in its more general signification, Nature of comprehends all kinds of earthen ware, which are white, porcelain, semitransparent, and have some degree of a vitreous texture. Hence, in this extensive meaning of the term, it includes all kinds of pottery, stoneware, delft ware, &c.; but in a more limited sense, the word Porcelain is employed to denote only the finer kinds of earthen ware; and because this kind of ware has been, from time immemorial, manufactured in the greatest degree of perfection in China, it has obtained the name of Chinese Porcelain, or China Ware.

In the Chinese language, porcelain is denoted by the Derivation word tse-ki, so that the derivation of the term is not to be sought for in that language; and hence it is supposed to be of European extraction, and to be derived from the Portuguese language; for in this language the word porcellana signifies a cup or vessel.

The first porcelain which was seen in Europe was Porcelain brought from Japan and China. Its whiteness, transparency, fineness of texture, with its elegance and beautiful colours, soon introduced it as an ornament of the tables of the rich and powerful, while at the same time it excited the admiration and industry of the European manufacturer. Accordingly attempts were made to imitate this kind of ware, in different countries of Europe. These attempts have succeeded so well, that the produce of the manufacture has acquired the name of Porcelain. The first European porcelains were made in Saxony; the manufacture was afterwards introduced into France, and successively into England, Germany, and Italy, where it has arrived at various degrees of perfection, according to the nature of the materials which can be obtained, and the industry and ingenuity of the artist who superintends and directs it; but after all, to whatever degree of perfection the manufacture of this ware has reached in Europe, it must still yield, in excellence and perfection, to the porcelain of eastern countries.

Of the antiquity of the manufacture of porcelain in Antiquity China, little precise information can be expected from the Chinese manufacturers, who have always shown themselves extremely averse to the freedom of intercourse with other nations; but it is said that the village or town of King-te-ching has furnished the emperors of China with porcelain since the year 442 of the Christian era, and that it is an object of so much attention to the Chinese government, that the manufacture is carried on under the superintendence of one or two mandarins sent from court. 1. History of the Manufacture of Porcelain in China.

The fullest account which has yet been received in Europe of the manufacture of Chinese porcelain, has been given by Father D'Entrecoulles, a Romanish missionary, who lived, for some time in the village or town where the principal manufactory is established. The account which is given of this village, and of the manufacture of porcelain, by this author, is the following:

This village or town, which is celebrated as producing the best porcelain of China, is in the province of Kiangsi, and it is said to be a league and a half in length, containing not less than 1,000,000 of inhabitants. Other manufactories, indeed, have been established in different parts of the Chinese empire, and particularly in those places which are convenient for the European trade, as in the provinces of Fo-kien and Canton; but the porcelain produced at these manufactories is said to be held in inferior estimation. A Chinese emperor wishing to have a manufacture of porcelain under his own inspection at Pekin, ordered workmen to be collected for the purpose, with all the necessary materials and implements; but after erecting furnaces and other expensive operations, the attempt failed, so that King-te-tching, in the time of our author, continued to be the most celebrated place in China for beautiful porcelain, and from this it was transported to all parts of the world.

The chief ingredients which enter into the composition employed in fine porcelain are petuntse and kaolin, two kinds of earth from the mixture of which the paste is obtained. The petuntse is of a pure white, and, when fully prepared, is in the form of an impalpable powder, so that it is very fine to the touch. The kaolin, he observes, is intermixed with small shining particles. These materials are carried to the manufactory in the shape of bricks. The petuntse is originally the fragments of rock dug out from certain quarries, and reduced to powder, and the colour of the stone which answers the purpose best, according to the Chinese, inclines somewhat to green. The fragments of rock are broken to pieces with a large iron club; they are then put into mortars, and by means of levers headed with hard stone, strongly secured with iron, they are reduced to the state of fine powder. The levers, it is scarcely necessary to observe, are moved either by the labour of men, or by water. The powder, which is afterwards collected, is thrown into a large vessel of water, which is strongly agitated with an iron shovel. When this mixture has been allowed to settle for some time, a substance resembling cream rises to the top, which is skimmed off, and poured into another vessel also filled with water. The water in the first vessel is again agitated, and the frothy substance which rises to the surface is collected as before, and the same operation is repeated till it appear that nothing remains but a coarse sediment which falls to the bottom by its own weight. This sediment is carefully collected, and again subjected to the process of pulverization.

The fluid in the second vessel is allowed to remain at rest till a sediment is produced, forming a kind of crust at the bottom; and when the water above seems to be quite transparent, it is poured off by gently inclining the vessel, that the sediment may not be disturbed. The paste is then put into large moulds, and allowed to dry slowly; but before it becomes quite hard, it is divided into small square cakes, which are sold by the hundred. Porcelain is the substance which is called by the Chinese petuntse, and the name is said to be derived from the colour and form of this paste.

The kaolin, the other substance which is employed in the fabrication of porcelain, requires fewer operations in its preparation than the former, as it is found in nature in a state almost ready for the manufacturer. Of this substance it is said, that there are extensive mines in certain mountains; the external strata of which are composed of a kind of red earth. The kaolin is found in these mines in small lumps, and it is formed into bricks by being subjected to a similar process with the petuntse, &c.

The fine porcelain, it has been observed, derives its nature, fabric and texture from the kaolin. It is to this that the fine qualities which it possesses of resisting the most powerful agents is owing; and it has been remarked as an extraordinary circumstance, that a soft earth should communicate strength and consistency to the petuntse, which is obtained from some of the hardest rocks. The author relates an anecdote which he received from a rich Chinese merchant, that the English and Dutch having purchased a quantity of petuntse, conveyed it to Europe for the purpose of manufacturing porcelain; but having procured none of the kaolin, the attempt failed. They wanted, added the Chinese with a smile, to form a body, the flesh of which would support itself without bones.

It is said that the Chinese have discovered of late several years a new substance which may be employed in the composition of porcelain. This stone is called hoa-chè, the first part of the word signifies glutinous, because it is of a saponaceous quality. Porcelain made with this substance is very rare, and bears a much higher price than any other. The grain is extremely fine, and the painting with which it is ornamented, when compared with that of common porcelain, seems to exceed it as much as vellum surpasses paper. This variety of porcelain, it is added, is also remarkable for its lightness. It is besides much more brittle, and it is found difficult to hit upon the proper degree of heat for tempering it. This substance, we are farther informed, is but rarely employed in the fabrication of the body of the porcelain; the reason of this perhaps is, the scarcity and high price of this precious article, in consequence of which the workman is contented with making it into a fine size, into which the vessel is immersed when it is dry, that it may receive a coat before it is painted and glazed; and by this process he finds that he can communicate to the ware a high degree of beauty. The previous processes in the preparation of this substance are similar to those which are followed in the preparation of kaolin. When hoa-chè is dug out from the mine, it is washed in rain or river water, for the purpose of separating a yellowish earth with which it is contaminated. It is then reduced to powder, thrown into a vessel filled with water, and then formed into cakes. The hoa-chè prepared in this manner, without the addition of any other earth, is said to be alone sufficient in the fabrication of porcelain. It is employed, as has been already noticed, as a substitute for kaolin; but, on account of its scarcity, is much dearer. The price of the former is three times that of the latter, and from this circumstance the value of porcelain made with hoa- The principal ingredients in the fabrication of porcelain are petuntse and kaolin; but to these must be added the glaze or varnish, or, as it is called in the account given of Chinese porcelain, the oil, on which depend its splendour and whiteness. This varnish is of a whitish colour, and is obtained from the same kind of stone which yields the petuntse; but for this purpose the whitest stone is always preferred. The glaze is obtained by a process similar to that which is followed in the preparation of petuntse. This stone is first washed and reduced to powder; it is then thrown into a vessel with water, and after being purified, a frothy matter rises to the surface. To 100 pounds of this matter, one pound of a substance called cho-kao, is added. This latter is a saline substance, somewhat like alum, which is put into the fire, and allowed to remain till it become red hot, when it is reduced to powder. By the addition of this substance the glaze acquires a greater degree of consistence, but at the same time a proper degree of fluidity must be preserved. The glaze prepared in this manner is not employed alone. Another glaze is mixed with it, which is obtained from lime and ashes; to 100 pounds weight of which is also added one pound of cho-kao, or the aluminous substance mentioned above. When the two substances are mixed, it is necessary to attend that they be nearly of the same consistence, and the workman ascertains this point by dipping into each of them some cakes of petuntse; and by a close examination of their surfaces after they are drawn out, he is able to judge of the consistence of the fluids. The proportions of the two which are usually employed, are 10 parts of the glaze obtained from the stone, to one of that which is prepared from the lime and from ashes.

In the manufacture of the Chinese porcelain, the first process after the separate preparation of the materials, is a second purification of the petuntse and kaolin; and when they are found to be in a state of sufficient purity, the workmen proceed to mix the two ingredients together. The proportions employed for the finer kinds of porcelain are equal parts of kaolin and petuntse; for an inferior kind, four parts of kaolin to six of petuntse are employed; and in some kinds of porcelain, only one part of the former is added to three of the latter. This is the smallest proportion of kaolin which is employed in the Chinese manufactories. When the proportions are fixed, and the mixture finished, the mass is thrown into a large pit, which is well paved and cemented. It is then trodden upon, and kneaded till it become hard. This is the most fatiguing part of the labour, for it must be continued without intermission. From the mass prepared in this manner the workmen detach different pieces, which they spread out upon large slates, where they knead and roll them in all directions, taking care that no vacuum be left, and that there be no mixture of any foreign body. The whole work would be entirely spoiled by the addition of a hair, or a particle of sand. When the paste has been properly prepared, the porcelain, when exposed to heat in the furnace, retains its form without becoming soft, or entering into fusion, and becomes semitransparent, without exhibiting cracks or superficial fissures; but when there is any defect in the mixture or preparation, the porcelain cracks, and becomes warped, or melts in the porcelain furnace.

The paste being thus prepared, the next operation is to form the vessels for which it is designed. All kinds of plain ware are formed with the wheel. When a cup, porcelain for instance, has undergone this operation, the outside ware of the bottom is quite round. The workman first gives it the requisite height and diameter, and it comes from his hands almost the moment he has received it. Great dexterity and expedition are absolutely necessary, on account of the low price of labour in these manufactories. A workman, it is said, scarcely receives a farthing per board, each board containing no less than 26 pieces. The cup then passes to a second workman, by whom the base is formed; it is then delivered to a third, who applies it to the mould, and gives it the proper form. When it is taken off the mould, it must be turned carefully, and not pressed more to one side than the other; for without this necessary precaution it would become warped or disfigured. The business of the fourth workman is to polish it with the chisel, especially round the edges, and diminish the thickness, to give it the proper degree of transparency. Having at length passed through the different hands from whom it receives its form and various ornaments, it then comes to the last workman, who forms the bottom with a chisel. It is wonderful, it is said, to see with how much dexterity and expedition the workmen convey the vessels from one to another; and it is added, that a single piece of porcelain, before it is completely finished, must pass through the hands of no fewer than 70 different workmen. It is indeed, we may observe, to this minute division of labour that its low price is owing; and on the same circumstance the remarkable dexterity and expedition which have been noticed, depend.

In the execution of large works of porcelain, different parts are first formed individually; and when all the pieces are finished, and nearly dry, they are put together and cemented with a paste formed of the same substance, and softened with water. Some time after, the seams are polished with a knife on both sides of the vessel, so that when it is covered with a varnish, or glazed, they are so completely concealed, that the least trace of them is not perceptible. It is in this way that spouts, handles, rings, and other parts of a similar nature, are united. In this way particularly are fabricated those pieces which are formed upon moulds, or by the hand, such as embossed works, grotesque images, idols, figures of trees or animals, and busts. All these are formed of four or five pieces joined together, which are afterwards brought to perfection by means of instruments proper for carving, polishing, and finishing the different traces which the mould has left imperfect. Flowers and ornaments which are not in relief, are either engraved, or the impression is made by means of a stamp; but ornaments in relief are prepared separately, and added to the pieces of porcelain to which they are destined.

The piece of porcelain being prepared according to the operations now described, is next conveyed to the painter: and in this art it is observed that the Chinese workmen follow no certain rule, and seem to be unacquainted with any of the principles of perspective. Their knowledge is the effect of practice, guided often by a whimsical imagination. The labour of painting porcelain in the Chinese manufactories is also divided among Porcelain, among a great number of hands. The business of one man, for instance, is solely limited to tracing out the first coloured circle with which the brim of the vessel is adorned; another designs the flowers, and a third paints them. One delineates waters and mountains, while it is the province of another to draw and paint birds and other animals. Of the painting on Chinese porcelain, it has been observed, that the human figure is often most indifferently executed.

A peculiar kind of glaze or varnish, we are informed, is obtained from white flint. This glaze, it is said, has the singular property of making the pieces of porcelain to which it is applied exhibit the appearance of veins distributed in all directions. Vessels glazed with this material seem as if the surface were cracked, without the fragments being separated or displaced. The colour of this glaze is whitish gray; and when it is applied to porcelain having an azure blue ground, it communicates a beautifully variegated appearance. Vases of Chinese porcelain are sometimes fabricated in a different manner. They are ornamented with a kind of fret-work, which has something of the appearance of fine lace, in the middle of which is placed a cup proper for holding any liquid; which constitutes one body with the surrounding fret-work.

We are informed that the Chinese workmen formerly possessed the secret of fabricating a kind of porcelain of a more singular nature. On the sides of the vessel thus formed were painted the figures of fishes, insects, and other animals, which could not be seen unless the vessel was filled with water. It is said that this secret is in a great measure lost; but the following is given as part of the process of preparing this kind of porcelain. The vessel which is to be painted, for the purpose of producing this peculiar effect, must be extremely thin and delicate. When it is dry, the colour is laid on, not on the outside, however, as is usually the case, but on the inside of the vessel, and it is laid on pretty thick. The figures which are painted upon it are usually fishes, as being more characteristic of the element in which they live. When the colour is perfectly dry, it is coated over with a kind of glaze, composed of porcelain earth, so that the azure is thus inclosed between two layers of earthy matter; and when the glaze becomes dry, the workman pours some oil into the vessel, and putting it upon a mould, applies it to the lathé. Porcelain fabricated in this manner, having received its consistence and body within, it is the object of the workmen to make it as thin as possible on the outside, without penetrating to the colour. The external surface is then dipped into a mixture for glazing, and when it is dry it is baked in a common furnace. This kind of porcelain is known by the name of kia-tsing, signifying pressed azure. It is supposed that the Chinese do not at present possess the art of making porcelain of this description, which requires a great deal of dexterity and delicate management; and it is added, that they have imperfectly succeeded in the attempts which have been occasionally made to discover the secret of this curious process.

The next process in the manufacture of porcelain is baking; but before we describe the method of arranging and managing the furnaces employed for this purpose, we shall give a short account of their construction. The Chinese furnaces for baking porcelain are furnished with a long porch, for the purpose of conveying air, and in some measure as a substitute for bellows. This porch answers the same purpose as the arch of a glass-house; but the furnaces which, as the author from whom the account is taken observes, were formerly only six feet in height, and the same in length, are now constructed upon a much more extensive plan. They are 12 feet high, and nearly four broad; and the roof and sides are so thick, that the powerful heat which is applied internally does not penetrate to the outside, at least so much as to be inconvenient to bear it on the application of the hand. The dome or roof is in the form of an inverted funnel, having a large aperture at the top by which the smoke escapes. Beside the principal aperture, there are five others of smaller dimensions, which are covered with broken pots in such a manner that the workman can increase or diminish the heat as he finds it necessary. Through these apertures also he is able to see the progress of the baking of the porcelain, and can judge when it is completed. By uncovering the hole which is nearest the principal opening, he opens with a pair of pincers one of the cases containing the pieces of porcelain, and if he perceives a bright fire in the furnace, and all the pieces brought to a red heat, as well as the colours of the porcelain appearing with a full lustre, he concludes that the process is finished. He then diminishes the fire, and entirely shuts up the mouth of the furnace for some time. In the bottom of the furnace there is a deep hearth about two feet in breadth, over which a plank is laid, in order that the workman may enter to arrange the porcelain. When the fire is kindled on the hearth, the mouth of the furnace is immediately closed up, and an aperture is left only sufficient for the admission of faggots, about a foot in length, but very narrow. The furnace is first heated for a day and a night, after which two men keep continually throwing wood into it, and relieve each other by turns. One hundred and eighty loads are consumed for one baking. As the porcelain is burning hot, the workman employs for the purpose of taking it out, long scarfs or pieces of cloth, which are suspended from his neck.

Having thus given a concise account of the construction of the Chinese furnaces, we proceed now to baking porcelain before our readers the method of baking porcelain which is followed in that country. After the porcelain has received its proper form, its colours, and all the intended ornaments, it is transported from the factory to the furnace, which is sometimes situated at the other end of the village already mentioned. In a kind of portico, which is erected before it, may be seen vast numbers of boxes and cases made of earth, for the purpose of inclosing the porcelain. Each piece, however inconsiderable it may be, has its own case; and the Chinese workman, by means of this procedure, imitates nature, which, in order to bring the fruits of the earth to maturity, clothes them in a covering, to defend them from the excessive heat of the sun during the day, and from the severity of the cold during the night.

A layer of fine sand is put into the bottom of these boxes, which is covered over with the powder of kaolin, to prevent the sand from adhering too closely to the bottom of the vessel. The piece of porcelain is then placed upon this bed of sand, and pressed gently down, in order that the sand may take the form of the bottom of the vessel, which does not touch the sides of its case; the case has no cover. A second, prepared in the same manner, With regard to small pieces of porcelain, such as tea-cups, they are inclosed in common cases about four inches in height. Each piece is placed upon a saucer of earth about twice as thick as a crown-piece, and equal in breadth to its bottom. These small cases are also sprinkled over with the dust of the kaolin. When the cases are large, the porcelain is not placed in the middle, because it would be too far removed from the sides, and consequently from the action of the fire.

These piles of cases are put into the furnace, and placed upon a bed of coarse sand six inches thick; those by which the middle space is occupied are at least seven feet high. The two boxes which are at the bottom of each pile remain empty, because the fire acts too feebly upon them, and because they are partly covered by the sand. For the same reason, the case which is placed at the top of each pile is also allowed to remain empty. The piles containing the finest porcelain are placed in the middle part of the furnace; the coarsest are put at its farthest extremity; and those pieces which have the most body and strongest colouring are near its mouth.

These different piles are placed very closely in the furnace; they materially support each other by pieces of earth, which bind them at the top, bottom, and middle, but in such a manner, that a free passage is left for the flame to insinuate itself everywhere around them.

The Chinese divide their porcelain into several kinds or classes, distinguishing each according to the different degrees of beauty and fineness. The whole of the first or most perfect kind is reserved for the emperor; none of it, we are assured, ever comes into the hands of the public, unless, on account of blemishes or imperfections, it is unworthy of being presented to the sovereign. Many have doubted whether at any time the largest and finest porcelain of China has ever been brought to Europe. None of that kind, at least, is offered to sale at Canton. The Chinese, who are apt to undervalue the productions of other countries, entertain a favourable opinion of the Dresden porcelain, and hold in still higher estimation the porcelain which is produced in the French manufactories.

The following is a short account of the Chinese porcelain manufactures by Sir George Staunton. "From the river," says he, "were seen several excavations made in extracting from the sides of the adjoining hills, the petuntse useful in the manufacture of porcelain. This material is a species of fine granite, or compound of quartz, feldspar, and mica, in which the quartz seems to bear the largest proportion. It appears from several experiments, that it is the same as the grown stone of the Cornish miners. The micaceous part, in some of this granite from both countries, often contains some particles of iron, in which case it will not answer the potter's purpose. This material can be calcined and ground much finer by the improved mills of England, than by the very imperfect machinery of the Chinese, and at a cheaper rate than the prepared petuntse of their own country, notwithstanding the cheapness of labour there.

"The kaolin, or principal matter mixed with the petuntse, is the grown clay also of the Cornish miners. The wha-she of the Chinese is the English soap-rock; and the she-kan is asserted to be gypsum. It was related by a Chinese manufacturer in that article, that the asbestos, or incombustible fossil stone, entered also into the composition of porcelain. A village, or univalled town, called Kin-te-chin, was not very far distant from this part of the present traveller's route, in which 3000 furnaces for baking porcelain were said to be lighted at a time, and gave to the place at night the appearance of a town on fire. The genius or spirit of that element is indeed, with some propriety, the principal deity worshipped there. The manufacture of porcelain is said to be precarious, from the want of some precise method of ascertaining and regulating the heat within the furnaces, in consequence of which their whole contents are baked sometimes into one solid and useless mass. Mr Wedgwood's thermometer, founded on the quality observed by him, of clay contracting in proportion to the degree of fire to which it is exposed, might certainly be of use to a Chinese potter*."

2. Inquiries of Reaumur into the Nature of Porcelain.

The first scientific investigation which was made into the nature of porcelain, was undertaken by the celebrated Reaumur; and the result of his researches was communicated to the French Academy of Sciences in the years 1727 and 1729. It was not the external form or appearance, nor was it the decorations of painting and gilding, which are by no means essential to porcelain, that constituted the object of his inquiries. His examination was particularly directed to the peculiar texture and fabric of this substance, with the view of ascertaining the nature and proportions of its constituent parts. For this purpose, he broke to pieces some of the Japanese, the Saxon, and the French porcelains, and carefully noted the peculiarities and differences in their texture. The grain or texture of the Japanese porcelain appeared to possess a considerable degree of closeness and compactness, with a smooth and somewhat shining aspect. He found that the Saxon porcelain was still more compact, and that it was smooth, and shining like enamel, but had nothing of the granular texture. In his examination of the French porcelain, he observed that it had much of the shining appearance, and that its grain was not so close and fine as that of the oriental porcelain, having some resemblance to the grain or texture of sugar. Such were the observations which occurred to the French philosopher at the commencement of his inquiries into the nature of porcelains, and hence he justly concluded, that they were characterised by very marked differences.

Proceeding in his investigation, the same philosopher subjected different porcelains to the action of heat; and heat on the result of his experiments with this powerful agent proved, that they might be distinguished by still more decisive characters; for it appeared that the porcelain of the east suffered no change from the action of the greatest heat, whereas that of European manufacture underwent fusion at no very high temperature. This remarkable difference between the Chinese and European porcelains, suggested to Reaumur an ingenious thought, which at last led him to the discovery of the Porcelain, true nature of the composition of porcelain. Having observed that all porcelains have some resemblance to glass in some of their general properties, although they are less compact, he considered them as in the state of a semivitrified substance. An earthy substance, he observed, may be in a semivitrified state in two ways. It may, in the first place, be entirely composed of vitrifiable or fusible matters; and this being the case, when it is exposed to the action of fire, provided the heat be sufficiently strong and long continued, it will be melted or vitrified. But as this change is not effected instantly, particularly where a violent degree of heat is not applied; and as it passes through different degrees, the progress of which may be more easily observed, according as the heat is managed and regulated; it followed, that by stopping in proper time the application of the heat to porcelain prepared in this way, the ware may be obtained in an intermediate state between those of crude earths and completely vitrified substances, while, at the same time, it possesses the semitransparency and other distinguishing properties of porcelain. Porcelain of this nature, it is well known, being exposed to a stronger degree of heat, undergoes perfect fusion and complete vitrification. All the European porcelains which were subjected to experiment by Reaumur, were found to be of this fusible nature.

But on the other hand, porcelain may be composed of fusible or vitrifiable matter, mixed in certain proportions with another matter, which is absolutely infusible in the strongest heat to which it can be exposed in the furnace; and hence, if a mixture of this kind be subjected to a heat sufficient to melt entirely the vitrifiable part of its composition, this will enter into fusion; but being mixed with another matter which is infusible, and which consequently retains its consistency and opacity, the whole will form a compound, partly opaque, and partly transparent, or, in other words, a semitransparent mass; that is, a semivitrified substance, or porcelain, but possessing qualities totally distinct from those of the former. For as the fusible part of the latter has been brought to its utmost degree of fusibility during the process of baking, although the compound may be exposed a second time to a still stronger degree of heat, it will not approach nearer to complete vitrification, that is, it will retain all the qualities of perfect porcelain. Reaumur found that the porcelain of the east was distinguished by the properties now described; and hence he concluded, that its component parts were arranged on the principle above alluded to. This opinion was afterwards confirmed by the most incontrovertible facts, deduced from a train of the most satisfactory and well directed experiments.

The ingredients which enter into the composition of the Chinese porcelain, namely, the petuntse and kaolin, were the next object of Reaumur's inquiries. Having obtained quantities of each, he subjected them separately to a strong heat, and he found that the petuntse entered into fusion, without addition; but it appeared that the kaolin was absolutely infusible. He then mixed the two ingredients, formed them into cakes, and exposed them in a furnace to the proper degree of heat; so that by baking they were converted into porcelain exactly similar to that of the Chinese. From these experiments it appeared, that the petuntse of the Chinese was a vitrifiable substance, and that the kaolin was of a different nature, quite refractory, and totally infusible.

After this discovery Reaumur, it would seem, entertained hopes that he might find materials in France, capable of making porcelain, possessing the same valuable qualities as that of China; but whether his researches in the discovery of proper materials in his own country, particularly that which corresponds to the petuntse of the Chinese, or whether he was prevented by other avocations from prosecuting his inquiries, it does not appear. But in his second memoir upon porcelain, we find, that he afterwards attempted to compose an artificial petuntse, by mixing vitrifiable stones with such saline bodies as were capable of rendering them fusible, or even by substituting for this artificial preparation glass readily formed, with the addition of such matters as he supposed might be successfully employed in the place of kaolin; but it would appear that he did not at the time prosecute his inquiries, for the subject was not resumed till the year 1739, when he announced the discovery of a process for converting common glass to a peculiar kind of porcelain, which has been since known by the name of Reaumur's porcelain.

Although it must appear, from the detail now given, that Reaumur was directed in his researches by the true spirit of philosophical inquiry, he seems to have been misled in certain points. One of his errors was relative to the Saxon porcelain, which he confounded with the other fusible porcelains of European manufacture, unless it be supposed that the porcelain of Saxony was formerly composed of entirely fusible or vitrifiable matters, and that it was porcelain of this description which he examined; for it is now certain, that all the porcelain of that country is capable of resisting the most powerful heat, and is therefore equally infusible with that of China or Japan. The appearance of the internal texture of the Saxon porcelain may have led the philosopher to this erroneous conclusion; for when it is broken, the internal surface does not exhibit a granular texture, but is uniform, smooth, shining, and compact, having much resemblance to white enamel. This appearance, however, so far from proving that the porcelain of Saxony is a fused or vitrified substance, shews, that it is not entirely composed of fusible matters. The internal surface of the most fusible porcelains, it is well known to those who are acquainted with the subject, is also the least dense, and the least compact; for no vitreous matter can be internally smooth and dense, without having been in a state of complete fusion. But if the density and shining appearance of the porcelain of Saxony depended only on the effects of the fusion of a vitreous matter, how is it to be supposed, that vessels formed of that fusible matter should have sustained the necessary degree of heat for producing the density and shining appearance, without having entirely lost their shape?

This peculiar quality of the Saxon porcelain, it is inferred, must then depend on another cause. Like every other porcelain, especially that of China and Japan, it contains a fusible substance, which has been in a state of complete fusion during the process of baking. The density and the internal lustre depend chiefly on this fused matter; but it is also certain, that the Saxon porcelain contains a large proportion of a substance which is absolutely infusible, and from which it derives its beautiful white appearance, its firmness and solidity, during It is this infusible substance which is to be considered as the substitute for the kaolin of China, and which possesses the property of considerably contracting its dimensions, while it unites with the fusible material. According to the observation of Macquer, if it be subjected to the most decisive trial, namely, the action of a violent fire, which is capable of melting every porcelain composed only of fusible materials, it appears as the result of numerous experiments, that it remains infusible, unless it be exposed to a heat which is also capable of melting the best and most perfect porcelain of Japan. The Saxon porcelain, therefore, is not to be confounded with porcelain manufactured of vitreous and fusible materials; for it seems to be equally excellent as that of Japan, and in some of its properties perhaps superior, as will appear from an examination of the qualities which constitute the peculiar excellence of porcelain.

Reaumur seems also to have taken an erroneous view of the nature of the Chinese kaolin. According to his account, this matter is a fine talky powder, from the mixture of which with petuntse, the porcelain of the east is manufactured. It is not impossible, it has been observed, that a porcelain similar to the Chinese might be produced from a talky substance of this nature mixed with petuntse; but it is well known to those who are at all familiar with the manufacture of any porcelain, that no vessels can be formed, unless the paste of which they are made possess that degree of ductility and tenacity which renders them fit for being worked upon the lathe, or fashioned in the mould. But substances of a talky nature, to whatever degree of fineness they may be reduced, never acquire the requisite ductility and tenacity which clays of all earthy substances only possess. But as it appears that the Chinese porcelain has been turned upon the lathe, it is obvious that they must have been formed of a very tenacious paste; and hence it is concluded, that kaolin is not purely a talky matter, but mixed with clay, otherwise the petuntse and kaolin, according to the supposition of Reaumur, are not the only ingredients which enter into the composition of Chinese porcelain; but the addition of a certain proportion of some matter of a tenacious quality is absolutely requisite.

3. Peculiar Properties of Porcelain.

It may be worth while now to consider the properties which constitute the perfection of porcelain; and here it is necessary, carefully to discriminate between the qualities which are to be regarded as only contributing to the external decoration, and the intrinsic and essential properties in which the fabric and perfection of porcelain consist. Those who have been occupied in experiments on this subject, have not found it difficult to form compositions which are very white, beautifully semi-transparent, and covered with a shining glazing; but which are extremely deficient in the more essential properties, as it appears they cannot be subjected to the necessary operations for want of a proper degree of tenacity; are not sufficiently compact; are quite fusible, subject to break by the sudden application of heat or cold, and from the softness of the glazing, which cracks and becomes rough, are soon deprived of their lustre. On the other hand, it is by no means difficult to form compositions of pastes, which are very tenacious, and which are capable of being easily worked and well baked, and in the process of baking which acquire the requisite degree of hardness and density; which are infusible, and capable of resisting the effects of sudden changes of heat and cold, and, in short, which possess all the qualities of the most excellent porcelain, excepting its whiteness and beauty. Materials fit for the composition of such porcelains, it will appear, may be found abundantly in most countries; but the difficulty in the manufacture of this ware is to unite beauty and goodness in one composition. The materials fit for the manufacture of the finer and more perfect porcelains, seem to be sparing productions of nature; and therefore the best kind of porcelain, it is presumed, will always be regarded as a valuable and high-priced commodity.

It may be observed, that the potteries called stone-ware, possess all the essential qualities of the Japanese porcelain; for, excepting the whiteness, on which alone the semitransparency depends, if we compare the properties of Japanese porcelain with those of our stoneware, little difference is found to exist between them. Both seem to possess the same granular texture; both have the same sonorous quality, when struck with a hard body; both have the same density; they possess also the same hardness, by which they strike fire with steel; they can resist the effects of the heat of boiling liquors without breaking, and are equally infusible when subjected to violent heat. Hence it is inferred, that if the earth which enters into the composition of stoneware, were free from foreign colouring matters, which prevent the whiteness and semitransparency, and if the vessels were carefully formed and coloured with a fine glaze, they would not be less perfect than the porcelain of the east. Earths fit for the production of the more perfect kinds of porcelain, are supposed to be more rare in Europe than in Japan and China; and hence probably it has happened, that, from the want of these earths, the first manufacturers of the porcelain in Europe confined themselves to an external imitation, by employing only vitrifiable matters with fusible salts, and a small quantity of white earth, from which fusible and vitreous porcelains were composed. Such might not improperly be denominated false porcelains; but great improvements have taken place since the first introduction of the manufacture of porcelain into Europe. Genuine white porcelains have been long ago produced in Germany, and especially in Saxony. These porcelains are in no respect inferior to those of China or Japan. They are found even to be considerably superior in beauty and whiteness to the productions of the eastern manufactories of modern times; for in these qualities the porcelains of the latter have greatly degenerated. And in one of the most valuable qualities of porcelain, namely, the property of resisting the effects of sudden changes of heat and cold, the European porcelain exceeds that of China or Japan. The quality of porcelain, it is to be observed, is not to be judged of by a slight trial; for as numerous circumstances concur to render a piece of porcelain capable or incapable of resisting the effects of heat or cold, boiling water may be at the same time poured into two vessels, one of which is good porcelain, and the other of an opposite quality, it is not impossible that the former may break, and the latter may remain entire. The true method of discovering Porcelain. ing what is good porcelain, is to examine several pieces of it which are in daily use; and it has been found, that in many such pieces of porcelain of oriental manufacture, which have been long used, cracks are always seen in the direction of their height, which are never perceived in the more perfect porcelains of European manufacture.

It has long been a very general opinion, that the Japanese porcelain is the most perfect; it has indeed continued to be the object of admiration and emulation, and has been held up as a model for the European manufacturer; a model which has not yet been equalled, and which, according to the opinion of some, cannot be equalled. In deciding on this subject, the Saxon porcelain is considered as inferior to the Japanese, on account of its greater smoothness, lustre, and less granular aspect of its internal texture, qualities in which it ought really to be regarded as superior to the porcelain from Japan. This surface has a near resemblance to that of glass, and it is supposed that this similarity has suggested the opinion; and it would be well founded, if the density and lustre of the European porcelain depended on the fusible and vitreous property of the ingredients of which it is composed: but this not being the case, and the Saxon porcelain being equally fixed and infusible as that of Japan, its superior density must be admitted as a valuable property. For in the comparison of different porcelains which are equal in other properties, that which is most firm and compact certainly claims the superiority. Hence it is that the internal texture of the Japanese porcelain is held in greater estimation, because it possesses a greater degree of density, compactness and lustre, than the European porcelain, which is composed only of vitreous sand or frit. For a similar reason the superior density of the Saxon porcelain ought to obtain for it a preference to that which is imported from the east. It is supposed besides, that it would be no difficult matter to communicate to the Saxon porcelain the granular texture of the Japanese, by mixing with the paste a certain proportion of sand or siliceous earth. But in this point, in producing by these means a nearer resemblance to the Japanese porcelain, those who conducted and brought to perfection the Saxon manufactures, were not insensible that their porcelain would sink in its valuable properties.

4. Porcelain Manufactories in different parts of Europe.

Manufactories of porcelain have been long established in almost every country of Europe. Besides that of Saxony, which was the first established in Europe, porcelain is made to a considerable extent at Vienna, at Frankenthal, and in the neighbourhood of Berlin, and in other places of the German states. The German porcelains are similar to those of Saxony, and are composed of similar materials, although from differences in the proportions, or in the modes of managing the manufactories, considerable differences arise in the porcelains manufactured at different places. Italy also is celebrated for its porcelain manufactures, the chief of which, it is said, are carried on at Naples. When M. de la Condamine travelled into Italy, he visited a manufacture of porcelain established at Florence, by the marquis de la Ginor, who was then governor of Leghorn. The French traveller was particularly struck with the large size of some of the pieces of this porcelain. Statues, and even groups of figures half as large as nature, and modelled from some of the finest antiques, were formed of it. The furnaces, he observed, in which the porcelain was subjected to the process of baking, were constructed with a great deal of ingenuity, and were lined with bricks made of the same materials as those which entered into the composition of the porcelain itself; and hence they were able to resist the effects of high degrees of heat. The paste of the porcelain manufactured at Florence appeared to be extremely beautiful, and to possess all the qualities of the best oriental porcelain. The glazing employed in this manufactory seemed to be inferior in whiteness, a circumstance which is supposed to be owing to the desire of using those materials only which are found in the country.

In France a greater number of manufactories of porcelain has been established than in any other country; and it must be allowed that the French have had wonderful success in the improvement and perfection of this manufacture. Some time even before Reaumur communicated the result of his inquiries, porcelain was manufactured at St Cloud, and in the suburb of St Antoine at Paris. This porcelain indeed was of the vitreous or fusible kind, but at the same time possessed no considerable degree of beauty. Since the period to which we allude, extensive manufactories of porcelain have been established at Villeroy, Chantilly, and Orleans, and at those places the manufacture has been brought to a great degree of perfection. But the productions of the celebrated porcelain manufactory at Sevres, on account of the pure shining white, the fine glazing and coloured grounds, the splendour and magnificence of the gilding, and the elegance and taste displayed in the shape and figures, are universally allowed to surpass every thing of the kind which has yet appeared.

In speaking of the French porcelain, we may notice the result of some researches which were made on this subject by Guettard, and of which an account appeared in the Memoirs of the Academy of Sciences for the year 1765. In the neighbourhood of Alençon, M. Guettard discovered a whitish argillaceous earth, in which mica considerably predominated. This earth he employed as a substitute for kaolin. The substance which he used in place of the petuntse, he obtained from a hard stone, which is described as a quartzose gritt stone, very abundant in that country, and with which the streets of Alençon are paved. With these materials Guettard instituted a series of experiments on porcelain, previous to the year 1751, and was associated in his inquiries with the duke of Orleans. For many years the count de Lauraguais, a member of the Academy of Sciences, was keenly engaged in prosecuting experiments to discover the true nature of porcelain, and the means by which the manufacture might be improved and perfected. To obtain the object of his researches, which was to produce porcelain in that its essential qualities might be equal to that of eastern countries, he spared no trouble or expense; and it would appear that he was not unsuccessful in his labours; for in the year 1766, when he exhibited some species of porcelain from his manufactory to the members of the Academy of Sciences, the persons who were appointed by that learned body to examine their properties, delivered it as their opinion, that of all the porcelain made in France, that The manufacture of porcelain has been brought to a great degree of perfection in England. In many of the essential qualities, and particularly in the beauty and richness of the paintings, as well as in the elegance of the forms, the English porcelain is little inferior to that of any other country. Manufactories of this ware have been established in different parts of England. This manufacture was first established at Derby about the year 1750, by Mr Duesbury, who is said to have been a very ingenious artist. Since his death the manufactories received very considerable improvement, and chiefly in the judicious methods pursued in the preparation of the paste, and increasing the beauty of the ornaments. The ware itself is said not to equal in fineness that which is manufactured in Saxony and France, although it is greatly superior in respect of decoration and workmanship. The paintings in general are rich, and executed with taste, and the gilding and burnishing are extremely beautiful. The body of the semi-vitreous kind, which is formed of a fine white clay, in combination with various proportions of different fusible matters, has obtained the name of porcelain. The best kind is wholly infusible, and is glazed with a vitreous substance which has not a single particle of lead in its composition.

The most famous manufactory of stone-ware, as well as of other kinds of pottery, is at Burslem in Staffordshire. This can be traced with certainty at least two centuries back; but of its first introduction no tradition remains. In 1686, as we learn from Dr Plot's Natural History of Staffordshire published in that year, only the coarse yellow, red, black, and mottled wares, were made in this country; and the only materials employed for them appear to have been the different coloured clays which are found in the neighbourhood, and which form some of the measures or strata of the coal-mines. These clays made the body of the ware, and the glaze was produced by powdered lead-ore, sprinkled on the pieces before firing, with the addition of a little manganese for some particular colours. The quantity of goods manufactured was at that time so inconsiderable, that the chief sale of them, the Doctor says, was "to poor cratesmen, who carried them on their backs all over the country."

About the year 1690, two ingenious artisans from Germany, of the name of Eller, settled near Burslem, and carried on a small work for a little time. They brought into this country the method of glazing stone-ware, by casting salt into the kiln while it is hot, and some other improvements of less importance; but finding they could not keep their secrets to themselves, they left the place rather in disgust. From this time various kinds of stone-ware, glazed by the fumes of salt in the manner above mentioned, were added to the wares before made. The white kind, which afterwards became, and for many succeeding years continued, the staple branch of pottery, is said to have owed its origin to the following accident. A potter, Mr Astbury, travelling to London, perceived something amiss with one of his horse's eyes; an hostler at Dunstable said he could soon cure him, and for that purpose put a common black Porcelain-flint stone into the fire. The potter observing it, when taken out, to be of a fine white, immediately conceived the idea of improving his ware by the addition of this material to the whitest clay he could procure: accordingly he sent home a quantity of the flint stones of that country, where they are plentiful among the chalk, and by mixing them with tobacco-pipe clay, produced a white stone-ware much superior to any that had been seen before.

Some of the other potters soon discovered the source of this superiority, and did not fail to follow his example. For a long time they pounded the flint stones in private rooms by manual labour in mortars; but many of the poor workmen suffered severely from the dust of the flint getting into their lungs, and producing dreadful coughs, consumptions, and other pulmonary disorders. These disasters, and the increased demand for the flint powder, induced them to try to grind it by mills of various constructions; and this method being found both effectual and safe, has continued in practice ever since. With these improvements, in the beginning of the present century, various articles were produced for tea and coffee equipages. Soon after attempts were made to furnish the dinner table also; and before the middle of the century, utensils for the table were manufactured in quantity as well for exportation as home consumption.

But the salt glaze, the only one then in use for this purpose, is in its own nature so imperfect, and the potters, from an injudicious competition among themselves for cheapness, rather than excellence, had been so inattentive to elegance of form and neatness of workmanship, that this ware was rejected from the tables of persons of rank; and about the year 1760, a white ware, much more beautiful and better glazed than ours, began to be imported in considerable quantities from France.

The inundation of a foreign manufacture, so much improved superior to any of our own, must have had very bad effects upon the potteries of this kingdom, if a new one, still more to the public taste, had not appeared soon after. In the year 1763, Mr Josiah Wedgwood, who had already introduced several improvements into this art, invented a species of earthen ware for the table quite new in its appearance, covered with a rich and brilliant glaze, bearing sudden alternations of heat and cold, manufactured with ease and expedition, and consequently cheap, and having every requisite for the purpose intended. To this new manufacture the queen was pleased to give her name and patronage, commanding Queen's it to be called Queen's ware, and honouring the inventor by appointing him her majesty's potter.

The common clay of the country is used for the ordinary sorts; the finer kinds are made of clay from Devonshire and Dorsetshire, chiefly from Biddeford; but the flints from the Thames are all brought rough by sea, either to Liverpool or Hull, and so by Burton. The convenience of plenty of coals, which abound in that part of the country, is supposed, and with good reason, to be the chief cause of the manufacture having been established here.

The flints are first ground in mills, and the clay prepared by breaking, washing, and sifting, and then they are mixed in the requisite proportions. The flints are bought Porcelain, bought first by the people about the country, and by them burnt and ground, and sold to the manufacturers by the peck.

The mixture is then laid in large quantities in kilns to evaporate the moisture; but this is a nice work, as it must not be too dry: next it is beaten with large wooden hammers, and then is in order for throwing, and is moulded into the forms in which it is to remain; this is the most difficult work in the whole manufacture. A boy turns a perpendicular wheel, which by means of thongs turns a small horizontal one, just before the thrower, with such velocity, that it twirls round the lump of clay he lays on it into any form he directs it with his fingers.

There are 300 houses, which are calculated to employ upon an average twenty hands each, or 6000 in the whole; but of all the variety of people that work in what may be called the preparation for the employment of the immediate manufacturers, the total number cannot be much short of 10,000, and it is increasing every day. Large quantities are exported to Germany, Ireland, Holland, Russia, Spain, the East Indies, and much to America; some of the finest sorts to France.

5. Different Processes in the Manufacture of Porcelain.

The basis of those porcelains which are known by the name of vitreous or fusible, and sometimes false porcelain, is denominated by the workmen a fritt. This is a mixture of sand or powdered flints, with a saline substance, capable of bringing it to a state of fusion when the mixture is exposed to a sufficient degree of heat. The fritt is then mixed with a proper proportion of clay or argillaceous earth, so that it may have such a degree of tenacity as to make it capable of being worked upon the wheel. The whole mixture is, after being well ground in a mill, to be made into a paste, which is to be formed, either upon the wheel or in moulds, into pieces of such forms or figures as may be required. Each of the pieces, when it is sufficiently dried, is put into a case made of earthen ware, and placed in the furnace, that it may be subjected to the process of baking. These cases are known among the English potters by the name of saggers or saggers, and they are generally formed of a coarser kind of clay, but this clay must possess the property of resisting the action of heat necessary for the baking of porcelain, without being fused. The porcelain contained in the cases is thus protected from the smoke of the burning fuel: the whiteness of the porcelain depends greatly on the purity of the clay of which it is made, so that being of a more compact texture, the smoke is more effectually excluded. These cases are arranged in the furnace or kiln in piles, one upon the other, to the very top of the furnace.

The furnaces are chambers or cavities of various forms and sizes, and they are so constructed that the fire-place is situated on the outside, opposite to one or more openings, which have a communication with the furnace internally. The flame of the fuel is drawn within the furnace, the air of which being rarefied, determines a strong current of air to the inside, as is the case in other furnaces. A small fire is first made, that the furnaces may be gradually heated, and it is to be increased more and more, till the process of baking is completed; that is, till the porcelain shall have acquired a proper degree of hardness and transparency. To ascertain this point, a good deal of attention is necessary; and this is done by taking out of the furnace from time to time, and examining, small pieces of porcelain placed for that purpose in the cases, which have lateral openings to render them accessible. When it appears from the examination of these pieces, that the porcelain is sufficiently baked, the fire is no longer to be supplied with fuel; the furnace is allowed to cool gradually, and the porcelain is afterwards taken out. In this state the porcelain has the appearance of white marble, having nothing of that shining surface which it acquires by covering it with a vitreous composition known by the name of glazing, a process which is afterwards to be described; but in the mean time we shall speak of the infusible porcelains.

The materials which enter into the composition of the infusible porcelains, and such as approach to the nature of stone ware, are first to be ground in a mill, and the earths or clays being well washed, are next to be carefully mixed and formed into a paste. The pieces at first receive a rude form from the wheel or lathe of the potter, according to their nature and magnitude. As the wheel and lathe are the principal machines employed in the manufacture of porcelain or pottery, we shall here give a short description of their construction. The potter's wheel, which is used for larger works, consists principally in the nut, which is a beam or axis, whose foot or pivot plays perpendicularly on a free-stone sole or bottom. From the four corners of this beam, which does not exceed two feet in height, arise four iron bars, wheel called the spokes of the wheel; which forming diagonal lines with the beam, descend, and are fastened at bottom to the edges of a strong wooden circle, four feet in diameter, perfectly like the felloes of a coach-wheel, except that it has neither axis nor radii, and is only joined to the beam, which serves it as an axis, by the iron bars. The top of the nut is flat, of a circular figure, and a foot in diameter; and on this is laid the clay which is to be turned and fashioned. The wheel thus disposed is encompassed with four sides of four different pieces of wood fastened on a wooden frame; the hind-piece, which is that on which the workman sits, is made a little inclining towards the wheel; on the fore-piece is placed the prepared earth; on the side pieces he rests his feet, and these are made inclining to give him more or less room. Having prepared the earth, the potter lays a round piece of it on the circular head of the nut, and sitting down turns the wheel with his feet till it has got the proper velocity; then, wetting his hands with water, he presses his fist or his finger-ends into the middle of the lump, and thus forms the cavity of the vessel continuing to widen it from the middle; and thus turning the inside into form with one hand, while he proportions the outside with the other, the wheel constantly turning all the while, and he wetting his hands from time to time. When the vessel is too thick, he uses a flat piece of iron, somewhat sharp on the edge, to pare off what is redundant; and when it is finished, it is taken off from the circular head by a wire passed under the vessel.

The potter's lathe is also a kind of wheel, but more simple and slight than the former: its three chief members are an iron beam or axis three feet and a half high, and two feet and a half diameter, placed horizontally. Porcelain, tally at the top of the beam, and serving to form the vessel upon; and another large wooden wheel, all of a piece, three inches thick, and two or three feet broad, fastened to the same beam at the bottom, and parallel to the horizon. The beam or axis turns by a pivot at the bottom of an iron stand. The workman gives the motion to the lathe with his feet, by pushing the great wheel alternately with each foot, still giving it a greater or lesser degree of motion as his work requires. He works with the lathe with the same instruments, and after the same manner, as with the wheel. The mouldings are formed by holding a piece of wood or iron cut in the form of the moulding to the vessel, while the wheel is turning round; but the feet and handles are made by themselves and set on with the hand; and if there be any sculpture in the work, it is usually done in wooden moulds, and stuck on piece by piece on the outside of the vessel. The lathe is employed for smaller works in porcelain.

After the first application of the pieces of porcelain to the wheel or lathe, they are allowed to become nearly dry; and to give the requisite form, or a greater degree of accuracy and perfection, they are again subjected to the same operation. They are afterwards introduced into the furnace, not, however, for the purpose of baking them completely, but only to apply a sufficient heat, to give them that firmness and solidity that they may undergo the various necessary manipulations without being disfigured or broken. In this state they are ready for the process of glazing. As the pieces of porcelain, after being subjected to this moderate degree of heat, are very dry, they readily imbibe water, and it is this property of absorbing water, which greatly assists in the application of the glazing; and having received this covering, the pieces of porcelain are again put into the furnace, to complete the process of baking. The heat is gradually raised, and at last brought to that degree that all the objects within the furnace shall be white, and the cases shall be scarcely distinguished from the flame. To ascertain when the porcelain is sufficiently baked, small pieces are taken out in the manner already described, after which the fire is withdrawn, and the furnace allowed to cool gradually. If the process of baking have succeeded properly, the pieces of porcelain will, after this operation, be sonorous, compact, having a moderate degree of lustre, and covered externally with a fine coat of glaze. If this porcelain is destined to receive the ornaments of painting and gilding, these operations are performed in the manner to be afterwards described.

After the porcelain has been subjected to the process of baking, and before it is glazed, it is said to be in the state of biscuit, in which it possesses various degrees of beauty and perfection, according to the nature and proportions of the materials employed. For particular purposes, the porcelain is sometimes allowed to remain in this state, and particularly when it is employed in smaller and finer pieces of sculpture, where the fineness of the workmanship and the sharpness of the figures are wished to be preserved, as it is well known that these will be greatly injured by being covered with a coat of Porcelain glazing. The celebrated manufactory of Sevres in France has been long distinguished for figures or small statues, and even for larger works, as ornamental vases, &c., which are left in the state of biscuit. The English manufactories, and particularly that of Mr Wedgwood, are probably not inferior in the delicacy and accuracy of execution of ornamental productions of this kind.

The next operation in the manufacture of porcelain Method of is the process of glazing. This process consists in covering the porcelain with a thin coat of vitreous or fusible matter, which adds greatly to its beauty, by its lustre or shining appearance. In preparing and applying the materials fit for glazing porcelain, it has been found that the same kind of glass will not admit of general application; for it appears that a glass which forms a fine glazing for one kind of porcelain, will not answer the same purpose when applied to another. In the former it may have all the necessary requisites, but in the latter it may crack in many places, may have no lustre, and may contain bubbles or be apt to scale off. The first thing then is to prepare a glass which shall be suited to the nature of the porcelain for which it is intended. The glazing must be appropriated to each kind of porcelain, that is, to the ingredients which enter into its composition, or to the degree of hardness or density of the ware. The materials of which the glazing is composed are prepared by previously fusing together all the substances of which they consist, and thus forming a vitreous mass (A). This mass of vitrified matter is to be finely ground in a mill, and the vitreous powder thus obtained is to be mixed with a sufficient quantity of water, so that the liquor shall have the consistence of cream of milk. The pieces of porcelain are to be covered with a thin coating of this matter, which is done by immersing them hastily in the liquid, and as they greedily imbibe the water, there remains on the surface a uniform covering of the glazing materials. This covering, which, it is necessary to observe, should be very thin, in a short time becomes so dry, that it does not adhere to the fingers when the pieces are handled. When they are sufficiently dry, they are replaced in the furnace in the same manner as in preparing the biscuit, and the heat is continued till the glazing be completely fused; but the degree of heat necessary for that purpose is far inferior to that which is requisite in baking the paste. The pieces of porcelain which are intended to remain white, are now finished, but those which are to be ornamented with painting and gilding must go through various other operations, of which the following is a general account.

The colours which are employed in painting porcelain are similar to those which are applied in the painting of enamel. They are all composed of metallic oxides or calces, combined with a very fusible, vitreous matter. The different colours are obtained from different metals. The oxides of iron afford a red colour; gold precipitated by means of tin, furnishes a purple and violet colour; copper precipitated from its solution in acids by means of an alkali, gives a fine green; cobalt, or

(A) The proportion of the materials employed for common white pottery-ware are 60 parts of litharge, 10 of clay, and 20 of ground flint. Porcelain, or when combined with vitreous matter, zaffar, as it is called, yields a fine blue. Earthy matters which are slightly ferruginous, produce a yellow colour, and brown and black colours are obtained from iron in different states, and from manganese. A coloured glazing has been recommended by O'Reilly*, which may be applied to coarse articles of earthen ware. It is obtained from the residuum after the distillation of oxymuriatic acid. The manganese contained in this residuum is said to communicate a blackish appearance like that of bronze, which, says the author, is far from being disagreeable to the eye. This glazing he employed several times by way of trial, first fusing it with sand in a potter's furnace, throwing it into cold water to facilitate its division, and grinding it in a mill, that it may be more completely diffused in water. This glazing is attended with the advantage of being free from those dangerous qualities so common in all preparations made from the oxides of lead. Whatever colouring matters are employed, they are finely ground with gum water, or with some essential oil, in which state they are fit to be employed for the painting of porcelain with figures of flowers, or any other design with which it is intended to be adorned.

In gilding porcelain, the oxide or calx of gold (B) is employed, and it is applied nearly in the same manner as the coloured enamels. The gold, which is in the state of very minute division, is mixed with gum water and borax, and in this state is applied to the clean surface of the porcelain with a fine camel's hair pencil. The painted and gilded porcelains are then exposed to such a degree of heat in the furnace as is capable of fusing the vitreous matter with which the metallic colours are mixed. The gold is fixed by means of the borax undergoing the process of vitrification, and thus strongly adhering to the porcelain. Most of the metallic colouring matters exhibit all their beauty when the porcelain is taken from the furnace; but to bring out the lustre and beauty of the gold, those parts of the porcelain which have been gilt are afterwards subjected to the operation of burnishing.

The use of platina in porcelain painting has been recommended by Klaproth; and experiments have been made on the subject by that celebrated chemist, with the view of ascertaining its effects for this purpose. The following is the conclusion of his observations.

"The process which I employ in the application of platina to painting on porcelain is simple and easy: it is as follows:—I dissolve crude platina in aqua regia, and precipitate it by a saturated solution of sal ammoniac in water. The red crystalline precipitate thence produced is dried, and being reduced to a very fine powder, is slowly brought to a red heat in a glass retort. As the volatile neutral salt combined with the platina in this precipitate, becomes sublimated, the metallic part remains behind in the form of a gray soft powder. This powder is then subjected to the same process as gold; that is to say, it is mixed with a small quantity of the same flux as that used for gold, and being ground with oil of spike, is applied with a brush on the porcelain; after which it is burnt-in under the muffle of an enameller's furnace, and then polished with a burnishing tool.

"The colour of platina, burnt into porcelain in this manner is a silver white, inclining a little to a steel gray. If the platina be mixed in different portions with gold, different shades of colour may be obtained; the gradations of which may be numbered, from the white colour of unmixed platina to the yellow colour of gold. Platina is capable of receiving a considerable addition of gold before the transition from the white colour to yellow is perceptible. Thus, for example, in a mixture of four parts of gold and one of platina, no signs of the gold were to be observed, and the white colour could scarcely be distinguished from that of unmixed platina: it was only when eight parts of gold to one of platina were employed that the gold colour assumed the superiority.

"I tried in the like manner, different mixtures of platina and silver; but the colour produced was dull, and did not seem proper for painting on porcelain.

"Besides this method of burning-in platina in substance on porcelain, it may be employed also in its dissolved state; in which case it gives a different result both in its colour and splendour. The solution of it in aqua regia is evaporated, and the thickened residuum is then applied several times in succession to the porcelain. The metallic matter thus penetrates into the substance of the porcelain itself, and forms a metallic mirror of the colour and splendour of polished steel."

The same substance has been applied as a glazing to porcelain in some of the English manufactories, but however valuable and important the application of platina to this purpose may be, the scarcity of that metal, and its consequent high price, must always prevent it from coming into very general use.

We have already noticed the establishment of the manufacture of porcelain in Derby. The following is a short detail of the method of conducting that manufacture. After the paste has been properly prepared, by grinding and other necessary operations, it is delivered to the workmen, by whose dexterity the shapeless mass is converted into various beautiful forms. Vessels of a round form are usually made by a man called a thrower, by whom they are worked on a circular block moving horizontally on a vertical spindle. They are next carried to the lathe; and being fixed to the end of a horizontal spindle, they are reduced to the proper form and thickness.

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(B) A powder of gold is prepared for this purpose in other two different ways. By one of those methods a quantity of gold leaf is put into a glass or earthen mortar, with a little honey or thick gum water, and ground till the gold is reduced to very minute particles; a little warm water is then added, which will wash out the honey or gum, and leave the gold behind: but the process by which the finest ground gold is obtained, is by gradually heating a gold amalgam in an open earthen vessel, and continuing the heat till the mercury is entirely evaporated, stirring the mixture with a glass rod, or tobacco pipe, that the particles of gold may be prevented from adhering as the mercury flies off. The gold remaining after the evaporation of the mercury is then ground with a little water in a Wedgwood-ware mortar, and after being dried is fit for use. Porcelain thickness. They are afterwards finished, and handled by other persons, if that should be necessary, and are then introduced into a stove, where the moisture is entirely evaporated, and they become fit for the process of baking. Vessels of an oval figure, such as tea-pots, tureens, &c., acquire their form by being pressed with the hand into moulds of plaster or gypsum. The pieces of porcelain being thus prepared, are put into the sagars or cases, which are of various sizes and dimensions, and these are set in the kiln or furnace, one upon the other, till they are filled up nearly to the top, in the manner already described. The furnace being full, the ware is baked, and after this first baking, the porcelain is in the state of biscuit.

The next process is the glazing, which, according to the description already given, is performed by dipping the pieces of porcelain in glaze of the consistence of cream. They are then conveyed to the glaze furnace, where they are again baked, but in a degree of heat inferior to that necessary for the first baking.

If the pieces of porcelain are to receive the additional ornaments of painting and gilding, they are next delivered to another set of workmen. The colouring matters, as already noticed, are extracted from mineral bodies, and after proper preparation, they are applied to the ware by the painters, in the form of landscapes or figures, according to the requisite pattern. After this process the ware is again conveyed to the furnace, and the colours are vitrified, to give them the proper degree of fixation and lustre. After every coat or layer of colour, a fresh burning is necessary. In the common kind of porcelain, once or twice is found sufficient for the ornaments it requires; but in the finer decorations, the colours must be laid on several times, and as often subjected to the action of heat, before the full effect can be produced. This completes the process for those articles of porcelain in which glazing and painting only are required.

But when the pieces of porcelain are to be farther decorated with gilding, they are pencilled with a mixture of oil and gold, dissolved or thrown down by quicksilver with the aid of heat, and are again introduced to the furnace. Here the gold returns to its solid state, but comes out with a dull surface; and to recover its lustre and usual brilliancy, it is furnished with bloodstones, and other polishing substances. Much care and attention are necessary in the latter part of the process; for if the gold be not sufficiently burnt, it will be apt to separate in thin flakes, and if it have been exposed to too great a heat, it is not susceptible of a fine polish. In this manufactory, when pieces of porcelain are to be finished in the highest style, they are frequently returned to the enamel furnace, where the colours are fluxed six or seven different times; and having gone through the processes now described, the porcelain is fit for the market.

White ware, or biscuit figures, are made at this manufactory, which are supposed to be equal in beauty and delicacy to any European productions of a similar kind. In this kind of porcelain, the lathe is of no use, for the figures are cast in moulds of plaster or gypsum. The materials of which they are composed being properly prepared, and previously reduced to a liquid of the appearance and consistence of thick cream, are poured into the moulds, which from the absorbent property of the plaster, imbibe the water contained in the mixture; so that the paste soon becomes sufficiently hard to part freely from the mould. The different parts of figures, as the head, arms, legs, &c., are cast in separate moulds, and after being dried and repaired, they are joined by a paste of the same kind, but of a thinner consistence. The porcelain pieces thus formed are then conveyed to the furnace, and after being subjected for a proper length of time, to a regular and continued heat, they come out extremely white and delicate.

Porcelain manufactories have been long established at Tournay in Flanders; one of these manufactories furnishes all Flanders with blue and white porcelain. At this manufactory they have a particular process in forming cups and other vessels, which is somewhat similar to that now described. They are neither turned on the lathe, nor is the clay compressed in a mould; but after being diluted in water, and when the liquid has acquired a proper consistency, the workmen pour it into moulds, two or three hundred of which are arranged together. When they have filled them all, they return to the first in the row. The liquid part is drawn off by a gentle inclination; the surplus adheres to the side of the vessel, and thus forms the piece which it is intended to make. The piece is detached from the mould by means of a slight stroke, and after being sufficiently dried, is conveyed to the furnace, to undergo the process of baking.

In the manufacture of utensils for chemical purposes, where they are to be subjected to the effects of powerful chemical agents, greater attention is necessary. Vessels of this description should be infusible at any degree of heat; possess a sufficient compactness of texture, to retain saline and other fluxes in fusion, without undergoing any change; and should bear sudden changes of temperature, particularly sudden heating, without cracking, or in any degree giving way. It has been found impracticable to have the three requisites now mentioned united in the same ware, so that it becomes necessary to select the kind of ware according to the purpose for which they are intended. For bearing high degrees of heat, Hessian crucibles are found to answer best; they are composed of a very refractory clay, mixed with sand, of which the finest part is separated by a sieve, and thrown away. These vessels are made by mixing the clay with a smaller proportion of water than usual, so that a stiffer mass is obtained, and the vessel brought to the requisite shape by ramming the clay strongly into an iron mould. In this way they are very compact, and for a considerable time retain saline fluxes. Ordinary crucibles, it is found, are rendered more retentive by lining them on the inside, before they are quite dry, with a thin coating of pure clay, without the addition of any other mixture. But the most refractory material known is a mixture of unburnt with burnt clay. Vessels made of this material are found capable of resisting the effects of saline fluxes longer than any other, and hence this material is employed in making large crucibles for glasshouses.

One of the most valuable qualities of porcelain ware, is to bear sudden changes of heat and cold; but in this quality some of the most perfect kinds of ware in other respects are extremely deficient, and can scarcely be subjected, without danger of cracking, to the draught of a wind furnace, even when the heat is slowly and gradually applied. This happens to the celebrated porcel- Porcelain, lain fire ware invented by an enlightened and philosophical manufacturer, the late Mr Wedgwood. This effect of cracking, on sudden changes of temperature, seems to depend on the hardness and closeness of texture; and the closeness of texture is found to be in proportion to the minute division of the materials before baking. The clay and flint of Wedgwood's ware are brought to a most impalpable powder before mixture, so that the texture is uncommonly hard and close. It may be worth while to mention, that Wedgwood's porcelain resists the effects of sudden heat and cold much better, by being covered with a thin coating of Windsor loam, or of a fire-lute composed of coarse sand and clay, and tow or horse-dung. When crucibles are intended merely for the fusion of metals, they are greatly improved by a mixture of black lead. This substance being involved in the clay, is protected from the access of air, and is then incombustible. It has no affinity for the earths at any temperature, and being absolutely infusible, it enables the clay to bear, without melting, the greatest degree of heat. The mixture of this substance, as a material for crucibles, has another advantage, that no part of the melted metal is detained in the crucible, as is the case in the common rough ware. It also bears sudden heating and cooling better than any other.

6. General Principles of the Manufacture of Porcelain.

Convinced that every accurate and scientific investigation into the nature and processes of any important art, will always be deemed of some value to the philosophic observer, or the enlightened manufacturer, we shall introduce the following observations on the principles of the manufacture of porcelain.

Observations by Vauquelin.

According to this celebrated chemist, four things may occasion difference in the qualities of earthen-ware: 1st, The nature or composition of the matter; 2d, The mode of preparation; 3d, The dimensions given to the vessels; 4th, The baking to which they are subjected. By composition of the matter, the author understands the nature and proportions of the elements of which it is formed. These elements, in the greater part of earthen ware, either valuable or common, are silex, argil, lime, and sometimes a little oxide of iron. Hence it is evident that it is not so much by the diversity of the elements that good earthen-ware differs from bad, as by the proportion in which they are united. Silex or quartz makes always two-thirds at least of earthen-ware; argil or pure clay, from a fifth to a third; lime, from 5 to 20 parts in the hundred; and iron from 0 to 12 or 15 parts in the hundred. Silex gives hardness, infusibility, and unalterability; argil makes the paste pliable, and renders it fit to be kneaded, moulded, and turned at pleasure. It possesses at the same time the property of being partially fused by the heat which unites its parts with those of the silex; but it must not be too abundant, as it would render the earthen-ware too fusible and too brittle to be used over the fire.

Hitherto it has not been proved by experience that lime is necessary in the composition of pottery: and if traces of it are constantly found in that substance, it is because it is always mixed with the other earths, from which the washings and other manipulations have not been able to separate it. When this earth, however, does not exceed five or six parts in a hundred, it appears that it is not hurtful to the quality of the pottery; but if more abundant, it renders it too fusible.

The oxide of iron, besides the inconvenience of communicating a red or brown colour, according to the degree of baking, to the vessels in which it forms a part, has the property of rendering them fusible, and even in a greater degree than lime.

As some kinds of pottery are destined to melt very penetrating substances, such as salts, metallic oxides, glass, &c., they require a fine kind of paste, which is obtained only by reducing the earths employed to very minute particles. Others destined for melting metals, and substances not very penetrating, and which must be able to support, without breaking, a sudden transition from great heat to great cold, require for their fabrication a mixture of calcined argil with raw argil. By these means you obtain pottery, the coarse paste of which resembles breche, or small-grained pudding-stone, and which can endure sudden changes of temperature.

The baking of pottery is also an object of great importance. The heat must be capable of expelling humidity, and agglutinating the parts which enter into the composition of the paste, but not strong enough to produce fusion; which, if too far advanced, gives to pottery a homogeneity that renders it brittle. The same effect takes place in regard to the fine pottery, because the very minute division given to the earths reduces them nearly to the same state as if this matter had been fused. This is the reason why porcelain strongly baked is more or less brittle, and cannot easily endure alternations of temperature. Hence coarse porcelain, in the composition of which a certain quantity of calcined argil is employed, porcelain retorts, crucibles, tubes, and common pottery, the paste of which is coarse, are much less brittle than dishes and saucers formed of the same substance, ground with more labour.

The general and respective dimensions of the different parts of vessels of earthen-ware have also considerable influence on their capability to stand the fire.

In some cases the glazing or covering, especially when too thick, and of a nature different from the body of the pottery, also renders them liable to break. Thus, in making some kinds of pottery, it is always essential, 1st, To follow the best proportion in the principles; 2d, To give to the particles of the paste, by grinding, a minuteness suited to the purpose for which it is intended, and to all the parts the same dimensions as far as possible; 3d, To carry the baking to the highest degree that the matter can bear without being fused; 4th, To apply the glazing in thin layers, the fusibility of which ought to approach as near as possible to that of the matter, in order that it may be more intimately united.

C. Vauquelin, being persuaded that the quality of good pottery depends chiefly on using proper proportions of the earthy matters, though it might be of importance, to those engaged in this branch of manufacture, to make known the analysis of different natural clays employed for this purpose, and of pottery produced by some of them, in order that, when a new earth is Porcelain is discovered, it may be known by a simple analysis whether it will be proper for the same object, and to what kind of pottery already known it bears the greatest resemblance.

| Hessian Argil of Porcelain Wedgwood's Crucibles Dreux Cap-nes Pyrometers | |-----------------------------|----------------|----------------|----------------|----------------| | Silex | 69 | 43.5 | 61 | 64.2 | | Argil | 21.5 | 33.2 | 28 | 25 | | Lime | 1 | 3.5 | 6 | 6 | | Oxide of iron | 8 | 1 | 0.5 | 0.2 | | Water | 18 | | | 6.2 |

Raw kaolin 100 parts.—Silex 74, argil 16.5, lime 2, water 7. A hundred parts of this earth gave eight of alum, after being treated with the sulphuric acid.

Washed kaolin 100 parts.—Silex 55, argil 27, lime 2, iron 0.5, water 14. This kaolin, treated with the sulphuric acid, gave about 45 or 50 per cent. of alum.

Petuntze.—Silex 74, argil 14.5, lime 5.5, loss 6. A hundred parts of this substance, treated with the sulphuric acid, gave seven or eight parts of alum. But this quantity does not equal the loss sustained.

Porcelain of retorts.—Silex 64, argil 28.8, lime 4.55, iron 0.59, loss 2.77. Treated with the sulphuric acid, this porcelain gave no alum.

There is a kind of earthen vessels, called Alcarrezes, used in Spain for cooling the water intended to be drunk. These vessels consist of 60 parts of calcareous earth, mixed with alumina and a little oxide of iron, and 364 of siliceous earth, also mixed with alumina and the same oxide. The quantity of iron may be estimated at almost one hundredth part of the whole. This earth is first kneaded into a tough paste, being for that purpose previously diluted with water; formed into a cake of about six inches in thickness, and left in that state till it begins to crack. It is then kneaded with the feet, the workman gradually adding to it a quantity of sea-salt, in the proportion of seven pounds to a hundred and fifty; after which it is applied to the lathe, and baked in any kind of furnace used by potters. The alcarrezes, however, are only about half as much baked as the better kinds of common earthen ware; and being exceedingly porous, water oozes through them on all sides. Hence the air, which comes in contact with it, by making it evaporate, carries off the caloric contained in the water in the vessel, which is thus rendered remarkably cool.

Observations of Brongniart.

The author of the following observations is superintendent of the celebrated porcelain manufactory at Sevres in France. The extensive views he has taken of the subject, and the general principles which he has advanced, will, we doubt not, be favourably received by the intelligent manufacturer, and meet with attention and consideration adequate to their importance and utility.

"The art of employing metallic oxides for colouring by fusion different vitreous matters, is of very great antiquity: every body knows that the ancients manufactured coloured glass and enamel, and that this art was practised in particular by the Egyptians, the first people who in this manner imitated precious stones. The practice of this art in modern times has been carried to a high degree of perfection: but the theory has been neglected; it is almost the only one of the chemical arts in which no attempt has yet been made to apply the new principles of that science.

"It is well known that all vitrifiable colours have for their basis metallic oxides; but all the metallic oxides are not proper for this purpose: besides, as they are not vitrifiable by themselves, they can scarcely ever be employed alone.

"Highly volatile oxides, and those which adhere little to the great quantity of oxygen they contain, either oxides cannot be employed in any manner, as the oxide of mercury and that of arsenic, or are employed only as agents. The colour they present cannot be depended on, since they must lose it in the slightest heat by losing a part of their oxygen: such are the puce-coloured and red oxides of lead, the yellow oxides of gold, &c. Oxides in which the proportions of oxygen are susceptible of varying with too much facility are rarely employed: the oxide of iron, though black, is never employed for that colour, and the green oxide of copper is, under many circumstances, very uncertain. I have said that oxides alone are not susceptible of fusion: however, as they are destined to be applied to thin strata on vitrifiable substances, they may be attached to them by a violent heat. But, except the oxides of lead and bismuth, they would give only dull colours. The violent heat, often necessary to fix them, would change or totally destroy the colours. A flux then is added to all metallic oxides.

"This flux is glass, lead, and silex; glass of borax, or a mixture of both. Its general effect is, to give splendour to the colours after their fusion; to fix them on the article which is painted, by promoting more or less the softening of its surface; to envelope the metallic oxides, and to preserve their colour by sheltering them from the contact of the air: in a word, to facilitate the fusion of the colour at a low temperature not capable of destroying it.

"I shall speak here only of the application of metal. Nature of lic colours to vitreous bodies or to vitreous surfaces. These bodies may be divided into three classes, very distinct by the nature of the substances which compose them, the effects produced on them by the colours, and the changes they experience. These classes are: 1st, Enamel, soft porcelain, and all crusts, enamels, or glass, that contain lead in a notable quantity. 2d, Hard porcelain, or porcelain which has a crust of feldspar. 3d, Glass in the composition of which no lead enters, such as common window-glass.

"I shall here examine in succession the principles of the composition of these colours, and the general phenomena they exhibit on these three kinds of bodies.

"It is well known that enamel is glass rendered opake by the oxide of tin, and exceedingly fusible by the oxide of lead. It is the oxide of lead, in particular, contained in it, that gives it properties very different from those of the other excipients of metallic colours. Thus all glass and glazing that contain lead will participate in the properties of enamel; and what we shall say of one may be applied to the rest with very trifling differences.

Such are the white and transparent glazing of stone ware, and the glazing of porcelain called soft glazing.

"Enamel..." Enamel or soft porcelain colours require less flux than others, because the glass on which they are applied becomes sufficiently soft to be penetrated by them. This flux may be either glass of lead and pure silex, called rocallie, or the same glass mixed with borax. Montamy asserts that glass of lead ought to be banished from among the enamel fluxes; and he employs only borax. He then dilutes his colours in a volatile oil. On the other hand, the painters of the manufactory of Sevres employ only colours without borax, because they dilute them in gum; and borax does not dilute well in that substance. I have found that both methods are equally good; and it is certain that Montamy was wrong to exclude fluxes of lead, since they are daily employed without any inconvenience, and as they even render the application of colours easier.

I have said that in the baking of these colours, the crust, softened by the fire, suffers itself to be easily penetrated by them. This is the first cause of the change which they experience. By mixing with the crust they become weaker, and the first heat changes a figure which appeared to be finished into a very light sketch.

The two principal causes of the changes which colours on enamel and soft porcelain are susceptible of experiencing do not depend in any manner on the composition of these colours, but on the nature of the glass to which they are applied. It follows from what has been said, that painting on soft porcelain has need of being several times retouched, and of several heats, in order that it may be carried to the necessary degree of strength. These paintings have always a certain faintness; but they are constantly more brilliant, and they never are attended with the inconvenience of detaching themselves in scales.

Hard porcelain, according to the division which I have established, is the second sort of excipient of metallic colours. This porcelain, as is well known, has for its base a very white clay called kaolin, mixed with a silicious and calcareous flux, and for its covering feldspar fused without an atom of lead.

This porcelain, which is that of Saxony, is much newer at Sevres than the soft porcelain. The colours applied to it are of two kinds: the first, destined to represent different objects, are baked in a heat very inferior to that necessary for baking porcelain. They are exceedingly numerous and varied. The others, destined to be fused in the same heat as that which bakes porcelain, lay themselves flat, and are much less numerous. The colours of painting are made nearly like those destined for soft porcelain; they only contain more flux. Their flux is composed of glass of lead and borax. When porcelain is exposed to heat in order to bake the colours, the covering of feldspar dilates itself and opens its pores, but does not become soft; as the colours do not penetrate it, they experience none of those changes which they undergo on soft porcelain. It must however be said that they lose a little of their intensity by acquiring that transparency which is given to them by fusion.

One of the greatest inconveniences of these colours, especially in the manufactory of Sevres, is the facility with which they scale off when exposed several times in the fire.

To remedy this defect without altering the quality of the paste, I was of opinion that the crust only ought to be softened by introducing into it more silicious or calcareous flux, according to the nature of the feldspar. This method has succeeded; and for about a year past the colours might be exposed two or three times to the fire without scaling, if not overcharged with flux, and if not laid on too thick.

The third sort of excipient of vitrifiable metallic colours is glass without lead.

The application of these colours to glass constitutes painting on glass; an art very much practised some centuries ago, and which was supposed to be lost because out of fashion; but it has too direct a dependence on painting in enamel and porcelain to be entirely lost.

The matters and fluxes which enter into the composition of the colours employed on glass are in general the same as those applied to porcelain. Neither of them differ but in their proportions; but there are a great number of enamel or porcelain colours which cannot be applied to glass, where they are deprived of the white ground which serves to give them relief.

Of Colours in particular.

After collecting the general phenomena exhibited by each class of vitrifiable colours, considered in regard to the body on which they are applied, I must make known the most interesting particular phenomena exhibited by each principal kind of colours employed on soft porcelain and glass in a porcelain furnace.

Of Reds, Purples, and Violets, made from Gold.

Carmine red is obtained by the purple precipitate of cassius; it is mixed with about six parts of its flux; and this mixture is employed directly, without being fused. It is then of a dirty violet, but by baking it acquires a beautiful red carmine colour: it is, however, exceedingly delicate; a little too much heat and carbonaceous vapours easily spoil it. On this account it is more beautiful when baked with charcoal than with wood.

This colour and the purple, which is very little different, as well as all the shades obtained from it, by mixing it with other colours, really change on all porcelain and in every hand. But it is the only one that changes on hard porcelain. Its place may be supplied by a rose-colour from iron which does not change; so that by suppressing the carmine made with gold, and substituting for it the rose oxide of iron here alluded to, you may exhibit a palette composed of colours none of which change in a remarkable manner. This rose-coloured oxide of iron has been long known; but it was not employed on enamel, because on that substance it changes too much. As the painters on enamel, however, have become the painters on porcelain, they have preserved their ancient method.

It might be believed that, by first reducing to a vitreous matter the colour called carmine already mixed with its flux, it might be made to assume its last tint. But the heat necessary to fuse this vitreous mass destroys the red colour, as I have experienced. Besides, it is remarked that, to obtain this colour very beautiful, it must be exposed to the fire as few times as possible.

The carmine for soft porcelain is made with fulminating gold slowly decomposed, and muriate of silver; no tin enters into it; which proves that the combination of the oxide of this metal with that of gold is not necessary to the existence of the purple colour. "POR [199] POR

Violet is made also with purple oxide of gold. A greater quantity of lead in the flux is what gives it this colour, which is almost the same crude or baked.

These three colours totally disappear when exposed to a great porcelain heat.

Carmine and purple have given us in glass tints only of a dirty violet. The violet, on the other hand, produces on glass a very beautiful effect, but it is liable to turn blue. I have not yet been able to discover the cause of this singular change, which I saw for the first time a few days ago.

Red, Rose, and Brown Colours, extracted from Iron.

These colours are made from red oxide of iron prepared with nitric acid. These oxides are further calcined by keeping them exposed to the action of heat. If heated too much, they pass to brown.

Their flux is composed of borax, sand, and minium, in small quantity.

These oxides give rose and red colours capable of supplying the place of the same colours made with oxide of gold. When properly employed on hard porcelain, they do not change at all. I have caused roses to be painted with these colours, and found no difference between the baked flower and that not baked, except what might be expected to result from the brilliancy given to colours by fusion.

These colours may be employed indiscriminately, either previously fused or not fused.

In a great heat they in part disappear, or produce a dull brick red ground, which is not agreeable.

The composition of them is the same both for soft porcelain and for glass. They do not change on the latter; but on soft porcelain they disappear almost entirely on the first exposure to heat, and to make anything remain they must be employed very deep.

This singular effect must be ascribed to the presence of lead in the crust or glazing. I assured myself of this by a very simple experiment. I placed this colour on window glass, and having exposed it to a strong baking, it did not change.

I covered several parts of it with minium; and again exposing it to the fire, the colour was totally removed in the places where the red oxide of lead had been applied.

By performing this operation on a larger scale in close vessels, a large quantity of oxygen gas was disengaged.

It appears to me that this observation clearly proves the action of oxidated lead on glass as a destroyer of colour: it is seen that it does not act, as was believed, by burning the combustible bodies, which might tarnish the glass, but by dissolving, discolouring, or volatilizing with it the oxide of iron, which might alter its transparency.

Yellows.

Yellows are colours which require a great deal of care in the fabrication on account of the lead which they contain, and which, approaching sometimes to the metallic state, produces on them black spots.

The yellows for hard and soft porcelain are the same: they are composed of the oxide of lead, white oxide of antimony, and sand.

Oxide of tin is sometimes mixed with them; and when it is required to have them livelier, and nearer Porcelain, the colour du souci, red oxide of iron is added, the too great redness of which is dissipated in the previous fusion to which they are exposed by the action of the lead contained in this yellow. These colours, when once made, never change: they disappear, however, almost entirely when exposed to a porcelain heat.

These yellows cannot be applied to glass: they are too opake and dirty. That employed by the old painters on glass has, on the contrary, a beautiful transparency, is exceedingly brilliant, and of a colour which approaches near to that of gold. The processes which they gave clearly showed that silver formed part of their composition; but, when exactly followed, nothing satisfactory was obtained. C. Miraud, whom I have already had occasion to mention, has found means to make as beautiful paintings on glass as the ancients, by employing muriate of silver, oxide of zinc, white argil, and yellow oxide of iron. These colours are applied on glass merely pounded, and without a flux. The oxide of iron brings the yellow to that colour which it ought to have after baking, and contributes with the argil and oxide of zinc to decompose the muriate of silver without deoxidating the silver. After the baking, there remains a dust which has not penetrated into the glass, and which is easily removed.

This yellow, when employed thicker, gives darker shades, and produces a russet.

Blues.

It is well known that these are obtained from the oxide of cobalt. All chemists are acquainted with the preparation of them. Those of Sevres, which are justly esteemed for their beauty, are indebted for it only to the care employed in manufacturing them, and to the quality of the porcelain, which appears more proper for receiving them in proportion to the degree of heat which it can bear.

I remarked respecting the oxide of cobalt a fact which is perhaps not known to chemists: it is volatile in a violent heat: it is to this property we must ascribe the blueish tint always assumed by white in the neighbourhood of the blue. I have placed expressly on purpose, in the same case, a white piece close to a blue one, and found that the side of the white piece next the blue became evidently blueish.

The blue of hard porcelain, destined for what is called the ground for a great heat (les fonds au grand feu) is fused with feldspar; that of soft porcelain has for its flux silex, potash, and lead: it is not volatilized like the preceding; but the heat it experiences is very inferior to that of hard porcelain.

These colours, when previously fused, do not change at all in the application.

Blues on glass exhibit the same phenomena as those on soft porcelain.

Greens.

The greens employed in painting are made with green oxide of copper, or sometimes with a mixture of yellow or blue. They must be previously fused with their flux, otherwise they will become black; but after this first fusion they no longer change.

They cannot stand a strong heat, as it would make them disappear entirely. Green grounds for a strong heat. Porcelain heat are composed with the oxides of cobalt and nickel, but a brownish green only is obtained.

"Blueish greens, called celestial blues, which were formerly colours very much in vogue, can be applied only upon soft porcelain; on hard porcelain they constantly become scaly, because potash enters into their composition.

"These greens cannot be applied on glass: they give a dirty colour. To obtain a green on glass, it is necessary to put yellow on one side, and blue, more or less pale, on the other. This colour may be made also by a mixture of blue with yellow oxide of iron. I hope to obtain from oxide of chrome a direct green colour. The trials I have made give me reason to hope for success. Pure chromate of lead, which I applied to porcelain in a strong heat, gave me a pretty beautiful green of great intensity and very fixed.

Bistres and Russets.

"These are obtained by mixtures in different proportions of manganese, brown oxide of copper, and oxide of iron from ombre earth. They are also previously fused with their flux, so that they do not change in any manner on soft porcelain, as lead has not the same action on oxide of manganese as on that of iron, as I assured myself by an experiment similar to that already mentioned.

"This colour fades very speedily on glass.

"Russet grounds in a great heat, known under the name of tortoise-shell grounds, are made in the same manner. Their flux is feldspar: no titanium enters into their composition, though said so in all printed works. Titanium was not known at the manufactory of Sevres when I arrived there. I treated this singular metal in various ways, and never obtained but grounds of a pale dirty yellow, and very variable in its tone.

Blacks.

"Blacks are the colours most difficult to be obtained very beautiful. No metallic oxide gives alone a beautiful black. Manganese is that which approaches nearest to it. Iron gives an opake, dull, cloudy black, which changes very easily to red: the colour-makers, therefore, to obtain a black which they could not hope for from the best theorist, have united several metallic oxides which separately do not give black, and have obtained a very beautiful colour, which, however, is liable to become scaly and dull.

"These oxides are those of manganese, the brown oxides of copper, and a little of the oxide of cobalt. The gray is obtained by suppressing the copper, and increasing the dose of the flux.

"The manufactory of Sevres is the only one which has hitherto produced beautiful blacks in a strong heat. This is owing rather to the quality of its paste than to any peculiar processes, since it does not conceal them. It is by darkening the blue by the oxides of manganese and iron that they are able in that manufactory to obtain very brilliant blacks.

"Having here made known the principles of the fabrication of each principal colour, it may be readily conceived that by mixing these colours together all the shades possible may be obtained. It is evident also that care in the preparation, choice in the raw materials, and a just proportion of doses, must produce in the results differences very sensible to an eye accustomed to painting. A mere knowledge of the composition of the colours does not give the talent of executing them well.

"In recapitulating the facts above mentioned, to present them under another general point of view, it is seen,

"1st, That among colours generally employed on hard porcelain one only is susceptible of changing, viz. vive carmine, and the tints into which it enters: that its laws no place may be supplied by the reds of iron, and that no pitiable colour then changes.

"I have presented to the Institute a head not baked, executed according to this method: and the painting of two roses, that of the one baked, and that of the other not baked. It has been seen that there was no difference between them.

"2d, That among the colours for soft porcelain and enamel, several change in a considerable degree. These are principally the reds of gold and iron, the yellows, the greens, the browns. They have not been replaced by others, because this kind of painting has been almost abandoned.

"3d, That several of the colours on glass change also by acquiring complete transparency. These in particular are the yellows and greens.

"4th, That it is neither by calcinating the colours in a higher degree, nor previously fusing them, as supposed by some, that they are prevented from changing, since these means really alter the changing colours, and produce no effect on the rest. The change which several colours experience on soft porcelain and on glass does not then depend on the nature of their composition, but rather on that of the body on which they are applied.

"Consequently, by suppressing from the colours of hard porcelain the carmine of gold, which is not indispensably necessary, we shall have a series of colours which do not change."

As it must be of no small importance to the chemical manufacturer to be acquainted with the results of experiments on the effects of heat, when applied to different proportions of the materials employed in making china porcelain, or other analogous ware, we shall insert the following tables, exhibiting those results. The first table contains the results of the numerous experiments of Achard and Morveau on the vitrification of earths with saline bodies. The mixture of the earths and salts was made in a clay crucible, and, in the experiments of Morveau, the crucible was exposed for two hours to a heat from $22^\circ$ to $26^\circ$ of Wedgwood's pyrometer; but in those of Achard, the crucible was kept for three hours in the heat of a strong wind furnace, in which the temperature was probably higher than the former.

The second table presents a view of the effects of the vitrification of earths by means of metallic oxides. The mixtures were exposed in earthen crucibles to the heat of a porcelain furnace during the whole time required to bake porcelain ware.

In the third table are exhibited the curious results of the effects of vitrifying materials on the crucibles in which the vitrification takes place. It is to be observed, that the effects of the same materials, and in the same proportions, are very different, in different vessels; and without attending to this circumstance, very erroneous conclusions will be drawn in estimating the action of vitrifiable substances on each other. This diversity of the effects of the same materials in different crucibles, Table I. Shewing the Results of the Vitrification of Earths with Saline Bodies.

| Mixture | Results | |--------------------------|-------------------------------------------------------------------------| | A. Silex | 1. A yellow glass, not hard enough to give sparks with steel. | | Carbonate of potash | | | M. Silex | 2. A colourless transparent glass, but deliquescent from the excess of alkali. | | Carbonate of soda (dry) | | | A. Silex | 3. A yellow glass, not scintillant. | | Carbonate of potash | | | A. Silex | 4. A vitriform mass, yellow, hard, and scintillant. | | Carbonate of potash | | | M. Silex | 1. A beautiful transparent glass, not at all soluble in water. | | Borax (calcined) | | | A. Silex | 2. A white porcellaneous mass, scarcely scintillant. | | Boracic acid | | | A. Silex | 3. A hard transparent glass—scintillant. | | Boracic acid | | | A. Silex | 4. A white opake melted porous mass—scintillant. | | Boracic acid | | | A. Silex | 5. A transparent glass—hard and scintillant. | | Calcined borax | | | A. Silex | 6. A mass resembling agate—but perfectly fused and scintillant. | | Calcined borax | | | A. Silex | 7. A green scintillant glass. | | Sulphate of soda | | | A. Silex | 8. A soft green transparent glass. | | Nitre | | | A. Silex | 9. Scoria—the crucible entirely destroyed. | | Common salt | | | M. Silex | 10. A white opake, puffy, vitreous mass, deliquescent, and reddening litmus. | | Phosphate of soda and ammonia | | | M. Lime | 11. A white spongy opake mass, crumbling between the fingers. | | Carbonate of soda | | | A. Chalk | 12. Partly, fused—the rest pulverulent—the crucible strongly corroded. | | Carbonate of potash | | | A. Chalk | 13. A well-fused, polished, black scintillant glass. | | Carbonate of potash | | | A. Chalk | 14. Remained a white powder. | | Carbonate of potash | | | M. Lime | 15. A fine transparent yellowish glass—the crucible strongly corroded. | | Borax | | | A. Chalk | 16. A well-fused, black, scintillant, polished mass. | | Borax | | | A. Chalk | 17. A yellow scintillant glass. | | Borax | | | A. Chalk | 18. A yellow glass—run through the crucible. | | Boracic acid | |

Vol. XVII. Part I. A. Chalk - 3. A hard yellow scintillant glass. Sulphate of soda - 1.

A. Chalk - 1. A hard brown scoria—the crucible totally destroyed. Sulphate of soda - 4.

A. Chalk - 1. A hard yellow glass. Nitrate of soda - 1.

A. Chalk - 1. A yellow scintillant glass—the crucible entirely destroyed. Common salt - 1.

M. Lime - 1. A white opake crumbly mass. Phosphate of soda and ammonia 2.

M. Alumine - 1. A gray opake ill-fused fritt, not cohering to the crucible and deliquescent. Carbonate of soda - 2.

A. Alumine - 4. Remained unmelted and uncohering. Carbonate of soda and potash in all proportions from 1 to 12.

A. Alumine - 1. Partially melted, but soft and friable. Carbonate of potash - 4.

M. Alumine - 1. A fine transparent clear green glass. Borax - 2.

A. Alumine - 1. Remained pulverulent. Borax - 1.

A. Alumine - 1. Part unfused and remaining pulverulent, the rest partially melted. Boracic acid - 4.

M. Alumine - 1. A green fritt easily friable. Phosphate of soda and ammonia 2.

M. Magnesia - 1. A white opake uncohering mass. Carbonate of soda - 2.

M. Magnesia - 1. A semi-transparent somewhat milky glass of a gelatinous appearance, but very hard and brilliant on the surface. Borax - 2.

M. Magnesia - 1. A white mass a little agglutinated but not adhering to the crucible. Phosphate of soda and ammonia 2.

M. Barytes (pure) - 1. A very hard semi-vitrified mass, of a clear green. Carbonate of soda - 2.

M. Barytes - 1. A beautiful transparent glass with a faint yellow tinge, strongly adhering to the crucible. Borax - 2.

M. Barytes - 1. A remarkably fine transparent glass. Phosphate of soda and ammonia 2.

**Table II. Containing the Results of the Vitrification of Earths by Metallic Oxides.**

| Mixture | Result | Colour and Texture | |------------------|-------------------------|----------------------------------------| | Silex | 1. Scoria | Black and polished—hard, giving sparks with steel. | | Oxide of iron | 1. Not fused | Black and friable. | | Silex | 2. Scoria run through the crucible | Black and hard—scintillant. | | Oxide of iron | 1. Not fused | | | Silex | 1. Not fused | | | Oxide of copper | 1. Not fused | | | Silex | 4. Not fused | | | Oxide of copper | 1. Not fused | | | Mixture | Result | Colour and Texture | |-------------------------|---------------------------------------------|----------------------------------------| | Silex | 1. A solid mass but not fused | White and hard | | Oxide of lead | 1. Fused, porous, and semi-vitrified | Yellow—not scintillant | | Silex | 2. Perfect glass | Green—not scintillant | | Oxide of tin | 1. A coherent mass | Gray—easily friable | | Silex | 2. Vitrified | Greenish yellow—not scintillant | | Oxide of bismuth | 1. Remained in powder | | | Silex | 2. Perfect glass | Deep yellow—not scintillant | | Oxide of antimony | 1. Glass | Colourless—scintillant | | Silex | 2. Not melted | Gray and friable | | Oxide of zinc | 1. Remained in powder | | | Silex | 2. Melted only where touching the crucible | White—hard | | Oxide of zinc | 3. Perfectly fused | Gray—scintillant | | Lime (carbonated) | 1. A melted porous mass | Black—scintillant | | Oxide of iron | 1. Melted, polished in the fracture, part of the copper reduced | Red—scintillant | | Lime | 2. Melted, but porous | The same | | Oxide of copper | 4. Part only melted, the rest pulverulent | Gray | | Lime | 1. Glass | Greenish yellow—scintillant | | Oxide of lead | 2. Glass run through the crucible | Yellow—scintillant | | Lime | 3. Remained in powder | | | Oxide of tin | 1. Semi-vitrified | Yellow—scintillant | | Lime | 2. Glass | Greenish yellow—scintillant | | Oxide of tin | 3. Melted only where touching the crucible | Gray | | Lime | 4. Glass | Greenish yellow—scintillant | | Oxide of bismuth | 1. Vitriform mass | Green | | Lime | 2. Glass penetrating the crucible | Yellow—scintillant | Porcelain.

Mixture. Result. Colour and Texture.

Lime Oxide of antimony 2. Remained in powder. Lime Oxide of antimony 1. Glass penetrating the crucible Deep yellow—scintillant. Lime Oxide of antimony 4. A semi-transparent polished mass Gray yellow—scintillant. Lime Oxide of zinc 1. Glass Deep yellow—scintillant. Alumine Oxide of iron 1. Only partially fused. Alumine Oxide of iron 3. A melted porous mass Black—scintillant. Alumine Oxide of copper 1. Only partially fused. Alumine Oxide of copper 4. The same. Alumine Oxide of lead 1. Remained in powder. Alumine Oxide of lead 3. The same. Alumine Oxide of lead 4. Glass Deep yellow—scintillant. Alumine Oxide of tin 2. A melted porous mass, not polished in the fracture Gray—scintillant. Alumine Oxide of bismuth 2. Partially fused. Alumine Oxide of antimony 4. Only partially fused. Alumine Oxide of antimony 1. Remained in powder. Magnesia Oxide of iron 3. Half fused, but not adhering. Magnesia Oxide of copper 3. A porous half-fused mass Gray—scintillant. Magnesia Oxide of lead 3. Not fused. Magnesia Oxide of lead 4. A porous melted mass, part of the oxide reduced. Magnesia Oxide of antimony 1. Beginning to fuse Gray—scintillant.

Table III. Shewing the Action of the Vitrifying matters on the Crucibles that contain them.

Substances used. Result in the Clay crucible (A). Result in the Chalk crucible (B). Result in the Charcoal crucible (C).

Common flint. Opake and milk-white, but without fusion. Opake and white, but with beginning fusion where in contact with the crucible. As in A.

Marble. Run into a green glass. No change. No change. Gypsum. Run into a radiated green glass. No change. No change. | Substances used. | Result in the Clay crucible (A.) | Result in the Chalk crucible (B.) | Result in the Charcoal crucible (C.) | |------------------|---------------------------------|----------------------------------|-------------------------------------| | Flour spar. | Melted and ran through the crucible. | Melted down with the crucible to a tough slag. | Scarcely altered, except slight fusion at the edges. | | Porcelain clay. | Compact, white and no signs of fusion. | Run into a hard blue clear glass. | As in A. | | Ditto, another kind. | A compact mass partially melted. | A perfectly black glass. | As in A. | | Reddle. | A black glass covered with a crust of reduced iron. | A semitransparent apple-green glass. | A brown scoria containing grains of iron. | | Jasper. | No fusion, but the colour changed to brown. | Completely fused in the parts touching the crucible. | As in A. | | Muscovy talc. | A black glass with interspersed grains of iron. | The whole crucible was penetrated with a scoria so as not to fall to powder on exposure to air. | As in A. | | Spanish chalk. | Only hardened. | A gray semitransparent glass | A green glass with many grains of iron. | | Basalt. | Brown-yellow glass with a crust of iron. | A green scoria, also with a crust of iron. | |

For an account of some valuable experiments of a similar nature, which were made by the celebrated Klapproth, in crucibles of clay and charcoal, in which the differences of the results are very striking, the reader is referred to his Analyt. Essays, or to Aikin's Dictionary of Chemistry and Mineralogy.

**Porcelain-Shell**, a species of Cypræa. See Cypræa, Conchology Index.

**Porch**, in Architecture, a kind of vestibule supported by columns; much used at the entrance of the ancient temples, halls, churches, &c.

A porch, in the ancient architecture, was a vestibule, or a disposition of insulated columns usually crowned with a pediment, forming a covert place before the principal door of a temple or court of justice. Such is that before the door of St Paul's, Covent-Garden, the work of Inigo Jones. When a porch had four columns in front, it was called a tetrasyle; when six, hexastyle; when eight, octostyle, &c.

**Porch**, in Greek ἀνάπηρον, a public portico in Athens, adorned with the pictures of Polygnotus and other eminent painters. It was in this portico that Zeno the philosopher taught; and hence his followers were called Stoics. See Stoics and Zeno.

**Porcupine**, See Hystrix, Mammalia Index.

**Porcupine-Man**, the name by which one Edward Lambert, who had a distempered skin, went in London. We have the following account of him in the Philosophical Transactions for 1755, by Mr Henry Baker, F. R. S. "He is now (says he) 40 years of age, and it is 24 years since he was first shown to the society. The skin of this man, except on his head and face, the palms of his hands, and the soles of his feet, is covered with excrescences that resemble an innumerable company of warts, of a brown colour and cylindrical figure; all rising to an equal height, which is about an inch, and growing as close as possible to each other at their basis; but so stiff and elastic as to make a rustling noise when the hand is drawn over them. These excrescences are annually shed, and renewed in some of the autumn or winter months. The new ones, which are of a paler colour, gradually rise up from beneath as the old ones fall off; and at this time it has been found necessary for him to lose a little blood, to prevent a slight sickness which he had been used to suffer before this precaution was taken. He has had the small-pox, and he has been twice salivated, in hopes to get rid of this disagreeable covering; but though just when the pustules of the smallpox had scaled off, and immediately after his salivations, his skin appeared white and smooth, yet the excrescences soon returned by a gradual increase, and his skin became as it was before. His health, during his whole life has been remarkably good; but there is one particular of his case more extraordinary than all the rest; this man has had six children, and all of them had the same rugged covering as himself, which came on like his own about nine weeks after the birth. Of these children only one is now living, a pretty boy, who was shown with his father. It appears therefore, as Mr Baker remarks, that a race of people might be propagated by this man, as different from other men as an African is from an Englishman; and that if this should have happened in any former age, and the accidental original have been forgotten, there would be the same objections against their being derived from the same common stock with others: it must therefore be admitted possible, that the differences now subsisting between one part of mankind and another may have been produced by some such accidental cause, long after the earth had been peopled by one common progenitor."

**Pore**, in Anatomy, a little interstice or space between the parts of the skin, serving for perspiration.

**Porella**, a genus of plants belonging to the Cryptogamia class. See Botany Index.

**Porentru**, a town of Switzerland, in Elsgaw, and capital of the territory of the bishop of Basle, which is distinguished only by its castle and cathedral. The bishop was formerly a prince of the empire. It is seated on the river Halle, near Mount Jura, 22 miles south of Basle. E. Long. 7. 2. N. Lat. 47. 34.

**Porism**, in Geometry, is a name given by the ancient geometers to two classes of mathematical propositions. Euclid gives this name to propositions which are involved in others which he is professedly investigating, and which, although not his principal object, are yet obtained along with it, as is expressed by their name porismata, "acquisitions." Such propositions are now called called corollaries. But he gives the same name, by way of eminence, to a particular class of propositions which he collected in the course of his researches, and selected from among many others on account of their great subserviency to the business of geometrical investigation in general. These propositions were so named by him, either from the way in which he discovered them, while he was investigating something else, by which means they might be considered as gains or acquisitions, or from their utility in acquiring further knowledge as steps in the investigation. In this sense they are porismata; for πορίσμα signifies both to investigate and to acquire by investigation. These propositions formed a collection, which was familiarly known to the ancient geometers by the name of Euclid's porisms; and Pappus of Alexandria says, that it was a most ingenious collection of many things conducive to the analysis or solution of the most difficult problems, and which afforded great delight to those who were able to understand and to investigate them.

Unfortunately for mathematical science, this valuable collection is now lost, and it still remains a doubtful question in what manner the ancients conducted their researches upon this curious subject. We have, however, reason to believe that their method was excellent both in principle and extent; for their analysis led them to many profound discoveries, and was restricted by the severest logic. The only account we have of this class of geometrical propositions, is in a fragment of Pappus, in which he attempts a general description of them as a set of mathematical propositions, distinguishable in kind from all others; but of this description nothing remains, except a criticism on a definition of them given by some geometers, and with which he finds fault, as defining them only by an accidental circumstance, "A Porism is that which is deficient in hypothesis from a local theorem."

Pappus then proceeds to give an account of Euclid's porisms; but the enunciations are so extremely defective, at the same time that they refer to a figure now lost, that Dr Halley confesses the fragment in question to be beyond his comprehension.

The high encomiums given by Pappus to these propositions have excited the curiosity of the greatest geometers of modern times, who have attempted to discover their nature and manner of investigation. M. Fermat, a French mathematician of the 17th century, attaching himself to the definition which Pappus criticises, published an introduction (for this is its modest title) to this subject, which many others tried to elucidate in vain. At length Dr Simson, Professor of Mathematics in the University of Glasgow, was so fortunate as to succeed in restoring the Porisms of Euclid. The account he gives of his progress and the obstacles he encountered will always be interesting to mathematicians. In the preface to his treatise De Porismatibus, he says, "Postquam vero apud Pappum legeram Porismata Euclidis Collectionem luisset artificiosissimam multarum rerum, quae spectant ad analysin difficiliorum et generalium problematum, magno desiderio tenebar, ali- quid de illis cognoscendi; quoque sapient et multis variisque vis tum Pappi propositionem generalem, mancam et imperfectam, tum primum lib. 1. porisma, quod, ut dictum fuit, solum ex omnibus in tribus libris integrum adhae- manet, intelligere et restituere conabar; frustra tamen, this subject distinctly, by considering them in the way in which it is probable they occurred to the ancient geometers in the course of their researches: this will at the same time show the nature of the analysis peculiar to them, and their great use in the solution of problems.

It appears to be certain, that it has been the solution of problems which, in all states of the mathematical sciences, has led to the discovery of geometrical truths: the first mathematical inquiries, in particular, must have occurred in the form of questions, where something was given, and something required to be done; and by the reasoning necessary to answer these questions, or to discover the relation between the things given and those to be found, many truths were suggested, which came afterwards to be the subject of separate demonstrations.

The number of these was the greater, because the ancient geometers always undertook the solution of problems, with a scrupulous and minute attention, insomuch that they would scarcely suffer any of the collateral truths to escape their observation.

Now, as this cautious manner of proceeding gave an opportunity of laying hold of every collateral truth connected with the main object of inquiry, these geometers soon perceived, that there were many problems which in certain cases would admit of no solution whatever, in consequence of a particular relation taking place among the quantities which were given. Such problems were said to become impossible; and it was soon perceived, that this always happened when one of the conditions of the problem was inconsistent with the rest. Thus, when it was required to divide a line, so that the rectangle contained by its segments might be equal to a given space, it was found that this was possible only when the given space was less than the square of half the line; for when it was otherwise, the two conditions defining, the one the magnitude of the line, and the other the rectangle of its segments, were inconsistent with each other. Such cases would occur in the solution of the most simple problems; but if they were more complicated, it must have been remarked, that the constructions would sometimes fail, for a reason directly contrary to that just now assigned. Cases would occur, where the lines, which by their intersection were to determine the thing sought, instead of intersecting each other as they did commonly, or of not meeting at all, as in the above-mentioned case of impossibility, would coincide with one another entirely, and of course leave the problem unresolved. It would appear to geometers upon a little reflection, that since, in the case of determinate problems, the thing required was determined by the intersection of the two lines already mentioned, that is, by the points common to both; so in the case of their coincidence, as all their parts were in common, every one of these points must give a solution, or, in other words, the solutions must be indefinite in number.

Upon inquiry, it will be found that this proceeded from some condition of the problem having been involved in another, so that, in fact, the two formed but one, and thus there was not a sufficient number of independent conditions to limit the problem to a single or to any determinate number of solutions. It would soon be perceived, that these cases formed very curious propositions of an intermediate nature between problems and theorems; and that they admitted of being enunciated in a manner peculiarly elegant and concise. It was to such propositions that the ancients gave the name of porisms. This deduction requires to be illustrated by an example: suppose, therefore, that it were required to resolve the following problem.

A circle ABC (fig. 1.), a straight line DE, and a point F, being given in position, to find a point G in the straight line DE such, that GF, the line drawn from it to the given point, shall be equal to GB, the line drawn from it touching the given circle.

Suppose G to be found, and GB to be drawn touching the given circle ABC in B, let H be its centre, join HB, and let HD be perpendicular to DE. From D draw DL, touching the circle ABC in L, and join HL; also from the centre G, with the distance GB or GF, describe the circle BKF, meeting HD in the points K and K'. It is evident that HD and DL are given in position and magnitude: also because GB touches the circle ABC, HBG is a right angle; and since G is the centre of the circle BKF, HB touches that circle, and consequently HB² = KH × HK'; but because KK' is bisected in D, KH × HK' + DK² = DH², therefore HI² + DK² = DH². But HI² + LD² = DI², therefore DK² = DL² and DK = DL. But DL is given in magnitude, therefore DK is given in magnitude, and consequently K is a given point. For the same reason K' is a given point, therefore the point F being given in position, the circle KFK' is given in position. The point G, which is its centre, is therefore given in position, which was to be found. Hence this construction:

Having drawn HD perpendicular to DE, and DL touching the circle ABC, make DK and DK' each equal to DL, and find G the centre of the circle described through the points K'FK; that is, let FK' be joined and bisected at right angles by MN, which meets DE in G, G will be the point required; or it will be such a point, that if GB be drawn touching the circle ABC, and GF to the given point, GB is equal to GF.

The synthetical demonstration is easily derived from the preceding analysis; but it must be remarked, that in some cases this construction fails. For, first, if F fall anywhere in DH, as at F', the line MN becomes parallel to DE, and the point G is nowhere to be found; or, in other words, it is at an infinite distance from D.—This is true in general; but if the given point F coincide with K, then MN evidently coincides with DE; so that, agreeable to a remark already made, every point of the line DE may be taken for G, and will satisfy the conditions of the problem; that is to say, GB will be equal to GK, wherever the point G is taken in the line DE: the same is true if F coincide with K. Thus we have an instance of a problem, and that too a very simple one, which, in general, admits but of one solution; but which, in one particular case, when a certain relation takes place among the things given, becomes indefinite, and admits of innumerable solutions. The proposition which results from this case of the problem is a porism, and may be thus enunciated:

"A circle ABC being given by position, and also a straight line DE, which does not cut the circle, a point K may be found, such that if G be any point whatever..." in DE, the straight line drawn from G to the point K shall be equal to the straight line drawn from G touching the given circle ABC."

The problem which follows appears to have led to the discovery of many porisms.

A circle ABC (fig. 2.) and two points D, E, in a diameter of it being given, to find a point F in the circumference of the given circle; from which, if straight lines be drawn to the given points E, D, these straight lines shall have to one another the given ratio of \(a\) to \(b\), which is supposed to be that of a greater to a lesser.

Suppose the problem resolved, and that F is found, so that FE has to FD the given ratio of \(a\) to \(b\); produce EF towards B, bisect the angle EFD by FL, and DFB by FM: therefore EL : LD :: EF : FD, that is in a given ratio, and since ED is given, each of the segments EL, LD, is given, and the point L is also given; again, because DFB is bisected by FM, EM : MD :: EF : FD, that is, in a given ratio, and therefore M is given. Since DFL is half of DFE, and DFM half of DFB, therefore LFM is half of \((DFE + DFB)\), that is, the half of two right angles, therefore LFM is a right angle; and since the points L, M, are given, the point F is in the circumference of a circle described upon LM as a diameter, and therefore given in position.

Now the point F is also in the circumference of the given circle ABC, therefore it is in the intersection of the two given circumferences, and therefore is found. Hence this construction: Divide ED in L, so that EL may be to LD in the given ratio of \(a\) to \(b\), and produce ED also to M, so that EM may be to MD in the same given ratio of \(a\) to \(b\); bisect LM in N, and from the centre N, with the distance NL, describe the semicircle LFM; and the point F, in which it intersects the circle ABC, is the point required.

The synthetical demonstration is easily derived from the preceding analysis. It must, however, be remarked, that the construction fails when the circle LFM falls either wholly within or wholly without the circle ABC, so that the circumferences do not intersect; and in these cases the problem cannot be solved. It is also obvious that the construction will fail in another case, viz. when the two circumferences LFM, ABC, entirely coincide. In this case, it is farther evident, that every point in the circumference ABC will answer the conditions of the problem, which is therefore capable of numberless solutions, and may, as in the former instances, be converted into a porism. We are now to inquire, therefore, in what circumstances the point L will coincide with A, and also the point M with C, and of consequence the circumference LFM with ABC. If we suppose that they coincide, EA : AD :: \(a\) : \(b\) :: EC : CD, and EA : EC :: AD : CD, or by conversion, EA : AC :: AD : CD — AD : AD :: 2DO, O being the centre of the circle ABC; therefore, also, EA : AO :: AD : DO, and by composition, EO : AO :: AO : DO, therefore EO × OD = AO². Hence, if the given points E and D (fig. 3.) be so situated that EO × OD = AO², and at the same time \(a\) : \(b\) :: EA : AD :: EC : CD, the problem admits of numberless solutions; and if either of the points D or E be given, the other point, and also the ratio which will render the problem indeterminate, may be found. Hence we have this porism:

"A circle ABC, and also a point D being given, another point E may be found, such that the two lines inflected from these points to any point in the circumference ABC, shall have to each other a given ratio, which ratio is also to be found." Hence also we have an example of the derivation of porisms from one another; for the circle ABC, and the points D and E remaining as before (fig. 3.), if, through D we draw any line whatever HDB, meeting the circle in B and H; and if the lines EB, EH be also drawn, these lines will cut off equal circumferences BF, HG. Let FC be drawn, and it is plain from the foregoing analysis, that the angles DFC, CFB, are equal; therefore if OG, OB, be drawn, the angles BOC, COG, are also equal; and consequently the angles DOB, DOG. In the same manner, by joining AB, the angle DBE being bisected by BA, it is evident that the angle AOF is equal to AOH, and therefore the angle FOB to HOG; hence the arch FB is equal to the arch HG. It is evident that if the circle ABC, and either of the points DE were given, the other point might be found. Therefore we have this porism, which appears to have been the last but one of the third book of Euclid's Porisms. "A point being given, either within or without a circle given by position. If there be drawn, anyhow through that point, a line cutting the circle in two points; another point may be found, such, that if two lines be drawn from it to the points in which the line already drawn cuts the circle, these two lines will cut off from the circle equal circumferences."

The proposition from which we have deduced these two porisms also affords an illustration of the remark, that the conditions of a problem are involved in one another in the porismatic or indefinite case; for here several independent conditions are laid down, by the help of which the problem is to be resolved. Two points D and E are given, from which two lines are to be inflected, and a circumference ABC, in which these lines are to meet, as also a ratio which these lines are to have to each other. Now these conditions are all independent of one another, so that any one may be changed without any change whatever in the rest. This is true in general; but yet in one case, viz. when the points are so related to another that the rectangle under their distances from the centre is equal to the square of the radius of the circle; it follows from the preceding analysis, that the ratio of the inflected lines is no longer a matter of choice, but a necessary consequence of this disposition of the points.

From what has been already said, we may trace the imperfect definition of a porism which Pappus ascribes to the later geometers, viz. that it differs from a local theorem, by wanting the hypothesis assumed in that theorem.—Now, to understand this, it must be observed, that if we take one of the propositions called loci, and make the construction of the figure a part of the hypothesis, we get what was called by the ancient geometers, a local theorem. If, again, in the enunciation of the theorem, that part of the hypothesis which contains the construction be suppressed, the proposition thence arising will be a porism, for it will enunciate a truth, and will require to the full understanding and investigation of that truth, that something should be found, viz. the circumstances in the construction supposed to be omitted.

Thus, when we say, if from two given points E, D, (fig. 3.) two straight lines EF, FD, are inflected to a third point F, so as to be to one another in a given ra- Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Plate CCCCXXXVII.

Porism.

Machine for draining Ponds without disturbing the Mud. tio, the point F is in the circumference of a given circle, we have a locus. But when conversely it is said, if a circle ABC, of which the centre is O, be given by position, as also a point E; and if D be taken in the line EO, so that EO × OD = AO²; and if from E and D the lines EF, DF be inflected to any point of the circumference ABC, the ratio of EF to DF will be given, viz. the same with that of EA to AD, we have a local theorem.

Lastly, when it is said, if a circle ABC be given by position, and also a point E, a point D may be found such that if EF, FD be inflected from E and D to any point F in the circumference ABC, these lines shall have a given ratio to one another, the proposition becomes a porism, and is the same that has just now been investigated.

Hence it is evident, that the local theorem is changed into a porism, by leaving out what relates to the determination of D, and of the given ratio. But though all propositions formed in this way from the conversion of loci, are porisms, yet all porisms are not formed from the conversion of loci; the first, for instance of the preceding cannot by conversion be changed into a locus; therefore Fermat's idea of porisms, founded upon this circumstance, could not fail to be imperfect.

To confirm the truth of the preceding theory, it may be added, that Professor Dugald Stewart, in a paper read a considerable time ago before the Philosophical Society of Edinburgh, defines a porism to be "A proposition affirming the possibility of finding one or more conditions of an indeterminate theorem," where, by an indeterminate theorem, he means one which expresses a relation between certain quantities that are determinate and certain others that are indeterminate; a definition which evidently agrees with the explanation which has been here given.

If the idea which we have given of these propositions be just, it follows, that they are to be discovered by considering those cases in which the construction of a problem fails, in consequence of the lines which by their intersection, or the points which by their position, were to determine the problem required, happening to coincide with one another. A porism may therefore be deduced from the problem to which it belongs, just as propositions concerning the maxima and minima of quantities are deduced from the problems of which they form limitations; and such is the most natural and obvious analysis of which this class of propositions admits.

The following porism is the first of Euclid's, and the first also which was restored. It is given here to exemplify the advantage which, in investigations of this kind, may be derived from employing the law of continuity in its utmost extent, and pursuing porisms to those extreme cases where the indeterminate magnitudes increase ad infinitum.

This porism may be considered as having occurred in the solution of the following problem: Two points A, B (fig. 4.) and also three straight lines DE, FK, KL, being given in position, together with two points H and M in two of these lines, to inflect from A and B to a point in the third line, two lines that shall cut off from KF and KL two segments, adjacent to the given points H and M, having to one another the given ratio of α to β.

Now, to find whether a porism be connected with this problem, suppose that there is, and that the following proposition is true. Two points A and B, and two straight lines DE, FK, being given in position, and also a point H in one of them, a line LK may be found, and also a point in it M, both given in position, such that AE and BE inflected from the points A and B to any point whatever of the line DE, shall cut off from the other lines FK and LK segments HG and MN adjacent to the given points H and M, having to one another the given ratio of α to β.

First, let AE', BE' be inflected to the point F, so that AE' may be parallel to FK, then shall EB' be parallel to KL; the line to be found; for if it be not parallel to KL, the point of their intersection must be at a finite distance from the point M, and therefore making as β to α, so this distance to a fourth proportional, the distance from H at which AE' intersects FK, will be equal to that fourth proportional. But AE' does not intersect FK, for they are parallel by construction; therefore BE' cannot intersect KL, which is therefore parallel to BE', a line given in position. Again, let AE'', BE'' be inflected to E'', so that AE'' may pass through the given point H: then it is plain that BE'' must pass through the point to be found M; for if not, it may be demonstrated just as above, that AE'' does not pass through H, contrary to the supposition. The point to be found is therefore in the line EB', which is given in position. Now if from E there be drawn EP parallel to AE', and ES parallel to BE', BS : SE :: BL : LN = SE × BL BS , and AP : PE :: AF : FG = PE = AF AP ; therefore FG : LN = PE × AF SE × BL AP BS :: PE × AF × BS : SE × BL × AP ; wherefore the ratio of FG to LN is compounded of the ratios of AF to BL, PE to ES, and BS to AP; but PE : SE :: AE' : BE', and BS : AP :: DB : DA, for DB : BS :: DE' : E' :: DA : AP; therefore the ratio of FG to LN is compounded of the ratios of AF to BL, AE' to BE', and DB to DA. In like manner, because E' is a point in the line DE, and AE', BE'' are inflected to it, the ratio of FH to LM is compounded of the same ratios of AF to BL, AE' to BE', and DB to DA; therefore FH : LM :: FG : NL (and consequently) :: HG : MN; but the ratio of HG to MN is given, being by supposition the same as that of α to β; the ratio of FH to LM is therefore also given, and FH being given, LM is given in magnitude. Now LM is parallel to BE', a line given in position; therefore M is in a line QM, parallel to AB, and given in position; therefore the point M, and also the line KLM, drawn through it parallel to BE', are given in position, which were to be found. Hence this construction: From A draw AE' parallel to FK, so as to meet DE in E'; join BE', and take in it BQ, so that α : β :: HF : BQ, and through Q draw QM parallel to AB. Let HA be drawn, and produced till it meet DE in E'', and draw BE'', meeting QM in M; through M draw KML parallel to BE', then is KML the line and M the point which were to be found. There are two lines which will answer the conditions of this porism; for if in QB, produced on the other side of B, there be taken Bq = BQ, and if qm be drawn parallel to AB, cutting MB in m; and if mλ be drawn parallel to BQ, the part mn, cut off by EB produced, will be equal to MN, and have to HG the ratio required. It is plain, that whatever be the ratio of \(a\) to \(b\), and whatever be the magnitude of EH, if the other things given remain the same, the lines found will be all parallel to BE. But if the ratio of \(a\) to \(b\) remain the same likewise, and if only the point H vary, the position of KL will remain the same, and the point M will vary.

Another general remark which may be made on the analysis of porisms is, that it often happens, as in the last example, that the magnitudes required may all, or a part of them, be found by considering the extreme cases; but for the discovery of the relation between them, and the indefinite magnitudes, we must have re- course to the hypothesis of the porism in its most gen- eral or indefinite form; and must endeavour so to con- duct the reasoning, that the indefinite magnitudes may at length totally disappear, and leave a proposition as- serting the relation between determinate magnitudes only.

For this purpose Dr Simson frequently employs two statements of the general hypothesis, which he compares together. As for instance, in his analysis of the last po- rism, he assumes not only E, any point in the line DE, but also another point O, anywhere in the same line, to both of which he supposes lines to be inflected from the points A, B. This double statement, however, cannot be made without rendering the investigation long and complicated; nor is it even necessary, for it may be avoided by having recourse to simple porisms, or to loci, or to propositions of the data. The following porism is given as an example where this is done with some diffi- culty, but with considerable advantage both with re- gard to the simplicity and shortness of the demonstration. It will be proper to premise the following lemma. Let AB (fig. 7.) be a straight line, and D, L any two points in it, one of which D is between A and B; also let CL be any straight line. Then shall

\[ \frac{LB}{CL} \cdot AD^2 + \frac{LA}{CL} \cdot BD^2 = \frac{LB}{CL} \cdot LA^2 + \frac{LA}{CL} \cdot LB^2 + \frac{AB}{CL} \cdot DL^2. \]

For place CL perpendicular to AB, and through the points A, C, B describe a circle, and let CL meet the circle again in E, and join AE, BE. Also draw DG parallel to CE, meeting AE and BE in H and G, and draw EK parallel to AB. Then, from the elements of geometry,

\[ CL : LB :: (LA : LE) : LA \times LE, \]

and hence \(LB \times LE = \frac{LB}{CL} \cdot LA^2\).

Also \(CL : LA :: (LB : LE) : LB \times LE\),

and hence \(LB \times LE = \frac{LA}{CL} \cdot LB^2\).

Now \(CL : LB :: LA : LE :: KE\) or \(LD : KH\), and \(CL : LA :: LB : LE :: KE\) or \(LD : KG\), therefore, (Geom. Sect. III. Theor. 8.)

\[ CL : AB :: (LD : GH) : LD^2 : EK \times GH, \]

and hence \(EK \times GH = \frac{AB}{CL} \cdot LD^2\).

From the three equations which we have deduced from the first, second, and fifth of these propositions, it is ma- nifest that

\[ \frac{LB}{LC} \cdot LA^2 + \frac{LA}{CL} \cdot LB^2 + \frac{AB}{CL} \cdot LD^2 = AB \times LE + EK \times GH. \]

Again, because

\[ CL : LA :: (LB : LE :: DB : DG) : DB^2 : DB \times DG, \]

therefore \(DB \times DG = \frac{LA}{CL} \cdot DB^2\).

And because

\[ CL : LB :: (LA : LE :: DA : DH) : DA^2 : DA \times DH, \]

therefore \(DA \times DH = \frac{LB}{CL} \cdot DA^2\). From the result of these two last propositions we have

\[ \frac{LB}{CL} \cdot DA^2 + \frac{LA}{CL} \cdot DB^2 = DA \times DH + BD \times DG; \]

but \(DA \times DH = twice trian. ADH\), and \(DB \times DG = twice trian. BDG\), and therefore \(DA \times DH + DB \times DG = 2 (trian. ADH + trian. BDG) = 2 (trian. AEB + trian. HEG) = AB \times LE + EK \times HG\). Now it has been proved, that \(DA \times DH + DB \times DG = \frac{LB}{CL} \cdot DA^2 + \frac{LA}{CL} \cdot BD^2\), and that \(AB \times LE + EK \times HG = \frac{LB}{CL} \cdot LA^2 + \frac{LA}{CL} \cdot LB^2 + \frac{AB}{CL} \cdot DL^2\), as was to be demonstrated.

**PORISM.** Let there be three straight lines AB, AC, CB given in position (fig. 5.); and from any point whatever in one of them, as D, let perpendiculars be drawn to the other two, as DF, DE, a point G may be found, such that if GD be drawn from it to the point D, the square of that line shall have a given ratio to the sum of the squares of the perpendiculars DF and DE, which ratio is to be found.

Draw AH, BK perpendicular to BC and AC; and in AB take L, so that \(AL : LB :: AH : BK :: AC : CB\). The point L is therefore given; and if a line N be taken, so as to have to AL the same ratio that \(AB^2\) has to \(AH^2\), N will be given in magnitude. Also, since \(AH^2 : BK^2 :: AL : LB\), and \(AH^2 : AB^2 :: AL : N\), ex equo, \(BK^2 : AB^2 :: LB : N\). Draw LO, LM perpendicular to AC, CB; LO, LM are there- fore given in magnitude. Now, because \(AB^2 : BK^2 :: \frac{LB}{N} \cdot AD^2 : DF^2, N : LB :: AD^2 : DF^2\), and \(DF^2 = \frac{LB}{N} \cdot AD^2\); and for the same reason \(DE^2 = \frac{AL}{N} \cdot BD^2\); but, by the preceding lemma, \(\frac{LB}{N} \cdot AD^2 + \frac{AL}{N} \cdot BD^2 = \frac{LB}{N} \cdot AL^2 + \frac{AL}{N} \cdot BL^2 + \frac{AB}{N} \cdot DL^2\); that is, \(DE^2 + DF^2 = LO^2 + LM^2 + \frac{AB}{N} \cdot DL^2\). Join LG, then by hypoth- esis \(LO^2 + LM^2\) has to \(LG^2\), the same ratio as \(DF^2 + DE^2\) has to \(DG^2\); let it be that of R to N, then \(LO^2 + LM^2\). LM = \frac{R}{N}LG^2; and therefore DE + DF = \frac{R}{N}LG^2 + \frac{AB}{N}DL^2; but DE + DF = \frac{R}{N}DG^2; therefore, \frac{R}{N}LG^2 + \frac{BA}{N}DL^2 = \frac{R}{N}DG^2 and \frac{AB}{N}DL^2 = \frac{R}{N}(DG^2 - LG^2); therefore DG^2 - LG^2 has to DL^2 a constant ratio, viz. that of AB to R. The angle DLG is therefore a right angle, and the ratio of AB to R that of equality, otherwise LD would be given in magnitude, contrary to the supposition. LG is therefore given in position; and since R : N :: AB : N :: LO^2 + LM^2 : LG^2; therefore the square of LG, and consequently LG, is given in magnitude. The point G is therefore given, and also the ratio of DE + DF to DG^2, which is the same with that of AB to N.

The construction easily follows from the analysis, but it may be rendered more simple; for since AH : AB :: AL : N, and BK : AB :: BL : N; therefore AH + BK : AB :: AB : N. Likewise, if AG, BG, be joined, AB : N :: AH^2 : AG^2, and AB : N :: BK^2 : BG^2; therefore AB : N :: AH^2 + BK^2 : AG^2 + BG^2, but it was proved that AB : N :: AH^2 + BK^2 : AB^2; therefore AG^2 + BG^2 = AB^2; therefore the angle AGB is a right one, and AL : LG :: LG : LB. If therefore AB be divided in L, so that AL : LB :: AH^2 : BK^2; and if LG, a mean proportional between AL and LB, be placed perpendicular to AB, G will be the point required.

The step in the analysis, by which a second introduction of the general hypothesis is avoided, is that in which the angle GLD is concluded to be a right angle; which follows from DG^2 - GL^2 having a given ratio to LD^2; at the same time that LD is of no determinate magnitude. For, if possible, let GLD be obtuse (fig. 6.), and let the perpendicular from G to AB meet it in V, therefore V is given; and since GD^2 - GL^2 = LD^2 + 2DL × LV; therefore, by the supposition, LD^2 + 2DL × LV must have a given ratio to LD^2; therefore the ratio of LD^2 to DL × VL, that is, of LD to VL, is given, so that VL being given in magnitude, LD is also given. But this is contrary to the supposition; for LD is indefinite by hypothesis, and therefore GLD cannot be obtuse, nor any other than a right angle. The conclusion that is here drawn immediately from the indetermination of LD would be deduced, according to Dr Simson's method, by assuming another point D' anyhow, and from the supposition that GD'^2 - GL'^2 : LD'^2 :: GD^2 - GL^2 : LD^2, it would easily appear that GLD must be a right angle, and the ratio that of equality.

These porisms facilitate the solution of the general problems from which they are derived: For example, let three straight lines AB, AC, BC (fig. 5.), be given in position, and also a point R, to find a point D in one of the given lines, so that DE and DF being drawn perpendicular to BC, AC, and DR, joined; DE + DF may have to DR a given ratio. It is plain, that having found G, the problem would be nothing more than to find D, such that the ratio of GD^2 to DR^2, and therefore that of GD to DR, might be given, from which it would follow, that the point D is in the circumference of a given circle, as is well known to geometers.

The same porism also assists in the solution of another problem. For if it were required to find D such that DE + DF might be a given space; having found G, DG^2 would have to DE + DF a given ratio, and DG would therefore be given; whence the solution is obvious.

The connection of this porism with the impossible case of the problem is evident; the point L being that from which, if perpendiculars be drawn to AC and CB, the sum of their squares is the least possible. For since DF^2 + DE^2 : DG^2 :: LO^2 + LM^2 : LG^2; and since LG is less than DG, LO^2 + LM^2 must be less than DF^2 + DE^2.

It is evident from what has now appeared, that in some instances at least there is a close connection between these propositions and the maxima or minima, and of consequence the impossible cases of problems. The nature of this connection requires to be farther investigated, and is the more interesting because the transition from the indefinite to the impossible case seems to be made with wonderful rapidity. Thus in the first proposition, though there be not properly speaking an impossible case, but only one where the point to be found goes off ad infinitum, it may be remarked, that if the given point F be anywhere out of the line HD (fig. 1.), the problem of drawing GB equal to GF is always possible, and admits of just one solution; but if F be in DH, the problem admits of no solution at all, the point being then at an infinite distance, and therefore impossible to be assigned. There is, however, this exception, that if the given point be at K in this same line, DH is determined by making DK equal to DL. Then every point in the line DE gives a solution, and may be taken for the point G. Here therefore the case of numberless solutions, and of no solution at all, are as it were continuous, and so close to one another, that if the given point be at K the problem is indefinite; but if it remove ever so little from K, remaining at the same time in the line DH, the problem cannot be resolved. This affinity might have been determined a priori: for it is, as we have seen, a general principle, that a problem is converted into a porism when one or when two of the conditions of it necessarily involve in them some one of the rest. Suppose, then, that two of the conditions are exactly in that state which determines the third; then while they remain fixed or given, should that third vary or differ ever so little from the state required by the other two, a contradiction will ensue: therefore if, in the hypothesis of a problem, the conditions be so related to one another as to render it indeterminate, a porism is produced; but if, of the conditions thus related to one another, some one be supposed to vary, while the others continue the same, an absurdity follows, and the problem becomes impossible. Wherever, therefore, any problem admits both of an indeterminate and an impossible case, it is certain, that these cases are nearly related to one another, and that some of the conditions by which they are produced are common to both.

It is supposed above, that two of the conditions of a problem involve in them a third; and wherever that happens, the conclusion which has been deduced will invariably take place. But a porism may in some cases be so simple as to arise from the mere coincidence of one condition with another, though in no case whatever any inconsistency can take place between them. There are, Porisms, however, comparatively few porisms so simple in their origin, or that arise from problems where the conditions are but little complicated; for it usually happens that a problem which can become indefinite may also become impossible; and if so, the connection already explained never fails to take place.

Another species of impossibility may frequently arise from the porismatic case of a problem which will affect in some measure the application of geometry to astronomy, or any of the sciences depending on experiment or observation. For when a problem is to be resolved by means of data furnished by experiment or observation, the first thing to be considered is, whether the data so obtained be sufficient for determining the thing sought; and in this a very erroneous judgment may be formed, if we rest satisfied with a general view of the subject; for though the problem may in general be resolved from the data with which we are provided, yet these data may be so related to one another in the case under consideration, that the problem will become indeterminate, and instead of one solution will admit of an indefinite number. This we have already found to be the case in the foregoing propositions. Such cases may not indeed occur in any of the practical applications of geometry; but there is one of the same kind which has actually occurred in astronomy. Sir Isaac Newton, in his Principia, has considered a small part of the orbit of a comet as a straight line described with an uniform motion. From this hypothesis, by means of four observations made at proper intervals of time, the determination of the path of the comet is reduced to this geometrical problem: Four straight lines being in position, it is required to draw a fifth line across them, so as to be cut by them into three parts, having given ratios to one another. Now this problem had been constructed by Dr Wallis and Sir Christopher Wren, and also in three different ways by Sir Isaac himself in different parts of his works; yet none of these geometers observed that there was a particular situation of the lines in which the problem admitted of innumerable solutions: and this happens to be the very case in which the problem is applicable to the determination of the comet's path, as was first discovered by the abbe Bosovich, who was led to it by finding, that in this way he could never determine the path of a comet with any degree of certainty.

Besides the geometrical there is also an algebraical analysis belonging to porisms; which, however, does not belong to this place, because we give this account of them merely as an article of ancient geometry; and the ancients never employed algebra in their investigations. Mr Playfair, formerly professor of mathematics, and now of natural philosophy in the university of Edinburgh, has written a paper on the origin and geometrical investigation of porisms, which is published in the third volume of the Transactions of the Royal Society of Edinburgh, from which this account of the subject is taken. He has there promised a second part to his paper, in which the algebraical investigation of porisms is to be considered. This will no doubt throw considerable light upon the subject, as we may readily judge from that gentleman's known abilities, and from the specimen he has already given us in the first part.

Such as are desirous of knowing more of this subject may consult Dr Simson's treatise De Porismatibus, which is contained in his Opera Reliqua, published after his death at the sole expense of the earl of Stanhope. We have already mentioned Dr Stewart's General Theorems which contain many beautiful porisms, but without demonstrations. A considerable number of them, however, have been demonstrated by the late Dr R. Small, of Dundee, in the Trans. R. S. Edin. vol. ii. There is also a paper upon the subject of porisms by Mr W. Wallace, now of the Royal Military College, in the fourth volume of the same work, entitled Some Geometrical Porisms, with examples of their application to the Solution of Problems.