in Philosophy, denotes any doctrines deduced from self-evident principles.

Sciences may be properly divided as follows: 1. The knowledge of things, their constitutions, properties, and operations: this, in a little more enlarged sense of the word, may be called Physics, or natural philosophy; the end of which is speculative truth. See Philosophy and Physics.—2. The skill of rightly applying these powers, mechanics: The most considerable under this head is ethics, which is the seeking out those rules and measures of human actions that lead to happiness, and the means to practise them (see Moral Philosophy); and the next is mechanics, or the application of the powers of natural agents to the uses of life (see Mechanics).—3. The doctrines of signs, semiotics; the most usual of which being words, it is aptly enough termed logic. See Logic.

This, says Mr Locke, seems to be the most general, as well as natural, division of the objects of our understanding. For a man can employ his thoughts about nothing but either the contemplation of things themselves for the discovery of truth; or about the things in his own power, which are his actions, for the attainment of his own ends; or the signs the mind makes use of both in the one and the other, and the right ordering of them for its clearer information. All which three, viz. things as they are in themselves knowable, actions as they depend on us in order to happiness, and the right use of signs in order to knowledge, being toto caelo different, they seem to be the three great provinces of the intellectual world, wholly separate and distinct one from another.

AMUSEMENTS OR RECREATIONS OF.

A DESIRE of amusement and relaxation is natural to man. The mind is soon fatigued with contemplating the most sublime truths, or the most refined speculations, while these are addressed only to the understanding. In philosophy, as in polite literature, we must, to please and secure attention, sometimes address ourselves to the imagination or to the passions, and thus combine the agreeable with the useful. For want of this combination, we find that pure mathematics (comprehending arithmetic, geometry, algebra, fluxions, &c.), notwithstanding their great and acknowledged utility, are studied but by few; while the more attractive sciences of experimental philosophy and chemistry, are almost universally admired, and seldom fail to draw crowds of hearers or spectators to the lectures of their professors. The numerous striking phenomena which these latter sciences present to our senses, the splendid experiments by which their principles may be illustrated, and the continual application which they admit, of those principles and experiments to the affairs of common life, have a powerful influence on the imagination; fix and keep alive the attention; excite the passions of joy, terror or surprise; and gratify that love of the marvellous which nature has implanted in the human mind. Even the more abstruse subjects of pure mathematics, especially arithmetic and geometry, may be sometimes enlivened by amusing examples and contrivances; and are found the more pleasing, in proportion as they are susceptible of such elucidation.

These experimental contrivances, and useful applications to the purposes of common life, constitute what we may term the Amusements or Recreations of Science. They have very properly been denominated rational recreations, as they serve to relax and unbend the mind after long attention to the cares of business, or to severer studies, in a manner more rational, and often more satisfactory, than those frivolous pursuits which too often employ the time, and injure the health of the rising generation.

In the preceding volumes of this work we have supplied our readers with many examples of scientific recreation. Thus, the articles Legerdemain and Pyrotechny may be regarded as entirely of this nature; and in the experimental parts of Chemistry, Electricity, Galvanism, and Magnetism; in the articles Acoustics, Hydrodynamics, Mechanics, Optics, and its correlative divisions, Catoptrics, Dioptrics, Perspective, and Microscope; in Pneumatics and Aerostation, we have related a variety of interesting experiments, and described many ingenious ous contrivances, calculated both for instruction and amusement. It is the object of the present article to bring these under one point of view, and to add a few of the more curious or useful experiments and contrivances which could not before be conveniently introduced. In particular, we propose to explain some of those scientific deceptions which have excited so much interest and admiration, and to describe several useful philosophical instruments, which either are of very late invention, or have been overlooked in the preceding parts of the work. We shall thus be enabled to supply several deficiencies (otherwise unavoidable), and shall render the present article a sort of general index or table of reference to the various subjects of scientific amusement which are dispersed through the Encyclopaedia.

For greater convenience, and more easy reference to preceding articles, we shall arrange the sections under which the various amusements of science may be reduced, in alphabetical order, according to the series of the principal mathematical and philosophical treatises. Thus the article will be divided into 13 sections, comprehending the recreations and contrivances that relate to Acoustics, Arithmetic, Astronomy, Chemistry, Electricity, Galvanism, Geography, Geometry, Hydrodynamics, Magnetism, Mechanics, Optics and Pneumatics.

It must not be supposed, from the title of this article, that the subjects which we are here to discuss are puerile or trifling. They will be such as are best calculated to excite the attention, quicken the ingenuity, and improve the memory of our young readers, and they will be similar to those pursuits which have employed the lighter hours of some of the most distinguished philosophers and mathematicians. The names of Bacon, of Boyle, of Newton, of Desaguliers, of Ozanam, of Montucla, and of Hutton, stamp a value on the recreations of science, and prevent us from considering them as frivolous or trifling.

The subject of scientific recreations must be regarded as entirely modern, as previous to the era of Lord Bacon, philosophers were much more attached to rigid demonstration and metaphysical reasoning, than to experimental illustration. Much may be found on these subjects in the works of Lord Bacon and Mr Boyle; but the earliest collection of scientific amusements which deserves notice, is the work of Ozanam, entitled Récréations Mathématiques et Physiques, published in 1692, in 2 vols 8vo, and afterwards several times republished with improvements and additions, till it was enlarged to 4 vols 8vo. This work was soon translated into most of the modern languages, and was given to the English reader by Dr Hooper, under the title of Rational Recreations, first published; we believe, in 1774, and again in 1783, in 4 vols 8vo. The original work of Ozanam has been lately recomposed and greatly improved by M. Montucla; and a translation of this improved edition into English was published in 1803, in 4 vols 8vo, by Dr Charles Hutton. In this English edition, the work is much better adapted than in any former copy, to the English reader, and is enriched by some of the latest improvements in natural philosophy and chemistry.

It may not be improper to add, to this notice of works on the amusements of science, a list of the best popular treatises on natural and experimental philosophy and chemistry, to which our younger readers may have recourse for an explanation of the principles of these sciences, if they should find some of the articles in this Encyclopaedia too abstruse or too mathematical.

To young people who have never read any work on these sciences, we may recommend Mr Joyce's Scientific Dialogues, Dialogues on Chemistry, and Dialogues on the Microscope, and Mr Frend's Evening Amusements. After attentively perusing these, they may enlarge their information by reading Brewster's edition of Ferguson's Lectures; Nicholson's Introduction to Natural Philosophy; Gregory's Economy of Nature; or Dr Young's Lectures on Natural Philosophy; and Henry's Epitome of Chemistry, 8vo edition.

Sect. I. Recreations and Contrivances relating to Acoustics.

In the article Acoustics, Vol. I. p. 159, we have related six amusing experiments and contrivances, and have explained them on the principles of acoustics. These are, the conversing statue, explained on the principle of the reflexion of sound; the communicative busts, and the oracular head, explained from the reverberation of sound; the solar sonata, the automation harpsichord, and the ventose symphony, explained partly on the principles of acoustics, and partly on those of mechanics. We have now to explain a deception connected with the conveyance of sound, well known to many of our readers, by the name of the invisible lady or invisible girl; and to notice some curious figures assumed by sand or other light bodies on the surface of vibrating plates.

Some years ago M. Charles, brother to the well-known philosopher of that name, exhibited in London, and afterwards in most of the large towns of Great Britain and Ireland, the experiment of the invisible girl. The apparatus by means of which this experiment was conducted, and the principal circumstances attending the exhibition, have been described by Mr Nicholson, in his Philosophical Journal, from which the following account is principally taken.

In the middle of a large lofty room, in an old house, where, from the appearance of the wainscot, and other circumstances, there seemed to be no situation for placing acoustic tubes or reflectors, was fixed a wooden railing, about 5 feet high, and as many wide, inclosing a square space. A perspective view of the apparatus is given at fig. 1. of Plate CCCCLXX, where A, A, A, A, represent the four upright posts. These posts were united by a cross rail near the top, BB, and by two or more similar rails at the bottom. The frame, thus constructed, stood upon the floor, and from the top of each of the four upright pillars proceeded a strong bended-brass wire a, a, a, a, so that they all met together at the top c, where they were secured by a crown and prince's feather, or other ornaments. From these four wires was suspended a hollow copper ball, about a foot in diameter, by means of slight ribbons, so as to cut off all possible communication with the frame. Round this ball were placed four trumpets, at right angles to each other, as represented at A, A, A, A, fig. 2., having their mouths opening externally.

Such was the apparent construction of the apparatus, and it was pretended that there resided within the ball an invisible lady, capable of giving answers to any questions that were put to her. When a question was pro-posed, AMUSEMENTS OF SCIENCE.

It was uttered in at the mouth of one of the trumpets, and an answer immediately proceeded from all the trumpets, so distinctly loud as to be heard by an ear applied to any of them, and yet so distant and feeble, that it appeared to come from a very diminutive being. In this consisted the whole of the experiment, except that the lady could converse in several languages, sing, describe all that happened in the room, and display a fund of lively wit and accomplishment that admirably qualified her to support the character she had undertaken.

The principles on which this experiment is constructed are similar to those of the oracular head described under Acoustics; except that in the present deception, an artificial echo is produced by means of the trumpets, and thus the sound is completely reversed, instead of proceeding in its original direction. Fig. 3 represents a section of the apparatus, and will explain the method by which the deception is effected. One of the posts A, A, as well as one-half of the hand-rail connected with it, is hollowed into a tube, the end of which opens on the inside of the rail, opposite the centre of the trumpet on that side, though the hole is very small, and is concealed by reeds or other mouldings. At the other end the tube communicates with a long tin pipe pp about half an inch in diameter, concealed below the floor of the room ff, and passing up the wall to a large deal case, k, almost similar to an inverted funnel, and large enough to contain the confederate, and a piano forte, on which tunes may be occasionally played. A small hole closed with glass is left through the funnel and side-wall of the room, as at h, so that the confederate may have an opportunity of observing and commenting on any circumstances which may take place in the room. Thus, when any question is asked at one of the trumpets, the sound is conveyed through the communicating tubes into the funnel-shaped case, so as to be heard by the confederate, who then gives the answer, which in like manner is conveyed through the tube below the floor to one of the trumpets, and is heard, either from that, or any of the rest.

On the Figures produced by Light Bodies on Vibrating Surfaces.

About the year 1787, Dr Chladni of Wittemberg drew the particular attention of philosophers to the nature of vibration, by investigating the curves produced by the moving points of vibrating surfaces. It is found that if sand, or a similar substance, be strewed on the surface of an elastic plate, such as glass or the sonorous metals, and if the plate be made to vibrate, the sand will arrange itself on particular parts of the surface, showing that these points are not in motion. These figures are often extremely curious, and may be varied according to the pleasure or address of the experimentalist. Some of the more remarkable are represented at figs. 5, 6, 10, 11.

To produce these figures, nothing is necessary but to know the method of bringing that part of the surface which we wish not to vibrate into a state of rest; and of putting in motion that which we wish to vibrate: on this depends the whole expertness of producing what are called vibration figures.

Those who have never tried these experiments may imagine that to produce fig. 5, it would be necessary to damp, in particular, every point of the part to be kept at rest, viz. the two concentric circles and the diameter, and to put in motion every part intended to vibrate. This, however, is not the case; for we need damp only the points a and b, and cause to vibrate one part c, at the edge of the plate; for the motion is soon communicated to the other parts which we wish to vibrate, and the required figure will in this manner be produced.

The damping may be best effected by laying hold of the place to be damped between the fingers, or by supporting it with only one finger. This will be more clearly comprehended by turning to fig. 8, where the hand is represented in the position necessary to hold the plate. In order to produce fig. 6, we must hold the plate horizontally, placing the thumb above at a, with the second finger directly below it; and besides this, we must support the point b on the under side of the plate. If the bow of a violin be then rubbed against the plate at c, there will be produced on the glass the figure which is delineated at fig. 6. When the point to be supported or damped lies too near the centre of the plate, we may rest it on a cork, not too broad at the end, brought into contact with the glass in such a manner as to supply the place of the finger. It is convenient also, when we wish to damp several points at the circumference of the glass, to place the thumb on the cork, and to use the rest of the fingers for touching the part which we wish to keep at rest. For example, if we wish to produce fig. 7, on an elliptic plate, the larger axis of which is to the less as 4 to 3, we must place the cork under c, the centre of the plate; put the thumb on this point, and then damp the two points of the edge p and q, as may be seen at fig. 8, and make the plate to vibrate by rubbing the violin bow against it at r. There is still another convenient method of damping several points at the edge when large plates are employed. Fig. 4 represents a strong square piece of metal a b, Fig. 4, a line in circumference, which is screwed to the edge of the table, or made fast in any other manner; and a notch, about as broad as the edge of the plate, is cut into one side of it by a file. We then hold the plate resting against this piece of metal, by two or more fingers when requisite, as at c and d, by which means the edge of the plate will be damped in three points d, c, e; and in this manner, by putting the plate in vibration at f, we can produce fig. 13. In cases of necessity, the edges of a table may be used, instead of the piece of metal; but it will not answer the purpose so well.

To produce the vibration at any required place, a common violin bow, rubbed with rosin, is the most proper instrument to be employed. The hair must not be too slack, because it is sometimes necessary to press pretty hard on the plate, in order to produce the tone sooner.

When we wish to produce any particular figure, we must first form it in idea upon the plate, in order that we may be able to determine where a line at rest, and where a vibrating part, will occur. The greatest rest will always be where two or more lines intersect each other, and such places must in particular be damped. For example, in fig. 9, we must damp the part n, and stroke with the bow in p. Fig. 13, may be produced with no less ease, if we hold the plate at r, and stroke with the bow. The strongest vibration seems always to be in that part of the edge which is bounded by a curve; for example, in figs. 10. and 11. at n. To produce these figures, therefore, we must rub with the bow at n, and not at r.

We must, however, damp not only those points where two lines intersect each other, but endeavour to support at least one which is suited to that figure, and to no other. For example, when we support a and b, fig. 5, and rub with the bow at c, fig. 9, also may be produced, because both figures have these two points at rest. To produce fig. 5, we must support with one finger the part e, and rub with the bow in c; but fig. 9 cannot be produced in this manner, because it has not the point e at rest.

One of the greatest difficulties in producing the figures, is to determine before-hand the vibrating and resting points which belong to a certain figure, and to no other. Hence, when we are not able to damp those points which distinguish one figure from another, if the violin bow be rubbed against the plate, several hollow tones are heard, without the sand forming itself as expected. We must therefore acquire by experience a readiness, in being able to search out among these tones, that which belongs to the required figure, and to produce it on the plate by rubbing the bow against it. When we have acquired sufficient expertness in this respect, we can determine before-hand, with tolerable certainty, the figures to be produced, and even the most difficult. It may be easily conceived, that we must remember what part of the plate, and in what manner we damped; and we may mark these points by scratching the plate with a piece of flint.

When the plate has acquired the proper vibration, endeavour to keep it in that state for some seconds; which can be done by rubbing the bow against it several times. By these means the sand will be more accurately formed.

Any sort of glass may be employed, provided its surface be smooth, otherwise the sand will fall into the hollow parts, or be thrown about irregularly. Common glass plates, when cut with a stone, are very sharp on the edge, and would soon destroy the hair of a violin bow; for which reason the edge must be smoothed by a file, or a piece of freestone.

We must endeavour to procure such plates as are uniformly thick, and of different sizes; such as circular ones from four to 12 inches in diameter. Sand too fine must not be employed. The plate must be equally besprewed with it; and not too thickly, as the lines will then be exceedingly fine, and the figures will acquire a better defined appearance.

The subject of ventriloquism, or that peculiar modification of voice by which sounds are made to appear as coming from situations at a distance from the person who utters them, is a deception connected with the subject of acoustics. This deception we have already explained under Physiology, No 251, 254.

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(a) Though it is not our intention in the present article, to explain all the experiments and contrivances so fully as to leave nothing to the ingenuity of the reader, we may remark, with respect to the present question, that as the obtained sum is derived merely from the first line of figures, all below this must be so contrived as to produce by their addition a line in which all the digits are 2's. Accordingly, it will be found that the addition of the first Most of our readers are well acquainted with the question in multiplication respecting the price of a horse from successively doubling a farthing as often as there are nails in the horse's shoes. (See Montucla's Recreations by Hutton, vol. i. or Sandford and Merton, vol. i.) The following question is of a similar nature, but appears still more surprising.

A courtier having performed some very important service to his sovereign, the latter wishing to confer on him a suitable reward, desired him to ask whatever he thought proper, promising that it should be granted. The courtier, who was well acquainted with the science of numbers, requested only that the monarch would give him a quantity of wheat equal to that which would arise from one grain doubled 63 times successively. What was the value of the reward?

The origin of this problem is related in so curious a manner by Al-Sepadi, an Arabian author, that it deserves to be mentioned. A mathematician named Sessa, says he, the son of Daher, the subject of an Indian prince, having invented the game of chess, his sovereign was highly pleased with the invention, and wishing to confer on him some reward worthy of his magnificence, desired him to ask whatever he thought proper, assuring him that it should be granted. The mathematician, however, asked only a grain of wheat for the first square of the chess-board, two for the second, four for the third, and so on to the last or 64th. The prince at first was almost incensed at this demand, conceiving that it was ill suited to his liberality, and ordered his vizir to comply with Sessa's request; but the minister was much astonished when, having caused the quantity of corn necessary to fulfill the prince's order to be calculated, he found that all the grain in the royal granaries, and that even of all his subjects, and in all Asia, would not be sufficient. He therefore informed the prince, who sent for the mathematician, who candidly acknowledged his inability to comply with his demand, the ingenuity of which astonished him still more than the game which he had invented.

To find the amount of this prodigious reward, to pay which even the treasury of a mighty prince was insufficient, we shall proceed most easily by way of geometrical progression, though it might be discovered by common multiplication and addition. It will be found by calculation, that the 64th term of the double progression, beginning with unity, is $9,223,372,036,854,775,808$. But the sum of all the terms of a double progression, beginning with unity, may be obtained by doubling the last term and subtracting from it unity. The number, therefore, of the grains of wheat equal to Sessa's demand, will be $18,446,744,073,708,551,615$. Now, if a standard English pint contain 9216 grains of wheat, a gallon will contain 73,728; and, as eight gallons make one bushel, if we divide the above result by 8 times 73,728, we shall have $31,274,997,412,295$ for the number of the bushels of wheat necessary to discharge the promise of the Indian king: and if we suppose that one acre of land be capable of producing in one year, 30 bushels of wheat, to produce this quantity would require $1,042,499,913,743$ acres, which make more than 8 times the surface of the globe: for the diameter of the earth being supposed equal to 7930 miles, its whole surface, comprehending land and water, will amount to very little more than $126,437,889,177$ square acres.

If the price of a bushel of wheat be estimated at 10s. (it is at present, August 1809, 12s. 6d. per bushel), the value of the above quantity will amount to $15,637,498,706,147l.$ 10s.; a sum which, in all probability, far surpasses all the riches on the earth.*

* Hutton's Recreations, vol. I.

To discover any Number thought of.

Of this problem there are several cases, differing chiefly in complexity of operation.

I. Desire the person who has thought of a number, to triple it, and to take the exact half of that triple if it be even, or the greater half if it be odd. Then desire him to triple that half, and ask him how many times that product contains 9; for the number thought of will contain double the number of nines, and one more if it be odd.

Thus, if 4 has been the number thought of, its triple will be 12, which can be divided by 2 without a remainder. The half of 12 is 6, and if this be multiplied by 3, we shall have 18, which contains 9 twice, the number will therefore be 4 equal twice 2, the number of nines in the last product.

II. Bid the person multiply the number thought of by itself; then desire him to add unity to the number thought of, and to multiply that sum also by itself; in the last place, ask him to tell the difference of those two products, which will certainly be an odd number, and the least half of it will be the number required.

Let the number thought of be 10, which multiplied by itself gives 100; in the next place 10 increased by 1 is 11, which multiplied by itself makes 121, and the difference of these two squares is 21, the least half of which being 10, is the number thought of.

This operation might be varied in the second step by desiring the person to multiply the number by itself, after it has been diminished by unity, and then to tell the difference of the two squares, the greater half of which will be the number thought of.

Thus, in the preceding example, the square of the number thought of is 100, and that of the same number, subtracting 1, is 81; the difference of these is 19, the greater half of which, or 10, is the number thought of.

III. Desire the person to add to the number thought of its exact half if it be even, or its greater half if it be odd, in order to obtain a first sum; then bid him add to this sum its exact half, or its greater half, according as

first right-hand column produces 92, and that of all the rest 20, which, with the addition of the 2 carried, supplies the other 2's in the line. From this it is evident, that though, for more easy illustration, we have given a question containing only five lines; seven, nine, or any unequal number may be employed, constructing the seventh, ninth, &c. on similar principles. Arithmetic as it is even or odd, to have a second sum, from which the person must subtract the double of the number thought of. Then desire him to take the half of the remainder, or its less half if it be an odd number, and continue halving the half till he comes to unity. When this is done, count how many subdivisions have been made, and for the first division retain two, for the second 4, for the third 8, and so of the rest, in double proportion. It is here necessary to observe, that 1 must be added for each time that the least half was taken, because, by taking the least half, one always remains; and that 1 only must be retained when no subdivision could be made; for thus you will have the number the halves of the halves of which have been taken; the quadruple of that number then will be the number thought of, in case it was not necessary at the beginning to take the greater half, which will happen only when the number thought of is evenly even, or divisible by 4; but if the greater half has been taken at the first division, 3 must be subtracted from the above quadruple, or only 2 if the greater half has been taken at the second division, or 5 if it has been taken at each of the two divisions, and the remainder then will be the number thought of.

Thus, if the number thought of has been 4; by adding to it its half, we shall have 6; and if to this we add its half, 3, we shall have 9; if 8, the double of the number thought of, be subtracted, there will remain 1, which cannot be halved, because we have arrived at unity. For this reason, we must retain 1; and the quadruple of this, or 4, will be the number thought of.

IV. Desire the person to take 1 from the number thought of, and to double the remainder; then bid him take 1 from this double, and add to it the number thought of. Having asked the number arising from this addition, add 3 to it, and the third of the sum will be the number required.

Let the number thought of be 5; if 1 be taken from it, there will remain 4, the double of which 8, being diminished by 1, and the remainder 7 being increased by 5, the number thought of, the result will be 12; if to this we add 3, we shall have 15, the third part of which, 5, will be the number required.

V. Desire the person to add 1 to the triple of the number thought of, and to multiply the sum by 3; then bid him add to this product the number thought of, and the result will be a sum, from which if 3 be subtracted, the remainder will be double of the number required. If 3 therefore be taken from the last sum, and if the cipher on the right be cut off from the remainder, the other figure will indicate the number sought.

Let the number thought of be 6, the triple of which is 18, and if unity be added it makes 19; the triple of this last number is 57, and if 6 be added it makes 63, from which if 3 be subtracted the remainder will be 60; now, if the cipher on the right be cut off, the remaining figure 6 will be the number required.

VI. Among the various methods contrived for discovering numbers thought of, we have seen none more ingenious than the following, which was lately communicated to us. This is a sort of puzzle, consisting of six slips of paper or pasteboard, on which are written numbers as expressed in the following columns.

The six slips being thus prepared, a person is to think of any one of the numbers which they contain, and to give to the expounder of the question those slips which contain the number thought of. To discover this number, the expounder has nothing to do but to add together the numbers at the top of the columns put into his hand. Their sum will express the number thought of.

Example. Thus, suppose we think of the number 14. We find that this number is in three of the slips, viz. those marked B, C, and D, which are therefore given to the expounder, who on adding together 2, 4, and 8, obtains 14, the number thought of.

This trick may be varied in the following manner. Instead of giving to the expounder the slips containing the number thought of, these may be kept back, and those in which the number does not occur be given. In this case the expounder must add together, as before, the numbers at the top of the columns, and subtract their sum from 63; the remainder will be the number thought of.

Example. Taking again the former number 14, the slips in which this is not contained are those marked A, E, and F. Adding together 1, 16, and 32, the expounder has 49, which subtracted from 63, leaves 14, the number thought of as before.

The slips containing the columns of numbers are usually Towards explaining the principles on which this puzzle has been constructed, we may remark, 1. That each column may be divided into sets of figures; those of each column consisting of as many figures as are represented by the number at the head of the column, one figure in each set in the column marked 1; two in that marked 2; four in four, &c. 2. That after each parcel there is a blank of as many figures as that parcel consists of, counting in a regular series from the last number of the parcel. 3. That the numbers of each parcel are in arithmetical progression, while those at the head of the columns are in geometrical progression. 4. That the first sets of all the columns taken together in regular series, compose the whole series of numbers in the columns from 1 to 63, and are consequently the most important, as any number thought of must be found in only one of these sets. 5. That the sum of all the terms of the geometrical progression is equal to the last or highest term of the arithmetical progression 63, and is also equal to the double of the last term of the geometrical progression diminished by unity.

Having premised these remarks, we shall not proceed farther than to hint, that, in constructing this ingenious puzzle, the author appears to have employed the properties of geometrical progressions, and their relations to arithmetical progressions, for which see the article SERIES.

To render these columns more portable, they may each be divided into three or more, and written on small cards, marked at the back with letters. In this form the first figure of the first column must be employed, like the first figure at the head of the slips; or the better to disguise the contrivance, the figures of each column may be placed in a confused order, and the letters alone employed.

Mr William Frend, well known as the author of the Evening Amusements, has rendered an important service to the rising generation, by the publication of his Tangible Arithmetic, or the Art of Numbering made easy, by means of an arithmetical toy. The toy which forms the basis of this method of numbering, is similar to what has been called the Chinese board, which is explained in the fourth volume of Mr Frend's Evening Amusements. This toy is so constructed as to be capable of expressing any number as far as 16,666,665, and is capable of performing a great variety of arithmetical operations, merely by moving a few balls. The author gives a variety of simple instances and amusing games, by which the first four rules of arithmetic may be explained and illustrated. The whole contrivance is very ingenious, and well deserves the attention of mothers and all teachers of children.

Sect. III. Recreations and Contrivances relating to ASTRONOMY.

Many scientific recreations may be derived from astronomy, and some of these have already been noticed in our treatise on that subject. Among the most useful of the astronomical amusements, however, is the method of discovering the several stars that compose the constellations; and this we shall here explain.

Before we can become acquainted with the stars that compose the constellations, we must be provided with learning accurate celestial charts, or a good planisphere, of such a size that stars of the first and second magnitudes can be readily distinguished on it. Having placed before us one of these charts, as that containing the north pole, or that part of the planisphere which contains the northern hemisphere, first find out the Great Bear, commonly called Charles's Wain (Plate CCCCLXXI., fig. Fig. 14.). It may be easily known, as it forms one of the most remarkable groups in the heavens, consisting of several stars of the second magnitude, four of which are arranged in such a manner as to represent an irregular square, and the other three a prolongation in the form of a very obtuse scalene triangle. Besides, by examining the figure of these seven stars, as exhibited in the chart, we shall easily distinguish those in the heavens which correspond to them. When we have made ourselves acquainted with these seven principal stars, we examine on the chart the configuration of the neighbouring stars, which belong to the Great Bear; and thence learn to distinguish the other less considerable stars which compose that constellation.

After knowing the Great Bear, we may easily proceed to the Lesser Bear; for nothing will be necessary but to draw, as may be seen in fig. 15., a straight line through the two anterior stars of the square of the Great Bear, or the two farthest distant from the tail; this line will pass very near the polar star, a star of the second magnitude, and the only one of that size in a pretty large space. At a little distance from it, there are two other stars of the second and third magnitudes, which, with four more of a less size, form a figure somewhat similar to that of the Great Bear, but smaller. This is what is called the Lesser Bear; and we may learn, in the same manner as before, to distinguish the stars which compose it.

Now if a straight line be drawn through those stars of the Great Bear, nearest to the tail, and through the polar star, it will conduct us to a very remarkable group of five stars arranged nearly in this form M (see fig. 16.). These are the constellation of Cassiopeia, in which a very brilliant new star appeared in 1572; though soon after it became fainter, and at length disappeared.

If a line, perpendicular to the above line, be next drawn through this constellation, it will conduct, on the one side, to a very beautiful star called Algol, which is in the back of Perseus; and in the other, to the constellation of the Swan (fig. 17.), remarkable by a star of the first magnitude. Near Perseus is the brilliant star of the Goat, called Capella, which is of the first magnitude, and forms part of the constellation of Auriga.

After this, if a straight line be drawn through the last two stars of the tail of the Great Bear, we shall come to the neighbourhood of Arcturus, one of the most brilliant stars in the heavens, which forms part of the constellation of Bootes (fig. 18.).

In this manner we may successively employ the knowledge which we have obtained of the stars of one constellation, to enable us to find out the neighbouring ones. In the article Astronomy we have described the usual instruments for ascertaining the situation, distances, &c. of the heavenly bodies. We must here add an account of an ingenious instrument for finding the rising and setting of the stars and planets, and their position in the heavens. This instrument is called an astrometer, and was originally invented by M. Jurat. An improved astrometer has been lately contrived by Dr David Brewster, and is thus described by him in Nicholson's Journal for May 1807, vol. xvi.

"This astrometer, represented in Plate CCCCLXXI. fig. 19, consists of four divided circumferences. The innermost of these is moveable round the centre A, and is divided into 24 hours, which are again subdivided into quarters and minutes, when the circle is sufficiently large. The second circumference is composed of four quadrants of declination, divided by means of a table of semidurnal arcs, adapted to the latitude of the place. In order to divide these quadrants, move the horary circle, so that 12 o'clock noon may be exactly opposite to the index B; then since the star is in the equator, and its declination 0, when the semidurnal arc is VI hours, the zero of the scales of declination will be opposite VI. VI.; and as the declination of a star is equal to the colatitude of the place, when its semidurnal arc is 0, or when it just comes to the south point of the horizon, without rising above it, the degree of declination at the other extremity of the quadrant, or opposite XII. XII., will be the same as the colatitude of the place, which in the present case is 39°, the latitude of the place being supposed 51° north. The intermediate degrees of declination are then to be laid down from a table of semidurnal arcs, by placing the degree of declination opposite to the arc to which it corresponds; thus the 10° of south declination must stand opposite V° 13' in the afternoon, and VI° 47' in the morning, because a declination of 10° south gives a semidurnal arc of V° 13'.

When the scales of declination are thus completed, the instrument is ready for showing the rising and setting of the stars. For this purpose move the horary circle till the index B points to the time of the star's southing; thus, opposite to the star's declination to the scale C, if the declination is south, or in the scale D if it is north, will be found the time of its rising above the horizon; and the degree of declination on the scales E and F, according as it is south or north, will point out on the horary circle the time of the star setting. If the rising of the star is known from observation, bring its declination to the time of its rising on the circle of hours, and the index B will point out the time at which it passed the meridian; and its declination on the opposite scale will indicate the time when it descends below the horizon. In the same way, from the time of the star setting, we may determine the time when it rises and comes to the meridian.

"The two exterior circles are added to the astrometer, for the purpose of finding the position of the stars and planets in the heavens. The outermost of these is divided into 360 equal parts; and the other, which is a scale of amplitudes, is so formed, that the amplitude of any of the heavenly bodies may be exactly opposite the corresponding degree of declination in the adjacent circle. The degree of south declination, for instance, in the latitude of 51°, corresponds with an amplitude of 15° 20', consequently the 15° of amplitude must be nearly opposite to the tenth degree of declination; so that by a table of amplitudes the other points of the scale may be easily determined. The astrometer is also furnished with a moveable index MN, which carries at its extremities two vertical sights m n, in a straight line with the centre A. The instrument being thus completed, let it be required to find the planet Saturn, when his declination is 15° north, and the time of his southing 9h 30' in the morning. The times of his rising and setting will be found to be 7h 15', and 10h 45', and his amplitude 24° north. Then shift the moveable index till the side of it which points to the centre is exactly above 24° of the exterior circle in the north-east quadrant, and when the line AB is placed in the meridian, the two sight holes will be directed to the point of the horizon where Saturn will be seen at 7h 15', the time of his rising. The same being done in the north-west quadrant, the point of the horizon where the planet sets will likewise be determined. In the same way the position of the fixed stars, and the other planets, may be easily discovered.

"If it is required to find the name of any particular star that is observed in the heavens, place the astrometer due north and south, and when the star is near the horizon, either at its rising or setting, shift the moveable index till the two sights point to the star. The sight of the index will then point out, on the exterior circle, the star's amplitude. With this amplitude enter the third scale from the centre, and find the declination of the star in the second circle. Shift the moveable horary circle till the time at which the observation is made be opposite to the star's declination, and the index B will point to the time at which it passes the meridian. The difference between the time of the star's southing, and 12 o'clock noon, converted into degrees of the equator, and added to the right ascension of the sun if the star comes to the meridian after the sun, but subtracted from it if the star souths before the sun, will give the right ascension of the star. With the right ascension and declination thus found, enter a table of the right ascensions and declinations of the principal fixed stars, and you will discover the name of the star which corresponds with these numbers. The meridian altitudes of the heavenly bodies may always be found by counting the number of degrees between their declination and the index B. The astrometer may be employed in the solution of various other problems; but the application of it to other purposes is left to the ingenuity of the young astronomer."

Sect. IV. Recreations and Contrivances relating to Chemistry.

The experiments which illustrate the principles of Chemistry afford abundant examples of scientific recreations. We cannot here enter on this extensive field, as we have already illustrated the subject very fully under the article Chemistry. In the present section, therefore, we shall do little more than enumerate some of the most striking experiments, referring our readers for for a description and explanation of them, to the above article, and to the principal elementary works on modern chemistry, especially the Epitome of Chemistry, by Dr William Henry (8vo edition), to which the following enumeration will chiefly refer.

Among the more curious and interesting experiments of chemistry, we may notice the combustion produced by wrapping nitrate of copper, slightly moistened, in a sheet of tin foil (Henry, p. 15); the reflection of heat and cold from the surface of concave mirrors (Chemistry, No. 170, or Henry, p. 28); the artificial production of great degrees of cold, so as to freeze mercury and alcohol (Chemistry, 274, or Henry, p. 36); the experiments of Dr Herschel, showing that the sun emits rays which heat without illuminating; others which illuminate without heating; and others which neither illuminate nor heat, but produce evident chemical changes (Chemistry, 172, or Henry, p. 48); the combustion of charcoal, phosphorus, and iron wires, in oxygenous gas, and more especially the combustion of metals in a combined stream of oxygen and hydrogen gases (Henry, p. 60); the explosion of hydrogenous and oxygenous gases, and consequent production of water (Chemistry, 382, and Henry, p. 70); the decomposition of water (Chemistry, 384, or Henry, p. 78); the effect of alkalies and acids in changing the colour of blue vegetable infusions to green and red (Henry, p. 102); the combustion produced by mixing nitric acid with essential oils, or other combustibles (Chemistry, 510, and Henry, p. 151); the combustion produced by throwing metallic particles into oxygenized muriatic acid gas (Henry, p. 181); the deflagration of hyperoxygenized muriate of potash, with phosphorus and other combustibles (Chemistry, 962, et seq., or Henry, p. 187); the production of phosphorated hydrogen gas, by throwing phosphuret of lime into water, (Henry, p. 197); and the decomposition of metallic solutions, so as to procure the metals in a pure or metallic state.

As these last experiments are only incidentally noticed in the article Chemistry, and in Dr Henry's Epitome, we shall here describe two of the most curious instances of what have been called metallic vegetations.

The first of these which we shall notice is called Arbor Diana, the tree of Diana, or the silver tree, as it is produced by decomposing a solution of silver, so that the silver is exhibited in the metallic state, and in an arborecent form. There are two methods of producing the Arbor Diana, one by Homberg, and the other by Beaumé.

According to Homberg's method, an amalgam is to be formed by rubbing a quarter of an ounce of very pure mercury, and half an ounce of fine silver reduced to leaves or filings, by triturating them together in a porphyry mortar, with an iron pestle. This amalgam is to be dissolved in four ounces of the purest nitric acid of a moderate strength, and the solution is to be diluted with about 24 ounces of distilled water. An ounce of this liquor is to be poured into a glass, and a small piece of a similar amalgam of mercury and silver, of the consistence of butter, is to be introduced. Soon after there may be seen rising from the ball of amalgam a multitude of small shining filaments, which visibly increase in number and size, and throw out branches, so as to form a kind of shrub.

Beaumé's method is as follows.—Six parts of a solution of silver in nitric acid, and four of a solution of mercury in the same acid, both in a state of saturation, are to be mixed together, and a small quantity of distilled water to be added. This mixture is to be poured into a conical glass vessel, containing six parts of an amalgam made of seven parts of mercury and one of silver. At the end of some hours there will appear on the surface of the amalgam a metallic precipitate in the form of a vegetation.

The other experiment which we have to describe is that of producing a leaden tree, which, as it may be performed on a large scale, and at a trifling expense, is preferable to the former. The method of effecting this decomposition which we have found most effectual, is the following.

Dissolve in distilled or pure rain water a quantity of acetate of lead (sugar of lead), not sufficient to saturate it; viz. in the proportion of four scruples of the salt to the English pint of water. When the solution has become clear, pour it into a cylindrical vessel, or a glass wine decanter of considerable size, and introduce into it an irregular piece of pure bright zinc, suspended by a string, or a piece of brass wire. In the course of a few hours, the zinc will be covered with a dusky grayish mass, having the appearance of moss, and from this are gradually shot out plates or leaves of a brilliant metallic substance. These will extend themselves towards the bottom of the vessel, and will form trunks, branches, and leaves, so as to resemble a leaden tree suspended by its roots from a mossy hill. In this way we have produced a vegetation that has nearly filled a cylindrical glass-jar of a foot in height, and four or five inches in diameter.

Sect. V. Recreations and Contrivances relating to Electricity.

The subject of electricity, like that of chemistry, affords ample room for scientific recreations. Of these we have given a large collection in our treatise on Electricity, and shall here only enumerate the more striking experiments.

These are, the phenomena produced by paper when excited by caoutchouc or Indian rubber (see Electricity, Part I. Chap. 3.); the experiments of the dancing-figures, dancing-balls, illustrating electrical attraction and repulsion; the electrical orrery, and electrified cotton, illustrating the action of points; the electrified spider; the magic picture, electrical jack, self-moving wheel, spiral tube, luminous conductor, aurora borealis, electrified can and chain, and the thunder-house.

Sect. VI. Amusements and Contrivances relating to Galvanism.

The subject of galvanism, though so nearly allied to electricity, is capable of supplying still more extraordinary experiments, many of which are often witnessed with surprise and admiration. Many of these have been related in our treatise of Galvanism. The most striking of these are, the muscular contractions produced in dead animals, especially those of Aldini (Galvanism, No. 35.); the combustion of charcoal (No. 42.); the deflagration of metals (No. 43.); and the decomposition of water (No. 44.). The experiments on deflagrating the metals, and on other perfect conductors, succeed best with a trough of very large plates of zinc and copper; but experiments on animal bodies, and other imperfect conductors, AMUSEMENTS OF SCIENCE.

Sect. VII. Recreations and Contrivances relating to GEOGRAPHY.

Some of the problems on the globes, and the use of the analemma engraved on Plate CCXXXV. constitute the principal recreations and contrivances relating to geography. To these we shall add only an easy method of approximating to the third problem on the terrestrial globe, (see Geography, No. 67.), namely, having the hour at any place given, to find what hour it is at other places on the earth.

Fig. 20. consists of an outer circle graduated at the edge into 96 equal parts, representing the 24 hours and their quarters, and is marked with two sets of hours from I. to XII. each; the XII. at the top of the figure representing noon, and the XII. at the bottom, midnight. The hours on the right hand are of course those of the evening, and those on the left are morning hours. About the centre of this large circle there is moveable a circular plate, having the figure of a globe in the middle, and having the circumference divided into 360 equal parts, comprehending so many degrees. The diameter marked O, 180, represents the meridian of London. It has the names of the principal places on the earth marked at its edge. Of these London is the principal, and is engraved in capitals. Now, by means of this contrivance, if the time at any one of these places be given, we can find very nearly the time at the other places marked on the inner circle. Thus, suppose it is X. o'clock in the forenoon at London, to find the hour at the other places in the inner circle, place the word LONDON opposite X. on the left hand; then we shall find that at Rome it is a quarter before XI.; at Berlin it is about XI.; at Stockholm about 20 minutes after XI.; at St Petersburg it is noon; at Bombay it is nearly III. in the afternoon; at Pekin it is nearly VI. in the evening; at Botany Bay it is about VIII. in the evening; at New Zealand it is X. at night; at Mexico it is about III. in the morning; at Philadelphia it is V.; and at the Leeward Islands about VI. in the morning.

The Abbé Gaultier has contrived a game, by which he shows how geography may be taught to young people by means of a set of toys. This method appears to be very ingenious, and is much extolled by those who are acquainted with it. As we have not been able to procure the apparatus, we cannot describe the method, according to which the game is conducted.

Mr Edgeworth proposes that geography should be taught to young people by means of a large globe made of silk, marked with the proper meridians and parallels, to be occasionally inflated; and that the places met with in reading should be laid down according to their proper longitudes and latitudes as they occur. See Practical Education, 8vo. vol. ii. p. 239.

Sect. VIII. Recreations and Contrivances relating to GEOMETRY.

From among the numerous problems which have been contrived by geometricians, we shall select a few of the most simple and curious.

To divide a Rectangular Gnomon into four equal and similar Gnomons.

Suppose we have the rectangular figure A, B, C, D, E, F. fig. 21. (A); it is required to divide it into four equal and similar rectangular figures.

On examining this figure, we find that the sides AB and BC are equal, and that if the sides AF and CD were produced, they would, by meeting, complete the square, of which the gnomon is evidently a part. The figure therefore forms three-fourths of a square, and may be divided into three squares, AHFE, EHBG, and DEGC. Each of these squares may in like manner be divided into four, as represented by the dotted lines. Thus we have the whole gnomon divided into 12 equal squares, and it is easy to see how from this division we may form four figures, each constituting three-fourths of a square, and consequently similar to the original figure.

From four unequal Triangles, of which three must be Right-angled, to form a Square.

As the triangles with which this problem is usually performed, are generally made mechanically, by cutting them from a square already formed, we shall for the more easy solution, follow the same method in our first illustration. The square A, B, C, D, fig. 22, is divided into the four triangles E, F, G, H, of which E, F, and G, are evidently right-angled triangles, while H is a scalene triangle.

If these triangles were separate, it would appear very difficult to unite them, so as to form a square. This may be done, however, by reflecting that three of the angles of the square must be formed by the angles of the right-angled triangles, so that these must first be placed as in the figure, while the scalene triangle fills up the vacant space, and by its most acute angle contributes with the most acute angles of the two other large triangles, to form the remaining right angle of the square.

These triangles may be constructed geometrically, without forming them immediately out of a square. For this purpose the following proportions may be employed. Two of the right-angled triangles must have one of the sides about the right angle of the same length in both. The other side about the right angle may be in one, two-thirds of the first side in the same triangle, while in the other it may be one-half. In the third right-angled triangle, one of the sides containing the right angle must, in the present case, be one-third, and the other one-half of the larger side containing the right angle in the two former triangles. Having these three triangles formed, the hypotenuses of which are evidently determined by the length of the sides containing the right angles, we may easily construct the remaining triangle from the hypotenuses of the three triangles already formed, according to the 22d proposition of the first book of Euclid.

To illustrate this by numbers, let us suppose that the side of the square to be formed is = four inches. One of the triangles, as E, will have its longer side = four inches, its shorter = three inches, and its hypotenuse = five inches. The second triangle, as F, will have its longer... To form a Square of five equal Squares.

Divide one side of each of four of the squares, as A, B, C, D, (fig. 23. No 1, and 2) into two equal parts, and from one of the angles adjacent to the opposite side draw a straight line to the point of division; then cut these four squares in the direction of that line, by which means each of them will be divided into a trapezium and a triangle, as seen fig. 23. No 1.

Lastly, arrange these four trapeziums and these four triangles around the whole square E, as seen fig. 23. No 2, and you will have a square evidently equal to the five squares given.

To describe an Ellipsis or Oval geometrically.

The geometrical oval is a curve with two unequal axes, and having in its greater axis two points so situated, that if lines be drawn to these two points, from each point of the circumference, the sum of these two lines will be always the same. See Conic Sections.

Let AB (fig. 24.) be the greater axis of the ellipsis to be described; and let ED, intersecting it at right angles, and divided into two equal parts, be the lesser axis, which is also divided into two equal parts at C; from the point D as a centre, with a radius = AC, describe an arc of a circle, cutting the greater axis in F and f; these two points are what are called the foci. Fix in each of these a pin, or, if you operate on the ground, a very straight peg; then take a thread or a cord, if you mean to describe the figure on the ground, having its two ends tied together, and in length equal to the line AB, plus the distance Ff; place it round the pins or pegs Ff; then stretch it as seen at FGf, and with a pencil, or sharp-pointed instrument, make it move round from B, through D, A, and E, till it return again to B. The curve described by the pencil on paper, or on the ground, by any sharp instrument, during a whole revolution, will be the curve required.

This ellipsis is sometimes called the gardener's oval, because, when gardeners describe that figure, they employ this method.

An oval figure approximating to the ellipse, may be described at one sweep of the compasses, by wrapping the paper on which it is to be described round a cylindrical surface. If a circle be described upon the paper thus placed, assuming any point as a centre, it is evident that when the paper is extended on a plain surface, we shall have an oval figure, the shorter diameter of which will be in the direction of the axis of the cylinder on which the oval was described. This figure, however, is by no means an accurate oval, though it may serve very well as the border of a drawing, or for similar purposes, where great accuracy is not required.

In no science are amusing contrivances more requisite to facilitate the progress of the young pupil than in geometry. We are therefore disposed to regard, with particular attention, every attempt to illustrate and render popular the elements of this science. We may say with Mr Edgeworth, that though there is certainly no royal road to geometry, the way may be rendered easy and pleasant by timely preparations for the journey. Without some previous knowledge of the country, or of its peculiar language, we can scarcely expect that our young traveller should advance with facility or pleasure. Young people should, from their earliest years, be accustomed to what are commonly called the regular solids, viz. the tetrahedron, or regular four-sided solid; the cube, or regular six-sided solid; the octahedron, or regular eight-sided solid; the dodecahedron, or regular 12-sided solid; and the icosahedron, or regular 20-sided solid. These may be formed of card or wood, and Mr Don, an ingenious mathematician of Bristol, has constructed models of these and other mathematical figures, and explained them in an Essay on Mechanical Geometry. Children should also be accustomed to the figures in mathematical diagrams. To these should be added their respective names, and the whole language of the science should be rendered as familiar as possible.

We have lately met with a contrivance for rendering familiar to children the terms of geometry by means of an easy trick. This contrivance is called Le Petit Euclid, and consists of two circular cards, which are represented at fig. 25. Plate CCCCLXXII, and fig. 26. Plate CCCCLXXXIII. Each of these circles is divided into eight compartments, marked 1, 2, 3, 4, 5, 6, 7, 8, and within each compartment are represented several mathematical figures or diagrams. In the centre of the card represented at fig. 25. is the word question, and in that at fig. 26. the word answer. On the latter the figures are distinguished by numbers, referring to their explanations in the following table.

| No | Description | |----|------------------------------| | 1 | The cone. | | 2 | Curve line. | | 3 | Quadrant. | | 4 | A point. | | 5 | Dotted cosine. | | 6 | Dotted secant. | | 7 | Cube. | | 8 | Pyramid. | | 9 | A perpendicular. | | 10 | Acute-angled triangle. | | 11 | Decagon. | | 12 | Hexagon. | | 13 | Square. | | 14 | Right-angled triangle. | | 15 | Sphere. | | 16 | Circular segment. | | 17 | An angle. | | 18 | Dotted length. | | 19 | Parallelopipedon. | | 20 | Dotted radius. | | 21 | A sector. | | 22 | Heptagon. | | 23 | The base. | | 24 | Dotted abscisse. | | 25 | Isosceles triangle. | | 26 | Dotted line subtending an angle. | | 27 | Dotted ordinate. | | 28 | Enneagon, or regular 9-sided figure. | | 29 | The foci of an ellipse. | | 30 | Octagon. | | 31 | Rhomboid. | | 32 | Equilateral triangle. | | 33 | Pentagon. | | 34 | Spindle. | | 35 | A scalene triangle. | | 36 | Parallelogram. | | 37 | Obtuse-angled triangle. | | 38 | Dotted height. | | 39 | Hyperbola. | | 40 | Dotted conjugate diameter. | | 41 | Dotted hypotenuse. | | 42 | Dotted parameter. | | 43 | Rhombus. | | 44 | Dotted diameter. | | 45 | Dotted sine. | | 46 | An obtuse angle. | | 47 | Parabola. | | 48 | Cylinder. | | 49 | External angle. | | 50 | Dotted tangent. | | 51 | Straight line. | | 52 | Ellipsis. | | 53 | Dotted diagonal. | | 54 | Circle. | | 55 | Dotted transverse diameter. | | 56 | Prism. | | 57 | Dotted. |

4 A 2 To form a trick with these cards, the teacher is to hold the question card, and the pupil the answer card. The teacher is to think of a figure in any one of his compartments, and to mention to the pupil both the number of the compartment in the question, and that in the answer card, on which the figure is found. The pupil is then to begin with the first or outmost diagram on the left hand of the compartment in his own card, where the figure thought on is said to be contained, and to count from this down the left-hand row towards the centre, and thence, if necessary, from the outmost diagram on the right hand of the same compartment towards the centre, till his counting reaches the number of the compartment in the question card, where the figure was at first found.

For example, let us suppose that the teacher thinks on a figure in the compartment of his card marked 2, and that he finds the same figure in the compartment of the answer card which is marked 6. The learner beginning to count from the first figure on the left hand in his sixth compartment, viz. that marked 48, comes immediately to the figure marked 30, which is that thought of by the teacher, and proves to be an octagon. Again, if the figure thought on be found in the sixth compartment of the question card, and in the fifth of the answer card, the learner beginning with the figure marked 15, and passing successively to 22, 24, 57, and 49, comes for his sixth place to 36, the figure thought of, which is a parallelogram.

The design of this contrivance is ingenious; but its execution, at least in the copy which we have seen, is extremely faulty. Many of the terms are misprinted, some of them inaccurate, and the explanation scarcely intelligible. We have endeavoured to rectify these defects, and trust we have succeeded.

Sect. IX. Recreations and Contrivances relating to Hydrodynamics.

In our treatise on Hydrodynamics, under which head we have included Hydrostatics and Hydraulics, we have described several entertaining experiments and useful contrivances, and explained them according to hydrostatical principles. Thus, at No. 49 and 50, we have explained the hydrostatic paradox, showing that the pressure on the bottoms of vessels filled with fluids does not depend on the quantity of fluid which they contain, but on its altitude; at No. 51, we have illustrated the upward pressure of fluids by the hydrostatic bellows; at No. 54 and 55, we have explained and illustrated the use of the syphon; at No. 112 and 113, we have shown how capillary attraction and the attraction of cohesion may be illustrated by experiment; in Chap. III. of Part III. we have described the various machines employed for raising water, such as pumps, fire engines, Archimedes's screw, the Persian wheel, &c. and explained their action; at No. 355, we have described Bramah's hydrostatic press, and at No. 356, &c. Method of constructing an hydraulic machine, in which a bird appears to drink up all the water that spouts up through a pipe, and falls into a basin.

Let ABDC, fig. 30, be a vessel, divided into two parts by an horizontal partition EF; and let the upper cavity be divided into two parts also by a vertical partition GH. A communication is formed between the upper cavity BF, and the lower one EC, by a tube LM, which proceeds from the lower partition, and descends almost to the bottom DC. A similar communication is formed between the lower cavity EC, and the upper one AG, by the tube IK, which, rising from the horizontal partition EF, proceeds nearly to the top AB. A third tube, terminating at the upper extremity in a very small aperture, descends nearly to the partition EF, and passes through the centre of a basin RS, intended to receive the water which issues from it. Near the edge of this basin is a bird with its bill immersed in it; and through the body of the bird passes a bent syphon QP, the aperture of which, P, is much lower than the aperture Q. Such is the construction of this machine, the use of which is as follows.

Fill the two upper cavities with water through two holes made for the purpose in the sides of the vessel, and which must be afterwards shut. It may be easily seen that the water in the cavity AG ought not to rise above the orifice K of the pipe KI. If the cock adapted to the pipe LM be then opened, the water of the upper cavity HF will flow into the lower cavity, where it will compress the air, and make it pass through the pipe KI into the cavity AG; in this cavity it will compress the air which is above it, and the air pressing upon it, will force it to spout up through the pipe NO, from whence it will fall down into the basin.

But at the same time that the water flows from the cavity BG, into the lower one, the air will become rarified in the upper part of that cavity; hence, as the weight of the atmosphere will act on the water already poured into the basin through the orifice O of the ascending pipe NO, the water will flow through the bent pipe QSP, into the same cavity BG; and this motion, when once established, will continue as long as there is any water in the cavity AG.

Sect. X. Recreations and Contrivances relating to Magnetism.

The attracting and repelling power of the opposite poles of a magnet, have furnished the writers on scientific recreations with a great variety of entertaining experiments. In our treatise on Magnetism, we have selected a few of these, viz. the communicating piece of money (Magnetism, No. 39); the magnetic table (No. 40); the mysterious watch (No. 41); the magnetic dial (No. 42); and the dividing circles (No. 43). We shall here describe a few other interesting experiments, and refer such of our readers as wish for a greater variety of these amusements, to the original work of Ozanam already mentioned in No. 3, or the Rational Recreations of Dr Hooper, and to the 51st part of the Encyclopédie Methodique, containing Amusements des Sciences, with the plates on Amusements de Physique, in the 42d part of the same work.

The dexterous Painter.

Provide two small boxes, as M and N (fig. 31.) four inches wide, and four inches and a half long. Let the box M be half an inch deep, and N two thirds of an inch. They must both open with hinges, and shut with a clasp. Have four small pieces of light wood (figs. 32, 33, 34, 35.) of the same size with the inside of the fig. 32, 33, box M (fig. 31.), and about one third of an inch thick, 34, 35. In each of these let there be a groove, as AB, EP, CD, GH; these grooves must be in the middle, and parallel to two of the sides. In each of these grooves place a strong artificial magnet, as fig. 36. The poles of these magnets must be properly disposed with regard to the figures that are to be painted on the boards; as is expressed in the plate. Cover the bars with paper to prevent their being seen; but take care, in pasting it on, not to wet the bars, as they will be rusted, and thus their virtue will be considerably impaired. When you have painted such subjects as you choose, you may cover them with a very thin clear glass. At the centre of the box N, place a pivot, (fig. 37.) on which a small circle of pasteboard OPQR (fig. 38.) is to turn quite free. Under this must be a touched needle S. Divide this circle into four parts, which are to be disposed with regard to the poles of the needle, as is expressed in the figure. In these four divisions paint the same subjects as are on the four boards, but reduced to a smaller compass. Cover the inside of the top of this box with a paper, M, (see fig. 31.) in which must be an opening, Fig. 31. D, at about half an inch from the centre of the box, that you may perceive successively, the four small pictures on the pasteboard circle just mentioned. This opening is to serve as the cloth on which the little painter is supposed to draw one of the pictures. Cover the top of the box with a thin glass. Then give the first box to any person, and tell him to place any one of the four pictures in it privately; and when he has closed it, to give it to you, then place the other box over it, when the moveable circle, with the needle, will turn till it comes in the same position with the bar in the first box. It will then appear that the little dexterous painter has already copied the picture that is enclosed in the first box.

The Cylindric Oracle.

Provide a hollow cylinder about six inches high, and three wide, as AB (fig. 39.) Its cover CD must be made to fix on in any position. On one side of this box or cylinder, let there be a groove, nearly of the same length with that side; in which place a small steel bar (fig. 40.) that is strongly impregnated, with the north pole next to the bottom of the cylinder. On the upper side of the cylinder describe a circle, and divide it into ten equal parts, in which are to be written the numbers from 1 to 10, as is expressed in fig. 41. Place a pivot at the centre of this circle, and have ready a magnetic needle. Then provide a bag in which there are several divisions. In each of these divisions put a number of papers, on which the same or similar questions are to be written. In the cylinder put several different answers to each question, and seal them up in the manner of small letters. On each of these letters or answers is to be written one of the numbers of the dial or circle at the top of the box. You are supposed to know the number of answers to each question. Then offer one of the divisions of the bag, (observing which division it is) to any person, and desire him to draw one Next put the top on the cylinder, with that number which is written on the answer directly over the bar. Then desire the person who drew the question to observe the number at which the needle stands, and to search in the box for a paper of the same number, which he will find to contain the answer.

The experiment may be repeated by offering another division of the bag to the same, or another person; and placing the number that corresponds to the answer over the magnetic bar, proceeding as before.

It is easy to conceive several answers to the same question. For example, suppose the question to be,

Is it proper for me to marry?

Ans. 1. While you are young, not yet; when you are old, not at all.

2. Marry in haste, and repent at leisure.

3. No, if you are apt to be out of humour with yourself; for then you will have two persons to quarrel with.

4. Yes, if you are sure to get a good husband (or wife), for that is the greatest blessing of life. But take care you are sure.

5. No, if the person you would marry is an angel; unless you would be content to live with the devil.

Fix a common ewer, as A (fig. 42.) of about 12 inches high, upon a square stand BC; on one side of which there must be a drawer D, of about four inches square, and half an inch deep. In the ewer place a hollow tin cone inverted, as AB (fig. 43.) of about four inches and a half diameter at top, and two inches at bottom; and at the bottom of the ewer there must likewise be a hole of two inches diameter.

Upon the stand, at about an inch distance from the bottom of the ewer, and directly under the hole, place a small convex mirror H, of such convexity that a person's visage, when viewed in it at about 15 inches distance, may not appear above 2½ inches long.

Upon the stand likewise at the point I, place a pivot of half an inch high, on which must be fixed a touched needle RQ, inclosed in a circle of very thin pasteboard OS (fig. 44.) of five inches diameter. Divide this pasteboard into four parts, in each of which draw a small circle; and in three of these circles paint a head; as x, y, z, the dress of each of which is to be different; one, for example, having a turban, another a wig, and the other a woman's cap. Let that part which contains the face in each picture be cut out, and let the fourth circle be entirely cut out, as it is expressed in the figure.

You must observe, that the poles of the needle are to be disposed in the same manner as in the figures.

Next provide four small frames of wood or pasteboard, N° 1, 2, 3, 4, each of the same size with the inside of the drawer. On these frames must be painted the same figures as on the circular pasteboard, with this difference, that there must be no part of them cut out. Behind each of these pictures place a magnetic bar, in the same direction as is expressed in the figures; and cover them over with paper, that they may not be visible. Matters being thus prepared, first place in the drawer the frame N° 4, on which there is nothing painted. Then pour a small quantity of water into the ewer, and desire the company to look into it, asking them if they see their own figures as they are. Then take out the frame N° 4, and give the three others to any one, desiring him to choose in which of those dresses he would appear. Then put the frame with the dress he has chosen in the drawer, and a moment after, the person looking into the ewer will see his own face surrounded with the dress of that picture.

For, the pasteboard circle (divided as above described, into four parts, in three of which are painted the same figures as on three of the boards, and the fourth left blank) containing a magnetic needle, and the four boards having each a concealed magnet; therefore when one of them is put in the drawer under the ewer, the circle will correspond to the position of that magnet, and consequently the person looking into the top of the ewer will see his own face surrounded with the head dress of the figure in the drawer. This experiment, well performed, is highly entertaining. As the pasteboard circle can contain only three heads, you may have several such circles, but must then have several other frames; and the ewer must be made to take off from the stand.

Provide a wooden box, about 13 inches long and 7 inches wide, as ABCD (fig. 45.) The cover of this box should be as thin as possible. Have six small boxes or tablets, about an inch deep, all of the same size and form, as E, F, G, H, I, K, that they may indiscriminately go into similar holes made in the bottom of the large box. In each of these tablets is to be placed a small magnetic bar, with its poles disposed as expressed in the figure. Cover each of these tablets with a thin plate of one of the six following metals, viz. gold, silver, copper, iron, pewter, and lead. Have also a magnetic perspective, at the end of which are to be two circles, one divided into six equal parts, and the other into four (as in fig. 46.), from the centre of which there must be drawn an index N, whose point is to be placed to the north. Therefore, when you are on the side CD of the box, and hold the perspective over any one of the tablets that are placed on the holes E, F, G, so that the index drawn on the circle is perpendicular to the side AB, the needle in the perspective will have its south pole directed to the letter that denotes the metal contained in that tablet. When you hold the perspective over one of the boxes placed in the holes H, I, K, so that the index drawn on the circle is perpendicular to the side CD, the south pole of the needle will, in like manner, express the name of the metal inclosed. If the under side of any of the tablets be turned upwards, the needle will be slower in its motion, on account of the greater distance of the bar. The gold and silver will still have the same direction; but the four other metals will be expressed by the letters on the interior circle. If any one of the metals be taken away, the needle will not then take any of the above directions, but naturally point to the north; and its motion will be much slower. Therefore, give the box to any one, and leave him at liberty to dispose all the tables in what manner and with what side upwards he pleases, and even to take any of them away. Then, by the aid of the perspective, you may tell him immediately the name of the metal on each tablet, and of that which he has taken away.

Construct a round box, ILNM (fig. 47.), of eight or nine inches diameter, and half an inch deep. On its bottom fix a circle of pasteboard, on which draw the central circle A, and the seven surrounding circles B, C, D, E, F, G, H. Divide the central circle into seven equal parts by the lines AB, AC, AD, AE, AF, AG, AH, which must pass through the centres of the other other circles, and divide each of them into two equal parts. Then divide the circumference of each of these circles into 14 equal parts, as in the figure. Have also another pasteboard of the same figure, and divided in the same manner, which must turn freely in the box by means of an axis placed on a pivot, one end of which is to be in the centre of the circle A (see fig. 48.) On each of the seven smaller circles at the bottom of the box, place a magnetic bar, two inches long, in the same direction with the diameters of those circles, and their poles in the situation expressed in the figure. There must be an index O (fig. 48.) like that of the hour hand of a dial, which is to be fixed on the axis of the central circle, and by which the pasteboard circle in the box may be turned about. There must also be a needle P, which must turn freely on the axis, without moving the circular pasteboard. In each of the seven divisions of the central circle write a different question; and in another circle, divided into 12 parts, write the names of the 12 months. In each of the seven circles write two answers to each question, observing that there must be but seven words in each answer, in the following manner. In the first division of the circle G (fig. 47.), which is opposite to the first question, write the first word of the first answer. In the second division of the next circle, write the second word, and so on to the last word, which will be in the seventh division of the seventh circle.

In the eighth division of the first circle, write the first word of the second answer; in the ninth division of the second circle, write the second word of the same answer, and so on to the 14th division of the seventh circle, which must contain the last word of that answer. The same must be done with all the seven questions, and to each of them must be assigned two answers, the words of which must be dispersed through the seven circles. At the centre of each of these circles place a pivot, and have two magnetized needles, the pointed end of one of which must be north, and the other south, QR (fig. 48.) Now, the index of the central circle being directed to any one of the questions, if you place one of the two magnetic needles on each of the seven lesser circles, they will fix themselves according to the direction of the bars on the correspondent circles at the bottom of the box, and consequently point to the seven words which compose the answer. If you place one of the other needles on each circle, it will point to the words that are diametrically opposite to those of the first answer; the north pole being in the place of the south pole of the other. Therefore, present this planetarium to any person, and desire him to choose one of the questions there written; and then set the index of the central circle to that question; putting one of the needles on each of the seven circles, turn it about; and when they all settle, they will point to the seven words that compose the answer. The two answers may be one favourable and the other unfavourable, and the different needles will serve to diversify the answers when the experiment is repeated.

There may be also a moveable needle to place against the names of the months; and when the party has fixed upon a question, place that needle against the month in which he was born, which will give the business a more mysterious air. On the centre of the large circle may be the figure of the sun; and on each of the seven smaller circles one of the characters of the principal planets. This experiment, well executed, is one of the most entertaining produced by magnetism.

Provide a box XY (fig. 49.), 18 inches long, nine wide, and two deep, the top of which is to slide off and on at the end Y. Towards the end X, describe a circle of six inches diameter, around which are to be fixed six small vases of wood or ivory, of an inch and a half high, and to each of them there must be a cover. At the end Y place an egg B, of ivory or some such material, about three inches and a half high, with a cover that shuts by a hinge, and fastens with a spring. It must be fixed on the stand C, through which, as well as the bottom of the egg, and the part of the box directly underneath, there is a hole of one-third of an inch diameter. In this cavity place an ivory cylinder F, that can move freely, and which rises or falls by means of the spring R. You must have a thin copper basin, A, of six inches diameter, which is to be placed on the centre of the circle next X, and consequently in the middle of the six vases. Let a proper workman construct the movement expressed by fig. 50., which is composed of a quadrant G, that has 16 teeth, and is moveable about an axis in the stand H, that has an elbow, by which it is screwed to the bottom of the box at L. To the quadrant there must be joined the straight piece K. The horizontal wheel M has 24 teeth, and is supported by the piece S, which is screwed to the end of the box next Y. On the axis of this wheel place a brass rod OP, five inches long; and at the part O place a large bar or horse shoe, of a semicircular form, and about two inches and a half diameter, strongly impregnated. The steel rod V, takes at one end the teeth of the quadrant G, by the pinion F, and at the other end the wheel M, by the perpendicular wheel N, of 30 teeth; the two ends of this rod are supported by the two stands that hold the other pieces. Under the piece K, that joins to the quadrant, must be placed the spring R, by which it is raised, and pushes up the cylinder that goes through the stand C into the egg. You must also have six small cases as Y, Y, Y, Y, Y, Y. These must be of the same circumference with the cylinder in the stand, and round at their extremities; their length must be different, that when they are placed in the egg, and the lower end enters the hole in which is the cylinder, they may thrust it down more or less, when the top of the egg against which they press is fastened down; and thereby lower the bar that is fixed to the end of the quadrant, and consequently by means of the pinion Z and wheels NM turn the horse shoe that is placed upon the axis of the last wheel. The exact length of these cases can be determined by trials only; but these trials may be made with round pieces of wood. In each of these cases place a different question, written on a slip of paper and rolled up, and in each of the vases put the answer to one of the questions; as you will know, by trials, where the magnetic bar or horse shoe will stop. Lastly, Provide a small figure of a swan, of cork or enamel, in which fix a touched needle, of the largest size of those commonly used in sewing.

Being thus prepared, offer a person the six cases, and desire him to choose any one of them, and conceal the rest, or give them to different persons. He is then to open his case, read the question to himself, and return the case, after replacing the question. You then put Mechanics the case in the egg, and placing the swan in the basin on the water, you tell the company she will soon discover in which of the vases the answer is contained. The same experiment may be repeated with all the cases.

Sect. XI. Recreations and Contrivances relating to Mechanics.

In the article Mechanics, we have described some recreations of the lighter experiments by which the principles of that science are illustrated, and have explained the construction and action of several ingenious and useful machines. In particular, we have described the windmill at No. 428.; several carriages that are capable of moving without horses, at Nos. 455, 456, 457, and 458.; a carriage that cannot be overturned, at No. 459.; Atwood's machine for illustrating the doctrines of accelerated and retarded motion, at No. 460.; a machine for illustrating the theory of the wedge, at 467.; a machine for illustrating the effects of the centrifugal force in flattening the poles of the earth, at 468.; a machine for trying the strength of materials, at 469.; a machine in which all the mechanical powers are united, 470.; Fiddler's balance at 471.; an improvement in the balance, 472.; a machine for showing the composition of forces, at 473.; Smeaton's machine for experiments on windmill sails, at 474.; Smeaton's machine for experiments on rotatory motion, at 475.; Prony's condenser of forces, at 476.; a portable stone crane for loading and unloading carts, with several other cranes, at 477, 478, 479, 480, and 482.; Bramah's jib for cranes, at 481.; the common worm-jack, at 483.; a portable loading and unloading machine, at 484.; Vailloue's pile engine, at 485.; and Bunce's pile engine at 486. We have also, in the articles Androïdes and Automaton, described several ingenious contrivances for producing various animal motions by means of machinery, or what is commonly called clock-work, especially M. Vaucanson's flute-player, and M. Kempell's chess-player.

In the present article we shall first present our readers with a few mechanical contrivances that may properly be called amusing; shall give the substance of an ingenious paper on the philosophical uses of a common watch; and shall conclude the section with an account of Edgeworth's Panorganon, or universal machine for illustrating the effect of the mechanical powers.

To support a pail of water by a stick, only one half of which, or less, rests on the edge of a table.

Let AB (fig. 51.) be the top of the table, and CD the stick that is to support the bucket. Convey the handle of the bucket over this stick, in such a manner, that it may rest on it in an inclined position, as HI, and let the middle of the bucket be a little within the edge of the table. That the whole apparatus may be fixed in this situation, place another stick as GFE, with one end, G, resting against the side of the bucket at the bottom, while its middle, F, rests against the opposite edge of the bucket at the top, and its other extremity, E, rests against the first stick CD, in which a notch should be cut to retain it. By these means the bucket will remain fixed in that situation, without inclining to either side; and if not already full of water, it may be filled with safety, for its centre of gravity being in the vertical line passing through the point H, which meets with the table, it is evident that the pail is in the same circumstances as if it were suspended from that point of the table where the vertical line would meet the edge. It is also evident that the stick cannot slide along the table, nor move on its edge, without raising the centre of gravity of the bucket, and of the water which it contains. The heavier it is, therefore, the more stable will be its position.

According to this principle, various other tricks of the same kind, which are generally proposed in books on mechanics, may be performed. For example, provide a bent hook DGF, as seen at the opposite end of the same figure, and insert the part, FD, in the pipe of a key at D, which must be placed on the edge of a table: from the lower part of the hook suspend a weight G, and dispose the whole in such a manner that the vertical line GD may be a little within the edge of the table. When this arrangement has been made, the weight will not fall; and the case will be the same with the key, which, had it been placed alone in that situation, would perhaps have fallen; and this resolves the following mechanical problem, proposed in the form of a paradox: A body having a tendency to fall by its own weight, how to prevent it from falling, by adding to it a weight on the same side on which it tends to fall.

To construct a figure which, without any counterpoise, shall always raise itself upright, and preserve or regain that position, however it may be disturbed.

Let a figure, resembling a man, ape, &c. be formed of some very light substance, such as the pith of elder, which is soft, and can easily be cut into any required figure. Then provide a hemispherical base of some very heavy substance, such as lead. The half of a leaden bullet made very smooth on the convex part will be very proper for this purpose. If now the figure be cemented to the plain part of this hemisphere; in whatever position it may be placed it will rise upright as soon as it is left to itself; for the centre of gravity of its hemispherical base being in the axis, tends to approach the horizontal plain as much as possible. This it cannot attain till the axis becomes perpendicular to the horizon; but as the small figure, on account of the disproportion between its weight and that of the base, scarcely deranges the latter from its place, the natural perpendicularity of the axis is easily regained in all positions.

According to this principle were constructed the small figures called Prussians, which some years ago constituted one of the amusements of young people. They were formed into battalions, and being made to fall down by drawing a rod over them, immediately started up again as soon as it was removed. On the same principle screens have been constructed, so as to rise of themselves when they happen to be thrown down.

To make a body ascend along an inclined plane in consequence of its own gravity.

Let a body be constructed of wood, ivory, or some such material, consisting of two equal right cones united by by their bases, as EF (fig. 52.) and let two straight, flat, smooth rulers, as A.B., CD, be so placed as to join in an angle at the extremities A, C, and diverge towards BD, where they must be a little elevated, so that their edges may form a gently inclined plane. If now the double cone be placed on the inclining edges, pretty near the angle, it will roll towards the elevated ends of the rulers, and thus appear to ascend; for the parts of the cone that rest on the rulers, growing smaller as they go over a larger opening, and thus letting down the larger part of the body, the centre of gravity descends, though the whole body seems to rise along the inclined plane.

To insure the success of this experiment, care must be taken that the height of the elevated ends of the rulers be less than the radius of the circle forming the base of the cones.

Explanation of the upright Position preserved in a Top or Tee-totum while it is revolving.

This is explained on the principle of centrifugal force, which teaches us that a body cannot move in a circular direction, without making an effort to fly off from the centre; so if it be confined by a string made fast in that centre, it will stretch the string in proportion as the circular motion is more rapid. See Dynamics. It is this centrifugal force of the parts of the top or tee-totum that preserves it in an upright position. The instrument being in motion, all its parts tend to fly off from the axis, and that with greater force the more rapid the revolution. Hence it follows that these parts are like so many powers acting in a direction perpendicular to the axis. As, however, they are all equal, and pass rapidly round by the rotation, the instrument must be in equilibrio on its point of support, or the extremity of the axis on which it turns. The motion is gradually impeded by the friction of the axis against the surface on which it moves; and we find that the instrument revolves for a longer time, in proportion as this friction is avoided by rendering very smooth the surfaces of the axis, and the plane on which it moves.

There are many observations and experiments in different departments of science, the accuracy of which depends greatly, and in some cases entirely, on the accurate measurement of minute portions of time; such, for instance, as the determination of the velocity of sound, the nature of the descent of falling bodies, the measure of the sun's diameter, the distance of two contiguous, or at least apparently contiguous, heavenly bodies taken at their passage over the meridian, and the distance of places from the difference of the velocity of light and sound. A pendulum for swinging seconds has usually been employed for these and similar purposes, and in an observatory is found to be very convenient; but a watch, by being more portable, is calculated to be more general in its application, and will measure smaller portions of time than any other instrument that has been invented. Besides, it possesses this peculiar advantage, that in all situations its beats may be counted by the ear, at the same time that the object of observation is viewed by the eye, so that no loss is incurred, as must inevitably happen, when the eye is used to view both the object and pendulum in succession, should this latter be ever so quick. But it will be objected here, that few watches measure time accurately, and that, from the mechanic different constructions of watches, the times corresponding to their beats vary in a very considerable degree. We allow these objections to be true, and conceive that to them the reason may be attributed, why the beat of a watch is not generally applied as the measure of the lowest denomination of subdivisions of time. We shall therefore endeavour to obviate these objections, by showing how any tolerably good watch, whatever be its construction, may be applied with advantage to many philosophical purposes.

We must, in the first place, consider, that the portions of time which we propose to measure by a watch are small, and those to be counted not by a second-hand, as is the custom with medical men, but altogether by the beats; in which case, if the watch be not liable to lose or gain time considerably in a day, the error in the rate of going will be extremely minute in the time corresponding to any number of beats that the memory can retain, or that the purposes to which we propose the application to be made will require; and even if the error in the rate of going be considerably so as to amount to several minutes in a day, as it is uniform, it may easily be allowed for by a correction. Thus, if the error were five minutes per day, the allowance would be upwards of \( \frac{1}{360} \)th part. Hence the first objection, which relates to the error occasioned by the rate of going of any watch, will constitute no real obstacle to its application in the ascertaining of small portions of time, provided a sudden change of temperature be avoided at the time of using it; for it will be necessary that the rate of going be estimated when the temperature is the same, as when the watch is used for philosophical purposes; so that if it is usually worn in the pocket, it may be held in the hand to the ear, but if it be hanging in a room or in the open air where the rate of going is ascertained, it must be hung near the ear, under similar circumstances, where any observation is intended to be made by it.

As to the other objection, which applies to the variation in the lengths of the beats of two different watches, owing to the difference of their constructions, though they indicate hours and minutes alike, it may be very readily removed. All common watches have the same number of wheels and pinions, which are known by the same names, and placed, no matter how variously, so as to act together without interruption; but all watches have not their corresponding wheels and pinions divided into the same number of teeth and spaces; and from this circumstance the beats of different watches differ from each other. As the rate of going of a watch is regulated by the lengthening or shortening of a spring, without any regard being had to the numbers which compose the teeth of the wheels and pinions, a great latitude is allowable in the calculation of those numbers; of which the different makers avail themselves according as the numbers on the engines they use for cutting the teeth require; but whatever the numbers may be of which the wheel-work consists, if we divide double the product of all the wheels, from the centre wheel to the crown wheel inclusively, by the product of all the pinions with which they act, the quotient will invariably be the number of beats of the watch in question in one hour; and again, if we divide this quotient by 3600, the number of seconds in an hour, this latter quotient will Mechanic will be the number of beats in every second, which may be carried to any number of places in decimals, and be copied upon the watch-paper for inspection whenever it may be wanted.

When any particular watch is cleaned, the workman may be directed to count, and return in writing, the numbers of the centre wheel, the third wheel, the contrate wheel, and the crown (balance) wheel, and also of the three pinions which they actuate, respectively, from which the calculation of the length of a beat is easily made by the rule just given, and, when once made, will apply in all instances where that individual watch is used. It may be remarked here, that no notice is taken of the wheels and pinions which constitute the dial work, or of the great wheel and pinion with which it acts; the use of the former of these is only to make the hour and minute hands revolve in their respective times, and may or may not be the same in all watches; and the use of the latter, the great wheel and its pinion, is to determine in conjunction with the number of spirals on the fusee, the number of hours that the watch shall continue to go, at one winding up of the chain round the barrel of the mainspring. All these wheels and pinions, therefore, it will be perceived, are unnecessary to be taken into the account in calculating the beats per hour. The reason why double the product of the wheels specified is taken in the calculation is, that one tooth of the crown wheel completely escapes the pallets at every two beats or vibrations of the balance.

A few examples of the numbers exhibited in the wheels of some common watches will render the general rule which we have laid down more intelligible. We shall take four examples, the first expressing the numbers of a common watch, as given by Mr Emmerson. In this watch the centre wheel contained 54 teeth, its pinion 6 teeth; the third wheel 48 teeth, its pinion 6; the contrate wheel 48 teeth, and its pinion 6; the crown wheel 15 teeth, besides 2 pallets. Now, we have

\[ \frac{54 \times 48 \times 48 \times 15 \times 2}{3732480} = \text{double the product of the specified wheels}, \]

and \( \frac{6 \times 6 \times 6}{216} = \text{the product of the specified pinions}; \)

also \( \frac{3732480}{216} = 17280 \) are the number of beats in an hour: accordingly Mr Emmerson says that this watch makes about 4.75 beats in a second. The number of spirals on the fusee is 7; therefore \( \frac{7 \times 48}{12} = 28 \), the number of hours that the watch will go at one winding up: likewise the dial work \( \frac{40 \times 36}{10 \times 12} = \frac{1440}{120} = 12 \) shews that whilst the first driving pinion of 10 goes 12 times round, the last wheel of 36 goes only once; whence the angular velocity of two hands carried by their hollow axles are to each other as 12 to 1.

In a second example the numbers in the calculation of beats per second will be as follows, \( \frac{60 \times 60 \times 60 \times 13 \times 2}{5616000} = \text{double the product of the wheels}, \)

and \( \frac{8 \times 8 \times 6}{384} = \text{the product of the pinions}; \)

then \( \frac{5616000}{384} = 14625 = \text{the number of beats in an hour}, \)

and \( \frac{14625}{3600} = 4.0625, \) the number of beats per second.

In a third watch the numbers require the following calculation, \( \frac{54 \times 52 \times 52 \times 13 \times 2}{3796416} = \text{for dou-} \)

ble the product of the wheels, and \( \frac{6 \times 6 \times 6}{216} = 216, \) the product of the pinions: therefore \( \frac{3796416}{216} = 17576, \)

the beats in an hour, and \( \frac{17576}{3600} = 4.882, \) beats per second.

In a fourth, \( \frac{56 \times 51 \times 50 \times 13 \times 2}{3712800} = \text{double the product of the wheels}, \)

and \( \frac{6 \times 6 \times 6}{216} = 216, \) the product of the pinions, consequently \( \frac{3712800}{216} = 17188, \)

beats in an hour, which, divided by 3600, gives 4.7746 for the beats per second.

It remains now to adduce an example or two of the mode of applying the beats of a watch to philosophical purposes.

For one example let us suppose with Dr Herschel, that the annual parallax of the fixed stars may be ascertained by observing how the angle between two stars, very near to each other, varies in opposite parts of the year. For the purpose of determining an angle of this kind, where an accurate micrometer is wanting, let a telescope that has cross wires be directed to the stars when passing the meridian, in such a manner that the upright wire may be perpendicular to the horizon, and let it remain unmoved as soon as the former of the two stars is just coming into the field of view; then fixing the eye to the telescope and the watch to the ear, repeat the word one along with every beat of the watch before the star is arrived at the perpendicular hair, until it is in conjunction with it, from which beat go on two, three, four, &c. putting down a finger of either hand at every twenty till the second star is seen in the same situation that the leading one occupied at the commencement of the counting; then, these beats divided by the beats per second, marked on the watch-paper, will give the exact number of uncorrected seconds, by which the following star passes later over the meridian than the leading one. When these seconds and parts of a second are ascertained, we have the following analogy for determining the angle, which includes also the correction, namely,—as 23° 56' 4", 098 (the length of a sidereal rotation of the earth), plus or minus the daily error in the rate of going, are to 360°; so is the number of observed seconds of time, to the quantity of the horizontal angle required. The watch is here supposed to be regulated to show solar time; but if it should be regulated exactly for sidereal time, instead of 23° 56' 4" 098, we must use exactly 24 hours in the analogy.

As a second instance, let it be required to ascertain the distance of the nearer of two electrified clouds from an observer when there are successive peals of thunder to be heard: a little time before the expected repetition of a flash of lightning place the watch at the ear, and commence the numbering of the beats at the instant the flash is seen, as before directed, and take care to cease with the beginning of the report. Then the beats converted into seconds, with the proportional part of the daily error added or subtracted, will give the difference of time taken up by the motion of the light and sound. If, lastly, we suppose light to be instantaneous at small distances, the distance of the nearer cloud will be had by multiplying the distance that sound is known to pass through in a second by the number of observed seconds obtained from the beats that were counted. Many more instances might be pointed out, in which the beats of a good watch would be extremely serviceable in the practical branches of philosophy; but the occurrence of such instances will always point out the propriety of the application, when it is once known and practised.

We shall therefore mention only one further advantage which seems peculiar to this mode of counting a limited number of seconds by a watch, namely, that it is free from any error which might arise from the graduations of a dial-plate, or unequal divisions in the teeth of wheels and pinions, where the seconds are counted by a hand.

In order to introduce this method of measuring small portions of time accurately, it is desirable that a watch be constructed so as to make an exact number of beats per second without a fraction, for then the reduction of beats into seconds would be more readily made. With the view of promoting this object, Mr William Pearson has calculated numbers for a watch, which will produce the desired effect, and which, as they are equally practicable with those in use, we shall here insert. By the method of arrangement already given, the numbers proper for such a watch, as will indicate hours, minutes, and seconds, by three hands, and also make just four beats per second, will stand thus, viz.

50 great wheel 10—60 centre wheel 8—64 third wheel 8—48 contrate wheel 6—15 crown wheel 2 palats.

Dial work as usual. Six spirals on the fusee—to go 30 hours.

By the preceding general rule for ascertaining the beats per second in any watch, the calculation of these numbers willbethus: $60 \times 64 \times 48 \times 15 \times 2 = 5529600$, and $8 \times 8 \times 6 = 384$; then $\frac{5529600}{384} = 14400$ the beats in an hour, and $\frac{14400}{3600} = 4$ exactly, for the beats per second; which agreement with the rule is a proof of the accuracy of the numbers.

Before we conclude this subject, we may caution medical gentlemen against an imposition which is practised by some watchmakers in the sale of watches with second hands. It is no uncommon thing with some of these workmen to put a second hand with a stop and an appropriate face to a watch, the wheel work of which is not calculated for indicating seconds. The second watch, the numbers of which are set down a little above, was of this kind. In this watch that part of the train which lay between the axle of the centre wheel and that of the contrate wheel on which the hands are placed, viz. $\frac{60}{8} \times \frac{60}{8} = 56.25$, instead of 60, so that 3.75 seconds are deficient in every minute, a deficiency which in 16 minutes is equal to a whole revolution of the second hand.

For the purpose of bringing to our assistance the sense of feeling, in teaching the use of the mechanic powers, Mr Edgeworth has constructed the following apparatus, to which he gives the name of panorganon.

It is composed of two principal parts, a frame for containing the moving machinery, and a capstan or windlass erected on a sill or plank that is sunk a few inches into the ground. By these means, and by braces or props, the frame is rendered steady. The cross rail or transom is strengthened by braces, and a king-post to make it lighter and cheaper. The capstan consists of an upright shaft, on which are fixed two drums (about either of which a rope may be wound), and two arms or levers, by which the capstan may be turned round. There is also an iron screw fixed round the lower part of the shaft, to show the properties of the screw as a mechanic power. The rope which goes round the drum, passes over one of the pulleys near the top of the frame, and below another pulley near the bottom. As two drums of different sizes are employed, it is necessary to have an upright roller, for conducting the rope to the pulleys in a proper direction, when either of the drums is used. Near the frame, and in the direction in which the rope runs, is made a platform or road of deal boards, one board in breadth and 20 or 30 feet long, on which a small sledge loaded with different weights may be drawn.

Fig. 53. represents the principal parts of this apparatus. FF, the frame; b, b, braces to keep the frame steady; a, a, angular braces, and a king post to strengthen the transom; S, a round taper shaft, strengthened above and below the mortises, through which the levers pass, with iron hoops; L, d, two arms or levers by which the shaft, &c. are to be moved round; DD, the drums, which are of different circumferences; R, the roller to conduct the rope; P, the pulley, round which the rope passes to the larger drum; P, another pulley to answer to the smaller drum; P, a pulley through which the rope passes when experiments are made with levers, &c.; P, another pulley through which the rope passes when the sledge is used; Ro, the road of deal boards for the sledge to move on; Sl, the sledge with pieces of hard wood attached to it to guide it on the road.

As this machine is to be moved by the force of men or children, and as this force varies, not only with the proportions of strength and weights of each individual, but also accordinging to the different manner in which that strength or weight is applied, we must in the first place establish one determinate mode of applying human force to the machine, as well as a method of determining the relative force of each individual, whose strength is employed in setting it in motion.

1. To estimate the force with which a person can draw horizontally by a rope over his shoulder.

Hang a common long scale-beam (without scales or chains) from the top or transom of the frame, so that one end of it may come within an inch of one side or post of the machine. Tie a rope to the hook of the scale-beam, where the chains of the scale are usually hung, and pass it through the pulley P, which is about four feet from the ground; let the person pull this rope from 1 towards 2, turning his back to the machine, and pulling the rope over his shoulder (fig. 58.) As the pulley may be either too high or too low to permit the rope to be horizontal, the person who pulls it should be placed 10 or 15 feet from the machine, which will lessen the angular direction of the cord, and thus diminish the inaccuracy of the experiment. AMUSEMENTS OF SCIENCE.

Hang weights to the other end of the scale-beam, till the person who pulls can but just walk forward, pulling fairly without knocking his feet against anything. This weight will estimate the force with which the person can draw horizontally by a rope over his shoulder.

Let a child who tries this, walk on the board with dry shoes; let him afterwards chalk his shoes, and then try it with his shoes soaped. He will find that he can pull with different degrees of force in these different circumstances. When he makes the following experiments, however, let his shoes be always dry, that he may always exert the same degree of force.

2. To show the force of the three different kinds of Levers.

The lever L (fig. 54.) is passed through a socket (fig. 55.) in which it can be shifted from one of its ends towards the other, so that it may be fastened, at any place by the screw of the socket. This socket has two gudgeons, upon which both the socket and the lever which it contains can turn. The socket and its gudgeons can be fitted out of the hole in which it plays between the rails RR (fig. 54.), and may be put into other holes at RR, (fig. 57.).

Hook the cord that comes over the person's shoulder to the end I, of the lever L. Loop another rope to the other end of this lever, and let the person pull as before. Perhaps it should be pointed out that the person must walk in a direction contrary to that in which he walked before, viz. from 1 towards 3 (fig. 53.). The height to which the weight ascends, and the distance to which the person advances, should be carefully marked and measured; and it will be found, that he can raise the weight to the same height, advancing through the same space as in the former experiment. In this case, as both ends of the lever moved through equal spaces, the lever only changed the direction of the motion, and added no mechanical power to the direct strength of the person.

3. Shift the lever to its extremity in the socket; the middle of the lever will now be opposite to the pulley (fig. 56.); hook to it the rope that goes through the pulley P 3, and fasten to the other end of the lever the rope by which the person is to pull. This will be a lever of the second kind, as it is called in books of mechanics; in using which, the resistance is placed between the centre of motion or fulcrum and the moving power. He will now raise double the weight that he did in experiment 2, and he will advance through double the space.

4. Shift the lever, and the socket which forms the axis, (without shifting the lever from the place in which it was in the socket in the last experiment) to the holes that are prepared for it at RR, (fig. 57.). The free end of the lever E will now be opposite to the rope, and to the pulley (over which the rope comes from the scale beam). Hook this rope to it, and hook the rope by which the person pulls to the middle of the lever. The effect will now be different from what it was in the last two experiments; the person will advance only half as far, and will raise only half as much weight as before. This is called a lever of the third kind.

The experiments upon levers may be varied at pleasure, increasing or diminishing the mechanical advantage, so as to balance the power and the resistance, to accustom the learners to calculate the relation between the power and the effect in different circumstances, always pointing out that whatever excess there is in the power, or in the resistance, is always compensated by the difference of space through which the power passes.

The experiments which we have mentioned are sufficiently satisfactory to a pupil, as to the immediate relation between the power and the resistance; but the different spaces through which the power and the resistance move when one exceeds the other, cannot be obvious, unless they pass through much larger spaces than levers will permit.

5. To show the different space through which the power and resistance move in different circumstances.

Place the sledge on the farthest end of the wooden road (fig. 53.): fasten a rope to the sledge, and conduct it through the lowest pulley P 4, and through the pulley P 3, so that the person may be enabled to draw it by the rope passed over his shoulder. The sledge must now be loaded, till the person can but just advance with short steps steadily upon the wooden road; this must be done with care, as there will be but just room for him beside the rope. He will meet the sledge exactly on the middle of the road, from which he must step aside to pass the sledge. Let the time of this experiment be noted. It is obvious that the person and the sledge move with equal velocity, there is therefore no mechanical advantage obtained by the pulleys. The weight that he can draw will be about half a hundred, if the weight be about nine stones; but the exact force with which the person draws is to be known by experiment 1.

6. To the largest drum (fig. 53.) fasten a cord, and pass it through the pulley P downwards, and then through the pulley P 4, to the sledge placed at the end of the wooden road which is farthest from the machine. Let the person, by a rope fastened to the extremity of one of the arms of the capstan, and passed over his shoulder, draw the capstan round; he will wind the rope round the drum, and draw the sledge upon the road. To make the sledge advance 24 feet upon its road, the person must have walked circularly 144 feet which is six times as far, and he will be able to draw about three hundred weight, which is six times as much as in the last experiment.

It may now be pointed out, that the difference of space, passed through by the power in this experiment, is exactly equal to the difference of weight which the person could draw without the capstan.

7. Let the rope be now attached to the smaller drum; the person will draw nearly twice as much weight upon the sledge as before; and will go through double the space.

8. Where there is a number of persons, left five or six of them, whose power of drawing (estimated as in experiment 1.) amounts to six times as much as the force of the person at the capstan, pull at the end of the rope which was fastened to the sledge; they will balance the force of the person at the capstan; either they or he, by a sudden pull may advance, but if they pull fairly, there will be no advantage on either side. In this experiment the rope should pass through the pulley P 3, and should be coiled round the larger drum. And it must also AMUSEMENTS OF SCIENCE.

also be observed, that in all experiments upon the motion of bodies, on which there is much friction, as where a sledge is employed, the results are never so uniform as under other circumstances.

9. Upon the pulley we shall say little, as it is in every body's hands, and experiments may be tried upon it without any particular apparatus. It should, however, be distinctly inculcated, that the power is not increased by a fixed pulley. For this purpose, a wheel without a rim, or, to speak with more propriety, a number of spokes fixed in a nave, should be employed, (fig. 61.). Pieces like the heads of crutches should be fixed at the ends of these spokes, to receive a piece of girthweb, which is used instead of a cord, because a cord would be unsteady; and a strap of iron with a hook to it should play upon the centre, by which it may sometimes be suspended, and from which at other times a weight may be hung.

Let this skeleton of a pulley be hung by the iron strap from the transom of the frame; fasten a piece of web to one of the radii, and another to the end of the opposite radius. If two persons of equal weight pull these pieces of girthweb, they will balance each other; or two equal weights hung to these webs, will be in equilibrium. If a piece of girthweb be put round the aftermost radius, two equal weights hung at the ends of it will remain immoveable; but if either of them be pulled, or if a small additional weight be added to either, it will descend, and the web will apply itself successively to the ascending radii, and will detach itself from those which are descending. If this movement be carefully considered, it will be perceived that the web, in unfolding itself, acts in the same manner upon the radii, as two ropes would, if they were hung to the extremities of the opposite radii in succession. The two radii which are opposite, may be considered as a lever of the first kind, when the centre is in the middle of the lever: as each end moves through an equal space, there is no mechanical advantage. But if this skeleton-pulley be employed as a common block or tackle, its motions and properties will be entirely different.

10. Nail a piece of girthweb to a post, at the distance of three or four feet from the ground; fasten the other end of it to one of the radii (see fig. 61.). Fasten another piece of web to the opposite radius, and let a person hold the skeleton-pulley suspended from the web; hook weights to the strap that hangs from the centre. The end of the radius to which the fixed girthweb is fastened will remain immovable; but if the person pulls the web which he holds in his hand upwards, he will be able to lift nearly double the weight which he can raise from the ground by a simple rope without the machine, and he will perceive that his hand moves through twice as great a space as the weight descends: he has therefore the mechanical advantage, which he would have by a lever of the second kind. Let a piece of web be put round the under radii, let one end of it be nailed to the post, and the other be held by the person, and it will represent the application of a rope to a moveable pulley; if its motion be carefully considered, it will appear that the radii, as they successively apply themselves to the web, represent a series of levers of the second kind.

Upon the wooden road lay down a piece of girthweb; nail one end of it to the road; place the pulley upon the web at the other end of the board; and bring-

ing the web over the radii, let the person taking hold of it, draw the loaded sledge fastened to the hook at the centre of the pulley; he will draw nearly twice as much in this manner as he could without the pulley.

Here the web lying in the road shows more distinctly, that it is quiescent where the lowest radius touches it; and if the radii, as they tread upon it, are observed, their points will appear at rest, while the centre of the pulley will proceed as fast as the sledge, and the top of each radius successively will move twice as far as the centre of the pulley and the edge.

If a person holding a stick in his hand, observes the relative motions of the top and the middle, and the bottom of the stick, whilst he inclines it, he will see that the bottom of the stick has only half the motion of the top. This property of the pulley has been considered more at large, because it elucidates the motion of a wheel rolling upon the ground; and it explains a common paradox, which appears at first inexplicable, the bottom of a rolling wheel never moves upon the road. This is asserted only of a wheel moving over hard ground, which, in fact, may be considered rather as laying down its circumference upon the road, than as moving upon it.

11. The inclined Plane and the Wedge.

The inclined plane is to be next considered. When a heavy body is to be raised, it is often convenient to lay a sloping artificial road of planks, upon which it may be pushed or drawn. This mechanical power, however, is but of little service without the assistance of wheels or rollers; we shall therefore speak of it as it is applied in another manner, under the name of the wedge, which is in fact a moving inclined plane; but if it be required to explain the properties of the inclined plane by the panorgamon, the wooden road may be raised and set to any inclination required, and the sledge may be drawn upon it as in the former experiments.

Let one end of a lever, N (fig. 59.), with a wheel at Fig. 59., one end of it, be hinged to the post of the frame, by means of a gudgeon driven or screwed into the post. To prevent this lever from deviating sideways, let a slip of wood be connected with it by a rail, which shall be part in the lever, but which may move freely in a hole in the rail. The other end of this slip must be fastened to a stake driven into the ground at three or four feet from the lever, at one side of it, and towards the end in which the wheel is fixed (fig. 62.), in the same manner as the treadle of a common lathe is managed, and as the treadle of a loom is sometimes guided.

12. Under the wheel of this lever place an inclined plane (fig. 59.) on the wooden road, with rollers under it, to prevent friction; fasten a rope to the foremost end of the wedge, and pass it through the pulleys (P 4 and P 3), as in the fifth experiment; let a person draw the sledge by this rope over his shoulder, and he will find, that as it advances it will raise the weight upwards; the wedge is five feet long, and elevated one foot. Now, if the perpendicular ascent of the weight, and the space through which he advances, be compared, he will find that the space through which he has passed will be five times as great as that through which the weight has ascended; and that this wedge has enabled him to raise five times as much as he could raise without it, if his strength were applied as in experiment 1, without any mechanical... Mechanical advantage. By making this wedge in two parts hinged together, with a graduated piece to keep them asunder, the wedge may be adjusted to any given obliquity; and it will always be found, that the mechanical advantage of the wedge may be ascertained by comparing its perpendicular elevation with its base. If the base of the wedge be 2, 3, 4, 5, or any other number of times greater than its height, it will enable the person to raise respectively 2, 3, 4, or 5 times more weight than he could do in experiment 1, by which his power is estimated.

13. The Screw.

The screw is an inclined plane wound round a cylinder: the height of all its revolutions round the cylinder taken together, compared with the space through which the power that it turns passes, is the measure of its mechanical advantage. Let the lever used in the last experiment be turned in such a manner as to reach from its gudgeon to the shaft of the Panorganon, guided by an attendant lever as before (fig. 60.). Let the wheel rest upon the lowest helix or thread of the screw; as the arms of the shaft are turned round, the wheel will ascend, and carry up the weight which is fastened to the lever. As the situation of the screw prevents the weight from being suspended exactly from the centre of the screw, proper allowance must be made for this in estimating the force of the screw, or determining the mechanical advantage gained by the lever. This can be done by measuring the perpendicular ascent of the weight, which in all cases is useful, and more expeditious, than measuring the parts of a machine, and estimating its force by calculation; because the different diameters of ropes, and other small circumstances, are frequently mistaken in estimates—both methods should be employed and their results compared. The space passed through by the moving power, and by that which it moves, are infallible data for estimating the powers of engines.

Two very material subjects of experiment yet remain for the Panorganon; friction, and wheels of carriages; but perhaps we may be thought to have extended this section beyond its just proportion to the rest of the article, in which it is not intended to write a treatise upon science, but to point out methods of initiating young people in the rudiments of knowledge, and of giving them a distinct view of those principles on which they are founded. No preceptor who has had experience will cavil at the superficial knowledge of a boy of 12 or 13 upon these subjects; he will perceive that the general view which we wish to give, must tend to form a taste for literature and investigation. The sciolist has learned only to talk—we wish to teach our pupils to think upon the various objects connected with the present article.

The Panorganon may be employed in ascertaining the resistance of air and water; the force of different muscles; and in a great variety of amusing and useful experiments. In academies and private families, it may be erected in the place allotted for amusement, where it will furnish entertainment for many a vacant hour. When it has lost its novelty, the shaft may from time to time be taken down, and a swing may be suspended in its place.*

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**SECT. XII. Recreations and Contrivances relating to Optics.**

In the articles CATOPTRICS, DIOPTRICS, MICROSCOPE and PERSPECTIVE, we have described a variety of optical recreations, viz. under CATOPTRICS, Sec. III., catoptrical illusions; the appearance of a boundless vista; a fortification apparently of immense extent; a surprising multiplication of objects; the optical paradox, by which opaque bodies are seemingly rendered transparent; the magician's mirror; the perspective mirror; the action of concave mirrors in inflaming combustible bodies, and the real apparition. Under DIOPTRICS, page 244 of Vol. VII., optical illusions; the optical augmentation, optical subtraction; the alternate illusion; the dioptrical paradox; the camera obscura; the method of showing the spots on the sun's disk, and magnifying small objects by means of the sun's rays; the diagonal opera glass; the construction and uses of the magic lantern; the nebulous magic lantern; method of producing the appearance of a phantom on a pedestal placed on the middle of a table; and the magic theatre. Under MICROSCOPE, besides fully explaining the construction of the several kinds of microscopes, and explaining their uses, we have given an account of a great variety of objects which are seen distinctly only by means of these instruments; such as the microscopic animalcula; the minute parts of insects; the structure of vegetables, &c.; and under PERSPECTIVE, we have described and explained the anamorphosis, an instrument for drawing in perspective mechanically, and the camera lucida of Dr Wollaston. Under OPTICS, Part III., Chap. I., we have explained the construction of the principal optical instruments, as multiplying glasses, mirrors, improvements on the camera obscura, by Dr Brewster and Mr Thomson; microscopes, telescopes, and various kinds of apparatus for measuring the intensity of light. Under PYROTECHNY, No. 150, we have shown how artificial fireworks may be imitated by certain optical deceptions.

At present we shall only describe one or two additional optical recreations, and explain the nature of the optical deception called Phantasmiagoria.

**Experiment to show the Blue Colour of Shadows formed in Day-Light.**

Darken a room in daylight, or towards twilight, so that only a small proportion of light may enter by the shutter. Then holding a lighted candle near the opening of the shutter, cast the shadow of an object, such as a small ruler, on a white paper. There will in general be seen two shadows, the one blue, and the other orange; the former of which resembles the blue colour of the sky in clear sunshine, and is of a greater or less intensity according as the object is brought nearer to a focus.

For explanations of the blue colour of the sky, see OPTICS, Part II., Sect. 4.

**The Air-drawn Dagger.**

An improved variety of the experiments described under CATOPTRICS, No. 14, by the name of the real apparition, is thus described by Montucla. Fig. 62 represents a different position of the mirror and partition from that described under CATOPTRICS, and one better adapted... adapted for exhibiting the fact by various objects. ABC is a thin partition of a room down to the floor, with an aperture for a good convex lens, turned outwards into the room nearly in a horizontal direction, proper for viewing by the eye of a person standing upright from the floor, or on a stool. D is a large concave mirror, supported at a proper angle, to reflect upwards through the glass in the partition B, images of objects at E, presented towards the mirror below. A strong light from a lamp, &c., being directed on the object E, and nowhere else; then to the eye of a spectator at F, in a darkened room, it is truly surprising and admirable to what effect the images are reflected up into the air at G.

Exhibitions of the appearances of spectres have sometimes been formed on the principles of this experiment; but the most striking deception of this kind is the phantasmaria, which some winters ago formed one of the principal public amusements at Paris and London.

This exhibition was contrived by Mr Philipsthal, and was conducted in a small theatre, all the lights of which were removed, except one hanging lamp, and this could be drawn up, so that its flame was perfectly enveloped in a cylindrical chimney, or opaque shade. In this gloomy and wavering light the curtain was drawn up, and presented to the spectators a sort of cave, with skeletons and other figures of terror, painted or moulded in relievo on the sides or walls. After a short interval the lamp was drawn up into its chimney, and the spectators were in total darkness, interrupted only by flashes of lightning succeeded by peals of thunder. These phenomena were followed by the appearance of figures of departed men, ghosts, skeletons, transmutations, &c. Several figures of celebrated men were thus exhibited with various transformations, such as the head of Dr Franklin, suddenly converted into a skull, &c. These were succeeded by phantoms, skeletons, and various terrific figures, which were sometimes seen to contract gradually in all their dimensions, till they became extremely small, and then vanished; while at others, instead of seeming to recede and then vanish, they were, to the surprise and astonishment of the spectators, made suddenly to advance, and then disappear, by seeming to sink into the ground.*

The principal part of these phenomena was produced by a modification of the magic lantern, having all its parts on a large scale, and placed on that side of a semi-transparent screen of taffeta which was opposite to the spectators, instead of the same side, as in the ordinary exhibitions of the magic lantern. To favour the deception, the sliders were made perfectly opaque, except in those places that contained the figures to be exhibited, and in these light parts the glass was covered with a more or less transparent tint, according to the effect required. The figures for these purposes have also been drawn with water colours on thin paper, and afterwards varnished. To imitate the natural motions of the objects represented, several pieces of glass placed behind each other were occasionally employed. By removing the lantern to different distances, and at the same time altering more or less the position of the lens, the images were made to increase or diminish, and to become more or less distinct at the pleasure of the exhibiter; so that, to a person unaccustomed to the effect of optical instruments, the figures appeared actually to advance and retire. In reality, however, figures exhibited in this way become much brighter as they are rendered smaller, while in nature the imperfect transparency of the air causes objects to appear fainter when they are remote, than when they are nearer the observer. Sometimes, by throwing a strong light on an object really opaque, or on a living person, its image was formed on the curtain, retaining its natural motions; but in this case the object must have been at a considerable distance, otherwise the images of its nearer and remoter parts could never be sufficiently distinct at once, as the refraction must either be too great for the remoter, or too small for the nearer parts; and there must also be a second lens placed at a sufficient distance from the first, to allow the formation of an inverted image between them, and to throw a second picture of this image on the screen in its natural erect position, unless the object be of such a nature that it can be inverted without inconvenience.*

Dr Thomas Young proposes the following apparatus for an exhibition similar to the phantasmaria. The light of the lamp A (fig. 63.) is to be thrown by the mirror B and the lenses C and D on the painted slider at E, and the magnifier F forms the image of the screen at G. This lens is fixed to a slider, which may be drawn out of the general support or box H; and when the box is drawn back on its wheels, the rod IK lowers the point K, and by means of the rod KL adjusts the slider in such a manner, that the image is always distinctly painted on the screen G. When the box advances towards the screen, in order that the images may be diminished and appear to vanish, the support of the lens F suffers the screen M to fall and intercept a part of the light. The rod KN must be equal to IK, and the point I must be twice the focal length of the lens F, before the object, L being immediately under the focus of the lens. The screen M may have a triangular opening, so as to uncover the middle of the lens only, or the light may be intercepted in any other manner.†

Mr Ezekiel Walker has lately constructed a new optical instrument, calculated for affording entertainment to those who derive pleasure from optical illusions. This instrument is called phantasmascope, and is so contrived, that a person standing before it sees a door opened, and a phantom make its appearance, coming towards him, and increasing in magnitude as it approaches, like those in the phantasmaria. When it has advanced about 3 feet, it appears of the greatest magnitude, and as it retires, becomes gradually contracted in its dimensions, till it re-enters the machine, when it totally vanishes. This phantom appears in the air like a beautiful painting, and has such a rich brilliancy of colouring, as to render it unnecessary to darken the room. On the contrary, this aerial picture is seen with rather greater perfection when the room is illuminated.

Fig. 64. represents a section of this machine, and will explain the principles of its construction.

ABCD, a wooden box, 96 inches by 21, and 22 deep. EF, a concave mirror, 15 inches diameter, placed near the end BD. AC, the other end, is divided into two parts at m by a horizontal bar, of which m is a section. A m, a door that opens to the left hand. n o a board with a circular opening, 10 inches diameter, covered with plate glass in that side next the mirror. GHI a drawer, opened at the end I, and covered at the top Gm with tin plate. It is represented in the fi- AMUSEMENTS OF SCIENCE.

In our treatise on Pneumatics, we have related several entertaining experiments, illustrating the principles of that science, such as experiments proving the fluidity of the air in No 52; that of Hero's fountain in No 54; experiments illustrating the application of hydrostatics to air, No 57, &c., &c.; a great variety of experiments with the air pump, No 160; the experiment of the syphon fountain, No 178; and experiments on the compressibility and expansibility of the air, No 196, &c. We have also, in that article, explained the construction and operation of the principal pneumatic engines, such as syringes, syphons, air-pumps, bellows, &c. The construction and uses of barometers have been explained under Barometer, and under Hydrodynamics, No 72. Those of thermometers under Chemistry from No 194 to 203; and those of common pumps under the article Pump.

As the account of the air-gun, referred to Pneumatics, has been omitted in that article, we must here describe the construction and action of that ingenious instrument.

The common air-gun is made of brass, and has two barrels; the inside barrel A, fig. 65, which is of a Fig. small bore, from whence the bullets are exploded; and a larger barrel BCDR on the outside of it. There is a syringe SMNP fixed in the butt of the gun, by which the air is injected into the cavity between the two barrels through the valve EP. The ball K is put down into its place in the small barrel, with the rammer, as in any other gun. At SL is another valve, which being opened by the trigger O, permits the air to come behind the bullet, so as to drive it out with great force. If this valve be opened and shut suddenly, one charge of condensed air may be sufficient for several discharges of bullets; but if the whole air be discharged on a single bullet, it will drive it out with a greater force. The discharge is effected by means of a lock, placed here as in other guns: for the trigger being pulled, the cock will go down and drive the lever O, fig. 65, which will open the valve, and let in the air upon the bullet K.

The air-gun has received very great improvements in its construction. Fig. 66. is a representation of one now made by several instrument-makers in the metropolis. For simplicity and perfection it exceeds any hitherto contrived. A is the gun-barrel, with the lock, stock, rammer, and of the size and weight of a common fowling-piece. Under the lock, at b, is a steel tube having a small moveable pin in the inside, which is pushed out when the trigger a is pulled, by the spring-work within the lock; to this tube b, is screwed a hollow copper ball c, so as to be perfectly air tight. This copper ball is fully charged with condensed air by the syringe B, fig. 67, previous to its being applied to the tube b of fig. 66. It is evident, that if a bullet be rammed down in the barrel, the copper ball screwed fast at b, and the trigger a pulled, that the pin in b will, by the action of the spring-work within the lock, forcibly strike out into the copper ball; and thereby pushing in suddenly a valve within the copper ball, let out a portion of the condensed air, which will rush up through the aperture of the lock, and forcibly act against the bullet, driving it to the distance of 60 or 70 yards, or farther. If the air be strongly condensed, at every discharge, only a portion of it escapes from the ball; therefore by recocking the piece, another discharge may be made; and this repeated 15 or 16 times.

The air in the copper ball is condensed by means of AMUSEMENTS OF SCIENCE.

The syringe B (fig. 67.), in the following manner. The ball c is screwed quite close in the top of the syringe at b, at the end of the steel pointed rod; a is a stout ring through which passes the rod k; upon this rod the feet are commonly placed, then the hands are to be applied to the two handles i, fixed on the side of the barrel of the syringe. Now by moving the barrel B steadily up and down on the rod a, the ball c will become charged with condensed air; and it may be easily known when the ball is as full as possible, by the irresistible action which the air makes against the piston while working the syringe. At the end of the rod k is usually a square hole, which with the rod serves as a key to make the ball c fast on the screw b of the gun and syringe close to the orifice in the ball c. In the inside is fixed a valve and spring, which gives way for the admission of air; but upon its emission comes close up to the orifice, shutting up the internal air. The piston rod works air-tight, by a collar of leather on it on the barrel B; it is therefore plain, that when the barrel is drawn up, the air will rush in at the hole b. When the barrel is pushed down, the air contained in it will have no other way to pass, from the pressure of the piston, but into the ball c at top. The barrel being drawn up, the operation is repeated, until the condensation is so strong as to resist the action of the piston.

The magazine air-gun was invented by that ingenious artist L. Colbe. By this contrivance 10 bullets are so lodged in a cavity, near the place of discharge, that they may be drawn into the shooting barrel, and successively discharged so fast as to be nearly of the same use as so many different guns.

Fig. 68. represents the present form of this machine, where part of the stock is cut off, to the end of the injecting syringe. It has its valve opening into the cavity between the barrels as before. KK is the small shooting barrel, that receives the bullets from the magazine ED, which is of a serpentine form, and closed at the end D when the bullets are lodged in it. The circular part a b c, is the key of a cock, having a cylindrical hole through it, i k, which is equal to the bore of the same barrel, and makes a part of it in the present situation. When the lock is taken off, the several parts Q, R, T, W, &c. come into view, by which means the discharge is made by pushing up the pin P p, which raises and opens a valve V to let in the air against the bullet I, from the cavity FF, which valve is immediately shut down again by means of a long spring of brass NN. This valve V being a conical piece of brass, ground very true in the part which receives it, will of itself be sufficient to confine the air.

To make a discharge, the trigger ZZ is to be pulled, which throws up the seer y a, and disengages it from the notch a, on which the strong spring WW moves the tumbler F, to which the cock is fixed. This, by its end u, bears down the end v of the tumbling lever R, which, by the other end m, raises at the same time the flat end of the horizontal lever Q; and by this means, of course, the pin P p, which stands upon it, is pushed up, and thus opens the valve V, and discharges the bullet. This is all evident, merely from the view of the figure.

To bring another bullet to succeed that marked I, instantaneously turn the cylindric cavity of the key of the cock, which before made part of the barrel KK, into the situation i k, so that the part i may be at K;

Vol. XVIII. Part II.