DYEING

DYEING.

1. DYEING is the art of communicating a permanent colour to any substance; but it is generally employed in a more limited sense, and is applied to the art of giving colours to wool, silk, cotton or flax, or to thread or cloth fabricated of these substances. To this more limited sense we propose to confine it in the following treatise; and for the dyeing or staining of other substances, as paper, wood, bone, leather, marble, the reader is referred to these articles.

2. Among the arts of life there are some which are essential to man even in the earliest period of his history; while others derive their origin from chance, and owe their improvement and perfection to the progress of refinement and luxury. Those arts which are connected with the means of providing food or

shelter are necessary even in the rudest state of man, and are practised with more or less dexterity and success according to the abundance or scantiness of the supply with which he is furnished, and the varieties of climate which he inhabits. But those arts which have been distinguished by the name of fine arts can only flourish and arrive at a high degree of perfection in the more luxurious ages of refined society. To this account of the origin and progress of the arts among mankind, the art of dyeing forms a remarkable exception. Totally unconnected with the means of providing food to satisfy the urgent calls of hunger, of preparing raiment to secure the body from cold, or of procuring shelter from the storm, this art might at first sight be considered as one of those which exclusively belong

belong to an age of luxury. But the history of mankind assigns to its origin a very different period. The art of dyeing seems to be almost co-eval with man. In the rudest state of his existence, his simple and scanty clothing is frequently coloured; and even the naked savage, while he is yet a houseless wanderer in the woods, has discovered the means of staining his body with different colours. And yet the art of dyeing in no respect contributes to relieve the real and primary wants of man. It renders not his raiment warmer, and it serves not to make his lodging more comfortable.

3. Whence then is the origin of this art? It depends not like others on the necessities of man, and it exists long before he is acquainted with refinement and luxury. It must therefore be traced to a different source.

We see that the desire of distinction is one of the most active principles in the human mind. This principle operates equally in the breast of the savage in the midst of his naked companions, and in that of the sage and the soldier in polished society. Man rarely rests satisfied with the solid, but frequently less obvious pre-eminence, which superior strength, genius, or learning, confers. The proofs of this superiority can be but seldom exhibited; they are often not generally understood or acknowledged, and therefore cannot always be fairly estimated. He who possesses any of those talents which give him a superiority to others, naturally wishes to be distinguished by certain marks by which he may more uniformly and more directly excite admiration and command respect. He seeks, therefore, for some adventitious circumstances, which may be regarded as a kind of symbolical representation of power and greatness; and as they are constantly present to the senses, they make a deep impression, and keep alive those feelings of admiration which are so gratifying to the vain and ambitious. Dress and its ornaments have been usually employed as external marks of distinction. Hence it is, that the chief or the warrior among rude nations is clothed with a finer and more beautiful skin; his head is decorated with flowers or feathers; or the leaves of the oak, or the laurel, simply adorn his brow. And in the progress of civilization and refinement, the diadem of gold, and the robe of purple or of scarlet, supplant these simpler decorations as characteristics of dignity and power. To increase still more the beauty and variety of those substances which are employed as clothing or as the ornaments of dress, the aid of colours has been called in; and accordingly we find that coloured clothing has been held in high estimation in all ages. This principle, therefore, the desire of distinction, seems to be the natural origin of the art of dyeing. Nature, however, furnishes the model, and may be regarded as the antetype of the art, in the gay plumage with which she has clothed the feathered tribes, and in the splendid colours and infinite variety of shades which are exhibited in her vegetable productions.

4. But without indulging farther in these speculations, which are to be considered as subjects of curious investigation, rather than as topics of practical utility, let us now take a short view of the history and progress of this art.

We have endeavoured to shew that the beauty of brilliant colours is one of the means of attracting at-

tention, and of acquiring distinction, which mankind in every period of society have employed. Even before the use of clothing has been introduced, the rude inhabitants of savage nations applied them first to their skins. This practice existed among the Britons in the time of Caesar; and the women of Gaul about the same period stained themselves of a brown olive colour. At this day, it is still the practice of many of the savage tribes of America, as well as of the natives of the South sea islands. But when mankind had made some progress in arts and civilization, and had begun to wear clothing, the colours which they admired were afterwards communicated to their garments. The art of dyeing, therefore, though in a rude and imperfect state, is indisputably of great antiquity; and indeed considering its nature and origin, this might have been expected.

5. India, the nursery of the arts and sciences, which in India were afterwards improved and brought to perfection among other nations, seems to have given birth to the art of dyeing; and it would appear that the knowledge of dyeing cotton had advanced as far in the time of Alexander the Great as at the present time, so stationary have the arts become in that country. The beautiful colours of the Indian linens would naturally lead to the supposition that the art had reached a very high degree of perfection; but it is known that the Indian processes are so tedious, complicated and imperfect, that they would be totally impracticable in any other country.

6. It was not till the time of Alexander the Great among the Greeks, that the art of dyeing cotton and linen, which had gradually spread from the east to the west, was known in Europe. The Greeks, however, as appears from many passages in the Iliad and Odyssey, were acquainted with the art of dyeing purple in the time of Homer. And it is supposed that they derived their knowledge of it from the Phoenicians, a people who were very early celebrated for the art of dyeing. But their art seems to have been confined to wool; silk, indeed, was at that time unknown, and linen was usually worn white.

7. Dyeing and coloured stuffs are frequently mentioned in the sacred writings. It would appear that the art had made considerable progress in the time of the patriarchs, from what is mentioned in the book of Genesis. The dyed stuffs which are described in the book of Exodus were purchased by the Jews from the Phoenicians.

8. The Egyptians, according to Pliny, practised a kind of topical dyeing or calico-printing, which from his general description seems to have been similar to that which was found many ages after to exist in different parts of India, and was from thence introduced into the different countries of Europe. He says, the Egyptians began by painting on white cloths, which were no doubt of linen or cotton, with certain drugs which were themselves colourless, but possessed the property of absorbing colouring substances. These cloths were afterwards immersed in a heated dyeing liquor which was of one uniform colour, and although they were formerly colourless, yet when they were taken out, they were found to be dyed of different colours, according to the different qualities of the substances which had been applied to their different parts; and these colours could not afterwards be discharged by

History. by washing. This art was probably borrowed from the natives of India.

Plin. lib. 9. The Tyrian purple, so celebrated among the ancients, was probably from the name discovered at Tyre, and perhaps contributed not a little to the opulence of that city. The liquor which was employed in dyeing the purple was extracted from two kinds of shell-fish, one of which, the larger, was called the purple, and the other was a species of whelk. Each of these species was subdivided into different varieties, and were otherwise distinguished, according to the places where they were found, and as they yielded more or less of a beautiful colour. It is in a vessel in the throat of the fish that the colouring liquor is found. Each fish only afforded a single drop. When a certain quantity of the liquor had been obtained, it was mixed with a proportion of common salt, macerated together for three days, and five times the quantity of water was added. The mixture being kept in a moderate heat, the animal parts which happened to be mixed with it, separated and rose to the surface. At the end of ten days, when these operations were finished, a piece of white wool was immersed, by which means they ascertained whether the liquor had acquired the proper shade.

Various processes were followed to prepare the stuff to receive the dye. By some it was immersed in lime water, and by others it was prepared with a kind of fucus, which acted as a mordant to give it a more fixed colour. Alkanet was used by some for the same purpose.

The liquor of the whelk did not alone yield a durable colour. The liquor from the other shell-fish served to increase its brightness; and thus two operations were in use to communicate this colour. A first dye was given by the liquor of the purple, and a second by that of the whelk; from which it was called by Pliny purpura dibapha, or purple twice dipped.

10. Some kinds of purple have been found to possess great durability. Plutarch, in his life of Alexander the Great, mentions that the Greeks discovered in the treasury of the king of Persia a great quantity of purple which was 190 years old, and still retained all its beauty.

11. The small quantity of liquor which could be obtained from each shell-fish, and the tedious process in its preparation and application to the stuffs, raised the price of purple so high, that in the time of Augustus a pound of wool of the Tyrian purple dye, could not be purchased for one thousand denarii, equal to about 361. sterling.

12. The purple, which has been almost everywhere a mark of distinction attached to high birth and dignity, was worn by those who held the first offices in Rome. The emperors at last reserved to themselves the right of wearing it, and prohibited all others from using it on pain of death.

13. The substances which have been discovered and used in dyeing by the moderns, and the superiority which they have obtained in many colours, have superseded the use of the purple of the ancients. The shell-fish from which the liquor is extracted, is supposed to be now as abundant as ever. Similar shell-fish have been found near Nicoya, a small Spanish town in South America, and they are at present used for dyeing.

VOL. VII. PART I.

ing cotton on the coasts of Guaiquil and Guatimala.

14. In the year 1683, Mr Cole of Bristol discovered, on the coast of England, the shell-fish which yields the purple liquor. The liquor was contained in a white vein, lying transversely in a little furrow or cleft, next to the head of the fish. He found by experiment, that letters or marks, made with this white liquor, appeared when first exposed to the air of a green colour. When exposed to the sun, it became of a deeper green, afterwards of a purplish red, and by the continued action of the sun's rays, of a deep purple red. Mr Cole sent some of the first linen marked with this liquor to Dr Plot, one of the secretaries of the Royal Society, in the year 1684. It was soon after shown to King Charles II. who greatly admired it, and desired that some of the shell-fish might be collected, and brought to town, that he might have an opportunity of seeing the liquor applied, and the successive changes of colour through which it passed.

A species of this shell-fish was also found by Plummer at the Antilles; and Reaumur made a number of experiments on whelks, which were collected on the coast of Poitou. Duhamel found the same shell-fish in great abundance on the coast of Provence. The experiments of these philosophers on this liquor afforded the same result as those of Mr Cole. They observed that, although at first white, it becomes by the action of light, of a yellowish green, then deepens to a kind of blue, which is afterwards changed to a red. In less than five minutes, the latter is converted into a fine deep purple, having all the characters of the purple of the ancients.

Eudocia Macrembolitissa, daughter of the emperor Constantine VIII. who lived in the 11th century, while the knowledge and practice of dyeing that colour for the use and at the expence of the Greek emperors still subsisted, has given a minute account of the mode of catching the shell-fish which produced the purple. Of this operation she herself, it would appear, was an eye-witness. As it was applied at that time, it did not acquire its full lustre and perfection of colour, till it had been exposed to the action of the sun's rays.

15. A liquor which yields the same colour, and has otherwise similar properties, is found in different parts of the world. Abundance of purple snails, it is said, are found in the islands opposite to Batavia. They are boiled and eaten by the Chinese, who polish the shells, and pick out of the middle of the snail a purple-coloured substance, which they use in colouring and making red ink. Dr Peysonnel describes what he calls the naked snail, which is found in the seas of the Antilles, and affords a liquor of a beautiful purple colour. This liquor is thrown out by the animal when it is disturbed, in the same way as the cuttle-fish discharges the ink. The liquor of the snail is naturally of a purple colour, without the application of light. Two shell-fishes, which yield a similar colouring liquor, are described by Dr Brown in his history of Jamaica. The one, he says, is frequent in the American seas, and emits on being touched a considerable quantity of viscid purple liquor, which thickens and colours water. The other is called the purple ocean shell, and yields a beautiful purple liquor, which seems to resemble the former. But investigations concern-

ing the nature and application of the purple dye from shell-fish are now to be considered merely as subjects of curiosity; because the colours which are obtained by the processes of the moderns are more beautiful, and far less expensive.

16. In the 5th century, during the irruption of the northern barbarians, the arts, which had been encouraged and protected by the Romans, were lost amidst the devastations of the western empire. A few, indeed, were preserved in Italy, but they were in a state of decay; and otherwise no traces remained of knowledge, industry, or humanity. A manuscript of the 8th century is quoted by Muratori, which contains a description of some dyes, principally for skins, as well as some processes connected with other arts; but from the barbarous Latin in which it is written, no distinct notion can be formed of the nature of these processes. The arts met with a better fate in the East, where they were protected and encouraged. So late as the 12th century, articles of luxury were procured by some of the great from eastern countries.

17. During the time of the crusades, Venice and other cities of Italy became rich and powerful, first by supplying with provisions the Europeans who engaged in these frantic and destructive expeditions, and afterwards by establishing an intercourse with the Grecian empire. By these means the arts, which had been preserved among the Greeks, were established in Italy. In the year 1338, the city of Florence contained 200 manufacturers, who are said to have produced from 70,000 to 80,000 pieces of cloth. In the year 1300, archil was accidentally discovered by a Florentine merchant. Observing that urine produced a fine colour on certain species of moss, he made experiments, and from these learned the mode of preparing this substance. The discovery was long kept secret. His posterity, a branch of which it is said still exists, have retained the appellation of Rucellai, from the Spanish word which signifies that kind of moss.

18. The arts, after being revived in Italy, continued for a long time to be cultivated and improved with increasing success. Along with these, the art of dyeing made considerable progress. The first collection of the processes employed in this art appeared at Venice in the year 1429. It was entitled Mariegola de l'arte de i tentori. To render this description more useful and extensive, a person of the name of Giovanni Ventura Rosetti, travelled through different parts of Italy, and the neighbouring countries, where the arts had begun to flourish, that he might acquire a knowledge of the processes which were employed by different dyers. These were collected and published in 1548, under the title of Plictho. This treatise has been by some considered as the leading step towards the perfection which the art of dyeing has attained; for it is the first in which the different processes are collected. No mention is made either of cochineal or of indigo; so that it would appear, these dyes were either not known, or not employed in Italy previous to the time in which it was written.

19. Italy, but especially Venice, for a long time almost exclusively possessed the art of dyeing, and this seems to have contributed greatly to the prosperity of the manufactures and commerce which the Italian states long enjoyed. By degrees it was introduced into

France, Holland, and Britain. The process for dyeing the true scarlet had been communicated to a person of the name of Gobelin, who established a manufactory near Paris, which still bears his name. At the time, this was considered so rash an enterprise, that it received the name of Gobelin's folly; but such was his success, and such was the ignorance of the times, that it was supposed he derived his knowledge of the processes he employed, from the devil!

20. The discovery of America brought the knowledge of the cochineal insect into Europe. The Spaniards observing that the Mexicans employed it in painting their houses, and in dyeing cotton, transmitted an account of the beauty of that colour to their government, whose attention was afterwards directed to encourage and promote the increase of this valuable insect from which it is obtained. The discovery of cochineal was soon followed by that of the process for dyeing scarlet, by means of a solution of tin. For this discovery we are indebted to a German chemist of the name of Kuster, or Kuffer, who carried the secret to London in the year 1643. Gluck or Kloeck, a Flemish painter, having obtained possession of this secret, communicated it to Gobelin, and afterwards the knowledge of it spread throughout all Europe. The use of indigo, which was a great acquisition to the art of dyeing, was more slowly established than that of cochineal. In the reign of Queen Elizabeth, the use of this substance, as well as of logwood, was strictly prohibited in England, and, if found in any manufactory, was ordered to be burned. This, as must appear at the present time, very strange prohibition, was not withdrawn till the reign of Charles II. It met with the same fate in Saxony. In the edict in which the use of it is forbidden, it is said to be a corrosive colour, and called food for the devil!

21. In France also, some prejudice was entertained against it, and although it was not entirely prohibited, the use of it was limited to a certain proportion. The reason on which this prejudice was founded, on a narrow view of the principles of political economy, might even in the present day be admitted as specious, if not satisfactory. It was held out by those who dyed blue, and were accustomed to use pastil and woad, that the introduction of indigo would supersede the use of these substances; and it was represented that their consumption would be destroyed, and the encouragement for the productions of the country diminished.

22. Previous to the administration of the celebrated Colbert, the industry and arts of France long remained in a state of languor and decay. By the wise measures which were adopted by this minister, she soon rose to distinction among the nations of Europe, and in a short time saw her commerce and manufactures greatly extended. He invited the most skillful artists, encouraged and rewarded their talents, and thus established many arts and manufactures. Among these, the art of dyeing received its share of attention. In the year 1672, he published a table of instructions for dyeing, which, although it contains many useless and improper restrictions, is on many accounts worthy of attention, and particularly the reasons which he has given for considering it as an object of consequence. As a proof of this, we may refer to the following extract.

History. tract from the instructions: "If, it is said, the manufactories of silk, wool, and thread, are to be reckoned among those which most contribute to the support of commerce; dyeing, which gives them that striking variety of colour, by which they resemble what is most beautiful in nature, may be considered as the soul of them, without which a body could scarcely exist.

"Wool and silk, the natural colour of which rather indicates the rudeness of former ages, than the genius and improvement of the present, would be in no great request, if the art of dyeing did not furnish attractions which recommend them, even to the most barbarous nations. All visible objects are distinguished and recommended by colours; but for the purposes of commerce, it is not only necessary that they should be beautiful, but that they should be good, and that their duration should equal that of the materials which they adorn."

23. But notwithstanding these just and liberal views, and many useful regulations, which were published for instruction in the art of dyeing, the restrictions imposed upon it, as we have already observed, were from mistaken views improper and injurious, because in this, as in every other art, these restraints infallibly operate as checks on industry and improvement. The effects of these prohibitions, however, were moderated by the facility with which they might be eluded, and by the rewards bestowed on those whose experiments promoted the progress of the art, and whose discoveries being afterwards published, served to modify the existing regulations. The effects of these prohibitions, too, were in a great measure obviated, by the judicious appointment of men of science, to whom the superintendence of arts and manufactures was entrusted. By their prudent exertions, and by the still more efficacious means of the diffusion of knowledge, this art, as well as others, has been encouraged and improved.

24. The French government continued to direct its attention to promote the plan which was thus begun by Colbert, and many eminent chemists have been employed to superintend and improve the processes of the art of dyeing. Dufay, Hellot, Macquer, and Berthollet, have been successively charged with the care of this department; and to their labours and exertions we are indebted for many valuable acquisitions which have been made in the art of dyeing, during the 18th century. Dufay was the first who entertained just views of the nature of colouring matters, and the powers by which they adhere. In the examination of certain processes he discovered great sagacity, and established the surest means which the state of knowledge at the time afforded, to ascertain the durability of a colour. Under his direction a new table of instructions, which superseded that of Colbert, was published in 1737. Hellot, who succeeded him, published in 1740 a methodical description of the processes for dyeing wool; and this treatise may be considered, even at the present day, as one of the best systems on the subject. Macquer in 1763 published a treatise on dyeing silk, in which he has given an accurate description of the processes, has discovered the combinations of the colouring principle of Prussian blue, and has endeavoured to make an application of it to the art of dyeing. Macquer died in 1784, and was succeeded in that de-

partment by the celebrated Berthollet, to whom was intrusted the superintendence of the arts connected with chemistry, and particularly that of dyeing. To his being placed in this department, we are probably indebted for the excellent work which he has published on this subject, and for different memoirs which have appeared in different periodical works. To these we must acknowledge ourselves greatly indebted for much of the information, both of the theory and practice of this art, which we propose to lay before our readers in the following treatise. He has endeavoured, he observes, to bring into one point of view the processes of industry, and the operations of nature; to take his situation between the philosopher and the artist. To the first he has shown, where it is that the phenomena of the art of dyeing and those of nature meet, and what are the principles which their discoveries have established. When these comprehensive views, we may add, are completed, the art of dyeing may be considered as perfect.

25. The art of dyeing has been long successfully State of, in practised in Britain, although little has been done to- Britain. wards the investigation of the theory on which it depends. At an early period of the Royal Society, it attracted the attention of some of its members; but nothing was published on the subject. Many years afterwards, some useful observations on dyeing were published by Dr Lewis, but these were limited to a very few processes. The only work with which the British dyers were acquainted, till within these few years, was a translation of the treatise of Hellot, mentioned above.

26. But since the progress of chemical science has improved so wide a field of investigation; and since all by chemistry the essential processes in the art of dyeing are to be considered as purely chemical, the attention of philosophers has been greatly occupied with its investigation and improvement. By their experiments and observations a great deal of new information has been accumulated, and much new light has been thrown upon the art.

27. The only treatise which has appeared in Sweden Authors on this subject, is that of Scheffer, accompanied with dyeing. notes by the celebrated Bergman. In Germany, experiments in different processes of dyeing have been published by Beckmann, Poerner, Vogler, and Francherville. The authors of the different treatises in France on this subject, which have greatly contributed to the improvement of the art, are D'Ambourney, D'Apligny, Haussmann, Chaptal, and Berthollet, whose works we have already mentioned. In Britain, two very valuable essays by Delaval and Henry have appeared: and to these we may add, the excellent treatise on the Philosophy of Permanent Colours, by Dr Bancroft.

In the following treatise, we propose to give a pretty full view, both of the theory and practice of dyeing. This subject naturally divides itself into two parts. In the first, we shall treat of dyeing in general, or of those departments of physical science, the knowledge and application of which may be considered as constituting the theory of the art. In the second part, we shall take a view of the different processes which are employed in communicating colours to different stuffs, or, in general terms, the practice of dyeing.

Of Colours, &c. UNDER this head we propose to take a general view of what may be regarded as the theory of dyeing; and investigate those principles of physical science which are immediately connected with the art, and by the application of which the phenomena of the art can only be accounted for, or satisfactorily explained. With this view we shall treat the subjects which come under this part in the four following chapters. In the first, we shall consider the nature of colours and colouring matters; in the second, we shall treat of the nature and operations of mordants; the third will include an account of the properties of the substances to which colours are communicated; and, in the fourth, we shall add some general observations on the operations of dyeing.

28. THE physical theory of light and vision properly belongs to optics; and the changes produced by the action of light on different substances are detailed under chemistry. In this place, therefore, we shall only make a few observations on the nature of light and colours, which are more immediately connected with the subject under consideration. For our knowledge of light and vision we are indebted to Sir Isaac Newton. It was first demonstrated by that sagacious philosopher, that the light of the sun is composed of seven rays which have different powers of refrangibility. The colours of these seven rays are red, orange, yellow, green, blue, indigo, violet. When these rays are separated by the prism, as they run gradually into each other, according to their different degrees of refrangibility, they produce every various shade of colour. The violet ray is the most refracted, the indigo next, and so on to the red, which is the least refracted of all the rays. The same rays of light also differ in their degrees of reflexibility. All known colours, and their different shades, are produced by mixing together the different rays. Thus, for instance, by mixing together red and yellow, an orange colour is obtained; yellow and blue give a green colour; and blue and red, according to their different proportions, produce a violet, purple, &c. and thus, as Sir Isaac Newton has observed, the variety of colours depends on the composition of light; for if the sun's light consisted but of one sort of rays, there would be but one colour.

Nature of light. 29. Colours in an object, the same philosopher farther observes, are nothing but a disposition to reflect this or that sort of rays more copiously than the rest; in the rays there are nothing but their dispositions to propagate this or that motion into the sensorium; and in the sensorium they are sensations of those motions under the forms of colours. In their power of reflecting light, bodies, it is well known, differ greatly from each other. Some bodies reflect it in such quantities, that the eye cannot bear it. Such, for instance, are metallic substances highly polished. Others again, as dark coloured or black substances, reflect it very feebly. It is found in general, that the quantity of

light reflected from a body depends greatly on the Of Colours &c. smoothness of its surface. On this account bodies which have the smoothest surface, or are most highly polished, are the brightest: that is, they reflect the greatest quantity of light. But there is also a very great difference among bodies, in the nature or quality of the rays of light which they have the power of reflecting. When all the rays of light are equally reflected by any body, that body is said to be white; but when a very few rays only are reflected from a body, that body is said to be black, because the greater number of the rays being absorbed by the body, the few that are reflected make a very faint impression on the organ of vision. A body which has the power of reflecting the red rays only, is said to be red; a body which reflects the blue rays, is said to be blue; the body reflecting only the yellow rays, is yellow: but when any two of these rays are reflected in combination with each other, a different colour is produced; as for instance, the red and the yellow rays afford an orange colour; and, as we have already observed, the various shades of colour exhibited by different bodies, depend on the different combinations of rays reflected from their surface. Thus it appears, that colour in bodies is to be ascribed to their disposition of absorbing certain rays, and reflecting the rest. In opaque bodies, it is owing to their disposition to absorb some rays, and to reflect the rest. In transparent bodies, it is owing to their disposition to absorb certain rays, and to transmit the rest.

30. Newton has demonstrated, that transparent Causes of colours in transparent bodies bodies reflect the rays of one colour, and transmit those of another, according to the difference of their thickness or density. He observes that transparent substances, such as glass, water, air, &c. when made very thin by being blown into bubbles, or otherwise formed into plates, exhibit various colours, according to their various thinness; although at a greater thickness they appear very clear and colourless. His method of conducting these experiments was the following. He took two object-glasses, the one a plano-convex for a 14 feet telescope, and the other a large, double convex, for one of about 50 feet; and upon this laying the other with its plain side downwards, he pressed them slowly together, to make the colours successively emerge in the middle of the circles, and then slowly lifted the upper glass from the lower, to make them successively vanish again, in the same place. The colour which, by pressing the glasses together, emerged last in the middle of the other colours, would, upon its first appearance, look like a circle of a colour almost uniform from the circumference to the centre; and by compressing the glasses still more, grow continually broader, until a new colour emerged in its centre, and thereby it became a ring, encompassing that new colour; and by compressing the glasses still more, the diameter of this ring would increase, until another new colour emerged in the centre of the last, and so on, until a third, a fourth, a fifth, and other following new colours successively emerged there, and became

Colours, came rings, encompassing the innermost colour, the last of which was the black spot. And on the contrary, by lifting up the upper glass from the lower, the diameter of the rings would decrease, and the breadth of their orbit increase, until their colours reached successively to the centre, and then, as they were of considerable breadth, he could more easily discern their species than before. By proceeding in this manner, he produced 25 different-coloured, circular rings, which he divided into seven orders, because the same colour was always repeated. They are reckoned from the central colour, which was always black, in the following order:

1. 1. Blue, white, yellow, and red.
2. 2. Violet, blue, green, yellow, red.
3. 3. Purple, blue, green, yellow, red.
4. 4. Green, red.
5. 5. Greenish blue, and red.
6. 6. Greenish blue, and pale red.
7. 7. Greenish blue, and reddish white.

But in the three last orders the colours were very indistinct, and terminated in perfect whiteness.

31. These colours were occasioned by the thin films of air which were included between the two glasses. For he found, he observes, by looking through the two object-glasses, that the interjacent air exhibited rings of different colours, as well by transmitting light, as by reflecting it. The film of air varies in thickness from the centre of the glasses to the circumference. In the centre where the film is thinnest the colour is black; and the other colours from the centre to the circumference are produced in their order by the gradual increase of the thickness of the film.

32. These experiments were repeated on films of water and also of glass; and it was found that the thickness of the films in these cases, reflecting any particular colour, was diminished, and this diminution appeared to be proportional to the density of the reflecting film. As there is no method of measuring the distance between the two glasses where the black spot appears, it is impossible to ascertain the absolute thickness of the films; but it certainly does not exceed the 1000th part of an inch. Newton, however, endeavoured by a mathematical investigation to measure the relative thickness of air, water, and glass, at which the several orders of colour appear. The following table exhibits the relative thickness of air which produced the coloured circles.

33. The conclusion which Newton drew from these experiments was, that the power or disposition of the

particles of bodies to reflect or transmit particular rays depended on the size and density of these particles; and proceeding on this theory he attempted to measure the size, or at least the thickness, of the particles of bodies, from the colours which they reflected or transmitted.

34. This subject was still farther investigated by Mr Delaval. In the year 1765, he published, in the Philosophical Transactions, an account of his "Experiments and Observations on the agreement between the specific gravities of the several metals, and their colours, when united to glass, as well as of their other preparations." In this paper, Mr Delaval treats of the difference of density, and of the colours produced by that cause; and yet he considers colours as arising from a difference of the size of the colouring particles. For since the particles of a coloured substance being separated they are removed to a greater distance from each other, and thus occupy a greater space, that substance must undergo a diminution of its specific gravity, while at the same time the size of its particles is smaller. According to Sir Isaac Newton, the refractive and reflective powers of bodies are nearly proportional to their densities, and the least refrangible rays require the greatest power to reflect them. From this, Mr Delaval supposed, that denser substances, by their greater reflective power, ought in similar circumstances to reflect the less refrangible rays; and that substances of less density should reflect rays proportionably more refrangible, and therefore appear of several colours in the order of their density. The densest bodies, he supposes, are the red; the next in density are the orange; the next are the yellow; and so, according to the order of the refrangibility of the different rays. Mr Delaval some time after extended his researches to animal and vegetable substances, and endeavoured to establish the theory of Newton by a great number of experiments, an account of which he published in an essay entitled, an Experimental Inquiry into the cause of the Permanent Colours of Opaque Bodies †.

35. According to the theory of Newton, with the exception of combustible bodies, which follow a different law, colour depends solely upon the size of the integrant particles of bodies, in which the density is the same; and upon the size and density of all bodies taken together. But the evidence for the truth of this theory can only be derived from experiment. Newton adduced but a small number of experiments in support of it. The experiments of Mr Delaval were more numerous and more varied; but they were made long before the important facts in chemical science, which have completely changed the views and opinions of philosophers, with regard to the nature and action of the constituent principles of bodies, were discovered; so that it is now universally acknowledged that they proceeded on a false hypothesis. It was supposed that alkalies enlarge, and that acids diminish, the size of the particles of bodies on which they act, without inducing any other change. This opinion, in the present state of chemical knowledge, will not readily find a place.

36. But if this theory were true, every change in the size of the integrant particles of bodies would occasion a different colour in these particles; and in all these changes, if they correspond with the theory, the

Of Colours, the colour produced must be precisely that colour
Sec. which is the result of a diminution or increase of
size.

Inconsistent with the facts. 37. But there is no such coincidence with the facts. The magnitude of the integrant particles of bodies cannot be ascertained; and there is no method by which the increase or diminution of the particles in the changes which they undergo can be measured; but the addition or abstraction of matter to particles can in many cases be distinctly determined. In the change which takes place on gold by the process of oxidation, that is, by combining with oxygen, an integrant particle of the oxide is larger than the integrant particle of gold in the metallic state; for it has united with one particle at least of oxygen. But if the theory were true, there should be a difference of colour between the oxide and the gold, which is not the case, for they are both yellow. In the amalgam of silver, a compound of silver and mercury, the colour is white, which is the colour of both metals; and yet an integrant particle of the compound must be larger than an integrant particle of either the mercury or the silver.

The same colours reflected in different orders. 38. But the same colour, it may be said, is reflected in the different orders of colours, in which the particles are of very different sizes. This circumstance, as Dr Bancroft* justly observes, proves incontestably, that although thickness or size of the particles may be one, it cannot be the only cause of the repeated variation of colour. It follows, therefore, that there must be some other cause. But besides, the most common colour remaining after an increase of the size of the integrant particles of bodies is white: and yet this colour does not appear in any of the orders except the first; its permanency, therefore, cannot be accounted for in any way which is at all compatible with this theory.

Colours of metals independent of density. 39. And in the changes of colour which are observed to follow the increase or diminution of the sizes of the particles of bodies, the order of these changes is not such as will correspond with the theory. It is obvious that the colours of metallic substances do not depend on their density. The colour of platina, the densest body known, is not red, as it should be according to the theory, but white; in this respect resembling tin, one of the metals which has the least density, and little more than one-third that of the former.

Chemical changes affect the colour. 40. The size of the particles of the green oxide of iron must be increased when they enter into combination with the prussic acid. But the colour of the compound is white; and, according to the theory, it should be accompanied with a diminution of the size of the particles, which is not the case. The colour of indigo is naturally green. The addition of oxygen, which must increase the size of the particles, converts it to a blue colour. This, then, is another case incompatible with the Newtonian theory; and from these facts it must appear, that this theory is deficient in accounting for the reflection or transmission of particular rays, and the absorption of the rest. It is not sufficient for the explanation of the causes of colour. The smallness and the density of particles are not the only circumstances which ought to be taken into the account, in explaining the cause of colour in bodies. It appears, from Newton's own experiments, that we must have recourse to the chemical properties of bodies, which have a considerable influence on their colour. It cannot be sup-

posed, that a force which acts powerfully in refracting or Colours the rays, will not also have great influence in their re- Sec. flection.

41. Numerous facts tend to prove that bodies have Affinity of a particular affinity for the rays of light; and indeed bodies for it is entirely upon these affinities that the phenomena certain rays of light depend. Coloured bodies have a certain affinity for some of the rays of light. Those rays for colour, which any body has a strong affinity, are absorbed by it, and retained; while the other rays, for which it has no affinity, are either reflected or transmitted, according to the nature of the body, as it may be opaque or transparent, and according to the direction of the incident ray. A red body, for instance, reflects only the red rays, because it has an affinity for all the other rays, excepting the red. It therefore absorbs them, if it be an opaque body, or transmits them if it be transparent. A green body absorbs all the rays excepting the green; a black body has a strong affinity for all the rays, and therefore they are all absorbed; while a white body, which has little affinity for any of the rays, if it be opaque, reflects, or if transparent, transmits them all.

Changes of bodies, may be conceived to be differences in size, density, and figure; and changes in these circumstances may account for all the varieties of affinity. If then affinity depends upon these circumstances, and of the particles, between their particles and the different rays of light, the cause of the colour of bodies, it seems obvious, is capable of being accounted for from the size, density, and figure of their particles. It cannot be accounted for, according to the theories of Newton and Delaval, solely on the variations in size and density.

43. If then the colour of bodies depends upon their affinity for light, and every body have some colour in consequence of the absorption of particular rays which it retains, and the reflection or transmission of all the rest, it is obvious, that it must continue of its first colour without suffering any change, till it is either saturated with the particular rays which it absorbs, or till the particles of the body have undergone some and to a change by decomposition or combination with new substances. As many substances have been long exposed to the action of light without their colours being changed, there is no certain evidence that the changes in the colours of bodies are to be ascribed to the first cause. The light which is absorbed either escapes unchanged or under some unknown form. But the action of the second cause which has been mentioned, may be traced in almost all cases where alterations of the colours of bodies have been observed. We may take as an example of this change of colour the green oxide of iron, which readily combines with oxygen, and is converted into the red oxide. The latter oxide, in combination with the gallic acid, assumes a black colour, and with prussic acid a blue colour. In these cases, where there is a change in the composition of the body, accompanied with a change of colour, the cause of this change is obvious; because every change in the composition of a body produces some change in the affinity, and therefore in the size, density, and figure of the particles; and it is not improbable in all of these circumstances together. But if the affinity of any body

Colours, &c. dy for other substances has undergone a change, it is natural to suppose that its affinity for light is also in some degree altered. This, however, although it happens in many instances, is not constant and uniform; because it may happen, that the changes in the size, density, or figure of the particles of the body, are such as to render it capable of combining with, or reflecting, the same rays of light as before it suffered any chemical change. Thus it must appear, that in most cases, the permanency of the colours of bodies will depend greatly on the permanency of their composition, and on the force of the affinities which they have for other bodies, to whose action they may be exposed.

44. In the ingenious experiments of Mr Delaval, which we have already alluded to, he has shown that coloured matters do not reflect any light. "Reflective media, (he observes), act indiscriminately on all the different rays. It does not appear from the optical phenomena which have hitherto been observed, that nature affords any kind of matter endowed with a power of reflecting one sort of rays more copiously than the other sorts; consequently no reflective substances are capable of separating the differently refrangible rays, and thereby producing colours. There are several experiments and observations in Sir Isaac Newton's optics, from which it might have been inferred, that coloured light is not reflected from coloured matter, but from white or colourless matter only. Although that great philosopher supposes that all coloured bodies reflect the rays of their own colours more copiously than the rest, yet he observes that they do not reflect the light of their own colours so copiously as white bodies do. If red-lead, for instance, and white paper, be placed in the red light of the coloured spectrum, made in a dark chamber by the refraction of a prism, the paper will appear more lucid than the red-lead, and therefore reflects the red-making rays more copiously than red-lead doth*.

"If it be supposed that the red particles of the minium reflect the red rays more strongly than the rest, what reason can be assigned why minium should not exhibit the red rays as vividly as white paper, which acts indifferently on all the rays? But if it be considered that in opaque coloured bodies, the rays which are reflected from white reflective matter pass back through the transparent coloured media with which the reflective matter is covered, it will evidently appear why the coloured light reflected from white paper is more copious and bright than that which is exhibited by red-lead.

"A considerable part of the incident light is lost in passing through transparent coloured media; therefore the light reflected immediately from the white paper, must be more copious and lucid than that which has

undergone a diminution in its passage to and from the reflective particles of the opaque coloured body, through the transparent coloured medium.

"When a small portion of colouring matter is mixed with a colourless medium, the mass appears tinged with colour; but when a great quantity of colouring matter is added, the mass exhibits no colour, but appears black; therefore, to attribute to colouring matter a reflective power, is to advance an inexplicable and contradictory proposition; for it is asserting that in proportion as more reflective colouring matter is opposed to the incident light, less colour is reflected; and that when the quantity of colouring matter is very great, no colour at all is reflected, but blackness is thereby produced."

45. "From these arguments it might have been shewn, that the reflective power does not exist in colouring matter, but in opaque white substances only. Nevertheless, in this disquisition, I have not entirely relied on arguments drawn from a few known and obvious appearances, but have endeavoured, by numerous experiments, to ascertain the cause of the colours of natural as well as artificial bodies, and the manner in which they are produced.

46. "M. Euler observed, that the colours of bodies are not produced by reflection. He supposes that the coloured rays are emitted by the colorific particles. This hypothesis, however, is not agreeable to experiment; for as the colouring matter acts upon light by transmission only, it is evident that bodies do not appear coloured, either by reflecting or emitting the rays. I have not attended to any other hypotheses which are unsupported by experiments. Sir Isaac Newton, and I believe all later philosophers, except M. Euler, have attributed to colouring matter a reflective power; and the artists whose works depend upon the preparation and use of colouring materials, seem in general to have adopted the same theory. As an instance of this agreement, I have cited, from M. Hellot, one of the most skilful and intelligent authors who have treated of the art of dyeing, a passage which comprises his opinion respecting the action of the tinging particles on the rays of light (A). All the other writers on the same subject, appear to agree in that established opinion; but they seem rather to have yielded to the authority of Sir Isaac Newton and other theorists, than to have appealed to the operations of their own art, from which the real cause and origin of colours is obviously deducible†."

47. The art of dyeing consists principally in covering white substances, from which light is strongly reflected, with transparent coloured media, which, according to their several colours, transmit more or less copiously the several rays reflected from the white substances.

(A) The passage from Hellot is the following. "At present we only know of two plants which afford a blue colour after their preparation. The one is the isatis or glastum, otherwise called pastel or wood. In the preparation of these plants, the fermentation is continued till the putrefactive process of all the parts of the plant, the root excepted, has been induced; consequently there takes place a separation of all their principles, with a new combination and arrangement of these same principles, from which results an assemblage of particles greatly divided, which being applied to any substance, reflect the light in a very different manner from what they did when those particles were combined with the other parts of the plant, previous to fermentation." Art de la Teinture des Laines, p. 117.

Of Colours, &c. stances. The transparent coloured media themselves reflect no light; and it is evident that, if they yielded their colours by reflecting instead of transmitting the rays, the whiteness or colour of the ground on which they are applied would not anywise alter or affect the colours which they exhibit. Such an erroneous conception of the principles of the art cannot fail greatly to obstruct its progress and improvement.

Coloured matters appear black by incident light. All colouring matter is black when viewed by incident light, and all substances inclined to blackness, in proportion as they are copiously stored with tinging particles.

48. As a farther illustration of this subject, we shall make another extract from the same author. "For the purpose," he observes, "of procuring masses made up of colouring particles, I reduced several transparent coloured liquors to a solid consistence by evaporation. When a gentle heat is employed in this operation, the colouring matter, which is thus concentrated, remains unimpaired, and capable of again imparting its colour unaltered, to other liquors. In this state the colouring particles reflect no colour; and as no light is transmitted through them, they are black. Among the liquors which I evaporated, were the tinctures and infusions of the colouring particles of red, purple, blue, and yellow flowers; of logwood, Brazilwood, fustic, turmeric, red sanders, alkanet, sap-green, kermes, and other transparent coloured liquors, which are capable of being reduced to a solid consistence, without undergoing such changes during their evaporation, as to render them opaque.

Effect of colours on white bodies. 49. "White paper and linen may be tinged by dipping them in the infusions of flowers of different colours; and by spreading upon those white grounds the expressed juices of such flowers, their colours may be communicated to the paper and the linen. These means of tinging are somewhat similar to the application of vegetable dyes to linen, and of transparent water colours to paper, many of which consist of the colouring matter of plants, such as indigo, litrus, gamboge, &c.

50. "The consideration of these white substances affords much insight into the manner in which the natural colours of vegetables are produced. When the colouring matter of plants is extracted from them, the solid fibrous parts, thus divested of their covering, display that whiteness which is their distinguishing character. White paper and linen are formed of such fibrous vegetable matter, which is bleached by dissolving and detaching the heterogeneous coloured particles. When these are dyed or painted with vegetable colours, it is evident that they do not differ, in their manner of acting on the rays of light, from natural vegetable bodies, both yielding their colours, by transmitting through the transparent coloured matter the light which is reflected from the white ground; for it appears, that no reflective power resides in any of their component parts, except in their white matter only."

51. Thus then it appears, that the colouring particles with which stuffs are dyed, being transparent, the reflected light must proceed entirely from the fibres of the cloth or stuff which are covered with the transparent colouring matter. If the stuff be already of a black colour, no other colour can be communicated to it; because it has not the power of reflecting any co-

lour, and therefore it cannot transmit any. And if or Colours &c. the stuff were of a red, blue, or yellow colour, it could not be dyed of any other colour excepting black; because the red, blue, or yellow rays only being reflected, no other rays could be transmitted. But these observations will strictly apply only when the whole of the surface of the cloth is of one uniform colour. They point out also the importance of the cloth being dyed of a pure white colour before it is dyed, especially dyed when it is to be dyed any bright colour; for then the rays are copiously reflected; so that any colour may be given by combining with it any colouring matter which has the power of transmitting only particular rays.

52. As it is by the force of affinity that the colouring matter enters into combination with the stuffs which are dyed, that this chemical action be complete, it is necessary that the matter be in a state of minute division. No permanent colour could be produced by merely covering the surface of the fibres of the stuffs with the colouring substance; for unless it adhere so strongly that it cannot be separated by mechanical action, or by means of any of the processes to which dyed stuffs must be subjected, it must appear to be of little value, and the object in view is not obtained. To allow the chemical action to take place between the colouring matter and the stuffs, the former is dissolved in some liquid, for which it has a weaker attraction than for the stuffs; so that when they are immersed in the solution, the colouring matter, in consequence of the stronger attraction which it has for the stuffs than for the solvent, combines with them, and thus they are dyed; and the facility with which this combination takes place, must obviously depend on the affinity between the colouring matter and the liquid holding it in solution, and the affinity between the cloth and the colouring matter. When these two affinities balance each other, no change takes place; but when the affinity between the stuff and the colouring matter prevails, the combination is effected, and the process proceeds more or less rapidly according to the force of this affinity.

53. Coloured bodies are compounds; and several substances enter into their composition. In all coloured bodies some of the component parts have a strong affinity for oxygen, which they attract from the atmosphere. The permanency of a colour consists in its power of resisting the action of all substances to which it is exposed. This power varies greatly according to the nature of the colour and the kind of stuff. The durability of the same colours on animal and vegetable matters is very different. But before the colour of a body can be permanent, all its component parts must be combined together by such strong affinities, that the substances which come in contact with them shall not be able to unite with any of these parts, and thus form a new compound. Should such a decomposition take place, the colour of the body cannot be permanent; and if the decomposition be suddenly effected, the colour is immediately destroyed. If the new combination proceeds slowly, the decay of the colour is also slow and gradual.

54. The combination of oxygen with some of the component parts of a coloured body, is one of the principal causes of the change of colours. The action of

Colours, of oxygen on bodies is greatly promoted in particular
&c. circumstances. With the assistance of heat, almost all
coloured bodies are decomposed by means of oxygen.

At the temperature of 448°, wheat flour is deprived of its white colour, becomes first brown, and then changes to black. The oxygen enters into combination with the hydrogen, one of the component parts of the vegetable matter, and in this state it is driven off. The action of light produces effects similar to those of heat. A decomposition of the colouring matter takes place by means of the light to which the body is exposed; and one of its component parts combines with oxygen. The effects of light on the colour of wood have been long observed. Wood kept in the dark retains its natural appearance; but when it is exposed to the light it becomes yellow, brown, or of some other shade. This effect is found to be subject to considerable variations in different kinds of wood, and bears some proportion to the intensity of the light. If the solution of the green part of vegetables in alcohol, which is of a fine green colour, be exposed to the light of the sun, it very soon assumes an olive hue, and in the course of a few minutes it is entirely deprived of its colour. When the light is weak the change proceeds more slowly; and if it be kept in the dark no change whatever takes place; at least it requires a great length of time. Light seems to favour the tendency to decomposition in many bodies, by producing combinations of some of their constituent principles, as when water is formed by the union of oxygen and hydrogen, or carbonic acid by the union of carbone and oxygen. Some bodies even are deprived of the whole or part of their oxygen by the action of light. Oxymuriatic acid exposed to the light, becomes common muriatic acid by losing its oxygen; and the nitrate of silver becomes black by a partial decomposition and loss of its oxygen.

55. Such then seem to be the most general causes, the action of which produces changes in the colour of coloured bodies. It is either by the decomposition of the substances, in consequence of new compounds formed by the combination of some of the constituent parts; by some of these parts combining with oxygen; or by the addition or abstraction of oxygen. And to such changes colouring matters must be subjected from their compound nature; since they are most generally derived from animal or vegetable substances. The selection of such substances as resist the action of these causes, must therefore be an object of the greatest importance in the art of dyeing. A colour too which is sufficiently permanent ought to be such as will resist the action of acids, alkalies, soap, and other substances to which dyed cloth may be exposed.

56. There is a great difference in colours with regard to their power of resisting the action of air and light; and as it is in this that their permanency chiefly consists, independent of their lustre, it becomes an object of great importance, to be able to ascertain by easy tests the durability or goodness of any colour. In France, where the art of dyeing was more under the regulation of government than in other countries, and a distinction was established by law between dyers of durable and fading colours, the means of ascertaining the permanency of colours became of still greater consequence. For the dyer of fading colours was subject

to punishment if he produced colours which were too Of Colours, permanent; so rigorous and capricious were the laws &c. which regulated these matters. The observations of M. Dufay on this subject laid the foundation of the regulations which were made to ascertain this point. For this purpose he made experiments by dyeing wool of all colours, with all kinds of colouring matters; and setting entirely aside the prejudices of the dyers, he collected most of the substances which he supposed might be employed in the art, and tried a great number of them, investigating their good or bad qualities with great care.

57. His first experiments were made on woollen yarn; Dufay's. but finding afterwards that pieces of white cloth were more suitable to the purpose, he employed them. And that he might distinguish between permanent and fading colours, he exposed to the action of the sun and air for the space of twelve days, patterns of all colours which he had dyed with known substances. In this time durable colours were little injured, but those which were of a fading nature were almost entirely obliterated. But as the action of the sun might be less intense in cloudy weather, and thus the test would be less severe when that happened than during twelve days of bright sunshine; to obviate this inconvenience and uncertainty, he selected one of the worst colours, that is, one on which the sun had the greatest effect in the same time. This colour served as a standard in his experiments; and whenever he exposed stuffs to the air to prove the colour, he exposed a piece of this stuff along with them. He did not calculate by the number of days, but by the change on the colour of the standard stuff. For he kept the pattern exposed to the air till it had lost as much as the standard would have done by the action of the sun during twelve days in summer. He found from these experiments that it required four or five days longer in winter than in summer to produce the same effect.

58. But by this method of exposure to the air he had another object in view. This was to discover the proper proof for each colour. By the application of this proof a stuff is tried whether its colour be permanent or not. The pattern for instance is boiled with alum, tartar, soap, vinegar, &c. and by the effect of these substances its quality is ascertained. But from the component parts of the substances employed being then unknown, and the imperfect state of chemical science, these proofs must appear now to have been extremely precarious and insufficient. Some which were applied, from their natural effects, destroyed good colours, and produced no effect whatever on bad colours.

59. As the method he employed may suggest the means of discovering others founded on more correct principles and more accurate knowledge of the substances whose action is investigated, we shall mention the ingenious process which he followed. Having observed the effects of air and light on each colour, whether it were a good or bad colour; he tried the same stuff with different proofs, and stopped as soon as he discovered one which produced the same effects as the air. He then noted the weight of the ingredients, the quantity of water, and the length of time; and thus he was certain of producing on a colour an effect similar to that which the air would have produced, on the

Of Colours, supposition that it was dyed in the same way with his, &c.

as was the case in France where all the processes were then regulated by law. In this way he was enabled to ascertain the qualities of any colour, by making an analysis of the ingredients of which it was composed. By means of the proofs which were invented by this ingenious chemist, as much of a colour which was not of a durable nature, could be discharged in a few minutes, as would be lost by the action of the air and light in twelve or fifteen days. But as general rules framed for such trials are liable to many exceptions, from different unavoidable causes, their application in many cases may be considered as too severe. For instance, light colours require less active proofs than those which are of a deeper dye, and are more loaded with colouring matter; in the latter case, a considerable proportion of colouring substance may be carried off without much visible change on the colour; but in the former, by means of the same active test, the colour would be entirely obliterated. Every variety of shade, therefore, would have required a separate proof. The sun and the air must always be considered as the true test; and those colours which undergo no change in a certain time by this exposure, may be considered permanent colours, although they may be greatly changed by the application of proofs. Scarlet, which is dyed with cochineal alone, assumes a purple colour when tried by means of alum: but if scarlet be exposed to the sun, it loses some of its brightness, and becomes of a deeper shade; but this shade is different from that which is produced by alum. In certain cases then the same effect is not to be expected from the action of proofs and that of air and light.

it is attended with the advantage of exhibiting nearly or the shades and changes through which a stuff must pass when it comes to be acted on by the air. Still, however, the same philosopher adds, the oxygenated muriatic acid is not to be considered as an infallible test; entire confidence can only be placed in the results obtained by the action of the air and light.

62. To prove the colours of silk, it has been thought sufficient to expose them to heat in acetic acid or lemon juice; and those colours which stand this test are considered as permanent. When the colours have been obtained from the woods or archil alone, they are reddened by means of a vegetable acid; but if the solution of tin has been used to dye with these substances, the colour which has been prepared in an acid liquor suffers no change from vegetable acids. Thus the colour which is the least expensive in the preparation may be reckoned good by the test, although it will prove the least permanent. For silk, therefore, the oxygenated muriatic acid should be employed; but more especially exposure to the air.

63. It must appear an object of much importance to the dyer to be able to estimate the relative qualities of colouring substances of the same kind. The oxygenated muriatic acid may also be employed as a test for this purpose. By its use we may ascertain the proportional quantity of colouring matter in those substances, the nature of whose colouring particles is the same; as, for instance, when different parcels of indigo are to be compared together. In this case no foreign affinity can interrupt the action of the acid. And even if it should happen, that any considerable difference exists in the nature of colouring particles supposed to be the same, the action of this acid, it is probable, would still be a measure of their comparative goodness. If then it is proposed to compare together two or more colouring substances of the same nature, and to ascertain the relative quantity and quality of the colouring particles in each, all that is necessary is to compare the quantity of the same oxygenated muriatic acid which is required to produce the same degree of change in equal weights of each. For the qualities of these substances, or the quantities of colouring particles they contain, are directly proportional to the quantities of liquor required to produce the same effect on each. In conducting this experiment it is scarcely necessary to observe, that the colouring matter of each substance should be dissolved in a proper liquor, and that all the circumstances attending the comparison should be as nearly as possible the same.

64. If different kinds of indigo are to be compared together, let an equal weight of each be carefully powdered and introduced into separate matrasses with eight times their weight of concentrated sulphuric acid, and let them remain for 24 hours in a heat of from 100° to 120° Fahrenheit. Each solution is then to be diluted with water, and filtered. What remains on the filter is to be collected, ground in a glass mortar, and again digested with a little more sulphuric acid. These last solutions are then to be diluted with equal quantities of water, filtered and added to its corresponding liquor. As much oxygenated muriatic acid is then to be added to each solution as will discharge the colour, or bring them to a shade of yellow:

60. An experiment by Heliot is added as a farther illustration of a colour resisting the effects of exposure to the air, and yet being destroyed by the action of other substances. Brazil wood, he mentions, like other woods loaded with colour, produces a fading dye. With this he prepared a red, much finer than madder reds, and as bright as those made with kermes. This red was exposed to the air for the two last months of the year 1740, in which much rain fell, and for the two first of 1741; and notwithstanding the rain and bad weather, it was so far from losing, that it gained body. Yet this red, so durable in the air, is incapable of resisting the trial by tartar. Colours then may be reckoned sufficiently durable when they resist the effects of the air, although they are decomposed or destroyed by means of powerful chemical agents. From these observations, it is therefore obvious, that the only sure mode of ascertaining the permanency of colours, is by exposing the dyed stuffs for a certain length of time to the action of light and air.

61. Berthollet* proposes to employ the oxygenated muriatic acid as a quick and easy method of ascertaining the degree of durability which a colour may possess; because it acts like the air itself. When a trial is to be made on any piece of stuff, all that is necessary is to put a pattern of it into the acid, along with one of a stuff which is known to have been dyed properly. The relative power of resisting its action, which appears in the two patterns, becomes the test or measure of the quality of the colour. This liquor having a very powerful action on the colouring particles, must be employed in a very diluted state. In the use of this proof,

low: Thus the qualities of the different kinds of indigo may be ascertained by the quantity of oxygenated muriatic acid which is required to discharge their colour.

65. The process is more simple to compare the qualities of those colouring matters which are soluble in water. To equal bulks of the decoction, containing the same weight of each substance, the oxygenated muriatic acid is added till they are all brought to the same shade; and the quality of the substance is proportionate to the quantity of acid required.

CHAP. II. Of Mordants.

66. THE term mordant, derived from the French word mordre, to bite or corrode, is applied to those substances which are employed in dyeing, to facilitate or modify the combination of the colouring particles with the stuff. This name was given to these substances, from a supposed mechanical action which they produced on the substance to which the colour was communicated; and as no equivalent word has yet been proposed, the original is retained in the English language.

67. The knowledge of this class of substances is not less important in the art of dyeing than that of colouring matters themselves, because on their action depend the variety, brightness, and durability of colours. The action of mordants is undoubtedly owing to chemical changes, so that more extensive observation and a complete knowledge of their effects, must greatly contribute to the improvement and perfection of the art of dyeing. It is by a new series of attractions which are introduced by their action, that the colouring particles are combined with the stuff, and the qualities and degrees of the colours are affected.

68. A mordant is not always to be considered as a simple agent; for, of the different ingredients which enter into its composition, new combinations are sometimes formed, so that the substances which are immediately employed, are not the direct agents in effecting the changes, but the new compounds which are produced.

69. Mordants are applied in different ways, according to their nature, according to the nature of the colouring matter, and that of the stuff to be dyed. Sometimes they are mixed with the colouring particles, and sometimes the stuffs to which the colour is to be communicated, are impregnated with them; and sometimes both these processes are combined. In some of the more complicated operations of dyeing, substances are successively applied to stuffs in which the action of the last only produces the effect. In such cases, there is a gradual progress of combination; but it is only by the effect of the last compound which is formed, that the colour is evolved.

70. The effects of mordants are well illustrated in many of the processes which are followed in the art of printing linen; and for the illustration of these effects, we shall extract from Berthollet a short account of some of these processes. For linens to which it is proposed to give different shades of red, the mordant employed is prepared by dissolving in eight pounds of hot water, three pounds of alum, and one pound of acetate of lead, or sugar of lead. To this solution two

ounces of potash, and afterwards two ounces of powdered chalk, are to be added. Our chemical readers will readily perceive, that the first change which takes place, is the decomposition of the alum, by means of the acetate of lead. The oxide of lead combines with the acid of the alum, and forms an insoluble salt, which is precipitated. The alumina which constitutes the base of the alum, unites with the acetic acid, and forms an acetate of alumina. The chalk and potash, according to Berthollet, serve to saturate the excess of acid; but it seems more probable that the addition of these substances is found necessary, on account of new decompositions which are effected by their action. Several advantages arise from the formation of the acetate of alumina, in the future changes which are to be effected. The alumina, or earthy basis of this salt, is retained in combination with the acid, by a much weaker affinity than when combined with sulphuric acid in the state of alum. Its affinity being thus weakened, it is more easily decomposed, and unites more readily with the stuff and colouring particles. Another advantage not less important is, that the effect of the acetic acid on the colouring matter being less powerful than the sulphuric acid, the acid liquor which remains after the separation of the alumina, does not produce such hurtful effects. And besides, as the acetate of alumina does not crystallize, the mordant which is thickened with starch or gum, to prepare it for being applied to the block on which the design is engraved, retains the same uniform consistence, which would not be the case if it contained alum, the latter being disposed to crystallize.

71. Let us now trace the different steps of the operation in printing a piece of cloth. When it has been impregnated with the mordant, in the manner determined by the design, it is immersed into a madder bath. Thus the whole of the cloth is coloured; but the colours are deeper on those parts to which the mordant has been communicated; because in those parts the colouring particles of the madder have entered into combination with the alumina and the stuff, forming a triple compound. The acetic acid separated from its earthy basis remains in the bath.

72. The effect of external agents on the colouring particles in this state of combination is much less considerable than when they are in a separate state, or only combined with the stuff, without the intermediate action of another substance. It is on this property that the subsequent operations depend. Having been immersed in the madder bath, the cloth is afterwards boiled with bran, and exposed to the open air by spreading it out on the grass; and the ultimate repetition of these operations is continued till the ground is whitened. The colouring particles of the madder which have not come in contact with the alumina are completely changed by entering into new combinations; while those which have united with it remain unaltered in consequence of the stronger affinity, so that those parts of the cloth which have been impregnated with the mordant, retain the colour and exhibit the design.

73. The decomposition of the colouring particles by boiling the stuff with bran, and exposure to the air, seems to be effected in a manner similar to the destruction of the colouring matter of flax, and is to be accounted

counted for in the same way. In the process of bleaching, indeed, alkaline substances are employed. But for the purpose of discharging the superfluous colouring-matter from printed cloths, bran is preferred as a substitute; because part of the colouring-matter, even when fixed by alumina, would be destroyed by the stronger action of alkalies; but as the action of the bran is much weaker, it affects only the colouring particles which have not come in contact with the alumina, and which by the action of the air are disposed to undergo a more easy solution.

74. Let us take another example with a different mordant. If, instead of alum, a solution of iron, as the acetate of iron, be employed, similar phenomena are exhibited. The solution of iron is decomposed by the particles of colouring-matter, and a triple compound is thus formed of the colouring-matter, the oxide of iron, and the stuff. But when this mordant is employed, a great variety of shades from brown to a deep black are obtained by the use of madder; and by a combination of alum and iron, the colours produced are of a mixed nature, inclining on the one hand to red, and to black on the other. And if another substance, as dyers weed, be substituted for the madder, other colours are obtained. Indeed the great variety of shades which are communicated to printed stuffs are derived from the colouring matter of madder, dyers weed, and indigo, fixed by alumina or the oxide of iron as mordants.

75. The different substances which enter into the composition of a mordant remain in combination till a new action is induced by the application of another substance. Thus, the affinity of the stuff for one of their constituent parts produces a decomposition and new combinations. But even this effect is sometimes incomplete, or does not at all take place without the action of another affinity, namely, that of the colouring-particles. We have an example of this in the mixture of alum and tartar, which is one of the most common mordants in the dyeing of wool.

76. The following experiments were made by Berthollet, to ascertain the effects of these substances as mordants. He dissolved equal weights of alum and of tartar; and he found that the solubility of the tartar was increased by the mixture. By evaporation and a second crystallization, the two salts were separated, so that no decomposition had taken place. Half an ounce of alum and one ounce of wool were boiled together for an hour, a precipitate was formed, which being carefully washed, was found to consist of filaments of wool incrusting with earth. To this sulphuric acid was added, and the solution being evaporated to dryness, crystals of alum were obtained, with the separation of some particles of carbonaceous matter. The liquid in which the wool had been boiled being evaporated, yielded only a few grains of alum; what remained would not crystallize. This being redissolved and precipitated by means of an alkali, the alumina which was thrown down was of a slate colour, became black when placed on red-hot coals, and emitted alkaline vapours. In this experiment it appears that the alum was decomposed by the wool, and part of the alumina had combined with its most detached filaments which were least retained by the force of aggregation; that part of its animal substance had been dis-

solved and precipitated by the alkali from the triple compound.

77. The same experiment was repeated with half an ounce of alum and two drams of tartar; but no precipitation followed. A small portion of the tartar, and some irregular crystals of alum, were obtained by crystallization: the remainder refused to crystallize; but being diluted with water, precipitated by potash, and evaporated, it yielded a salt which burned like tartar. The wool which was boiled with the alum had a harsh feel; but the other retained all its softness. The first, after being subjected to the process of maddering, had a duller and lighter tint; but the colour of the latter was fuller and brighter.

78. In the first of these experiments the wool had effected a decomposition of the alum, had united with part of the alumina; and even part of the alum which retained its alumina had dissolved some portion of the animal matter. In the second experiment it appears, that the tartar and alum, between which there seems to exist a balance of affinities, can only act on each other by the intermediate action of the wool. The principal use of the tartar seems to be to moderate the action of the alum on the wool, by which it is injured. In the aluming of silk and thread, whose action on alum is less powerful than that of wool, tartar is not found requisite.

79. Whatever be the mode adopted in aluming, or whatever be the chemical changes which are produced, its final effect is the union of the alumina with the stuff. At first this combination has probably been incomplete, and a partial separation only of the acids has taken place; but it is perfected after the cloth has been boiled with the madder, as appeared in the case of printed stuffs.

80. The principal substances which are employed for the purposes of mordants in the process of dyeing, are earths, metallic oxides, and some astringent matters. Alumina, which is now one of the most important, and in most general use, was very early employed as a mordant. This earth, as has been proved by direct experiment, and which is still farther confirmed by daily practice and observation, is useful in the art of dyeing, in consequence of the affinity which exists between it, the stuffs to be dyed, and the colouring matter. The affinity of alumina for animal matters, as wool and silk, as much stronger than that for vegetable productions, as cotton and linen; and hence the difference in the facility of fixing the colours on these different substances, and in their durability.

81. When alumina is employed as a mordant, it is always in a state of combination, either in that of alum, which is the sulphate of alumina and potash, or united with the acetic acid, forming the acetate of alumina. Alum was employed at a very early period as a mordant. It was used by the ancients as it was found native, and therefore far from being in a state of purity. But as the nature of the constituent parts of alum was long unknown, its use in dyeing, as well as that of mordants in general, can only be ranked among the discoveries of modern chemistry. Alumina is also employed for a similar purpose, in combination with the acetic acid. This combination of alumina seems to have been first introduced about the beginning of the 18th century, and its introduction, like other valuable improvements,

improvements, was owing to accident. It was first employed by the calico-printers; but at what time, or by whom it was first used, is not exactly known. In one of the earliest recipes for preparing the mixtures employed as mordants in calico-printing, which Dr Bancroft, in his investigation of this subject, informs us he examined, the substances directed to be used are alum, sal ammoniac, saltpetre, red orpiment, and kelp; and these were to be mixed with water. In another, which he observes probably followed this, these ingredients were to be dissolved in vinegar. Sugar-of-lead was afterwards added in small quantity, and among a great variety of other substances which were employed at different times, litharge and white-lead came into use. In cases where vinegar was employed as the solvent, after different decompositions had taken place, a portion of acetate of alumina was formed, and the use of it was found to be followed with good effects. The quantity of sugar-of-lead, from observing the advantages derived from it, was gradually increased, and the employment of many of the other substances which were found by experience to be useless, was omitted. As the introduction of acetate of alumina was at first owing to chance, and as the changes and decompositions which took place in its formation were entirely unknown, it is not to be wondered at that the discovery or invention of this substance as a mordant, should not be distinctly ascertained.

82. The usual method of preparing the acetate of alumina is by pouring acetate of lead into a solution of alum. Both the salts are decomposed, by an exchange of their constituent parts. The sulphuric acid and the lead having a stronger affinity than the sulphuric acid and the alumina, combine together, and fall to the bottom in the form of an insoluble powder. The alumina at the same time enters into combination with the acetic acid, and remains dissolved in the liquid. But the application and effects of this substance in dyeing have been fully illustrated in treating of mordants in general.

83. Lime is the only earth, besides alumina, which is employed in dyeing. The affinity of lime for cloth is sufficiently strong; it is, however, found to answer the purpose of a mordant less perfectly than alumina, on account of the colour, which is not so good. It is employed, either in the state of lime water, or in that of sulphate of lime dissolved in water.

84. Metallic oxides have a strong affinity for animal substances. They have also so great an attraction for many colouring matters, that they separate from the acids with which they are combined, and are precipitated in combination with the colouring matters. In consequence of these different affinities, metallic oxides are of great importance in dyeing, and hence they were early applied in that art, and are now extensively used. But besides the affinity of these oxides for the colouring particles, and for animal substances, their solutions in acids possess properties by which they are more or less fit to be employed as mordants. Thus, those oxides which easily part with their acids, such as that of tin, are capable of entering into combination with animal substances, without the aid of colouring particles. All that is necessary is to impregnate the wool or the silk with a solution of tin. Some metallic

substances yield only in combination, a white and colourless basis; but there are others which, by means of their own colour, produce modifications on the peculiar colour of the colouring particles. But the effects of many metallic oxides are extremely different, according to the proportion of oxygen with which they are combined; and this proportion is variable.

85. The affinity of metallic oxides for vegetable matters is considerably weaker than that which they have for animal substances. Metallic solutions, therefore, are found not to answer so well as mordants for colours in dyeing cotton or linen. Iron, indeed, is an exception, the oxide of which, it is well known, has a strong affinity for vegetable substances. Iron moulds on cotton or linen are owing to a combination of the oxide of iron with the vegetable matter.

86. Although almost all metallic oxides have an affinity for animal and vegetable matters, and might therefore be employed as mordants, yet two only, either because they are found to answer the purpose better, or because they are cheaper, are used to any extent. These are the oxides of tin and of iron.

87. The use of the oxide of tin seems to have been first discovered by a German chemist of the name of tin. Kuster or Kuffler. Observing the effects of a solution of tin in nitric acid, in giving a more vivid colour to stuffs dyed with cochineal, he was led to the discovery of the method of producing what has since been denominated cochineal scarlet. This discovery has been ascribed by others to Drebel, a Dutch chemist: and Macquer, who is of this opinion, supposes that the first solutions of tin were made with nitro-muriatic acid; but Dr Bancroft thinks that there is good reason to believe, that nitric acid only was used for some years for this purpose. According to Mr Delaval, the use of tin in dyeing was known to the ancients; and he supposes that the tin which the Phœnicians carried from Britain, was employed in this way, because he thinks that it is necessary to the production of red colours, whether from animal or vegetable matter. Dr Bancroft, however, has proved, that this opinion is founded in mistake.

88. About the year 1543, Kuster brought his secret to London, and it appears that it was first employed for this purpose at Bow. Hence the scarlet colour thus produced was denominated in this country the Bow dye. It seems too, that this mode of dyeing scarlet was very early introduced into Holland. A Frenchman of the name of Gobelin, received an account of the process from a Flemish painter called Kloeck, to whom it had been communicated by Kuster himself, and established it in France. Hence the Bow dye of England was known in other parts of Europe under the names of Dutch scarlet, scarlet of the Gobelins.

89. We have mentioned above, that the effects of metallic oxides as mordants in dyeing, depend on the different proportions of oxygen with which they may be combined. Thus, there are two oxides of tin containing different proportions of oxygen; the one contains 30 parts of oxygen in the 100, and the other contains 40. The oxide having the smaller proportion of oxygen, being exposed to the air, combines with a new portion of oxygen, and is soon converted into the oxide with the greater proportion, or the white oxide. It is

this last which is the mordant, for if the other were applied to the stuff, it would soon be converted into the white oxide, by combining with an additional portion of oxygen.

90. Tin was first used as a mordant dissolved in nitric acid; but this preparation was found not to answer well, because the nitric acid readily converted the tin to the state of white oxide, in which state it is incapable of dissolving it. A precipitation of the tin took place, to prevent which, different substances were added, as common salt, or sal ammoniac; and thus a nitro-muriatic acid was produced, by which means the white oxide of tin was held in solution. It appears, however, that it was a considerable time before this method came into general use. Hellot, in an account of the process employed in his time for dyeing scarlet at Carcassonne, mentions that the tin was dissolved only in diluted nitric acid, adding that a Mr Baron was the first in that city who employed nitro-muriatic acid for the solution of tin, to prevent the precipitation of the oxide.

91. The ordinary solution of tin is made with that species of nitric acid called single aquafortis, and as it is usually prepared, it is found capable of dissolving about $\backslash frac\{1\}\{2\}$ part of its weight of granulated tin. To each pound of aquafortis from one to two ounces of sea salt, or, what is deemed preferable by some, of sal ammoniac, are added. The acid is commonly diluted with a little water. The solutions which are made most slowly, and with the least separation of vapours, are found to succeed best. Two ounces of granulated tin are usually allowed for each pound of aquafortis; and the metal should be added at different times to moderate the rapidity of the solution. The water added to the acid should be weighed or measured, that a solution of the same strength may be always obtained. Eighteen or 20 pounds of this solution (B) are required to give a full cochineal scarlet to 100 pounds of woolen cloth.

92. But in the dyeing of scarlet, according to the ordinary process, a quantity of tartar is dissolved in the water, along with the nitromuriate of tin; and if the tartar be employed in sufficient quantity, the mordant is not to be considered as a nitromuriate of tin, but a tartrate or combination of tin with tartaric acid, in consequence of the decomposition which takes place, when these substances are brought to act on each other; for the nitromuriatic acid enters into combination with the potash or the tartar, while the acid of the tartar forms a compound with the oxide of tin.

93. It has been proposed by Haussman to employ the acetate of tin as a mordant for cotton and linen, instead of the nitromuriate. The acetate of tin is prepared by mixing together acetate of lead and nitromuriate of tin; and as the affinity between metallic oxides and vegetable substances is less powerful than the affinity between these oxides and animal matters, this mordant has been found preferable for cotton and linen stuffs; for the affinity of the oxide of tin for the acetic acid being weaker than for the nitromuriatic acid, it is more easily decomposed.

94. Dr Bancroft* tried the solution of tin in sulphuric acid, but found that it would not answer, on account of its destructive action on the cochineal colour; but he found afterwards, that, by the use of muriatic acid combined with $\backslash frac\{1\}\{2\}$ its weight of sulphuric acid, good effects were obtained. The proportions which he employed were about 14 ounces of tin in a mixture of two pounds of sulphuric acid of the ordinary strength, with about 3 pounds of muriatic acid. This preparation may be made in the cold; but the solution is very rapidly promoted with a sand heat. The solution of tin made in these proportions, Dr Bancroft observes, is perfectly transparent and colourless; and in the space of three years, during which time he kept a solution of it, no precipitation had taken place. It produces, he adds, full twice as much effect as the dyer's spirit, or nitromuriatic solution of tin, and at less than one-third of the expence.

95. Iron exists in two states of combination with oxygen. In the state of green oxide it contains the smaller proportion of oxygen, and in that of red oxide the greater proportion. In the last state it can only be employed as a mordant in dyeing; for if it be applied in the state of green oxide, in consequence of its strong affinity for oxygen, it attracts it from the atmosphere, and is soon converted into red oxide. The difficulty of removing iron spots or mould from cotton or linen shows with what force of affinity the red oxide of iron adheres to cloth. Iron is employed as a mordant in two states of combination, either in that of sulphate or acetate of iron. The sulphate of iron is generally employed for wool. The stuff is immersed in the solution of the salt in water. In this state it may be also used for cotton; but it is more commonly preferred in the state of acetate of iron. This is the combination of iron with the acetic acid, and it is usually prepared by dissolving iron in vinegar or sour beer; and the longer it is retained in the solution, it is found to act more powerfully as a mordant, because it is then in a state of more complete oxidation.

96. Some other saline bodies are also employed as mordants, to facilitate the combination of the colouring matter with the cloth, or to produce greater variety of shades of colour. Among these substances may be mentioned common salt, sal ammoniac, acetate of lead, sulphate and acetate of copper, sulphate of zinc.

97. Besides the mordants obtained from the class of Animal salts, vegetable and animal substances also serve a similar purpose. In the process for dyeing the Turkey red, which will be afterwards described, the cotton stuffs should be impregnated with an animal substance, as oil; and the astringent principle is often employed as a medium of combination between colouring particles and stuffs. Tan, or the astringent principle, having a strong affinity for cloth, is found extremely useful as a mordant. It is commonly prepared by infusing nut-galls in water. The cloth is immersed in this solution, and allowed to remain till it is sufficiently impregnated with the tan. Sumach, which is the shoots of the Rhus coriaria Lin. a shrub which grows in the southern parts of

(B) This solution is called spirit by the dyers in this country.

Europe, is often used and prepared in the same way as the nut galls.

98. Mordants have a very considerable effect on the colour; and, by varying the mordant, very different colours, and a great variety of shades, may be obtained from the same colouring matter. Some mordants themselves may be considered as communicating a colour without the addition of any colouring substance; and although, when the latter is added, a new set of affinities is brought into action, yet there is little doubt that the mordant also has a considerable share in fixing the shades of colour. Let us take an example in dyeing with cochineal. When the aluminous mordant is employed, the colour produced is crimson; but when the oxide of iron is substituted for the alumina, the colour obtained is black. The effect is obviously produced by a change in the action of the affinities between the colouring matter and the mordant, and the colouring matter and light. In the use of mordants, therefore, it is necessary to attend to their combined effects with the colouring matter employed, and to be able to communicate particular colours to stuffs with any degree of certainty, to know the amount of that effect.

99. Even in the mode of applying mordants, the variety of shades may be greatly multiplied. Different effects, for instance, are produced by previously impregnating the stuff with the mordant, or by mixing it with the bath. Different effects also arise from using heat, or, as the stuff is more or less rapidly dried; and this must appear to be the case, if we consider the different affinities which are in action, and the change on the action of these affinities in these different circumstances, as well as in others which can scarcely be appreciated. The combination of these substances which have an affinity for the stuff, and the decompositions which are the result of that combination, are greatly facilitated by the evaporation of the water or other liquid which held these substances in solution; because by its affinity, which is opposed to the action of the affinity between these substances and the stuff, the affinity of the latter produces a more limited effect. But in dyeing, the process should proceed slowly, that the substances may not be separated before their mutual affinities have begun to operate.

100. Considerable differences must be observed in the mode of employing the mordant, as the force of affinity between the stuff and the colouring matter is greater or less. When this affinity is strong, the mordant and the colouring substance may be mixed together; the compound thus formed, immediately enters into combination with the stuff. But if the affinity between the stuff and the colouring particles be weak, the compound formed of the latter and the mordant may separate, and a precipitation take place, before it can be attached to the stuff; and hence it is in these cases, that the mordant which is to serve as the medium of union between the stuff and the colouring matter, must be combined with the former, before the application of the latter. It is from these differences that different processes must be followed in fixing colouring matters on animal and vegetable productions; as for instance, in dyeing wool or silk black, or with cochineal.

101. In estimating the effects of mordants, and in judging of the most advantageous manner of applying them, it is necessary to attend to the combinations which may be formed, either by the action of the ingredients of which they are composed, or, by that of the colouring matter and the stuff. It is necessary also, to take into consideration the circumstances which may tend to bring about these combinations with more or less rapidity, or that may render them more or less perfect. The action which the liquor in which the stuff is immersed may have, either on its colour or texture, must also be considered; and to be able accurately to judge of the extent of this action, we must know the proportions of the principles of which the mordant is composed; which of these principles remains in an uncombined state in the liquor, and the proportion or quantity which is thus separated.

CHAP. III. Of the Nature and Properties of the Substances to which Colours are communicated in the Processes of Dyeing.

102. In the more limited sense to which we have here restricted the art of dyeing, the substances to which colours are usually communicated by means of this art, are wool, silk, cotton, flax, and hemp. Of these, the two first are animal substances, and the three latter are derived from the vegetable kingdom. These two classes of bodies present striking differences, not only in structure, but also in their composition and chemical properties.

103. Animal substances are distinguished from those which have a vegetable origin, by the nature of their constituent parts. The former contain a large proportion of azote, which exists sparingly in the latter. Hydrogen, or the base of hydrogen gas or inflammable air, is found in greater abundance in animal matters, than in vegetable productions. In the distillation of animal and vegetable substances, the difference of their constituent parts is not less remarkable. The former afford a large proportion of ammonia, or volatile alkali; the latter yield very little, and sometimes give out an acid substance. Animal matters afford much oil, while vegetable substances sometimes do not afford it in any perceptible quantity. From the nature of their component parts, animal substances produce a bright flame in burning; and their combustion is accompanied with a penetrating odour, which is owing to the formation and emission of ammonia and oil. Animal matters run rapidly into the putrefactive process, while vegetable substances more slowly undergo the changes which are induced by the vinous or acetous fermentation.

104. The constituent principles of animal substances have a stronger tendency than those which enter into the composition of vegetable matters, to assume the elastic form. On this account the cohesive force existing between the particles of the former is inferior to that of the particles of the latter. Hence animal matters are more disposed to combine with other substances, more liable to be destroyed by different agents, and to enter into combination with colouring particles. Thus, animal substances are destroyed by the caustic fixed alkalis, and they are decomposed by the nitric and sulphuric

phuric acids. The action of acids and alkalies on silk is less powerful than upon wool, and it is less disposed to combine with the particles of colouring matter. In this respect it bears some resemblance to vegetable substances; but on vegetable matters, the action of alkalies and acids is less powerful than on animal substances; and the action of acids is more feeble on cotton than on flax or hemp. It is even decomposed with considerable difficulty by means of nitric acid.

In the four following sections, we shall consider the peculiarities of these substances at greater length.

SECT. I. Of Wool.

Structure. 105. Wool, which is well known as the covering of sheep, derives its value from the length and fineness of its filaments. The filaments of wool are considerably elastic, for they may be drawn out beyond their usual length, and when the force is removed, they recover it again. The surface of the filaments of wool or hair is not perfectly smooth; for although no roughness or inequality can be discovered by the microscope, yet they seem to be formed of small laminae placed over each other in a slanting direction, from the root of the filament towards its point, resembling the arrangement of the scales of a fish, which cover each other from the head of the animal to its tail; or perhaps they consist of zones placed over each other, as is observed in the horns of animals. This peculiarity of structure of the filaments of hair and wool is proved by a simple experiment. If a hair be laid hold of by the root in one hand, and drawn between the fingers of the other hand, from the root towards the point, scarcely any friction or resistance is perceived, and no noise is heard; but if it be grasped by the point, and passed in the same manner between the fingers from the point towards the root, a resistance is felt, and a tremulous motion is perceptible to the touch, while the ear is sensible to a slight noise. Thus it appears, that the texture of the surface of hair or wool is not the same from the root towards the point, as it is from the point towards the root. This is farther confirmed by another experiment. If a hair be held between the thumb and forefinger, and they are rubbed against each other in the longitudinal direction of the hair, it acquires a progressive motion towards the root. This effect depends not on the nature of the skin of the finger, or on its texture, for if the hair be turned, and the point placed where the root formerly was, the motion is reversed, that is, it will still be towards the root.

Felting. 106. On this peculiarity of structure, which was observed by M. Monge, depend the processes of felting and fulling, to which hair and wool are subjected, for different purposes. In the process of felting, the flocculi of wool are struck with the string of the bow, by which the filaments are separately detached, and dispersed in the air. These filaments fall back on each other in all directions on the table, and when a layer of a certain thickness is formed, they are covered with a cloth, on which the workman presses with his hands in all parts. By this pressure the filaments of wool are brought nearer to each other; the points of contact are multiplied; the progressive motion towards the root is pro-

duced by the agitation; the filaments entangle each other; and the laminae of each filament, taking hold of those of the other filaments, which are in an opposite direction, the whole is retained in the state of close texture.

107. Connected with this operation is that of fulling. The roughness on the surface of the filaments of wool, and their tendency to acquire a progressive motion towards the root, produces considerable inconvenience in the operations of spinning and weaving. These inconveniences are obviated by covering the filaments with a coat of oil, which fills up the cavities, and renders the asperities less sensible. When these operations are finished, the stuff must be freed from the oil, which would prevent it from taking the colour with which it is to be dyed. For this purpose it is taken to the fulling-mill, where it is beaten with large beetles, in a trough of water, through which clay has been diffused. The clay unites with the oil, which being thus rendered soluble in the water, is carried off by fresh portions of water, conveyed to it by proper apparatus. In this way the stuff is scoured; but this is not the sole object of the operation. By the alternate pressure of the beetles, an effect similar to that of the hands in the operation of felting, is produced. The filaments composing a thread of warp or woof, acquire a progressive motion, are entangled with the filaments of the adjoining threads; those of the latter into the next, and so on, till the whole threads are felted together. The stuff is now contracted in all its dimensions, and participating both of the nature of cloth and of felt, may be cut without being subjected to ravel; and when employed to make a garment, requires no hemming. In a common woollen stocking web, after this operation, the stitches, when one happens to slip, are now no longer subject to run, and the threads of the warp and woof being less distinct from each other, the whole stuff is thickened, and forms a warmer clothing.

108. The various manufactures of which wool constitutes the basis, are justly regarded among the most important to man in civilized society. Accordingly, the production of fine wool, and the causes which retard or improve the breed of sheep from which it is obtained, have greatly occupied the attention of economists and philosophers in our own, as well as in other countries. The wool of different breeds of sheep, in different countries, it is well known, possesses very different qualities, both with regard to the fineness of the filament, and the colour. Some is of a white, or yellow, and some of a reddish, and black colour. Excepting the wool of the breed of sheep in Andalusia, the Spanish wool was formerly all of a brownish black colour. This was preferred by the native Spaniards; and even at this day, the dress of some religious orders in Roman Catholic countries, consists of cloth manufactured from this wool, and retaining its natural colour. But for the purposes of dyeing, white wool is now always preferred, because it is found susceptible of receiving better and more durable colours.

109. Wool is naturally covered with a kind of grease or oil, which is found to preserve it from insects or moths, and on this account this greasy matter is not removed, or the wool is not scoured, till it is to be dyed.

or spun (c). The process for scouring wool is the following. It is put for about a quarter of an hour into a kettle, with a sufficient quantity of water, to which a fourth part of putrid urine has been added. It is then heated to such a degree as the hand can bear, occasionally stirred, and after being taken out, is allowed to drain. It is then put into a basket, and exposed to a stream of running water, and moved about till the grease is so completely separated, that it no longer renders the water turbid. After being drained, it is sometimes found to lose by this operation above one-fifth of its weight. It is almost unnecessary to observe, that the more carefully and completely this process is performed, the better the wool is fitted to receive the colouring matter. Our chemical readers will readily perceive the nature of the changes which are effected in this process of scouring. The ammonia, or volatile alkali, which exists in the urine, combines with the oil of the wool, and forms a soap, which being soluble in water, is dissolved, and carried off.

110. Wool is either dyed in the fleece, or after it is spun into threads, or when it has been manufactured into cloth. For the purpose of forming cloths of mixed colours, it is dyed before it is spun; for the purposes of tapestry, it is dyed in the state of thread; but most commonly it is subjected to this process after it has been manufactured into cloth. In these different states, the quantity of colouring matter which is taken up is very different. The proportion is largest when it is dyed in the fleece, because then the filaments being more separated, a greater surface is exposed to the action of the colouring particles. For a similar reason the quantity of colouring matter taken up is greater when in the state of thread or yarn, than when it is formed into cloth. But cloths themselves must vary greatly in this respect, according to their different qualities. Their different degrees of fineness, or closeness of texture, will produce considerable variations; and besides, the difference in the quantity and dimensions of the substances to be dyed, the different qualities of the ingredients employed in the process, and the different circumstances in which it is performed, should be a caution against trusting to precise quantities, regulated by weight or measure, which are recommended according to general rules. According to the fineness of the texture of the wool, and the nature of the colouring matter employed, it is found to be more or less penetrated with this matter. The coarse wool from the thighs and tails of some sheep, receives colours with difficulty, and the finest cloth is never completely penetrated with the scarlet dye. The interior of the cloth appears always, when cut, of a lighter shade, and sometimes even white.

SECT. II. Of Silk.

111. Silk, which forms the basis of one of the richest and most splendid parts of dress, among the wealthy and luxurious, in civilized society, is the production of different species of insects. The phalaena bombyx, or silk-worm, which is a native of China, attracted the

attention of mankind in that country, from the earliest ages. The honour of having first collected and prepared silk from the cocoons or balls in which it is wound up by the insect, during its metamorphosis, is ascribed by the Chinese historians, to the wife of an emperor. The phalaena atlas, Lin. which is also a native of China, is said to form larger cocoons, and to yield a stronger silk. The silk-worm was first carried from China to Hindostan, and afterwards to Persia. Silk seems not to have been known to the Greeks or Romans till the time of Augustus. Its nature and origin were little understood, and for many ages it was so scarce, that it could only be purchased at a price which was equal to its weight in gold. The emperor Aurelian, it is said, from a principle of economy, resisted the urgent solicitations of his empress, who wished to have a silken robe, alleging the extravagance of the expence. About the middle of the sixth century, two monks returned from India to Constantinople, and brought with them a considerable number of silk-worms, with instructions for managing and breeding them, as well as for collecting, preparing, and manufacturing the silk. Establishments were thus formed at Corinth, Athens, and other parts of Greece. The crusades, which greatly contributed to the diffusion of different kinds of knowledge, by the intercourse which took place between different countries, proved useful in disseminating the knowledge of rearing the silk-worm, and preparing and manufacturing its valuable productions. Roger, king of Sicily, about the year 1130, returning from one of these frantic expeditions, brought with him from Athens and Corinth, several prisoners, who were acquainted with the management of silk-worms, and the manufacturing of silk. Under their superintendence, manufactories were established at Palermo and Cagliari in Sicily. This example was soon adopted, and followed in different parts of Italy and Spain. In the time of James I. an attempt was made to establish the silk-worm in England. For this purpose the culture of the mulberry-tree, on which the insects feed, was strongly recommended by that prince to his subjects; but the attempts which were made have been hitherto unsuccessful.

112. The fibres of silk are covered with a coating or Scouring, natural varnish of a gummy nature. To this are ascribed its stiffness and elasticity. Besides this varnish, the silk which is usually met with in Europe is impregnated with a substance of a yellow colour, and for most of the purposes to which silk is applied, it is necessary that it should be deprived, both of the varnish and of the colouring matter. On this account it must be subjected to the operation of scouring; but for silks which are to be dyed, this process should not be carried so far as for those which are merely to be whitened; and different colours, it is observed, require different degrees of this operation. The quantity of soap constitutes the chief difference. A hundred pounds of silk boiled in a solution of 20 lbs. of soap for three or four hours, adding new portions of water during the evaporation, are sufficiently prepared for receiving common

(c) According to an observation of Reaumur, rubbing any stuff with greasy wool, is sufficient to preserve it from moths.

Of Substances to be coloured. For blue colours, the proportion of soap must be increased; and scarlet, cherry-colour, &c. require a still greater proportion, for the ground must be whiter for these colours.

Process, when employed white. 113. Silk which is to be employed white, must undergo three operations. In the first the banks are immersed in a hot but not boiling solution of 30 lbs. of soap to 100 of silk. When the immersed part is freed from its gum, which is known by its whiteness, the banks are shaken over, as the workmen term it, so that the part which was not previously immersed may undergo the same operation. They are then wrung out as the process is completed. In the second operation the silk is put into bags of coarse cloth, each bag containing 20 or 30 lbs. These bags are boiled for an hour and a half, in a solution of soap prepared as before, but with a smaller proportion of soap; and that they may not receive too much heat, by touching the bottom of the kettle, they must be constantly stirred during the operation. The object of the third operation is to communicate to the silk different shades, to render the white more agreeable. These are known by different names, as China-white, silver-white, azure-white, or thread-white. For this purpose a solution of soap is also prepared, of which the proper degree of strength is ascertained by its manner of frothing by agitation. For the China-white, which is required to have a slight tinge of red, a small quantity of anatto is added, and the silk is shaken over in it till it has acquired the shade which is wanted. In other whites, a blue tinge is given by adding a little blue to the solution of soap. The azure-white is communicated by means of indigo. To prepare the azure, fine indigo is well washed two or three times in moderately warm water, ground fine in a mortar, and boiling water poured upon it. It is then left to settle, and the liquid part only, which contains the finer and more soluble parts, is employed.

114. Some use no soap in the third operation; but when the second is completed, they wash the silks, fumigate with sulphur, and azure them with river water, which should be very pure. But all these operations are not sufficient to give silk that degree of brightness which is necessary, when it is to be employed in the manufacture of white stuffs. For this purpose it must undergo the process of sulphuration, in which the silk is exposed to the vapour of sulphur; for an account of which see BLEACHING. But before the silk which has been treated in this way is fit for receiving colours, and retaining them in their full lustre, the sulphur which adheres to it must be separated by immersion and agitation for some time in warm water, otherwise the colours are tarnished and greatly injured.

Mode of extracting its colouring matter. 115. It has long been an object of considerable importance, to deprive silk of its colouring matter, without destroying the gum, on which its stiffness and elasticity depend. A process for this purpose was discovered by Beaumé, but as it was not made public, others have been led to it by conjecture and experiment. The following account, given by Berthollet, is all that has transpired concerning this process. A mixture is made with a small quantity of muriatic acid and alcohol. The muriatic acid should be in a state of purity, and particularly should be entirely free from nitric acid, which would give the silk a yellow colour. In the mixture, thus prepared, the silk is to be immersed.

One of the most difficult parts of the process, especially when large quantities are operated upon, is to produce a uniform whiteness. In dyeing the whitened silk, there is also considerable difficulty to prevent its curling, so that it is recommended to keep it constantly stretched during the drying. The muriatic acid seems to be useful in this process, by softening the gum, and assisting the alcohol to dissolve the colouring particles which are combined with it. The alcohol which has been impregnated with the colouring matter may be again separated from it and purified, that it may serve for future operations, and thus render the process more economical. This may be done by means of distillation with a moderate heat, in glass or stone-ware vessels.

116. The preparation with alum is a very important preliminary operation in the dyeing of silk. Without this process, few colours would have either beauty or durability. Forty or fifty pounds of alum, previously dissolved in warm water, are mixed in a vat, with forty or fifty pails of water; and to prevent the crystallization of the salt, the solution must be carefully stirred during the mixture. The silk being previously washed and beetled, to separate any remains of soap, is immersed in this alum liquor, and at the end of eight or nine hours is wrung out, and washed in a stream of water. A hundred and fifty pounds of silk may be prepared in the above quantity of liquor; but when it begins to grow weak, which may be known by the taste, 20 or 25 lbs. of dissolved alum are to be added, and the addition repeated till the liquor acquires a disagreeable smell. It may then be employed in the preparation of silk intended for darker colours, till its whole strength is dissipated. This preparation of silk with alum must be made in the cold; for when the liquor is employed hot, the lustre is apt to be impaired.

SECT. III. Of Cotton.

117. Cotton is the down or wool contained in the pods of a shrubby plant, which is a native of warm climates. Of this genus of plants (Gossypium Lin.) there are four species, one of which only is perennial; the other three are annual plants; but of these there are many varieties, occasioned by the difference of soil or temperature in which they are produced. The principal differences among cottons consist in the length and fineness of the filaments, and in their strength and colour.

118. The peculiar structure of the fibres of cotton is not well known. According to the microscopic observations of Leeuwenhoek, they have two sharp sides, to which are ascribed the irritation and inflammation of wounds and ulcers, when they are dressed with cotton instead of lint. This peculiarity of structure, it is also supposed, may occasion some difference in the conformation, and number of the pores, on which alone the disposition of cotton to admit and retain colours better than linen, seems to depend. In this respect, however, it is inferior to wool and silk, because, on account of its vegetable nature, its affinity for colouring matter is less powerful.

119. It is well known that silk, cotton, and linen have a weaker affinity for colouring matter than wool. Le Pileur d'Apligny attempts to explain this by supposing that matter.

Substances to wool, and that the colouring particles enter them less easily and freely. But according to the observation of Dr Bancroft, the reverse of this seems to be the fact; for there is little difficulty in making silk, cotton, and linen, imbibe colouring matter, even when it is applied cold, without any artificial dilatation of the pores, which is always necessary in the dyeing of wool. The only real difficulty is to make them retain the colours after the matter has been imbibed; because being admitted so readily into their undilated pores, the particles cannot be afterwards compressed and retained by the contraction of these pores, as is the case with wool. It requires double the quantity of cochineal which is necessary for wool to communicate a crimson colour to silk; a certain proof that it can take up a greater quantity, and consequently that the pores are sufficiently large and accessible. Unbleached cotton is always preferred for dyeing Turkey red; because in this state the colour is found to be most permanent; and this is ascribed to the pores or interstices being less open than after it has undergone the process of bleaching. The same thing is observed of raw or unscoured silk. It is found to combine more easily with the colouring matter, and to receive a more permanent colour in this state than after it has been scoured and whitened. "The openness of cotton and linen (says Dr Bancroft), and their consequent readiness to imbibe, both colouring particles, and the earthy or metallic bases employed to fix most of them, are circumstances upon which the art of dyeing and calico-printing is in a great degree founded." But is not this too mechanical an explanation of the phenomenon? Might it not rather be alleged that it is owing to a difference of affinities which exists between the particles of colouring matter and the substance which is separated from the silk or cotton by the process of bleaching or scouring? This substance probably acts the part of a mordant; and having a stronger affinity for the stuff and for the colouring matter than the stuff has for the latter, the colour communicated is more durable when silk or cotton is dyed in the unbleached or unscoured state.

120. To prepare cotton stuffs for receiving the dye, several operations are necessary. It must first undergo the process of scouring. By some it is boiled in sour water, or in alkaline ley. It should be kept boiling for two hours, then wrung out, and rinsed in a stream of water till the water comes off clear. The stuffs to be prepared should be soaked for some time in water, mixed with not more than $\backslash frac\{1\}\{50\}$th part of sulphuric acid, and then carefully washed in a stream of water, and dried. In this operation the acid combines with a portion of calcareous earth and iron, which would have interrupted the full effect of the colouring matter in the process of dyeing.

121. Aluming is another preliminary process in the dyeing of cotton. The alum is to be dissolved in the manner already described, in preparing silk. Each pound of cotton stuff requires four ounces of alum. By some a solution of soda, about $\backslash frac\{1\}\{50\}$th part of the alum, and by others a small quantity of tartar and arsenic are added. The thread is to be impregnated by working it in small quantities with this solution. The whole is then put into a vessel, and the remaining part of the

liquor is poured upon it. In this state it is left for 24 hours, after which it is removed to a stream of water, and allowed to remain for an hour and a half, or two hours, to extract part of the alum. It is then to be washed. By this operation, cotton is found to gain an addition of about $\backslash frac\{1\}\{50\}$th part of its weight.

122. The operation of galling is another preparatory process in the dyeing of cotton stuffs. The quantity of astringent matter employed must be proportioned to its quality, and the amount of the effect required. Powdered galls are boiled for two hours in a proportion of water, regulated by the quantity of thread to be galled. This solution being reduced to such a temperature as the hand can bear, is divided into a number of equal parts, that the thread may be wrought pound by pound. The whole stuff is then put into a vessel, and the remaining liquor poured upon it, as in the former process. It is then left for 24 hours, if it is to be dyed black, but for other colours, 12 or 15 hours are found sufficient. It is then wrung out and dried.

In the galling of cotton stuffs, which have already received a colour, the precaution should be observed of performing this operation in the cold, otherwise the colour is subject to injury.

123. Berthollet informs us, that cotton which had been alumed acquired more weight in the galling than that which had not previously undergone that process; for although alum adheres but in small quantities to cotton, it communicates to it a greater power of combining, both with the astringent principle, and with the colouring particles. This, we may add, may be considered as a good instance of the action of intermediate affinities, and of the advantage to be derived to the art of dyeing, from investigating and observing this action.

SECT. IV. Of Flax.

124. Flax and hemp nearly resemble each other in their general properties; and so far as relates to the process of dyeing, what is said of the one may be applied to the other. Flax or lint is obtained from the bark of Linum usitatissimum, and hemp from that of Cannabis sativa.

125. Before flax is properly prepared to receive the dye, it must be subjected to several processes. One of the most important is that of watering, by which the fibrous parts of the plant are separated, and brought to that state in which they can be spun into threads. As the quantity and quality of the product depend much on this preliminary operation, it becomes of the greatest consequence that it be properly conducted. During this process, carbonic acid and hydrogen gas are given out. The extrication of these gases is owing to a glutinous juice which holds the green colouring part of the plant in solution, and which is the medium of union between its cortical and ligneous parts, undergoing a certain degree of putrefaction. This substance seems to resemble the glutinous part which is held dissolved in the juice obtained from plants by pressure; is separated from the colouring particles by means of heat; readily becomes putrid, and by distillation affords ammonia. But although it is held in solution with the expressed juice, it would appear that it cannot be separated from the cortical parts completely, by means of water; and hence it happens, that hemp or flax watered

Operations of Dyeing. watered in too strong a current, has not the requisite softness and flexibility. But on the other hand, if the water employed in this operation be stagnant and in a putrid state, the hemp or flax becomes of a brown colour, and loses its firmness. In the one case, the putrefactive process is interrupted; in the other it is continued too long, and carried too far. This process, therefore, is performed with the greatest advantage in places near the banks of rivers, where the water may be changed so frequently as to prevent such a degree of putrefaction as would be injurious to the flax, as well as prejudicial to the workmen, from noxious exhalations; and, at the same time, not so frequently as to retard or interrupt those changes which are necessary for rendering the glutinous substance soluble in water.

126. By the process of watering flax, and by drying before and after that process, the green coloured particles undergo a similar change to that which is observed in the green substance of the plants exposed to the action of air and light. The next part of the process, therefore, after watering, is to spread it out upon the grass, and thus expose it for some time to the air and sun. By this means the colour of the lint is improved, and the ligneous part becomes so brittle, that it is easily separated from the fibrous part. This operation, as is well known, is usually performed by machinery.

Structure. 127. The fibres of lint possess no perceptible degree of elasticity, and they appear to be perfectly smooth. No roughness or inequality can be detected by the feel, and no asperities can be perceived, even with the assistance of the microscope. Experience shows, that it produces no irritation on wounds or sores which are dressed with it, as is known to happen from a similar application of cotton stuffs.

Preparations for dyeing. 128. Flax which is intended for dyeing must be subjected to a similar series of operations with cotton, in the different processes of scouring, aluming and galling. A repetition of the mode of performing these operations is therefore unnecessary.

CHAP. IV. Of the Operations of Dyeing.

129. BEFORE we proceed to the detail of the processes of dyeing, we shall throw out a few hints on the operations in general, some of which may perhaps be useful to the practical dyer.

Advantages of large manufactories. 130. The works which are carried on in extensive manufactories, it has been observed, are followed with advantages which are unknown to those which are conducted on a limited scale or in a detached manner. By the subdivision of labour, each workman directing his attention to one or a few objects, acquires a great facility and perfection of execution, by which means the saving of time and labour becomes considerable. This principle is particularly applicable to the art of dyeing, because the preparation which remains after one operation may often be advantageously employed in another. A bath from which the colouring matter has been in a great measure extracted in the first operation, may be used as a ground for other stuffs, or with the addition of a fresh portion of ingredients may form a new bath. The galls which have been applied to the galling of silk may answer a similar purpose for

cotton or wool. From this it must appear that the limitations and restrictions under which the art of dyeing labours in some countries must tend to obstruct its progress and improvement. An extensive plan of operations, by which the different branches of the art are connected together, would effectually prevent the loss of ingredients, time, fuel, and labour.

131. A dye-house, which should be set down as near Dye-house as possible to a stream of water, should be spacious and well lighted. It should be floored with lime and plaster; and proper means should be adopted to carry off water or spent baths by forming channels or gutters, so that every operation may be conducted with the utmost attention to cleanliness.

132. The size and position of the caldrons are to be regulated by the nature and extent of the operations for which they are designed. Excepting for scarlet and other delicate colours, in which the tin is used as a mordant, in which case tin vessels are preferable, the caldrons should be of brass or copper. Brass, being less apt than copper to be acted on by means of chemical agents, and to communicate spots to the stuffs, is fitter for the purpose of a dyeing vessel. It is scarcely necessary to say that it is of the greatest consequence that the coppers or caldrons be well cleaned for every operation; and that vessels of a large size should be furnished at the bottom with a pipe and stop-cock for the greater convenience of emptying them: and there must be a hole in the wall or chimney above each copper to admit poles for the purpose of draining the stuffs which are immersed, so that the liquor may fall back into the vessel, and no part may be lost.

133. Dyes for silk, where a boiling heat is not found necessary, are prepared in troughs or backs, which are long copper or wooden vessels. The colours which are used for silk are extremely delicate. They must therefore be dried quickly, that they may not be long exposed to the action of the air, and there may be no risk of change. For this purpose, it is necessary to have a drying room heated with a stove. The silk is stretched on a moveable pole, which by the dyers is called a shaker. This is hung up in the heated chamber, and kept in constant motion to promote the evaporation.

134. For pieces of stuffs, a winch or reel must be constructed; the ends of which are supported by two of iron forks which may be put up at pleasure in holes made in the curb on which the edges of the copper rest. The manipulations in dyeing are neither difficult nor complicated. Their object is to impregnate the stuff to be dyed with the colouring particles, which are dissolved in the bath. For this purpose, the action of the air is necessary, not only in fixing the colouring particles, but also in rendering them more vivid; while those which have not been fixed in the stuff are to be carefully removed. In dyeing whole pieces of stuff, or a number of pieces at once, the winch or reel mentioned above must be employed. One end of the stuff is first laid across it, and by turning it quickly round, the whole passes successively over it. By turning it afterwards the contrary way, that part of the stuff which was first immersed, will be the last in the second immersion, and thus the colouring matter will be communicated as equally as possible.

135. In dyeing wool in the fleece, a kind of broad ladder

ladder with very close rounds, called by the dyers of this country, a scravo, or scray, is used. This is placed over the copper, and the wool is put upon it, for the purpose of draining and exposure to the air, or when the bath is to be changed. If wool is dyed in the state of thread, or in skains, rods are to be passed through them, and the hanks turned upon the skain sticks in the liquor. This is called shaking over. When silk or thread is in the same state, it undergoes a similar operation.

136. To separate the superabundant colouring particles, or those which have not been fixed in the stuff, silk or thread, after being dyed, it must be wrung out. This operation is performed with a cylindrical piece of wood, one end of which is fixed in the wall, or in a post. This operation is often repeated a number of times successively, for the purpose of drying the stuffs more rapidly, and communicating a brighter lustre.

137. When, after a certain quantity of fresh ingredients is added to a liquor, and it is stirred about, it is said to be raked, because it is mixed with the rake.

138. In dyeing, one colour is frequently communicated to stuffs, with the intention of applying another upon it, and thus a compound colour is produced. The first of these operations is called giving a ground.

139. When it is found necessary to pass stuffs several times through the same liquor, each particular operation is called a dip.

140. A colour is said to be rosed, when a red colour having a yellow tinge, is changed to a shade inclining to a crimson or ruby colour; and the conversion of a yellow red to a more complete red, is called heightening the colour.

141. In addition to these general remarks, we might give more minute details of the different operations which are employed in dyeing; but as we cannot presume that they would be of much advantage to the practical dyer, we shall not indulge ourselves in useless description. "Although the manipulations of dyeing," says Berthollet, "are not very various, and appear extremely simple, they require very particular attention, and an experienced eye, in order to judge of the qualities of the bath, to produce and sustain the degree of heat suited to each operation; to avoid all circumstances that might occasion inequalities of colour, to judge accurately whether the shade of what comes out of the bath suits the pattern, and to establish the proper gradations in a series of shades."

142. We shall conclude this chapter with a few observations on the qualities and effects of different kinds of water, which may be considered as one of the most essential agents in the art of dyeing. It is almost unnecessary to say, that water which is muddy, or contains putrid substances, should not be employed; and indeed no kind of water which possesses qualities distinguished by the taste, ought to be used. Water which holds in solution earthy salts, has a very considerable action on colouring matters, and it is chiefly by means of these salts. Such, for instance, are the nitrates of lime and magnesia, muriate of lime and magnesia, sulphate of lime, and carbonate of lime and of magnesia.

143. These salts which have earthy bases, oppose the solution of the colouring particles, and by entering into combination with many of them, cause a precipita-

tion, by which means the colour is at one time deeper, and at other times duller and more faint than would otherwise be the case. Waters impregnated with the carbonates of lime and magnesia, yield a precipitate when they are boiled; for the excess of carbonic acid which held them in solution is driven off by the heat; the earths are thus precipitated, and adhering to the stuffs to be dyed, render them dirty, and prevent the colouring matter from combining with them.

144. It is of much consequence to be able to distinguish the different kinds of water which come under the denomination of hard water, that they may be avoided in the essential operations of dyeing; but to detect different principles contained in such waters, and to ascertain their quantity with precision, require great skill, and very delicate management of chemical operations, which the experienced chemist only can be supposed to possess. For the methods to be followed when such accuracy is required, we must refer to the analysis of mineral waters, of which a full view is given in the treatise on chemistry, and content ourselves with mentioning some simple tests which are of easy application.

145. One of these tests is the solution of soap, by which it may be discovered whether water contain so large a portion of any of these saline matters as may be injurious to the processes. Salts which have earthy bases, have the property of decomposing soap by the action of double affinity. The acid of the salt combines with the alkali of the soap, and remains in solution, while the earth of the salt and the oil of the soap enter into combination, and form an earthy soap which is insoluble in water, and produces the curdling appearance which is the consequence of this new combination. Water, then, which is limpid and not stagnant, which has no perceptible taste or smell, and has the property of dissolving soap without decomposition, may be considered as sufficiently pure for the processes of dyeing. All waters which possess these qualities will be found equally proper for these purposes.

146. But, as it is not always in the power of the Method of dyer to choose pure water, means of correcting the water purifying, which would be injurious to his processes, and particularly for the dyeing of delicate colours, have been proposed. Water in which bran has been allowed to become sour, is most commonly employed for this purpose. This is known by the name of sours, or sour water. The method of preparing sour water is the following. Twenty-four bushels of bran are put into a vessel that will contain about 10 hogsheads. A large boiler is filled with water, and when it is just ready to boil, it is poured into the vessel. Soon after the acid fermentation commences, and in about 24 hours the liquor is fit to be applied to use. Water which is impregnated with earthy salts, after being treated in this way, forms no precipitate by boiling. It is probable that the sour water decomposes the carbonate of lime and magnesia, because the vegetable acid which is formed during the fermentation, combines with the earthy basis, and sets the carbonic acid at liberty.

147. Some of the substances, with which waters are impregnated, or those which are merely diffused in them in a state of very minute division, may be separated by means of mucilaginous matters. The mucilage coagulates.

Practice of coagulates by means of heat, and carrying with it the earths separated by boiling, as well as those substances which are simply mixed with the water, and render it turbid, rises to the surface, and forming a scum, may be easily removed.

148. Saline matters having earthy bases, which in general are injurious in dyeing, may in some cases be useful, because by their action, modifications of different colours may be produced. A water of this kind, for instance, would have the effect of communicating to the colour of cochineal a crimson shade.

149. River water, which is apt to be impregnated

with earthy salts, may, at different times, contain very different proportions of these salts; and although the dyer may follow exactly the same process, he may be surprised to find considerable variations in the shades of his colours. This arises from the different degrees of impregnation with these saline matters which the water undergoes, as the bed of the river is of greater or less extent, or the waters flow over those places from which they derive these earthy salts. To obtain the same result in the process, therefore, it would be necessary to make certain variations according to the state of impregnation of the water.

PART II. OF THE PRACTICE OF DYEING.

150. IN the preceding part, we have endeavoured to give a general view of the principles on which the art of dyeing depends. We have considered the physical and chemical properties of colours and colouring matters, the nature of the substances to which colours are communicated, and the agents or means by which this is effected; and from the experiments and observations of philosophers, whose investigations have been directed to this subject, it appears that these changes are entirely owing to chemical affinities, by which decompositions are effected, and new combinations formed, among the constituent parts of the substances employed. A precise and full knowledge of the effects of these chemical agents would render the theory of dyeing complete; and although much has been already done by the chemical philosophers whom we have had occasion frequently to quote, yet experiments and observations are still wanting to form a theory of this art on fixed and rational principles. This, it is obvious, can only be done by chemical investigations. To the practical dyer, therefore, the study of chemical science must be essentially requisite, as this only can be his true guide in estimating and managing the complicated changes in the different processes of his art. It is only by the application of the principles of chemistry that this art can be improved and perfected. But the application of these principles must be made by the practical dyer himself, not by the chemist in his laboratory, or during an occasional visit to the manufactory. For in the complicated processes of dyeing conducted on an extensive scale, a thousand circumstances will be overlooked by the most acute and discerning chemist, which will not escape the habitual observation of the philosophical artist. Convinced ourselves of the incalculable advantages which the art of dyeing may derive from chemical science, and the innumerable resources which ingenuity and address may discover in the proper application of its principles towards the improvement of the different processes of this art, we shall not be thought, we hope, too sanguine in looking forward to a degree of perfection which is little to be expected from its present state.

The processes of the art of dyeing form the subject of the second part of this treatise, the consideration of which we are now to enter upon.

151. Colours have been usually distributed by dyers into two classes. These have been denominated simple

and compound colours. Simple colours, which are commonly reckoned four in number, are such as cannot be produced by the mixing together different colours. Colours denominated compound may be produced by the mixture of any two of the simple colours in different proportions. Thus red, yellow, and blue are incapable of being produced by any combination of others, and are therefore considered as simple colours. Blue and red, which compose a purple, blue and yellow, a green, and red and yellow, an orange, are compound colours; but none of these, by any composition whatever, will afford a red, yellow, or blue.

152. Dr Bancroft, in his elaborate treatise on the philosophy of permanent colours, divides colouring matters into two classes. The first includes those colouring substances which, being in a state of solution, may be permanently fixed on any stuff without any mordant, or the intermediate action of earthy or metallic bases. In the second class are comprehended those matters which cannot be fixed without the action of mordants. The first he has denominated substantive colours; because the colour is fixed without the aid of any other body; and the second adjective; because they become permanent only with the addition of a mordant. The celebrated purple produced by the liquor obtained from shell-fish and indigo, are examples of substantive colours. Prussian blue and cochineal are adjective colours.

The usual division of colours into simple and compound seems to form an arrangement equally convenient and perspicuous. We shall therefore adopt it in the following chapters. In the first we shall treat of simple colours; in the second of compound colours; and to these we shall add a third chapter on topical dyeing, or calico printing.

CHAP. I. Of Simple Colours.

153. SIMPLE colours, we have already observed, are such as cannot be produced by the mixture of other colours. They are the foundation of all other colours, and therefore come naturally to be first treated of. The simple colours are four, viz. 1. Red. 2. Yellow. 3. Blue. 4. Black. To these a fifth is added by some; namely, brown, or fawn colour; although it may be produced by the combination of other colours. The nature of the colouring substances which are employed

sample to produce these colours, and the processes by which they are fixed on the several stuffs, will form the subject of the four following sections.

SECT. I. Of Red.

154. Red colours, from different degrees of intensity, have received different names, as crimson, scarlet, besides a great variety of shades which are less striking, and come under no particular denomination. In this section we shall treat of the nature and properties of the substances which are employed in dyeing red, and then give an account of the different processes which are followed in fixing these colouring matters on animal and vegetable productions.

1. Of the Substances employed in Dyeing Red.

The colouring matters which are principally employed in dyeing red, are madder, cochineal, kermes, lac, archil, carthamus, brazil wood, and logwood.

155. Madder is very extensively employed in dyeing. It is the root of a plant (rubia tinctorum, Lin.) of which there are two varieties. It is cultivated in different parts of Europe, and the best, it is said, is brought from Zealand. Madder, as it is prepared for dyeing, is distinguished into different kinds. What is called grape madder, is obtained from the principal roots; the none grape is produced from the stalks, which by being buried in the earth, are converted into roots, and are called layers. When the roots are gathered, these layers are separated, with such of the fibres of the roots as do not exceed a certain degree of thickness, as well as those which are too thick; the latter containing a great deal of woody matter. The best roots are about the thickness of a goose quill, they have some degree of transparency; are of a reddish colour, and have a strong smell, and a smooth bark. When the madder is gathered, it must be dried, to render it fit for being reduced to powder, and being preserved. This operation is performed in warm climates in the open air. In Holland, stoves are employed for the same purpose; but when treated in this way, it is often injured, from too great a degree of heat, and being mixed with particles of soot. The superiority of madder from the Levant is ascribed to its having been dried in the open air.

156. The roots being dried, and the earthy matters which adhere to them being separated, by shaking them in a bag, or beating them lightly on a wooden hurdle, they are reduced to powder by means of manual labour, or with the aid of machinery. All the parts of madder do not yield the same colouring matter. The outer bark, and the ligneous part within, give a yellowish dye, which injures the red. These parts may be separated, in consequence of the different degrees of facility with which they are reduced to powder. The outer bark and woody parts are more easily powdered than the parenchymatous parts, which contain the fine red dye. To effect the separation of these different parts, three operations are performed. After the first, the madder is passed through a sieve, by which, what is called the short madder, (courte of the French), intended for tan, and inferior colours, is obtained. What remains is again ground and sifted. What the French call mirobie, is obtained by this

operation. A third operation of the same kind affords the robee or finer kind of madder.

157. The result of the experiments of D'Amourney show, that the fresh root of madder may be used with as much advantage in dyeing, as when it is dried and powdered. Four pounds of fresh madder, he observed, are equal to one of the dry, although in drying it loses seven-eighths of its weight. When the fresh roots are to be used, they are to be well washed in a current of water, immediately after they are taken out of the ground, and afterwards cut into pieces and bruised. In dyeing with the fresh roots, allowance should be made for the quantity of water which they contain, so that a smaller proportion should be put into the bath. Beckmann seems to be of the same opinion with regard to the use of the fresh roots of madder, and yet he has frequently observed that it is more fit for dyeing after it has been preserved for two or three years.

158. The madder which is cultivated in the neighbourhood of Smyrna, and in the island of Cyprus, affords a brighter red than the European madder, and therefore it is preferred in the preparation of the Adrianople red. This is known by the name lizar. Berthollet informs us that it is cultivated in Provence in France, and Beckmann has been very successful in raising it at Gottingen.

159. The colouring matter of madder is soluble in alcohol, and by evaporation a deep-red residuum is formed. In this solution sulphuric acid produces a fawn-coloured precipitate; fixed alkali, one of a violet colour, and the sulphate of potash, a precipitate of a fine red. Alum, nitre, chalk, acetate of lead, and muriate of tin, afford precipitates in the solution of madder in alcohol, of various shades. The colouring matter of madder is also soluble in water. By maceration in several portions of cold water successively, the last receives only a fawn colour, which appears entirely different from the peculiar colouring particles of this substance. It resembles what is extracted from woods and other roots, and perhaps exists only in the ligneous and cortical parts. By repeated boiling, Berthollet exhausted the madder of all its colouring particles which are soluble in water. It still retained, however, a deep colour, and yielded a considerable quantity of colouring matter to an alkali. There was an inconsiderable residuum, which still remained coloured. The pulp, therefore, appears entirely composed of colouring matter, part of which is insoluble in simple water. When oxymuriatic acid is employed in sufficient quantity, to change an infusion of madder from red to yellow, it produces a small portion of a pale-yellow precipitate; the supernatant liquor is transparent, and retains more or less of a deep yellow colour, according to the proportion and strength of the acid. Double the quantity of acid is required to discharge the colour of a decoction of madder of what is necessary to destroy that of the same weight of Brazil wood. This shows that the colouring matter of madder is more durable than that of Brazil wood. The infusion of madder in water is of a brownish orange colour. The colouring matter may be extracted, either by cold or hot water; in the latter the colour is most beautiful. The decoction is of a brownish colour. The colouring matter of madder.

der cannot be extracted without a great deal of water. Two ounces of madder require three quarts of water. Alum forms, in the infusion of madder, a deep brownish red precipitate; the supernatant liquor is yellowish, inclining to brown. Alkaline carbonates precipitate from this last liquor a lake of a blood-red colour; with the addition of more alkali, the precipitate is redissolved, and the liquor becomes red. Calcareous earth precipitates a darker and browner coloured lake than alkalies. Carbonate of magnesia forms a clear blood-red precipitate, which by evaporation produces a blood-red extract, soluble in water. The solution of this extract is employed as a red ink, but it becomes yellow by exposure to the sun. Metallic salts also form precipitates in a solution of madder. The precipitate with acetate of lead is of a brownish red colour; with nitrate of mercury and sulphate of manganese, a purplish brown; with sulphate of iron, a fine bright brown.

160. Cochineal, which furnishes a valuable dye stuff, and about the nature of which there was at first a good deal of uncertainty, is an insect. It is produced on different species of the cactus, or Indian fig. The most perfect variety of the cochineal insect, is that which breeds on the cactus coccinillifer, Lin. To this plant the Mexican Spaniards gave the name of nojal. When the Spaniards first arrived in Mexico, they saw the cochineal employed by the native inhabitants, in communicating colours to some part of their habitations, ornaments, and in dyeing cotton. Struck with its beautiful colour, they transmitted accounts of it to the Spanish ministry, who about the year 1523, ordered Cortes to direct his attention to the propagation of this substance. The inhabitants of Europe were long mistaken concerning the nature and origin of cochineal, by supposing it to be the grain or seed of a plant. This opinion was first contradicted in a paper published in the third volume of the Philosophical Transactions in 1668; and four years afterwards, Dr Lister, in the seventh volume of the same work, throws out a conjecture, that cochineal may be a sort of kermes. Different opinions concerning the origin of this substance were entertained, till about the beginning of the year 1757, Mr Ellis obtained some of the joints of the plant on which the insects breed, from South Carolina, and presented them the same year to the Royal Society. These specimens, Mr Ellis observes, were full of the nests of this insect, in which it appeared in its various states, in the most minute when it walks about, to the state when it becomes fixed, and wrapt up in a fine web, which it spins about itself. With the assistance of the microscope, Mr Ellis discovered the true male insect in the parcels which had been sent to him from America; and in August 1756, in consequence of Mr Ellis's discovery, Dr Garden caught a male cochineal fly, which he observes is rarely to be met with.

He supposes that there may be 150 or 200 females for one male. These discoveries proved indisputably, that the cochineal is an animal production.

161. The body of the female insect is flat on the belly, and hemispherical on the back, and transversely wrinkled. The skin is dark brown; it has no wings, but is furnished with six short brown legs. The body of the male, which is of a deep red colour, is rather long, and covered with two wings, extending horizontally, and crossing a little upon the back. It has two small antennæ, and six legs which are larger than those of the female. It has a fluttering kind of motion. The life of the male is only of a month duration, but the fecundated female lives a month longer. The female is sometimes oviparous and sometimes viviparous; but this is not a peculiarity confined to this insect. It belongs to some others, and seems to be regulated by the temperature and season of the year. The female cochineal insect adheres to the same spot of the tree on which it is produced during her whole life. As soon as the female is delivered of its numerous progeny, it becomes a mere husk and dies. In Mexico it is therefore an object of great importance to prevent this, and to collect them in the fecundated state. For this purpose they are picked from the plants, put into a linen bag, which is immersed in hot water, to destroy the life of the young insects, and then carefully dried. In this state they are imported into Europe.

162. There are two kinds of cochineal. The best, varia, or domesticated kind, is called by the Spaniards, grana fina. This variety breeds upon the cactus coccinillifer, or nojal; and being of a larger size, and containing a greater proportion of colouring matter, it is always preferred. The other variety is the grana sylvestris of the Spaniards, or wild cochineal. It is produced from other species of the cactus. It is smaller than the other, and as it is covered with a downy matter, produced by the insect to defend itself against the cold, this increases the weight, but is of no use in dyeing. An equal weight of the wild cochineal yields a smaller quantity of colouring matter, and is therefore less valuable. It ought, however, to be observed, that it can be reared with greater facility, and at much less expence; and when it is bred upon the nojal, it acquires double the size, and has a smaller quantity of downy matter for its covering, so that it approaches, by this management, to the nature of fine cochineal.

163. As the quantity of cochineal consumed in Europe is very great (D), and as the Spaniards have hitherto enjoyed the exclusive advantages of rearing and supplying the market with this valuable substance, it has become an object with other nations to share them. Attempts have therefore been made to form establishments for rearing these insects in those colonies whose soil and climate seem suitable for the purpose.

(D) The average quantity, says Dr Bancroft, of fine cochineal annually consumed in Europe, amounts to about 3000 bags, or 600,000 lbs. weight, of which about 1200 bags, or 240,000 lbs. weight may be considered as the present annual consumption of Great Britain. A greater quantity comes to the kingdom, but the surplus is again exported to other countries. These 1200 bags may be supposed to cost 180,000. sterling, valued at 15s. per lb. which has been about the average price for some years past. Philosophy of Permanent Colours, p. 258.

164. One of the most successful of these attempts was made by M. Thiery de Menonville, in 1777. He exposed himself to great danger, by going to Mexico that he might observe the mode of rearing the cochineal insect, and procure that valuable production, to plant it in St Domingo. He proceeded by the Havannah to La Vera Cruz, where he was informed that the finest cochineal insects were reared at Guaxaca, 70 leagues distant. On the pretence of ill health, he received permission to use the baths of the river Magdalena: but instead of accepting this privilege, which was not his object, he directed his course, not without much difficulty and danger, to Guaxaca; where having obtained the information he wanted, and having purchased a quantity of nopals, covered with the insects of the fine or domestic breed, which he pretended were of great use in preparing an ointment for his feigned disorder, the gout, he put them into boxes along with other plants, and succeeded in bringing them away without notice or suspicion. On his return, he was driven by a storm into the bay of Campeachy, where he found a living cactus of a species which was fit for the nourishment of the fine cochineal. He returned in safety towards the end of the same year, to St Domingo, with his prize, and immediately formed a plantation of nopals, with the view of propagating both varieties of the cochineal. Soon after his return, he found the wild kind living naturally on the cactus pereskia, a native of that island. Unfortunately, however, for the establishment, Thiery de Menonville died in the year 1780, through disappointment and vexation, it is said, at seeing his patriotic endeavours so little assisted, and his services so sparingly rewarded by government; and soon after his death, the fine cochineal perished. But the discovery of the wild kind in St Domingo was not neglected. M. Bruley succeeded in his attempts to rear this species of cochineal. A posthumous work of Thiery de Menonville was published by the Royal Society of arts and sciences at Cape Françoise, containing minute instructions with regard to every thing respecting the cultivation of the nopal, and the other species of cactus, which may be more or less successfully substituted for breeding or rearing the cochineal. Of this Berthollet has given an extract in the 5th volume of the Annales de Chimie. Some of our own countrymen, a few years ago, succeeded in procuring some of the fine cochineal insects; and attempts have been made, with what success we know not, to rear them in the East Indies.

165. Fine cochineal, if it has been properly prepared and kept, ought to be of a gray colour, with a shade of purple. The gray colour is owing to a powder with which it is naturally covered, and part of which it still retains. The colouring matter extracted by the water in which the insect has been killed, produces the purple shade. In a dry place, cochineal may be kept for a long time, without losing any of its properties. Hellot made experiments on cochineal 130 years old, and found that it produced the same effect

as if it had been quite new. Cochineal yields its colouring matter to water; and the decoction, which is of a crimson colour, inclining to violet, may be kept for a long time, without losing its transparency, or becoming putrid. If this decoction be evaporated, and the residuum or extract be digested in alcohol, the colouring part dissolves, and leaves a residuum of the colour of wine lees, of which fresh alcohol cannot deprive it. The alcohol of cochineal affords, by evaporation, a transparent residuum of a deep red, which, being dried, has the appearance of a resin. A small quantity of sulphuric acid added to the decoction of cochineal, produces a red colour, inclining to yellow, and a small quantity of a beautiful red precipitate. With muriatic acid the same change is produced, but there is no precipitate. A solution of tartar converts the decoction to a yellowish red colour. A precipitate of a pale red colour is slowly formed, and the supernatant liquor remains yellow; but with the addition of an alkali becomes purple. With the yellow liquor, solution of tin forms a rose-coloured precipitate; solution of alum brightens the colour of the infusion, gives it a redder hue, and produces a crimson precipitate. With a mixture of alum and tartar the colour is brighter, more lively, and inclines to a yellowish red. Muriate of tin occasions a copious sediment of a beautiful red. The supernatant liquor is colourless and transparent, and no change is produced on it by adding an alkali. Sulphate of iron forms a brown violet precipitate, and the supernatant liquor remains clear, with a slight darkish hue. Sulphate of zinc gives a deep violet precipitate; the supernatant liquor remains colourless and transparent. The precipitate with sulphate of copper is of a violet colour, and forms slowly: the supernatant liquor is also violet and transparent. Acetate of lead gives a purple violet precipitate, and the supernatant liquor remains limpid.

166. The experiments of Berthollet and Bancroft shew, that the colouring matter of cochineal is not entirely extracted by means of water. Dr Bancroft found, that after the whole of it which could be extracted by water was obtained, by adding a little potash to the seemingly exhausted sediment, and pouring on it fresh boiling water, it yielded a new quantity of colouring matter, equal to one-eighth of what had been given out to the water; and Berthollet found the same effect produced with the addition of tartar; from which he concludes that tartar favours the solution of the colouring part of the cochineal.

167. Kermes (E), another animal substance, which Kermes is extensively employed in dyeing, is an insect, (coccus ilicis, Lin.) which breeds on a species of oak (quercus coccifera, Lin.) which grows in most of the southern parts of Europe, and in many parts in Asia. Kermes History. was known to the ancients, under the names of coccum scarlatinum, coccus bapticus, coccus infectorius, granum tinctorium. Kermes is chiefly obtained from Languedoc, Spain, and Portugal. The insects are collected in the month of May or June, when the female, which alone

(E) This word is supposed to have been derived from the Arabic language, and signifies a little worm, vermiculus; and from this we have the word vermilion, the pigment in the manufacture of which it is the principal ingredient.

alone is useful, is distended with eggs. To destroy the young insects, the kermes is exposed to the steam of vinegar for about half an hour, or steeped in vinegar for 10 or 12 hours. They are afterwards dried on linen cloths, and brought to market.

168. When the living insect is bruised, it gives out a red colour. The smell is somewhat pleasant; the taste is bitter and pungent. It gives out its colouring matter both to water and alcohol, to which also it imparts its smell and taste. The colour is also retained in the extract which is obtained, both from the tincture, and from the infusion. Kermes is one of the most ancient dyeing drugs; and although the colours which it communicates to cloth are less bright and vivid than those of cochineal, and on that account it has been less extensively employed in dyeing since the latter was known, yet they have been found to be exceedingly permanent. The fine blood-red colour which is to be seen on old tapestries in different parts of Europe, was produced from kermes, with an aluminous mordant, and seems to have suffered no change, though some of them are 200 or 300 years old. The colour obtained from kermes was formerly called scarlet in grain, because it was supposed that the insect was a grain; and from the chief manufactory having been at one time in Venice, it was called Venetian scarlet.

169. Lac is an animal production which has been long known in India, and used for dyeing silk and other purposes. It is the nidus of the coccus lacca, Lin. and is generally produced on the small branches of the croton laciferum. Three kinds of lac are well known in commerce: 1. Stick lac is the substance or comb, in its natural state, forming a crust on the small branches or twigs. Seed lac is said to be only the above, separated from the twigs, and reduced into small fragments. Mr Hatchett, who has examined this substance with his usual skill and precision, found the best specimens considerably deprived of their colouring matter*. According to the information which he received from Mr Wilkins, the silk dyers in Bengal produce the seed lac by pounding crude lac into small fragments, and extracting part of the colouring matter by boiling. 3. Shell lac is prepared from the cells, liquefied, strained, and formed into thin transparent laminae. There is also a fourth kind called lump lac, which is obtained from the seed lac by liquefaction, and afterwards formed into cakes. The best lac is of a deep red colour; when it is pale, and pierced at the top, the value is greatly diminished, for then the insects have left their cells, and it can no longer be of use as a dye stuff.

170. The decoction of powdered stick lac in water, gives a deep crimson colour. With one-fifth of borax, lac becomes more soluble in water. Pure soda, and carbonate of soda, completely dissolve the different kinds of lac, and produce a deeper colour than that which is obtained by means of borax. Pure potash speedily dissolves all the varieties of lac; the colour approaches to purple. Pure ammonia and carbonate of ammonia readily act on the colouring matter of lac. Alcohol dissolves a considerable part of the lac; and according to Geoffroy, yields a fine red colour. When the solution is heated it becomes turbid. Sulphuric acid dissolves the colouring matter of lac, as well as muriatic and acetic acids. In the use of lac in

dyeing, it has been considered superior to kermes, because it is able to bear the action of a solution of tin, without the colour being changed to yellow.

171. Archil is a vegetable substance of great use in dyeing. It is employed in the form of a paste, which is of a red violet colour. It is chiefly obtained from two species of lichen, rocella, and parellus, Lin. The first, which is called Canary archil, because the lichen from which it is prepared grows abundantly in the Canary islands, is most valued. It is prepared by reducing the plant to a fine powder, which is afterwards passed through a sieve, and slightly moistened with stale urine. The mixture is daily stirred, each time adding a certain proportion of soda in powder, till it acquire a clove colour. It is then put into a wooden cask, and urine, lime-water, or a solution of sulphate of lime, (gypsum) is added in sufficient quantity to cover the mixture. In this state it is kept; but to preserve it any length of time, it is necessary to moisten it occasionally with urine. By a similar preparation, other species of lichen may be used in dyeing. In this country the lichen omphalodes and tartareus are frequently employed for dyeing coarse cloths.

172. Archil gives out its colouring matter to water, ammonia, and alcohol. The infusion of archil is of a crimson colour, with a shade of violet. The addition of an acid converts it to a red colour. Fixed alkalies only render it of a deeper shade; because its natural colour has been already modified by the ammonia with which it is combined in the preparation. Alum produces in the solution of archil a dark-red precipitate; the supernatant liquor is of a yellowish red colour. With solution of tin a reddish precipitate is formed, which subsides slowly; and the liquor retains a slight tinge of red. This infusion loses its colour in a few days if it be entirely excluded from the air. To cold marble the aqueous infusion of archil communicates a fine violet colour, or blue inclining to purple. The affinity between the stone and the colouring matter is so strong, that it resists the action of the air longer than colours which it gives to other substances. The colour thus communicated to marble, has remained for two years unchanged.

173. Archil is also soluble in alcohol. This tincture is employed for making spirit of wine thermometers. A singular phenomenon was observed by the Abbé Nolle when the tincture was excluded from the air. In a few years it was entirely deprived of its colour. The contact of air restored the colour; but it was again destroyed when deprived of it.

174. Carthamus, or bastard saffron, a vegetable substance used in dyeing, is the flower of an annual plant which is cultivated in Spain, Egypt, and the Levant. There are two varieties of this plant, the one with larger, the other with smaller leaves. The variety with larger leaves is cultivated in Egypt.

175. The method of preparing the flowers of carthamus in Egypt, as it is described by Hasselquist, is the following. After being pressed between two stones, to squeeze out the juice, they are washed several times with salt water, pressed between the hands, and spread out on mats in the open air to dry. In the day time they are covered, that they may not dry too fast with the heat of the sun, but they are left exposed to the dew of the night. When they are sufficiently dry, they are put

Simple put up, and kept for sale, under the name of saffron. Care should be taken afterwards, not to keep it in too dry a place; for unless it is a little moist, its properties are considerably impaired.

176. Carthamus contains two colouring substances, a yellow substance, which is soluble in water; and as it is of no use, it is extracted by the process mentioned above, by squeezing the flowers between stones till no more colour can be pressed out. The flowers become reddish in this operation, and lose nearly one half of their weight. The other colouring matter, which is red, is soluble in alkaline carbonates, and it is precipitated by means of an acid. A vegetable acid, as lemon juice, has been found to produce the finest colour. Next to this, sulphuric acid produces the best effect, provided too great a quantity, which would alter and destroy the colour, be not employed. The juice of the berries of the mountain-ash, or rowan tree, (serbus aucuparia, Lin.) is recommended by Scheffer as a substitute for lemon juice, and it is thus prepared. The berries are bruised in a mortar with a wooden pestle, and the expressed juice, after it has been allowed to ferment, is bottled up. The clear part, which is most acid, becomes fitter for use the longer it is kept; but this operation requires a period of some months, and can only be conducted in summer.

177. From the colouring matter extracted by means of an alkali, and precipitated with an acid, is procured the substance called rouge, which is employed as a paint for the skin. The solution of carthamus is prepared with crystals of soda, and precipitated with lemon juice which has stood some days to settle. After being dried on delft plates with a gentle heat, the precipitate is separated, and ground accurately with talc which has been previously reduced to a very subtile powder; and on the fineness of the talc depends the difference between the cheaper and dearer kinds of rouge.

178. Brazil wood is of very extensive use in dyeing. It is the wood of the caesalpinia crista, Lin. and is a native of America and the West Indies. It is known under different names, according to the place where it is produced; as, Fernambouc, Brazilotto, wood of St Martha, and of Sapan. It has a very hard wood, and has so much density as to sink in water. When fresh cut, it is of a pale colour, but becomes reddish by exposure to the air; and it has a sweetish taste.

179. The colouring matter of Brazil wood is soluble in water, and the whole of it may be extracted by continuing the boiling for a sufficient length of time. The decoction is of a fine red colour. The residuum, which is black, yields a considerable portion of colouring matter to alkalies. The colouring matter is also soluble in alcohol, and in ammonia, and the colour is deeper than that of the aqueous solution. The tincture of Brazil wood in alcohol gives to hot marble a red colour, which afterwards changes to violet. The fresh decoction yields, with sulphuric acid, a small portion of a red precipitate, inclining to fawn colour. Nitric acid first produces a yellow colour, but by adding more, a deep orange. Oxalic acid produces a precipitate of an orange red. Tartar furnishes a small precipitate: with the addition of a fixed alkali, the decoction becomes of a deep crimson or violet colour. Ammonia gives a brighter purple: alum produces a copious

red precipitate, inclining to crimson. Sulphate of iron occasions a black colour in the tincture, with a copious precipitate of the same colour. Sulphate of copper also produces an abundant precipitate, the liquor remaining transparent, and of a brownish red. A copious precipitate, of a fine deep red, is produced with acetate of lead, and that obtained with muriate of tin is abundant, and of a fine rose colour. With the addition of corrosive sublimate, a light precipitate, which is of a brown colour, is obtained. The liquor remains transparent, and of a fine yellow colour. Brazil wood, which has been changed to a yellow colour by means of tartar and acetic acid, with a solution of nitro-muriate of tin, yields a copious rose-coloured precipitate; and if to the solution, rendered yellow by an acid, a greater quantity of the same acid, or a stronger acid, as the sulphuric, be added, the red colour is restored. Some salts also possess the property of restoring the red colour of Brazil wood, which has been destroyed by means of acids*. The decoction of Brazil wood, which is called juice of Brazil, is found to answer better for the process of dyeing, when it has been kept some time, and has even undergone some degree of fermentation, than when it has been fresh prepared. The colour, by keeping, becomes of a yellowish red.

180. Logwood, sometimes called India or Cam-Logwood, peachy wood, (Hamatoxylon Campeachianum, Lin.) is a tree which grows to a considerable size in Jamaica, and the eastern shore of the bay of Campeachy. Its specific gravity is greater than that of water; it has a fine grain, and is susceptible of a fine polish. Logwood yields its colouring matter, which is a fine red, readily and copiously to alcohol. It is more sparingly soluble in water, and the decoction inclines a little to violet or purple. When it is left some time to itself, it becomes yellowish, and at length black. It becomes yellowish also by the action of acids; alkalies produce a deeper colour, and convert it to a purple or violet. Sulphuric, nitric, and muriatic acids form a small proportion of precipitate, which separates slowly: the precipitate formed with sulphuric acid is of a dark red; with muriatic, a lighter red, and with the nitric, feuille morte. With sulphuric or muriatic acids, the supernatant liquor is of a deep red colour; with nitric it is yellowish, and in all transparent. Oxalic acid produces a precipitate of a light marone colour; the liquor remains transparent, and is yellowish red. Acetic acid produces a similar effect, but the colour of the precipitate is somewhat deeper. A similar precipitate is obtained by means of tartar; but the liquor, which is more inclined to yellow, remains turbid. No precipitate is produced by means of fixed alkali; the decoction becomes of a deep violet, which is afterwards converted to a brown colour. Alum yields a copious precipitate, of a lightish violet colour; the colour of the liquor remains the same, and it is nearly transparent. A copious, dark red precipitate is produced with alum and tartar; the liquor is yellowish red and transparent. Sulphate of iron occasions a bluish black colour; a copious precipitate of the same colour is formed, and the liquid remains long turbid. With sulphate of copper, a very copious precipitate, of a dark brown colour, is obtained; the liquor, which is also of a deep brown, or yellowish red, remains transparent. Acetate of lead yields a black precipitate, with

Or Simple
Colours. with a slight tinge of red; the colour of the liquor is like that of pale beer, and it remains transparent. Nitro-muriate of tin gives a precipitate of a fine violet or purple colour; the liquor remains clear and colourless.

2. Of the Processes for Dyeing Wool Red.

181. All red colouring matters with which we are acquainted, come under that class of colours to which Dr Bancroft has given the name of adjective colours; that is, such colours as require the aid of mordants to render them permanent. Red colours, we have already observed, are of various shades, according to the nature and proportion of the colouring matters employed. Hence we have madder red, scarlet, crimson, and other shades.

Madder-red. 182. Madder Red.—Madder is only employed for dyeing coarse woollen stuffs, and the following is the process. The stuffs are first boiled for two or three hours with alum and tartar: they are then left to drain, slightly wrung out, put into a linen bag, and carried into a cool place, where they are to remain for some days. The quantities and proportions of the alum and tartar are varied according to the views of the dyer, and the shade of colour which is wanted. Some recommend five ounces of alum and one ounce of tartar to each pound of wool. By increasing the proportion of tartar to a certain degree, a deep and permanent cinnamon colour, instead of a red, is produced. This arises from the yellow tinge which is induced by means of the acid on the colouring particles of the madder. Others propose to diminish the proportion of tartar, and to employ only a seventh part. In conducting the process of dyeing with madder, the bath should not be brought to the boiling point, because at that temperature the fawn-coloured particles would be dissolved, and a different shade obtained from that which is desired. When the water is at that degree of temperature which the hand can bear, Hellot recommends the addition of half a pound of grape madder for every pound of wool to be dyed. It is then to be well stirred before the wool is introduced, which must remain for an hour without boiling, excepting for a few minutes towards the end of the process, that the combination of the colouring particles with the stuff may be more certain.

Rosing. 183. Madder reds are sometimes rosed, as it is called, with archil and Brazil wood. In this way they become more beautiful and velvety, but this brightness is not permanent. But madder reds, even when they are most perfect, are far inferior to those obtained from lac and cochineal, and even to that produced by kermes; but as the expence of the materials is comparatively small, they are employed, as we have already observed, for coarse stuffs.

Proportion of madder. 184. Different authors recommend different proportions of madder. Poerner proposes to employ one-third of the weight of the wool, while Scheffer limits the quantity to one-fourth. In one process, Poerner added to the alum and tartar, a quantity of solution of tin, equal in weight to the tartar, and after two hours boiling, allowed the cloth to remain in the bath, which had been left to cool for three or four days. He then dyed it in the usual way, and thus obtained a fine red. According to another process, he prepared the

cloth by the common boiling, and dyed it in a bath of slightly heated, with a larger proportion of madder, tartar, and solution of tin. The cloth remained 24 hours in the bath, and when it had become cold, he put it into another bath, made with madder only, where it remained for 24 hours. By this process he got a fine red, somewhat brighter than the common, but inclining a little to yellow. Scheffer informs us that he obtained an orange red by boiling wool with a solution of tin, and one-fourth of alum, and then by dyeing with one-fourth of madder. A cherry colour is obtained, according to Bergman, by dyeing with one part of a solution of tin, and two of madder, without previously boiling the wool. By exposure to the air, this colour becomes deeper. By boiling the wool for two hours with one-fourth of sulphate of iron, then washing it, and afterwards immersing it in cold water with one-fourth of madder, and then boiling for an hour, the result is a coffee colour. But if the wool has not been soaked, and if it be dyed with one part of sulphate of iron and two of madder, the colour is a brown approaching to red.

185. When sulphate of copper is employed as the mordant, the madder dye yields a clear brown, inclining somewhat to yellow; and a similar colour may be produced by dyeing the wool simply soaked in hot water, with one part of sulphate of copper, and two of madder. But when this mordant and dye-stuff are used in equal proportions, the yellow is somewhat more obscure, approaching to green; and in both these instances, exposure to the air does not produce a darker colour. Berthollet informs us that he employed a solution of tin in various ways, both in the preparation and the application of the madder; and by the use of different solutions of tin, he found, that although the tint was somewhat brighter than what is obtained by the common process, it was always more inclined to yellow or fawn colour.

186. Scarlet.—The finest and most splendid of all colours is scarlet. This, like other colours, is of various shades, according to the quality and proportion of the colouring matter employed. The scarlet dye is communicated to woollen stuffs by means of cochineal, the history and properties of which we have already detailed. The Mexicans, as appears from their history, employed alumina as the basis or mordant, to fix the colour of cochineal; and previous to the discovery of the solution of tin, the use of the same substance seems to have prevailed in Europe. The fine colour obtained from the latter, received, as we have already mentioned, different names in different places; as that of bow dye in England, scarlet of the Gobelins in France, and in Holland Dutch scarlet.

187. In the process for dyeing scarlet, two operations are necessary. The first is denominated the boiling, and the second is distinguished by the name of finishing or reddening. The operation of boiling, which is the first part of the process, is conducted in the following manner. For 100 pounds of cloth, 6 pounds of pure tartar are added to the water, which is made pretty warm. The bath is then to be briskly stirred, and when the heat has increased a little more, half a pound of powdered cochineal is to be added, and the whole is then to be well mixed. The next moment five pounds of a very clear solution of tin are to be poured

Simple poured in, and carefully mixed. When the bath be-
gins to boil, the cloth is introduced, and briskly moved
for two or three turns: after which it is moved more
slowly. The boiling having continued for two hours,
the cloth is taken out, exposed to the air, and carried
to the river to be well washed.

188. In the preparation of the second bath, which is
for the reddening, the boiler is to be emptied, and when
the bath has just reached the boiling point, five pounds
and three quarters of cochineal, previously powdered
and sifted, are to be added. These are to be carefully
mixed; and after having ceased stirring, when a crust
has formed on the surface, and opened of itself in sev-
eral places, 13 or 14 pounds of solution of tin are poured
in. Should the bath, during the boiling, rise above the
edge of the boiler, it may be cooled with a little cold
water. This solution being well mixed, the cloth is
put in, and two or three times quickly turned. It is
then boiled in the bath for an hour, taking care to keep
it under the surface. It is afterwards taken out, ex-
posed to the air, and when it has cooled, washed in the
river and dried.

189. There are no determinate proportions of cochineal
and solution of tin in either of these operations.
Hellot informs us, that some dyers employ two-thirds
of solution of tin, and one-fourth of cochineal, in
the boiling or first operation, and the other one-third
of the solution of tin with the remaining three-fourths
of the cochineal in the second operation, or the red-
dening. He adds farther, that the use of tartar gives
a greater degree of permanency to the colour, provided
the proportion do not exceed one half the weight
of the cochineal employed. According to Berthollet,
several dyers at present adopt this practice. Tartar,
he observes, promotes the solution of the colouring
matter; and this effect is greater when it is ground
with the cochineal, after which it is found that the
residuum is more completely exhausted. But this con-
sideration is of inferior consequence, when the opera-
tions are successively performed, because any colouring
matter that may remain in the residuum, is employed
in the next operation. It ought not, however, to be
overlooked, that the tartar communicates to the colour
a rosy hue.

190. It is the practice of some dyers not to remove
the cloth out of the boiling. They merely refresh it,
and perform the operation of reddening in the same
bath. When this is done, the infusion of cochineal,
made in a separate vessel, and mixed with the proper
proportion of solution of tin, is added. By conducting
the process in this way the scarlet is supposed to be
equally fine, and there is a considerable saving of time
and fuel.

191. To give scarlet the bright lively red which,
as it approaches to the colour of fire, has been distin-
guished by the name of fiery scarlet, a yellow tinge is
communicated by boiling fustic in the first bath, or by
adding a little turmeric to the cochineal. A larger
proportion of the solution of tin also produces this
yellow shade, but it renders the cloth harsh, and li-
mits the action of the colouring matter. The use of
fustic or turmeric, therefore, although the colour ob-
tained from them is not permanent, is preferable to an
excess of the solution of tin. When these substances
are used, the inside of the cloth, when it is cut, ap-

pears yellow; but in the ordinary processes, the cochineal, it is found, does not penetrate the cloth, for when no other substance is employed, the cloth is internally white.

192. The use of tin boilers is recommended in dye-
ing scarlet. When copper boilers are employed, the
acid acts on the metal, and thus forming a solution, in-
jures the beauty of the colour. Tin boilers, however,
are attended with several inconveniences. It is diffi-
cult to procure them of sufficient size, and they are apt
to be melted by the incautious continuance of the fire,
after they have been emptied. In the use of copper
boilers, there are several necessary precautions. They
must be kept very clean; the acid liquor should not be
allowed to remain in them for any length of time, and
some contrivance should be adopted to prevent the cloth
from touching the metal, either by using a net, or a
wicker basket.

193. Different proportions of materials, we have
observed, are recommended by different authors. For
the boiling, Scheffer directs an ounce and a half of
solution of tin, with an equal quantity of starch, and
as much tartar, to every pound of cloth. The effect
of the starch is to give more uniformity to the colour.
When the water boils, a dram of cochineal is to be
added; it is then to be well stirred, and after the
wool is introduced, to be boiled an hour, taken out, and
washed. The proportions for the reddening bath, in
which the wool is to be boiled half an hour, are half an
ounce of starch, three-fourths of an ounce of solution
of tin, half an ounce of tartar, and 7 drams of cochineal.
In Scheffer's process, it may be observed, the propor-
tion of solution of tin is smaller than in that of Hellot,
but the quantity of tin in the solution of the former is
greater than in that of the latter.

194. Poerner has described three principal processes,
according to the variety of the shade of the scarlet.
He uses no cochineal in the boiling; the materials
of which are one ounce and six drams of tartar, and an
equal weight of solution of tin, the latter being added
after the tartar is dissolved, for every pound of cloth.
As soon as the boiling has commenced, the cloth is in-
troduced, and it is boiled for two hours. For the red-
dening of the first process he employs two drams of tar-
tar and one ounce of cochineal, adding gradually after-
wards two ounces of solution of tin. For the red-
dening of the second process, the same quantity of
cochineal and solution of tin, without any tartar, is em-
ployed. In the reddening of the third process, two
drachms of tartar with one ounce of solution of tin, one
ounce of cochineal, and two ounces of common salt,
are directed to be used. The colour produced in the
first process has the deepest shade; that of the sec-
ond is more lively, while that of the third is paler and
brighter.

195. By the use of tartar in the reddening in differ-
ent proportions, various shades of scarlet may be ob-
tained. When it is employed, the shade is deeper and
fuller; but when it is entirely omitted, the scarlet ap-
proaches to an orange colour. The shade of colour
also is subject to considerable variety, from the differ-
ent degrees of strength of the solution of tin. To
ascertain this effect, Berthollet made a number of ex-
periments. He found that a solution of tin composed
of sixteen parts of nitric acid, two of muriate of am-
monia,

monia, and three of tin, produced a deeper shade than when the proportions of the acid and muriate of ammonia were equal, with only two parts of tin. The last proportions, he observes, succeeded best. Four parts of water were mixed with the solution. When the proportion of muriate of ammonia amounted only to half a part, the colour was brighter, and inclining to orange.

196. Common salt has the effect of increasing the brightness of scarlet, while it is also attended with the advantage of causing the colour to penetrate deeper into the cloth. It seems difficult to explain why common salt, which gives a deeper shade to the colour of the infusion of cochineal, and indeed produces a similar effect on colours in general, should diminish the intensity of the colour of scarlet. The proportion of common salt mentioned above (194) is, according to Poerner, the greatest that can be employed. When less is used, the shade, though lighter, is more agreeable. By adding five ounces of white sugar to the ingredients of the second process, a fine colour, which is always lighter than that of the first process, will be obtained. The colour, it is said, is more permanent, and the shade more agreeable, when the cloth is left 24 hours in the boiler after it has cooled.

197. It has been generally supposed, Dr Bancroft observes, that after the discovery of the effects of tin on the cochineal colour, to produce a scarlet, it was only necessary to apply the colour so produced as a dye to wool; or that a nitric or nitro-muriatic solution of tin might change the natural crimson of cochineal to a scarlet. This opinion, however, he considers to be quite erroneous; for the nitric solution of tin invariably produces with cochineal a crimson or rose colour, and not a scarlet, unless other means are employed to incline the cochineal colour to a yellow shade. This effect is produced by means of the tartar, which seems to have been accidentally stumbled upon, and has been for many ages used, without knowing its true effect. Tartar was long employed with the aluminous mordant, in the preparation of the ordinary boiling liquor for woollen cloths; and it is probable that its good effects being observed in this combination, the use of it was continued after the introduction of the solution of tin; and the more so, after the result of the combination was observed in the brilliancy of the colour which was produced. Dr Bancroft has particularly directed his attention to the process for dyeing scarlet; and in the progress of his investigations, he has found that it is by no means absolutely necessary to follow the usual process which we have described above. He has often, he says, produced that colour very well at a single boiling, by mixing the whole quantity of tartar, solution of tin, and cochineal together; the affinity of the wool for the colouring matter, and for the oxides of tin, being sufficiently strong to combine with them readily, and to retain them permanently. The only objection to simplifying the process in this manner is, that the colouring matter of the dyeing liquor is less perfectly exhausted than when two operations are performed. He farther adds, that he has often produced a beautiful scarlet, by preparing and boiling the cloth with the whole quantity of solution of tin and tartar at once, and afterwards dyeing it unrinsed, with the whole of the cochineal, dissolved only in pure water. In this

way he found the colouring particles completely taken up; that the liquor had become quite colourless, and that the cloth had received a durable dye.

198. "It is remarkable," says Dr Bancroft, "that during the 18th century, no considerable improvement has been made in the process for dyeing scarlet; a circumstance which is the more extraordinary, since the pre-eminent lustre and costly nature of this dye, have rendered it an object of particular attention, not only to dyers, but to eminent chemists, by whose researches we might have expected that at least every obvious improvement therein would have been long since attained." To attain this object, this ingenious philosopher instituted a set of experiments about the year 1786. Dr Bancroft's experiments. Having, by repeated affusions of boiling water, extracted the whole of the colouring matter from powdered cochineal, he found that the addition of a little potash to the seemingly exhausted sediment, and a fresh quantity of boiling water, extracted a new portion of colouring matter, equal to about one-eighth of what had been given out to the pure water. He repeatedly extracted this colouring matter by means of potash, and afterwards dyed small pieces of cloth scarlet with it, which he found similar to other pieces dyed with the more soluble colouring matter of cochineal. It was in the course of these inquiries that he perceived scarlet to be a compound colour, consisting of about three-fourths of pure crimson or rose colour, and one-fourth of pure bright yellow. He conceived, therefore, that when the natural crimson of the cochineal is made scarlet, by the usual process, there must be a change produced, equivalent to a conversion of one-fourth of the colouring matter of cochineal from its natural crimson to a yellow colour. From this he concludes that there might be a great saving of cochineal, by substituting a cheaper substance, which at the same time might yield a better yellow colour. It was therefore his object to combine with this crimson or rose colour, a suitable portion of a lively golden yellow, capable of being permanently fixed, and reflected by the same basis. Such a yellow he had discovered in quercitron bark, (quercus nigra, Lin.) which will be afterwards described; and it had the advantage, not only of being the brightest, but also the cheapest, of all the yellows which he had tried.

199. With the view of diminishing the quantity of cochineal employed in producing a scarlet dye, Dr Bancroft made a number of experiments under the authority of government. In these experiments, the mordant used was the ordinary dyers spirit, or the nitro-muriate of tin; but he found that they were not attended with the advantages which he expected. In some of his earliest experiments, he observes, that the solution of tin by means of sulphuric acid destroyed the cochineal colour, and this naturally led him to reject the use of this acid, till accident brought him to dissolve a quantity of tin in muriatic acid, combined with one-fourth of sulphuric acid. The application of this solution in dyeing, was not accompanied with the corrosive effects of the muriate and nitro-muriate which he had employed in the experiments above alluded to, and which proved unsuccessful. After trying different proportions of these acids, he found the following to answer best. In a mixture of 2lbs. of sulphuric acid of the ordinary strength, and about 3lbs. of muriatic acid,

Simple acid, he dissolved about 14 oz. of tin. The muriatic acid is first poured on a large quantity of granulated tin, in a large glass receiver, and the sulphuric acid is then slowly added. The solution is more rapidly promoted by means of a sand heat, but it will take place in the cold, requiring only a greater length of time. This murio-sulphate of tin is transparent and colourless, and may be kept for several years without any precipitation. It produces twice the effect of the dyers spirit, at less than one-third of the expence, and raises the colours not only more than the dyers spirit, but also full as much as the tartrate of tin, without converting the crimson of cochineal to a yellowish shade.

200. In the use of this solution of tin as a mordant, to produce the compound scarlet colour with the cochineal crimson and quercitron yellow, Dr Bancroft recommends the following process. "Nothing," says he, "is necessary but to put the cloth, suppose 100 lb. weight, into a proper tin vessel, nearly filled with water, in which about eight pounds of the murio-sulphuric solution of tin have been previously mixed, to make the liquor boil, turning the cloth as usual through it, by the winch, for a quarter of an hour; then turning the cloth out of the liquor, to put into it about four pounds of cochineal, and two pounds and a half of quercitron bark in powder, and having mixed them well, to return the cloth again into the liquor, making it boil, and continue the operation as usual until the colour be duly raised, and the dyeing liquor exhausted, which will be the case in about fifteen or twenty minutes; after which the cloth may be taken out and rinsed as usual. In this way the time, labour, and fuel, necessary for filling and heating the dyeing vessel a second time, will be saved; the operation finished much more speedily than in the common way; and there will be a saving of all the tartar, as well as of two-thirds of the cost of spirit, or nitro-muriatic solution of tin, which for dyeing 100 lb. of wool, commonly amounts to 10s.; whereas 8 lb. of the murio-sulphuric solution will only cost about 3s. There will be moreover a saving of at least one-fourth of the cochineal usually employed (which is generally computed at the rate of one ounce for every pound of cloth), and the colour produced will certainly not prove inferior in any respect to that dyed with much more expence and trouble in the ordinary way. When a rose-colour is wanted, it may be readily and cheaply dyed in this way, only omitting the quercitron bark, instead of the complex method now practised of first producing a scarlet, and then changing it to a rose by the volatile alkali contained in stale urine, set free or decomposed by potash or by lime: and even if any one should still unwisely choose to continue the practice of dyeing scarlet without quercitron bark, he need only

employ the usual proportions of tartar and cochineal, with a suitable quantity of the murio-sulphate of tin, which, while it costs so much less, will be more effectual than the dyers spirit.

201. "Several hundreds of experiments warrant my assertion, that at least a fourth part of the cochineal generally employed in dyeing scarlet, may be saved by obtaining so much yellow as is necessary to compose this colour from the quercitron bark; and indeed nothing can be more self-evident, than that such an effect, ceteris paribus, ought necessarily to result from this combination of different colouring matters, suited to produce the compound colour in question. Let it be recollected that the cochineal crimson, though capable of being changed by tartar towards the yellow hue on one hand, is also capable by other means of being changed towards a blue on the other, and of thereby producing a purple without indigo or any other blue colouring matter: yet I am confident that nobody would believe a pound of cochineal so employed capable alone of dyeing as much cloth, of any particular shade of purple, as might be dyed with it, if the whole of its colouring matter were employed solely in furnishing the crimson part of the purple, whilst the other (blue) part thereof was obtained from indigo. To say that a pound of cochineal alone could produce as much effect or colour as a pound of cochineal and a pound of indigo together, would be an improbability much too obvious and palpable for human belief; and there certainly would be a similar improbability in alleging that a pound of cochineal, employed in giving another compound colour (scarlet), could alone produce as much effect as a pound of cochineal and a pound of quercitron bark, when the colour of this last was employed only in furnishing one of the component parts of the scarlet, for which a considerable portion of the colouring matter of the cochineal must otherwise have been expended, which certainly happens in the new mode of dyeing scarlet, because the colour produced with an addition of the quercitron yellow inclines no more towards a yellow, than the scarlet produced by yellowing a part of the cochineal colour in the usual method with tartar. I retain, therefore, at this moment, as much confidence as I ever had in the reality and importance of my proposed improvements in this respect (x).

202. "The scarlet composed of cochineal crimson and quercitron yellow, is moreover attended with this advantage, that it may be dyed upon wool and wool-len yarn without any danger of its being changed to a rose or crimson, by the process of fulling, as always happens to scarlet dyed by the usual means. This last being in fact nothing but a crimson or rose colour, yellowed by some particular action or effect of the tartar, is liable to be made crimson again by the application of many

(x) "Of the benefit which I formerly expected to obtain by employing potash to extract a part of the cochineal colour, which water alone did not appear capable of extracting, it must be remarked that I have some time since convinced myself of its being an illusion; for, by repeated trials, I have found that the solid parts of powdered cochineal remaining after it has been boiled with the solution of tin, as in the common dyeing process, yield no colour worth notice, upon the application of potash, the solution of tin enabling the water to extract the colour sufficiently; so that in truth there is no such waste of cochineal colour as I had supposed in the usual way of employing that drug."

many chemical agents, (which readily overcome the changeable yellow produced by the tartar), and particularly by calcareous earths, soap, alkaline salts, &c. But where the cochineal colouring matter is applied and fixed merely as a crimson or rose colour, and is rendered scarlet by superadding a very permanent quercitron yellow, capable of resisting the strongest acids and alkalies, (which it does when dyed with solutions of tin), no such change can take place, because the cochineal colour having never ceased to be crimson, cannot be rendered more so, and therefore cannot suffer by those impressions or applications which frequently change or spot scarlet dyed according to the present practice."

203. "There is also a singular property attending the compound scarlet dyed with cochineal and quercitron bark; which is, that if it be compared with another piece of scarlet dyed in the usual way, and both appear by day-light exactly of the same shade, the former, if they be afterwards compared by candle-light, will appear to be at least several shades higher and fuller than the latter; a circumstance of some importance, when it is considered how much this and other gay colours are generally worn and exhibited by candle-light during a considerable part of the year."

204. "To illustrate more clearly the effects of the muri-sulphuric solution of tin with cochineal in dyeing, I shall state a very few of my numerous experiments therewith; observing, however, that they were all several times repeated, and always with similar effects."

"1st, I boiled one hundred parts of woollen cloth in water, with eight parts of the muri-sulphuric solution of tin, during the space of ten or fifteen minutes; I then added to the same water four parts of cochineal, and two parts and a half of quercitron bark in powder, and boiled the cloth fifteen or twenty minutes longer; at the end of which it had nearly imbibed all the colour of the dyeing liquor, and received a very good, even, and bright scarlet. Similar cloth dyed of that colour at the same time in the usual way, and with a fourth part more of cochineal, was found upon comparison to have somewhat less body than the former; the effect of the quercitron bark in the first case having been more than equal to the additional portion of cochineal employed in the latter, and made yellow by the action of tartar."

"2d, To see whether the tartrite of tin would, besides yellowing the cochineal crimson, contribute to raise and exalt its colour more than the muri-sulphate of that metal, I boiled one hundred parts of cloth with eight parts of the muri-sulphuric solution, and six parts of tartar, for the space of one hour; I then dyed the cloth, unrinsed, in clean water, with four parts of cochineal, and two parts and a half of quercitron bark, which produced a bright aurora colour, because a double portion of yellow had been here produced, first by the quercitron bark, and then by the action of tartar upon the cochineal colouring matter. To bring back this aurora to the scarlet colour, by taking away or changing the yellow produced by the tartar, I divided the cloth whilst unrinsed into three equal parts, and boiled one of them a few minutes in water slightly impregnated with potash; another in water with a lit-

tle ammonia; and the third in water containing a very little powdered chalk, by which all the pieces became scarlet; but the two last appeared somewhat brighter than the first, the ammonia and chalk having each rose the cochineal colour rather more advantageously than the potash. The best of these, however, by comparison, did not seem preferable to the compound scarlet dyed without tartar, as in the preceding experiment; consequently this did not seem to exalt the cochineal colour more than the muri-sulphate of tin; had it done so, the use of it in this way would have been easy, without relinquishing the advantages of the quercitron yellow."

"3d, I boiled one hundred parts of woollen cloth with eight parts of the muri-sulphuric solution of tin, for about ten minutes, when I added four parts of cochineal in powder, which, by ten or fifteen minutes more of boiling, produced a fine crimson. This I divided into two equal parts, one of which I yellowed or made scarlet by boiling it for fifteen minutes with a tenth of its weight of tartar in clean water; and the other, by boiling it with a fortieth part of its weight of quercitron bark, and the same weight of muri-sulphuric solution of tin; so that in this last case there was an addition of yellow colouring matter from the bark, whilst in the former no such addition took place, the yellow necessary for producing the scarlet having been wholly gained by a change and diminution of the cochineal crimson; and the two pieces being compared with each other, that which had been rendered scarlet by an addition of quercitron yellow, was, as might have been expected, several shades fuller than the other."

"4th, I dyed one hundred parts of woollen cloth scarlet, by boiling it first in water with eight parts of muri-sulphate of tin, and twelve parts of tartar, for ten minutes, and then adding five parts of cochineal, and continuing the boiling for fifteen minutes. This scarlet cloth I divided equally, and made one part crimson, by boiling with a little ammonia in clean water; after which I again rendered it scarlet, by boiling it in clean water, with a fortieth of its weight of quercitron bark, and the same weight of muri-sulphate of tin; and this last, being compared with the other half to which no quercitron yellow had been applied, was found to possess much more colour, as might have been expected. A piece of the cloth, which had been dyed scarlet by cochineal and quercitron bark, as in the first experiment, being at the same time boiled in the same water with ammonia, did not become crimson, like that dyed scarlet without the bark."

205. "In this way of compounding a scarlet from cochineal and quercitron bark, the dyer will at all times be able, with the utmost certainty, to produce every possible shade between the crimson and yellow colours, by only increasing or diminishing the proportion of bark. It has indeed been usual at times, when scarlets approaching nearly to the aurora colour were in fashion, to superadd a fugitive yellow either from turmeric, or from what is called young fustic (Rhus Cotinus); but this was only when the cochineal colour had been previously yellowed as much as possible by the use of tartar, as in the common way of dyeing scarlet; and therefore that practice ought not to be confounded

confounded with my improvement, which has for its object to preclude the loss of any part of the cochineal crimson, by its conversion towards yellow colour, which may be so much more cheaply obtained than the quercitron bark. By sufficient trials, I have satisfied myself that the cochineal colours, dyed with the mureo-sulphuric solution of tin, are in every respect at least as durable as any which can be dyed with any other preparation of that metal; and they even seem to withstand the action of boiling soap suds somewhat longer, and therefore I cannot avoid earnestly recommending its use for dyeing rose and other cochineal colours, as well as for compounding a scarlet with the quercitron bark."

206. Dr Bancroft afterwards tried a great variety of earthy and metallic salts, as mordants, for the purpose of fixing the colour of cochineal on wool; and he found that, besides the metallic oxides and solutions, the aluminous, calcareous and siliceous earths, as well as magnesia and barytes, might be employed with different success in dyeing with the colouring matter of cochineal: but for the detail of these experiments which he has given, we refer our readers to the treatise itself*.

207. To produce different shades of scarlet, and the other colours which are derived from it, all that is necessary, is to vary the proportions of cochineal, tartar, and solution of tin; and for the shades which incline most to yellow, the addition of quercitron bark, or fustic, is requisite. The use of the tartar is to deepen the colour, and the solution of tin produces a shade of orange. When the shade of colour required to be communicated to the stuff is light, the time of conducting the process must be shortened†.

208. Crimson.—The processes which are employed to dye wool a crimson colour, are two. The stuff is either dyed crimson at once, or the crimson shade is communicated to it, after being previously dyed of a scarlet colour. To dye crimson by a single process, a solution of two ounces and a half of alum, and an ounce and a half of tartar for every pound of stuff, is employed for the boiling, and the stuff is afterwards to be dyed with an ounce of cochineal. It is usual also to employ solution of tin, but in smaller proportion than for dyeing scarlet. The processes employed, it is scarcely necessary to observe, must vary, according as the shade wanted is deeper or lighter, or more or less distant from scarlet. Common salt is also employed by some in the boiling. To render the crimson deeper, and to give it more bloom, archil and potash are frequently used; but this bloom, it ought to be observed, is extremely fugacious. By adding tartar and alum, the boiling for crimson is sometimes prepared after a scarlet reddening, and it is said that the colour possesses more bloom, when both the boiling and reddening are made after scarlet, than when the crimson is dyed in a fresh bath prepared on purpose. In dyeing these colours, the wild cochineal may be employed, but as it contains a smaller proportion of colouring matter, the quantity must be greater.

209. Different substances, as the alkalies, alum, and earthy salts in general, convert the colour of scarlet to crimson, which is the natural colour of cochineal. To effect this, the stuff previously dyed scarlet is boiled for an hour in a solution of alum, the strength of which

is to be regulated by the depth of shade required. In conducting this process, it is necessary to observe, that water impregnated with earthy salts has a considerable effect in varying the shade; so that the quantity of alum employed must be proportioned to the purity of the water. Hellot tried soap, soda, potash, and some other substances, and although they produced the crimson, yet it was of a deeper shade, and had less lustre, than what was produced by means of alum. Ammonia produced a good effect; but from its great volatility, a considerable proportion must be put into the bath, moderately heated, with a little sal ammoniac, and an equal quantity of potash. By this process the stuff became of a bright rosy colour, and thus rendered a smaller quantity of cochineal necessary. Poerner directs the stuff, previously dyed scarlet, to remain 24 hours in a cold solution of sal ammoniac and potash.

210. To produce crimsons, as well as scarlets, in half grain, madder is to be substituted for half the crimson, quantity of the cochineal; or in other proportions, according to the shade desired. The same boiling is given as for scarlet in grain, and the other parts of the process are to be conducted as for reddening the scarlet or crimson. Even the common madder red assumes a greater degree of lustre, when the boiling is made after the reddening for scarlet†.

3. Of the Processes for dyeing Silk Red.

211. Madder red.—The colour which is obtained from madder does not possess sufficient brightness for processes with madder. We shall here, however, describe some of the processes which are employed for this purpose. That of De la Folie, is the following. Half a pound of alum is to be dissolved in each quart of hot water, and two ounces of potash are afterwards to be added. When the effervescence has ceased, and the liquor has become clear, the silk must be kept in it for two hours, after which it is to be washed, and put into the madder-bath. The silk which is dyed in this way becomes more beautiful by means of the soap proof. The process of Scheffer is somewhat different. For each pound of scoured silk, he directs a solution of four ounces of alum, and six drams of chalk, to be prepared. When the sediment has formed, the solution is to be decanted, and having become quite cold, the silk is immersed in it, and left for 18 hours. It is then taken out, and dried, and afterwards dyed with an equal weight of madder. The colour thus obtained is of a dark shade. Mr Guliche describes another process. For every pound of silk he proposes a bath of four ounces of alum and one ounce of solution of tin. When the liquor has become clear, it is decanted, and the silk carefully soaked in it for 12 hours, after which it is to be immersed in a bath with half a pound of madder softened by boiling, with an infusion of galls in white wine. The bath is to be kept moderately hot for an hour, and then made to boil for two minutes. The silk being taken from the bath is to be washed in a stream of water, and dried in the sun. The colour thus obtained is very permanent. By leaving out the galls it is clearer. The brightness of the first colour may be considerably increased, by passing the stuff through a bath of Brazil-wood, to which one ounce of solution of tin is added.

In this way the colour becomes extremely beautiful and durable.

212. Silk is sometimes dyed with Brazil wood, and the colour thus obtained has been distinguished by the name of false crimson, to distinguish it from the more durable colour which is produced by cochineal. The silk, after being boiled with soap, is to be alumed. It is then to be refreshed at the river, and dipped in a bath more or less charged with Brazil juice, according to the depth of shade required. If pure water be employed, the colour will be too red for crimson; but to remedy this, the stuff may be passed through a weak alkaline solution, or a little alkali may be added to the bath, or the stuff may be washed in hard water till it has acquired the proper shade. To deepen the shade of false crimsons, or dark reds, the solution of logwood is added to the Brazil bath, the silk being previously impregnated with the latter; or a little alkali may be added, according to the shade required.

213. The crimson produced by cochineal is called grain crimson, to distinguish it from false crimson. The silk, being well cleansed from the soap at the river, is to be immersed in an alum liquor of the full strength, and to remain for a night. It is then to be washed, and twice beetled at the river. The bath is prepared by filling a long boiler two-thirds with water, to which are added, when it boils, from half an ounce to two ounces of powdered white galls for every pound of silk. When it has boiled for a few moments, from two to three ounces of cochineal, also powdered and sifted, for every pound of silk, are put in, and afterwards one ounce of tartar to every pound of cochineal. When the tartar is dissolved, one ounce of solution of tin is added for every ounce of tartar. In the preparation of this solution of tin, the following proportions are recommended by Macquer. For every pound of nitric acid two ounces of sal ammoniac, six ounces of fine grain tin, and twelve ounces of water are employed. When these ingredients are mixed together, the boiler is to be filled up with cold water, and the proportion of the bath for every pound of silk is about eight or ten quarts of water. In this the silk is immediately immersed, and turned on the winch, till it appear to be of a uniform colour. The fire is then increased, and the bath is kept boiling for two hours, taking care to turn the silk occasionally. The fire is afterwards put out, and the silk put into the bath, where it is allowed to remain for a few hours longer. It is then taken out, washed at the river, twice beetled, wrung, and dried. Two processes are recommended by Scheffer and Macquer. In that of the former, a greater proportion of cochineal is employed in the dye-bath; but, in that of the latter, a yellow ground is previously communicated to the silk. The colour which is thus obtained resists the action of soap, and is more durable than that which is produced by means of carthamus.

214. To obtain other shades of red, the above processes must be varied. If, after the silk has been wrung out of the solution of tin, it is steeped for a night in a cold solution of alum, in the proportion of one ounce to a quart of water, wrung and dried, then washed and boiled with cochineal, it will only appear of a pale poppy-red; but a fine poppy-red may be produced by steeping it twelve hours in the solution of tin, diluted with eight parts of water, then left all night in

the solution of alum, washed, dried, and passed through two baths of cochineal, taking care to add to the second bath a small quantity of sulphuric acid. The same colour may be produced by dyeing the silk previously with anotta, and then passing it successively through a number of baths prepared with an alkaline solution of carthamus, to which lemon juice has been added, till it acquire a fine cherry-colour. To brighten the colour, the silk, after being dyed, may be immersed in hot water acidulated with lemon juice.

215. Other shades of red, as a cherry-red, and flesh-red, are also produced by means of carthamus. For a cherry-red, it is not necessary that the stuff be previously dyed with anotta, and the proportion of colouring matter is smaller. A flesh-red colour is obtained by adding a little soap to the bath, which has the effect of softening the colour, and of retarding the action of the colouring matter on the stuff. To produce dark shades, it is sometimes usual to mix archil, and by this means the expense is diminished.

216. Those who have produced a colour on silk which comes nearest to scarlet, Berthollet observes, begin with dyeing the silk crimson. It is then dyed with carthamus, and lastly it is dyed yellow without heat. By this process a fine colour is obtained; but the dye of the carthamus is not permanent, as it is destroyed by the action of the air, and the colour becomes deeper. The following is Dr Bancroft's process. In a solution of muriate of tin, diluted with five times its weight of water, the silk is to be soaked for two hours; and after being taken out, it is to be wrung and partially dried. It is then to be dyed in a bath prepared with four parts of cochineal, and three of quercitron bark. In this way a colour approaching to scarlet is obtained. To give the colour more body, the immersion may be repeated both in the solution of tin, and in the dyeing bath; and the brightness of the scarlet is increased by means of the addition of carthamus. A lively rose-colour is produced by omitting the quercitron bark, and dyeing the silk with cochineal only; and by adding a large proportion of water to the cochineal, a yellow shade is obtained, which changes the cochineal to the compound scarlet colour*.

4. Of the Process of dyeing Cotton and Linen Red.

217. Madder is most commonly employed for dyeing cotton and linen a red colour; and indeed in this kind of dyeing it is the most useful of all colouring matters. The affinity of the colouring matter of madder for cotton is stronger than for linen; but it has been found that the processes which are most successful in dyeing the one are the most preferable for the other. There are two kinds of madder reds: the one is called simple madder red; and the other, which is much brighter, has been distinguished by the name of Turkey or Adrianople red, because it comes from the Levant, and has rarely been equalled in brightness and permanency. In communicating this beautiful red colour to cotton, by means of madder, a great many useless and ridiculous directions have been given. According to some processes, the period of a month is scarcely sufficient to finish all the operations which are considered as indispensably necessary for obtaining this dye.

218. The principal mordants which are employed in dyeing cotton with madder, are oil, gall-nuts, and alum. The colouring matter of madder cannot be fixed on cotton, till the latter has been impregnated with oil. A cold soapy liquor is formed by a combination of oil and a weak solution of soda. By the use of this alkaline ley the oil is diluted and divided, and can be easily and equally applied to all the parts of the cotton. According to Chaptal, potash produces the same effect as soda; and attention to this is of some importance, from the difference of price of the two substances. All kinds of soda or oil are not fit for this preliminary preparation. The soda must be in the caustic state, and its causticity must be the effect of calcination; because if it has been rendered caustic by means of lime, it becomes of a brown colour. The soda also should contain little muriate, for when this neutral salt prevails, the combination of the oil and the soda is greatly retarded. The most proper oil is not of a fine kind, but that which contains a large portion of the extractive principle. As the ley of soda is only employed for the purpose of diluting and conveying the oil equally to all the parts of the cotton, there must be a perfect combination of the oil and the soda. Indeed this is of so much importance, that many place the whole secret of a strong colour in the choice of good oil and soda. From this it follows, that the oil should be in excess, otherwise it would abandon the stuff in washing, and the colour would remain dry.

219. The cotton, being impregnated with oil, is subjected to the operation of galling. The use of gall-nuts is attended with several advantages. 1. The gallic acid which they contain decomposes the saponaceous liquor with which the cotton is impregnated, and fixes the oil on the stuff. 2. The other properties which the galls possess, predispose the cotton to receive the colouring matter. 3. The astringent principle unites with the oil, and forms with it a compound, which on drying becomes black, is not very soluble in water, and has a strong affinity with the colouring matter of madder.

220. From these principles some practical observations may be deduced. 1. Gall-nuts furnish the most proper astringent matter for this kind of dye. 2. To effect a speedy and perfect decomposition, the galls ought to be strained as hot as possible. 3. The galled cotton should be speedily dried, for otherwise it might assume a black colour, which would injure the brightness of the red. 4. The process of galling should be performed in dry weather, because when the weather is moist, the astringent principle produces a black colour, and dries slowly. 5. The cotton should be pressed together with great care, that the decomposition may be equally effected at every point of the surface. 6. It is necessary to attend to the proportion between the gall-nuts and the soap, for if the former predominate the colour is black, and if the soap is in excess, the portion of oil uncombined with the astringent principle, escapes in the washings, and impoverishes the colour.

221. Alum is also employed as a mordant in dyeing cotton red. This substance not only heightens the red of madder, but contributes also, by its decomposition, and the fixation of its alumina, to give solidity to the

colour. When cotton, after it has been galled, is immersed in a solution of alum, it immediately changes its colour, and becomes gray. No precipitate appears in the bath, because the operation takes place in the tissue of the cloth itself. But if the solution of alum be employed at too high a temperature, part of the galls escapes from the stuff, and the decomposition of the alum is then effected in the bath. This, which should be guarded against, must obviously diminish the proportion of the mordant, and render the colour poorer.

222. This mordant, which is the most complicated known in dyeing, requires great attention in its application. In this, indeed, consists the whole difficulty of dyeing cotton a madder or Turkey red. In this mordant there is a combination of three principles, oil, the astringent principle, and alumina; and on their proper combination, the perfection of the colour depends. When any one of them is employed separately, the colour is neither so bright, nor so completely fixed.

223. After these preliminary observations, we shall now give a fuller detail of some of the processes which are followed in dyeing cotton Turkey red. The following is that which is practised at Astracan, of which an account has been given by Professor Pallas.

"The cotton to be dyed red is first washed exceedingly clean in running water, and, when the weather is clear, hung up on poles to dry. If it does not dry before the evening, it is taken into the house, on account of the saline dews so remarkable in the country around Astracan, and again exposed to the air next morning. When it is thoroughly dry it is laid in a tub, and fish oil is poured over it till it is entirely covered. In this state it must stand all night, but in the morning it is hung up on poles, and left there the whole day; and this process is repeated for a week, so that the cotton lies seven nights in oil, and is exposed seven days to the atmosphere, that it may imbibe the oil and free itself from all air. The yarn is then again carried to a stream, cleaned as much as possible, and hung up on poles to dry.

224. "After this preparation, a mordant is made of three materials, which must give the grounds of the red colour. The pulverized leaves of the sumach are first boiled in copper kettles; and when their colouring matter has been sufficiently extracted, some powdered galls are added, with which the liquor must be again boiled; and by these means it acquires a dark dirty colour. After it has been sufficiently boiled, the fire is taken from under the kettle, and alum put into the liquor yet hot, where it is soon dissolved. The proportion of these three ingredients I cannot determine with sufficient accuracy, because the dyers make use of different quantities at pleasure. The powder of the sumach leaves is measured into the kettle with ladles; the water is poured in according to a gauge, on which marks are made to shew how high the water must stand in the kettle to soak six, eight, ten, &c. puds of cotton yarn. The galls and alum are added in the quantity of five pounds to each pud of cotton. In a word, the whole mordant must be sufficiently yellow, strong, and of an astringent taste.

225. "As soon as the alum is dissolved, no time must be lost in order that the mordant may not be suffered

O. Simple to cool. The yarn is then put into hollow blocks of wood shaped like a mortar, into each of which such a quantity of the mordant has been poured as may be sufficient to moisten the yarn without any of it being left. As soon as the workman throws the mordant into the mortar, he puts a quantity of the yarn into it, and presses it down with his hand till it becomes uniformly moistened, and the whole cotton yarn has struck. By this it acquires only a pale yellow colour, which however is durable. It is then hung up on poles in the sun to dry, again washed in the stream, and afterwards dried once more.

226. "By the yellow dye of the sumach leaves, the madder dye becomes brighter and more agreeable; but the galls damp the superfluous yellow, and together with the alum prepare the yarn for its colour. Some dyers however omit the use of these leaves altogether, and prepare their mordant from galls and alum only, by first boiling the galls in due proportion with the requisite quantity of water, then dissolving the alum with boiling water in a separate vessel, afterwards pouring both liquors together into a tub, and suffering the cotton to remain in them an hour, or an hour and a half; after which it is dried gradually, then washed, and again dried once more. By this process the yarn acquires a dirty reddish colour.

227. "The next part of the process is to prepare the madder dye. The madder, ground to a fine powder, is spread out in large troughs, and into each trough is poured a large cup full of sheep's blood, which is the kind that can be procured with the greatest facility by the dyers. The madder must be strongly mixed in it by means of the hand, and then stand some hours in order to be thoroughly soaked by it. The liquor then assumes a dark red appearance, and the madder in boiling yields more dye.

228. "After this process water is made hot in large kettles, fixed in brick-work; and as soon as it is warm the prepared red dye is put into it, in the proportion of a pound to every pud of cotton. The dye is then suffered to boil strongly; and when it is boiled enough, which may be tried on cotton threads, the fire is removed from under the kettle, and the prepared cotton is deposited near it. The dyer places himself on the edge of the brick-work that encloses the kettle; dips the cotton yarn, piece by piece, into the dye; turns it round, backwards and forwards; presses it a little with his hands; and lays each piece, one after the other, in pails standing ready for the purpose. As soon as all the cotton has received the first tint, it is hung up to dry: as the red, however, is still too dull, the yarn which has been already dyed once, and become dry, is put once more into the dyeing kettle, and must be left there to seethe for three hours over a strong fire, by which it acquires that beautiful dark red colour which is so much esteemed in the Turkey yarn. The yarn is now taken from the dye with sticks; the superfluous dye which adheres to it is shaken off; the hanks are put in order, and hung up, one after another, to dry. When it is thoroughly dry, it is washed in the pure stream and again dried. The only fault of the Astra-

can dyers is, that the colour is sometimes brighter and sometimes darker, probably because they do not pay sufficient attention to the proportions, or because the madder is not always of the same goodness.

229. "In the last place, the above-mentioned soda (kalakar) is dissolved with boiling water in tubs destined for that purpose; and it is usual here to allow twenty pounds of soda to forty pounds of cotton, or half the weight. Large earthen jars, which are made in Persia of very strong clay, a yard and a half in height, almost five spans wide in the belly, and ending in a neck a span and a half in diameter, enclosed by means of cement in brick-work over a fire-place, in such a manner that the necks only appear, are filled with the dyed cotton yarn. The ley of dissolved soda, which is blackish and very sharp, is then poured over it till the jars be filled; and some clean rags are pressed into their mouths, that the uppermost skains of yarns may not lie uncovered. A fire is then made in the fire-place below, and continued for 24 hours; and in the mean time the steam which arises from the jars is seen collected among the rags in red drops. By this boiling the dye is still more heightened, and is made to strike completely; every thing superfluous is removed, and all the fat matter which still adheres to the yarn is washed out: nothing more is then necessary for completing the dye of the yarn but to rinse it well several times in running water, and then to dry it.

230. "That the dye of madder might be made very penetrating by other methods, and through the means of other oily and resinous substances, is shewn by the process of the Tungusians to dye horse, goat's and reindeer's hair, which they use for ornamenting their dresses, of a beautiful red colour, with the roots of the cross-wort, or northern madder (galium), and narrow-leaved woodroof (asperula tinctoria), which have a resemblance to those of madder. They boil the fresh or dried roots with about the same quantity of agaric (agaricus officinarum), which, as is well known, is abundant in resinous gummy particles, and is used by the people of Jakut instead of soap; they then lay in it the white hair which they wish to dye, and suffer it to seethe slowly until it be sufficiently red. Cotton cloth is dyed with madder at Astracan in the same manner: but many pursue a fraudulent process, by dyeing with red wood, and then sell their cloth as that which has been dyed in the proper manner."

231. The processes which are employed in the Greco-Turkish manufactures for dyeing Turkey red, as they have been described by C. Felix, in a memoir in the French annals of chemistry, are somewhat different from the above. "In these manufactures," he observes, "the workmen dye at one time a mass of skains weighing thirty-five occas (G); each occa being equal to about fifty ounces. The first process is that of cleaning the cotton, for which purpose three leys are employed; one of soda, another of ashes, and a third of lime. The cotton is thrown into a tub, and moistened with the liquor of the three leys in equal quantities; it is then boiled in pure water, and washed in running water.

232. "The second bath given to the cotton is composed of soda and sheep's dung dissolved in water. To facilitate the solution, the soda and dung are pounded in a mortar. The proportions of these ingredients employed, are, one occa of dung, six of soda, and forty of water. When the ingredients are well mixed, the liquor expressed from them is strained, and being poured into a tub, six occas of olive oil are added to it, and the whole is well stirred till it becomes of a whitish colour, like milk. The cotton is then besprinkled with this water, and when the skains are thoroughly moistened, they are wrung, pressed, and exposed to dry. The same bath must be repeated three or four times, because it is this liquor which renders the cotton more or less fit for receiving the dye. Each bath is given with the same liquor, and ought to continue five or six hours. It is to be observed that the cotton, after each bath, must be dried without being washed, as it ought not to be rinsed till after the last bath. The cotton is then as white as if it had been bleached in the fields.

233. "The bath of sheep's dung is not used in our manufactories (H); it is a practice peculiar to the Levant. It may be believed that the dung is of no utility for fixing the colours; but it is known that this substance contains a great quantity of volatile alkali, in a disengaged state, which has the property of giving a rosy hue to the red. It is therefore probable that it is to this ingredient that the red dyes of the Levant are indebted for their splendour and vivacity. This much, at any rate, is certain, that the Morocco leather of the Levant is prepared with dog's dung; because it has been found that this dung is proper for heightening the colour of the black. The bath of dung is followed by the process of galling.

234. "The galling is performed by immersing the cotton in a bath of warm water, in which five occas of pulverised gall-nuts have been boiled. This operation renders the cotton more fit for being saturated with the colour, and gives to the dye more body and strength. After the galling comes aluming, which is performed twice, with an interval of two days, and which consists in dipping the cotton into a bath of water in which five occas of alum have been infused, mixed with five occas of water alkalized by a ley of soda. The aluming must be performed with care, as it is this operation which makes the colouring particles combine best with the cotton, and which secures them in part from the destructive action of the air. When the second aluming is finished, the cotton is wrung; it is then pressed, and put to soak in running water, after being inclosed in a bag of thin cloth.

235. "The workmen then proceed to the dyeing.— To compose the colours they put in a kettle five occas of water and thirty-five occas of a root which the Greeks call ali-zari, or painting colour, and which in Europe is known under the name of madder. The madder, after being pulverised, is moistened with one occa of ox or sheep's blood. The blood strengthens the colour, and the dose is increased or lessened according to the shade of colour required. An equal heat is maintained below the kettle, but not too violent; and when the liquor ferments, and begins to grow warm, the skains are then gradually immersed, before the liquor becomes too hot. They are then tied with pack-thread to small rods, placed crosswise above the kettle for that purpose, and when the liquor boils well, and in an uniform manner, the rods from which the skains were suspended are removed, and the cotton is suffered to fall into the kettle, where it must remain till two-thirds of the water is evaporated. When one-third only of the liquor remains, the cotton is taken out and washed in pure water.

236. "The dye is afterwards brought to perfection by means of a bath alkalized with soda. This manipulation is the most difficult and the most delicate of the whole, because it is that which gives the colour its tone. The cotton is thrown into this new bath, and made to boil over a steady fire till the colour assumes the required tint. The whole art consists in catching the proper degree: a careful workman, therefore, must watch with the utmost attention for the moment when it is necessary to take out the cotton, and he will rather burn his hand than miss that opportunity. It appears that this bath, which the Greeks think of so much importance, might be supplied by a ley of soap; and it is probable that saponaceous water would give the colour more brightness and purity.

237. "When the colour is too weak, the Levantines know how to strengthen it by increasing the dose of the colouring substances; and when they wish to give it brightness and splendour, they employ different roots of the country, and, in particular, one named sussari, specimens of which I have sent to France. The ali-zari, which is the principal colouring matter employed in the Greek dye-houses, is collected in Natolia, and is brought to Greece from Smyrna: some of it comes also from Cyprus and Mesopotamia. The superiority of this Levantine plant to the European madder is acknowledged by all those acquainted with the art of dyeing, and may arise from two causes: the manner in which it is cultivated, and the method employed for its desiccation (1)."

(1) "The chief manufactories (continues our author), for dyeing spun cotton red, established in Greece, are in Thessaly. There are some at Baba, Rapsani, Tournavos, Larissa, Pharsalia, and in all the villages situated on the sides of Ossa and Pelion. These two mountains may be considered as the alembics that distil the eternal vapours with which Olympus is crowned, and which distribute them throughout the beautiful valleys situated around them. Of these valleys, that of Tempe has at all times been distinguished by the beauty of its shady groves and of its streams. These streams, on account of their limpidness, are very proper for dyeing, and supply water to a great number of manufactories, the most celebrated of which are those of Ambelakia.

Ambelakia, on account of the activity which prevails in it, has a greater resemblance to a town of Holland than a village of Turkey. This village, by its industry, communicates life and activity to all the neighbouring country, and gives birth to an immense trade, which connects Germany with Greece in a thousand ways. Its population,

238. To these processes we shall add the account of another, which was long successfully practised at Glasgow by Mr Papillon, a native of France, and was communicated by him, for a suitable premium, to the commissioners and trustees for manufactures in Scotland, to be by them published for the benefit of the public, at the end of a certain term of years. This transaction took place in 1790, and the period having expired, the trustees announced it to the public in 1803. The process, which consists of nine different steps, is the following.

For 100 lib. cotton you must have
100 lib. of Alicante barilla,
20 lib. of pearl ashes,
100 lib. quicklime.

The barilla is mixed with soft water in a deep tub, which has a small hole near the bottom of it, stopped at first with a peg.—This hole is covered in the inside with a cloth supported by two bricks, that the ashes may be prevented from running out at it, or stopping it up while the ley filters through it.

Under this tub is another to receive the ley; and pure water is repeatedly passed through the first tub to form leys of different strength, which are kept separate at first until their strength is examined. The strongest required for use must swim or float an egg, and is called the ley of six degrees of the French hydrometer, or peseliqueur. The weaker are afterwards brought to this strength, by passing them through fresh barilla. But a certain quantity of the weak, which is of 2 degrees of the above hydrometer, is reserved for dissolving the oil, and gum, and the salt, which are used in subsequent parts of the process. This ley of 2 degrees is called the weak barilla liquor, the other is called the strong.

Dissolve the pearl-ashes in 10 pails, of 4 gallons each, of soft water, and the lime in 14 pails.

Let all the liquors stand till they become quite clear, and then mix ten pails of each.

Boil the cotton in the mixture five hours, then wash it in running water and dry it.

Take a sufficient quantity (20 pails) of the strong

barilla water in a tub, and dissolve or dilute in it 2 pails of sheep's dung, then pour into it 2 quart bottles of oil of vitriol, and 1 lib. of gum arabic, and 1 lib. of sal ammoniac, both previously dissolved in a sufficient quantity of the weak barilla water, and lastly, 25 lib. of olive oil, which has been previously dissolved or well mixed with 2 pails of the weak barilla water.

The materials of this steep being well mixed, tramp or tread down the cotton into it, until it is well soaked; let it steep 24 hours, and then wring it hard and dry it.

Steep it again 24 hours, and again wring and dry it. Steep it a third time 24 hours, after which wring and dry it, and lastly wash it well and dry it.

This part of the process is precisely the same with the last, in every particular, except that the sheep's dung is omitted in the composition of the steep.

Boil 25 lib. of galls bruised in 10 pails of river water until 4 or 5 are boiled away; strain the liquor into a tub, and pour cold water on the galls in the strainer, to wash out of them all their tincture.

As soon as the liquor is become milk-warm, dip your cotton hank by hank, handling it carefully all the time, and let it steep 24 hours.

Then wring it carefully and equally, and dry it well without washing.

Dissolve 25 lib. of Roman alum in 14 pails of warm water, without making it boil, skim the liquor well, and add 2 pails of strong barilla water, and then let it cool until it be lukewarm.

Dip your cotton and handle it hank by hank, and let it steep 24 hours, and wring it equally and dry it well without washing.

Is performed in every particular like the last, but after the cotton is dry, you steep it 6 hours in the river, and wash and dry it.

population, which has been tripled within these fifteen years, amounts at present to 4000, and all these people exist by dyeing. None of those vices or cares produced by idleness are known here. The hearts of the inhabitants are pure, and their countenances unclouded. Servitude, which degrades the countries watered by the Peneus, has not ascended to these hills: no Turk can reside or live among these people; and they govern themselves, like their ancestors, by their protoyeros and their own magistrates. Twice have the savage mussulmans of Larissa, envious of their ease and happiness, attempted to scale their mountains in order to plunder their houses; and twice have they been repulsed by hands which suddenly quitted the shuttle to assume the musket.

"All hands, and even those of the children, are employed in the dye-houses of Ambelakia; and while the men dye the cotton, the women are spinning and preparing it. The use of wheels is not known in this part of Greece: all the cotton is spun on a distaff: the thread, indeed, is certainly not so round or equal, but it is softer, more silky, and more tenacious; it is less apt to break, and lasts longer; it is also more easily whitened, and more proper for being dyed. It is a pleasing spectacle to see the women of Ambelakia, each spinning from a distaff, and sitting conversing together on the threshold of their doors; but as soon as a stranger appears, they instantly retire and conceal themselves in their houses, manifesting, like Galatea, in their precipitate retreat, a desire of flying and of shewing themselves:

Et fugit ad salices, et se cupit ante videri."

The cotton is dyed by about 10 lib. at once, for which take 2½ gallons of ox blood, and mix it in the copper with 28 pails of milk-warm water, and stir it well; then add 25 lib. of madder, and stir all well together. Then having beforehand put the 10 lib. of cotton on sticks, dip it into the liquor, and move and turn it constantly one hour, during which you gradually increase the heat, until the liquor begin to boil at the end of the hour. Then sink the cotton, and boil it gently one hour longer; and, lastly, wash it and dry it.

Take out so much of the boiling liquor, that what remains may produce a milk-warm heat with the fresh water with which the copper is again filled up, and then proceed to make up a dyeing liquor as above, for the next 10 lib. of cotton.

Mix equal parts of the gray steep liquor, and of the white steep liquor, taking 5 or 6 pails of each. Tread down the cotton into this mixture, and let it steep six hours, then wring it moderately and equally, and dry it without washing.

Ten lib. of white soap must be dissolved most carefully and completely in 16 or 18 pails of warm water; if any little bits of the soap remain undissolved, they will make spots in the cotton. Add four pails of strong barilla water, and stir it well. Sink your cotton in this liquor, keeping it down with cross sticks, and cover it up and boil it gently two hours, then wash and dry it, and it is finished.

The number of vessels necessary for this business is greater in proportion to the extent of the manufactory; but, in the smallest work, it is necessary to have four coppers of a round form.

1st, The largest, for boiling and for finishing, is 28 inches deep by 38 or 39 wide in the mouth, and 18 inches wide in the widest part.

2d, The second, for dyeing, is 28 deep, by 23 or 24 in the mouth.

3d, The third, for the alum steep, is like the second.

4th, The fourth, for boiling the galls, is 20 deep, by 28 wide.

A number of tubs or larger wooden vessels are necessary, which must all be of fir, and hooped with wood or with copper.

Iron must not be employed in their construction, not even a nail; but where nails are necessary, they must be of copper.

By the pail is always understood a wooden vessel, which holds four English gallons, and is hooped with copper.

In some parts of the above process, the strength of the barilla liquor or liquors is determined, by telling to what degree a peseliqueur or hydrometer sunk in them.

The peseliqueur is of French construction. It is similar to the glass hydrometer used by the spirit-dealers

in this country; and any artist who makes these instruments, will find no difficulty in constructing one with a scale similar to that employed by M. Papillon, when he is informed of the following circumstances:

1st, The instrument, when plunged in good soft water, such as Edinburgh pipe water, at temperature 60 degrees, sinks to the 0, or beginning of the scale, which stands near the top of the stem.

2d, When it is immersed in a saturated solution of common salt, at the same temperature of 60 degrees, it sinks to the 26th degree of the scale only, and this falls at some distance from the top of the ball.

This saturated solution is made by boiling, in pure water, refined sea or common salt, till no more is dissolved, and by filtering the liquor when cold through blotting paper.

It should also be observed, that whenever directions are given to dry yarn, to prepare it for a succeeding operation, that this drying should be performed with particular care, and more perfectly than our dryest weather is in general able to effect. It is done therefore in a room heated by a stove to a great degree.

239. There is still another process, which is recommended by Haussmann. This process, (says he) obtains a beautiful and durable red. He makes a caustic ley of one part of common potash dissolved in four of boiling water, and a half part of quicklime, which is afterwards slaked in it. He then dissolved one part of powdered alum in two of boiling water, and to this solution, while it was yet warm, he added that of the caustic ley. The solution of alumina being left at rest, formed, on cooling, a precipitate of sulphate of potash. A 33d part of linseed oil was then mixed with the alkaline solution of alumina, which then formed a milky saponaceous liquid. When the mixture is to be used, it ought to be well shaken, because the oil separates. The stuffs of cotton or linen must be successively immersed in it, and equally pressed, and must be dried under shelter from rain in summer, and in a warm place in winter; and being left in that state for 24 hours, are then washed in pure running water, and again dried. The same process in the immersion in alkaline ley is again to be repeated, taking care to introduce first those stuffs which were last in the first solution. The whole of the mixture should be consumed each time, as it would attract carbonic acid from the air, and suffer the alumina to be precipitated.

240. Two immersions in the alkaline solution of alumina mixed with linseed oil, afford a beautiful red: but by impregnating the stuffs a third, or even a fourth time, in the same manner, the most brilliant colours are obtained. The intensity of the colour is in proportion to the quantity of madder. A quantity of madder equal in weight to the stuffs, will yield a red, which, by clearing becomes of a rosy shade; and shades of crimson of different degrees of brightness are obtained, by using two, three, or four times the weight of madder; but unless the water employed in the processes contains some portion of lime, the addition of the chalk should never be omitted.

241. The scarlet colour communicated to cotton by Scarlet means of cochineal, is far from being permanent; but with cochineal if this colour is wished to be communicated to cotton, Dr Bancroft recommends to steep the cotton, previously moistened, for half an hour, in a diluted solution of mario-

murio-sulphate of tin, and then having wrung the cotton, to plunge it into water, in which as much potash has been dissolved as will neutralize the acid adhering to the cotton, so that the oxide of tin may be more copiously fixed on the fibres of the cotton. The stuff being afterwards rinsed in water, may be dyed with cochineal and quercitron bark, in the proportion of four pounds of the former, to two and a half or three pounds of the latter. A full bright colour is thus given to the cotton, which will bear slight washings with soap, and exposure to the air. Indeed the yellow part of the colour derived from quercitron bark will bear long boiling with soap, and will resist the action of acids.

242. With the aluminous mordant, as it is usually applied by calico printers for madder reds, cotton dyed with cochineal receives a beautiful crimson colour, which will bear several washings, and resist the weather for some time. It is not, however, to be considered as a fixed colour. Dr Bancroft is of opinion, that the addition of a small portion of cochineal in dyeing madder reds upon the finer cottons, would be highly advantageous to the calico-printers. By this addition the madder reds are rendered more beautiful, and the fawn colour, or brownish yellow hue, which injures these reds, would be thus overcome *.

243. In dyeing yellow, it is necessary to employ mordants, because the affinity of yellow colouring matters for either animal or vegetable stuffs is not sufficiently strong to produce durable colours. Yellow colours, therefore, belong to that class which Dr Bancroft has denominated adjective colours. As in the former section, we shall first give a short description of the nature and properties of the substances employed in dyeing yellow, and then point out the most approved modes of communicating their colours to woollen, silk, cotton, and linen stuffs.

The substances capable of giving a yellow colour to different stuffs are very numerous; they do not all produce similar quantities of colouring matter; their dye is not equally free; the colours they impart incline more or less to orange or green; they possess various degrees of brightness and permanency, and differ considerably in price; circumstances by which the choice of the dyer ought always to be regulated. But those commonly employed in dyeing yellow, are weld, fustic, anotta, and quercitron bark.

244. Weld (reseda luteola, Lin.) is a plant which grows wild in Britain, and in different European countries. Its leaves are long, narrow, and of a bright green, but the whole plant is made use of in the dyeing of yellow. There are two kinds of weld, cultivated and wild, the former of which is deemed more valuable than the latter, as it yields a much greater proportion of colouring matter. When this plant is fully ripe, it is pulled, dried, and bound up in bundles for the use of the dyer. The wild species grows higher and has a stronger stalk than that which is cultivated, by which the one may be readily distinguished from the other.

245. A strong decoction of weld is of a brownish yellow colour, and if very much diluted with water the co-

lour inclines to a green. An alkali gives to this decoction a deeper colour, and the precipitate it occasions is not soluble in alkalies. Most of the acids give it a paler tinge, occasioning a little precipitate which is soluble in alkalies. Alumina has so strong an affinity for the colouring matter of weld, that it can even abstract it from sulphuric acid, and the oxide of tin produces a similar effect. The greater part of metallic salts throw down similar precipitates, which vary in their shades of colour according to the metal employed. A solution of common salt renders the liquor turbid, and a solution of tin yields a copious yellow precipitate, while the liquor long continues turbid, and slightly coloured.

246. Fustic (morus tinctoria, Lin.) is procured from Fustic, a tree of considerable magnitude, which grows in the West Indies. The wood is yellow, as its name imports, with orange veins. Ever since the discovery of America it has been used in dyeing, as appears from a paper in the Transactions of the Royal Society, of which Sir William Petty was the author. Its price is moderate, the colour it imparts is permanent, and it readily combines with indigo, which properties give it a claim to attention as a valuable ingredient in dyeing. Before it can be employed as a dye-stuff, it must be cut into chips and put into a bag, that it may not fix in, and tear the stuff, to which it is to impart its colouring matter.

247. When a decoction of yellow wood or fustic is made very strong, the colour is of a reddish yellow, and when diluted it is of an orange yellow, which it readily yields to water. It becomes turbid by means of acids, its colour is of a pale yellow, and the greenish precipitate may be re-dissolved by alkalies. The sulphates of zinc, iron, and copper, as well as alum, throw down precipitates composed of the colouring matter and the different bases of the salts employed.

In examining the causes of the fixity of yellow colours, obtained from vegetables, Chaptal discovered that the durability of the pale yellow depended on the tanning principle, which is found united with the yellow colouring matter. He obtained by analyzing fustic, 1. A resinous or gummy matter, which can communicate a beautiful yellow colour. 2. An extractive matter, which is also yellow, and affords a beautiful colour. 3. A tanning principle of a pale yellow colour, which becomes black by boiling, or exposure to the air. This latter diminishes the brilliancy of the two former; but it may be separated by a simple process. Chaptal boiled with the wood some animal substance containing gelatinous matter, such as bits of skin, strong glue, &c. The tanning principle was thus precipitated with the gelatinous matter, and the bath held in solution only the colouring matters which yield a bright full yellow; and by means of this process he procured colours from several vegetables, equally bright with those which are communicated by yellow wood and quercitron bark *.

248. Anotta is a species of paste of a red colour, obtained from the berries of the bixa orellana, Lin. which is a native of America. The anotta of commerce is imported from America to Europe in cakes of two or three pound weight, where it is prepared from the seeds of the tree mentioned above; but the Americans are said to be in possession of a species of anotta superior to that which they export, both for the brilliancy and

simple and permanency of the colour it imparts. They bruise the seeds with their hands moistened with oil, separating with a knife the paste as it is formed, and drying it in the sun; but the seeds are pounded with water when designed for sale, and allowed to undergo the process of fermentation.

247. Anotta yields its colouring matter more readily to alcohol than to water, on which account it is used in yellow varnishes to which an orange tinge is intended to be given. Acids form a precipitate with a decoction of anotta of an orange colour, which is soluble in alkalies; but solutions of common salt produce no sensible change. It yields an orange precipitate with a solution of alum, and the sulphates of copper and iron produce effects of nearly a similar nature. With a solution of tin, the precipitate is of a lemon colour and slowly deposited.

248. Quercitron, as it is denominated by Dr Bancroft, is the quercus nigra of Linnaeus, and is a large tree which grows spontaneously in North America. The bark of it yields a considerable quantity of colouring matter, which was first discovered by Dr Bancroft in the year 1784, in whom the use and application of it in dyeing were exclusively vested for a certain term of years by virtue of an act of parliament. To prepare it for use, the epidermis is taken off and pounded in a mill, the result of which process is a number of filaments and a fine light powder; but as these do not contain equal quantities of colouring matter, it will be proper to employ them in their natural proportions.

249. Quercitron bark readily imparts its colouring matter to water at 100° of Fahrenheit, which is of a yellowish brown, capable of being darkened by alkalies, and brightened by acids. With muriate of tin the precipitate is copious, and of a yellow colour; with sulphate of tin it is a dark olive; and with sulphate of copper it is yellow, but inclining to an olive. Nitromuriate of tin yields a yellow extremely beautiful, probably owing to the oxide of tin combining with the colouring matter in a greater proportion than some other salts.

250. Besides the substances already mentioned as employed in the dyeing of yellow, we may add saw-wort to the number (serratula tinctoria, Lin.) a plant which yields a colouring matter nearly similar to that of weld, and may of consequence be used as a proper substitute. Dyers broom (genista tinctoria) produces a yellow of very indifferent nature, and is therefore only employed in dyeing stuffs of the coarsest kind. Turmeric (curcuma longa) is a native production both of the East and West Indies, and yields a more copious quantity of colouring matter than any other yellow dye-stuff; but it will probably never be of any essential service in dyeing yellow, as no mordant has yet been discovered, capable of giving permanency to its colour.

251. Chamomile (anthemis tinctoria) yields a faint yellow colour, the hue of which is not unpleasant, but is far from being durable, and even mordants are not capable of fixing it. Sulphate of lime, tartar and alum, bid fairest for success.

252. Fenugreek (trigonella fenugraecum) yields seeds which, when ground, communicate to stuffs a pale yellow of tolerable durability; and the best mordants are found to be alum and muriate of soda, or common salt. American hickory (juglans alba) is a tree,

the bark of which yields a colouring matter in every respect resembling that of the quercus nigra, but in quantity greatly inferior. French berries (rhamnus infectorius) produce a tolerable yellow colour, but it is by no means permanent. When used in the process of dyeing, they are to be employed in the same manner as weld. According to Scheffer, a fine yellow colour may be imparted to silk, thread, and wool, by means of the leaves of the willow: but Bergman informs us that only the leaves of the sweet willow (salix pentandra) are proper for producing a permanent colour, as a few weeks exposure to the sun extracts that which is produced by the colouring matter from the leaves of the common willow.

253. In Switzerland and in England, the seeds of purple trefoil are sometimes employed in the art of dyeing, on which Vogler made a number of experiments, in order to ascertain what colours they would produce: and he found that a fine deep yellow was afforded by a bath made of a solution of these seeds with potash; that sulphuric acid yielded a light yellow, and sulphate of copper or blue vitriol, a yellow inclining to green. M. Dizé informs us, that the seeds of trefoil impart to wool a beautiful orange, and to silk a greenish yellow; and that while aluming is necessary in the process of dyeing with the seeds of trefoil, a solution of tin cannot be employed.

II. Of the Processes for Dyeing Wool Yellow.

254. In dyeing woollen stuffs with weld, the mordants employed are alum and tartar, and by their means a pure, permanent yellow is obtained. The boiling is to be conducted in the usual way; and according to Hellot, four ounces of alum to one ounce of tartar are to be employed. Other dyers, however, employ half as much tartar as alum. The colour is rendered paler, but more lively, by means of the tartar.

255. The bath is prepared by boiling the plant inclosed in a thin linen bag, and keeping it from rising by means of a wooden cross. Some boil it till it sinks to the bottom of the vessel; while others, after it is boiled, take it out, and throw it away. From three to four lbs. of weld, and sometimes less, are allowed for every lb. of stuff; but the quantity must be regulated by the intensity of the shade desired. Some dyers add a small quantity of quicklime and ashes, which are found to promote the extraction of the colouring matter. These substances at the same time heighten the colour, but render it less susceptible of resisting the action of acids.

256. With other additions, and different management, for different shades may be obtained. Thus, lighter shades are produced by dyeing after deeper ones, adding water at each dipping, and keeping the bath at the boiling temperature. These shades, however, are less lively than when fresh baths are employed, with a suitable proportion of weld. The addition of common salt or sulphate of lime to the weld bath communicates a richer and deeper colour. With alum it is paler and more lively, with tartar still paler, and with sulphate of iron the shade inclines to brown. According to Scheffer, by boiling the stuff two hours, with one-fourth of its weight of a solution of tin, and the same proportion of tartar, and then washing and boiling it with an equal weight of weld, a fine yellow is produced; but if the stuff

Of Simple stuff be in the state of cloth, its internal texture is not Co'ours. penetrated. Poerner recommends a similar preparation as for dyeing scarlet, and by these means the colour is brighter, more permanent, and lighter.

With querc. 257. Dr Bancroft recommends the quercitron bark citron bark. as one of the cheapest and best substances for dyeing wool yellow. The following is the simple process which he has proposed for its application. The bark is to be boiled up with about its weight, or one-third more, of alum, in a suitable proportion of water, for about 10 minutes. The stuff previously scoured is then to be immersed in the bath, taking care to give the higher colours first, and afterwards the paler straw colours.

Cheap pro- By this cheap and expeditious process, colours which cess. are not wanted to be of a full or bright yellow, may be obtained. The colour may be considerably heightened by passing the unrinsed stuff a few times through hot water, to which a little clean powdered chalk, in the proportion of about 1 lb. for each 100 lb. of stuff has been previously added. The bark, when used in dyeing, being first reduced to powder, should be tied up in a thin linen bag, and suspended in the liquor, so that it may be occasionally moved through it, to diffuse the colouring matter more equally.

Process for 258. But although the above method possesses the permanent advantages of cheapness and expedition, and is fully colours. sufficient for communicating pale yellows; to obtain fuller and more permanent colours, the common mode of preparation, by previously applying the aluminous mordant, ought to be preferred. The stuff, therefore, should be boiled for about one hour or one hour and a quarter, with one-sixth, or one-eighth of its weight of alum, dissolved in a proper proportion of water. The stuff is then to be immersed, without being rinsed, into the dyeing bath, with clean hot water, and about the same quantity of powdered bark tied up in a bag, as that of the alum employed in the preparation. The stuff is then to be turned as usual through the boiling liquor, until the colour appears to have acquired sufficient intensity. One pound of clean powdered chalk for every 100 lb. of stuff is then to be mixed with the dyeing bath, and the operation continued for eight or ten minutes longer. This addition of the chalk raises and brightens the colour.

259. Orange Yellow.—To communicate a beautiful orange yellow to woollen stuffs, 10 lbs. of quercitron bark, tied up in a bag, for every 100 lb. of stuff, are to be put into the bath with hot water. At the end of six or eight minutes, an equal weight of murio-sulphate of tin is to be added, and the mixture well stirred for two or three minutes. The cloth, previously scoured, and completely wetted, is then immersed in the dyeing liquor, and briskly turned for a few minutes. By this process the colouring matter fixes on the cloth so quickly and equally, that after the liquor begins to boil, the highest yellow may be produced in less than 15 minutes.

260. High shades of yellow, somewhat similar to those obtained from quercitron bark by the above process, are frequently given with young fustic (rhus cotinus, Lin.) and dyers spirit, or nitro-muriate of tin; but this colour is much less beautiful and permanent, while it is more expensive than what is obtained from the bark.

261. Bright golden Yellow.—This colour is produ-

ced by employing 10 pounds of bark for every 100 lbs. of cloth, the bark being first boiled a few minutes, and then adding seven or eight lbs. of murio-sulphate of tin, with about five pounds of alum. The cloth is to be dyed in the same manner as in the process for the orange yellow.

262. Bright yellows of less body are produced by employing a smaller proportion of bark, as well as by diminishing the quantity of murio-sulphate of tin and alum. And indeed every variety of shade of pure bright yellow may be given by varying the proportions of the ingredients.

263. To produce the lively delicate green shade, which, for certain purposes, is greatly admired, the addition of tartar, with the other ingredients, only is necessary, and the tartar must be added in different proportions, according to the shade which is wanted. For a full bright yellow, delicately inclining to the greenish tinge, it will be proper to employ eight pounds of bark, six of murio-sulphate of tin, with six of alum, and four of tartar. An additional proportion of alum and tartar renders the yellow more delicate, and inclines it more to the green shade; but when this lively green shade is wanted in the greatest perfection, the ingredients must be used in equal proportions. The delicate green lemon yellows are seldom required to have much fulness or body. Ten pounds of bark, therefore, with an equal quantity of the other ingredients, are sufficient to dye three or four hundred pounds of stuffs.

264. To produce the exquisitely delicate and beautiful pale green shades, the surest method, Dr Bancroft observes, is to boil the bark with a small proportion of water, in a separate tin vessel for six or eight minutes, and then to add the murio-sulphate of tin, alum, and tartar, and to boil them together for about fifteen minutes. A small quantity of this yellow liquor is then to be put into a dyeing vessel, which has been previously supplied with water sufficiently heated. The mixture being properly stirred, the dyeing process is to be conducted in the usual way, and the yellow liquor, as it is wanted, gradually added from the first vessel. In this way, the most delicate shades of lively green lemon yellows are dyed with ease and certainty. Weld is the only dye-stuff from which similar shades of colour can be obtained; but it is four times more expensive. The yellows dyed from quercitron bark, Dr Bancroft adds, with murio-sulphate of tin and alum as mordants, do not exceed the expence of one penny for each pound of stuff; besides a considerable saving of time, labour, and fuel.

265. A greenish shade may also be produced without tartar, by substituting verdigris dissolved in vinegar, along with the bark; but it is neither so permanent, nor so bright and delicate, as that produced by means of tartar. Sulphate of indigo also, in very small proportion, communicates a similar shade, when it is employed with the bark, murio-sulphate of tin, and alum; but it is apt to take unequally on the stuff, and besides, in the language of the dyers, the colour has a tendency to cast or fly in the finishing.

266. Small proportions of cochineal, employed along with the bark and other ingredients, raise the colour to a beautiful orange, and even to an aurora. Madder may be also employed with the same view, for it heightens the yellow obtained from quercitron bark, although

although the colour thus obtained is inferior in beauty to that from cochineal. The madder may also be employed with weld for the same purpose †.

267. The colours obtained from quercitron bark, by the processes which we have now described, are very durable. They resist the action of the air, of soap, and of acids. It is by the effects of alum, but especially of tartar, that these colours become so fixed as to remain permanent by exposure to the air. It is observed of the highest yellows, even when they approach to the orange, and which are best dyed, either with muriate or muri-sulphate of tin and bark, that although they resist the action of soap and acids, they are apt to lose their lustre and become brown by the effect of the sun and air; but this also happens to yellows dyed with nitro-muriate of tin, both with the bark and with weld, but in a still greater degree with other yellow vegetable colouring matters. In some of these this defect is less easily obviated by alum and tartar, than it is in the yellow obtained from weld and quercitron bark *.

III. Of the Processes for Dyeing Silk Yellow.

268. To dye silk a plain yellow colour, the only ingredient which was formerly employed is weld. The following is the process. The silk being previously scoured in the proportion of 20 lbs. of soap to the 100 of stuff, and then alumed and washed after the aluming, or, as it is called, refreshed, the bath is prepared with two pounds of weld for every pound of silk; and, having boiled for 15 minutes, it is to be passed into a vat through a sieve or cloth. When the temperature is such as the hand can bear, the silk is introduced, and turned, until it has acquired a uniform colour. While this operation is going on, the weld is to be boiled a second time in fresh water; one half of the first bath is taken out, and its place supplied with a fresh decoction. The temperature of the fresh bath may be a little higher than the former, but it is necessary to guard against too great a degree of heat, that the colouring matter already fixed may not be dissolved. The stuff is to be turned as before, and afterwards taken out of the bath. A quantity of soda is to be dissolved in a part of the second decoction, and a larger or smaller proportion of this solution is to be added to the bath, according to the intensity of the shade required. When the silk has been turned a few times, a skain is wrung out, that it may be examined whether the colour be sufficiently full, and have the proper golden shade. To render the colour deeper, and to give it the gold cast, an addition of the alkaline solution is to be made to the bath, and to be repeated till the shade has acquired sufficient intensity. The alkaline solution may also be added along with the second decoction of the weld, observing the precaution, that the temperature of the bath be never too great.

269. To produce other shades of yellow, having more of a gold or jonquille colour, a quantity of anotta, proportioned to the shade required, is to be added to the bath, along with the alkali. Lighter shades of yellow, such as pale lemon, or Canary-bird colour, are obtained, by previously whitening the silk, and regulating the proportion of ingredients in the bath by the shade required. To communicate a yellow having a tinge of green, a little indigo is added to the bath, if

the silk has not been previously azure. To prevent the intensity of the shade from being too great, the silk may be more slightly alumed than usual.

270. But, according to Dr Bancroft, the different shades of yellow obtained from weld, may be given to silk with equal facility and beauty, and at a cheaper rate, by employing quercitron bark as a substitute. A quantity of bark powdered and enclosed in a bag, in proportion to the shade of colour wanted, as from one to two pounds for every twelve pounds of silk, is put into the dyeing vat while the water is cold. Heat is then applied; and when it has become rather more than blood warm, or of the temperature of 100°, the silk having previously undergone the aluming process, is to be immersed and dyed in the usual way. If a deep shade is wanted, a small quantity of chalk or pearl-ashes may be added towards the end of the operation. To produce a more lively yellow, a small proportion of muri-sulphate of tin may be employed; but it should be cautiously used, as it is apt to diminish the lustre of the silk. To produce such a shade, the proportions of the ingredients may be four pounds of bark, three of alum, and two of muri-sulphate of tin. These are to be boiled with a proper quantity of water for ten or fifteen minutes; and the temperature of the liquid being so much reduced as the hand can bear it, the silk is immersed and dyed as usual, till it has acquired the proper colour. Care should be taken to keep the liquor constantly agitated, that the colouring matter may be equally diffused *.

271. To dye silk of an aurora or orange colour, after being properly scoured, it may be immersed in an alkaline solution of anotta, the strength of which is to be regulated by the shade required; and the temperature of the bath should be between tepid and boiling water. When the desired shade has been obtained, the silks are to be washed and twice beetled, to free them from the superfluous colouring matter, which would injure the beauty of the colour. When raw silk is to be dyed, that which is naturally white should be selected, and the bath should be nearly cold; for otherwise the alkali, by dissolving the gum of the silk, destroys its elasticity. Silk is dyed of an orange shade with anotta, but the stuff must be reddened with vinegar, alum, or lemon juice. The acid, by saturating the alkali employed to dissolve the anotta, destroys the yellow shade produced by the alkali, and restores its natural colour, which inclines to a red. But although beautiful colours are obtained by this process, they do not possess any great degree of permanency.

272. Several kinds of mushrooms afford lively and durable yellow dyes. A bright shining dye of this description has been extracted from the boletus hirsutus, which commonly grows on walnut and apple trees. The colouring matter is contained both in the tubular part, and also in the parenchyma of the body of the mushroom. To extract the colouring matter, it is pounded in a mortar, and the liquor which is thus obtained, is boiled for a quarter of an hour in water. An ounce of liquor is sufficient to communicate colouring matter to six pounds of water. After the liquor has been strained, the stuff to be dyed is immersed in it, and boiled for fifteen minutes. When silk is subjected to this process, after being dyed, it is made to pass through a bath of soft soap, by which it acquires a shining

ing golden yellow colour, which has a near resemblance to the yellow of the silk employed to imitate embroidery in gold. This has been hitherto brought from China, and bears a very high price, the method of dyeing it being unknown in Europe. All kinds of stuff receive this colour, but it is less bright on linen and cotton, and seems to have the strongest affinity for silk. The use of mordants, it is supposed, would modify and improve it greatly *.

IV. Of the Processes for Dyeing Cotton and Linen Yellow.

273. The process which has been usually followed in dyeing cotton and linen yellow, is by scouring it in a bath prepared in a ley with the ashes of green wood. It is afterwards washed, dried, and alumed, with one-fourth of its weight of alum. After 24 hours, it is taken out of the aluming, and dried, but without being washed. The cotton is then dyed in a weld bath, in the proportion of one pound and a quarter of weld for each pound of cotton, and turned in the bath till it has acquired the proper colour. After being taken out of the bath, it is soaked for an hour and a half in a solution of blue vitriol (sulphate of copper), in the proportion of one-fourth of the weight of the cotton, and then immersed, without washing, for nearly an hour, in a boiling solution of white soap, after which it is well washed and dried.

274. A deeper yellow is communicated to cotton, by omitting the process of aluming, and employing two pounds and a half of weld for each pound of cotton. To this is added a dram of verdigrise, mixed with part of the bath. The cotton is then to be dipped and worked till the colour become uniform. It is then taken out of the bath, that a little solution of soda may be added, after which it is returned, and kept for fifteen minutes. It is then wrung out and dried.

275. Other shades of yellow may be obtained, by varying the proportion of ingredients. Thus, a lemon colour is dyed by using only one pound of weld for every pound of cotton, and by diminishing the proportion of verdigrise, or using alum as a substitute †.

276. But a better method, as it affords more permanent and more beautiful colours, and at a smaller expense, is recommended by Dr Bancroft. This is by the use of quercitron bark, and the calico printers aluminous mordant, or the sugar of lead. The following is the process which he proposes to employ, for producing bright and durable yellow colours. One pound of sugar of lead, and three pounds of alum, are to be dissolved in a sufficient quantity of warm water. The cotton or linen, after being properly rinsed, is to be soaked in this mixture, heated to the temperature of 100°, for two hours. It is then taken out, moderately pressed over a vessel, to prevent the waste of the aluminous liquor. It is then dried in a stove heat, and after being again soaked in the aluminous solution, it is wrung out and dried a second time. Without being rinsed, it is to be barely wetted with lime water, and afterwards dried, and if a full, bright, and durable yellow is wanted, it may be necessary to soak the stuff in the diluted aluminous mordant, and after drying, to wet it a second time with lime water. After it has been soaked for the last time, it should be well rinsed in clean water, to separate the loose particles of the

mordant, which might injure the application of the colouring matter. By the use of the lime-water, a greater proportion of alumina combines with the stuff, besides the addition of a certain proportion of lime.

277. In the preparation of the dyeing bath, from 12 to 18 lbs. of powdered quercitron bark are inclosed in a bag for every 100 lbs. of the stuff, varying the proportion according to the intensity of the shade desired. The bark is put into the water while it is cold; and immediately after, the stuff is immersed and agitated or turned for an hour, or an hour and a half, during which the water should be gradually heated, and the temperature raised to about 120°. At the end of this time the heat is increased, and the dyeing liquor brought to a boiling temperature; but at this temperature the stuff must remain in it only for a few minutes, because otherwise the yellow assumes a brownish shade. The stuff having thus acquired a sufficient colour, is taken out, rinsed and dried.

278. Dr Bancroft observes, that when the aluminous mordant is employed, without the addition of water, one soaking only, and an immersion in lime water, may be sufficient; but he thinks that greater advantage is derived from the application of a more diluted mordant at two different times, or even by the immersion of the stuff a greater number of times, alternately in the diluted aluminous mordant, and lime water, and drying it after each immersion. By this treatment he found, that the colour always acquired more body and durability.

279. Chaptal has proposed a process, for communicating to cotton a nankeen yellow, which at the same time that it affords a durable colour, has the advantage of being cheap and simple. When cotton is immersed in a solution of any salt of iron, it has so strong an affinity for the oxide, that it decomposes the salt, combines with the iron, and assumes a yellow colour. The process recommended by Chaptal is the following. The cotton to be dyed is put into a cold solution of copperas (sulphate of iron) of the specific gravity 1.02. It is afterwards wrung out, and immediately immersed in a ley of potash of the specific gravity 1.01. This ley must have been previously saturated with a solution of alum. When the stuff has been kept for four or five hours in this bath, it may be taken out, washed and dried. By varying the proportion of sulphate of iron, every variety of shade of nankeen yellow may be obtained.

280. We shall lay before our readers another process for dyeing nankeen colour, which is proposed and followed by Mr Brewer, a practical dyer. It is as follows.

"Mix as much sheep's dung in clear water as will make it appear of the colour of grass; and dissolve in clear water one pound of best white soap for every ten pounds of cotton yarn, or in that proportion for a greater or lesser quantity.

"Observe:—The tubs, boards, and poles, that are used in the following preparations must be made of deal; the boiling pan of either iron or copper.

First Operation.—"Pour the soap liquor prepared as above into the boiling pan; strain the dung liquor through a sieve; add as much thereof to the soap liquor in the pan as will be sufficient to boil the yarn, intended to be dyed, for five hours. When the liquor are

Simple are well mixed in the pan, enter the yarn, light the fire under the pan, and bring the liquor to boil in about two hours, observing to increase the heat regularly during that period. Continue it boiling for three hours; then take the yarn out of the pan, wash it, wring it, and hang it in a shed on poles to dry. When dry, take it into a stove or other room where there is a fire; let it hang there until it be thoroughly dry.

N. B. "The cotton yarn, when in the shed, should not be exposed either to the rain or sun: if it is, it will be unequally coloured when dyed.

Second Operation.—"In this operation use only one half of the soap that was used in the last, and as much dung liquor (strained as before directed) as will be sufficient to cover the cotton yarn, when in the pan, about two inches. When these liquors are well mixed in the pan, enter the yarn, light the fire, and bring the liquor to boil in about one hour; then take the yarn out, wring it out without washing, and hang it to dry as in the former operation.

Third Operation.—"This operation the same as the second in every respect.

Fourth Operation.—"For every ten pounds of yarn make a clear ley from half a pound of pot or pearl-ashes. Pour the ley into the boiling-pan, and add as much clear water as will be sufficient to boil the yarn for two hours; then enter the yarn, light the fire, and bring it to boil in about an hour. Continue it boiling about an hour, then take the yarn out, wash it very well in clear water, wring it, and hang it to dry as in former operations.

N. B. "This operation is to cleanse the yarn from any oleaginous matter that may remain in it after boiling in the soap and dung liquors.

Fifth Operation.—"To every gallon of iron liquor (K) add half a pound of ruddle or red chalk (the last the best) well pulverized.

"Mix them well together, and let the liquor stand four hours, in order that the heavy particles may subside; then pour the clear liquor into the boiling-pan, and bring it to such a degree of heat as a person can well bear his hand in it; divide the yarn into small parcels, about five hanks in each; soak each parcel or handful very well in the above liquor, wring it, and lay it down on a clean deal board. When all the yarn is handed through the liquor, the last handful must be taken up and soaked in the liquor a second time, and every other handful in succession till the whole is gone through; then lay the yarn down in a tub, wherein there must be put a sufficient quantity of ley made from pot or pearl-ashes, as will cover it about six inches. Let it lie in this state about two hours, then hand it over in the ley, wring it, and lay it down on a clean board. If it does not appear sufficiently deep in colour, this operation must be repeated till it has acquired a sufficient degree of darkness of colour: this done, it must be hung to dry as in former operations.

N. B. "Any degree of red or yellow hue may be given to the yarn by increasing or diminishing the quantity of ruddle or red chalk.

Sixth Operation.—"For every ten pounds of yarn

make a ley from half a pound of pot or pearl-ashes; pour the clear ley into the boiling pan: add a sufficient quantity of water thereto that will cover the yarn about four inches; light the fire, and enter the yarn when the liquor is a little warm; observe to keep it constantly under the liquor for two hours; increase the heat regularly till it come to a scald; then take the yarn out, wash it, and hang it to dry as in former operations.

Seventh Operation.—"Make a sour liquor of oil of vitriol and water: the degree of acidity may be a little less than the juice of lemons; lay the yarn in it for about an hour, then take it out, wash it very well and wring it; give it a second washing and wringing, and lay it upon a board.

N. B. "This operation is to dissolve the metallic particles, and remove the ferruginous matter that remains on the surface of the thread after the fifth operation.

Eighth Operation.—"For every ten pounds of yarn dissolve one pound of best white soap in clear water, and add as much water to this liquor in your boiling-pan as will be sufficient to boil the yarn for two hours. When these liquors are well mixed, light the fire, enter the yarn, and bring the liquor to boil in about an hour. Continue it boiling slowly an hour; take it out, wash it in clear water very well, and hang it to dry as in former operations: when dry, it is ready for the weaver.

N. B. "It appears to me, from experiments that I have made, that less than four operations in the preparation of the yarn will not be sufficient to cleanse the pores of the fibres of the cotton, and render the colour permanent."

281. A method of dyeing cotton and linen a durable yellow colour is practised in the east. The object of this process, which is tedious, is to increase the affinity between the alumina and the stuff, so that it may adhere with sufficient force to produce a permanent colour. For this purpose three mordants are employed: these are oil, tan, and alum. The cotton is soaked in a bath of oil, mixed with a weak solution of soda. Animal oil, as it is found to answer best, is preferred. Glue has also been tried, and is found to answer very well. The soda must be in the caustic state, for in that state it combines with the oil, and produces on the cloth an equal absorption. The stuff is then to be washed, and afterwards put into an infusion of nut-galls of the white kind, and the infusion should be used hot. The tan combines with the oil, while the gallic acid carries off any portion of alkali which may adhere to the cloth. When the stuff is removed from the bath, it should be quickly dried; and too great an excess of galls beyond a proper proportion with the oil should be avoided, as it is apt to darken the shade of colour. After this preparation the stuff is to be immersed in a solution of alum; and in consequence of the affinity which exists between tan and alumina, the alum is decomposed, and its earth combines with the tan. After these preliminary steps, the cotton is to be dyed with quercitron bark, according to the process which has been already described.

SECT.

282. The next of the simple colours is blue. We shall first treat of the substances which are employed in dyeing blue, and then describe the processes which are followed in fixing this colour.

The only substances which are used in dyeing blue, are indigo and woad.

283. Indigo was not used for the purpose of dyeing in Europe till near the middle of the 16th century. A substance is mentioned by Pliny*, which was brought from India, and termed indicum, which seems to have been the same as the indigo of the moderns; but it does not appear that either the Greeks or the Romans knew how to dissolve indigo, or its use in dyeing, although it was applied as a paint. It was, however, long before known as a dye in India. The first indigo which was employed for the purpose of dyeing by Europeans, was brought by the Dutch from India. One of the species of the plant from which it is obtained, was discovered by the Portuguese in Brazil, where it grows spontaneously, as well as in other parts of America. Being afterwards successfully cultivated in Mexico, and some islands of the West Indies, the whole of the indigo employed in Europe was supplied from these countries. The indigo from the East Indies has, however, of late recovered its character, and is imported into Britain in considerable quantities.

284. There are three species of the indigo plant, which are usually cultivated in America. The first is the indigofera tinctoria, Linn. which besides being a smaller and less hardy plant, is inferior to the others on account of its pulp; but as it yields a greater proportion, it is generally preferred. The second is the indigofera disperma, Linn. or Guatimala indigo plant. This is a taller and hardier plant, and affords a pulp of a superior quality to the former. The third is the indigofera argentea, Linn. which is the hardest of the three species; yields a pulp of the finest quality, though in smallest proportion.

285. When the indigo plant has arrived at maturity, it is cut a few inches above the ground, disposed in strata in a large vessel or steamer, and being kept down with boards, is covered with water; and in this state it is left to ferment till the pulp is extracted. The process commences by the evolution of heat, and the emission of a great quantity of carbonic acid gas. When the fermentation has continued for a sufficient length of time, which is known by the tops becoming tender and pale, the liquor, which is now of a green colour, is drawn off into large flat vessels, called beaters, where it is agitated with buckets, or other convenient apparatus, till blue floccules begin to appear. To promote the granulation or separation of the floccules, it is usual to add clear lime water till the liquor in which they are suspended become quite colourless. The liquor being sufficiently impregnated with the lime water, is left at rest, to allow the particles of the colouring matter to precipitate; after which the supernatant liquor is drawn off, and the sediment collected into linen bags, which are suspended for some time to let the water drain off. It is then put into square boxes, or

formed into lumps and dried in the shade. The indigo thus prepared is in a state fit for the market.

286. The indigo which is produced in this operation differs greatly, not only according to the quality of the plant from which it is obtained, but according to the mode of preparation. But the difference of quantity seems to depend entirely on the heterogeneous substances with which it is mixed, and on the degree of consistence which it has acquired in drying. The lightest kind, which is brought from Guatimala, is called light indigo; it is of a fine blue colour, and is the most valuable, because it is of the finest quality. Indigo exhibits various shades of colour, which is also owing to the mixture of foreign substances. The most common shades are blue, violet, and copper colour.

287. Other plants have also been discovered, which by a process somewhat similar, afford indigo, and in particular the nerium tinctorium, or rose bay, an account of which, with the method of manufacturing indigo from its leaves, has been given by Dr. Roxburgh. This tree grows in great abundance in different parts of the East Indies; and plantations of it, raised from seeds, have succeeded well in Bengal. The leaves of the nerium afford indigo, not only when they are fresh gathered, but also when they are nearly dried; but they yield the best indigo after being kept a day or two. The leaves collected the preceding day are put into a copper, so as nearly to fill it without pressing. The copper is filled with water till within three inches of the top; and hard spring water, which increases the quantity of indigo, and improves its quality, is preferred. The fire is then applied, and kept up, till the liquid becomes of a green colour in the vessel. The leaves then become of a yellowish colour, and the heat of the liquor about 150°, or 160°. The leaves should be constantly agitated, that they may be equally heated, as well as to promote the operation, by the expulsion of the carbonic acid gas. When the process exhibits the above appearances, the liquor is to be drawn off, passed through a hair-cloth, and agitated while hot in the usual way, till granulation takes place, or the appearance of blue flakes is observed. About $\backslash frac\{1\}\{2\}$th part of strong lime water is then added, to promote the precipitation of the indigo, and the remaining part of the process is similar to that described above, for the manufacture of indigo from indigofera †.

288. The object of the processes which are followed in the manufacture of indigo, is to extract from the plants which yield it, a green substance, which is soluble in water. This substance, which has a strong affinity for oxygen, gradually attracts it from the air, becomes of a blue colour, and is then insoluble in water. This absorption is greatly promoted by agitation, for then a greater surface is exposed to the action of the air; and the lime water, by combining with carbonic acid, which exists in the green matter, also promotes the separation of the indigo.

289. Indigo is insoluble in water, alcohol, ether, and oils, and the only acids which produce any effect upon it, are the sulphuric and nitric. By the latter it is soon changed to a dirty white colour, and is at last entirely decomposed. When the acid is concentrated, the indigo is inflamed; but when it is diluted, the indigo becomes brown, and crystals like those of oxalic and

Simple and tartarous acids make their appearance: and when the acids and crystals are washed off, there remains behind a kind of resinous matter. Sulphuric acid in the concentrated state dissolves indigo, with the evolution of a great deal of heat. The solution is opaque and black, but when diluted with water, it changes to a deep blue colour. Dr Bancroft has denominated this solution sulphate of indigo, which has been long known by the name of liquid blue. The fixed alkalies in the state of carbonate precipitate slowly from sulphate of indigo, a blue coloured powder, which has the properties of indigo, but is found to be soluble in most of the acids and alkalies. Pure alkalies destroy the colour of sulphate of indigo, as well as that which is precipitated.

290. Indigo is employed in dyeing, both in the state of liquid blue, or sulphate of indigo, from which is obtained the beautiful colour called Saxon blue; and also in the state of simple indigo, or the indigo of commerce. In dyeing with indigo, it must be reduced to the state of the green matter as it exists in the plants, or when it is first extracted from them. It must be deprived of the oxygen, to the combination of which the blue colour is owing. In this state it becomes soluble in water by means of the alkalies. To effect this separation of the oxygen, the indigo must be mixed with a solution of some substance which has a stronger affinity for oxygen than the green matter of indigo. Such substances are green oxide of iron and metallic sulphurets. Lime, green sulphate of iron, and indigo, are mixed together in water, and during this mixture the indigo is deprived of its blue colour, becomes green, and is dissolved, while the green oxide of iron, is converted into the red oxide. In this process, part of the lime decomposes the sulphate of iron, and as the green oxide is set at liberty, it attracts oxygen from the indigo, and reduces it to the state of green matter, which is immediately dissolved by the action of the rest of the lime. Indigo is also deprived of its oxygen, and prepared for dyeing, by another process. Some vegetable matter is added to the indigo mixed with water, with the view of exciting fermentation; and quicklime or an alkali is added to the solution, that the indigo, as it is converted into the green matter, may be dissolved.

291. Another plant, known under the name of pastel or woad (isatis tinctoria), is employed for dyeing blue. Another species (isatis lusitanica), which is a smaller plant, is also employed in dyeing. The isatis tinctoria is cultivated in France and in England. When the plant has reached maturity, it is cut down, washed in a river, and speedily dried in the sun. It is then ground in a mill, and reduced into a paste, which is formed into heaps, covered up to protect them from the rain, and at the end of a fortnight, the heap is opened to mix the whole well together. It is afterwards formed into round balls, which are exposed to the wind and sun, that the moisture may be separated. The balls are heaped upon one another, become gradually hot, and exhale the smell of ammonia. To promote the fermentation, which is stronger in proportion to the quantity heaped up, and the temperature of the season, the heap is to be sprinkled with water till it falls down in the state of coarse powder, in which state it appears in commerce. The blue colour obtained from woad is very permanent, but has little lustre. But its colour

is not only inferior in beauty to that obtained from indigo; it affords also a smaller proportion of colouring matter, so that since the discovery of indigo, the use of woad has diminished.

II. Of the Processes for Dyeing Wool Blue.

292. The preparation for dyeing blue is made in a Preparation large wooden vessel or vat, which should be so constructed of the vat, as to retain the heat, which is a matter of considerable importance in the process. The vat is therefore set up in a separate place from the coppers, and is sunk so far in the ground as to be only breast high above it. Before the introduction of indigo, blue was dyed with woad, which furnished a permanent, but not a deep colour; but a very rich blue is obtained by mixing indigo with the woad, and these are almost the only substances which are now employed for dyeing woollen stuffs. The proportions of these substances are varied by different dyers, and according to the shade which is required. The following is the account of the preparation of a vat, as it is given by Quatremere. Into a vat of about seven and a half feet deep, and five and a half in diameter, are thrown two balls of pastel or woad, which are previously broken, and together amount to about 400 pounds weight; 30 pounds of weld are boiled in a copper for three hours, in a sufficient quantity of water, to fill the vat. To this decoction are added 20 pounds of madder and a basket full of bran. The boiling is then continued half an hour longer. This bath is cooled with 20 buckets of water, and after it is settled, and the weld taken out, it is poured into the vat, which must be stirred with a rake all the time that it is running in, and for 15 minutes longer. The vat is then covered up very hot, and allowed to stand for six hours, when it is uncovered, and raked again for 30 minutes. The same operation must be repeated every three hours. When the appearance of blue streaks is perceived on the surface of the vat, eight or nine pounds of quicklime are added; the colour then becomes of a deeper blue, and the vat exhales more pungent vapours. Immediately after the lime, or along with it, the indigo, which has been previously ground in a mill, with the smallest possible quantity of water, is put into the vat. The quantity is to be regulated by the intensity of the shade required. From ten to thirty pounds may be put into a vat such as we have now described. If on striking the vat with a rake, a fine blue scum arises, no other previous preparation is required than to stir it with the rake twice in the space of six hours, to mix the ingredients completely. Great care should be taken not to expose the vat to the air, except during the time of stirring it. When that operation is finished, it is covered with a wooden lid, on which are spread thick cloths, to retain the heat as much as possible; but after all these precautions, at the end of eight or ten days it is greatly diminished, and is at last entirely dissipated, so that the liquor must be again heated, by pouring the greater part of the liquor of the vat into a copper under which a large fire is made. When the liquor has acquired a sufficient temperature, it is returned into the vat, and carefully covered up.

293. Vats of this description are sometimes liable to Accidents. A vat is said to be repelled, when having to which previously afforded fine shades of blue, it appears the vat is black, liable.

black, without any blue streaks; and if it be stirred, the black colour becomes deeper; the vat at the same time exhales, instead of a sweetish smell, a pungent odour; and the stuff dyed in a vat in this state, comes out of a dirty gray colour. These effects are ascribed to an excess of lime.

294. Different means are employed to recover a repelled vat. Some are satisfied with merely reheating it; while others add tartar, bran, urine, or madder. Hellot recommends bran and madder as the best remedy. If the excess of lime be not very great, it is sufficient to leave it at rest five or six hours, putting in a quantity of bran and three or four pounds of madder, which are to be sprinkled on the surface, and then it is to be covered up, and after a certain interval, to be tried again. But if the vat has been so far repelled as to afford a blue only when it is cold, it must be left at rest to recover, and sometimes must remain whole days without being stirred with the rake. When it begins to afford a tolerable pattern, the bath must be reheated. In general, this revives the fermentation. The addition of bran or madder, or a basket or two of fresh woad, produces the same effect.

295. This vat sometimes runs into the putrefactive process. When this happens, the colour of the vat becomes reddish, the paste rises from the bottom, and a fetid smell is exhaled. This accident is owing to a deficiency of lime, and it must be corrected by adding a fresh quantity. The vat is then to be raked; after two hours more lime is added, and the process of raking again performed. These operations are to be repeated till the vat is recovered.

296. Nothing requires more attention in treating a vat of this kind, than the distribution of the lime, the principal use of which is to moderate the tendency to putrefaction, and to limit the fermentation to that degree which is necessary to deprive the indigo of its oxygen. If too much lime be added, the necessary fermentation is retarded, and if there be too little, the putrefactive process commences.

297. Two hours previous to the dyeing operation, the vat should be raked; and to prevent the stuff coming in contact with the sediment, which would produce inequalities in the colour, a cross of wood is introduced. The stuff is then to be completely wetted with pure water a little heated; and being wrung out, it is dipped into the vat, where it is moved about for a longer or a shorter time, according to the depth of shade required. During this operation it is taken out occasionally, to be exposed to the air, the action of which is necessary to change the green colour of the bath into a blue. Stuff dyed blue in this manner must be carefully washed, to carry off the loose particles of colouring matter; and when the shade of blue is deep, they ought even to be cleansed, by fulling with soap. This operation does not alter the colour.

298. When a vat is prepared entirely of indigo, without pastel or woad, it is called an indigo vat. The vessel employed for this purpose is of copper, into which water is poured according to its capacity, to the amount of 40 buckets, in which have been boiled six pounds of potash, twelve ounces of madder, and six pounds of bran. Six pounds of indigo ground in water are then put in, and after it has been carefully raked, the vat is to be covered. A slow fire is to be kept up, and

twelve hours after it is filled, it is to be raked a second time. This operation is to be repeated every twelve hours, till it come to a blue colour, which will generally be the case in about 48 hours. If the bath is properly managed, it will be of a fine green, exhibiting on the surface coppery scales, and a blue scum or flower. In this vat the indigo is rendered soluble in water, by means of the alkali instead of lime. The dyeing operation is to be conducted in the same manner as the preceding.

299. Two vats have been described by Hellot, in which the indigo is dissolved by means of urine. Madder is added to it, and in the one vinegar, in the other alum and tartar, of each a quantity equal in weight to that of the indigo. The proportion of urine must be considerable. In considering the theory of this process, it seems probable that the indigo, deprived of its oxygen by the urine and madder during the fermentation, is dissolved by the ammonia which is formed in the urine. When the solution of alum and tartar is added, an effervescence, which Hellot observed, is produced. This, it is probable, has a tendency to retard or stop the putrefaction. But in vats of this description, operations on a large scale cannot be carried on; they seem only adapted for small dye-houses.

III. Of the Processes for Dyeing Silk Blue.

300. Silk is dyed blue with indigo alone, without any proportion of woad. The proportion of indigo mentioned in the preparation of the indigo vat, and sometimes a larger proportion, is employed, with six pounds of bran, and about twelve ounces of madder. According to Macquer, half a pound of madder for each pound of potash, renders the vat greener, and produces a more fixed colour in the silk. When the vat is come to, it should be refreshed with two pounds of potash, and three or four ounces of madder; and after being raked, in the course of four hours it is fit for dyeing. The temperature should be so moderated, that the hand may be held in it without uneasiness.

301. The silk, after being boiled with soap, in the proportion of 30 pounds of soap to 100 of silk, and then well cleaned by repeated beatings in a stream of water, must be dyed in small portions, because it is apt to take on an uneven colour. When it has been turned once or oftener in the bath, it is wrung out, and exposed to the air, that the green colour may change to a blue. When the change is complete, it is thrown into clear water, and afterwards wrung out. Silk dyed blue should be speedily dried. In damp weather and in winter, it is necessary to conduct the drying in a chamber heated by a stove. The silk should be hung on a frame kept constantly in motion. To dye light shades, some dyers employ vats that are somewhat exhausted; but it ought to be observed, that the colour thus obtained is less beautiful and less permanent than when fresh vats, containing a smaller quantity of indigo, are employed.

302. Some addition is required to be made to the indigo, to give silk a deep blue. A previous preparation is necessary, by giving it another colour or ground. For the Turkey blue, which is the deepest, a strong bath of archil is first prepared. Cochineal is also sometimes used, instead of archil, for the ground, to render the colour more permanent. A blue is given to silk

silk by means of verdigris and logwood, but possesses little durability. It might be rendered more permanent, by giving it a lighter shade in this bath, then dipping it in a bath of archil, and finally in the indigo vat.

303. When raw silk is to be dyed blue, such as is naturally white should be selected. Being previously soaked in water, it is put into the bath in separate hanks, as already directed for scoured silks; and as raw silk is found to combine more readily with the colouring matter, the scoured silk, when it can be conveniently done, should be first put into the bath. If archil, or any of the other ingredients which have been already mentioned, are required to give more intensity to the colour, the mode of application is the same as that directed for scoured silk.

IV. Of the Processes for Dyeing Cotton and Linen Blue.

304. For dyeing cotton and linen blue, Pileur d'Apligny recommends a vat containing about 120 gallons. From six to eight pounds of indigo, reduced to powder, are boiled in a ley drawn off from a quantity of lime, equal in weight to the indigo, and a quantity of potash double its weight. During the boiling, which is to be continued till the indigo is completely penetrated with the ley, the solution must be constantly stirred, to prevent the indigo from being injured, by adhering to the bottom of the vessel.

305. During this process, another quantity of quicklime, equal in weight to the indigo, is to be slaked. Twenty quarts of warm water are added, in which is to be dissolved a quantity of copperas (sulphate of iron) equal to twice the weight of the lime. The solution being completed, it is poured into the vat, which is previously half filled with water. To this the solution of indigo is added, with that part of the ley which was not employed in the boiling. The vat must now be filled up to within two or three inches of the top. It must be raked twice or thrice a day till it is completely prepared, which is generally the case in 48 hours, and sometimes sooner, as it depends on the temperature of the atmosphere. A small proportion of bran, madder, and woad, is recommended by some, to be added to such a vat as we have now described.

306. The process which is followed at Rouen, and described by Quatremere, is simpler. The vats, which are constructed of a kind of flint, are coated within and without with fine cement, and are arranged in one or more parallel lines. Each vat contains four hogsheads of water. The indigo, to the amount of 18 or 20 pounds, being macerated for a week in a caustic ley, strong enough to bear an egg, is ground in a mill; three hogsheads and a half of water are put into the vat, and afterwards 20 pounds of lime. The lime being thoroughly slaked, the vat is raked, and 36 pounds of copperas are added; and when the solution is complete, the ground indigo is poured in through a sieve. It is raked seven or eight times the same day, and after being left at rest for 36 hours, it is in a state fit for dyeing.

307. In extensive manufactories, it is necessary to have vats set at different times. In conducting the process of dyeing, the stuffs are first dipped in the most exhausted vat, and then regularly proceeding from the weakest to the strongest, if they have not previously at-

tained the desired shade. The stuffs should remain in the bath only about five or six minutes, for in that time they combine with all the colouring matter they can take up. After the stuffs have been dipped in a vat, it should not be used again, till it has been raked, and stood at least 24 hours, unless it has been lately set, when a shorter period is sufficient.

308. After the stuffs have been dipped three or four times in a vat, it begins to change. It becomes black, and no blue or copper-coloured streaks are seen on the surface after raking it. It must then be renewed, by adding four lbs. of copperas, with two of quicklime, after which it must be raked twice. In this way a vat may be renewed three or four times; but the additional quantity of ingredients must be diminished, as the strength of the vat is exhausted.

309. A vat which is still more simple and more easily prepared, has been recommended by Bergman. The proportion of the ingredients which he has directed to be employed, is the following. To three drachms of indigo reduced to powder, three drachms of copperas, and three of lime, add two pints of water. Let it be well raked, and in the course of a few hours it will be in a proper state for dyeing.

310. Haussmann employs a still smaller proportion of Haussmann's indigo. For 3000 lbs. of water, he takes 36 lbs. of quicklime slaked in 200 lbs. of water, with which the indigo in the proportion of from 10 to 20 lbs. well ground, is to be mixed. He then dissolves 30 lbs. of copperas in 120 lbs. of hot water. The whole being left at rest for fifteen minutes, the vat is filled, and gently and constantly stirred. When a deeper shade is wanted, and particularly when linen is to be dyed, the proportion of indigo should be greater; but the shade depends very much on the time the stuffs remain in the vat, and the times it has been used. When the vat becomes turbid, the process of dyeing must be interrupted, till it has been again raked, and the supernatant liquor become transparent. If the effects of the lime fail, a new quantity, fresh slaked, must be added; and if the iron cease to produce the effect on the indigo, a new portion must be also added, observing the precaution to have a greater quantity of lime than what is necessary to saturate the sulphuric acid. When the indigo seems to be exhausted, fresh portions ground in water are also to be added; the vat is to be raked several times, and allowed to settle, after which it is again fit for use. In this way Mr Haussmann informs us he preserved a vat for the space of two years; and had it not been for the accumulation of sediment, which prevented the stuffs from being immersed to a sufficient depth, it might have been continued in use for a much longer time. It is worth while to add, that Mr Haussmann found, that a pattern of cloth dipped in water acidulated with sulphuric acid, immediately after it was taken out of the bath, became of a much deeper blue than a similar pattern exposed to the air, or another dipped in river water.

311. Another convenient and expeditious vat is mentioned by Bergman, and described by Scheffer. Indigo reduced to fine powder, in the proportion of three drachms to a quart, is added to the strong ley of the soap boiler. After a few minutes, when the colouring matter is well penetrated by the ley, six drachms of powdered orpiment are to be added. In a few minutes after the bath has been well raked, it becomes green,

Of Simple and the blue streaks appear on the surface. Heat is to be applied; when the operation of dyeing may commence.

312. The preparation employed for printing cottons is similar to the above bath, excepting in the proportions of orpiment and indigo, which are greater in the former; but these proportions are very different in different manufactories.

313. Saxon Blue.—The colour which is obtained by dyeing with a solution of indigo in sulphuric acid is known under the name of Saxon blue, because the process was first carried on at Grossenhayn in Saxony, by Counsellor Barth, who made the discovery about the year 1740. This discovery was for some time kept secret, and the method seems to have been originally very complicated. Alumina, antimony, and some other substances, were previously added to the sulphuric acid. These, however, are now omitted, and the indigo alone is dissolved in the acid.

314. From a great number of experiments which were made on this process by Bergman, he concluded, that in those cases where the sulphate of indigo afforded only a fading colour, the acid employed had been too weak. Quatremere observes that, among several processes for dyeing with sulphate of indigo, he discovered only two, in which the stuffs were completely penetrated with colouring matter. To effect this, he employed an alkali, in the proportion of one ounce to an ounce of indigo, and six ounces of sulphuric acid. With these proportions of the ingredients he obtained a deep vivid blue, equally intense through every part of the stuff. Poerner, who has paid great attention to this preparation, also employs an alkali, by means of which a more pleasing colour, which penetrates deeper, is produced. The proportions which he recommends are four parts of sulphuric acid to one of indigo. The indigo is first reduced to a fine powder, and the sulphuric acid, in the concentrated state, is poured upon it. The mixture is stirred for some time, and having stood twenty-four hours, one part of dry potash in fine powder, is added; and after the whole is again stirred, it remains for twenty-four hours longer. It is then to be diluted with eight times its weight of water, which must be gradually added, or a greater or less proportion as may be wanted.

Dr Bancroft seems to be of opinion, that a more durable blue may be obtained by diluting the acid with an equal quantity of water, when the indigo is put in, and allowing the mixture to remain forty-eight hours; for he thinks by this slower and more moderate action, the basis of the indigo is less injured. Instead of the potash employed by Poerner, Dr Bancroft uses chalk; and even in such a quantity as to saturate the acid. In this case the indigo is precipitated along with the chalk; and, when collected into a solid mass, communicates a blue colour to wool, but more slowly than by the common method, in which the combination is very rapid and the dyeing unequal. This inconvenience he thinks might be obviated by the use of chalk*.

315. To produce a Saxon blue colour on woollen stuffs, they are prepared with alum and tartar. And in proportion to the shade required, the quantity of solution of indigo put into the bath must be regulated. When a deep shade of Saxon blue is wanted, the stuff must be passed different times through vessels contain-

ing such a quantity of colouring matter as is sufficient to give light colours. In this way, by repeated applications, the colours become more uniform.

316. The sulphate of indigo is also employed to dye silk. For this purpose, attempts have been made to unite the advantages of the indigo vat and its solution in sulphuric acid. A process of this kind is greatly recommended by Gubliche, which produces beautiful colours, and is at the same time cheap and convenient. The bath is composed of one pound of indigo, three pounds of quicklime, three of copperas, and one and a half of orpiment. The indigo is first to be carefully ground and mixed with water, put into a wooden vat, and diluted with water, according to the shade of colour wanted. The lime is then to be added, and the mixture being well stirred, it is covered up, and allowed to remain at rest for some hours. After this the copperas in the state of powder is added, the whole well stirred, and the vat covered up. And lastly, at the end of some hours, the orpiment reduced to powder is thrown in, and the whole left at rest for several hours. The mixture is afterwards to be stirred, and then left to settle, till the liquor becomes clear; when the blue streaks or flower which covers it is removed, and the silk previously dipped in warm water, is to be dyed hank by hank. When it is removed from the bath, it is to be washed in a stream of water, and dried.

317. This process is recommended as the means of obviating a greenish cast, which is sometimes observed in Saxon blue, and which is supposed to be owing to some change in the particles of indigo, by means of the sulphuric acid.

318. The colour denominated English blue is produced by means of the sulphate of indigo. To give this colour, it is first to be dyed a light blue; and, when taken out of this bath, it is dipped in hot water, washed in a stream, and left in a bath composed of the sulphate of indigo, to which a little of the solution of tin has been added, until the proper shade is obtained, or the bath is exhausted. Previous to its being put into this bath, it may be dipped in a solution of alum, in which it should only remain a very short time. Silk, which has been dyed according to this process, is free from the reddish shade which it derives from the blue vat, as well as from the greenish cast of the Saxon blue†.

319. The sulphate of indigo has been hitherto only applied for the purpose of dyeing wool and silk. The affinity of indigo for vegetable substances is not sufficiently strong to effect the decomposition of the sulphate. It cannot, therefore, be employed with advantage in dyeing cotton and linen.

320. Attempts have been made to dye with Prussian blue. The process which was followed by Macquer with thread, in a solution of alum and sulphate of iron, and afterwards in an alkaline solution, which was partly saturated with prussic acid. He then immersed the stuffs in water, acidulated with sulphuric acid, for the purpose of dissolving that part of the oxide of iron which remained uncombined with the prussic acid, and which the uncombined alkali had precipitated. By successive repetitions of these immersions he obtained a fine blue, but very unequal. Berthollet justly remarks on this experiment,

experiment, that an alkali saturated with prussic acid should be employed, or lime water or magnesia, both of which have the property of combining with that acid. In a second experiment Macquer boiled the stuffs in a solution of tartar and alum, and then passed them through a bath which contained prussian blue merely diffused in it. The colour was faint, and could not be made deeper; but it was equal, and soft to the touch.

321. In the process proposed by Abbé Menon for thread and cotton, they are first dyed black, and soaked for a few minutes in prussiate of alkali, and afterwards boiled in a solution of alum. In this way they acquired a deep blue. When a lighter blue is wanted, the stuffs must be passed through a weak acid.

322. Similar to the second experiment of Macquer is the process of Roland de la Platiere. He takes prussian blue in the proportion of a pound to a piece of stuff, powdered, and passed through a very fine sieve, and adds muriatic acid till it is reduced to the consistence of syrup. It is to be constantly stirred for about half an hour while it ferments. It is then well diluted, and stirred every hour for a day, till the fermentation ceases. The particles are thus in a state of minute division. Seven or eight buckets of water for one piece of velvet, are put into a trough; then add the mixture, which has been previously well diluted in a separate vessel, and poured into the bath through a very fine sieve. When the piece is placed on the winch, over the trough, let the bath be briskly stirred, and the piece speedily let down; and the same operation must be continued as quickly as possible for several hours. This colour requires great management, for as the particles of the prussian blue are only in a state of minute division, and heavy, they are quickly deposited on the stuff. Hence the colour appears very unequal and in patches, even with the utmost care; and nothing can be done to avoid it, but repeating the operations again and again. The stuff should be put into the bath thoroughly wet, for when it is dry, it penetrates with difficulty, and is always unequal. Between the dryings the stuff is always to be washed and beetled, excepting the last time, when it is not washed, but dried in the open air, either in the sun or in the shade; observing, however, that it be well stretched. This beautiful colour is not changed by the air; it resists the action of acids, and is little altered by boiling with alum; but it is soon tarnished by friction, or particles of dust that adhere to it. It is scarcely necessary to add, that it is instantly decomposed by alkaline liquors. Guhliche employs a solution of tin in nitro-muriatic acid, as a substitute for muriatic acid, in the process of dyeing with prussian blue*.

323. Dr Bancroft made a number of experiments in dyeing both vegetable and mineral matters, with prussian blue, and particularly with the view of obviating the difficulties which had occurred to others in the use of it. He boiled up copperas with quercitron bark, fustic, and logwood, separately, in what he thought the best proportions; and in each of these mixtures he dyed a piece of woollen cloth by boiling it for 10 or 15 minutes. The stuffs were afterwards separately immersed in warm diluted prussiate of potash neutralized by sulphuric acid. They acquired an equal and beautiful blue. This, however, was not the uniform result; for when too much copperas was employed in dyeing with quercitron bark, there was an excess of oxide of iron,

which combining with the fibres of the wood, gave the prussian blue a greenish tinge; but this he found could be remedied, by passing the cloth through warm water, slightly acidulated with muriatic acid. The prussian colouring matter, Dr Bancroft observes, must always be applied in a moderate heat, otherwise it will be precipitated by the sulphuric acid, and rendered unfit for this purpose, till it is again dissolved by potash, lime, or some other substance.

324. He then tried to fix prussian blue by means of the aluminous mordant; but at the end of 15 minutes, after being immersed in a solution of prussiate of potash, it had acquired no colour. The addition of a small proportion of a solution of iron in muriatic acid, communicated a blue colour. All parts of the cloth, as well as those to which the mordant had been applied, received the colour. The cloth being washed with soap, the whole of the colour was discharged, excepting where it had been impregnated with alumina, and even there it had become fainter. A piece of the same cotton was immersed in a solution of ammonia (volatile alkali); the pale blue was greatly heightened. Another piece was put into water slightly tinctured with a solution of copper in ammonia. The blue colour became suddenly of an intensely deep garter-blue or violet, and it resisted the action of soap. Into water mixed with a little of a solution of muriate of copper, he put another piece of the same cotton, and it soon became of a deeper blue, without any of the purple or violet shade. This resisted the action of soap, and after long exposure to the weather, the colour was little diminished; and when the colour remained in any degree weakened, immersion in water slightly acidulated with sulphuric acid, completely restored it. From these facts it would appear to be advantageous to prepare woollens by the usual boiling with alum, or alum and tartar, before they are dyed with copperas and quercitron bark, fustic or logwood, for a prussian blue; but a greater proportion of sulphuric acid, in the prussiate of potash or lime, that the excess of acid may discharge the vegetable colouring matters, becomes necessary*.

325. Dr Bancroft afterwards tried pieces of silk and cotton in the diluted prussiates of potash, soda, lime, &c. with solutions of most of the metals in different acids and alkalies; and from the different metallic solutions he obtained a very full, lively colour, which he calls the red copper colour, from the different solutions of copper in sulphuric, nitric, muriatic, and acetic acids; the same effect succeeded well from a solution in ammonia. He obtained also the same colour from the nitrates of silver and of cobalt. The prussian colouring matter fixed by these metallic mordants resisted the action of acids, washings with soap, and exposure to the weather for the greatest length of time; but in all these cases there must be a double application. The prussian colouring matter must first be applied to the linen, cotton or silk, which must be afterwards allowed to dry. It must then be immersed in the metallic solution, or the metallic solution must be applied first, and then the solution of prussiate of potash, soda, lime, &c.

SECT. IV. Of Dyeing Black.

The next of the simple colours is black, of which we shall treat as in the former sections; first describing the substances which are employed, and then giving an

* Phit. of
Perm. Col.
217.

For silk and
cotton.

Of Simple account of the processes which are followed in dyeing different stuffs of a black colour.

gen gas, diminish its volume, so that some portion of it is absorbed.

I. Of the Substances employed in Dyeing Black.

326. There are few substances which have the property of producing a permanent black colour, without any addition. The juice of some plants produces this effect on cotton and linen. A black colour is obtained from the juice of the cashew nut, which will not wash out, and even resists the process of boiling with soap or alkalies. The cashew nut of India is employed for marking linen. That of the West Indies (anacardium occidentale, Lin.) also yields a permanent dye, but the colour has a brownish shade. The juice of some other plants, as that of the toxicodendron, or sloc, affords a durable blueish black colour; but these substances cannot be obtained in sufficient quantity, even if they afforded colours equal to those produced by the common processes.

327. The principal substances which are employed to give a black colour are gall-nuts which contain the astringent principle, or tan, and the red oxide of iron (L). For a particular account of the nature and properties of tan, see CHEMISTRY Index. The black colour is produced by the combination of the astringent principle with the oxide of iron, held in solution by an acid, and fixed on the stuff. When the particles are precipitated from the mixture of tan and a solution of iron, they have only a blue colour; but after they are exposed for some time to the air, and moistened with water, the colour becomes deeper, although the blue shade is still perceptible. After the particles are fixed on the stuff, the shade becomes much deeper.

328. Logwood is not to be considered as affording a black dye, but is much employed to give a lustre to black colours. We have (180.) already described its nature and properties, among the substances from which red colouring matters are obtained.

329. Black colours are rarely produced by a simple combination between the colouring matter and the stuff; but are usually fixed by means of mordants, as in the case of the black particles which are the result of a combination of the astringent principle and the oxide of iron, held in solution by an acid. But when the particles are precipitated from the mixture of an astringent and a solution of iron, they have only a blue colour. By being exposed to the air, and moistened with water, the colour becomes deeper, although the blue shade is still perceptible. No fine black colour is ever obtained, unless the stuffs are freely exposed to the air. In dyeing black, therefore, the operations must be conducted at different intervals. Berthollet has observed, that black stuffs, when brought in contact with oxy-

II. Of the Processes for Dyeing Woollen Black.

330. In dyeing woollen stuffs black, if a full and fine deep colour is wanted, it is necessary that they are previously dyed of a deep blue colour. To remove all the blue particles of colouring matter which happen to be loosely attached to the stuff, it should be washed in a river as soon as it is taken out of the vat, and afterwards cleansed at the fulling mill. After these preliminary processes, the stuffs are ready to receive the black colouring matter. The process of Hellot is the following.

For every hundred pounds of stuff, ten pounds of log-wood, and ten pounds of galls reduced to powder, are put into a bag, and boiled in a middle-sized copper, with a sufficient quantity of water, for 12 hours. A third of this bath is put into another copper, along with two pounds of verdigrise. The stuff is immersed in this bath, and continually stirred for two hours. The bath should be kept hot, but it ought not to boil. At the end of two hours the stuff is taken out, and a similar portion of the bath is put into the copper, with eight pounds of copperas (sulphate of iron). During the solution of the copperas, the fire is diminished, and the bath is allowed to cool for half an hour, stirring it well the whole time. The remainder of the bath is then to be added, and after making this addition, the bag containing the astringent matters should be strongly pressed, to separate the whole. A quantity of sumach from 15 to 20 pounds, is now to be added, and the bath is just raised to the boiling temperature; and when it has given one boil, it is to be immediately stopped with a little cold water. A fresh quantity of sulphate of iron, to the amount of two pounds, is then added, and the stuff is kept in it for another hour, after which it is taken out, washed and aired; it is again put into the copper, and constantly stirred for an hour. It is then carried to the river, well washed, and filled. To soften the black colour, and make it more firm, another bath is prepared with weld. This is made to boil for a moment, and when it has cooled, the stuff is passed through it. By this process, which is indeed somewhat complicated, a beautiful black colour is produced.

331. But the processes usually followed for dyeing black, are more simple. Cloth which has been previously dyed blue, is merely boiled in a vat of galls for two hours. It is then kept two hours, but without boiling, in the bath of logwood and sulphate of iron, and afterwards washed and filled. According to Hellot's process, a bath is to be prepared of a pound and a half of yellow wood, five pounds of logwood, and ten pounds of sumach, which is the proportion of the ingredients.

(L.) Oak bark has been recommended as a substitute for gall-nuts in dyeing black, and particularly in dyeing hats; and it is said that the colour thus obtained is fuller, more beautiful and durable, while the operation is easier and less liable to accident. It was first proposed in the year 1782 by Stephanopoli, a Corsican, and a surgeon in the French army. The examination of the process was referred by the French government to Macquer, who gave a favourable report of it; and afterwards to Berthollet, who gave a different opinion. The process has since been examined, and promises to be more economical and advantageous, especially for dyeing hats.

Simple ingredients for every 15 yards of deep blue cloth; and the cloth having boiled in this bath for three hours, ten pounds of sulphate of iron are added; the cloth is allowed to remain for two hours longer, when it is taken out to be aired, after which it is again returned to the bath for an hour, and then washed and fulled.

332. When stuffs are to be dyed at a less expence, instead of the blue ground, a brown or root-coloured ground may be substituted. This brown or fawn colour is communicated by means of the root of the walnut tree, or green walnut peels. The stuffs are then to be dyed black, according to some of the processes already described.

333. The proportions of the ingredients employed by the English dyers are, for every hundred pounds of cloth previously dyed a deep blue, about five pounds of sulphate of iron, five pounds of galls, and 30 of logwood. The first step in the process is to gall the cloth, after which it is passed through the decoction of logwood, to which the sulphate of iron has been added.

334. The leaves of the arbutus uva ursi have been recommended, and employed as a substitute for galls. The leaves must be carefully dried, so that the green colour may be preserved. A hundred pounds of wool are boiled with 16 pounds of sulphate of iron, and eight of tartar, for two hours. The day following the cloth is to be rinsed as after aluming. A hundred and fifty pounds of the leaves of uva ursi are then to be boiled for two hours in water, and after being taken out, a small quantity of madder is to be added to the liquor, putting in the cloth at the same time, which is to remain about an hour and a half. It is then taken out and rinsed in water. By this process, it is said, blue cloth receives a pretty good black, but white cloth becomes only of a deep brown. It is said, too, that the madder and tartar are useless ingredients.

335. After the different operations for dyeing the cloth have been finished, it is washed in a river, and fulled, till the water comes off clear and colourless. Soap suds are recommended by some in fulling fine cloths, but it is found difficult to free the cloth entirely from the soap. After the cloth has come from the fulling mill, some propose to give it a dip in a bath of weld, by which it is said to be softened, and the colour better fixed; but according to Lewis, this operation, which in other cases is of some advantage, is useless after the cloth has been treated with the soap suds.

III. Of the Processes for Dyeing Silk Black.

336. In communicating a black colour to silk, different operations are necessary, such as boiling, galling, repairing the bath, dyeing, and softening.

337. To give a deeper shade to silk, it is necessary to deprive it of the gummy substance to which its stiffness and elasticity are owing. This is done by boiling the silk four or five hours with one-fifth its weight of white soap, and afterwards beetling and carefully washing it.

338. In conducting the process of galling silk, three-fourths of its weight of galls are to be boiled for three or four hours, but the proportion of galls must depend on their quality. After the boiling, the liquor is allowed to remain at rest for two hours; the silk is then put into the bath, and left there from 12 to 36 hours, when it

is to be taken out, and washed in the river. But as silk is capable of combining with a great proportion of the astringent principle, or tan, from which it receives a considerable increase of weight, it is allowed to remain for a longer or shorter time, as the silk is required to have more or less additional weight. To communicate, therefore, to silk, what is called a heavy black, it is allowed to remain longer in the gall liquor: the process is repeated oftener, and the silk is also dipped in the dye a greater number of times.

339. While silk is preparing for the process of dyeing, the bath is to be heated, and should be occasionally stirred, that the grounds which fall to the bottom may not acquire too much heat. It should always be kept under the boiling temperature. Gum and solution of iron are added in different proportions, according to the different processes. When the gum is dissolved, and the bath near the boiling temperature, it is left to settle for about an hour. The silk, which in general is previously divided into three parts, that each may be successively put into the bath, is immersed in it. Each part is then to be three times wrung, and after each wringing hung up to air. The silk being thus exposed to the action of the air, acquires a deeper shade. This operation being finished, the bath is again heated, with the addition of gum and sulphate of iron; and this is repeated two or three times, according as the black required is light or heavy. When the process of dyeing is finished, the silk is rinsed in a vessel with some cold water, by turning or shaking it over.

340. Silk, after it has been taken out of the dye, is extremely harsh, to remove which it is subjected to the operation of softening. A solution of four or five pounds of soap for every hundred pounds of silk, is poured through a cloth into a vessel of water. The solution being completed, the silk is immersed, and allowed to remain in it for about 15 minutes; it is then to be wrung out and dried.

341. When raw silk is to be dyed, that which has a natural yellow colour is preferred. The galling operation must be performed in the cold, if it be proposed to preserve the whole of the gum, and the elasticity which it gives to the silk; but if part only of the gum is wished to be preserved, the galling is to be performed in the warm bath.

342. The dyeing operation is also performed in the cold. All that is necessary is to add the sulphate of iron to the water in which the stuff is rinsed. By this simple process, the black dye is communicated. It is then washed, once or twice beetled, and dried without wringing, that its elasticity may not be destroyed. Raw silk may be dyed by a more speedy process. After a speedier galling, it may be turned or shaken over in the cold bath; and thus by alternately dipping and airing the stuff, the operation may be completed. It is then to be washed and dried as in the former processes.

343. The method of dyeing velvet at Genoa, which has been simplified and improved in France, is thus described by Macquer. For every 100 pounds of silk, 20 pounds of Aleppo galls, reduced to powder, are boiled in a sufficient quantity of water for an hour. The bath is allowed to settle till the galls have fallen to the bottom; they are then taken out, and two pounds and a half of sulphuric acid, twelve pounds of iron filings, and 20 pounds of gum, are put into a cop-
per.

per vessel, or cullender, furnished with two handles. This vessel is immersed in the bath, and supported that it may not touch the bottom. The gum, which is allowed to dissolve for an hour, is to be occasionally stirred; and if it appear that the whole of the gum is dissolved, three or four pounds more are to be added. Excepting during the operation of dyeing, the cullender is to remain in the copper, which must be kept hot the whole time, but at a temperature below the boiling point. In galling the silk, one-third of Aleppo galls is employed, and the stuff should remain six hours in the liquor the first time, and twelve hours the second. By frequent additions of sulphate of iron, and repeated immersions of the stuff, a fine black, according to Lewis, has been obtained. In the above process, the proportion of sulphate of iron is too small, and the gum, according to some, being carried off in the washing, may be considered as useless. Berthollet thinks that, although the quantity be excessive, it has some effect in keeping up the bath; and he adds, if it is to be diminished, it would be useful to add the sulphate of iron in separate portions during each interval.

344. To diminish the quantity of galls, which are an expensive ingredient in dyeing silk black, other substances have been proposed as substitutes. With this view the following process is recommended.

The silk being boiled and washed, is immersed in a strong decoction of green walnut peels, and allowed to remain till the colouring matter of both is exhausted. It is then to be slightly wrung out, dried and washed (M). To give the silk a blue ground, logwood and verdigrise are employed, in the proportion of one ounce of the latter for every pound of silk. The verdigrise is dissolved in cold water, and the silk is allowed to remain two hours in this solution. It is then immersed in a strong decoction of logwood, slightly wrung out, dried, and afterwards washed at the river. The bath is prepared by macerating two pounds of galls and three of sumach in 25 gallons of water, over a slow fire, for twelve hours. The liquid being strained, three pounds of sulphate of iron, and the same quantity of gum arabic, are to be dissolved in it. The silk is dipped in this solution at two different times; it is to remain in the bath two hours each time, and it must be aired and dried between each dip. After being twice beattled at the river, it is dipped a third time, and left in the bath four or five hours, after which it is to be dried, washed and beattled as before. The temperature of the bath should not exceed 120°. After the first dipping, it may be necessary to add half a pound of sulphate of iron, and an equal quantity of gum arabic.

345. Silk which has been previously dyed blue with indigo, it is said, takes only a mealy black; but when it has been prepared with logwood and verdigrise, it acquires a velvety lustre. A fine black may be obtained from green walnut peel; but the addition of logwood and verdigrise renders a smaller quantity of sulphate of iron necessary, and this is of importance, because it is apt to weaken the silk. The only use of galls, according to some, is to increase the weight of

the silk; for the purposes of dyeing, sumach is considered sufficient*.

IV. Of the Processes for Dyeing Cotton and Linen Black.

346. It is more difficult to communicate a fine black to linen or cotton than to silk or woollen stuffs. To succeed in producing a black colour of that degree of intensity which will resist soap, it is necessary to adopt particular processes. In dyeing animal matters black, as silk and wool, the best colours are obtained on those which have been previously dyed blue. This also is an essential preliminary process in dyeing linen and cotton black; for it is found that the process which succeeds best, is first to give a deep blue grain to the cotton or linen.

347. The first part of the process is the operation of galling. The stuffs which have been previously dyed blue, wrung out and dried, are kept 24 hours in the gall-liquor, composed of four ounces of galls to every pound of thread. A bath is then prepared of a solution of iron in acetic acid. This solution is obtained by saturating the acid with oxide of iron. In France, vinegar, small beer, or small wine, is employed for this purpose. To promote the acid fermentation, rye meal, or some other substance, is added, and pieces of old iron are thrown into the liquid, which are allowed to remain for six weeks or two months, that the acid may be saturated with the iron. This solution, called iron liquor in this country, is prepared from fermented worts, to which old iron is added, as is described above. Five quarts of the iron-liquor for every pound of stuffs, are put into a vessel. In this the stuffs are wrought with the hand, pound by pound, for 15 minutes: they are then wrung out and aired. This operation is to be again repeated, taking care to add a fresh quantity of the iron-liquor, which should be carefully scummed, after which the stuffs are to be wrung out, aired, and washed at the river. In the next operation, a pound of alder bark for every pound of stuff is boiled in a sufficient quantity of water for an hour. One half of the bath which was employed in the galling, and about one half the quantity of sumach as of alder bark, are then added. The whole is boiled together for two hours, and strained through a sieve. When this liquid is cold, the stuffs are immersed, wrought pound by pound, and occasionally aired. They are afterwards put into the bath, and after remaining for 24 hours, are wrung out and dried. The above is the process which, according to D'Apligny, is followed at Rouen, for dyeing cotton and linen.

348. The process followed at Manchester, which is described by Mr Wilson, is the following. For the operation of galling, galls or sumach are employed. The stuff is afterwards dyed in a bath consisting of a solution of iron in acetic acid. This bath is also frequently composed of alder bark and iron. After having passed through this bath, the stuff is dipped in a decoction of logwood, to which a small quantity of verdigrise has been added. This process is to be repeated

(M) The decoction of walnut peels is prepared by boiling for 15 minutes, after which it is taken from the fire. After it has subsided, the silk, which has been previously immersed in warm water, is dipped in it.

Simple peated till a black of sufficient intensity is obtained, observing to wash and dry after each operation.

349. According to Gubliche, a solution of iron may be prepared by the following process. A pound of rice is to be boiled in 12 or 15 quarts of water, till the whole is dissolved. A sufficient quantity of old iron made red hot, to reach half way to the surface of the liquor, is thrown into the solution. The vessel in which the solution is kept must be under cover, but exposed to the air and light, at least for a week. In another vessel, containing a quantity of warm vinegar equal to the solution of rice, an equal quantity of red-hot iron is to be put. This vessel must also be exposed in the same way to the air and light. After several days, the contents of both vessels are mixed together, and the mixture is to be exposed for a week to the open air, after which it is to be decanted and kept for use in a close vessel. To give a sufficient black to linen and cotton, it is only necessary, it is said, to steep them 29 hours in this solution: and if it should appear that the liquor is exhausted of colouring matter, a fresh portion is to be employed. In this way a fine permanent black is obtained. According to the same author, this solution may be advantageously employed as a substitute for sulphate of iron, in dyeing silk and wool. But to give them a fine black, silk and woollen stuffs must be dipped in a decoction of logwood after they are taken from the bath.

SECT. V. Of Brown.

350. The last of the simple colours is brown. This is also known under the name of fawn colour, (faune, Fr.). It is that brown colour which has a shade of yellow, and might perhaps be considered as a compound colour, although it is communicated to stuffs by one process.

I. Of the Substances employed in Dyeing Brown.

351. The vegetable substances which are capable of inducing a fawn or brown colour on different stuffs, are very numerous, but those chiefly employed for this purpose are walnut peels and sumach. The peels constitute the green covering of the nut; they are internally of a white colour, which is converted into brown or black by exposure to the air. The skin, when impregnated with the juice of walnut peels, becomes of a brown or almost black colour. When the inner part of the peel, taken fresh, is put into weak oxymuriatic acid, it assumes a brown colour. If the decoction of walnut peels be filtered and exposed to the air, its colour becomes of a deep brown; the pellicles on evaporation are almost black; the liquor detached from these yields a brown extract completely soluble in water. The colouring particles are precipitated from a decoction of walnut peels, by means of alcohol, and they are soluble in water. No apparent change is at first produced by a solution of potash; but it gradually becomes turbid, and the colour is deepened. A copious precipitate of a fawn colour, approaching to an ash colour, is produced in a decoction of walnut peels by means of a solution of tin, and the remaining liquor has a slightly yellow tinge.

352. A decoction of walnut peels yields a small quantity of fawn-coloured precipitate by means of a

solution of alum, and the liquor remains of the same colour. Sulphate of copper renders it slowly turbid, and throws down a small quantity of precipitate of a brownish green colour, leaving the supernatant liquor of the same colour. Sulphate of iron deepens the colour; when diluted, the colour becomes brownish green, without the deposition of any sediment. Sulphate of zinc also deepens the colour, and produces no precipitate. The same properties are exhibited by a decoction of the walnut-tree wood, but the colouring matter is not obtained from it in such abundance as from the peels; and the bark may also be used with advantage in dyeing.

353. The affinity of the colouring matter of walnut peels for wool is very strong; and it readily imparts to it a durable colour, which even mordants do not seem capable of increasing, but they are generally understood to give it additional brightness. A lively and very rich colour is obtained with the assistance of alum. Walnut peels afford a great variety of pleasing shades; and as they require not the intervention of mordants, the softness of the wool is preserved, and the process of dyeing becomes both cheap and simple.

354. Walnut peels are not gathered till the nuts are Preparation completely ripe, when they are put into large casks, along with as much water as is sufficient to cover them. When used in dyeing at the Gobelins in Paris, Berthollet informs us, they are kept for upwards of a year, and very extensively used; but if not made use of till the end of two years, they yield a greater quantity of colouring matter, at which time their odour has become peculiarly disagreeable and fetid. The peels separated from the nuts before they arrive at maturity, may likewise be used in dyeing, but in this state they do not keep so long.

355. Sumach (rhus coriaria, Linn.) is a shrub pro-Sumach. duced naturally in Palestine, Syria, Portugal, and Spain, being carefully cultivated in the two last of these countries. Its shoots are annually cut down, dried, and reduced to powder in a mill, by which process they are prepared for the purposes of dyeing.

356. The infusion of sumach, which is of a fawn co-Properties. lour with a greenish tinge, is changed into a brown by exposure to the air. A solution of potash has little action on the recent infusion of sumach; its colour is changed to yellow by the action of acids; the liquor becomes turbid by means of alum, a small quantity of precipitate being at the same time formed, and the supernatant liquor remaining yellow. A copious precipitate of a yellowish green colour is thrown down by sulphate of copper, and the liquor remains clear. No change is speedily produced by muriate of soda (common salt), but it becomes rather turbid at the end of some hours, and its colour is rather clearer. Sulphate of copper produces a copious precipitate of a yellowish green, which after standing some hours, changes to a brownish green; the supernatant liquor, which is slightly yellow, remains clear. Sulphate of zinc renders the liquor turbid, darkens its colour, and produces a deep blue precipitate; but when the sulphate of zinc is pure, the precipitate, which is of a brownish fawn colour, is in very small quantity. Acetate of lead gives a copious precipitate, of a yellowish colour; the supernatant liquor is of a clear yellow colour. No astringent has so strong a resemblance to galls as sumach; but the precipitate

Compound Colours. Precipitate thrown down from an infusion of it by a solution of iron, is not so copious as that which is yielded by an equal quantity of galls, on which account sumach may be generally employed as a substitute for galls, only its quantity will require to be increased.

Bark of birch. 357. The bark of the birch tree (betula alba, Lin.) yields a decoction of a clear fawn-colour, but it soon becomes turbid and brown. The addition of a solution of alum in the open air, produces a copious yellow precipitate; a solution of tin gives also a copious precipitate of a clear yellow colour. With solutions of iron the decoction of the birch-tree strikes a black colour, and it dissolves in considerable quantity the oxide of iron, but in smaller proportion than the decoction of walnut peels. On account of this property, it is employed in the preparation of black vats for dyeing thread.

Sandal wood. 358. Sanders or sandal wood, is also employed for the purpose of giving a fawn colour. There are three kinds of sandal wood, the white, the yellow, and the red. The last only, which is a compact heavy wood, brought from the Coromandel coast, is used in dyeing. By exposure to the air it becomes of a brown colour; when employed in dyeing, it is reduced to fine powder, and it yields a fawn colour with a brownish shade, inclining to red. But the colouring matter which it yields of itself is in small quantity, and it is said that it gives harshness to woollen stuffs. When it is mixed with other substances, as sumach, walnut peels, or galls, the quantity of colouring matter is increased; it gives a more durable colour, and produces considerable modifications in the colouring matter with which it is mixed. Sandal wood yields its colouring matter to brandy, or diluted alcohol, more readily than to water.

Soot. 359. Soot communicates to woollen-stuffs a fawn or brown colour, of a lighter or deeper shade, in proportion to the quantity employed; but the colour is fading, and its affinity for wool is not great; and besides leaving a disagreeable smell, it renders the fibres harsh. In some manufactories, it is employed for browning certain colours, and it produces shades which could not otherwise be easily obtained.

II. Of the Processes for Dyeing Woollen, &c. a Fawn or Brown Colour.

With walnut peels. 360. In dyeing with walnut peels, a quantity proportioned to the quantity of stuff, and the intensity of shade wanted, is boiled for fifteen minutes in a copper. All that is necessary in dyeing with this substance is, to moisten the cloth or yarn with warm water, previous to their immersion in the copper, in which they are to be carefully stirred till they have acquired the proper shade. This is the process, if the aluminous mordant is not employed. In dyeing cloth, it is usual to give the deepest shades first, and the lighter ones afterwards; but in dyeing woollen yarn, the light shades are given first, and the deeper ones afterwards. An additional quantity of peels is joined to each parcel.

Berthollet's Experiments. 361. Berthollet made a number of experiments to ascertain the difference of colour obtained from the simple decoction of walnut peels, and the addition of metallic oxides as mordants. The oxide of tin, he found, yielded a clearer and brighter fawn colour than that of the simple decoction. The oxide of zinc pro-

duced a still clearer colour, inclining to ash or gray. The colour from oxide of lead had an orange cast, while that from oxide of iron was of a greenish brown*. Compound Colours. Elements of Dyeing, p. 266.

362. A fawn colour, which has a shade of green, is obtained from sumach alone; but to cotton stuffs which have been impregnated with printers' mordant, or acetate of alumina, sumach communicates a good and durable yellow. Here, however, some precaution is necessary in the use of this substance for this purpose; for as the colouring matter is of so fixed a nature, the ground of the stuff cannot be bleached by exposure on the grass. This inconvenience is avoided by impregnating the whole of the stuff with different mordants, producing in this way a variety of colours, and leaving no part white. With an- dal wool.

363. Vogler employed the tincture of sanders wood for dyeing patterns of wool, silk, cotton and linen, having previously impregnated them with a solution of tin, and afterwards washing and drying them. Sometimes he used the solution unmixed, and at other times added six or ten parts of water, and in whatever way he employed it, he obtained a poppy colour. When the mordant employed was solution of alum, the colour was a rich scarlet; with sulphate of copper it was a clear crimson, and with sulphate of iron a beautiful deep violet†. †Cell An. 1790.

CHAP. II. Of Compound Colours.

364. A MIXTURE of two colouring substances, it is well known, produces a very different shade from that of either of the uncombined colouring matters; hence compound colours are obtained, which are merely mixtures of simple colours. It would undoubtedly be a desirable thing to ascertain with accuracy the peculiar shade produced by the combination of two colouring matters; but these results can only be certainly known by experiment, because by the action of different substances in the bath, they are subject to great variations in their effects, according to the affinities which are brought into action, and the new combinations which are formed. What is natural to colouring particles is not to be considered as a constituent part of compound colours, but only the difference of shade which they ought to assume, with a particular mordant, or in a particular bath. The effects, therefore, of the chemical agents employed in these processes, and the result of different combinations, ought to be particularly attended to. It is in dyeing compound colours that skill and ingenuity are most conspicuous, and their application of greatest utility, to enable the dyer to vary his processes according to the shade desired, and at the same time to accomplish his operations by the shortest and cheapest means. Nature of compound colours.

365. As compound colours are obtained by the mixture of simple colours, very different shades will be obtained from different proportions of the simple colours; hence compound colours exhibit an indefinite variety of shade, and the processes by which they are produced are very numerous. It would extend this treatise to an unusual length, were we to attempt to describe every variety of shade which is obtained from the mixture of simple colours. We shall therefore limit our observations to some of the principal compound colours, and Great variety of shades.

Compound colours, leaving it to our readers, who have made themselves familiar with the principles already detailed, to vary these colours, by employing different proportions and different combinations of simple colouring matters.

366. Compound colours have been usually divided into four classes, namely, green, purple, orange, and gray or drab colour. These are obtained from mixtures of the following simple colours.

1. 1. Blue and yellow produce a green.
2. 2. Red and blue, a purple, &c.
3. 3. Red and yellow, orange.
4. 4. Black and other colours, gray, &c.

The following sections will be occupied in a short detail of the methods which are usually employed in producing these different compound colours.

SECT. I. Of the Mixture of Blue and Yellow, or Green.

367. Green colours, from the great variety of shades which they exhibit, have been long known by different names, by which the intensity of shade is characterised, such as sea-green, apple-green, meadow or grass-green, pea-green, parrot-green, &c. Many plants afford a green colour, such as brome grass (bromus secalinus, Lin.) green berries of rhhamnus frangula, wild chervil (chierophyllum sylvestre, Lin.), purple clover (trifolium pratense), common reed (arundo phragmites). These colours, however, do not possess sufficient permanency. According to D'Ambourney, indeed, a permanent green may be obtained from the fermented juice of the berries of the berry-bearing alder (rhhamnus frangula). Having previously prepared the cloth with tartar, solution of nitrate of bismuth, and common salt, he added to the fermented juice of the berries, after it was warmed, a small proportion of acetate of lead; and in this bath he communicated to the cloth an intermediate shade between parrot and grass green. But it is usually from the mixture of blue and yellow that green is obtained; and it may be observed, that it requires much skill and experience, especially in giving light shades, to produce a colour which is uniform, and entirely without spots.

I. Of the Processes for Dyeing Woollen Stuffs Green.

368. To dye woollen green, either the yellow or the blue dye may be given to it first. But when the stuff is first dyed yellow, and in this state is introduced into the blue vat, part of the yellow colouring matter being dissolved in the vat, communicates to it a green colour, which renders it unfit for dyeing any other colour than green. To avoid this inconvenience, therefore, the blue colour is first given, and afterwards the yellow. It would be quite unnecessary to resume the account of any part of the processes for dyeing blue, which have been already detailed. It is proper, however, to add, that the intensity of the blue shade must be proportioned to the green, or to the depth of the green colour which is wished to be obtained. Thus, for instance, to produce a parrot green, a ground of sky blue is given, and for the green like that of a drake's neck, a deep blue is required. When the blue dye has been communicated, the yellow is afterwards given, according to some of the processes which have been al-

ready described for dyeing yellow. The proper ground being communicated to the cloths, they are washed in the fulling mill, and boiled as for the common process of welding; but when the shade is light, the proportion of salts should be less. Cloths which are to receive light shades are first boiled, and when these are taken out, tartar and alum are added in fresh portions, till the cloths which are intended for the darkest shades are boiled. The process of welding is conducted in the same way as for dyeing yellow, with this difference, that a larger proportion of weld is employed, excepting for lighter shades, when the proportion must be smaller. In dyeing green, it is usual to have a succession of shades at the same time; the process is begun with the deepest, and ends with the lightest. Between each dip there should be an interval of one-half or three quarters of an hour, and at each interval water is added to the bath. It is the practice of some dyers to give each parcel two dips, beginning the first time with the deep shades, and the second with the lighter ones; but when this practice is followed, the time of immersion should be shortened. In dyeing very light shades, the bath should never be permitted to reach the boiling temperature. For deep greens, a browning is given with logwood, and a small proportion of sulphate of iron.

369. For some kinds of green, sulphate of indigo is Saxon employed; and in this case either the blue and yellow green are dyed separately, or the whole of the ingredients are mixed together in the bath, and the whole process is finished at a single operation. The colour thus obtained has been distinguished by the name of Saxon green. The following is the process recommended by Dr Bancroft.

370. "The most beautiful Saxon green (says he) may be produced very cheaply and expeditiously, by combining the lively yellow which results from quercitron bark, murio-sulphate of tin, and alum, with the blue afforded by indigo when dissolved in sulphuric acid, as for dyeing the Saxon blue.

"To produce this combination most advantageously, the dyer, for a full-bodied green, should put into the dyeing vessel after the rate of six or eight pounds of powdered bark, in a bag, for every 100 lb. weight of cloth, with only a small proportion of water as soon as it begins to grow warm; and when it begins to boil, he should add about six pounds of murio-sulphate of tin (with the usual precautions), and a few minutes after, about four pounds of alum; these having boiled together five or six minutes, cold water should be added, and the fire diminished so as to bring the heat of the liquor nearly down to what the hand is able to bear; and immediately after this, as much sulphate of indigo is to be added as will suffice to produce the shade of green intended to be dyed, taking care to mix it thoroughly with the first solution by stirring, &c.; and this being done, the cloth previously scoured and moistened, should be expeditiously put into the liquor, and turned very briskly through it for a quarter of an hour, in order that the colour may apply itself equally to every part, which it will certainly do in this way with proper care. By these means, very full, even, and beautiful greens may generally be dyed in half an hour; and during this space, it is best to keep the liquor at rather less than a boiling heat. Murio-sulphate

Compound of tin is infinitely preferable, for this use, to the dyer's spirit; because the latter consists chiefly of nitric acid, which, by its highly injurious action upon indigo, would render that part of the green colour very fugitive, as I have found by repeated trials. But no such effect can result from the murio-sulphate of tin, since the muriatic acid has no action upon indigo; and the sulphuric is that very acid which alone is proper to dissolve it for this use.

“Respecting the beauty of the colour thus produced, those who are acquainted with the unequalled lustre and brightness of the quercitron yellows, dyed with the tin basis, must necessarily conclude, that the greens composed therewith will prove infinitely superior to any which can result from the dull muddy yellow of old fustic; and in point of expence, it is certain that the bark, murio-sulphate of tin, and alum, necessary to dye a given quantity of cloth in this way, will cost less than the much greater quantity (six or eight times more) of fustic, with the alum necessary for dyeing it in the common way, the sulphate of indigo being the same in both cases. But in dyeing with the bark, the vessel is only to be filled and heated once; and the cloth, without any previous preparation, may be completely dyed in half an hour; whilst in the common way of producing Saxon greens, the copper is to be twice filled: and to this must be joined the fuel and labour of an hour and a half's boiling and turning the cloth, in the course of preparation, besides nearly as much boiling in another vessel to extract the colour of the fustic; and after all the dyeing process remains to be performed, which will be equal in time and trouble to the whole of the process for producing a Saxon green with the bark; so that this colour obtained from bark will not only prove superior in beauty, but in cheapness, to that dyed as usual with old fustic.”

II. Of the Processes for Dyeing Silk Green.

371. In giving silk a green colour, greater precaution is necessary, to preserve uniformity of colour, and to prevent spots and stripes. Silk which is intended to receive a green colour, is scoured in the same way as for other colours; but for light shades, the scouring must be as complete as for blue. Silk which is to be dyed green, is first dyed yellow, and being well alumed, it is slightly washed at the river, and divided into small parcels, that it may receive the colouring matter uniformly, and then carefully turned in the weld bath. When the ground is supposed to have acquired a sufficient degree of intensity, a pattern is put into the blue vat, to ascertain the proper shade. When this is the case, the silk is taken out of the bath, washed, and immersed in the blue vat. To produce a deeper colour, and at the same time to give variety of shade, a decoction of logwood, fustic, or anotta, is added to the yellow bath, after the weld has been taken out. For very light shades, such as apple and sea green, it is scarcely necessary to add, that a weaker ground is to be given. For all light shades, except sea green, the process is found to succeed better when the yellow is communicated by baths which have been already used; but these baths should not contain any logwood or fustic.

372. Saxon green is produced by means of sulphate of indigo. This is a brighter, but less durable colour than the former. This process is conducted by boiling

as for welding, after which the cloth is washed. Fustic Compound in chips is enclosed in a bag, put into the same bath, and boiled for an hour and a half, when it is taken out, and the bath allowed to cool till the hand can bear it. A pound and a quarter of sulphate of indigo for each piece of cloth of eighteen yards, is added. The cloth is at first to be turned quickly, and afterwards more slowly, and it should be taken out before the bath boils. Some dyers put in only two-thirds of the solution at first; and after two or three turns, take out the cloth, and add the other one-third. By this means the colour is more uniform.

373. To produce Saxon green at one operation, the following process is recommended by Dr Bancroft. A bath is prepared of four pounds of quercitron bark, three pounds of alum, and two pounds of murio-sulphate of tin, with a sufficient quantity of water. The bath is boiled ten or fifteen minutes, and when the liquor is so far reduced in temperature as the hand can bear it, it is fit for dyeing. By adding different proportions of sulphate of indigo, various and beautiful shades of green may be obtained, and the colour thus produced is both cheap and uniform. Care should be taken to keep the bath constantly stirred, to prevent the colouring matter from subsiding. Those shades which are intended to incline most to the yellow, should be dyed first; and by adding sulphate of indigo, the green, having a shade of blue, may be obtained. This process, Dr Bancroft observes, is the most commodious and certain for dyeing most beautiful Saxon greens upon silk.

374. To produce English green, which is more beautiful than common green, and is said to be more durable than the Saxon green, Guhlische gives the following process. He first dyes the silk of a light blue in the cold vat already described (316.), then soaks it in warm water, washes it in a stream, and dips it in a weak solution of alum. He then prepares a bath of sulphate of indigo, one ounce of solution of tin, with the tincture of French berries made with aceto-citric acid. The silk is kept in this bath till it has obtained the desired colour. It is then washed and dried in a shady place. Lighter shades may be dyed afterwards.

III. Of the Processes for Dyeing Cotton and Linen Green.

375. Cotton and linen, after being scoured in the usual way, are first dyed blue; and after being cleansed, they are dipped in the weld bath, to produce a green colour. The strength of the blue and yellow is proportioned to the shade of green which is wanted. But as it is difficult to give to cotton velvet an uniform colour in the blue vat, it is first dyed yellow with turmeric, and the process is completed by giving it a green with sulphate of indigo. The same result, however, will be obtained by commencing the process either with the yellow or the blue.

376. The process which D'Apligny describes for dyeing cotton velvet, or cotton thread, a sea or apple green, in one bath, is the following. A quantity of verdigris is dissolved in vinegar, and the mixture is kept excluded from the air in the heat of a stove for fifteen days. A quantity of potash equal in weight to the verdigris employed is dissolved in water, and four

Compound colours. hours before dyeing it is added to the solution of verdigrise. The mixture is to be kept hot. One ounce of alum in five quarts of water for each pound of stuff being prepared, the cotton thread or velvet is soaked in this solution. It is then taken out, and the verdigrise mixture being added to the solution of alum, it is again introduced to be dyed.

377. The different shades of olive green, and drake's neck green, are given to thread after it has received a blue ground, by galling it, and dipping it in a weaker or stronger bath of iron liquor, then in the weld bath, to which verdigrise has been added, and afterwards in the bath with sulphate of copper. The colour is lastly to be brightened with soap.

378. Cotton dyed with Prussian blue may be dyed green by previously aluming while it is still wet with the blue, and then dipping in a weld bath, the strength of which is proportioned to the shade required. The colour from weld is more lively than that obtained from fustic. But fustic which gives a deeper shade than weld, and diminishes the brightness of the blue, is to be preferred when a green with an olive shade is wanted.

379. The shade of green given to any stuff, it is obvious, must vary according to the intensity of the blue shade, the strength of the yellow bath, and the nature of the yellow colouring matter employed. Yellow colours are rendered more intense by means of alkalies, sulphate of lime and ammoniacal salts; but become fainter by means of acids, alum, and solutions of tin. In dyeing Saxon green the result will be different according to the process which is followed. The effects will be different by adding a yellow to a Saxon blue, from the process in which the sulphate of indigo is mixed with the yellow ingredients; because in the latter case the sulphuric acid has a considerable action on the colouring matter, and thus diminishes the intensity of the yellow. As the particles of indigo have a stronger affinity for the stuff than the yellow colouring matter, in dyeing a succession of shades in a bath in which both are mixed, the bath being first exhausted of the indigo, the last shades incline more to the yellow on account of the predominance of the yellow colouring matter.

SECT. II. Of the Mixture of Red and Blue, or Purple, &c.

380. By the mixture of red and blue, violet, purple, dove-colour, lilac, and a great variety of other shades, according to the proportion of the substances employed, or the predominance of the blue or the red, are produced. In stuffs which are to be dyed violet, a deeper blue must be given, but for purple colours, the ground requires to be of a lighter blue; but in lilac and similar light colours, it is necessary that both the blue and the red have a light shade.

I. Of Dyeing Wool Violet, Purple, &c.

381. In the attempts which have been made to communicate a violet or purple colour to a scarlet ground, according to the observations of Hellot, the colour is very unequal. It becomes therefore necessary to give the blue colour first; and for violets or purples, the shade of blue ought not to be deeper than that of sky

blue. The stuff being dyed blue, is boiled with alum, and two-fifths of tartar, and is afterwards dipped in a bath composed of nearly two-thirds the quantity of cochineal required for scarlet, with the addition of tartar. The same process, indeed, as for dyeing scarlet, is followed. It is a common practice to dye these colours after the reddening for scarlet, making such additions of cochineal and tartar as the intensity of the shade may require.

382. For lighter shades, as lilacs, dove-colours, &c. Lilac, &c. the stuff may be dipped in the bath which has served for violet and purple, and is now somewhat exhausted, taking care to add a quantity of alum and tartar. For reddish shades, such as peach blossom, a small proportion of solution of tin is added. It may be observed, in general, that although the proportion of cochineal is less in dyeing lighter shades, the quantity of tartar must not be diminished.

383. To obtain the same colours, a shorter and less expensive process is recommended by Poerner. In this and shorter process he employs sulphate of indigo. He boils the stuff in a solution of alum, in the proportion of three ounces of the latter to one pound of the former, for an hour and a half, and afterwards allows it to remain in the liquid for a night after it has cooled. The dyeing bath is prepared with an ounce and a half of cochineal, and two ounces of tartar, which are boiled for three quarters of an hour: two ounces and a half of sulphate of indigo are then added, the whole is stirred, and boiled gently for 15 minutes. The dyeing operation is conducted in the usual way, and a beautiful violet is thus obtained. To have all the variety of shades which are produced by the mixture of red and blue, the proportion of the sulphate of indigo is increased or diminished. It is sometimes increased to five ounces, and diminished to five drachms, for each pound of stuff. The quantity of cochineal is also varied, but when it is less than an ounce, the colour is dull. Different proportions of tartar are also employed. To produce variety of shades, the stuff is also prepared with different proportions of solution of tin.

384. To communicate a purple colour to wool, as well as some other shades, logwood, with the addition of galls, has been employed. The stuff is previously dyed blue, and to give a brown shade, sulphate of iron is used; but the colours thus obtained are not permanent. By the following process, described by Decroizille, a durable dye is produced, by means of this wood. He dissolved tin in sulphuric acid, to which were added common salt, red acidulous tartrate of potash, and sulphate of copper; or it may be more conveniently done by making a solution of tin in a mixture of sulphuric acid, common salt, and water, to which are to be added the tartrate and sulphate in the state of powder. Of this mordant not less than 1500 quarts were made in twenty-four hours, in a leaden vessel to which a moderate heat was applied. A very lucrative trade was carried on for three years by Decroizille, who sold it at the rate of 1s. 3d. sterling per pound.

385. If wool in the fleece is to be dyed, it will require a third of its weight of this mordant, while a fifth Process. is a proportion sufficient for stuffs. A bath is prepared of such a degree of temperature as the hand can bear, with which the mordant is properly mixed, and the wool or stuff dipped in it and stirred, the same degree

Compound of temperature being kept up for two hours, and increased a little towards the end: after which it is taken out, aired, and well washed. A fresh bath of pure water is prepared at the same temperature, to which is added a sufficient quantity of the decoction of logwood; the stuff is then immersed, stirred, and the heat increased to the boiling temperature, which is to be continued for 15 minutes, after which the stuff being taken out, aired, and carefully rinsed, the process of dyeing is completed. If for every three pounds of wool, one pound of decoction of logwood has been used, and a proportionate quantity for stuffs which require less, a fine violet colour is produced, to which a sufficient quantity of Brazil wood imparts the shade known in France by the name of prune de Monsieur.

Different shades from other substances. 386. Logwood and Brazil, fustic and yellow wood, are colouring substances which may be fixed with advantage upon wool by means of this mordant. The colour communicated by the two first of these is liable to be changed in the fulling by the action of the soap or urine employed for that purpose; but this change, which is always produced by alkaline substances, is remedied by a slightly acid bath a little hot, called brightening, for which the sulphuric acid has the preference. The colour becomes as deep, and frequently much brighter than before the change. Wools which have been dyed by means of this mordant, are said to admit of being spun into a finer and more beautiful thread than by the use of alum. If the use of sulphate of copper is omitted, more beautiful colours are produced by fustic and yellow wood, as well as by weld. An orange red colour is communicated by madder, but not so deep as with a similar quantity of alum. When sulphate of copper is omitted, the wool is said to become much harsher, and the mordant thus prepared yields but indifferent colours with logwood, and in particular with Brazil wood. The use and carriage of this mordant are inconvenient, on account of the heavy sediment by which the vessel is half filled under a corrosive liquor, capable only of being kept in stone ware. These inconveniences may be remedied by the omission of the water in the receipt, which leaves only a paste more conveniently used, and the carriage of it two-fifths cheaper.

Nature of the process. 387. The above process is thus explained by Berthollet. The decomposition of the muriate of soda is effected by the action of the sulphuric acid; and the muriatic acid being thus disengaged, dissolves the tin, part of which is precipitated by means of the tartaric acid, producing the sediment already mentioned. The oxide of copper produces the blue with the colouring particles of the logwood; the violet is formed by the oxide of tin with the same wood, and the red, with the colouring matter of the Brazil wood. The same ingenious chemist farther observes, that as an excess of acid is retained in the liquor, it might probably be of advantage to employ acetate as a substitute for sulphate of copper, in which case the action of the free acid would be moderated. He thinks it would still be more advisable to make use of verdigrise; because the uncombined part of the oxide of copper would, in that case, unite with the excess of acid, on which account a smaller quantity of acid would remain in the liquor; and probably the quantity of tartar might be diminished.

ed, as a smaller quantity of tin would thus be precipitated *.

II. Of Dyeing Silk Violet or Purple.

388. Silk is capable of receiving two kinds of violet colours, denominated the fine and the false, the latter of which is produced by means of archil or Brazil wood. When the fine violet colour is required, the silk must first be passed through cochineal, and dipped afterwards in the vat. The preparation and dyeing of the silk with cochineal are the same as for crimson, with the omission of tartar and solution of tin, by means of which the colour is heightened. The quantity of cochineal made use of is always proportioned to the required shade, whether it is more or less intense; but the usual proportion for a fine violet colour is two ounces of cochineal for each pound of silk. When the silk is dyed, it is washed at the river, twice beetled, dipped in a vat more or less strong, in proportion to the depth of the violet shade, and then washed and dried with precautions similar to those which all colours require that are dyed in the vat. If the violet is to have greater strength and beauty, it is usual to pass it through the archil bath, a practice which, though frequently abused, is not to be dispensed with for light shades, which would otherwise be too dull.

389. When silk has been dyed with cochineal according to the above directions, only a very light shade is requisite for purple; the shades which are deepest are dipped in a weak vat, while dipping them in cold water is sufficient for such as are lighter, the water having been incorporated with a small quantity of the liquor of the vat, because in the vat itself, however weak it might be, they would acquire too deep a tinge of blue. In this manner are the light shades of this colour, such as gilly-flower, peach blossom, &c. produced by diminishing the quantity of cochineal.

390. There are various ways of imparting to silk what are denominated the false violets; but those which are most frequently used, and possessed of greatest beauty, are prepared with archil, the bath of which is, in point of strength, to be suited to the colour required. Having been beetled at the river after scouring, the silk is turned in the bath on the skein sticks; and when the colour is deemed sufficiently deep, a pattern is tried in the vat, to ascertain whether it takes the violet colour intended to be produced. If the shade is found to have acquired the proper depth, the silk is beetled at the river and dipped in the vat, in the same way as for the fine violet colours; and less either of the blue or of the archil colour is given, according as it is meant that the red or blue shade of the violet colour should predominate.

391. The process recommended by Gubliche for communicating a violet colour to silk is the following. A pound of silk is to be soaked in a bath of two ounces of alum, and a like quantity of solution of tin, after having carefully poured off the sediment formed in the mixture. The dye-bath is prepared with two ounces of cochineal reduced to powder with a dram of tartar, and the remaining part of the bath which has answered the purpose of a mordant, with the addition of a sufficient quantity of water. When slightly boiled, such a quantity of solution of indigo is added as may communicate

compound cate to the bath a proper shade of violet; after which the silk is immersed, and boiled till it has acquired the intended shade. It is then wrung, washed in a stream, and like every other delicate colour, must be dried in the shade. The light shades exhaust the bath. But it ought to be observed, that this colour, which is said to be a beautiful violet, possesses but little durability, and is apt to assume a reddish tinge, owing to the colour of the indigo fading first.

392. A violet colour may be imparted to silks, by immersing them in water impregnated with verdigrise, as a substitute for aluming, and next giving them a bath of logwood, in which they assume a blue colour, which is converted to a violet, either by the addition of alum to the bath, or by dipping them in a weaker or stronger solution of that substance, which communicates a red colour to the particles of logwood. This violet possesses but a small degree of beauty, and little durability. But if alumed silk be immersed in a bath of brazil-wood, and next in a bath of archil, after washing it at the river, a colour is obtained possessing a much higher degree of beauty and intensity. The process described above (385.), for dyeing wool, succeeds equally well, according to M. Decroizille, in communicating to silk a violet colour.

III. Of Dyeing Cotton and Linen Violet.

393. The most ordinary mode by which a violet colour is communicated to cotton and linen stuffs is first to give them a blue ground in the vat, proportioned to the required shade, and to dry them. They are afterwards galled, in the proportion of three ounces of galls to a pound of stuff, and being left in this bath for 12 or 15 hours, are wrung out and dried again. They are next passed through a decoction of logwood, and when thoroughly soaked and taken out, the bath receives an addition of two drams of alum, and one of dissolved verdigrise for each pound of cotton or thread. The skeins are then dipped again on the skein sticks, and turned for about 15 minutes, when they are taken out and aired. They are next immersed in the bath for 15 minutes, taken out and wrung. To complete the process, the vat employed is emptied; half of the decoction of logwood not formerly made use of is now poured in, with the addition of two drams of alum, and the thread is again dipped in it till it has acquired the shade proposed, which must always regulate the strength or weakness of the decoction of logwood. This colour resists in a considerable degree the action of the air, but in point of permanency is much inferior to that which is obtained from the use of madder.

SECT. III. Of the Mixtures of Yellow and Red, or Orange.

394. Orange is the usual result of a composition of yellow and red colours; but an almost endless variety of shades may be produced, according as we vary the proportion of the ingredients, and the particular nature of the yellow made use of. It is sometimes the practice of dyers to combine blue with yellow and red, the result of which is the colour denominated olive. Many varieties may be obtained from the use of weld, saw-wort, dyers-weed, and other yellows, and by employing tartar, alum, sulphate of zinc, or sulphate of

copper in the bath, or in the preparation of the compound cloth.

I. Of Dyeing Wool Orange.

395. By a process exactly the same as that which is followed in communicating to stuffs a scarlet colour, an orange may be given to wool; but the quantity of red must be diminished, and that of the yellow increased. If wool is dyed a red colour by means of madder, and afterwards yellow with weld, the resulting compound is a cinnamon colour, and the most proper mordant in this case is a mixture of alum and tartar. The shades may be varied at pleasure by substituting other yellow dye stuffs instead of weld, and by varying the proportions as circumstances may require. Wool may receive a reddish yellow colour by passing it through a madder bath, after it has undergone the usual process for yellow, which has already been described. The strength of the madder bath is always to be proportioned to the shade required. Brasil-wood is sometimes employed with yellow substances, or mixed with cochineal and madder. Snuff, chesnut, musk, and other shades are produced, by substituting walnut-tree root, walnut peels or sumach, for weld.

II. Of Dyeing Silk, Orange, &c.

396. Logwood, brasil-wood, and fustic, communicate to silk a marone and cinnamon colour, together with all the intermediate shades. The silk is scoured in the usual manner, alumed, and a bath is prepared, by mixing together decoctions of the three different woods mentioned above, made separately, varying the quantity of each according to the shade intended to be given; but the proportion of fustic should be greatest. The silk is turned in the bath on the skein sticks, and when it is taken out, if the colour be uniform, it is wrung and again dipped in a second bath of these three ingredients, according to the effect produced by the first in order to obtain the shade required.

397. The blue vat is not made use of, when an olive colour is to be communicated to silk. After being alumed, it is dipped in a bath of weld, which is made very strong. To this is afterwards added the juice of logwood, with a small quantity of solution of alkali when the silk is dipped. This converts it into green, and gives the olive colour. It is dipped again in this bath till it has acquired the shade wanted.

398. To communicate to it the colour known by the name of rotten olive, fustic and logwood are added to the bath after welding, without any alkali. If the colour wanted is to incline more to a red, the addition of logwood alone is sufficient. A sort of reddish olive may likewise be obtained, by dyeing the silk in a fustic bath, to which a greater or lesser quantity has been added of sulphate of iron and logwood.

III. Of Dyeing Cotton and Linen Orange, &c.

399. A cinnamon colour is communicated to thread and cotton, by commencing the process for dyeing them with verdigrise and weld; they are afterwards to be dipped in a solution of sulphate of iron, denominated by the French bain d'assurage, and then wrung out and dried. As soon as they are dried, they are galled in the

Compound the proportion of three ounces to the pound of stuff; then dried again, alumed as for red colours, and maddered. After being washed and dried, they are put into hot soap suds, and turned till they have acquired a sufficient degree of brightness. It is the practice of some dyers to add to the aluming a decoction of fustic.

Olive. 400. By boiling four parts of weld and one of potash in a sufficient quantity of water, M. d'Apligny informs us, a fine olive colour is communicated to cotton and thread. Brasil wood, which has been steeped for a night, is boiled separately with a small quantity of verdigrise, and these solutions are mixed together in various proportions, according to the particular shade required. The thread or cotton is dipped in the compound solution in the usual way.

SECT. IV. Of the mixture of Black with other Colours.

Brown. The compound colours which are obtained from the mixture of black and other colours, are brown, gray, drab, &c. according to the nature and proportions of the simple colours employed.

I. Of Dyeing Woollen Stuffs Brown, Gray, &c.

401. To give a browning to cloth, as soon as it has been dyed, it is dipped in a solution of sulphate of iron, with the addition of an astringent, which makes a black bath. It is more common to mix a small quantity of solution of iron with a bath of water, adding more till the dyed stuff dipped in it has received the intended shade. Sulphate of iron is sometimes added to the dye bath; but by dipping the dyed stuff in a solution of this salt, the end is more easily attained. It is the usual practice of M. Poerner to soak the stuff in a solution of sulphate of iron, to which other ingredients are sometimes added, and after having taken it out of the mordant, it is dipped in the dye bath.

Coffee-colour. 402. In order to obtain coffee and damascene colours, with other shades of browns of the common dye, the first method is adopted; a colour more or less deep is communicated to them, according to the shade intended to be obtained by the browning; and a bath is made of galls, sumach, and alder bark, with the addition of sulphate of iron. Those stuffs are first dipped to which the lightest shades are to be communicated, and when these are finished, the browner ones are dipped; a quantity of sulphate of iron being added for each operation, proportioned to the effect intended to be produced.

Gray. 403. Bluish grays are communicated to stuffs, according to Poerner, by the solution of indigo in sulphuric acid, combined with a mixture of decoction of galls and sulphate of iron, varying the shades according to the different quantities of these ingredients made use of. If to a bath composed of cochineal, fustic and galls, sulphate of iron be added, other shades are obtained.

404. For marone, and such other colours as bear a strong resemblance to it, sanders and galls are employed, and sometimes a browning with the addition of logwood. If dyed in the remains of a cochineal bath, these colours may be made to incline to a crimson or purple, and the same effect is produced by adding a small quantity of madder or cochineal to the

bath. A little tartar gives a greater degree of brightness to the colour. With a mixture of galls, fustic, and logwood, and a greater or smaller quantity of madder, with the addition of a little alum, those colours may be communicated to stuffs which are known by the name hazel.

405. M. Guhlliche produces what is called a puce colour, by boiling for fifteen minutes a pound of woollen stuff with two ounces of alum, a certain proportion of vinegar and solution of iron, after which he leaves it in the mordant for twelve hours. He then makes a bath with the decoction of two ounces of white galls carefully poured off from the sediment, and mixed with four ounces of madder, in which, when it grows hot, the stuff is immersed, after being taken out of the mordant, allowing it to remain there, while the temperature is gradually increased, till the colour intended has been imparted to it; after which it is boiled for two minutes, washed, and dried in the sun. The colour thus obtained possesses a great degree of durability. It is of a deeper brown by the omission of the alum and vinegar in the mordant; and after these colours the lighter shades are dyed. Sumach may be employed as a substitute for half of the madder. Different brown colours possessing considerable permanency, may likewise be produced by the use of brasil and logwood, if more or less of a solution of iron be mixed with a decoction of these substances. The wool being previously alumed and galled, is dyed in it.

II. Of Dyeing Silk with Mixtures of Black, &c.

406. M. Guhlliche imparts to silk a purple violet purple without a blue ground, with a mixture of one part of galls dissolved in white wine, with three parts of water, in which a pound of silk is macerated for twelve hours, soaked in a mordant made up of two ounces of alum, one ounce of solution of tin, and half an ounce of muriatic acid. After wringing the stuff, it is dyed in a bath composed of two ounces of cochineal and a small quantity of solution of iron, till the intended shade has been communicated; and for shades which are lighter, the residua of these baths are sufficient, either separately or mixed together. Madder may be used in the same way, macerating a pound of silk in a solution of alum, mixed with an ounce of muriatic acid, and a quantity of solution of iron. When the stuff is wrung out, it is dyed in a bath made of eight ounces of madder. When deeper colours are wanted, some of the solution of galls in white wine is mixed with the madder and cochineal baths.

407. Silk may be dyed in a bath made of equal parts of brasil and logwood juice, adding a certain quantity of solution of iron, after the stuff has been soaked in a solution of two ounces of alum, and an ounce of muriatic acid. If solution of galls be added, the colour becomes deeper.

Colours resembling that of brick, may be produced, by immersing silk in an anotta bath, after preparing it with a solution of galls mixed with a certain quantity of solution of iron. By the mixture of brasil, logwood, archil, and galls, and by a browning with sulphate of iron, a number of different shades are produced; but the whole of them have more or less

a tendency to fade, although their brightness is very pleasing to the eye.

III. Of Dyeing Silk with Mixtures of Black, &c.

408. A permanent violet colour may be given to thread and cotton, when scoured in the ordinary way, by preparing a mordant with two quarts of the bath of what is called the black cask, and four quarts of water for each pound of stuff, which is made to boil, and the scum is removed which forms on the surface, till it wholly disappears. The liquor is poured into a vat, and, when warm, four ounces of sulphate of copper and one ounce of nitre are dissolved in it. The skeins are left to soak in it for ten or twelve hours, wrung out, and dried. If it is required to produce a deep violet colour, two ounces of verdigrise must be added to the bath; and if the nitre be omitted, the colour becomes still deeper by galling the thread more or less, prior to its being put into the mordant. If the nitre be increased, and the sulphate of copper be diminished, the violet colour becomes more inclined to lilac. A number of various shades may be produced, by different modifications of the mordants employed.

409. Cotton is galled, dipped, and wrought in the common way, when different shades of marone colour are wanted. To the bath employed must be added more or less of the liquor of the black cask. The cotton is then washed in a bath mixed with verdigrise, next welded, and dyed to a fustic bath, to which a solution of soda and alum is sometimes added. When the cotton prepared in this manner has been thoroughly washed, it is next well maddered, dipped in a weak solution of sulphate of copper, and last of all in soap suds.

410. For some hazel and snuff colours, a browning is communicated to stuffs by means of soot, after the welding and madder bath, to which galls and fustic have been added; sometimes soot is mixed with this bath, and a browning is likewise imparted by means of a solution of sulphate of iron; and for browning colours, walnut peels are sometimes employed as a substitute for solutions of iron. For such wools as are designed for the manufacture of tapestry, they are very advantageous, because the colour is not changed into yellow by exposure to the air, as is the case in browning which is imparted by means of iron; but remains a considerable time without any sensible change. The hue is indeed rather dull; but its goodness and very moderate price are sufficient to recommend a more extensive use of it for grave colours, which in common stuffs are sometimes fashionable.

CHAP. III. Of Calico-printing.

411. THIS may be defined to be the art of communicating different colours to particular spots on the surface of cotton or linen cloth, while the rest of the stuff retains its original white colour.

The wonderful and truly ingenious art of calico-printing seems to have been first known in India, and for more than two centuries before the commencement of the Christian era. Although the Egyptians were well acquainted with this art in the days of Pliny, as he himself informs us, it can scarcely be doubted that they derived the knowledge of it from India, as that

country rather than Egypt, produced the colouring and other materials for carrying it on. If we consider its present improved state, the elegance of different patterns, the beauty and durability of the colours which can now be imparted to cotton or linen stuffs, and the dispatch with which the various operations of this art are conducted, we must be astonished at the rapidity of its improvements, when we recollect that it has been known in Europe for little more than a century. Perhaps no other art has risen to such perfection in so short a period.

412. Our readers will not expect that our account of this subject should be tedious or elaborate, since the artist is presumed to be already acquainted with the different processes which are employed in calico-printing; and to such as wish only for a general knowledge of the art, in a theoretical point of view, prolixity would be disagreeable.

413. The art of calico-printing consists in impregnating with a mordant, such parts of cotton or linen stuffs as are to have particular colours communicated to them, and then dyeing them in the usual manner with some colouring substance. Those parts of the cloth only which receive the mordant are intimately united with the colouring matter, although the whole surface must be more or less tinged; but the parts which have not received the mordant are restored to their original brightness by means of washing, and afterwards bleaching it upon the grass for some days, taking care to turn the wrong side towards the sun. If red stripes are to be communicated to a piece of white cotton cloth, those parts of its surface upon which stripes are intended to appear, are marked out by a pencil dipped in acetate of alumina; after which it is dyed with madder in the usual way. When it is first taken out of the dyeing vessel, its whole surface is red; but when it is washed and bleached, it resumes its original whiteness, the stripes only excepted, which, being impregnated with the acetate of alumina, remain red. By a similar process may yellow or any other stripes be fixed upon cotton or linen, by the substitution of quercitron bark, weld, &c. in the room of madder.

414. When different parts of the cloth are to receive different coloured stripes at the same time, different mordants must be employed. If stripes are delineated on its surface with the acetates of alumina and iron, and if it be then dyed with madder in the ordinary way, it will, after being washed and bleached as formerly directed, exhibit stripes of a red and brown colour. If the same mordants are employed, but quercitron bark used instead of madder, the stripes will then be yellow, and olive or drab.

415. The mordants known by the names of acetate of alumina and acetate of iron, which are made use of in calico-printing, may either be applied to stuffs with a pencil, as already mentioned, or still more expeditiously by means of blocks, on which the intended patterns are cut. Being designed only for particular parts of the surface of the cloth, great caution is necessary to prevent them from spreading to any part of it which is to remain white, and to prevent their interference when the application of more than one is required. Such a degree of consistence must of consequence be given to the mordants employed, as will prevent this disagreeable effect, which cannot fail to destroy the beauty and

and elegance of the print. If blocks are to be made use of, the mordants may be brought to a proper consistence by means of starch; but gum arabic must be mixed with them, when the pencil is to be employed. The thickness should not exceed what is absolutely necessary to prevent the mordants from spreading; because, if carried too far, the cotton is frequently not saturated with the mordant, in consequence of which the dye is but imperfectly communicated.

416. To distinguish those parts of the cloth which are impregnated with mordants, it is a common practice to give the mordants some particular tinge by which they may be known; and for this purpose printers commonly make use of the decoction of brasil wood. Dr Bancroft objects to this practice, because he is of opinion that the process of dyeing is impeded by the colouring matter of brasil wood. The affinity of the dye stuff for the mordant displaces the colouring matter of the brasil wood; and without such affinity it would be impossible to strike the colour. Some of the dye stuff to be employed afterwards is recommended by Dr Bancroft for colouring the mordant, who prohibits the use of a larger quantity than what is sufficient to render it distinguishable when an application of it is made to the cloth. Should too large a quantity be united with the mordant, a considerable proportion of the latter would be combined with colouring matter, by which means its affinity for the cloth would be diminished, and therefore a permanent colour could not be expected to result from such a partial combination.

417. It is necessary to dry the cloth completely after the application of the mordants, for which purpose artificial heat may be employed, which has a tendency to promote the separation of the acetous acid from its base, and assist its evaporation, and thus the combination of the mordant with the cloth will be facilitated.

418. When the cloth is thoroughly dried, it is customary to wash it with warm water and cow-dung, till every particle of the starch or gum arabic which had been employed to give a proper consistence to the mordants, and those parts of them which do not combine with the cloth, are entirely removed. The loose particles of the mordant are entangled by means of the cow-dung, and prevented from being attached to those parts of the cloth which are to remain white. After this, it must be completely rinsed in pure water.

419. Indigo, madder, quercitron bark, and weld, are the chief dyeing ingredients made use of by calico-printers; but the last of these is seldom used by the printers of this country, except for the purpose of communicating yellows of a delicate greenish shade. Quercitron bark, on account of its inferior price, and capacity of imparting colours equally good, as well as requiring a less degree of heat, is employed as a substitute. It is usual to apply indigo at once, either by means of the block or pencil, because it requires not the intervention of a mordant to fix it. This preparation is made by boiling together indigo, potash reduced to the caustic state by means of quicklime, and orpiment; afterwards thickening the solution with gum. Dr Bancroft recommends the use of coarse brown sugar as a substitute for orpiment, which operates as powerfully in the decomposition of the indigo, and in promo-

ting its solubility, answering at the same time all the purposes of gum.

420. When the cloth is thoroughly cleansed after it has been impregnated with the mordant, the dyeing process is conducted in the usual manner. As the whole of it receives a tinge of the dye, it must be completely washed and bleached for some days on the grass, as formerly mentioned, by which means the colour is entirely removed from those parts of the cotton not impregnated with the mordant, while all the other parts of it retain the colouring matter as powerfully as at first.

421. One of the most common colours imparted to Nankeen cotton prints is a species of nankeen yellow of different shades, and for the most part in stripes or spots. It is produced by means of a block on which is cut the intended pattern, rubbed over with acetate of iron brought to a proper consistence with gum or starch, and applied to the cotton; which, being dried and cleansed in the ordinary way, is immersed in a ley of potash. It is proper to observe, that the quantity of acetate of iron must be proportioned to the particular shade required.

422. In order to produce a yellow colour, the block is rubbed over with acetate of alumina; and the cloth, after being impregnated with this mordant, is dyed with quercitron bark in the common manner, and then bleached.

423. If madder be substituted for the quercitron bark, a red colour is given to cotton by the same process.

424. To communicate to stuffs the fine light blue colours which we frequently behold upon cotton, the block is rubbed over with a composition consisting partly of wax, by means of which all those parts of its surface are to remain white. It is next dyed in a cold vat of indigo, and when it is dried, the wax composition may be removed by the use of hot water.

425. Lilac and blackish brown colours are communicated by acetate of iron, proportioning the quantity to the particular shade required, and adding a little sumach for such shades as are to be very deep. The cotton is then dyed with madder, and bleached in the usual manner. Dove colour and drab are produced by means of acetate of iron and quercitron bark.

426. When a variety of different colours are to be made on the same print, a greater number of operations are unavoidably necessary. Upon each of the blocks to be employed is cut that particular part of the pattern which is to have one appropriate colour; and when these blocks are rubbed over with their respective mordants and thus applied to the cloth, the dyeing process is afterwards conducted in the ordinary manner. If, for example, three different blocks are to be made use of, the first rubbed over with acetate of alumina brought to a proper consistence, the second with acetate of iron, and the third with a composition of these two, the colours resulting, after the dyeing and bleaching processes are finished, will be the following.

It is proper to observe, that these are the results when quercitron bark is employed; but by the substitution of madder the following colours will be obtained.

When it is required to produce at the same time both those colours which are imparted by madder, and likewise by the use of quercitron bark, mordants are first applied for one part of the pattern, after which the cotton is dyed in a bath of madder, and then bleached. The rest of the mordants are then applied in a similar manner, after which the cotton is dyed with the quercitron bark, and bleached as before. The colours which the madder communicates are very little affected by the second dyeing, because the mordants by which their permanency is secured, are previously saturated. A new mordant may be applied to some of the colours resulting from the use of madder, by which means they receive a new durable colour from the bark. And by means of the indigo liquor other new colours may still be communicated after the last bleaching.

427. The following colours may be communicated to cotton, by means of the different processes which have been described.

Madder Dye.

Dark Dye.

Indigo Dye.

Thus may twelve different colours be communicated to the same print by these different processes.

428. If durable colours could be directly applied to cotton by means of the block or pencil, without the help of mordants, nothing could be conceived more simple than the art of calico-printing; but with the single exception of indigo, the communicating of permanent colours requires the process of dyeing. Yellow, indeed, which is a compound colour, and some others, may be communicated to cotton at once, by mixing together an infusion of quercitron bark and acetate of alumina, while the same mordant with a decoction of madder, imparts to it a red colour; but those which are produced in this way are far from being durable, since they are destroyed by washing, and sometimes even by exposure to the air.

429. But as it is not always practicable for calico-printers to avoid the application of colours in this manner, every endeavour to give them a greater degree of permanency becomes an object of importance. The following composition has been recommended for a yellow printing colour. Three pounds of alum, and three ounces of pure chalk are to be dissolved in a gallon of hot water, to which are to be added two pounds of acetate of lead. This mixture is to be occasionally

stirred for 24 or 36 hours, after which it is to remain at rest during 12 hours. The clear liquor is then to be poured off, and as much more hot water added to the residuum, as will, after being stirred and allowed to settle, amount to three quarts when added to the first quantity. Into a tinned copper vessel put six pounds, or at most a quantity not exceeding eight pounds, of quercitron bark sufficiently ground, and boil it for an hour in four or five gallons of clean soft water, adding afterwards a little more water if the bark is not properly covered. When the liquor is thoroughly boiled, let it be removed from the fire, and left to settle for half an hour, when the clear decoction is to be poured off through a fine sieve. Six quarts more of pure water are then to be put upon the same bark, and boiled for a quarter of an hour, being previously well stirred. When it has stood a sufficient time to settle, the clear liquor is to be strained off, and being mixed with the former, both are put into a shallow wide vessel to be evaporated by boiling, till the whole, in addition to the mordant already mentioned, and the gum or paste for bringing it to a proper consistence, does not exceed three gallons. It will be proper not to add the three quarts of aluminous mordant till the decoction has been cooled down almost to the natural heat of blood. Let gum arabic or gum senegal be taken for thickening, if the pencil is to be used, and starch or flour when blocks are to be employed.

430. If a pound of muriol-sulphate of tin be used as a substitute for the aluminous mordant in the composition described above, a mixture will be produced which is capable of imparting to cotton a very bright yellow, and considerably permanent.

431. A cinnamon colour possessed also of a sufficient degree of permanency may be given to cotton, by means of a mixture of sulphate of tin and a decoction of the quercitron bark.

432. If the decoctions of this bark and of logwood are boiled together, and proper quantities of sulphate of copper and verdigrise added to them, together with a small proportion of carbonate of potash, there results a compound which communicates to cotton a green colour. Although the expectations of Dr Bancroft were not fully answered by the trials which he made of this substance, he deemed his success sufficient to encourage him to a farther investigation of it.

433. A permanent drab colour may be given to cotton by means of acetate of iron mixed with a decoction of quercitron bark, and reduced to a proper consistence. This mixture will also produce an olive, if added to the olive colouring liquor already mentioned; and the colours may be made still more permanent, if a solution of iron in diluted nitric or muriatic acid be used as a substitute for iron liquor. They ought, however, to be used sparingly and with caution, that the texture of the cotton or linen to which they are applied may not be injured.

434. Dr Bancroft made a number of experiments with the decoction of quercitron bark, to ascertain its effects when combined with different metallic salts as mordants. The sulphate, nitrate, and muriate of zinc, with this decoction, yielded brownish yellow colours of different shades; but none of them were found sufficiently permanent when they were applied topically to linen or cotton. Mercury in the different acids pro-

duced with the decoction of bark different shades of brown or yellowish brown colours; but they did not prove more durable than the former. The nitro-muriate of platina with a proper proportion of decoction of quercitron bark, afforded, when topically applied to linen or cotton, strong full-bodied snuff colours, which were found sufficiently permanent, and capable of resisting the action of acids, and of the sun and air. Nitrate of silver with a decoction of the bark, when applied topically to linen or cotton, produced strong dark brown and cinnamon colours of considerable durability. Nitrate of lead with the same decoction gave, by topical application, a drab colour which was not less durable than the former. Nitrate of bismuth produced with the decoction of bark a very full and strong brownish yellow. This colour, however, is attended with the inconvenience of becoming almost black when exposed to the action of the alkaline sulphurets, sulphurated hydrogen gas, or even by the action of common soap. Muriate of bismuth with the decoction gives a drab colour: sulphate of the same metal affords a yellow; but these colours when applied to cotton or linen are not durable. Nitro-muriate of antimony produced with the decoction of bark something of a snuff colour, which applied to linen and cotton possess some degree of durability. Nitrate and muriate of cobalt with the quercitron bark gave different shades of brown; but these colours were extremely fugitive; they soon faded by exposure to the sun and air.

435. The art of calico-printing has been hitherto al-

most solely limited to linens and cottons. Many colouring matters have such an affinity for these stuffs that they readily enter into combination with them at the ordinary temperature of the atmosphere. This is also the case with silk, so that colouring matters might be applied topically to the latter by means of similar operations as to linen and cotton. Attempts, however, have been made to extend the process of topical dyeing or printing to woollen stuffs, and particularly those kinds known by the name of kerseymeres, which are employed after being prepared in this way for waistcoat patterns. When it is recollected that woollen stuffs when they are to be dyed generally must be exposed to a considerable degree of heat, it is easy to conceive that it will be difficult to communicate spots or figures by printing to woollen stuffs. The means by which this difficulty is obviated in those manufactories where this operation is conducted have been hitherto kept secret. The preparation of colouring matter, whether such as may be employed simply or require the use of mordants to fix them, will be easily understood from what we have already fully detailed in the course of this treatise. The application of the colours is made in the usual way; and it is said that, after the woollen stuffs are printed, they are wrapped up in two or three folds of thick paper, to prevent the access of moisture which might cause the colours to run, and exposed to the steam of boiling water for such a length of time as may be supposed necessary for the colouring matter to combine with the stuffs.

APPENDIX.

AFTER that part of the preceding treatise to which it properly belongs, was printed off, the following account of the Indian method of dyeing cotton cloth and cotton thread a red colour came under our notice. It was communicated to the Society for the Encouragement of Arts, &c. by Mr MacLachlan of Calcutta. The insertion of it may perhaps excite the curiosity of some of our countrymen into farther inquiries into the state of this as well as of other arts in India, where, from being long known and practised, many of them have arrived at a high degree of simplicity and perfection.

Directions for dyeing a bright Red, four yards of three-fourths broad Cotton Cloth.

1st. The cloth is to be well washed and dried, for the purpose of clearing it of lime and congee, or starch, generally used in India for bleaching and dressing cloths; then put into an earthen vessel, containing twelve ounces of chaya or red root, with a gallon of water, and allow it to boil a short time over the fire.

2d. The cloth being taken out, washed in clean water, and dried in the sun, is again put into a pot with one ounce of myrobalans, or galls coarsely powdered, and a gallon of clear water, and allowed to boil to one half: when cool, add to the mixture a quarter of a pint of buffalo's milk. The cloth being fully soaked in this, take it out, and dry it in the sun.

3d. Wash the cloth again in clear cold water, and

dry it in the sun; then immerse it into a gallon of water, a quarter of a pint of buffalo's milk, and a quarter of an ounce of the powdered galls. Soak well in this mixture, and dry in the sun. The cloth, at this stage of the process, feeling rough and hard, is to be rolled up and beated till it becomes soft.

4th. Infuse into six quarts of cold water, six ounces of red wood shavings, and allow it to remain so two days. On the third day boil it down to two-thirds the quantity, when the liquor will appear of a good bright red colour. To every quart of this, before it cools, add a quarter of an ounce of powdered alum; soak in it your cloth twice over, drying it between each time in the shade.

5th. After three days wash in clean water, and half dry in the sun; then immerse the cloth into five gallons of water, at about the temperature of 120° of Fahrenheit, adding 50 ounces of powdered chaya, and allowing the whole to boil for three hours; take the pot off the fire, but let the cloth remain in it until the liquor is perfectly cool; then wring it gently, and hang it up in the sun to dry.

6th. Mix intimately together, by hand, about a pint measure of fresh sheep's dung, with a gallon of cold water, in which soak the cloth thoroughly, and immediately take it out, and dry it in the sun.

7th. Wash the cloth well in clean water, and spread it out in the sun on a sand-bank (which in India is universally preferred to a grass-plat) for six hours, sprinkling

Me-ling it from time to time, as it dries, with clean water, for the purpose of finishing and perfecting the colour, which will be of a very fine bright red.

Directions for dyeing of a beautiful red, eight ounces of Cotton Thread.

7th. Repeat the process of yesterday, and dry the thread in the sun. Indian Method of Dyeing Red.

8th. The same process to be repeated.

9th. First repeat the ash-ley process three or four times, as under the operations 3, 4, and 5, and then prepare the following mixture: One pint of sheep-dung water; one gill of Gingelly oil; one pint and a half of ash-ley.—In this squeeze and roll the thread well, and dry it in the sun.

10th. Repeat the same process.

11th. Do. Do.

12th. Do. Do.

13th. Do. Do.

14th. Do. Do.

15th. Wash the thread in clean water, and squeeze and roll it in a cloth until almost dry; then put it into a vessel containing a gill of powdered chaya root, one pint by measure of cashan leaves, and ten pints of clear water; in this liquor squeeze and roll it about well, and allow it to remain so till next day.

16th. Wring the thread, and dry it in the sun, and repeat again the whole of the 15th process, leaving the thread to steep.

17th. Wring it well, dry it in the sun, and repeat the same process as the day before.

18th. Do. Do.

19th. Do. Do.

20th. Wring and dry it in the sun, and with the like quantity of chaya root in ten pints of water; boil the thread for three hours, and allow it to remain in the infusion until cold.

21st. Wash the thread well in clear water, dry it in the sun, and the whole process is completed.

INDEX.

O.
riv, communicated to cloth in ca-
lico-printing by acetate of
iron, No 426
and by the acetates of alumina
and iron combined, ib.
orange colour, how produced, 271
a compound of red and yel-
low, 366
various shades of, 394

P.
apillon, Mr, his process for dyeing
red, 238
enciling, colours for, 429
latiere, De la, his method of dye-
ing with Prussian blue, 322
ppy-red, how obtained, 214
process for dyeing wool yellow, 258
Prussian blue, how to dye with, 320
rpk, Tyrian, celebrated by the
ancients, 9
a compound of red and yel-
low, 366
liquor, preparation of, 9
stuffs, how prepared to re-
ceive, ib.
permanency of, 10
high price of, 11
worn by the Romans, 12
still used in dyeing, 13
found in snails, 15

Q.
ercitron bark, history of, 248
properties, 249
for dyeing wool
yellow, 257

R.
d substances for dyeing, 155—180
how to obtain different shades of, 195
madder, for cotton, 217
Grecian method of ob-
taining, 231
how improved in the
Levant, 237
how communicated in
calico-printing, 423
re-colour, how obtained, 216
rge, preparation of, 177
madder, for wool, 182
silk, 211
cotton and linen, 217
scarlet, 186
crimson, 208

S.
t, common, use of, in dyeing scar-
let, 196
Sidal wood, use of, in dyeing, 358
son blue, discovery of, 313
how to dy with, 314
green, process for dyeing wool, 369

Saxon green, process for dyeing silk, No 372
Scarlet, process for dyeing, 187
with cochineal, 197
process for boiling, 18
reddening, 188
how to give a bright red to,
a compound colour, 198
different shades of, 207
Shell-fish, producing a purple liquid,
found on the French coast,
method of catching, 14
ib.
Silk, how produced, 111
scoured, 112
treated when used white,
to extract the colouring
matter of, 113
alumed, 115
process for dyeing red, 211
with madder, 116
brazil wood, 212
cochineal, 213
weld, 268
how prepared for a blue colour,
Turkey blue, 301
black, 336
how galled, 338
softened, 340
raw, how to dye, 342
how dyed green, 371
purple, 389
a process for dyeing, 392
how dyed olive, 397
purple-violet, 406
brick colour, 407
how dyed with the black cask, 408
Soot, use of, in dyeing, 359
Stuffs to be dyed should be white, 51
Sumach, properties of, 356
use of, in dyeing, 362

T.
Terms for different shades of colour, 140
Tests for silks, 62
dye-stuffs, 63
Tin, oxide of, used in dyeing,
brought to London by
Kuster, 88
solution of, how prepared, 91
acetate of, recommended by
Haussman as a mordant, 93
Trefoil, leaves of, used in dyeing, 253

V.
Vats, how liable to accidents,
recovered, 293
preserved from putrefaction, 294
made with indigo, 298
for blue, recommended by
D'Apligny, 304
by Quatremere 306
on a large scale, 307
recommended by Bergman, 309

Vats recommended by Haussman, No 310
Velvet, how dyed black, 343
substances used instead of galls
for, 344
Verdigrise, use of, instead of tartar in
dyeing, 265

W.
Walnut-peels, for dyeing brown,
properties of, 351
preparation of, 352
Water, importance of, in dyeing,
different kinds how distin-
guished, 144
method of purifying, 141
tests for, 145
Weld, use of, in dyeing yellow,
properties of, 244
Willows, sweet, leaves of, used in dye-
ing, 252
Woad, use of, in dyeing blue, 291
Wool, different modes of dyeing,
structure of, 105
felting of, 106
how fulled, 107
importance of, 108
dyed red with madder, 182
process for dyeing, scarlet, 186
crimson, 208
yellow, 254
blue, 315
brown, 360
black, 330
green, 368
purple, 381
lilac, 382
orange, 395
coffee-co-
lour, 402
gray, 403
puce colour, 405
dyed purple with logwood,
process for obtaining, 384
Woollen stuffs, printing, 436

Y.
Yellow, substances employed for dye-
ing, 244
mordants necessary for a per-
manent, 243
with an orange shade,
bright golden, 259
greenish, 263
pale green, 264
process for a cheap,
how communicated in calico-
printing, 422
produced by acetate of alu-
mina, 426
composition for, in calico-
printing, 430
bright, 431

1. DYNAMICS is that branch of physico-mathematical science which includes the abstract doctrine of moving forces; that is, the necessary results of the relations of our thoughts concerning motion, the immediate causes of motion, and its changes.

2. Motion and its general properties are the first and principal object of mechanical philosophy. This science indeed presupposes the existence of motion; and we may consider it as universally admitted and recognized. With regard to the nature of motion, however, philosophers are greatly divided in opinion. The most obvious and simplest conception of motion is the successive application of the moving body to the different parts of indefinite space, which are considered as the place of the body. This idea of motion supposes a space whose parts are penetrable and immoveable; a doctrine directly contrary to that of the followers of Des Cartes, who regarded extension and matter as one and the same thing. To have a distinct idea of motion, it seems requisite to conceive two kinds of extension; the one, which is considered as impenetrable, and which constitutes what we properly call matter or body; the other, which being simply considered as extended, without taking any other property into account, is the measure of the distance of one body from another; and whose parts being supposed fixed and immoveable, enable us to judge of the rest or motion of bodies. We may therefore conceive bodies to be placed in indefinite space, whether real or supposed; and motion as a change in the state or condition of a body from one part of space to another. We must indeed consider motion as a state or condition of existence of a body, which would remain till it is changed by some cause; otherwise we could not have any idea of motion in the abstract. From the changes which we observe, we infer agency in nature; and in these changes we are to discover what we know of their causes.

3. In mechanical disquisitions, the simplest, and at the same time the most usual conception of space, is mere extension. We think only of the distance between two places. The path along which any body moves in passing from one place or point in space to another, is said figuratively to be the path described by that body. Space is considered by the geometer not only as having length but also breadth. In this case it is called a surface. But to have a more complete notion of the capaciousness of any portion of space, thickness, as well as length and breadth, is taken into consideration. This is called a solid space. By this, however, is meant only the susceptibility of measure in three ways, or extension of three dimensions. The adjacent parts or portions of space are distinguished from each other by their mutual boundaries. Contiguous portions of a line are separated by points; contiguous portions of a surface are separated by lines; and contiguous portions of a solid are separated by surfaces. The boundaries of any portions of space are not to be considered as parts of the contiguous portions. They must be conceived as common to both; as the places where

one portion ends and another begins. Space cannot be said to have any bounds or limits; it is therefore said to be infinite or unbounded.

4. Any portion of space may be considered in relation to its place or situation among other portions of space. This portion of space which is occupied by any body has been called the relative place of that body. But this portion of space may be considered as a determinate portion of infinite space; and this portion of infinite space occupied by any body has been called the absolute place of that body. Space, it is obvious, taken in this meaning, is immoveable; for it cannot be conceived that this identical portion of space can be removed from one place to another. The body which occupies that space may be removed, but the space remains. We have no perception of the absolute space of any object. This may be illustrated by the motion of the earth or that of a ship. A person in the cabin of a ship does not consider the table as changing its place while it remains fixed to the same spot on the deck. While a mountain is observed to retain the same situation among other objects, few persons think that it changes its place.

5. The idea of time is acquired by means of the power of memory in observing the succession of events. We conceive time as unbounded, continuous, homogeneous, unchangeable in the order of its parts, and infinitely divisible. It is conceived as a proper quantity made up of its own parts, and measured by them. But as the relation of the parts of time is unknown, the only means which we can employ to discover this relation, is to find out some other relation which is more obvious and better known, to which it may be compared. We shall then have discovered the simplest measure of time, if we compare in the simplest manner possible the relation of the parts of time with those relations which are most familiar. Hence it follows, that uniform motion is the simplest measure of time. For, on the one hand, the relation of the parts of a right line is that which is most easily conceived; and, on the other hand, there are no relations more susceptible of comparison with each other than equal relations. Now, in uniform motion, the relation of the parts of time is equal to that of the corresponding parts of the line described. Uniform motion then gives us at once, both the means of comparing the relation of the parts of time with that which is most obvious to our senses, and also of making this comparison in the simplest manner. In uniform motion, then, we find the simplest measure of time. It may be added, that the measure of time by uniform motion, is, independent of its simplicity, that which is the most natural to think of employing. Indeed as there is no relation with which we are acquainted more accurate than that of the parts of space; and, as in general, a motion, the law of which is given, would lead us to discover the relation of the parts of time, by the known analogy with that of the parts of space passed over, it is evident that such a motion would be the most accurate measure of time, and

and that which ought to be employed in preference to every other. In the actual measurement of time, some event which is imagined always to require an equal time for its accomplishment is selected; and this time is employed as a unit of time or duration, in the same way as a foot rule is employed as a measure of extension. During any observed operation, as often as this event is accomplished, so often is it supposed that the time of the operation contains this unit. While a heavy body falls 16 feet, a pendulum, 39½ inches long, makes one vibration; but it makes three vibrations, while the same body falls 144 feet. It is therefore said that the time of a body falling 144 feet, is thrice as great as the time of falling 16 feet.

6. Between the affections of time and space, there is an obvious analogy; and hence in most languages the same words are employed to express the affections of both. Thus it is that time may be represented by lines and measured by motion; since uniform motion is the simplest succession of events that can be conceived. In the order of situation all things are placed in space. In the order of succession all events happen in time.

Having made these preliminary observations, we propose to divide the following treatise into two parts. In the first, we shall consider motion in general. In the second, we shall treat of moving forces, or of dynamics.

PART I. OF MOTION.

BEFORE we enter on the consideration of the different kinds of motion, it may be necessary to notice some general circumstances regarding it.

7. It is impossible to conceive that any motion can be instantaneous. A moving body, in passing from the beginning to the end of its path, must pass through all the intermediate points. Now to suppose the motion along even the most minute portions of the space passed through instantaneous, is to suppose that the moving body is in every intervening point at the same instant; which is impossible.

8. Relative motion is the change of situation with regard to other objects. Absolute motion is the change of absolute place. These two motions, it may be observed, may not only be different, but even contrary to each other. From the relative motions of things which are the differences of their absolute motions, we cannot find out what are the absolute motions. It is often a subject of elaborate and intricate investigation to discover and determine the absolute motions, by means of observing the relative motions.

9. The affections or circumstances of motion are various with regard to its quantity and direction. That affection of motion by which the quantity is determined, is called velocity. The length of the line, which is uniformly described or passed over during some given portion or unit of time, is the proper measure of this velocity. When a ship sails six miles per hour, she describes a length of line equal to six miles in the space of a given portion or unit of time, namely the hour; and thus the velocity of the ship is said to be ascertained.

10. Another affection or circumstance of motion is its direction. This is the position of the straight line along which the motion is performed. The straight line which a body describes or tends to describe is called its direction. The motion is said to be in the direction AB, fig. 1. when the body moved passes along the line AB from A to B. In common language, it is not unusual to express the direction of motion in a manner quite the reverse of this. We have an instance of this kind in speaking of the direction of the winds. A current of air or wind which moves eastward is said to be a westerly wind, deriving its name from the point or quarter from which it proceeds, not as in other cases, and in strict expression, from the point to which it is directed.

11. Motions are of different kinds. They are either rectilinear, deflected, or curvilinear. In a rectilinear motion the direction remains unchanged during the whole time that the motion is continued, as when a body moves from A to B, fig. 1. In a deflected motion it is performed along two contiguous straight lines in succession. Thus if a body moves from A to B, fig. 2. and at the point B its direction is changed from that of AD to BC; this change has been called deflection, the quantity of which may be measured either by the angle DBC, or by a line DC drawn from the point D to which the body would have arrived in the same time, if its motion had remained unchanged, in which it has actually reached the point C. When a body in moving along describes the sides of a polygon, the deflections are repeated, with the intervention of undeflected motions. In curvilinear motion the deviation and deflection are supposed to be continual. Continual deflection therefore constitutes curvilinear motion. Let the motion be performed along a curve line ABCDE (fig. 3.), the direction is continually changing. When the body is in the point C the direction is that of the tangent CF; because this direction alone lies between any pair of polygonal directions, such as CE and Ca, or CB and CD, however near the points A and E, or B and D, are taken to the point C.

12. Motions have been divided into uniform motions, variable, compound, and curvilinear. These we shall consider separately in the following sections.

SECT. I. Of Uniform Motion.

13. It is of great importance in mechanical disquisitions, to have the characters of uniform or unchanged motion fixed. For in our conceptions of motion in general, in which we do not turn the attention to its alterations, the motion is supposed to be equal and rectilinear. By the deviations from such motion only can we determine the marks and measures of all changes; and hence also we are to obtain the measures of all changing causes, or in other words of the mechanical powers of nature.

PROPOSITION I.

14. In uniform motions, the velocities are in the proportions of the spaces described in the same or in equal times.

times; or as it is sometimes expressed, The velocities are proportional to the spaces described in equal times.

The spaces described are the measures of the velocities, and things are proportional to their measures. Let the spaces described in the time $T$, be represented by $S$ and $s$, and let the velocities be represented by $V$ and $v$. We have the analogy $V\; :\; v\; =\; S\; :\; s$. Or, as it may be expressed by the proportional equation, $v\; =\; s$.

15. In uniform motions with equal velocities, the times are in the proportion of the spaces described during their currency. Or, as it is also expressed, The times are proportional to the spaces described with equal velocities.

For in uniform motions, equal spaces are described in equal times. The successive portions of time therefore are equal, in which equal spaces are described in succession; and the sums of the equal times must be proportional to the corresponding sums of equal spaces. In all cases, therefore, which are susceptible of being represented by numbers, this proposition is evident. And it may be extended to all other cases, in a way similar to that in which Euclid has demonstrated that triangles of equal bases are in the proportion of their bases.

16. As proportion can only take place between quantities of the same kind, all that is to be understood by the expressions in the above propositions, which are far from being accurate, is, that the proportions of the velocities and the times are the same with the proportions of the spaces. For as space and time are quantities of a different nature, it is evident that we cannot divide space by time. Thus when it is said that the velocities are as the spaces divided by the times, it is an abridged mode of expression, which signifies that the velocities are as the relations of the spaces to the same common measure, divided by the relations of the times to the same measure. Thus, for example, if we take a foot for the measure of the spaces, and a minute for the measure of the times, the velocities of two bodies which move uniformly, are to each other as the number of feet described, divided by the number of minutes which the bodies require to describe the portion of space passed through, and not as the feet divided by the same minutes.

17. Hence it is that uniform motion is universally employed as a measure of time. But it is often difficult to find out whether the motion which is proposed for the measure of time be perfectly uniform. What then are the means to ascertain this? To this it may be answered that there is no motion which is not uniform, the law of which we can determine exactly; so that this difficulty only proves that we cannot ascertain the relation of the parts of time with mathematical precision; but it does not follow that uniform motion from its nature may not be the first and simplest measure. And having no strictly accurate measure of time, we endeavour to discover the measure which comes nearest in the motions which approach nearest to uniformity.

18. There are three ways by which it may be ascertained that a motion is nearly uniform. 1. When the moving body describes equal spaces in times which we nearly judge to be equal; and we can determine that the

times are equal, after having observed from repeated experience that similar events take place in the same times. Thus we conclude that the times which the same clypeus requires to be emptied are equal; so also the times in which the same quantity of sand runs in the sandglass; the times in which the shadow moves over the same space on the sun-dial; the times of the same number of vibrations of a pendulum of the same length; and the times of the revolution of the heavenly bodies through the same spaces—are equal. If then it is found by observation that a body during the same time passes over equal spaces, we conclude that the motion is uniform. 2. Another method of ascertaining how far any motion is uniform, is when the effect of the accelerating or retarding cause, if such operate, is imperceptible. It is by combining these two methods that we conclude the motion of the earth round its axis to be uniform; and this inference is not only not opposed by any of the celestial phenomena, but seems to be in perfect accord with them. 3. By a third method of determining the uniformity of any motion, we compare it with others; and when the same law is observed in both the one and the other, we may conclude that the motion compared is uniform. Thus if several bodies move at such a rate that the spaces described in the same time are always to each other, either precisely or very nearly so, in the same ratio, the motion of these bodies, we conclude, is either precisely, or at least very nearly uniform. For if a body $A$ which moves uniformly passes through the space $E$ during the time $T$ taken at pleasure, and another body $B$ also moving uniformly, passes through the space $e$ during the same time $T$, the relation of the spaces $E,\; e$ will be always the same, whether the two bodies have begun to move in the same or in different instants; and it is only to uniform motion that this property belongs. Wherefore if we divide the time into parts, whether equal or unequal, and if it be observed that the spaces passed through by two bodies during one part of the time, are always in the same relation, the greater the number the parts of the time taken, the more there is reason to conclude that the motion of each body is uniform. None of these methods, it has been observed, possesses geometrical precision; but they are sufficient, especially when they are repeated and taken together, to afford a satisfactory conclusion, if not with regard to absolute uniformity of motion, at least with regard to a near approximation to uniform motion.

19. In uniform motions, the spaces described are in the compound ratio of the velocities and the ratio of the times. This proposition is frequently expressed otherwise thus; The spaces described with a uniform motion are proportional to the products of the times and the velocities; Or otherwise thus; The spaces described with a uniform motion are proportional to the rectangles of the times and the velocities.

For let $S$ be the space described with the velocity $V$, in the time $T$, and let $s$ be the space described with the velocity $v$, in the time $t$. Let another space $Z$ be described in the time $T$ with the velocity $v$.

Then by proposition 1st we have $S\; :\; Z\; =\; V\; :\; v$,
And by proposition 2d $Z\; :\; s\; =\; T\; :\; t$.

By composition of ratios therefore (or by VI. 23. Euclid), we have $V\; \backslash times\; T\; :\; v\; \backslash times\; t\; =\; S\; \backslash times\; Z\; :\; s\; \backslash times\; Z$; that is, $S\; :\; s$.

The above are all equivalent expressions which are demonstrated by the same composition of ratios. The products or rectangles of the times and velocities, are the products of numbers which are as the times, multiplied by numbers which are as the velocities; or the rectangles whose bases are as the times, and whose heights are as the velocities.

COROLLARY.

20. If the spaces described in two uniform motions be equal, the velocities are in the reciprocal proportion of the times.

For in this case the products $VT$ and $vt$ are equal, and therefore $V\; :\; v\; =\; t\; :\; T$, or $V\; :\; v\; =\; \backslash frac\{1\}\{T\}\; :\; \backslash frac\{1\}\{t\}$. Or, because the rectangles $AC$, $DF$ (fig. 4.) are in this case equal, we have (by VI. 14. Euclid) $AB\; :\; BF\; =\; BD\; :\; BC$, that is $V\; :\; v\; =\; t\; :\; T$.

PROP. IV.

21. In uniform motions, the times are as the spaces, directly, and as the velocities, inversely.

For by Prop. III. $S\; :\; s\; =\; VT\; :\; vt$;

Therefore, $Svt\; =\; sVT$;

And, $T\; :\; t\; =\; Sv\; :\; sV$.

Or, $T\; :\; t\; =\; \backslash frac\{S\}\{V\}\; :\; \backslash frac\{s\}\{v\}$;

And, $t\; =\; \backslash frac\{S\}\{V\}\; \backslash cdot\; \backslash frac\{v\}\{s\}$.

PROP. V.

22. In uniform motions, the velocities are as the spaces, directly, and as the times, inversely.

For by Prop. IV. $Svt\; =\; sVT$;

Therefore $V\; :\; v\; =\; S\; :\; s\; =\; T\; :\; t$.

Or, $V\; :\; v\; =\; \backslash frac\{S\}\{T\}\; :\; \backslash frac\{s\}\{t\}$.

And, $v\; =\; \backslash frac\{S\}\{T\}\; \backslash cdot\; \backslash frac\{t\}\{s\}$.

23. The values of the results of these propositions are not changed by the absolute magnitudes of the space and time, if both are changed in the same ratio.

The value of $\backslash frac\{12\; \backslash text\{\; feet\}\}\{24\text{'}\text{'}\}$, or of $\backslash frac\{8\; \backslash text\{\; feet\}\}\{16\text{'}\text{'}\}$, is the same with half a foot per second.

Therefore, if $s\text{'}$ be the expression of an extremely minute portion of space described with this velocity in the small portion of time $t\text{'}$, the velocity $v$ is still accurately expressed by $\backslash frac\{s\text{'}\}\{t\text{'}\}$.

And the accurate expression of the time $t\text{'}$ is $\backslash frac\{s\text{'}\}\{v\}$.

SECT. II. Of Variable Motions.

24. In observing the phenomena of nature, it rarely happens that the motions to which our attention is directed are perfectly uniform. These motions, however,

we distinctly conceive, with all their properties; and it is obviously of the utmost importance that all the deviations from uniform motions be clearly understood; because these deviations afford the only marks and measures of the variations, and therefore of the causes which produce these changes.

25. When a body continues to move uniformly in the same direction, its motion, or circumstances with respect to motion, have suffered no change. The condition of that body, therefore, must be allowed to be the same in any two portions of its path, whatever the distance of these portions may be. And because a change of place is involved in the very conception of motion, the difference of place does not imply any change. Two bodies, therefore, moving with the same velocity in this path, or in two lines parallel to it, their condition in respect of motion must be allowed to be the same. Their direction is the same, and their rate of motion is the same. The velocity, therefore, and direction of a body, are the only circumstances which seem to enter into our conception of the state of a body, in respect of motion. Changes either in the velocity, or in the direction, or in both of these circumstances, include all the changes of which this condition is susceptible. Let us now consider the first of these changes, namely, changes of velocity.

Of Accelerated and Retarded Motions.

26. It has been ascertained by experiment and observation, that a stone in falling is carried downward with greater rapidity in every successive period of its fall. During the first second it falls 16 feet; during the next, it falls 48 feet; during the third, it falls 80 feet; during the fourth, it falls 112 feet; continuing to fall, during every successive second 32 feet more than during the preceding second. A body moving in this manner is said to have an accelerated motion. But if a body be projected perpendicularly upwards, the very reverse takes place in the circumstances of its motion. It is observed to rise with a motion which is continually retarded. These bodies therefore are conceived to be in every succeeding instant in different states of motion. The velocity of the falling body is conceived to be greater in a certain instant than in any preceding instant; as, for example, when it has fallen 144 feet, its velocity is said to be thrice as great as when it has fallen only 16 feet. But this inference, it is evident, cannot be made directly by comparing the spaces described in the following moments; for in these it falls 112 and 48 feet; or by comparing the spaces immediately preceding; for in these the body fell 80 and 16 feet. But in this expression it is supposed that the variable condition of a body, called its velocity, is in every instant susceptible of any accurate measure; and yet in no moment, however short, does the body describe uniformly a space which can be taken as the measure of its velocity at the beginning of that moment; because the space described in any moment is too great for measuring the velocity at the beginning of the moment, and too small for the measure of its velocity at the end of it. Till however such a measure is obtained, the mechanical condition of the body is not known.

27. But in a continually accelerated motion, no such measure can be obtained. No space is described

Variable Motion. ed in an instant: for this requires time. In that instant, however, the body possesses what has been called a potential velocity, that is, a certain tendency or determination, which remaining unchanged, causes it to describe a certain space uniformly during some assignable portion of time. At another instant it has another determination, by which, if it be not changed, another space will be uniformly described in an equal portion of time. Now it is in the difference of those two determinations that its difference of mechanical condition consists. The marks and measures of these determinations are known from the spaces which would be uniformly described. These therefore must be carefully investigated as the measures of the velocities; and the proportions of these spaces are to be taken as the proportions of the velocities.

28. Let the straight line ABD (fig. 5.) be described with a motion continually varied; it is required to determine the proportion of the velocity in the point A, to the velocity in any other point C.

Let the right line $a\; b\; d$, represent the time of this motion along the path AD, so that the points $a,\; b,\; c,\; d$, may denote the instants of the moving body being in A, B, C, D, and the proportions $a\; b,\; b\; c,\; c\; d$, may express the times of describing AB, BC, CD, that is, may be in the proportion of those times; and let $a\; e$, perpendicular to $a\; d$, express the velocity of the moving body at the instant $a$, or in the point A. Let $e\; g\; h$ be a line, so related to the axis $a\; d$, that the areas $a\; b\; f\; c,\; b\; c\; g\; f,\; c\; d\; h\; g$, comprehended between the ordinates $a\; e,\; b\; f,\; c\; g,\; d\; h$, all perpendicular to $a\; d$, may be proportional to the spaces AB, BC, CD, described in the times $a\; b,\; b\; c,\; c\; d$, and let this relation hold in every part of the figure. Then the velocity in A is to the velocity in B, or C, or D, as $a\; e$ to $b\; f$, or $c\; g$, or $d\; h$. Or it may be expressed in other words, If the abscissa $a\; d$, of a curve $e\; g\; h$, be proportional to the time of any motion, and the areas interrupted by parallel ordinates be proportional to the spaces described, the velocities are proportional to those ordinates.

Make $b\; c$ and $c\; d$ equal, so as to represent very small and equal moments of time, and make $p\; a$ equal to one of them. Complete the rectangle $p\; a\; e\; q$. This will represent the space uniformly described in the moment $p\; a$, with the velocity $a\; e$ (Propos. 3.). Let PA be that portion of space thus uniformly described in the moment $p\; a$. Let the lines $i\; m,\; k\; n$, parallel to $a\; d$, making the rectangles $b\; c\; m\; i$, and $c\; d\; n\; k$, respectively equal to the areas $b\; c\; g\; f$, and $c\; d\; h\; g$. If the motions along the spaces PA and BC had been uniform, the velocities would have been proportional to the spaces described (Propos. 1.) because the times $p\; a$, and $b\; c$ are equal. That is, the velocity in A would be to the velocity in C, as the rectangle $p\; a\; e\; q$ to the area $b\; c\; g\; f$, that is, as $p\; a\; e\; q$ to $b\; c\; m\; i$, that is, as the base $a\; e$ to the base $c\; m$, because the altitudes $p\; a$ and $b\; c$ are equal.

But the motion along the line BC is not represented as uniform; for the line $f\; g\; h$ diverges from the axis $b\; d$, the ordinate $c\; g$ being greater than $b\; f$. And therefore the spaces measured by these areas increase faster than the times; and thus the figure represents an accelerated motion. Therefore the velocity with which

BC would be uniformly described during the moment $b\; c$, is less than the velocity at the end of that moment, that is, at the instant $c$, or in the point C of the path; and therefore it must be represented and measured by a line greater than $c\; m$.

In the same manner it is proved that $c\; k$ represents and measures the velocity with which CD would be uniformly described during the moment $c\; d$. And therefore, since the motion along CD is also accelerated, the velocity at the beginning of that moment is less than the velocity with which it would be uniformly described in the same time, and must be represented by a line less than $c\; k$.

Therefore the velocity in A, is to that in C, in a less ratio than that of $a\; e$ to $c\; m$, but in a greater ratio than that of $a\; e$ to $c\; k$. But in this case, as long as the instant $b$ is prior, and $d$ posterior, to the instant $c$, $c\; m$ is less, and $c\; k$ is greater, than $c\; g$. Therefore the velocity in A is to that in C in a ratio that is greater than any ratio less than that of $a\; e$ to $c\; g$. And, consequently the velocity in A is to that in C, as $a\; e$ to $c\; g$.

It may be proved in the same way, with respect to the velocity in any other point D; and therefore the proposition may be considered as demonstrated. And had the motion along BCD, instead of being accelerated as in this case, been retarded, the same reasoning would still apply.

29. Cor. 1. The velocities in different points of the path AD, are in the ultimate ratio of the spaces described in equal small moments of time. Draw $g\; o$ parallel to $a\; d$. Then the velocity in the instant $a$, is to that in the instant $c$, as $a\; e$ to $c\; g$, that is, as the rectangle $p\; e$ to the rectangle $c\; o$, that is, as $p\; a\; e\; q$ to $c\; d\; h\; g$, nearly. As the moments are diminished, the difference $g\; o\; h$ between the rectangles $c\; g\; o\; d$ and $c\; g\; h\; d$, diminishes nearly in the duplicate ratio of the moment. If then the moment be taken $\backslash frac\{1\}\{2\}$, $\backslash frac\{1\}\{4\}$, or $\backslash frac\{1\}\{8\}$ of $c\; d$, the error $g\; o\; h$ is diminished to $\backslash frac\{1\}\{4\}$, $\backslash frac\{1\}\{8\}$, or $\backslash frac\{1\}\{16\}$: the corollary is now manifest; for the ultimate ratio of $c\; g\; o\; d$ to $c\; g\; h\; d$ is the ratio of equality. That is, the velocity in A is to that in C, in the ultimate ratio of PA to BC described in equal small moments.

There are many cases in which the spaces described in very small moments can be measured, and yet the ultimate ratio cannot be ascertained. These spaces must then be taken as measures of the velocity. And by taking half the sum of the spaces BC and CD, for the measure of the velocity in the point C, the error is almost reduced to nothing.

30. Cor. 2. The momentary increments of the spaces described, are in the compound ratio of the velocities, and the ultimate ratio of the moments.

For the increments PA, CD are as the rectangles $p\; e$ and $c\; o$ ultimately, (Propos. 3.); and these are in the compound ratio of the base $a\; e$ to the base $c\; o$, and the ultimate ratio of the altitude $p\; a$, to the altitude $c\; d$. This may be expressed by the proportional equation $\backslash dot\{s\}\; \backslash dot\{t\}\; =\; v\; t$.

31. Consequently $v\; =\; \backslash frac\{\backslash dot\{s\}\}\{t\}$; and $\backslash dot\{t\}\; =\; \backslash frac\{\backslash dot\{s\}\}\{v\}$. The equation $\backslash dot\{s\}\; =\; v\; t$.

Variable motions. $\backslash dot\{s\}\; =\; \backslash dot\{v\}t$, $v\; =\; \backslash frac\{\backslash dot\{s\}\}\{t\}$, and $\backslash dot\{t\}\; =\; \backslash frac\{\backslash dot\{s\}\}\{v\}$ seem to be the same with those in (23), but there the same space $s\text{'}$ was described uniformly, and the equations were absolute. In 32 and 35, $s$ does not represent a space uniformly described. But $\backslash dot\{S\}$: $\backslash dot\{s\}$ expresses the ultimate ratio of $S\text{'}$ to $s\text{'}$ when they are diminished continually, and vanish together. Therefore the meaning of the equation $\backslash dot\{s\}\; =\; \backslash dot\{v\}t$ is, that the ultimate ratio of $S\text{'}$ to $s\text{'}$, is the same with that of $VT\text{'}$ to $vt\text{'}$.

32. The following is the converse of this proposition.

If the abscissa $ad$ of the line $efh$, represent the time of a motion along the line $ABD$, and if the ordinates be as the velocities in the points then the areas are as the spaces described. This is proved by an indirect demonstration, thus:

For if the spaces $AB,\; AD$, be not proportional to the areas $abfe,\; adhe$, they must be proportional to some other, $abfe,\; adhe$, of another line $efh$, passing through $e$. Assuming this to be true, then (by Propos. 6.) the velocity in $A$ is to that in $B$, as $ae$ to $bf$. Therefore $ae\; :\; bf\; =\; ae\; :\; bf$, which is absurd.

33. The relation between the space described and the time which elapses is the only immediate observation to be made on these variable motions. By means of the foregoing proposition, the mechanical condition of the body, or rather the effect and measure of this condition, denominated velocity, is inferred. The same inference is made in another way. Sir Isaac Newton often represents the uniform lapse of time by the uniform increase of an area during the motion along the line taken for the abscissa. The velocities or determinations to motion in the different points of this line, are inversely proportional to the ordinates of the curve which bounds this area.

Along the straight line $AD$, (fig. 6.) let a point move with a motion any how continually changed, and let the curve line $LIH$ be so related to $AD$, that the area $LICB$ is to the area $LHDB$ as the time of moving along $BC$ to that of moving along $BD$. Let this be true in every point of the line $AD$. Let $Cc,\; Dd$, be two very small spaces described in equal times, draw the ordinate $ic,\; hd$, and draw $ik,\; hl$ perpendicular to $IC,\; HD$.

The areas $ICci$ and $HDdh$ must be equal, because they represent equal moments of time. It is evident also, that as the spaces $Cc$ and $Dd$ are continually diminished, the ratio of $ICci$ and $HDdh$ to the rectangles $kCci$ and $lDdh$ continually approximates to that of equality, and that the ratio of equality is the limiting or ultimate ratio. Since, therefore, the areas $ICci$ and $HDdh$ are equal, the rectangles $kCci$ and $lDdh$ are ultimately in the ratio of equality. Therefore their bases $ic$ and $hd$ are inversely as their altitudes $Cc$ and $Dd$, that is, $ic\; :\; hd\; =\; Dd\; :\; Cc$. But as $Cc$ and $Dd$ are described in equal times, they are ultimately as the velocities in $c$ and $d$ (29). Therefore $ic$ and $hd$, are inversely as the velocities in $c$ and $d$. And as the same reasoning may be applied to every point of the abscissa, the proposition is demonstrated.

34. In all cases, then, in which the relation between the spaces described, and the times elapsed can be discovered by observation, we discover the mechanical

condition of the moving body, or its velocity. But in the practical application of these conclusions, recourse must always be had to arithmetical conclusions; and the indications of these are the algebraic symbols of geometrical reasonings. Thus any ordinate $eg$ (fig. 5.) is represented by $v$, and the portion $cd$ of the abscissa by $t$, and the area $cdhg$, or its equal, the rectangle $cdog$, by $vt$. This rectangle then being as the corresponding portion $CD$ of the line of motion, and $CD$ being represented by $\backslash dot\{s\}$, we have the equation $\backslash dot\{s\}\; =\; vt$.

35. The mathematical consequences of these representations may now be assumed to be true; and therefore $\backslash dot\{t\}\; =\; \backslash frac\{\backslash dot\{s\}\}\{v\}$, as in (23). Algebraic symbols being the representations of arithmetical operations, they represent more remotely the operations of geometry, and only because the area of a rectangle is analogous to the product of numbers which are proportional to its sides. The symbol $\backslash int\; vt$ being used to represent the sum of all these rectangles, expresses the whole area $adh$, as well as the whole line of motion $AD$; and the equation may be stated $s\; =\; \backslash int\; vt$. In like manner $\backslash int\; \backslash frac\{\backslash dot\{s\}\}\{v\}$ will be equivalent to $\backslash int\; t$, that is, to $t$, and will express the whole time $ad$. It is plain too that $\backslash frac\{\backslash dot\{s\}\}\{v\}$ represents the

ordinate $DH$ of the line $LKIH$ (fig. 6.) because any portion $Dd$ of its abscissa, is properly represented by $s$, and the ordinates are reciprocally proportional to the velocities, that is, are proportional to the quotients of some constant number divided by the velocities, and therefore to $\backslash frac\{1\}\{v\}$. And as $\backslash dot\{t\}$ is represented by the rectangle $kCci$, which is also represented by $\backslash dot\{s\}\; \backslash times\; \backslash frac\{1\}\{v\}$, we have $\backslash dot\{t\}\; =\; \backslash frac\{\backslash dot\{s\}\}\{v\}$, and $t\; =\; \backslash int\; \backslash frac\{\backslash dot\{s\}\}\{v\}$, as above.

36. In one case of varied motion, when the line $efgh$ (fig. 5.) is a straight line, the characters are very particular and useful. Let this case of motion be represented along the line $AD$ (fig. 7.), and let $pa,\; bc,\; cd$, represent equal moments of time, in which the moving body describes $PA,\; BC,\; CD$; and draw $fm,\; gn,\; es$, parallel to the abscissa $ad$. Now it is evident that $mg$ and $nh$ are equal, or that equal increments of velocity are acquired in equal times; $eq,\; er,\; es$, are also proportional to $qf,\; rg,\; sh$, and therefore the increments $qf,\; rg,\; sh$, of velocity are proportional to the times $ab,\; ac,\; ad$, in which they are acquired. This motion may very properly be denominated uniformly accelerated; for here the velocity increases in the same ratio with the times, and equal increments are acquired in equal times. If the line $eh$ cut the abscissa in $v$, it will represent a motion uniformly accelerated from rest during the time $vd$, and thus exhibit the relations between the spaces, velocities, and times in such motions.

Hence it follows from this mode of expressing these relations,

Variable Motions. relations, that in motions uniformly accelerated from a state of rest, the acquired velocities are proportional to the times from the beginning of the motion. For $a\; e$, $b\; f$, $c\; g$, $d\; h$, represent the velocities gained during the times $v\; a$, $v\; b$, $v\; c$, $v\; d$, and are in the same proportion with those lines.

37.—1. Also, the momentary increments of velocity, are as the moments in which they are acquired.

2. Also, the spaces described from the beginning of the motion, are as the squares of the times.

3. Also, the increments of the spaces are as the increments of the squares of the times; reckoning from the beginning of the motion.

4. Also, the spaces described from the beginning of the motion, are as the squares of the acquired velocities.

5. Also, the momentary increments of the spaces are as the momentary increments of the squares of the velocities.

6. Also, the space described during any portion of time by a motion uniformly accelerated from rest, is one half of the space uniformly described in the same time with the final velocity of the accelerated motion.

7. And the space described during any portion of the time of the accelerated motion, is equal to that which would be described in the same time with the mean between the velocities at the beginning and end of this portion of time.

In the investigation of all other varied motions, the properties of uniformly accelerated motion stated above, will be found extremely useful, and especially in cases where approximation only can be easily obtained. But for the fuller illustration of these properties the reader is referred to Robison's Elements of Mechanical Philosophy, p. 38.

38. Supposing the acceleration to be always the same, we conceive of this constancy, that in equal times there are equal increments of velocity; and therefore that the augmentations of velocity are proportional to the times in which they are required. That acceleration then, according to this supposition, must be accounted double, or triple, &c. where the velocity acquired is double or triple. And, acceleration being considered as a measurable quantity, the augmentation of velocity uniformly acquired in any given time is its measure.

COROLLARY.

39. Therefore accelerations are proportional to the spaces described in equal times, with motions uniformly accelerated from a state of rest. For in this case the spaces are the halves of what would be uniformly described in the same time with the acquired final velocities, and are therefore proportional to these velocities, or to the accelerations, since the velocities were acquired in equal times.

40. It is then said that accelerations are proportional to the increments of velocity uniformly acquired, directly, and to the times in which they are acquired, inversely.

This relation between acceleration, velocity, and time, is also true, in uniformly accelerated motion, with respect to all momentary changes of velocity, as well as

to those cases of motion passing through all degrees of velocity from nothing to the final magnitude $v$. For the velocity increasing at the same rate with the time, we have $v\; :\; v\text{'}\; =\; t\; :\; t\text{'}$; and $v\text{'}$ and $t\text{'}$ express the simultaneous increments of velocity and time.

41. But if the augmentation of velocity be the measure of the acceleration, and therefore proportional to it, and if in uniformly accelerated motions, the velocity increases at the same rate with the times, the increments of velocity are as the accelerations and as the times jointly. Hence the proportional equation

42. It appears from (39.), that when the velocity has uniformly increased from nothing, the spaces described in equal times are proper measures of acceleration. And in (37.—3.) uniformly accelerated motions, the spaces are as the squares of the times. Therefore, when the acceleration continues the same, the fraction $\backslash frac\{s\}\{t^2\}$ must also remain of the same value, and $a$

is proportional to $\backslash frac\{s\}\{t^2\}$. And therefore, accelerations are proportional to the spaces described with a motion uniformly accelerated from rest, directly, and to the squares of the times inversely.

43. And since $a\; =\; \backslash frac\{v\}\{t\}$, we have $a\; =\; \backslash frac\{v\}\{t\}$; but $v\; =\; \backslash frac\{s\}\{t\}$, therefore $a\; =\; \backslash frac\{v^2\}\{s\}$. Therefore we have another measure of acceleration, viz. Accelerations are directly as the squares of the velocities, and inversely as the spaces along which the velocities are uniformly augmented.

44. But when the spaces are equal, we have $a\; =\; \backslash frac\{v^2\}\{s\}$, and in uniformly accelerated motions, that is, when $a$ remains constant, the space being increased in any proportion, $v^2$ increases in the same proportion; it follows that $v^2$ increases in the proportion both of the acceleration and of the space. And therefore, in general, we have $v^2\; =\; a\; s$. And, as in 41, 42, we shall have $v^2\; =\; a\; S$, and $V^2\; -\; v^2\; =\; a\; S\; -\; a\; s$, or $\backslash frac\{V^2\; -\; v^2\}\{S\; -\; s\}$, which may be thus expressed, $\backslash frac\{V^2\; -\; v^2\}\{S\; -\; s\}\; =\; a$, that is, in a motion uniformly accelerated, the momentary change of the square of the velocity is proportional to the acceleration and to the space jointly. Thus it appears, that the acceleration continued during a given time $t$, or $t\text{'}$, produces a certain augmentation of the simple velocity; but the acceleration continued along a given space $s$ or $S\text{'}$, produces a certain augmentation of the square of the velocity.

45. But accelerations which are constant and uniform, and such as have been considered, are very rare in the phenomena of nature. They are as variable as velocities, and therefore it is not less difficult to discover their actual measure. By changes of velocity only we obtain any knowledge of the changing cause. From the continual acceleration of a falling body we learn, that the same power which makes it press on the hand, presses it downward, as it falls through the air; and whatever be the rapidity of its descent, it is from observing that it acquires equal increments of velocity in equal times, that we know the downward pressure to be the same.

In the same way that we obtain measures of a velocity which is continually varying, we may obtain accurate measures of a similarly varying acceleration. A line may be conceived to increase along with the velocity, and at the same rate; and this rate of increase of velocity is what is called acceleration, in the same way as the rate at which the line increases, is what is called velocity. If, then, we consider the areas (fig. 5.) or the line AD, as representing a velocity; the ordinates to the line $egh$, which were demonstrated to be proportional to the rate of variation of the area, will be proportional to the variation of the velocity, that is, to the acceleration.

46. If the abscissa $a$ of a curve line $egh$ represent the time of a motion, and if the areas $abfe$, $acge$, $adh$, &c. are proportioned to the velocities at the instants $b$, $c$, $d$, &c. then the ordinates $ae$, $bf$, $cg$, $dh$, &c. are proportional to the acceleration at the instants $a$, $b$, $c$, $d$, &c.

By substituting the word acceleration for the word velocity, the same demonstration may be applied here as in Prop. 6. (28.). From this proposition may be deduced some corollaries of practical use in mechanical discussions.

47. The momentary increments of velocity are as the accelerations, and as the moments jointly.

For the increment of velocity in the moment $cd$ is accurately represented by the area $cdhg$, or by the rectangle $cdnk$; and $cd$ accurately represents the moment. Also, the ultimate ratio of $ck$ to such another ordinate $bi$, is the ratio of $cg$ to $bf$; that is, the ratio of the acceleration in the instant $c$ to that in the instant $b$. And therefore the increment of velocity during the moment $pa$ is to that during the moment $cd$ as $pa\; \backslash times\; a$ to $cd\; \backslash times\; dg$. Or it may be expressed by the proportional equation $v\; \backslash dot\{=\}\; at$.

48. Conversely. The acceleration $a$ is proportional to $\backslash frac\{v\}\{t\}$, as in the case when the motion is uniformly accelerated (40.).

And as the area of this figure is analogous to the sum of all the inscribed rectangles, when the circumstances of the case admit of its being measured, it may be expressed by $\backslash int\; a\; i$; and thus is obtained the whole velocity acquired during the time $AC$, and we say $v\; \backslash dot\{=\}\; \backslash int\; a\; i$.

The intensities (or at least their proportions) of the accelerating power of nature in the different points of the path being frequently known, we wish to discover the velocities in those points. This may be done by the following proposition.

49. If the abscissa $AE$ (fig. 8.) of a line $ace$ be the space along which a body moves with a motion continually varied, and if the ordinates $Aa$, $Bb$, $Cc$, &c. are proportional to the accelerations in the points $A$, $B$, $C$, &c. then the areas $ABba$, $ADda$, $AEea$, &c. are proportional to the augmentations of the square of the velocity in $A$ at the points $B$, $D$, $E$, &c.

Take $BC$, $CD$, as two very small portions of the line $AE$, and draw $bf$, $cg$, parallel to $AE$. Then, supposing the acceleration $Bb$, to continue through the space $BC$, the rectangle $BbfC$ will express the augmentation made on the square of the velocity in $B$. In the same way $CcgD$ will express the augmentation of the square of the velocity in $C$; and, in like manner, the rectangles inscribed in the remainder of the figure will express the increments of the squares of the velocity acquired, while the body moves over the corresponding portions of the abscissa. And, therefore, the whole augmentation of the square of the velocity in $A$ (should there be any velocity in that point) during the time of moving from $A$ to $B$, will constitute the aggregate of these partial increments. The same thing must be affirmed of the motion from $B$ to $E$. And, when the subdivision of $AE$ is carried on without end, it is plain that the ultimate ratio of the area $AEea$ to the aggregate of inscribed rectangles, is that of equality; that is, when the acceleration varies continually, the area $ABba$ will express the increment made on the square of the initial velocity in $A$, while the body moves along $AB$; and the same must be affirmed with respect to the motion along $BE$. And, therefore, the intercepted areas $ABba$, $BDdb$, $DEed$, are proportional to the changes made on the squares of the velocities in the points $A$, $B$, and $D$.

50. COR. 1. If the body had no velocity in $A$, the areas $ABba$, $ADda$, &c. are proportional to the squares of the velocity acquired in the points $B$, $D$, &c.

Cor. 2. The momentary change on the square of the velocity, is as the acceleration and increment of the space jointly; or we have $v\; \backslash dot\{=\}\; as$.

Cor. 3. $v\; \backslash dot\{v\}$ being equal to half the increment of the square of the velocity, it follows that the area $AEea$, or the fluent $\backslash int\; a\; s$ is only equal to $\backslash frac\{V^2\; -\; v^2\}\{2\}$, taking $v$ and $V$ as the velocities in $A$ and $E$.

51. What has now been said of the acceleration of motion, is equally applicable to motions that are retarded, whether these motions be uniform or unequal. The momentary variations in this case are to be taken as decrements of velocity instead of increments. A moving body, subject to uniform retardation till it come to rest, will continue in motion during a time proportional to the initial velocity; and describe a space proportional to the square of this velocity; and the space which is so described, is one half what it would have been if the initial velocity had continued undiminished.

52. HAVING obtained the marks and measures of every variation of velocity, we are to discover similar characteristics for every change of direction. In the above investigation of the general marks of any change of motion, it is plain that the change being the same in any two or more instances, the ostensible marks must also be the same, whatever may have been the previous

Compound previous condition of the moving bodies. In every case of change, some circumstance in the difference between the former motions and the new motions must be observed, which is exactly the same both in respect of velocity and of direction. One of the bodies then may be supposed to have been at rest; and thus the change produced on it, is the motion which it has acquired, or the determination to this motion. Therefore, a change of motion is itself a motion, or determination to motion. In the above case, it is the new motion only; but it is not the new motion in every other case. For supposing the previous condition of the body to have been different from that of a body at rest, and supposing the same change produced on it, the new condition of the one body must be different from the new condition of the other. The change, therefore, being the same in both cases, the new condition cannot be that change. But, when the same change happens in any previous motion, the difference between the former motion and the new motion, must indicate something that is equivalent to the motion produced in a body previously at rest, or the same with that motion, this body having received the same change. And the difference between the new motions of the two bodies will be such as shall indicate the difference between the previous conditions of each body. The change of motion then is itself a motion; and this being assumed as a principle, we are now to endeavour to discover a motion which alone shall produce that difference from the former motion, which, in all cases, is observed in the new motion. This is to be considered as the proper characteristic of the change.

53. The following motions may serve as an illustration of these conditions. Let it be supposed that the straight line AB (fig. 9.) lies east and west, and that it is crossed by the line AC from north to south. Suppose this line AC to be a rod or wire, and to be carried along the line AB in one minute, but always in the same position, that is, lying north and south. The end of the rod or wire A having moved uniformly one-third of AB at the end of 20", it will be in the position Dd; at the end of 40" it will have the position Ee; and at the end of the minute it will be in the position Bb.

Let the line AB, in the mean time (supposing it also to be material) be uniformly moved from north to south, and always parallel to its first position AB. When it has passed over one-third of AC, at the end of 20", it will be in the position m d n; at the end of 40" it will have the position o e p, and A o is two-thirds of AC. At the end of the minute, it will have the position C d b. It is evident that the common intersection of these two lines will be always in the diagonal A b of the parallelogram A C b B; for the parallelogram A m d D is similar to the parallelogram A C b B, because $AD\; :\; AB\; =\; Am\; :\; AC$; and, in like manner, A o e E is a parallelogram similar to A C b B. Therefore, these parallelograms are about a common diagonal A b.

Again, the motion of the point of intersection of these lines is uniform; for $AD\; :\; AB\; =\; Ad\; :\; A\; b$, and $AE\; :\; AB\; =\; Ae\; :\; A\; b$, &c. Therefore the spaces A d, A e, A b are proportional to the times.

Thus the intersection of two lines having each a uniform motion in the direction of the other, moves uniformly in the direction of the diagonal of the parallel-

gram, which is formed by the lines in their first or last position; and the velocity of the intersection is to the velocity of each of the motions of the lines as the diagonal is to the side in the direction of which the motions are made. This motion of the intersection is very properly said to be compounded of two motions in the direction of the sides; for when the point d of the line D d moves eastward, the same point d of the line m d n is at the same instant moving southward. The point d, therefore, may be considered as a point of both lines, partaking in every instant of both motions. The motion along A b then contains both motions along AB and AC, and being identical with a motion compounded of these motions, indicates both, or the determination to both. In every situation of the point of intersection, its velocity is compounded of the velocity AB and AC. A body, therefore, whose motion continued unchanged, would have described AB in one minute; but when it reaches the point A, it turns aside, and describes A b uniformly in the same time; the change then which the body sustains in the point A is a motion AC. For suppose the body had been at rest in the point A, and it is observed to describe AC in one minute, the motion AC is the change which it has sustained. The motion A b is not the change: for if AF had been the primitive motion, the same motion A b would have been the result of compounding with it the motion AG. But since AF is different from AB, the same change cannot produce the same new conditions. But, farther, there is no other motion which, by compounding it with AB, will produce the motion A b; and the motion AC is the only circumstance of sameness between changing the motion AB into the diagonal motion A b, and giving the motion AC to a body which was previously at rest. —From these conditions it follows, that a change of motion, is that motion, which by composition with the previous state of motion, produces the new motion.

54. This composition of motion has been considered and is in a different way. While a body is supposed to move uniformly in the direction AB, the space in which this motion is performed, is supposed to be carried in the direction AC. But it cannot be conceived that any portion of space is moved from its place. A distinct notion of this composition may be obtained, by supposing a person walking along a line AB, while this is drawn on a piece of ice, and the ice is floating in the direction AC. But the motion on moving ice is not precisely a composition of two determinations to motion; for this is completed in the first instant. When the motion in the direction and with the velocity A b begins, no farther exertion is needed; the motion continues, and A b is described. It serves, however, to exhibit to the mind the mathematical composition of two motions. In the result of this combination, all the characteristics of the two determinations are to be found; for the point of intersection, in whatever way it is considered, partakes of both motions.

55. Thus a general characteristic of a change of motion is obtained, and this corresponds with the mark and measure of every moving cause; for it is the very motion which it is conceived to produce. It may perhaps even be considered as the foundation of former measures; for in every acceleration, retardation, or deflection, there is a new motion compounded with the former.

former. What is taken for the beginning of motion in every observation of surrounding bodies, is nothing more than a change induced on a motion already produced.

56. The actual composition of motion being so general in the phenomena of the universe, it obtains in all motions and changes of motion produced or observed, and the characteristic which has been assumed of a change of motion being the same, whatever may have been the previous motion, and this being equally applicable to simple motions, it is evident that a knowledge of the general results of this composition of motion will be of essential service in acquiring a knowledge of mechanical nature.

57. The following is the general theorem to which all others may be reduced.

PROP. IX.

Two uniform motions, having the directions and velocities represented by the sides AB, AC, of a parallelogram, compose a uniform motion in the diagonal. The demonstration of this has been already given. The motion of the point of intersection of these two lines, each moving uniformly in all its points, in the direction of the other, is, in every instant, composed of the two motions. It is the same as if a point described AB uniformly, while AB is carried uniformly in the direction AC. This motion is along the diagonal Ab, and it has been already shewn to be uniform. And, because AB and Ab are described in the same time, the velocities of the motions along AB, AC, and Ab are proportional to those lines.

COROLLARIES.

Cor. 1. The motion Ab, which is compounded of the two simple motions AB and AC, is in the same plane with these motions. For a parallelogram lies all in the same plane.

Cor. 2. The motion Ab may be produced by the composition of any two uniform motions having the direction and velocities which are represented by the sides of any parallelogram, AFbG, or ACbB, which has Ab for its diagonal.

58. Cases are not unfrequent in which the directions of two simple motions composing an observed motion may be discovered; but the proportion of the velocities is unknown. This velocity may be ascertained by means of this last proposition. For the direction of the three motions, namely the two simple and the compound motions, determines not only the species of parallelogram, but also the ratio of the sides. Again, in those cases in which the direction and the velocity of one of the simple motions are known, and therefore its proportion to that of the observed compound motion, the direction and velocity of the other may be also found by means of the same proposition; because from these data the parallelogram may be determined.

59. This motion in the diagonal is called the equivalent motion, or the resulting motion; for it is equivalent to the combined motions in the sides. Thus, if the moving body first describe AB, and then Bb or AC, it will be in the same point, as if it had described Ab, namely, in the point b.

60. It is often highly useful in investigations of this kind to substitute such motions for an observed motion,

as will produce it by composition. This has been denominated the resolution of motions. By this manner of proceeding, a ship's change of situation at the end of a day, having sailed in different courses, is computed. Thus the distance sailed to the eastward or the westward, as well as that to the northward or southward, on each course, is observed and marked. The whole of the eastings, and the whole of the southings, are added together; and then it is supposed that the ship has sailed for the whole day on that course, which would be produced by combining the same easting and southing.

61. It is also useful to consider how much the body has been advanced in a certain direction by means of the observed motion; let us suppose in the direction AB (fig. 10.). The motion CD is first considered as Fig. 10. composed of a motion CE parallel to the given line AB, and another motion CF perpendicular to AB. CD is the diagonal of a parallelogram CEDF, one of whose sides CE is parallel to AB, and the other CF is perpendicular to AB. It is evident, that the body has advanced in the direction of AB as much as if it had moved from G to H, instead of moving from C to D, so that the motion CF has no effect either in obstructing or promoting the progress in AB. This is called estimating a motion in a given direction, or reducing it to that direction.

62. A motion is also said to be estimated in a given plane, when it is considered as composed of a motion perpendicular to the plane, and of another parallel to it. In a given plane ABCD (fig. 11.), let EF be a motion compounded of a motion GE perpendicular to the plane, and EH parallel to it. For if the lines GE, FH are drawn perpendicular to the plane, they cut it in two points e and f, and EH is parallel to ef.

63. In the same way a compound motion may be formed of any number of motions. Let AB, AC, AD, AE, &c. (fig. 12.) be any number of motions, of which Fig. 12. the motion AF is compounded. The motion which is the result of this composition is thus ascertained. The motion AG is compounded of AB and AC; and the motion AG compounded with AD, gives the motion AH; which latter being compounded with AE, produces the motion AF. And the same place, or final situation F, will be found by supposing the different motions AB, AC, AD, AE, to be performed successively. The moving body first describes AB; then BG, equal and parallel to AC; then GH, equal and parallel to AD; and lastly, HF, equal and parallel to AE. In this case it is not requisite that all the motions lie in the same plane.

64. Three motions which have the direction and proportions of the sides of a parallelopiped, compose a motion having the direction of its diagonal. Let AB, AC, AD (fig. 13.), be these motions, the compound- Fig. 13. ed motion is in the diagonal AF of the parallelopiped; because AB and AC compose the motion AE; and AE and AD compose the motion AF.

It is in this way that the mine-surveyor proceeds. He sets down a gallery of a mine, not directly by its real position, but marks the easting and westing, the northing and southing, as well as its dip and rise. All these measures are referred to three lines, of which one runs east and west, one north and south, and a third is perpendicular. These three lines are obviously analogous.

Compound motions to the angular boundaries of a rectangular box, as AC, AB, AD.

Other compound motions. 65. The composition of uniform motions only has yet been considered. But it is easy to conceive that any motions may be compounded. It is a case of this kind when a man is supposed to walk on a field of ice along a crooked path, while the ice floats down a crooked stream. Suppose a uniform motion in the direction AB (fig. 14.), to be compounded with a uniformly accelerated motion in the direction AC.

A stone falling from the mast head of a ship, while she sails uniformly forward in the direction AB, affords an example of this kind of motion; for the stone will be observed to fall parallel to a plummet hung from the mast head. But the real motion of the stone is a parabolic arch $A\; b\; f\; g$, which AB touches in A; for while the mast head describes the equal lines AB, BF, FG, the stone has fallen to $\backslash beta$ and $\backslash phi$ and $\backslash gamma$, and the line AC is in the positions BB', FF', GG', so that A$\backslash beta$ is four times A$\backslash beta$; and A$\backslash gamma$ is nine times A$\backslash beta$. Therefore A$\backslash beta$, A$\backslash phi$, A$\backslash gamma$, are as the squares of $\backslash beta\; b$, $\backslash phi\; f$, $\backslash gamma\; g$, and the line $A\; b\; f\; g$ is a parabola.

66. Knowing the direction and velocities of each of the simple motions in any instant, of which two motions, however variable, are compounded, we may discover the direction and velocities of the compound motions in that instant. For it may be supposed that each motion at that instant proceeds unchanged: a parallelogram is then constructed; the sides of which have the direction and proportions of the velocities of the simple motions; and the diagonal of this parallelogram will express the direction and velocity of the compound motion. But, on the other hand, if the direction and velocity of the compound motion, with the directions of each of the simple motions, be known, we may discover their velocities.

67. In cases where a curvilinear motion, as ABC (fig. 15.), is the result of two motions compounded, of which the direction is known to be AD and AE, we discover the velocities of the three motions in any point B, by drawing the tangent BF, and the ordinate BG, parallel to one of the simple motions, and from any point H in that ordinate drawing HF parallel to the other motion, and cutting the tangent in the point F. The three velocities are in the proportion of the three lines FH, HB, and FB.

68. As the motions which are observed in nature are very different from what they are taken to be, it is not easy to avoid mistakes with respect to the changes of motion, and consequently with respect to the inference of its cause. Without considering the real motion of any body, we are apt to judge only of the changes of distance and direction in relation to ourselves. Thus it is that our inferences with regard to the planetary motions are very different from the motions themselves, if the rapid motion of our earth be considered.

69. The motion of one body in relation to another body, or as it is seen from another body, which is also in motion, is compounded of its own real motion, and the opposite of the real motion of the second body.

Let A (fig. 16.) be a body in motion from A to C, as seen from B, which is another body in motion from

B to D the motion of A is compounded of its own real motion, and of the opposite to the real motion of B. Join AB, and draw AE equal and parallel to BD. Complete the parallelogram ACFE, and join ED and DC. Produce EA, and make AL equal to AE or BD. Complete the parallelogram LACK, and draw AK and BK. If then A had moved along AE while B moves along BD, the two bodies would have been at E and D, at the same time, and would have the same relative situation; they would have the same bearing and distance as before. And if the spectator in B is not sensible of his own motion, A will appear not to have changed its place. In the same way two ships becalmed in an unknown current, seem to the persons on board to be at rest. The real position, therefore, and distance DC, are the same with BK; and if a spectator in B imagines himself at rest, the line AK will be taken as the motion of A. And this motion, it is obvious, is composed of the motion AC its real motion, and the motion AL which is the equal and opposite motion to that of BD.

Again, if BH be drawn equal and opposite to AC, and the parallelogram BHGD be completed, and BG and AG be drawn, the diagonal BG will be the motion of B as it is seen from A. Now as KAGB is a parallelogram, the relative situation and distances of A and B at the end of the motion will appear to be the same as in the former case. For B appears to have moved along BG, which is equal and opposite to AK. Hence it follows that the apparent or relative motions of two bodies are equal and opposite, whatever their real motions may be; and therefore they do not afford any information of their real motions.

70. Suppose equal and parallel motions are compounded with all and each of the motions of any number of bodies, moving in any manner of way, then their relative motions are not consequently changed. For if it be compounded with the motion of any one of the bodies which may be called A, the real motion of this body is changed; but its apparent motion, as seen from another body B, is compounded of the real change, and of the opposite to the real change in A, which therefore destroys that change, and the relative motion of A is the same as before. Thus it is that the motions in the cabin of a ship are not affected by the ship's progressive motion; and the motion of the earth round the sun produces no perceptible effect on the relative motions on its surface. And indeed it is only by observing other bodies which are not affected by these common motions, and to which we refer as to fixed points, that we arrive at any knowledge of them.

71. CURVILINEAL motions are cases of continual deflection. They are susceptible of great varieties; and the investigation of their modifications and chief properties is attended with no small difficulty. Uniform motion in a circular arch is an example of the simplest case of curvilinear motion; for here the deflections from rectilinear motion are equal in equal times. If, however, the velocity be increased, the momentary deflection must also be augmented; for a greater arch will be described, and the end of this greater arch is at

tion at a greater distance from the tangent. But the proportionally portion of this augmentation is difficult to be ascertained.

When a uniform rectilinear motion AB (fig. 17.) is deflected into another BC, the lineal deflection is ascertained by drawing a line from the point c, at which point the body would have arrived, had it not been deflected to the point C at which it has arrived. The result is the same, whether the lines d D or c C be drawn in this manner; for being proportional to B d, B c, they always give the same measure of the velocities; and here the lines of deflection are all parallel, indicating the direction of the deflection in the point B. But this is not the case in any curvilinear motion. It rarely happens that d D, c C, are parallel; and it is never found that $d\; D\; :\; c\; C\; =\; B\; d\; :\; B\; c$. We cannot therefore discover which lines should be taken for the indication of the direction of the deflection at B, or for the measure of its magnitude. A greater velocity, then, in the same curve, produces a greater deflection; but if the path be more incurvated, an arch of the same length, described with the same velocity, causes a farther deviation from the tangent. If therefore a body have a uniform motion in a curve of variable curvature, the deflection is greatest where the curvature is greatest.

Thus it appears that the direction and measure of the deflections by which a body deviates continually into a curvilinear path cannot be ascertained, but by investigating the ultimate positions and ratios of the lines, which join the points of the curve with the simultaneous points of the tangent, as the points d and C are taken nearer to B. In some cases, but rarely, the lines joining the simultaneous points are parallel. But in most cases the direction of the deflection is discovered by observing to what direction it approximates. The following proposition which was discovered by Newton is of great importance in this investigation.

72. If a body describe a curve line ABCDEF (fig. 18.) being in the same plane, and if in this plane there be a point S so situated, that the lines SA, SB, SC, &c. drawn to the curve, cut off areas ASB, ASC, ASD, &c. proportional to the times of describing the arches AB, AC, AD, &c. then the deflections are always directed to the point S.

Suppose first that the body describes the polygon ABCDEF, formed of the chords of this curve, and that it describes each chord uniformly, and is deflected only in the angles B, C, D, &c. Suppose also that the sides of the polygon are described in equal times, so that, according to the hypothesis, the triangles ASB, BSC, CSD, are all equal. Continue the chords AB, BC, &c. beyond the arches, making B c equal to AB, and C d equal to BC, and so on. Join c C, d D, &c. and draw c S, d S, &c.; draw C b parallel to c B or BA, cutting BS in b, and join b A, and draw CA, cutting B b in o. And lastly, make a similar construction at E.

Then, because c B is equal to BA, the triangles ASB and BSc are equal, and therefore BSc is equal to BSC. And being on the same base SB, they are therefore between the same parallels; that is, c C is

parallel to BS, and BC is the diagonal of a parallelogram B b C c. The motion BC is therefore compounded of the motions B c and B b, and B b is the deflection, by which the motion B c is changed into the motion BC; and therefore the deflection in B is directed to S. By similar reasoning it may be shown that f F, or E i, is the deflection at E, and is likewise directed to S; and the same demonstration will apply to every angle of the polygon.—This point S has been called the centre of deflection.

If the sides of the polygon are diminished, and their number infinitely increased, the demonstration remains the same, and continues, when the polygon coalesces with the curvilinear area, and its sides with the curvilinear arch.

But when the whole areas are proportional to the times, equal areas are described in equal times. In such motion, therefore, the deflections are always directed to S.

73. If the deflection by which a curve line is described, be continually directed to a fixed point, the figure will be in one plane, and areas will be described round that point proportional to the times. Let ADF (fig. 18.) be the curve line described, and let the deflections be directed to the point S, this curve line is in the same plane. For BC is the diagonal of a parallelogram, and is in the plane of SB and B c; and c C is parallel to BS, and the triangles SBC, SB c, and SBA, are equal. But equal areas are described in equal times; and therefore areas are described proportional to the times.

74. Cor. 1. The velocities in different points of the curve are inversely proportional to the perpendiculars S r and S t (fig. 19.) drawn from S on the tangents A r, E t in those points of the curve. For since the elementary triangles ASB, ESF, are equal, their bases AB, EF, are inversely as their altitudes S r, S t. And these bases being described in equal times are as the velocities, and ultimately coincide with the tangents at A and E; and therefore the velocity in A is to that in E as S t to S r.

COR. 2. The angular velocities round S are inversely as the squares of the distances. For if we describe round the centre S the small arches B a, F d, they may be considered as perpendiculars on SA and SE. Describe also with the distance SF the arch g h. It is evident that g h is to F d as the angle ASB to the angle ESF. And since the areas ASB, ESF are equal, we have B a : F d = SE : SA.

75. Let us now proceed to determine the magnitude of the deflection, or to compare its magnitude in any two points, as for example the magnitude in B (fig. 18.) with its magnitude in E. The deflection in B is to that in E as the line B b to the line E i; for B b and E i are the motions, which, by being compounded with the motions B c and E f make the body describe BC and EF. And therefore when the sides of the polygon

Motions continually diminished, the ultimate ratio of $Bb$ to $Ei$ is the ratio of the deflection at $B$ to the deflected flection at $E$.

To obtain a convenient expression of this ultimate ratio, let $ABCXZY$ be a circle which passes through the points $A,\; B,\; C$. Draw $BSZ$ through the point $S$, and draw $CZ,\; AZ$. Now the triangles $BCb$ and $AZC$ are similar, for $Cb$ was drawn parallel to $cB$ or $BA$; and therefore the angle $CbB$ is equal to the alternate angle $bBA$ or $ZBA$, which is equal to the angle $ZCA$, because it is subtended by the same chord $ZA$; and because they stand on the same chord $CZ$, $CBb$, or $CBZ$, is equal to $CAZ$. And therefore the remaining angles $bCB$ and $CZA$ are equal, and the triangles are similar. Therefore $Bb\; :\; CA\; =\; BC\; :\; AZ$.

Now if the sides of the polygon are continually diminished, the points $A$ and $C$ continually approach to $B$, and $CA$ continually approaches to $cA$, or to $2cB$, or $2CB$, and is ultimately equal to it; and $AZ$ is ultimately equal to $BZ$.

Therefore ultimately, $Bb\; :\; 2BC\; =\; BC\; :\; BZ$, and $Bb\; \backslash times\; BZ\; =\; 2BC^2$, and $Bb\; =\; \backslash frac\{2BC^2\}\{BZ\}$.

Also, at the point $E$, we have $Ei$ ultimately equal to $\backslash frac\{2EF^2\}\{Ez\}$, for $Ez$ is that chord of the circle through $D,\; E$, and $F$, which passes through $i$.

Therefore $Bb\; :\; Ei\; =\; \backslash frac\{2BC^2\}\{BZ\}\; :\; \backslash frac\{2EF^2\}\{Ez\}$.

The ultimate circle, when the three points $A,\; B,\; C$, coalesce, is called the circle of equal curvature, or the equicurve circle, which coalesces with the curve in $B$ in the closest manner; and the chord $BZ$ of this circle, having the direction of the deflection in $B$, is called its deflective chord. And since $BC$ and $EF$ are described in equal times, they are proportional to the velocities in $B$ and $E$. This proposition therefore may be expressed as follows.

In curvilinear motions, the deflections in different points of the curve, are proportional to the square of the velocities in those points directly, and to the deflective chords of the equicurve circles, inversely.

It ought, however, to be remarked, that this theorem is not limited to curvilinear motions, in which the deflections tend always to the same fixed point; it may be extended to all curvilinear motions whatever. A symbolical expression of this theorem will be convenient. If therefore the deflective chord of the equicurve circle be represented by $c$, and the deflection by $d$, the theorem may be thus expressed,

76. The line $Bb$ is the linear deflection by which the uniform motion in the chord $AB$ is changed into a uniform motion in the chord $BC$, or it is the deviation $cC$ from the point to which the moving body would have arrived, if the deflection at $B$ had not taken place. In the case of curvilinear motion which we are now considering, the lines $Bb$ and $Bc$ are expressions of the measures of the velocities of these motions. $Bc$ is to $Bb$ as the velocity of the progressive motion is to the velocity of the deflection, generated in the time that the arch $BC$ is described. But the deflection in the arch has been continual, and, like acceleration, it

may be measured by the velocity generated during any moment of time. It may therefore be measured by the velocity generated during the time the arch $BC$ is described. This measure will therefore be double of the space through which the body is actually deflected from the tangent in $B$ in that time. The space described will be $BO$, or only one half of $Bb$. This is exactly what happens; for the tangent is ultimately parallel to $OC$, and it bisects $cC$; therefore the velocity gradually generated is that which constitutes the polygonal motion in the chords, although the deflection from the tangent to the curve is only half of the deflection from the produced chord to the curve.

77. In any point of a curvilinear motion, the velocity is that which would be generated by the deflection in that point, if continued through one fourth of the deflective chord of the equicurve circle. Take $x$ for the space along which a body is to be accelerated that it may acquire the velocity $BC$.

We have $Bb^2$, or $4BO\; :\; BC^2\; =\; B\; :\; x$ (37.—1.); and therefore $x\; =\; \backslash frac\{BC^2\; \backslash times\; BO\}\{4BO^2\}\; =\; \backslash frac\{BC^2\}\{4BO\}$, and $4x\; =\; \backslash frac\{BC^2\}\{BO\}$, or $BO\; :\; BC\; =\; BC\; :\; 4x$. But $BO\; :\; BC\; =\; BC\; :\; BZ$; therefore $x\; =\; \backslash frac\{1\}\{4\}\; BZ$.

78. We have now obtained characteristic expressions or marks and measures of the principal affections of motion. These expressions may be brought into one view as follows.

The acceleration $a$ is $\backslash frac\{v\}\{t\}$ (48.), or $\backslash frac\{v^2\}\{s\}$ (49.), or $\backslash frac\{s\}\{t^2\}$ (42.).

The momentary variation of velocity $\backslash dot\{v\}\; =\; a\; t$ (48.).

The momentary variation of the square of velocity $2v\backslash dot\{v\}\; =\; 2a\; s$ (49.).

The momentary deflection $d\; =\; \backslash frac\{\backslash text\{arc\}^2\}\{\backslash text\{chord\}\}$ (76.).

The deflective velocity $\backslash frac\{2v^2\}\{c\}$ (75.).

79. But for the application of these doctrines, it is necessary to select some point in any body of sensible magnitude, or in any system of bodies, by whose position or motion, a distinct and accurate notion of the position or motion of the body or system may be formed. The condition by which the propriety of this selection is ascertained, is, that the position, distance, or motion of this point shall be the medium or average of the positions, distances, and motions of every particle of matter in the aggregate or system.

This will happen, if the point be so situated, that when a plane is made to pass through it in any direction whatever, and perpendiculars being drawn to this plane from every particle of matter in this aggregate or system, the sum of the perpendiculars on the one side of the plane is equal to the sum of the perpendiculars on the other side. And that such a point, which is called the centre of position, may be found in every body, is proved by the following demonstration.

For let $P$ (fig. 20.) be a point so situated, and let $QR$ be the section of a plane perpendicular to the paper, and at any distance from it, the distance $Pp$ of the point $P$ from this plane is the average of all the distances of each particle from it. Let the plane $APB$ pass through $P$, and parallel to $QR$. The distance $CS$

Motions
originally
deflected.

CS of any particle C from the plane QR is equal to DS—DC, or to $Pp—DC$. And the distance GT of a particle G on the other side of APB, is equal to $HT+GH$, or to $Pp+GH$. Let $n$ be the number of particles on that side of AB which is nearest to QR, and let $o$ be the number of particles on the other side of AB. Let $m$ be the number of particles in the whole body; we have then $m=n+o$. It is evident that the sum of all the distances of all the particles such as CS, is $n\; \backslash times\; Pp$—the sum of all the distances, such as CD. Also the sum of all the distances of the particles, such as G, is $o\; \backslash times\; Pp$, + the sum of the distances GH. And therefore the sum of both sets is $n+o\; \backslash times\; Pp$+the sum of GH—the sum of DC, or $m\; \backslash times\; Pp$+the sum of GH—the sum of DC. But by the supposed property of the point P, the sum of GH wanting the sum of DC is nothing; and therefore $m\; \backslash times\; Pp$ is the sum of all the distances, and $Pp$ is the $m$th part of this sum, or the average distance.

Suppose the body to have changed both its place and its position with respect to the plane QR, and that P (fig. 21.) is still the same point of the body, and $\backslash alpha\; P\; \backslash beta$ a plane parallel to QR. Make $p\; \backslash pi$ equal to $p\; P$ of fig. 20. It is plain that $Pp$ is still the average distance, and that $m\; \backslash times\; Pp$ is the sum of all the present distances of the particles from QR, and that $m\; \backslash times\; \backslash pi\; p$ is the sum of all the former distances. Therefore $m\; \backslash times\; P\; \backslash pi$ is the sum of all the changes of distance, or the whole quantity of motion estimated in the direction $\backslash pi\; P$. $P\; \backslash pi$ is the $m$th part of this sum, and is therefore the average motion in this direction. The point P has therefore been properly selected; and its position, and distance, and motion, in respect of any plane, is a proper representation of the situation and motion of the whole.

Hence it follows, that if any particle C (fig. 20.) moves from C to N, in the line CS, the centre of the whole will be transferred from P to Q, so that PQ is the $m$th part of CN; for the sum of all the distances has been diminished by the quantity CN, and therefore the average distance must be diminished by the $m$th part of CN, or PQ is $=\; \backslash frac\{CN\}\{m\}$.

But it may be doubted whether there is in every body a point, and but one point, such that if a plane pass through it, in any direction whatever, the sum of all the distances of the particles on one side of this plane is equal to the sum of all the distances on the other.

It is easy to shew that such a point may be found, with respect to a plane parallel to QR. For if the sum of all the distances DC exceed the sum of all the distances GH, we have only to pass the plane AB a little nearer to QR, but still parallel to it. This will diminish the sum of the lines DC, and increase the sum of the lines GH. We may do this till the sums are equal.

In like manner we can do this with respect to a plane LM (also perpendicular to the paper), perpendicular to the plane AB. The point wanted is somewhere in the plane AB, and somewhere in the plane LM. Therefore it is somewhere in the line in which these two planes intersect each other. This line passes through the point P of the paper where the two lines AB and LM cut each other. These two lines represent planes, but are, in fact, only the intersection of those planes with the plane of the paper. Part of the body must be conceived as being above the paper, and

part of it behind or below the paper. The plane of the paper therefore divides the body into two parts. It may be so situated, therefore, that the sum of all the distances from it to the particles lying above it shall be equal to the sum of all the distances of those which are below it. Therefore the situation of the point P is now determined, namely, at the common intersection of three planes perpendicular to each other. It is evident that this point alone can have the condition required in respect of these three planes.

It still remains to be determined whether the same condition will hold true for the point thus found, in respect to any other plane passing through it; that is, whether the sum of all the perpendiculars on one side of this fourth plane is equal to the sum of all the perpendiculars on the other side.

Let AGRB (fig. 22.), AXYB, and CDEF, be three planes intersecting each other perpendicularly in the point C; and let CIKL be any other plane, intersecting the first in the line CI, and the second in the line CL. Let P be any particle of matter in the body or system. Draw PM, PO, PR, perpendicular to the first three planes respectively, and let PR, when produced, meet the oblique plane in V; draw MN, ON, perpendicular to CB. They will meet in one point N. Then PMNO is a rectangular parallelogram. Also draw MQ perpendicular to CE, and therefore parallel to AB, and meeting CI in S. Draw SV; also draw ST perpendicular to VP. It is evident that SV is parallel to CL, and that STRQ and STPM are rectangles.

All the perpendiculars, such as PR, on one side of the plane CDEF, being equal to all those on the other side, they may be considered as compensating each other; the one being considered as positive or additive qualities, the other as negative or subtractive. There is no difference between their sums; and the sum of both sets may be called o or nothing. The same must be affirmed of all the perpendiculars PM, and of all the perpendiculars PO.

Every line, such as RT, or its equal QS, is in a certain invariable ratio to its corresponding QC, or its equal PO. Therefore the positive lines RT are compensated by the negative, and the sum total is nothing.

Every line, such as TV, is in a certain invariable ratio to its corresponding ST, or its equal PM, and therefore their sum total is nothing.

Therefore the sum of all the lines PV is nothing; but each is in an invariable ratio to a corresponding perpendicular from P on the oblique plane CIKL. Therefore the sum of all the positive perpendiculars on this plane is equal to the sum of all the negative perpendiculars, and the proposition is demonstrated, viz. that in every body, or system of bodies, there is a point such, that if a plane be passed through it in any direction whatever, the sum of all the perpendiculars on one side of the plane is equal to the sum of all the perpendiculars on the other side.

80. If A and B (fig. 23.) be the centres of position of two bodies, whose quantities of matter (or numbers of equal particles) are $a$ and $b$, the centre C lies in the straight line joining A and B, and $AC\; :\; CB\; =\; b\; :\; a$, or its distances from the centres of each are inversely as their quantities of matter. For let $\backslash alpha\; C\; \backslash beta$ be any plane passing

passing through C. Draw $A\backslash alpha$, $B\backslash beta$, perpendicular to this plane. Then we have $a\; \backslash times\; A\backslash alpha\; =\; b\; \backslash times\; B\backslash beta$, and $A\backslash alpha\; :\; B\backslash beta\; =\; b\; :\; a$, and, by similarity of triangles, $CA\; :\; CB\; =\; b\; :\; a$.

If a third body D, whose quantity of matter is $d$, be added, the common centre of position E of the three bodies is in the straight line DC, joining the centre D of the third body with the centre C of the other two, and $DE\; :\; EC\; =\; a\; +\; b\; :\; d$. For, passing the plane $\backslash partial\; E\backslash alpha$ through E, and drawing the perpendiculars $D\backslash delta$, $C\backslash epsilon$, the sum of the perpendiculars from D is $\backslash delta\; \backslash times\; D\backslash delta$; and the sum of the perpendiculars from A and B is $\backslash epsilon\; \backslash times\; C\backslash epsilon$, and we have $d\; \backslash times\; D\backslash delta\; =\; a\; \backslash times\; C\backslash epsilon$; and therefore $DE\; :\; EC\; =\; a\; +\; b\; :\; d$.

In like manner, if a fourth body be added, the common centre is in the line joining the fourth with the centre of the other three, and its distance from this centre and from the fourth is inversely as the quantities of matter; and so on for any number of bodies.

81. If all the particles of any system be moving uniformly, in straight lines, in any directions, and with any velocities whatever, the centre of the system is either moving uniformly in a straight line, or is at rest.

For, let $m$ be the number of particles in the system. Suppose any particle to move uniformly in any direction. It is evident from the reasoning in a former paragraph, that the motion of the common centre is the $m$th part of this motion, and is in the same direction. The same must be said of every particle. Therefore the motion of the centre is the motion which is compounded of the $m$th part of the motion of each par-

particle. And because each of these was supposed to be of Motion uniform and rectilinear, the motion compounded of Forces them all is also uniform and rectilinear; or it may happen that they will so compensate each other that there will be no diagonal, and the common centre will remain at rest.

82. Cor. 1. If the centres of any number of bodies move uniformly in straight lines, whatever may have been the motions of each particle of each body, by rotation or otherwise, the motion of the common centre will be uniform and rectilinear.

Cor. 2. The quantity of motion of such a system is the sum of the quantities of motion of each body, reduced to the direction of the centre's motion. And it is had by multiplying the quantity of matter in the system by the velocity of the centre.

Cor. 3. The velocity of the centre is had by reducing the motion of each particle to the direction of the centre's motion, and then dividing the sum of those reduced motions by the quantity of matter in the system.

83. If on any two bodies of such an assemblage equal and opposite quantities of matter be impressed, the motion of the centre of the whole is not at all affected by it. Because the motion of the centre, arising from the motion of one of the bodies being compounded with the equal and opposite motion of the diagonal of the parallelogram, becomes a point; or these motions destroy one another; and therefore no change is effected on the motion of the centre.

84. HAVING in the former part considered the general doctrine of motion, which is the foundation of mechanical investigations, we now proceed to treat of moving forces or dynamics, properly so called.

It has been already observed, that dynamics includes the abstract doctrine of moving forces, or the necessary results of the relations of our thought concerning motion, the immediate causes of motion, and its changes; and that from the changes observed, we infer agency in nature; and in these changes we are to discover what we know of their causes.

85. When we cast our eyes around us, it cannot escape observation, that the changes which we perceive in the state or condition of any body in respect of motion, are constantly and distinctly related to the situation and distance of other bodies. The motions of the moon, or of a stone projected through the air, have a palpable relation to the earth; the motions of the tides have also an obvious relation to the moon; and the motions of a piece of iron have a palpable dependence on a magnet. The vicinity of the one of these bodies seems to be the occasion, at least, of the motions of the other; and the causes of these motions have an evident connection with, or dependence on, the other body. Such dependences have been called the mechanical relations of bodies. They are indications of properties or distinguishing qualities. They accompany the bodies wherever they are, and are usually conceived

to be inherent in them. They at least ascertain and determine what is called the mechanical nature of bodies.

86. The mutual relation of bodies is differently considered according to the interest we may have in the Mutual phenomenon. The cause of the approach of the iron bodies to the magnet is generally ascribed to the magnet. It is said to attract the iron. The approach of a stone to the earth is ascribed to the stone. It is said to tend to the earth. But it is probable that the procedure of nature is the same in both; that both bodies are affected alike, and that the property is distinctive of both. For in all cases that have been observed, the indicating phenomenon is equally connected with both bodies; as in the case of magnetism the magnet and the iron approach each other; and an electrified body and another body near it approach each other. This property is therefore equally inherent in both bodies, between which there is a mutual attraction. But, according to some philosophers, no such mutual tendencies exist either in the one body or the other. The observed approaches or mutual separations of bodies, or their attractions and repulsions, are supposed to depend on the extraneous action of an ethereal fluid.

87. These qualities thus inherent in bodies, which constitute their mechanical relations, or the mechanical affections of matter, have been called powers or forces. The event which is indicated by their presence, is considered

considered as the effect and mark of their agency. Thus the magnet is said to act on the iron, the earth is said to act on the stone which falls to its surface; and the iron and the stone are said to act on the magnet and the earth. But all this, it must be observed, is figurative language. Power, force, and action, when used in their original strict sense, express only the notions of the power, force, and action of sentient, active beings; and cannot be predicated of any thing but the exertions of such beings; for such beings only are agents. In strict propriety, it is perhaps only the exerted influence of the mind on the body which ought to be called action. Language having begun among simple men, such denominations were very properly given to their own exertions; because to move a body they found it necessary to exert their force or power, or to act. But when the changes of motion, observed in the occurrence or vicinity of bodies, were attended to by speculative men, and it was found that the phenomena greatly resembled the results or effects when they exerted their own strength, similar terms were employed to express these occurrences in nature. The old term was retained, in preference to the invention of a new language, to express things which had so near a resemblance. The danger of confounding things from the use of the same terms, was avoided from the differences in other circumstances of the case. It is not, however, to be imagined, that they supposed inanimate bodies exerted force or strength in the same way as living beings. But, in the progress of refinement, the word power or force came at last to be employed to express any efficiency whatever; and hence the common expressions, the force of arguments, the action of motives, the power of an acid to dissolve a metal, &c. It is to this idea of convenience, that the use of the terms attraction, repulsion, pressure, impulsion, as well as of the words power and force, which express efficiency in general, is to be ascribed. But these terms, excepting in those cases when they are applied to the exertions or actions of living beings, are metaphorical. On account, however, of the resemblance between the phenomena and those which are observed when we draw a thing towards us, push it from us, forcibly compress it, or kick it away, these different actions being analogous to attraction, repulsion, pressure, and impulsion, these words are employed as terms of distinction. The action of the mind on the body is perhaps the only case of pure unfigurative action. But this action being always exerted with the view of effecting some change on external bodies, our attention is only directed to them. The instrument passes unnoticed; and hence it is said that we act on the external body. The real action is only the first movement in a long succession of events, and is only the remote cause of the interesting event. In many cases of mechanical phenomena, we find the resemblance to such actions to be very strong. The following is of this description. A ball is projected from a man's hand by the motion of his arm; and in the same way a ball is impelled by the unbending of a spring. In all circumstances there is a resemblance between these two events, excepting in the action of the mind on the corporeal organ. And, hence in general, because the ultimate results of the mutual influence of bodies on each other have a strong resemblance to the ultimate results of our actions on bodies, no new or ap-

propriate terms have been invented; but, as has been already observed, mankind have remained satisfied with the use of those terms that are employed to express their own actions, or the exertions of their own powers or forces.

88. When power or force is spoken of as existing or residing in a body, and the effect is ascribed to the exertion of this power, one body considered as possessing it, is said to act on another. Thus a magnet is said to act on a piece of iron; a billiard ball is said to act on one which it strikes. But if it be attempted to fix the attention on this action, independent both of the agent and the thing acted on, we shall find that there is no object of contemplation. The exertion or procedure of nature in effecting the change is kept out of view; and if we limit our attention to the action as a thing distinct from the agent, we shall find that it is not the action, strictly speaking, but the act, that is brought under consideration. And in the same way, it is only in the effect produced that the action of a mechanical power can be conceived.

89. In the very nature of action some change is implied. Without producing some effect, a man is never said to act. Thought is the act of a thinking principle; and the motion of the limb is the act of the mind on it. In mechanics too there is action only in so far as some mechanical effect is produced. For instance, to begin motion on a piece of ice, or to slide along it, we must act violently; we must exert force; and this force being exerted produces motion. In all cases, the productions of motion are conceived as the exertions of force; but to continue the motion which has been begun along the ice, no exertion seems requisite. Being conscious of no exertion, we ought to infer that no force is necessary for the continuation of motion. It is not the production of any new effect, but the permanency or continuation of an effect already produced. Motion is indeed considered as the effect of some action; but there would be no effect or no change, if the body were not moving. Motion is not to be considered as an action, but the effect of an action.

90. Mechanical actions or forces have been divided into pressures and impulsions. The idea of pressure is very familiar; perhaps it enters into every distinct conception that we can form of a moving force, when the attention is endeavoured to be fixed on it. Changes of motion by the collision of moving bodies are produced by impulsion. Pressures and impulsions are usually considered as of different kinds, the actions or exertions of different powers. It is supposed that there is an essential difference between pressure and impulsion. That we may obtain all the knowledge that these distinctions can give us, let us state some examples of these kinds of forces, instead of attempting to define or describe them.

Let us first take some examples of pressure. Pressure is known to be a moving force; for if a ball lying on the table be gently pressed on one side, it moves towards the other side of the table. If it be followed with the finger, the pressure being continued, its motion is continually increased. There is an acceleration of its motion. By pressing in the same way on the handle of a common kitchen jack, the fly begins to move; and if the pressure be continued on the handle, the motion of the fly becomes very rapid; and there

is also a continual acceleration. Such motions as these are the effects of genuine pressure. The unbending of a spring would urge the ball in the same way along the table, and would produce a continually accelerated motion; and a spring coiled up round the axis of the handle of the jack would, by uncoiling itself, urge round the fly with a similar accelerated motion. By comparing the pressure of the finger on the ball with the effects of the spring, we perceive distinctly the perfect similarity. These exertions or actions, or influences, are denoted by the word pressure, which is derived from the most familiar instance of them.

The same motion may be produced in the ball or fly, by pulling the ball or machine by means of a thread having a weight suspended to it. Both being motions accelerated in the same manner, the action of the thread on the ball or machine comes under the same denomination of pressure. Weight is therefore considered as a pressing power. And indeed the same compression is felt from the real pressure of a man on the shoulders and a load laid on them. But in the instance above, the weight acts by the intervention of the thread. By the pressure of the weight it pulls at that part of the thread to which it is attached; this part pulls at the next by the force of cohesion; and this at a third, and so on, till the most remote pulls at the ball or machine. In this way elasticity, weight, cohesion, and other forces, perform the office of a genuine power; and their result being always a motion beginning from nothing, and accelerating to any velocity by perceptible degrees, from this resemblance we are led to give them one familiar name.

91. If the thread by which the weight is suspended be cut, it falls with an accelerated motion. This also is ascribed to some pressing power which acts on the weight; and it is even considered as the cause of the body's weight, which word is a name by which this instance of pressing power is distinguished. Gravitation, therefore, comes under the denomination of pressure. For the same reason the attractions and repulsions of the magnet, or of electric bodies, belong to this class of phenomena; for on bodies placed between them they produce actual compressions, as well as motions which are continually accelerated, in the same way as gravitation does. To all these powers, therefore, the descriptive name of pressures may be given, although this name, properly speaking, belongs to one of them only. This great class has been subdivided by some philosophers into pressures and solicitations. Gravity is considered as a solicitation ab extra, by which a body is urged downward. The forces of electricity and magnetism, with many other attractions and repulsions, are also called solicitations. But this classification seems to be of little use.

92. We have a familiar instance of impulsion in one ball striking another, and putting it in motion. In this case the appearances are very different from the phenomena of pressure. For the body that is struck acquires in the instant of impulse a sensible quantity of motion. But after the stroke this motion is neither accelerated nor retarded, unless by the action of some other force. The rapidity of the motion, it is observed, depends on the previous velocity of the striking ball. If for instance a clay ball, moving with any velocity, strike another equal ball which is at rest, the

ball which is struck moves with one half of the velocity of the other. It is farther observed that the striking ball always loses as much motion as the ball which is struck gains. From this remarkable fact there seems to have arisen an indistinct notion of a kind of transference of motion from one body to another. It is not said that the one ball produces motion or causes it in the other, but it is said to communicate motion to it; and the phenomenon is usually termed the communication of motion. This, however, is a very inaccurate mode of expression. We distinctly conceive the cause or communication of heat, the communication of saltiness, of sweetness, and of many other things; but we have no clear conception of part of the identical motion which existed in one body being transferred to another. From this, therefore, it appears that motion is not a thing which can exist independently, and is susceptible of actual transference; but is a state or condition of which bodies are susceptible, which may be produced in bodies, and which is the effect or characteristic of certain natural properties or powers.

The notion of the actual transference of something formerly possessed by the striking body, and now separated from it, or transfused into the body which is struck, has obtained support from the remarkable circumstance in the phenomenon, that a rapid motion requiring for its production the action of a pressing power, continued for a sensible, and frequently a long time, is or seems to be effected instantaneously by impulsion. Here then we find room for the employment of metaphor, both in thought and language. We see the striking body affect the body which is struck. It possesses the power of impulsion, or of communicating motion, but it only possesses this power while it is itself in motion; and we therefore conclude that this power is the efficient distinguishing cause of its motion. Hence it has been called inherent force, the force inherent in a moving body, vis insita corpori moto. This force is communicated to the body impelled, or transfused into it; the transference is instantaneous, and the body thus impelled continues in motion till it is changed by a new force. But if we attend scrupulously to those feelings which have given rise to this metaphorical conception, we shall find, that although at first sight this train of observation seems very plausible, we should entertain very different notions. To begin the motion of sliding on a smooth piece of ice, we are conscious of exertion; but when the ice is very smooth, no exertion that we are conscious of seems requisite to continue the motion. No exertion of power is here necessary; and therefore we have no primitive feeling of power while we slide along. And indeed we cannot think of moving forward without effort otherwise than as a certain mode of existence. It has however been imagined that those who support this opinion have in some way deduced it from their feelings. To move forward in walking, we must continue the exertion with which we began; and unless this power of walking be continually exerted, we must stop our progress. But this is inaccurate observation. In the action of walking there is much more than the continuance in progressive motion. It is the repeated and continued lifting the body up a small height, and allowing it to come down again, and this repeated ascent requires repeated exertion.

93. From the consideration of the instantaneous production of rapid motion by impulse, some distinguished philosophers have been led to suppose that the force or power of impulse is not susceptible of being compared with a pressing power. It has been asserted that impulse when compared with pressure is infinitely great. But the similarity of the ultimate results of impulse and pressure, have always led them to adopt a different view. There is no difference between the motion of two balls which move with equal rapidity, one of which descends from a height by the force of gravity, while the other has been struck by another body. In this struggle of the mind attached to preconceived opinions, and at the same time accommodating these opinions to observed phenomena, other singular forms of expression have arisen. Pressure is considered as an effort to produce motion. And here we have another instance of metaphorical expression as well as thought. The weight of a ball on the table is called a power; and this weight is continually endeavouring to move the ball downward. But these efforts being ineffectual, the power in this case is said to be dead. It is called vis mortua, in contradistinction to the force of impulse, which is called a living power, vis viva. But this mode of expression must appear very inaccurate, if we consider the case of the impelling ball falling perpendicularly on the other ball lying on the table. No motion is induced by this impulse; and if the table be conceived to be annihilated, the power of gravity becomes a vis viva.

To prove that impulse is infinitely greater than pressure, numerous familiar instances have been adduced by those who support this doctrine. A nail is driven with a moderate blow of a hammer, which would require a pressure many hundred times greater than the impelling effort of the person who employs the hammer. A hard body may be shivered to pieces with a moderate blow, which would support an inconceivable weight gradually applied. This prodigious superiority in impulse leaves it a difficult matter to account for the production of motion by means of pressure; because the motion of the hammer might have been acquired in consequence of the continued pressure of the carpenter's arm. It is considered as the aggregate of an infinite number of succeeding pressures repeated in every instant of its continuance. The smallness of each effort is compensated by their number.

94. After all, it does not appear clear that there are two kinds of mechanical force which are essentially different in their nature. It is, indeed, in a great measure given up by those who support the doctrine that impulse is infinitely greater than pressure: Some method might perhaps be found of explaining satisfactorily this remarkable difference between the two modes of producing motion. But there seems to be no considerable advantage in thus arranging the phenomenon under two distinct heads.

95. The nature of the sole moving force in nature has given rise to much discussion among mechanicians, and produced no small diversity of opinion. According to some, all motion is the effect of pressure; for when impulse is considered as equivalent to the aggregate of an infinite number of pressures, every pressure, however small, is supposed to be a moving force.

The sole cause of motion, according to other philoso-

phers, is impulse. Bodies are observed in motion; they impel others, and produce motion in them; and this production of motion is said to be regulated by such laws, that there is only one absolute quantity of motion in the universe, which quantity remains invariably the same. Some portion of this motion, therefore, must be transferred or transfused when bodies come into collision with each other. But besides, there are some cases in which it is perfectly obvious that motion produces pressure. Cases, which are indeed both whimsical and complicated, have been adduced by Euler, to show that an action, in all respects similar to pressure, may be produced by motion. Such a case is the following. If two balls are connected by a thread, they may be struck in such a way, that they shall not only move forward, but at the same time also wheel round. When this happens, the thread by which they are connected is stretched. Since then, according to this reasoning, motion is observed, and pressure is produced by motion, it would be absurd to suppose that pressure is any thing else than the result of certain motions. The philosophers who are attached to this doctrine of moving forces, proceed to account for those pressing powers or solicitations to motion which are observed in the acceleration of falling bodies, the phenomena of magnetism and electricity, and others of the same kind, where motion is induced on certain bodies which are in the vicinity of other bodies, or, as it is expressed in common language, by the action of other bodies at a distance. To say that a magnet can act on a piece of iron at a distance, is to say that it acts where it is not; which is no less absurd than to say that it acts, when it is not. Euler assumed it as an axiom, nihil movetur, nisi à contiguo et moto.

The methods proposed by these philosophers to produce pressure, are less ingenious and not more satisfactory than that adduced by Euler which was mentioned above; and indeed they do not seem to be very anxious about the manner in which these motions are produced. The phenomena of magnetism are induced, or a piece of iron is put in motion, when it is in the vicinity of a magnet, by a stream of fluid which issues from one pole of a magnet, passes in a circle round the magnet, and enters at the other pole. By this stream of fluid the iron is impelled, and brought to arrange itself in certain determined positions. In the same way all bodies are impelled in lines perpendicular to the surface of the earth by a stream of fluid which is in continual motion towards its centre. In the same way similar phenomena are accounted for, and thus these motions are reduced to simple cases of impulse. But to say nothing worse of this doctrine, it is not very compatible with the dictates of common sense. It proceeds on the supposition that something acts which we do not see; and of the existence of which there is not the smallest proof.

96. Pressure, according to the opinion of others, is or pressure, the only moving force in nature; but it is that kind of pressure which has been termed solicitation, not what arises from the mutual contact of solid bodies. Gravitation is an instance of the kind of pressure here alluded to. It is affirmed by these philosophers, that there is no such thing as contact on the instantaneous communication of motion by the real collision of bodies. It is said that the particles of solid bodies exert very strong repulsions—

Of Moving Forces. repulsions to a small distance; and when they are brought by any motion sufficiently near to another body, they exert a repulsive force, and are equally repelled by this body. Motion is thus produced in the one body, while it is diminished in the other. It is then shown by scrupulously considering the state of the bodies, while the one advances and the other retires, in what way they attain a common velocity, the quantity of motion before collision remaining the same, and the one body gaining exactly as much as the other loses. Cases also are adduced, of such mutual action between bodies, where it is obvious they have never come into contact; but where the result is exactly the same as when the motion seemed to be instantaneously changed. And hence it is concluded that there is no such thing as instantaneous communication, or transfusion of motion, by contact in collision or impulse. All moving forces, according to these philosophers, are of that kind which have been named solicitations; such as gravity is.

97. Different names have been given to the exertions of mechanical forces, according to the reference that is made to the result. In wrestling, when my antagonist exerts his strength to prevent being thrown down, and I am sensible of his exertion, I thus discover that he resists. But if I oppose him only to prevent him throwing me, I am said to resist. If I strike or endeavour to throw him, I am said to act. The same distinction is applied to the exertion of mechanical powers. If, for instance, one body A change the motion of another body B, the change in the motion of B may be considered either as the indication and measure of the power of A in producing motion, or as the indication and measure of the resistance made by A in being brought to rest, or having any change induced on its motion. The distinction which is here made is not in the thing itself, but exists only in the reference which we are disposed to make of its effect, from other considerations. If a change of motion take place when one of the powers ceases to be exerted, it is conceived that this power has resisted. But this language is metaphorical. Resistance, effort, endeavour, are all words which express motions that relate to sentient beings. There is perhaps no word preferable to the word reaction, to express the mutual force which is observed in all the operations of nature which have been successfully investigated.

98. A difficulty has been started with regard to the opinion of those who affirm that all mechanical phenomena are dependent on attracting and repelling forces; because it is here supposed that bodies act on each other at a distance, and however small this distance may be, this is conceived to be absurd. It may however be observed, that the mutual approaches or recesses of bodies may be ascribed to tendencies to, or from each other. Without thinking of any intermediate connection between the iron and the magnet, we conceive the iron to be affected by the magnet; and if this be conceivable, it is not absurd. Our knowledge of the essence or nature of matter is not such as to render this tendency of the iron to the magnet impossible. We do not indeed see intuitively why the iron should approach to the magnet; but this is by no means sufficient to pronounce it impossible or inconsistent with the nature of matter. To suppose therefore in the production of

motion, the impulse of an invisible fluid, of which we know not any thing, and of whose existence there is no evidence, is a rash and unwarrantable assumption. But farther, if it be true that bodies do not come into contact, even when one ball strikes another, and drives it before it, the supposition of the existence of this invisible fluid will not assist us in solving the difficulty; for the same difficulty would occur in the action of any one particle of the fluid in the body. At any rate the production of motion without any observed contact, is more familiar to us than the production of motion by one body acting on another by impulse. Every case of gravitation is an instance of this.

99. In those cases where the exertions of any mechanical power are observed to be always directed toward any body, that body is said to attract. Thus a boat is attracted toward a man when he pulls it toward him by means of a rope. This is a case of pure attraction. But when the other body always moves off, the body exhibiting this phenomenon is said to repel; and it is a case of pure repulsion when a person pushes any body from him. And because there is a resemblance to the results of real attraction and repulsion, the same terms are employed to express the mechanical phenomena of nature. But that our conceptions may not be embarrassed or rendered obscure by the use of such metaphorical expressions, it is requisite to be careful not to allow these words to suggest to us any opinion about the manner in which mechanical forces produce their effects. If the opinion which is held of the existence of an invisible fluid on which mechanical action depends be well founded, it is obvious that there can be neither attraction nor repulsion in the universe.

100. Forces are conceived as measurable quantities. Thus we conceive one man to possess double the strength of another man, when we observe that he can resist the combined efforts of two others. It is in this way that animal force is conceived as a quantity made up of its own parts and measured by them. This however seems not to be a very accurate conception. Our conception of one strain being added to another is obscure, although we have a distinct notion of their being combined. There are no words to express the difference of these two notions in our minds; but we think that the same difference is perceived by others. We have a clear conception of the addition of two lines or two minutes; but our notions of two forces combined are indistinct; although it cannot be affirmed that two equal forces are not double of one of them. They are measured by the effects which they are known to produce.

101. In the same way mechanical forces are conceived as measurable by their effects, and thus become the subject of mathematical discussion. We speak of the proportions of magnetism, electricity, &c. and even of the proportion of gravity to magnetism. These, however, considered in themselves, are quite dissimilar, and do not admit of any proportion; but some of their effects are measurable, and these assumed measures being quantities of the same kind are susceptible of comparison. The acceleration of motion in a falling body, is one of the effects of gravity; magnetism accelerates the motion of a piece of iron; and these two accelerations may be compared together. But because none of the measurable effects of magnetism with which we are acquainted

Moving acquainted, are of the same kind with any of the effects of heat, magnetism and heat are not susceptible of comparison.

When it is said that the gravitation of the moon is the 3600th part of the gravitation of a stone at the sea-shore, it is meant that the fall of a stone in a second is 3600 times greater than the fall of the moon in the same time. But to express the proportion of the tendency of gravitation more purely, if a stone hung on the spring of a steelyard, draw out the rod of the steelyard to the mark 3600, the same stone carried up to the distance of the moon will draw it out only to the mark one. And if the stone at the sea-shore draw out the rod to any mark, it will require 3600 such stones to draw the rod out to the same mark at the distance of the moon. Now, it is not in consequence of an immediate perception of the proportion of gravitation at the moon to that at the surface of the earth that such an assertion is made. It is because these motions being considered as its effects in such situations, and being magnitudes of the same kind, are susceptible of comparison, and have a proportion which can be determined by observation. And although the proportions of the causes or forces are spoken of, yet it is only the proportions of the effects which come under contemplation.

102. In order that these assumed measures may be accurate, they must be always connected with the magnitudes which they are employed to measure; and the connection must be of that kind, that the degrees of the one must change in the same manner with the degrees of the other. The same thing must also be known of the measure which is employed; the precise and constant relation must be seen. But how is this to be accomplished? Force as a separate existence is not a perceptible object. We do not perceive its proportions, so as to be able to ascertain that they are the same with the proportions of the measures. On the contrary, the very existence of this force is inferred from observation of the acceleration, and its degree is also an inference from the observed extent or magnitude of the acceleration. The measures which are thus assumed are therefore necessarily connected with the magnitudes, and their proportions are the same; the one is an inference from the other both in kind and degree.

103. It now appears that this subject is susceptible of mathematical investigation. After having selected our measures, and observing certain mathematical relations of those measures, every inference deduced from the mathematical relations of the proportions of those representations is true of the proportions of the motions, and therefore it is also true of the proportions of the forces. Thus then Dynamics may be reckoned a demonstrative science.

104. Moving forces are considered as differing also in kind, that is, in direction. The direction of the observed change of motion is assigned to the force; which is not only the indication, but also the measure of the changing force. This force is called an accelerating, retarding, or deflecting force, according as it is observed, that the motion is accelerated, retarded, or deflected. And from these terms it must appear, that we have no knowledge of the forces different from our knowledge of the effects. They are either descriptive of the effects, or they have a reference to the substances in which the forces are supposed to be inherent.

Thus of the first kind are the terms accelerating, attractive, or repulsive forces; of the second, are the terms magnetism, electricity, &c.

Of the Laws of Motion.

105. Such then being our notions of mechanical forces, of the causes of the production of motion and its changes, there are certain results, which by the constitution of the human mind, necessarily arise from the relations of these ideas. These results are laws of human judgment, independent of all experience of external nature. Some of these laws may be intuitive, presenting themselves to the mind as soon as the ideas which they involve are presented to it. These may be called axioms. Others may be as necessary results from the relations of these notions, are less obvious, and may require a process of reasoning to establish their truth.

Of these laws there are three, which were first distinctly proposed by Sir Isaac Newton. These may be considered as the first principles of all discussions in mechanical philosophy, give a sufficient foundation for all the doctrines of Dynamics, and to these principles we may refer for the elucidation of all the mechanical phenomena of nature.

First Law of Motion.

106. Every body continues in a state of rest, or of uniform rectilinear motion, unless it is affected by some mechanical force.

On the truth of this proposition the whole of mechanical philosophy chiefly depends. But with regard to its truth and the foundation on which it rests, the opinions of philosophers are very different. In general these opinions are obscure and unsatisfactory; and, as is usual, they influence the discussions of those who hold them in all their investigations.

107. It is not only the popular opinion that a state of rest is the natural state of body, and that motion is something foreign to it, but the same opinion has been supported by many philosophers. They allow that matter unless it is acted on by some moving force will remain at rest; and nothing seems necessary for matter to remain where it is, but its continuing to exist. But the case is widely different, according to these philosophers, with respect to matter in motion. For here the relations of the body to other things are continually changing; and as there is the continual production of an effect, the continual agency of a changing cause is necessary. This metaphysical argument, it is said, is fully confirmed by the most familiar observations. All motions, whatever may have been their violence, terminate in rest, and for their continuance the continual exertion of some force is necessary.

108. It is affirmed by these philosophers, that the continual action of the moving cause is essentially requisite for the duration of the motion. But their opinions of the nature of this cause are not uniform. According to some, all the motions in the universe are produced and continued by the direct agency of the Deity himself. By others all the motions and changes of every particle of matter are ascribed to a sort of mind which is inherent in it. This is called an elemental mind. It is the same as the physis and the energeia of Aristotle. Every thing, according to these philosophers,

Of Moving phers, which moves, is mind, and every thing which
Forces. is moved is body. But this elemental mind is only
known and characterized by the effects which are as-
cribed to its action; and these are observed in the mo-
tions or changes which are produced. These, we learn
from uniform experience, are regulated by laws equally
precise with the laws of mathematical truth. But there
is nothing which indicates any thing like intention or
purpose; none of the marks or characters by which
mind was brought first into view. They resemble the
effects produced by the exertions of corporeal force;
and hence the word force has been applied to express
the causes of motion.

No body is 109. A state of rest, it has been supposed, is the natu-
in absolute rest. ral state of matter. But it does not appear that the con-
tinued action of some cause is necessary for continuing
matter in motion. Experience gives us no authority
for supposing that the natural condition of matter is a
state of rest. It cannot be affirmed of any body what-
ever, that it has ever been seen in absolute rest. All
the parts of the planetary system are in motion; and
even the sun himself with his attendant planets is car-
ried in a certain direction with a great velocity. There
is no unquestionable evidence that any of the stars are
absolutely fixed; and many of them, it has been ascer-
tained by observation, are in motion. Rest, therefore,
being so rare a condition of matter, no experience which
we have, supports the notion that this is its natural con-
dition. This opinion seems to be derived from our own
experiments on matter. To continue the motion of a
body, we find that the continued action of some mov-
ing force is necessary, otherwise the motion becomes
gradually slower, and at last terminates in rest. Since
then we see that our own exertions are constantly ne-
cessary in the production of motion, and especially in
those cases where we are interested; we are thus in-
duced to ascribe to matter something that is naturally
quiescent and inert, and even something that is slug-
gish and averse from motion. But this is an erroneous
conception, which is suggested to our thoughts from
the imperfection of language. We ascribe animation
to matter, to give it motion, and endow it with a kind
of moral character in order to explain the phenomena
of motion.

Matter has 110. But more accurate and more extended obser-
no aptitude vation leads us to conclude that matter has no peculiar
rest. aptitude to a state of rest. Every observed retardation
has a distinct reference to external circumstances.
Wherever there is a diminution of motion, it is invari-
ably accompanied by the removal of obstacles; as in
the case when a ball moves through sand, or air, or wa-
ter. The diminution of motion is also owing to oppo-
site motions which are destroyed. And it is found
that the more these obstacles are kept out of the way,
the less is the diminution of motion. The vibration of
a pendulum in water soon ceases; it continues longer
in air; and much longer in the exhausted receiver. The
conclusion then from these observations is, that if all
obstacles could be completely removed, motion would
continue for ever. This conclusion is strongly support-
ed by the motions of the heavenly bodies. These mo-
tions, so far as we know, are retarded by no obstacles;
and accordingly they have been observed to retain
them without perceptible diminution for thousands of
years.

111. The inactivity of matter has been denied by other philosophers. According to them it is essentially active, and continually undergoing changes in its con-
dition. Some traces of this doctrine are to be found in the writings of some of the ancient philosophers; but it was reduced to a systematic form by Leibnitz. According to this philosopher, every particle of matter is end-
owed with a principle of individuality. This he calls a monad, which is supposed to have a kind of percep-
tion of its place in the universe, and of its relation to all
other parts of the universe. This monad too is supposed
to act on the particle of matter in the same way as the
soul acts on the body. The motion of the material
particle is modified by the monad, and thus are produ-
ced, according however to unalterable laws, all the ob-
served modifications of motion. And thus matter, or
the particles of matter, are continually active and conti-
nually changing their situation. No information in
any way useful can be obtained from this fanciful hy-
pothesis. It is not unlike the system of elemental
minds. And should its existence be admitted, it would
not, any more than the actions of animals, invalidate
the general proposition which is considered as the fun-
damental law of motion. The powers of the monads
or of the elemental minds are supposed to be the causes
of all the changes; but the particle of matter itself is
subject to the law, and any change of motion which it
exhibits is ascribed to the exertion of the monad.

112. By another set of philosophers, the law of mo-
tion is deduced from the want of a determining cause.
At the head of this sect is Sir Isaac Newton, who main-
tains the doctrine affirmed in the proposition. But these
philosophers are not uniform in their opinion of the foun-
dation on which it rests. It is asserted by some that it is
a kind of necessary truth which arises from the nature
of the thing. If, for instance, a body be in a state of
rest, and if it be asserted that it will not remain at rest,
it must move in some direction; and if it be in motion in
any direction, and with any velocity, and do not contin-
ue its equable, rectilinear motion, it must be either
accelerated or retarded; it must either turn to one side
or to some other side. The event, whatever it be, is in-
dividual and determinate; but no cause which can de-
termine it being supposed, the determination cannot
take place, and no change with respect to motion will
happen in the condition of the body. It will either re-
main at rest, or persevere in its rectilinear and equable
motion. But to this argument of sufficient reason, as
it has been called, considerable objections may be made.
In the immensity and perfect uniformity of time and
space, there is no determining cause why the visible
universe should exist in one place rather than in another,
or at this time rather than at another. It is essentially
necessary that there should be a cause of determination;
for a determination may be without a cause, as well as
a motion without a cause.

113. Other philosophers deduce this law of motion
from experience. They consider it merely as an experi-
mental truth, of the universality of which there are in-
numerable proofs. When a stone is thrown from the
hand, it is pressed forward, and when the hand has the
greatest velocity that we can give it, the stone is let go,
and it continues in that state of motion which it gradu-
ally acquired along with the hand. A stone may be
thrown much farther by means of a sling, because with

Having a very moderate motion of the hand, the stone being whirled round acquires a very great velocity, and when it is let go, it continues its rapid motion. We have a similar illustration in the case of an arrow shot from a bow. The string which presses hard on the notch of the arrow carries it forward with an accelerated motion as it becomes a straight line by the unbending of the bow; and there being nothing to check the arrow, it flies off. In these simple cases of perseverance in a state of motion the procedure of nature is easily traced; it is perceived almost intuitively. In many other phenomena it is not less distinct, although somewhat more complicated. A man can stand on the saddle of a horse at a gallop, and step from it to the back of another horse that gallops along with him at the same rate; and this he seems to do with the same ease as if the horses were standing still. The man is carried along with the same velocity as the horse which gallops under him, and he retains the same velocity while he steps from the back of one horse to that of the other. But if the horse to which he steps were standing still, he would fly over his head, because he is carried forward with the velocity of the galloping horse; or if he stepped from the back of a horse standing still to that of one at a gallop, he would be left behind; because he has not acquired the velocity of the galloping horse. In the same way a man tosses oranges from one hand to the other while he is carried forward with the motion of a horse at a gallop, or while he swings on the slack-wire. In both cases the oranges have the same motion as the man, and while they are in the air are moving forward with the same velocity, so that they drop into the hand at a considerable distance from the place in which they were thrown from the other hand. While a ship sails forward with a rapid motion a ball dropped from the mast head falls at the foot of the mast: for it retains the motion which it had previous to its being dropped, and follows the mast during the whole time of its fall.

114. Familiar instances may also be given of a body in a state of rest. A vessel filled with water drawn suddenly along the floor, leaves the water behind, which is dashed over the posterior side of the vessel; and when a boat or coach is suddenly dragged forward, the persons in it find themselves strike against the hinder part of the carriage or boat; or rather it should be said the carriage strikes on them, for it sooner acquires motion from the action of the force applied. A ball discharged from a cannon will pass through a wall and move onward; but the wall remains behind.

115. Common experience is perhaps insufficient for establishing the truth of this fundamental proposition. It must be granted, that we have never seen a body either at rest, or in uniform rectilinear motion; yet this seems necessary before it can be said that the proposition is experimentally established. What is supposed in our experiments to be putting a body, formerly at rest, into motion, is in fact only producing a change of a very rapid motion—a motion not less than 90,000 feet per second.

116. For the purpose of obtaining such experimental proof of the truth of this proposition, it will be necessary to resort to other observations. The relative motions of bodies, which are the differences of their absolute motions, only can be measured. We cannot measure their absolute motions. If then it can be shown by experi-

ment that bodies have equal tendencies to resist the augmentation and diminution of their relative motions, they thus have equal tendencies to resist the augmentation or diminution of their absolute motions.

Let A and B two bodies be put into such a situation that they cannot persevere in their relative motions. The change which we observe produced on A is the effect and measure of the tendency of B to persevere in its former state. From the proportion of these changes therefore we derive the proportion of their tendencies to remain in their former condition. This will be illustrated by the following experiment, which should be made at noon.

117. Let the body moving at the rate of three feet per second to the westward, strike the equal body B which is apparently at rest. Different cases of the results of the changes thus produced may be supposed.

1st. Let A impel B forward without having its own velocity at all diminished. From this result it appears that B shows no tendency to maintain its motion unchanged, but that A retains its motion without diminution.

2d. Suppose that A stops, and that B remains at rest. This case shows that A does not resist a diminution of motion, and that the motion of B is not changed.

3d. Let it be supposed that both move westward at the rate of one foot per second. There is in this case a diminution of the velocity in A, equal to two feet per second. This then is to be considered as the effect and measure of the tendency of B to maintain its velocity unaugmented. B has received an augmentation of one foot per second in its velocity. From this change it appears that the tendency is but half of the former; and the result shows that the resistance to a diminution of velocity is only equal to one half of the resistance to augmentation; and perhaps equal only to one quarter, since the change on B has effected a double change on A.

4th. Let it be supposed that both bodies move forward with the velocity of one and a half feet per second. In this case it is obvious that the tendencies of the two bodies to maintain their states unchanged are equal.

5th. But suppose that $A\; =\; 2B$, and that the velocity of both after collision is equal to two feet per second. The body B has then received an addition of two feet per second to its former velocity; and this is the effect and measure of the whole tendency of A to preserve its motion undiminished. One half of this change on C measures the persevering tendency of one half of A; but it is supposed that A, which formerly moved with the apparent or relative velocity three, now moves with the velocity two, and thus has lost the velocity of one foot per second. Therefore each half of A has lost this velocity; and the whole loss of motion is two. This then is the measure of the tendency of B to maintain its former state unaugmented; and it is the same with the measure of the tendency of A to preserve its former state undiminished. From such a result therefore the conclusion would be, that bodies have equal tendencies to maintain their former states of motion unaugmented and undiminished.

The suppositions made above in the 4th and 5th cases are the result of all the experiments which have been made; and in all the changes of motion which are produced

produced by the mutual action of bodies on impulsion, this is the regulating law. To this there is no exception. And thus it appears that there exists in bodies no preferable tendency to rest. No fact can be adduced which should lead us to suppose that a motion having once begun should suffer any diminution without the intervening action of some changing cause.

118. It must, however, be observed that this is a very imperfect way of establishing the first law of motion. It is inapplicable to those cases where experiment cannot be made; and at best it is subject to all the inaccuracies of the best managed experiments. If this proposition be examined by means of the general principles which have been adopted in the article PHILOSOPHY (which see), an accurate decision of this question may be given. These principles, which are the foundation of all our knowledge, shew that this proposition is an axiom or intuitive consequence of the relations of those ideas which we have of motion, of its changes, and of their causes.

119. Powers or forces, it has been shewn, are not the immediate objects of our perceptions. Their existence, kind, and degree, are inferences from the motions which we observe. And hence it follows, that when no change of motion is observed, no such inference is made; no force or power is supposed to act. But when any change of motion is observed, the inference is made; a power or force is supposed to have acted. By a similar conclusion, it is said, that when no change of motion is supposed, no force is thought of or supposed; and whenever a change of motion is supposed, it always implies a changing force. On the other hand, when the action of a changing force is supposed, the change of motion is also supposed; the action of this force and the change of motion being the same thing. The mind does not admit the idea of the action, without at the same time thinking of the indication of the action, and this indication is the change of motion. And in the same way, when we do not think of the changing force, or do not suppose the action of a changing force, we suppose, although it be not expressed in terms, that there is no indication of this changing force; that there is no change. If, therefore, it be supposed that no mechanical force acts on a body, we suppose in fact that the body remains in its former condition with respect to motion. And if it be supposed that nothing accelerates or retards, or deflects the motion, it is conceived as neither accelerated nor retarded, nor deflected. Hence it follows, that we suppose the body to continue in its former state of rest or motion, unless we suppose that it is changed by some mechanical force.

120. This proposition then does not depend on the properties of body as a matter of experience or contingency. It is to us a necessary truth. It is not so much any circumstances with regard to body that are expressed in the proposition, as the operations of the mind in considering these circumstances. The truth of the proposition will not be invalidated by taking into view, that it may be essential to move in some particular direction; that it may be essential to body to stop when the moving cause ceases to act; or gradually to diminish its motion, and at last to come to rest. The circumstances in the nature of body which render those modifications essentially necessary, are the causes of those modifications; and they are to be considered as changing forces.

If we should suppose that body of its own nature is or is not capable of producing a change in its condition, this change must be effected according to some law which characterizes the nature of body. But the knowledge of this law can be obtained only by observing the deviations from uniform rectilinear motion. It then becomes indifferent whether external causes operate those changes, or they depend on the nature of the thing; for in considering the various motions of bodies, we must first consider the nature of matter as one of its mechanical affections which operates in every instance; and this brings us back to the law contained in the proposition. This is rendered more certain by reflecting, that the external causes, such for instance as gravity and magnetism, which are acknowledged to operate changes of motion, are not less unknown to us than this essential property of matter. They are, like it, only inferences from the phenomena.

121. Many philosophers, among which number may be included Newton himself, have introduced modes of expression, which suggest inadequate notions, and such as are incompatible with the doctrine of the proposition; for although they allow that rest is the natural condition of body, and that force is necessary for the continuation of motion, yet they speak of a power or force residing in a moving body by which it perseveres in its motion. This has been called the vis insita, or the inherent force of a moving body. Now if the motion be supposed to be continued in consequence of a force, that force must be supposed to be exerted, and it is supposed that if it were not exerted the motion would cease. The proposition, therefore, must be false. To obviate this objection, it is indeed sometimes said, that the body continues in uniform rectilinear motion, unless it is acted on by some external cause. This mode of expression, however, subjects us to the impropriety of asserting that gravity, electricity, and other mechanical forces, are external to the bodies on which they are supposed to act and to put in motion. Every thing which produces a change of motion is very properly called a force; and when a change of motion is observed, the action of such a force is very properly inferred. But to give the same name to what has not this property of producing a change, and to infer the action of a force when no change is observed, is not a very accurate or consistent expression. This error has arisen from the use of analogical language in philosophical discussions.

122. But motion is not, as philosophers have imagined, the continual production of an effect. We can conceive there is such a thing as a moving cause, to which the name of force has been given. This produces motion, and the character of motion in body, which is a continual change of place. Motion is the effect of an action; and previous to the commencement of the motion, this action is equally incomplete as it is the minute after. The immediate effect of a moving force is a determination to motion, which if not obstructed by some cause would go on for ever. In this determination only the condition of the body differs from a state of rest. Motion then is a condition or mode of existence, which no more requires the continued agency of the moving cause than colour or figure. Some mechanical cause is required to change this condition into the state or condition of rest. When a moving

moving body is brought to rest, some cause of this cessation of motion never fails to occur to the mind. A cause is no less necessary to stop the motion of body than it is to produce it. Now this cause must either reside in the body or be external to it. If it reside in the body, then it possesses a self-determining power or force, by which it may be able to stop its own motion as well as to produce it.

123. Taking this view of the subject, the opinion of a force residing in a moving body by which its motion is continued must be given up; and the remarkable difference between a body in a state of motion and a state of rest must be explained on other principles. Motion, it cannot be doubted, is necessary in the impelling body to permit the forces which are inherent in one or both bodies to continue the pressure long enough for the production of sensible motion. But whether bodies be in the condition of motion or rest, these forces are inherent in them. If we reflect on the motions that are involved in the general conception of one body being impelled and put in motion by another, we shall see that there is nothing individual transferred from the one to the other. Before collision took place, the determination to motion existed only in the impelling body. After collision, both bodies possessed this condition or determination. But we have no conception, we can form no notion, of the thing transferred.

124. An expression not less vague and indefinite is also very common among mechanical philosophers. This is the phrase inertia, or vis inertiae. This expression, which was introduced by Kepler, seems to have been generally employed by him, as well as by Newton, to express the fact of the perseverance of body in a state of motion or rest. Sometimes, however, it has been employed by these philosophers to express something like indifference to motion or rest; and this is supposed to be manifested by body requiring the same quantity of force to make an augmentation of its motion, as is necessary to produce an equal diminution of it. To suppose resistance from a body at rest seems to be in direct contradiction to the common use of the word force; and yet this expression vis inertiae is very common. It is not less absurd to say that a body remains in the condition of rest by the exertion of a vis inertiae, than to affirm that it maintains itself in a state of motion by the exertion of an inherent force. Such expressions, which are metaphorical, should be carefully avoided, because they are apt to lead to misconception of the procedure of nature.

125. In the phenomena of motion the force employed always produces its complete effect. No resistance whatever is observed. When one man throws down another, and he finds that no more force has been required than to throw down a similar and equal mass of inanimate matter, he concludes that no resistance has been made; but if more force be necessary, the conclusion is that resistance has been made. When, therefore, the exerted force produces its full effect, there is no such thing as resistance properly so called. It is therefore misconceiving the mode in which mechanical forces operate in the collision of bodies, to say that there is any resistance: for there is no more in these cases than in other natural changes of condition. It may be observed, that these terms, inherent force and inertia, may be employed for the purpose of abbreviating language, provided they are used only for expressing either the simple fact of persevering in the former state, or the necessity of a determinate force to produce a change on that state, being careful to avoid all thought of resistance.

126. Thus it appears that deviations from uniform motions are only the indications of the existence and from uniformity of mechanical forces. This indication is simply change of place; and it can only indicate what is very simple, something competent to the production of the observed motion. The same thing is indicated by two similar changes of motion. A compass needle in a state of rest, can be moved some degrees by means of the finger, a magnet, an electrified body, or by the unbending of a spring, &c. in all which cases the indication is precisely the same; and therefore the thing indicated must also be the same. This is the intensity and direction of some moving power. The circumstances of resemblance by which the affections of matter are to be characterized are impulsiveness, intensity, and direction. This leads us to consider the second law of motion.

Second Law of Motion.

Every change of motion is proportional to the force impressed, and it is made in the direction of that force.

127. This law of motion also may almost be considered as an identical proposition. It is equivalent to saying that the changing force is to be measured by the change produced, and the direction of this force is the direction of the change. Considering the force only in the sense of its being the cause of motion, and withdrawing the attention from the manner or form of its exertion, there can be no doubt of this. In whatever way a body is put in motion, whether by the expansive force of the air, by the unbending of a spring, or by any similar pressure, when it moves off in the same direction, and with the same velocity, the force or the exertion of the force is considered as the same. Even when it is put in motion by instantaneous percussion from a smart stroke, although in this case the manner of the effect being produced is essentially different from the other cases, we cannot conceive the propelling force, as such, but as precisely one and the same. The expression of this law of motion by Newton is equivalent to saying, "that the changes of motion are taken as the measures of the changing forces, and the direction of the change is taken as the indication of the direction of the forces; for it cannot be said that it is a deduction from the acknowledged principle, that effects are proportional to their causes. This law is not affirmed from the proportion of the forces and the proportion of the changes, and that these proportions are the same, having been observed; and that this universally holds in nature. For forces are not objects of observation, and we do not know their proportions. In this way it would be established as a physical law, as indeed it is so in fact. But according to the definition of the term, this does not establish it as a law of motion; or as a law of human thought, the result of the relations of our ideas. Philosophers having attempted to prove this as a matter of observation, have produced great diversity of opinion in the mode of estimating forces. A bullet, it is well known, which moves with double velocity, penetrates four times as far. This is confirmed.

confirmed by other similar facts; and to generate this double velocity in the bullet, it has been observed by philosophers, four times the force is expended, four times as much powder is required. This is the invariable result; and in cases of this kind, it would appear that the ratio of the forces employed has been very accurately ascertained. The conclusion therefore is, that moving forces are not proportional to the velocities produced, but to the squares of the velocities. This is strongly confirmed by observing that moving bodies seem to possess forces in this very proportion, and to produce effects in this proportion; when, for instance, the velocity is only twice as great, they penetrate four times as deep.

128. If this mode of estimation be just, it is irreconcilable with the concession of those, who admit that the velocity is proportional to the force impressed, in those cases where no previous observation can be had of the ratio of the forces, and of its equality to the ratio of the velocities. Such a case is the force of gravity, which these philosophers also measure by its accelerating power, or the velocity generated in a given time. This must be granted; for there are cases in which the force can be measured by the actual pressure which it exerts. Thus a spring steelyard can be constructed, the rod of which is divided by hanging on successively a number of perfectly equal weights. In the different states of tension of the spring, its elasticity is proportional to the pressures of gravity which it balances. If it be found, that at Quito in Peru, a weight will pull out the rod to the mark 312, and that the same weight at Spitzbergen draws it out to 313, it seems to be a fair inference to say, that the pressure of gravity at Quito is to its pressure at Spitzbergen as 312 to 313; and this is affirmed on the authority of effects being proportional to their causes. Such cases, however, are very rare; for it is seldom, that the whole of a natural power, accurately measured in some other way, is employed in producing the observed motion. Part of it is generally otherwise expended, and therefore it frequently happens that the motions are not in the proportion with the supposed forces. And allowing that this could be done with accuracy, it would only be the proof of a general law or fact: but these philosophers attempt to establish it as an abstract truth.

129. It seems to be considered by Sir Isaac Newton only as a physical law. And in this sense good arguments are not wanting. A ball which moves with a double, triple, or quadruple velocity, generates by impulse in another, a double, triple, or quadruple velocity, or it generates the same velocity in a double, triple, or quadruple quantity of matter, and losing at the same time similar proportions of its own velocity.

Two bodies, having equal quantities of motion, meeting together mutually stop each other.

When two forces, which act similarly during equal times, produce equal velocity in a third body, they will, by acting together during the same time, produce a double velocity.

If a pressure which acts for a second, produce a certain velocity, a double pressure acting during a second, will produce in the same body a double velocity.

A force which is known to act equably, produces in

equal times equal increments of velocity, whatever the velocities may be. Of Moving Forces.

In all the examples above adduced, the forces are observed to be in the same proportion with the change of motion effected by them in a similar way.

But the curious discoveries of Dr Hooke, about the middle of the 17th century, seemed to shew, from a great collection of facts, forces to be in a very different proportion. In the production of motion it was found, that four springs equal in strength, and bent to the same degree, generated only a double velocity in the ball which they impelled: nine springs generated only a triple velocity, &c. In the extinction of motion, it was found, that a ball moving with a double velocity, will penetrate four times as deep into a uniformly resisting mass; and a triple velocity will make it penetrate nine times as far, &c.

130. These facts were brought forward by Leibnitz in support of his own pretensions to the discovery of the real nature and measure of mechanical action and force, which he said had been hitherto totally mistaken. He affirmed that the inherent force of a moving body, was in the proportion of the square of the velocity. In this argument he was supported by John Bernoulli, who adduced many simple facts to confirm the relation between the inherent force of a moving body and its velocity. One of the strongest arguments urged by Leibnitz is, that the inherent force of a moving body is to be estimated by all that it is able to do before the total extinction of its motion; and therefore when it penetrates four times as far, it is to be considered as having produced a quadruple effect. In this mode of estimation many things are gratuitously assumed, many contradictions are incurred; and it is only because forces are assumed as proportional to the velocities which they generate, that these facts come to be proportional to the squares of the same velocity. When Leibnitz assumes the quadruple penetration as the proof of the quadruple force of a body having twice the velocities, he has not considered that a double time is employed during this penetration. But a double force, acting equably during a double time, should produce a quadruple effect. This circumstance is lost sight of in all the facts which this philosopher has adduced. It may, however, be observed, that Leibnitz, as well as his followers, holds no difference of opinion in all the consequences which are deduced from the measure which is here adopted. They admit, that a force producing an uniformly accelerated motion must be constant; they agree with the followers of Des Cartes in the valuations both of accelerating and deflecting forces; and have assiduously and successfully cultivated the philosophy of Newton, which proceeds on the principle of estimating the measure of moving forces by the velocity generated.

131. It ought here to be observed, that moving forces only are taken into consideration. When a ball has acquired a certain velocity, whether it has been impelled by the elasticity of the air, by a spring, or struck off by a blow, or urged forward by means of a stream of air or water, or has obtained its velocity by falling; in all these cases it is conceived that it has sustained the same action of moving force. The only distinct notion, perhaps, which we are able to form, is pressure; but

moving but it is from experience that we derive the information that pressure produces motion. Whatever may be the difference of the circumstances of mechanical forces, in one, namely, production of motion, they all agree. In this circumstance of resemblance they are capable of comparison; and from this they derive a name, moving force, which is expressive of this comparison. And therefore the particular faculty of pressure, elasticity, &c. may be measured by the change of motion produced by pressure. In whatever proportion pressure may act on a body in a state of rest, the magnitude of the change of motion measures the pressure actually exerted in its production; and as this is the only change of mechanical condition effected by the pressure in the body moved by it, it may be measured by the velocity. When, therefore, pressure produces the same change of velocity on a soft clay ball, the pressure really exerted is the same whether the velocity has been augmented or diminished. In both cases the same dimple will be observed. The changes of motion, therefore, are proportional to the exerted pressures.

132. The notions which we form of a constant or invariable force lead to the same conclusion. By such a force equal effects or changes of motion are produced in equal times. But equal augmentations of motion are equal augmentations of velocity. This notion of an invariable accelerating force is confirmed by what is observed in the case of a falling body, which receives equal additions of velocity in equal times; and this force, so far as we know, is invariable. The inference then is, that whatever be the force exerted in one second, it will be four times as much in four seconds. And this is really the case, if it be granted that a quadruple velocity is the indication of a quadruple force; but it does not hold in any other estimation of force. Besides, it may be observed, that four springs applied to an ounce ball impel it only twice as fast as one spring does; and if the same four springs be applied to a four-ounce ball, they produce in it the same velocity that one spring produces on an ounce ball. In the last case, it may be demonstrated, that the four springs act during the same time with one spring.

133. The proper measure, therefore, of a changing force is a change of motion in all its circumstances of velocity and direction. This also is the proper measure of a moving force. For, in different states of motion, bodies may sustain the same change of motion. Supposing then one of these bodies to be previously in a state of rest, the change and the motion acquired are the same thing. The force, therefore, producing a change of motion in a moving body, is precisely the same with that force which produces in a body, previously at rest, a motion equivalent to this change; and in this case it is simply a moving force.

This opinion of Leibnitz about the measure of forces has influenced the sentiments of many writers, and in the mechanical investigations of some of them, has not a little affected their practical deductions. No dispute probably could have occurred if philosophers had not been led to consider force as something existing in body; the term on the contrary being only used to express the phenomenon, which is conceived to be its fall effect and adequate measure. The simple change of motion observed is the measure of the force by which it is produced.

The following is the enunciation, adapted to the characteristic and measure of a change of motion.

Law of the Changes of Motion.

PROP. XII.

134. In every change of motion, the new motion is compounded of the former motion, and of the motion which the changing produces in a body at rest.

Let the change of motion be from AB (fig. 23.) to Fig. 23. AD, this new motion AD is compounded of the former motion AB and of the motion AC.

For it has been shewn, that the change in any motion, is that motion, which when compounded with the former motion, produces the new motion; and the new motion (55.) is the compound of the former motion and the changing motion. Since then the change of motion is the mark and measure of the changing force (133.) by which both the direction and intensity or velocity produced, are determined, the truth of the proposition will appear of course.

135. It has been already observed (54.), that the composition of motions and the similar composition of forces are very different things. The first is a pure mathematical truth; the second, is a physical question dependent on the nature of the mechanical forces as they exist in the universe. Our notions are not very distinct of two forces, each of which separately produces motions, having the directions and velocities expressed by the sides of a parallelogram, producing by their joint action a motion in the diagonal. The demonstrations which have been frequently given, are altogether inconclusive, and only include the composition of motions; while gratuitous postulates have been assumed by those who endeavoured to accommodate their reasonings to physical principles. The celebrated Daniel Bernoulli gave the first legitimate demonstration of this proposition, in which, however, he employs a series of many propositions, some of which are very abstruse. It was greatly simplified by D'Alembert, Mem. Acad. des Sciences 1769, still, however, requiring many propositions. Ingenious demonstrations have also been given by other celebrated mechanicians. In the following demonstration by Professor Robison, this distinguished philosopher has attempted to combine the demonstration of Bernoulli, D'Alembert, and others, thus rendering it more expeditious, and at the same time legitimate. This demonstration is entirely limited to pressures, without at all considering or employing the motions supposed to be produced by them.

(A) If two equal and opposite pressures or incitements to motion act at once on a material particle, it suffers no change of motion; for if it yields in either direction by their joint action, one of the pressures prevails, and they are not equal.

Equal and opposite pressures are said TO BALANCE each other; and such as balance must be esteemed equal and opposite.

(B) If $a$ and $b$ are two magnitudes of the same kind, proportional to the intensities of two pressures which act in the same direction, then the magnitude $a+b$ will measure the intensity of the pressure, which is equivalent, and may be called equal, to the combined effort of the other two; for when we try to form a notion of pressure as a measurable magnitude, distinct from motion.

Of Moving Forces. tion or any other effect of it, we find nothing that we can measure it by but another pressure. Nor have we any notion of a double or triple pressure different from a pressure that is equivalent to the joint effort of two or three equal pressures. A pressure $a$ is accounted triple of a pressure $b$, if it balances three pressures, each equal to $b$, acting together. Therefore, in all proportions which can be expressed by numbers, we must acknowledge the legitimacy of this measurement; and it would surely be affectionate to omit those which the mathematicians call incommensurable.

The magnitude $a-b$, in like manner, must be acknowledged to measure that pressure which arises from the joint action of two pressures $a$ and $b$ acting in opposite directions, of which $a$ is the greatest.

(C) Let $ABCD$ and $A\; b\; c\; d$ (fig. 24.) be two rhombuses, which have the common diagonal $AC$. Let the angles $B\; A\; b$, $D\; A\; d$, be bisected by the straight lines $A\; E$ and $A\; F$.

If there be drawn from the points $E$ and $F$ the lines $E\; G$, $E\; H$, $F\; g$, $F\; h$, making equal angles on each side of $E\; A$ and $F\; A$, and if $G\; g$, $H\; h$ be drawn, cutting the diagonal $AC$ in $I$ and $L$: then $A\; I\; +\; A\; L$ will be greater or less than $A\; Q$, the half of $AC$, according as the angles $G\; E\; H$, $g\; F\; h$, are greater or less than $G\; A\; H$.

Draw $G\; H$, $g\; h$, cutting $A\; E$, $A\; F$, in $O$ and $o$, and draw $O\; o$, cutting $AC$ in $K$.

Because the angles $A\; E\; G$ and $E\; A\; G$ are respectively equal to $A\; E\; H$ and $E\; A\; H$, and $A\; E$ is common to both triangles, the sides $A\; G$, $G\; E$ are respectively equal to $A\; H$, $H\; E$, and $G\; H$ is perpendicular to $A\; E$, and is bisected in $O$; for the same reasons, $g\; h$ is bisected in $o$. Therefore the lines $C\; g$, $O\; o$, $H\; h$, are parallel, and $I\; L$ is bisected in $K$. Therefore $A\; I\; +\; A\; L$ is equal to twice $A\; K$. Moreover, if the angle $G\; E\; H$ be greater than $G\; A\; H$, $A\; O$ is greater than $E\; O$, and $A\; K$ is greater than $K\; Q$. Therefore $A\; I\; +\; A\; L$ is greater than $A\; Q$; and if the angle $G\; E\; H$ be less than $G\; A\; H$, $A\; I\; +\; A\; L$ is less than $A\; Q$.

(D) Two equal pressures, acting in the directions $AB$ and $AC$ (fig. 25.) at right angles to each other, compose a pressure in the direction $AD$, which bisects the right angle; and its intensity is to the intensity of each of the constituent pressures as the diagonal of a square to one of the sides. It is evident, that the direction of the pressure, generated by their joint action, will bisect the angle formed by their directions; because no reason can be assigned for the direction inclining more to one side than to the other.

In the next place, since a force in the direction $AD$ does, in fact, arise from the joint action of the equal pressures $AB$ and $AC$, the pressure $AB$ may be conceived as arising from the joint action of two equal forces similarly inclined and proportioned to it. Draw $E\; A\; F$ perpendicular to $AD$. One of these forces must be directed along $AD$, and the other along $A\; E$. In like manner, the pressure $AC$ may arise from the joint action of a pressure in the direction $AD$, and an equal pressure in the direction $A\; F$. It is also plain that the pressures in the directions $A\; E$ and $A\; F$, and the two pressures in the direction $AD$, must be all equal. And also any one of them must have the same proportion to $AB$ or to $AC$, that $AB$ or $AC$ has to the force in the direction $AD$, arising from their joint action.

Therefore, if it be said that $AD$ does not measure or measure the pressure arising from the joint action of $AB$ and $AC$, let $A\; d$, greater than $AD$, be its just measure, and make $A\; d\; :\; AB\; =\; AB\; :\; A\; g\; =\; AB\; :\; A\; c$. Then $A\; g$ and $A\; c$ have the same inclination and proportion to $AB$ that $AB$ and $AC$ have to $A\; d$. We determine, in like manner, two forces $A\; f$ and $A\; g$ as constituents of $AC$.

Now $A\; d$ is equivalent to $AB$ and $AC$, and $AB$ is equivalent to $A\; c$ and $A\; g$; and $AC$ is equivalent to $A\; f$, and $A\; g$. Therefore $A\; d$ is equivalent to $A\; c$, $A\; f$, $A\; g$, and $A\; g$. But $A\; c$ and $A\; f$ balance each other, or annihilate each other's effect; and there remain only the two forces or pressures $A\; g$, $A\; g$. Therefore their measure is a magnitude equal to twice $A\; g$. But if $A\; d$ be greater than the diagonal $AD$ of the square, whose sides are $AB$ and $AC$; then $A\; g$ must be less than $A\; I$, the side of the square whose diagonal is $AB$. But twice $A\; g$ is less than $AD$, and much less than $A\; d$. Therefore the measure of the equivalent of $AB$ and $AC$ cannot be a line $A\; d$ greater than $AD$. In like manner it cannot be a line $A\; d$ that is less than $AD$. Therefore it must be equal to $AD$, and the proposition is demonstrated.

(E) Two equal forces $AB$, $AC$, acting at right angles, will be balanced by the force $AO$, equal and opposite to $AD$, the diagonal of the square whose sides are $AB$ and $AC$; for $AO$ would balance $AD$, which is the equivalent of $AB$ and $AC$.

(F) Let $A\; E\; C\; F$ (fig. 26.) be a rhombus, the acute angle of which $E\; A\; F$ is half of a right angle. Two equal pressures, which have the directions and measures $A\; E$, $A\; F$, compose a pressure, having the direction and measure $A\; C$, which is the diagonal of the rhombus.

It is evident, in the first place, that the compound force has the direction $AC$, which bisects the angle $E\; A\; F$. If $AC$ be not its just measure, let it be $A\; P$ less than $AC$. Let $A\; B\; C\; D$ be a square described on the same diagonal, and make $A\; P\; :\; A\; Q\; =\; A\; E\; :\; A\; O$, $=\; A\; F\; :\; A\; o$. Draw $K\; O\; G$, $K\; o\; g$ perpendicular to $A\; E$, $A\; F$; draw $G\; I\; g$, $O\; H\; o$, $E\; G$, $E\; K$, $F\; g$, $F\; K$, $P\; F$, and $P\; E$.

The angles $C\; A\; B$ and $F\; A\; E$ are equal, each being half of a right angle. Also the figures $A\; E\; P\; F$ and $A\; G\; E\; K$ are similar, because $A\; P\; :\; A\; Q\; =\; A\; E\; :\; A\; O$. Therefore $F\; A\; :\; A\; P\; =\; K\; A\; :\; A\; E$, and $F\; A\; :\; A\; P\; =\; G\; A\; :\; A\; E$. Therefore, in the same manner that the forces $A\; E$, $A\; F$ are affirmed to compose $A\; P$, the forces $A\; G$ and $A\; K$ may compose the force $A\; E$, and the forces $A\; g$ and $A\; K$ may compose the force $A\; F$. Therefore (B) the force $A\; P$ is equivalent to the four forces $A\; G$, $A\; K$, $A\; g$, $A\; K$. But (D) $A\; G$ and $A\; g$ are the sides of a square, whose diagonal is equal to twice $A\; I$; and the two forces $A\; K$, $A\; K$ are equal to, or are measured by, twice $A\; K$. Therefore the four forces $A\; G$, $A\; K$, $A\; g$, $A\; K$, are equivalent to $2\; A\; I\; +\; 2\; A\; K\; =\; 4\; A\; H$.

But because $A\; P$ was supposed less than $AC$, the angle $F\; P\; E$ is greater than $F\; A\; F$, and $G\; E\; K$ is greater than $G\; A\; K$, $A\; O$ is greater than $O\; E$, and $A\; H$ is greater than $H\; Q$, and $4\; A\; H$ is greater than $A\; Q$; and therefore $4\; A\; H$ is greater than $AC$, and much greater than

moving than AP. Therefore AP is not the just measure of the force composed of AE and AF.

In like manner, it is shewn, that AE and AF do not compose a force whose measure is greater than AC. It is therefore equal to AC; and the proposition is demonstrated.

(G) By the same process it may be demonstrated, that if BAD be half a right angle, and EAF be the fourth of a right angle, two forces AE, AF will compose a force measured by AC. And the process may be repeated for a rhombus whose acute angle is one-eighth, one-sixteenth, &c. of a right angle; that is, any portion of a right angle that is produced by continual bisection. Two forces, forming the sides of such a rhombus, compose a force measured by the diagonal.

(H) Let ABCD, $A\; b\; c\; d$ (fig. 27.) be two rhombuses formed by two consecutive bisections of a right angle. Let AECF be another rhombus, whose sides AE and AF bisect the angles BAB and DA d.

The two forces AE, AF, compose a force AC.

Bisect AE and AF in O and o. Draw the perpendiculars GOH, $g\; o\; h$, and the lines GIg, OK o, HL h, and the lines EG, EH, Fg, Fh.

It is evident, that AGEH and $A\; g\; F\; h$ are rhombuses; because $AO=OE$, and $A\; o=o\; F$. It is also plain, that since $b\; A\; d$ is half of BAD, the angle GAH is half of $b\; A\; d$. It is therefore formed by a continual bisection of a right angle. Therefore (G) the forces AG, AH, compose a force AE; and $A\; g$, $A\; h$, compose the force AF. Therefore the forces AG, AH, $A\; g$, $A\; h$, acting together, are equivalent to the forces AE, AF acting together. But AG, $A\; g$ compose a force $=\; 2\; AI$; and the forces AH, $A\; h$ compose a force $=\; 2\; AL$. Therefore the four forces acting together are equivalent to $2\; AI\; +\; 2\; AL$, or to $4\; AK$. But because $AO$ is $\backslash frac\{1\}\{4\}\; AE$, and the lines $G\; g$, $O\; o$, $H\; h$, are evidently parallel, $4\; AK$ is equal to $2\; AQ$, or to AC; and the proposition is demonstrated.

(I) Let us now suppose, that by continual bisection of a right angle we have obtained a very small angle $a$ of a rhombus; and let us name the rhombus by the multiple of $a$ which forms its acute angle.

The proposition (G) is true of $a$, $2a$, $4a$, &c. The proposition (H) is true of $3a$. In like manner, because (G) is true of $4a$ and $8a$, proposition (H) is true of $6a$; and because it is true of $4a$, $6a$, and $8a$, it is true of $5a$ and $7a$. And so on continually till we have demonstrated it of every multiple of $a$ that is less than a right angle.

(K) Let RAS (fig. 28.) be perpendicular to AC, and let ABCD be a rhombus, whose acute angle BAD is some multiple of $2a$ that is less than a right angle. Let $A\; b\; c\; d$ be another rhombus, whose sides $A\; b$, $A\; d$ bisect the angles RAB, SAD. Then the forces $A\; b$, $A\; d$ compose a force AC.

Draw $b\; R$, $d\; S$ parallel to BA, DA. It is evident, that $A\; R\; b\; B$ and $A\; S\; d\; D$ are rhombuses, whose acute angles are multiples of $a$, that are each less than a right angle: Therefore (I) the forces AR and AB compose the force $A\; b$, and AS, AD compose $A\; d$; but AR and AS annihilate each other's effect, and there remains only the forces AB, AD. Therefore

$A\; b$ and $A\; d$ are equivalent to AB and AD, which compose the force AC; and the proposition is demonstrated.

(L) Thus is the corollary of last proposition extended to every rhombus, whose angle at A is some multiple of $a$ less than two right angles. And since $a$ may be taken less than any angle that can be named, the proposition may be considered as demonstrated of every rhombus; and we may say,

(M) Two equal forces, inclined to each other in any angle, compose a force which is measured by the diagonal of the rhombus, whose sides are the measures of the constituent forces.

(N) Two forces AB, AC (fig. 29.) having the direction and proportion of the sides of a rectangle, compose a force AD, having the direction and proportion of the diagonal.

Draw the other diagonal CB, and draw EAF parallel to it; draw BE, CF parallel to DA.

AEBG is a rhombus; and therefore the forces AE and AG compose the force AB. AFGC is also a rhombus, and the force AC is equivalent to AF and AG. Therefore the forces AB and AC, acting together, are equivalent to the forces AE, AF, AG, and AG acting together, or to AE, AF, and AD acting together: But AE and AF annihilate each other's action, being opposite and equal (for each is equal to the half of BC). Therefore AB and AC acting together, are equivalent to AD, or compose the force AD.

(O) Two forces, which have the direction and proportions of AB, AC (fig. 30.) the sides of any parallelogram, compose a force, having the direction and proportion of the diagonal AD.

Draw AF perpendicular to BD, and BG and DE perpendicular to AC.

Then AFBG is a rectangle, as is also AFDE: and AG is equal to CE. Therefore, (N) AB is equivalent to AF and AG. Therefore AB and AC acting together, are equivalent to AF, AG, and AC acting together; that is, to AF and AE acting together; that is (N) to AD; or the forces AB and AC compose the force AD.

Hence arises the most general proposition.

If a material particle be urged at once by two pressures or incitements to motion, whose intensities are proportional to the sides of any parallelogram, and incitements which act in the directions of those sides, it is affected in the same manner as if it were acted on by a single force, whose intensity is measured by the diagonal of the parallelogram, and which acts in its direction: Or, two pressures, having the direction and proportion of the sides of a parallelogram, generate a pressure, having the direction and proportion of the diagonal.

136. Thus is demonstrated from abstract principles the perfect similarity of the composition of pressures and the composition of forces measured by the motions which are produced. A separate demonstration seems indispensably necessary; for what may be deduced from the one case is not always applicable to the other. The change produced on a motion already existing by a deflecting force, cannot be explained by any composition of pressure; because the changing pressure is the only one that exists, and there is none with which it may be compounded.

Of Moving Forces. compounded. Nor, on the other hand, will our notions of the composition of motions explain the composition of pressures, without assuming that the pressures are proportional to the velocities.

137. Considering this law of motion merely as a universal fact or physical law, abundant proof may be adduced in support of it.

1. The joint action of different forces is quite familiar. A lighter, for example, is dragged in different directions by two ropes on different sides of the canal, the lighter moving in an intermediate direction, as if dragged in that direction by one rope only. A ball moving in a particular direction, which receives a stroke across this direction, takes a direction lying between that of the first motion and that of the transverse stroke.

2. If a particle of matter A (fig. 23.) be urged at once by two pressures in the directions AB and AC; and if AB and AC be proportional to the intensities of those pressures, the joint action of these two pressures is equivalent to the action of a third pressure in the direction of the diagonal AD, and having its intensity in the proportion of AD. This is proved by observing, that the point A is withheld from moving by a pressure AE, which is equal and opposite to AD. But pressures are moving forces, producing velocities when they act similarly during equal times, proportional to their intensities. The proportion, therefore, is true with respect to pressures, considered merely as such, and also with respect to the motions which may be produced by their composition.

3. The weight of a ball which is suspended by a thread, and drawn aside from its position in a state of rest, urges it downwards, and the ball is supported obliquely by the thread. Supposing this proposition to be true, the directions and intensities of the forces inciting it to motion in any position, as well as the result of the velocities, can be precisely ascertained.

4. The motions of the planets, computed on these principles of the composition of forces, do not exhibit any perceptible deviation from calculation, at the end of thousands of years.

Nothing, therefore, can be relied on with greater confidence than the perfect agreement between the composition of motions, and the composition of the forces, which, separately taken, would produce those motions, and which are measured by the velocities produced. But it ought to be remarked, that if the moving forces are measured by the squares of the velocities which they generate, the composition cannot possibly hold; namely, from two forces which are represented by the sides of a parallelogram made proportional to the squares of the velocities, there will not result a force which can be represented by the diagonal. But supposing the composition of forces to be as the velocities, nature exhibits them exactly.—This proposition, therefore, whether it be considered as an abstract truth or as a physical law, may be received as fully established. The following is the converse of this proposition.

138. The force by which the motion AB (fig. 23.) is changed into AD, is that which would produce in a body at rest, the motion AC, and this compounded with AB produces the observed motion AD.

139. The force which will produce in a body at rest a motion having the direction and velocity represented by AC, (fig. 23.) when applied to a body moving with the velocity and in the direction AB, will change its motion into the motion AD, which is the diagonal of the parallelogram ABDC. For the new motion must be that which is compounded of AB and AC, that is, it must be the motion AD.

The combination of these two propositions gives rise to the following, which is still more general.

140. A body A (fig. 23.) being urged at once by two forces which separately would cause it to describe AB and AC, the sides of a parallelogram ABDC, the body by their joint action will describe the diagonal AD in the same time.

For if the body had been already moving with the velocity and in the direction AB, and if it had been acted on in A by the force AC, it would describe AD in the same time. But it matters not at what time it acquired the determination to describe AB. Let it be then at the instant that the force AC is applied to it. And because its mechanical condition in A, which has the determination to the motion AB, is the same as in any other point of that line, it must describe AD.

Two forces acting on a body in the same or in opposite directions, will cause it to move with a velocity equal to the sum or to the difference of the velocities which it would have received from the forces separately. For if AC (fig. 23.) approach continually to AB by diminishing the angle BAC, the points C and D will at last fall on c and d, and then AD is equal to the sum of AB and AC. But if the angle BAC increase continually, the points C and D will at last fall on * and †, and then A‡ becomes equal to the difference of AB and AC. In the last case, it is evident, that if AC be equal to AB, the point D or ‡ will coincide with A, and the two forces being equal, and acting in opposite directions, there will be no motion.

141. In such cases the equal and opposite forces AC and AB are said to balance each other; and it is generally said, that these forces, by whose joint operation no change of motion is produced, balance each other. Such forces are accounted equal and opposite, each producing on the body a change of motion equal to what it would produce on a body at rest, and at the same time equal to the motion produced by the other force on a body at rest. The two motions being equal and opposite, the forces are therefore equal and opposite.

142. What has been demonstrated concerning the affections with respect to the affections of compound motions, may now be applied to the combination of forces; taking care, however, to recollect the essential difference between the composition of motions and the composition of forces. In the combination of forces, the composition is complete, when the determination has been given to the body to move with the proper velocity in the diagonal. When the body has acquired this determination there is no farther composition; and it continues its uniform motion, till its condition be changed.

Moving changed by some new force. On the other hand, in the composition of two or more motions, the constituent forces. motions are supposed to continue; and it is only during their continuance that the compound motion exists. If it be possible, which does not appear to be the case, that any force can generate a finite velocity by its instantaneous action, two such forces generate in an instant the determination in the diagonal. But supposing the action to continue for some time, to generate the velocities AB or AC, there must be a continuance of the joint action during the same time to produce the velocity AD. And although the moving powers of the two forces may vary in their intensity, yet it is necessary that they retain the same proportion to each other during the whole time of their joint action. Overlooking this circumstance, experiments have been made for the purpose of comparing this doctrine with the phenomena; and they have been found to exhibit very different results. But experiments made by the combination of pressures, such as weights pulling a body by means of threads, coincide precisely with this doctrine; for it is always found that two weights pulling in the directions AB, AC, and proportional to those lines, are balanced by a third weight in the proportion of AD, and pulling in the direction AE. In this way the composition of pressures is clearly proved; and having no other distinct conception of a moving force, these experiments may be considered as sufficient. But we may go farther; for there is the clearest proof by experiment, that pressures produce motions in proportion to their intensities by their similar action during equal times. In the planetary motions, the directions and intensities of the compound forces are accurately known as moving forces. These motions afford a complete proof of the physical law, by their perfect coincidence with the calculations which proceed on the principles of this doctrine. This coincidence must be acknowledged as a full proof of the propriety of the measure which has been assumed. The assumption of any other measure would exhibit results quite different from the phenomena.

143. Forces which produce motions along the sides of a parallelogram are called simple forces or constituent forces. And the force which singly produces the motion in the diagonal, is called the equivalent force, the compound force, or the resulting force.

144. Some general conclusions may now be pointed out, which will facilitate greatly the use of the parallelogram of forces.

GENERAL COROLLARIES.

1. The constituent and the resulting forces, or the simple and compound forces, act in the same plane; for the sides and diagonal of a parallelogram are in one plane.

2. The simple and the compound forces are proportional to the sides of any triangle which are parallel to their directions. For if any three lines $ab$, $bd$, $ad$, be drawn parallel to AB, AC, and AD (fig. 31.), they will form a triangle similar to the triangle ABD. For the same reasons they are proportional to the sides of a triangle $abd$, which are respectively perpendicular to their directions.

3. Therefore each is proportional to the sine of the opposite angle of this triangle; for the sides of any tri-

angle are proportional to the sines of the opposite angles. Of Moving Forces.

4. Each is proportional to the sine of the angle contained by the directions of the other two; for AD is to AB as the sine of the angle ABD to the sine of the angle ADB. Now the sine of ABD is the same with the sine of BAC contained between the directions AB and AC, and the sine of ADB is the same with the sine of CAD; also AB is to AC, or BD, as the sine of ADB (or CAD) to the sine of BAD.

145. Let us now proceed to the application of this fundamental proposition. And we observe, in the first of the place, that since AD may be the diagonal of an infinite number of parallelograms, the motion or the pressure AD may result from the joint actions of many pairs of forces. It may be produced by forces which would separately produce the motions AF and AG. This generally gives us the means of discovering the forces which concur in its production. If one of them, AB, is known in direction and intensity, the direction AC, parallel to BD, and the intensity, are discovered. Sometimes we know the directions of both. Then, by drawing the parallelogram or triangle, we learn their proportions. The force which deflects any motion AB into a motion AD, is had by simply drawing a line from the point B (to which the body would have moved from A in the time of really moving from A to D) to the point D. The deflecting force is such as would have caused the body move from B to D in the same time. And, in the same manner, we get the compound motion AD, which arises from any two simple motions AB and AC, by supposing both of the motions to be accomplished in succession. The final place of the body is the same, whether it moves along AD or along AB and BD in succession.

146. This theorem is not limited to the composition of two forces only; for since the combined action of many two forces puts the body into the same state as if their equivalent alone had acted on it, we may suppose this to have been the case, and then the action of a third force will produce a change on this equivalent motion. The resulting motion will be the same as if only this third force and the equivalent of the other two had acted on the body. Thus, in fig. 32. the three forces AB, AC, AE, may act at once on a particle of matter. Complete the parallelogram ABDC; the diagonal AD is the force which is generated by AB and AC. Complete the parallelogram AEFD; the diagonal AF is the force resulting from the combined action of the forces AB, AC, and AE. In like manner, completing the parallelogram AGHF, the diagonal AH is the force resulting from the combined action of AB, AC, AE, and AG, and so on of any number of forces.

This resulting force and the resulting motion may be much more expeditiously determined, in any degree of composition, by drawing lines in the proportion and direction of the forces in succession, each from the end of the preceding. Thus draw AB, BD, DF, FH, and join AH; AH is the resulting force. The demonstration is evident.

147. In the composition of more than two forces, we are not limited to one plane. The force AD is in the same plane with AB and AC; but AE may be elevated above this plane, and AG may lead below it.

Of Moving Forces AF is in the plane of AD and AE, and AH is in the plane of AF and AG.

Complete the parallelograms ABLE, ACKE, ELFK. It is evident that ABLEFKC is a parallelopiped, and that AF is one of its diagonals. Hence we derive a more general and very useful theorem.

Three forces having the proportion and direction of the three sides of a parallelopiped, compose a force having the proportion and direction of the diagonal.

148. In the investigation of very complicated phenomena, the mechanician considers every force as resulting from the joint action of three forces at right angles to each other, and he takes the sum or difference of these in the same or opposite directions. Thus he obtains the three sides of a parallelopiped, and from these computes the position and magnitude of the diagonal. This is the force resulting from the composition of all the partial ones. This process is called the estimation or reduction of forces. Forces may be estimated in the direction of a given line or plane, or they may be reduced to that direction, as has been done with respect to motion. See Cor. 2. Propos. 9. in art. 57.

The laws of motion which have now been considered, are necessary consequences of the relations of those conceptions which we form of motion and mechanical force, and they are universal facts or physical laws. To these Sir Isaac Newton has added another, which is the following.

Third Law of Motion.

149. Every action is accompanied by an equal and contrary reaction, or the actions of bodies on one another are always mutual, equal, and in contrary directions.

In all cases which can be accurately examined, this holds to be a universal fact. Newton has made this affirmation on the authority of what he conceives to be a law of human thought; namely, that the qualities discovered in all bodies on which experiments and observations can be made, are to be considered as universal qualities of body. But if the term law of motion be limited to those consequences that necessarily flow from our notions of motion, of the causes of its production and changes, this proposition is not such a result. Because a magnet causes the iron to approach toward it, it by no means follows, from this observation, that the pressure of the iron shall be accompanied by any motion or change of state of the magnet, or it does not appear to be necessarily supposed that the iron attracts the magnet. When this was observed, it was accounted a discovery, and a discovery which is to be ascribed to the moderns. Dr Gilbert, who first mentions it, affirms that the magnet and the iron are observed mutually to attract each other, as well as all electrical substances, and the light bodies which are attracted by them. The discovery was made by Kepler, that a mutual attraction exists between the earth and the moon. Newton discovered that the sun acts on the planets, and that the earth acts on the moon. It had been observed too by Newton that the iron reacts on the magnet, that the actions of electrified bodies are mutual, and that all the actions of solid bodies are accompanied by an equal and contrary reaction. On the authority of the rule of philosophizing which he had laid down, he affirmed that the planets react on the sun, and that the sun is

not at rest, but is continually agitated by a small motion round the general centre of gravitation; and he pointed out several of the consequences of this reaction. As the celestial motions were more narrowly examined by astronomers, these consequences were found to obtain, and to produce disturbances in the planetary motions. This reciprocity of action is now found to hold with the utmost precision through the whole of the solar system; and therefore this third proposition of Newton is to be considered as a law of nature. And it is true with respect to all bodies on which experiment or observation can be made.

150. This then being a universal law, we cannot divest our minds of the belief that it depends on a general principle, by which all the matter in the universe is influenced. It strongly induces the persuasion of the ultimate particles of matter being alike, that a certain number of properties belong in the same degree to each atom, and that all the sensible differences of substance which are observed, arise from a different combination of those primary atoms in the formation of a particle of those substances. All this is no doubt perfectly possible. But if each primary atom be so constituted, no action of any kind of particle or collection of particles can take place on another, which is not accompanied by an equal reaction in the opposite direction.

151. Let us now direct our attention to the application of these laws. This answers a twofold purpose. The first is to discover the mechanical powers of natural substances by which they are fitted to become parts of a permanent universe. This is accomplished by observing the changes of motion which always accompany those substances. It is from those changes that the only characteristics of power are derived; and thus is discovered the power of gravity, of magnetism, &c. Another purpose in the employment of these laws is, that, after having obtained the mechanical character of any substance, we may ascertain what will be the result of its being in the vicinity of the bodies mechanically allied, or we may ascertain what is the change induced on the condition of the neighbouring bodies.

152. The mechanical powers of bodies occasionally produce accelerations, retardations, and deflections in the motions of other bodies. These names have been given, because nothing is known of their nature, or of the manner in which they are effective; they are therefore named, as they are measured by the phenomena which are observed and considered as their effects. Let us now attend a little to the principal circumstances relating to the action of these forces.

Of Accelerating and Retarding Forces.

153. Changes of motion are the only marks and measures of changing forces; and having no other mark of the force but the acceleration, it has obtained the name of an accelerating force. When the motion is retarded, it is called retarding force. Nor is there any other measure of the intensity of an accelerating force, but the acceleration which it produces. To investigate therefore the powers which produce all the changes of motion, it is necessary to obtain measures of the acceleration. What has been said of accelerations and retardations of motion is equally descriptive of the effects of accelerating and retarding forces. Hence the following proposition.

If the abscissa $a\; d$, fig. 5. represent the time of and motion, and if the areas $a\; b\; f\; e$, $a\; c\; g\; e$, &c. are as the velocities at the instants $b\; c$, &c. the ordinates $a\; e$, $b\; f$, $c\; g$, &c. are as the accelerating forces at those instants.

Cor. 1. The momentary change of velocity is as the force $f$ and the time $t$ jointly. It may be thus expressed,

Also, the accelerating or retarding force is proportional to the momentary variation of the velocity, directly, and to the moment of time in which it is generated, inversely (48.)

Indeed all that we know of force is that it is something which is always proportional to $\backslash frac\{\backslash dot\{v\}\}\{t\}$.

Cor. 2. Uniformly accelerated or retarded motion is the indication of a constant or invariable accelerating force. For, in this case, the areas $a\; b\; f\; e$, $a\; c\; g\; e$, &c. increase at the same rate with the times $a\; b$, $a\; c$, &c. and therefore the ordinates $a\; e$, $b\; f$, $c\; g$, &c. must all be equal; therefore the forces represented by them are the same, or the accelerating force does not change its intensity, or, it is constant. If, therefore, the circumstances mentioned in articles 37 and 38, are observed in any motion, the force is constant. And if the force is known to be constant, those propositions are true respecting the motions.

Cor. 3. No finite change of velocity is generated in an instant by an accelerating or retarding force. For the increment or decrement of velocity is always expressed by an area, or by a product $f\; t$, one side or factor of which is a portion of time. As no finite space can be described in an instant, and the moveable must pass in succession through every point of the path, so it must acquire all the intermediate degrees of velocity. It must be continually accelerated or retarded.

Cor. 4. The change of velocity produced in a body in any time, by a force varying in any manner, is the proper measure of the accumulated or whole action of the force during this time. For, since the momentary change of velocity is expressed by $f\; t$, the aggregate of all these momentary changes, that is, the whole change of velocity, must be expressed by the sum of all the quantities $f\; t$. This is equivalent to the area of the figure employed in art. 148, and may be expressed by $\backslash int\; f\; t$.

154. If the abscissa $A\; E$ (fig. 8.) of the line $a\; c\; e$ be the path along which a body is urged by the action of a force, varying in any manner, and if the ordinates $A\; a$, $B\; b$, $C\; c$, &c. be proportional to the intensities of the force in the different points of the path, the intercepted areas will be proportional to the changes made on the square of the velocity during the motion along the corresponding portions of the path.

For, by art. 49. the areas are in this proportion when the ordinates are as the accelerations. But the accelerations are the measures of, and are therefore proportional to, the accelerating forces. Therefore the proposition is manifest.

The momentary change on the square of the velocity is as the force, and as the small portion of space along which it acts, jointly;

and

155. It deserves remark here, that as the momentary change of the simple velocity by any force $f$ depends only on the time of its action, it being $=\; f\; t$ (148.) Cor. 1. so the change on the square of the velocity depends on the space, it being $=\; f\; s$. It is the same, whatever is the velocity thus changed, or even though the body be at rest when the force begins to act on it. Thus, in every second of the falling of a heavy body, the velocity is augmented 32 feet per second, and, in every foot of the fall, the square of the velocity increases by 64.

156. The whole area $A\; E\; e\; a$, expressed by $\backslash int\; f\; s$, expresses the whole change made on the square of the velocity which the body had in $A$, whatever this velocity may have been. We may therefore suppose the body to have been at rest in $A$. The area then measures the square of the velocity which the body has acquired in the point $E$ of its path. It is plain that the change on $v^2$ is quite independent on the time of action, and therefore a body, in passing through the space $A\; E$ with any initial velocity whatever, sustains the same change of the square of that velocity, if under the influence of the same force.

157. This proposition is the same with the 39th of the First Book of Newton's Principia, and is perhaps the most generally useful, of all the theorems in Dynamics, in the solution of practical questions. It is to be found, without demonstration, in his earliest writings, the Optical Lectures, which he delivered in 1669 and following years.

158. One important use may be made of it at present. It gives a complete solution of all the facts which were observed by Dr Hooke, and adduced by Leibnitz with such pertinacity in support of his measure of the force of moving bodies. All of them are of precisely the same nature with the one mentioned in art. 157, or with the fact, "that a ball projected directly upwards with a double velocity, will rise to a quadruple height, and that a body, moving twice as fast, will penetrate four times as far into a uniformly tenacious mass." The uniform force of gravity, or the uniform tenacity of the penetrated body, makes a uniform opposition to the motion, and may therefore be considered as a uniform retarding force. It will therefore be represented, in fig. 8. by an ordinate always of the same length, and the areas which measure the square of the velocity lost will be portions of a rectangle $A\; E\; \backslash cdot\; a$. If therefore $A\; E$ be the penetration necessary for extinguishing the velocity 2, the space $A\; B$, necessary for extinguishing the velocity 1, must be $\backslash frac\{1\}\{4\}$ of $A\; E$, because the square of 1 is $\backslash frac\{1\}\{4\}$ of the square of 2.

159. What particularly deserves remark here, is, that this proposition is true, only on the supposition that forces are proportional to the velocities generated by them in equal times. For the demonstration of this proposition proceeds entirely on the previously established measure

Of Moving of acceleration. We had $v\; \backslash propto\; ft$; therefore $v\; \backslash propto\; f\; i\; v$.
Forces. But $i\; v\; \backslash propto\; s$; therefore $v\; \backslash propto\; f\; s$, which is precisely this proposition.

160. Those may be called similar points of space, and similar instants of time, which divide given portions of space or time in the same ratio. Thus, the beginning of the 5th inch, and of the 2d foot, are similar points of a foot, and of a yard. The beginning of the 21st minute, and of the 9th hour, are similar instants of an hour, and of a day.

Forces may be said to act similarly when, in similar instants of time, or similar points of the path, their intensities are in a constant ratio.

161. Lemma. If two bodies be similarly accelerated during given times $ac$ and $hk$ (fig. 33.), they are also similarly accelerated along their respective paths $AC$ and $HK$.

Let $a,\; b,\; c$, be instants of the time $ac$, similar to the instants $h,\; i,\; k$ of the time $hk$. Then by the similar accelerations, we have the force $ae\; :\; hl\; =\; bf\; :\; im$. This being the case throughout, the area $af$ is to the area $hm$ as the area $ag$ to the area $hn$. These areas are as the velocities in the two motions (48.) Therefore the velocities in similar instants are in a constant ratio, that is, the velocity in the instant $b$ is to that in the instant $i$, as the velocity in the instant $c$ to that in the instant $k$.

The figures may now be taken to represent the times of the motion by their abscissæ, and the velocities by their ordinates, as in art. 28. The spaces described are now represented by the areas. These being in a constant ratio, as already shewn, we have $A,\; B,\; C$, and $H,\; I,\; K$, similar points of the paths. And therefore, in similar instants of time, the bodies are in similar points of the paths. But in these instants, they are similarly accelerated, that is, the accelerations and the forces are in a constant ratio. They are therefore in a constant ratio in similar points of the paths, and the bodies are similarly accelerated along their respective paths (155.).

162. If two particles of matter are similarly urged by accelerating or retarding forces during given times, the whole changes of velocity are as the forces and times jointly; or $v\; \backslash propto\; ft$.

For the abscissæ $ac$ and $hk$ will represent the times, and the ordinates $ae$ and $hl$ will represent the forces, and then the areas will represent the changes of velocity, by art. 47. And these areas are as $ac\; \backslash times\; ae$ to $hk\; \backslash times\; hl$.

163. If two particles of matter are similarly impelled or opposed through given spaces, the changes in the squares of velocity are as the forces and spaces jointly; or $s\; \backslash propto\; f\; t^2$.

This follows, by similar reasoning, from art. 49.

It is evident that this proposition applies directly to the argument so confidently urged for the propriety of the Leibnitzian measure of forces, namely, that four springs of equal strength, and bent to the same degree, generate, or extinguish only a double velocity.

164. If two particles of matter are similarly impelled through given spaces, the spaces are as the forces and the squares of the times jointly.

For the moveables are similarly urged during the same times of their motion (converse of 156.). Therefore $v\; \backslash propto\; ft$, and $v^2\; \backslash propto\; f^2\; t^2$; but (158.) $v^2\; \backslash propto\; fs$. Therefore $fs\; \backslash propto\; f^2\; t^2$ and $s\; \backslash propto\; f\; t^2$.

COROLLARY.

$t^2\; \backslash propto\; \backslash frac\{s\}\{f\}$, and $f\; \backslash propto\; \backslash frac\{s\}\{t^2\}$. That is, the squares of the times are as the spaces, directly, and as the forces, inversely; and the forces are as the spaces, directly, and as the squares of the times, inversely.

165. The quantity of motion in a body is the sum of the motions of all its particles. Therefore, if all are moving in one direction, and with one velocity $v$, and if $m$ be the number of particles, or quantity of matter, $mv$ will express the quantity of motion $q$, or $q\; \backslash propto\; mv$.

166. In like manner, we may conceive the accelerating forces $f$, which have produced this velocity $v$ in each particle, as added into one sum, or as combined on one particle. They will thus compose a force, which, for distinction's sake, it is convenient to mark by a particular name. We shall call it the MOTIVE FORCE, and express it by the symbol $p$. It will then be considered as the aggregate of the number $m$ of equal accelerating forces $f$, each of which produces the velocity $v$ on one particle. It will produce the velocity $mv$, and the same quantity of motion $q$.

167. Let there be another body, consisting of $n$ particles, moving with one velocity $u$. Let the moving force be represented by $\backslash pi$. It is measured in like manner by $nu$. Therefore we have, $p\; :\; \backslash pi\; =\; mv\; :\; nu$, and $v\; :\; u\; =\; \backslash frac\{p\}\{m\}\; :\; \backslash frac\{\backslash pi\}\{n\}$; that is,

The velocities which may be produced by the similar action of different motive forces, in the same time, are directly as these forces, and inversely as the quantities of matter to which they are applied.

REMARK.

168. In the application of the theorems concerning accelerating or retarding forces, it is necessary to attend carefully to the distinction between an accelerative and a motive force. The caution necessary here has been generally overlooked by the writers of Elements, and this has given occasion to very inadequate and erroneous notions of the action of accelerating powers. Thus, if a leaden ball hangs by a thread, which passes over a pulley, and is attached to an equal ball, moveable along a horizontal plane, without the smallest obstruction, it is known that, in one second, it will descend 8 feet, dragging the other 8 feet along the plane, with a uniformly accelerated motion, and will generate in it the velocity 16 feet per second. Let the thread be attached to three such balls. We know that it will descend 4 feet in a second, and generate the velocity 8 feet per second. Most readers are disposed to think that it should generate no greater velocity than $5\backslash frac\{1\}\{3\}$ feet per second, or $\backslash frac\{1\}\{3\}$ of 16, because it is applied to three times as much matter (162.). The error

error lies in considering the motive force as the same in both cases, and in not attending to the quantity of matter to which it is applied. Neither of these conjectures is right. The motive force changes as the motion accelerates, and in the first case it moves two balls, and in the second it moves four. The motive force decreases similarly in both motions. When these things are considered, we learn by articles 202 and 207, that the motions will be precisely what we observe.

Of Deflecting Forces, in General.

169. It was observed, in art. 71, that a curvilinear motion is a case of continual deflection. Therefore, when such motions are observed, we know that the body is under the continual influence of some natural force, acting in a direction which crosses that of the motion in every point. We must infer the magnitude and direction of this deflecting force by the magnitude and direction of the observed deflection. Therefore, all that is affirmed concerning deflections in the 71st and subsequent articles, may be affirmed concerning deflecting forces. It follows, from what has been established concerning the action of accelerating forces, that no force can produce a finite change of velocity in an instant. Now, a deflection is a composition of a motion already existing with a motion accelerated from rest by insensible degrees. Supposing the deflecting force of invariable direction and intensity, the deflection is the composition of a motion having a finite velocity with a motion uniformly accelerated from rest. Therefore the linear deflection from the rectilinear motion must increase by insensible degrees. The curvilinear path, therefore, must have the line of undeflected motion for its tangent. To suppose any finite angle contained between them would be to suppose a polygonal motion, and a subsultory deflection.

Therefore no finite change of direction can be produced by a deflecting force in an instant.

170. The most general and useful proposition on this subject is the following, founded on art. 75.

The forces by which bodies are deflected from the tangents in the different points of their curvilinear paths are proportional to the squares of the velocities in those points directly, and inversely to the deflective chords of the equicurve circles in the same points. We may still express the proposition by the same symbol,

where $f$ means the intensity of the deflecting force.

171. We may also retain the meaning of the proposition expressed in article 76, where it is shewn that the actual linear deflection from the tangent is the third proportional to the deflective chord and the arch described in a very small moment. For it was demonstrated in that article (see fig. 18.) that $BZ\; :\; BC\; =\; BC\; :\; BO$.

We see also that $Bb$, the double of $BO$, is the measure of the velocity, generated by the uniform action of the deflecting force, during the motion in the arch $BC$ of the curve.

172. The art. 77. also furnishes a proposition of frequent and important use, viz.

The velocity in any point of a curvilinear motion is that which the deflecting force in that point would generate

rate in the body by uniformly impelling it along the fourth part of the deflective chord of the equicurve circle. Of Moving Forces.

REMARK.

137. The propositions now given proceed on the supposition that, when the points $A$ and $C$ of fig. 18. after continually approaching to $B$, at last coalesce with it, the last circle which is described through these three points has the same curvature which the path has in $B$. It is proper to render this mode of solving these questions more plain and palpable.

If $ABCD$ (fig. 34.) be a material curve or mould, and a thread be made fast to it at $D$, this thread may be lapped on the convexity of this curve, till its extremity meets it in $A$. Let the thread be now unrolled or EVOLVED from the curve, keeping it always tight. It is plain that its extremity $A$ will describe another curve line $Abc$. All curves, in which the curvature is neither infinitely great nor infinitely small, may be thus described by a thread evolved from a proper curve. The properties of the curve $Abc$ being known, Mr Huyghens (the author of this way of generating curve lines) has shewn how to construct the evolved curve $ABC$ which will produce it.

From this genesis of curves we may infer, 1st, that the detached portion of the thread is always a tangent to the curve $ABC$; 2dly, that when this is in any situation $Bb$, it is perpendicular to the tangent of the curve $Abc$ in the point $b$, and that it is, at the same time, describing an element of that curve, and an element of a circle $abx$, whose momentary centre is $B$, and which has $Bb$ for its radius. 3dly, That the part $bA$ of the curve, being described with radii growing continually shorter, is more incurvated than the circle $abx$, which has $Bb$ for its constant radius. For similar reasons the arch $bc$ of the curve $Abc$ is less incurvated than the circle $abx$. 4thly, That the circle $abx$ has the same curvature that the curve has in $b$, or is an equicurve circle. $Bb$ is the radius, and $B$ the centre of curvature in the point $b$.

$ABC$ is the CURVA EVOLUTA or the EVOLUTE. $Abc$ is sometimes called the INVOLUTE of $ABC$, and sometimes its EVOLUTRIX.

174. By this way of describing curve lines, we see clearly that a body, when passing through the point $b$ of the curve $Abc$ may be considered as in the same state, in that instant, as in passing through the same point $b$ of the circle $abx$; and the ultimate ratio of the deflections in both is that of equality, and they may be used indiscriminately.

The chief difficulty in the application of the preceding theorems to the curvilinear motions which are observed in the spontaneous phenomena of nature, is in ascertaining the direction of the deflection in every point of a curvilinear motion. Fortunately, however, the most important cases, namely those motions, where the deflecting forces are always directed to a fixed point, afford a very accurate method. Such forces are called by the general name of

Central Forces.

175. If bodies describe circles with a uniform motion, the deflecting forces are always directed to the centres of the

Of Moving the circles, and are proportional to the square of the velocities, directly, and to their distances from the centre, inversely.

For, since their motion in the circumference is uniform, the areas formed by lines drawn from the centre are as the times, and therefore (72.) the deflections, and the deflecting forces (164.) are directed to the centre. Therefore, the deflective chord is, in this case, the diameter of the circle, or twice the distance of the body from the centre. Therefore, if we call the distance from the centre $d$, we have $f\; \backslash propto\; \backslash frac\{v^2\}\{d\}$.

176. These forces are also as the distances, directly, and as the square of the time of a revolution, inversely.

For the time of a revolution (which may be called the PERIODIC TIME) is as the circumference, and therefore as the distance, directly, and as the velocity, inversely. Therefore $t\; \backslash propto\; \backslash frac\{d\}\{v\}$, and $v\; \backslash propto\; \backslash frac\{d\}\{t\}$, and $v^2\; \backslash propto\; \backslash frac\{d^2\}\{t^2\}$, and $\backslash frac\{v^2\}\{d\}\; \backslash propto\; \backslash frac\{d\}\{t^2\}$.

177. These forces are also as the distances, and the square of the angular velocity, jointly.

For, in every uniform circular motion, the angular velocity is inversely as the periodic time. Therefore, calling the angular velocity, $\backslash omega$, $\backslash omega\; \backslash propto\; \backslash frac\{1\}\{t\}$, and $\backslash frac\{d\}\{t^2\}\; \backslash propto\; d\backslash omega^2$, and therefore $f\; \backslash propto\; d\backslash omega^2$.

178. The periodic time is to the time of falling along half the radius by the uniform action of the centripetal force in the circumference, as the circumference of a circle is to the radius.

For, in the time of falling through half the radius, the body would describe an arch equal to the radius (37.—6.) because the velocity acquired by this fall is equal to the velocity in the circumference (167.). The periodic time is to the time of describing that arch as the circumference to the arch, that is, as the circumference is to the radius.

179. When a body describes a curve which is all in one plane, and a point is so situated in that plane, that a line drawn from it to the body describes round that point areas proportional to the times, the deflecting force is always directed to that point (72.)

180. Conversely. If a body is deflected by a force always directed to a fixed point, it will describe a curve line lying in one plane which passes through that point, and the line joining it with the centre of forces will describe areas proportional to the times (73.)

The line joining the body with the centre is called the RADIUS VECTOR. The deflecting force is called CENTRIPETAL, or ATTRACTIVE, if its direction be always toward that centre. It is called REPULSIVE, or CENTRIFUGAL, if it be directed outwards from the centre. In the first case, the curve will have its concavity toward the centre, but, in the second case, it will be convex toward the centre. The force which urges a piece of iron towards a magnet is centripetal, and that which causes two electrical bodies to separate is centrifugal.

181. The force by which a body may be made to describe circles round the centre of forces, with the angular velocities which it has in the different points of its

curvilinear path, are inversely as the cubes of its distances from the centre of forces. For the centripetal force in circular motions is proportional to $d^3$ (172.). But when the deflections (and consequently the forces) are

directed to a centre, we have $a\; \backslash propto\; \backslash frac\{1\}\{d^2\}$ (75.) and $a^2\; \backslash propto\; \backslash frac\{1\}\{d^4\}$, therefore $d^3\; a^2\; \backslash propto\; d\; \backslash times\; \backslash frac\{1\}\{d^4\}\; \backslash propto\; \backslash frac\{1\}\{d^3\}$, therefore $f\; \backslash propto\; \backslash frac\{1\}\{d^3\}$.

This force is often called centrifugal, the centrifugal force of circular motion; and it is conceived as always acting in every case of curvilinear motion, and to act in opposition to the centripetal force which produces that motion. But this is inaccurate. We suppose this force, merely because we must employ a centripetal force, just as we suppose a resisting vis inertiae, because we must employ force to move a body.

182. If a body describe a curve line ABC by means of a centripetal (fig. 35.) force directed to S, and varying according to some proportion of the distances from it, and if another body be impelled toward S in the straight line a b S by the same force, and if the two bodies have the same velocity in any points A and a which are equidistant from S, they will have equal velocities in any other two points C and c, which are also equidistant from S.

Describe round S, with the distance SA, the circular arch A a, which will pass through the equidistant point a. Describe another arch B b, cutting off a small arc AB of the curve, and also cutting AS in D. Draw DE perpendicular to the curve.

The distances AS and a S being equal, the centripetal forces are also equal, and may be represented by the equal line AD and a b. The velocities at A and a being equal, the times of describing AB and a b will be as the spaces (14.). The force a b is wholly employed in accelerating the rectilinear motion along a S. But the force AD, being transverse or oblique to the motion along AB, is not wholly employed in thus accelerating the motion. It is equivalent to the two forces AE and ED, of which ED, being perpendicular to AB, neither promotes nor opposes it, but incurs the motion. The accelerating force in A therefore is AE. It was shewn, in art. 48, that the change of velocity is as the force and as the time jointly, and therefore it is as $AE\; \backslash times\; AB$. For the same reason, the change of the velocity at a is as $a\; b\; \backslash times\; a\; b$, or $a\; b^2$. But, as the angle ADB is a right angle, as also AED, we have $AE\; :\; AD\; =\; AD\; :\; AB$, and $AE\; \backslash times\; AB\; =\; AD^2\; =\; a\; b^2$. Therefore, the increments of velocity acquired along AB and a b are equal. But the velocities at A and a were equal. Therefore the velocities at B and b are also equal. The same thing may be said of every subsequent increase of velocity, while moving along BC and b c; and therefore the velocities at C and c are equal.

The same thing holds when the deflecting force is directed in lines parallel to a S, as if to a point S' infinitely distant, the one body describing the curve line VA'B', while the other describes the straight line VS.

183. The propositions in art. 73. and 74. are also true in curvilinear motions by means of central forces.

When the path of the motion is a line returning into itself, like a circle or oval, it is called an ORBIT; otherwise it is called a TRAJECTORY.

The time of a complete revolution round an orbit is called the PERIODIC TIME.

184. The formula $f\; =\; \backslash frac\{v^2\}\{c\}$ serves for discovering the law of variation of the central force by which a body describes the different portions of its curvilinear path; and the formula $f\; =\; \backslash frac\{d\}\{t^2\}$ serves for comparing the forces by which different bodies describe their respective orbits.

185. It must always be remembered, in conformity to art. 77. that $f\; =\; \backslash frac\{v^2\}\{c\}$ or $f\; =\; \backslash frac\{\backslash text\{arc\}^2\}\{c\}$ expresses the linear deflection from the tangent, which may be taken for a measure of the deflecting force, and that $f\; =\; \backslash frac\{2v^2\}\{c\}$,

or $f\; =\; \backslash frac\{2\; \backslash text\{\; arc\}^2\}\{c\}$ expresses the velocity generated by this force, during the description of the arc, or the velocity which may be compared directly with the velocity of the motion in the arc. The last is the most accurate, because the velocity generated is the real change of condition.

186. A body may describe, by the action of a centripetal force, the direction of which passes through C (fig. 36.), a figure VPS, which figure revolves (in its own plane) round the centre of forces C, in the same manner as it describes the quiescent figure, provided that the angular motion of the body in the orbit be to that of the orbit itself in any constant ratio, such as that of m to n.

For, if the direction of the orbit's motion be the same with that of the body moving in it, the angular motion of the body in every point of its motion is increased in the ratio of m to n + m, and it will be in the same ratio in the different parts of the orbit as before, that is, it will be inversely as the square of the distance from S (75.). Moreover, as the distances from the centre in the simultaneous positions of the body, in the quiescent and in the revolving orbit, are the same, the momentary increments of the area are as the momentary increments of the angle at the centre; and therefore in both motions, the areas increase in the constant ratio of m to n (75.). Therefore the areas of the absolute path, produced by the composition of the two motions, will still be proportional to the times; and therefore (73.) the deflecting force must be directed to the centre S; or, a force so directed will produce this compound motion.

187. The differences between the forces by which a body may be made to move in the quiescent and in the moveable orbit are in the inverse triplicate ratio of the distances from the centre of forces.

Let VKSBV (fig. 36.) be the fixed orbit, and upk be the same orbit moved into another position; and let

Vpn No Nt QV be the orbit described by the body in absolute space by the composition of its motion in the orbit with the motion of the orbit itself. If the body be supposed to describe the arch VP of the fixed orbit while the axis VC moves into the situation uC, and if the arch up be made equal to VP, then p will be the place of the body in the moveable orbit, and in the compound path Vp. If the angular motion in the fixed orbit be to the motion of the moving orbit as m to n, it is plain that the angle VCP is to VCP as m to n + n. Let PK and pk be two equal and very small arches of the fixed and moving orbits. PC and pc are equal, as are also KC and kc, and a circle described round C with the radius CK will pass through k. If we now make VCK to VCn as m to n + n: the point n of the circle Kkn will be the point of the compound path, at which the body in the moving orbit arrives when the body in the fixed orbit arrives at K, and pn is the arch of the absolute path described, while PK is described in the fixed path.

In order to judge of the difference between the force which produces the motion PK in the fixed orbit and that which produces pn in the absolute path, it must be observed that, in both cases, the body is made to approach the centre by the difference between CP and CK. This happens, because the centripetal forces, in both cases, are greater than what would enable the body to describe circles round C, at the distance CP, and with the same angular velocities that obtain in the two paths, viz. the fixed orbit and the absolute path. We shall call the one pair of forces the circular forces, and the other the orbital. Let C and c represent the forces which would produce circles, with the angular velocities which obtain in the fixed and moving orbits, and let O and o be the forces which produce the orbital motions in these two paths.

These things being premised, it is plain that o — c is equal to O — C, because the bodies are equally brought towards the centre by the difference between O and C, and by that between o and c. Therefore o — O is equal to c — C (A). The difference, therefore, of the forces which produce the motions in the fixed and moving orbits is always equal to the difference of the forces which would produce a circular motion at the same distances, and with the same angular velocity. But the forces which produce circular motions, with the angular motion that obtains in an orbit at different distances from the centre of forces, are as the cubes of the distances inversely (175.). And the two angular motions at the same distance are in the constant ratio of m to n + n. Therefore the forces are in a constant ratio to each other, and their differences are in a constant ratio to either of the forces. But the circular force at different distances is inversely as the cube of the distance (121.). Therefore the difference of them in the fixed and moveable orbits is in the same proportion. But the difference of the orbital forces is equal to that of the circular. Therefore, finally, the difference of the centripetal

(A) For let A o, AO, Ac, AC represent the four forces o, O, c, and C. By what has been said, we find that o — c = O — C. To each of these add O c, and then it is plain that o — O = c — C, that is, that the difference of the circular forces c and C is equal to that of the orbital forces o and O.

Of Moving Forces. petal forces by which a body may be retained in a fixed orbit, and in the same orbit moving as determined in article 130. is always in the inverse triplicate ratio of the distances from the centre of forces.

In this example, the motion of the body in the orbit is in the same direction with that of the orbit, and the force to be joined with that on the fixed orbit is always additive. Had the orbit moved in the opposite direction, the force to be joined would have been subtractive, unless the retrograde motion of the orbit exceeded twice the angular motion of the body. But in all cases, the reasoning is similar.

188. Thus we have considered the motions of bodies influenced by forces directed to a fixed point. But we cannot conceive a mere mathematical point of space as the cause or occasion of any such exertion of forces. Such relations are observed only between existing bodies or masses of matter. The propositions which have been demonstrated may be true in relation to bodies placed on those fixed points. That continual tendency towards a centre, which produces an equable description of areas round it, becomes intelligible, if we suppose some body placed in the centre of forces, attracting the revolving body. Accordingly, we see very remarkable examples of such tendencies towards a central body in the motions of the planets round the sun, and of the satellites round the primary planet.

But, since it is a universal fact that all the relations between bodies are mutual, we are obliged to suppose that whatever force inclines the revolving body towards the body placed in the centre of forces, an equal force (from whatever source it is derived) inclines the central body towards the revolving body, and therefore it cannot remain at rest, but must move towards it. The notion of a fixed centre of forces is thus taken away again, and we seem to have demonstrated propositions inapplicable to any thing in nature. But more attentive consideration will shew us that our propositions are most strictly applicable to the phenomena of nature.

189. For, in the first place, the motion of the common centre of position of two, or of any number of bodies, is not affected by their mutual actions. These, being equal and opposite, produce equal and opposite motions, or changes of motion. In this case, it follows from art. 115. that the state of the common centre is not affected by them.

190. Now, suppose two bodies S and P, situated at the extremities of the line SP (fig. 37.). Their centre of position is in a point C, dividing their distance in such a manner that SC is to CP as the number of material atoms in P to the number in S or $SC\; :\; PC\; =\; P\; :\; S$. Suppose the mutual forces to be centripetal. Then, being equal, exerted between every atom of the one, and every particle of the other, the vis motrix may be expressed by $P\; \backslash times\; S$. This must produce equal quantities of motion in each of the bodies, and therefore must produce velocities inversely as the quantities of matter. In any given portion of time, therefore, the bodies will move towards each other, to $s$ and $p$, and $Ss$ will be to $Pp$, as $P$ to $S$, that is, as $SC$ to $PC$. Therefore we shall still have $sC\; :\; pC\; =\; SC\; :\; PC$. Their distances from C will always be in the same proportion. Also we shall have $SC\; :\; SP\; =\; P\; :\; S\; +\; P$, and $sC\; :\; pC\; =\; P\; :\; S\; +\; P$; and therefore $SC\; :\; SP\; =\; sC\; :\; sP$. Consequently, in whatever manner the mutual forces vary by a va-

riation of distance from each other, they will vary in the same manner by the same variation of distance from C. And, conversely, in whatever manner the forces vary by a change of distance from C, they vary in the same manner by the same change of distance from each other.

Let us now suppose that when the bodies are at S and P, equal moving forces are applied to each in the opposite directions SA and PB. Did they not attract each other at all, they would, at the end of some small portion of time, be found in the points A and B of a straight line drawn through C, because they will move with equal quantities of motion, or with velocities SA and PB inversely as their quantities of matter. Therefore $SA\; :\; PB\; =\; SC\; :\; PC$, and A, C, and B are in a straight line. But let them now attract, when impelled from S and P. Being equally attracted towards each other, they will describe curve lines $Sa$ and $Pb$, so that their deflections $Aa$ and $Bb$ are as $SC$ and $PC$; and we shall have $aC\; :\; bC\; =\; SC\; :\; PC$. As this is true of every part of the curve, it follows that they describe similar curves round C, which remains in its original place.

Lastly, If the motion of P be considered by an observer placed in S, unconscious of its motion, since he judges of the motion of P only by its change of direction and of distance, we may make a figure which will perfectly represent this motion. Draw the line EF equal and parallel to PS, and EG equal and parallel to $ab$. Do this for every point of the curve $Sa$ and $Pb$. We shall then form a curve FG similar to the curves $Sa$ and $Pb$, having the homologous lines equal to the sum of the homologous lines of these two curves. Thus the bodies will describe round each other curve lines which are similar and equal (lineally) to the lines which they describe round their common centre by the same forces. They may appear to describe areas proportional to the times round each other; and they really describe areas proportional to the times round their common centre of position, and the forces, which really relate to the body which is supposed to be central, have the same mathematical relation to their common centre.

Thus it appears that the mechanical inferences, drawn from a supposed relation to a mere point of space, are true in the real relations to the supposed central body, although it is not fixed in one place.

191. The time of describing any arch FG of the curve described round the other body at rest in a centre of forces (where we may suppose it forcibly withheld from moving) is to the time of describing the similar arch $Pb$ round the common centre of position in the subduplicate ratio of $S+P$ to $S$, that is, in the ratio of $\backslash sqrt\{S+P\}$ to $\backslash sqrt\{S\}$. For the forces being the same in both motions, the spaces described by their similar actions, that is, their deflections from the tangent, are as the squares of the times $T$ and $t$ (204.). That is, $HG\; :\; Bb\; =\; T^2\; :\; t^2$, and $T\; :\; t\; =\; \backslash sqrt\{HG\}\; :\; \backslash sqrt\{Bb\}\; =\; \backslash sqrt\{S+P\}\; :\; \backslash sqrt\{S\}$.

Hence it follows that the two bodies S and P are moved in the same way as if they did not act on each other, but were both acted upon by a third body, placed in their common centre C, and acting with the same forces on each; and the law of variation of the forces by a change of distance from each other, and from this third body, is the same.

192. If a body P (fig. 38.) revolve around another Fig. 38. body

Fig. 1. 1800

Fig. 2. 1800

Fig. 28.

A geometric diagram showing a quadrilateral with vertices labeled A (top), B (left), C (bottom), and D (right). Internal lines connect A to B, C, and D, and B to C and D. Points R, U, and S are on the top edge AB. Points a, b, c, and d are on the bottom edge CD. Other points labeled include b, b, and d.

Fig. 29.

A geometric diagram showing a quadrilateral with vertices A (top-left), B (top-right), C (bottom-left), and D (bottom-right). Internal lines connect A to B, C, and D, and B to C and D. Points E and F are on the top edge AB. Point G is the intersection of the diagonals AC and BD.

Fig. 30.

A geometric diagram showing a rectangle with vertices A (left), B (top), C (right), and D (bottom). Internal lines connect A to B, C, and D, and B to C and D. Points F and E are on the top edge AB. Point G is on the bottom edge CD.

Fig. 32.

A complex geometric diagram showing a central point A connected to several other points B, C, D, E, F, G, H, I, K, and L. The figure consists of multiple overlapping triangles and quadrilaterals.

Fig. 31.

A complex geometric diagram showing a central point A connected to several other points B, C, D, E, F, G, and a, b. The figure consists of multiple overlapping triangles and quadrilaterals.

Fig. 33.

A geometric diagram showing a series of vertical and horizontal lines. Points are labeled A, B, C on the left vertical line, H, I, K on the right vertical line, and a, b, c, d, e, f, g, h, i, k, l, m, n on the horizontal lines.

Fig. 34.

A large geometric diagram showing a curved line with points A, B, C, and D marked along it. Other points are labeled a, b, c, e, f, g, h, i, k, l, m, and n.

Fig. 35.

A geometric diagram showing a curved line with points A, B, C, and D marked along it. Other points are labeled a, b, c, d, e, f, g, h, i, k, l, m, and n.

Fig. 36.

A geometric diagram showing a circle with center O and points A, B, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, U, V, W, X, Y, and Z marked along its circumference and internal lines.

Fig. 37.

A geometric diagram showing a series of lines and points labeled A, B, C, D, E, F, G, H, I, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, and Z.

Fig. 38.

A geometric diagram showing a circle with center O and points A, B, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, U, V, W, X, Y, and Z marked along its circumference and internal lines.

body S, by the action of a central force, while S moves in any path ASB, P will continue to describe areas proportional to the times round S, if every particle in P be affected by the same accelerating force that acts, in that instant, on every particle in S. For, such action will compound the same motions Pp and Ss with the motions of S and P, whatever they are; and it was shown in art. 69. that such composition does not affect their relative motions. This is another way of making a body describe the same orbit in motion which it describes while the orbit is fixed (186.)

Such is the view of the abstract doctrines of motion and of moving forces which we proposed to lay before our readers. Those who have heard the excellent lecture of the late Professor Robison of the university of Edinburgh will probably see that we have availed ourselves of his valuable instructions; and the learned reader will readily perceive that we have enriched our treatise with much important matter by borrowing freely from the writings of the same distinguished philosopher.

DYNANOMETER, an instrument for ascertaining the relative strength of men and animals. Of an instrument of this kind, invented by Regnier, and of which a description is given in vol. ii. Jour. de l'Ecole Polytechnique, the author thus speaks. "Some important knowledge, says he, might be acquired, had we the easy means of ascertaining, in a comparative manner, our relative strengths at the different periods of life, and in different states of health. Buffon and Gueneau, who had some excellent ideas on this subject, requested me to endeavour to invent a portable machine, which, by an easy and simple mechanism, might conduct to a solution of this question, on which they were then engaged. These philosophers were acquainted with that invented by Graham, and improved by Dr Desaguliers, at London; but this machine, constructed of wooden work, was too bulky and heavy to be portable; and, besides, to make experiments on the different parts of the body, several machines were necessary, each suited to the part required to be tried. They were acquainted also with the dynamometer of Citizen Leroy of the Academy of Sciences at Paris. It consisted of a metal tube 10 or 12 inches in length, placed vertically on a foot like that of a candlestick, and containing in the inside a spiral spring, having above it a graduated shank terminating in a globe. This shank, together with the spring, sunk into the tube in proportion to the weight acting upon it, and thus pointed out, in degrees, the strength of the person who pressed on the ball with his hand.

"This instrument, though ingenious, did not appear sufficient however to Buffon and Gueneau; for they wished not merely to ascertain the muscular force of a finger or hand, but to estimate that of each limb separately, and of all the parts of the body. I shall not here give an account of the attempts I made to fulfil the wishes of these two philosophers, but only observe, that in the course of my experiments I had reason to be convinced that the construction of the instrument was not so easy as might have been expected. Besides the use which an enlightened naturalist may make of this machine, it may be possible to apply it to many other important purposes. For example, it may be employed with advantage to determine the strength of draught cattle; and, above all, to try that of horses, and compare it with the strength of other animals. It may

serve to make known how far the assistance of well-constructed wheels may favour the movement of a carriage, and what is its vis inertiae in proportion to the load. We might appreciate by it, also, what resistance the slope of a mountain opposes to a carriage, and be able to judge whether a carriage is sufficiently loaded in proportion to the number of horses that are to be yoked to it. In the arts, it may be applied to machines of which we wish to ascertain the resistance, and when we are desirous to calculate the moving force that ought to be adapted to them. It may serve, also, as a Roman balance to weigh burdens. In short, nothing would be more easy than to convert it into an anemometer, to discover the absolute force of the wind, by fitting to it a frame of a determined size filled up with wax cloth; and it would not be impossible to ascertain by this machine the recoil of fire-arms, and consequently the strength of gun-powder.

"This dynamometer, in its form and size, has a near resemblance to a common graphometer. It consists of a spring twelve inches in length, bent into the form of an ellipse; from the middle of which arises a semicircular piece of brass, having engraved upon it the different degrees that express a force of the power acting on the spring. The whole of this machine, which weighs only two pounds and a half, opposes, however, more resistance than may be necessary to determine the action of the strongest and most robust horse." For a fuller description, see Phil. Mag. vol. i.

DYNASTY, among ancient historians, signifies a race or succession of kings of the same line or family. Such were the dynasties of Egypt. The word is formed from the Greek δυναστεία, of δύναμις, to be powerful, or king.

The Egyptians reckon 30 dynasties within the space of 36,525 years; but the generality of chronologists look upon them as fabulous. And it is very certain, that these dynasties are not continually successive, but collateral.

DYRRACHIUM, in Ancient Geography, a town on the coast of Illyricum, before called Epidamnus, or Epidamnus, an inauspicious name, changed by the Romans to Dyrrachium; a name taken from the peninsula on which it stood. Originally built by the Corcyreans. A Roman colony (Pliny). A town famous in story: its port answered to that of Brundusium, and the passage