BALANCE, a machine for ascertaining the weight of substances. There are several kinds of balances, as the common balance or scales, the steelyard, the Danish or Swedish balance, the Chinese balance, the hydrostatic balance, &c. The same name is also given to certain kinds of apparatus employed for measuring or comparing the intensities of very small forces, as the balance of torsion, the electric balance, &c.

The common balance, which is of the most extensive use in the affairs of life, as well as in the arts and experimental[7:4:304] physics, consists of a beam, AB (fig. 1, Plate CIII.), supported in the middle by a fulcrum or prop C, round which it turns freely, and having a scale or dish attached to each of its extremities A, B, one of which holds the weight, and the other the substance to be weighed. The balance, therefore, in reference to the mechanical powers, is a lever of the first kind; that is to say, having the fulcrum placed between the power and the weight to be raised; hence its theory is easily deduced from the statical properties of the lever. Let P represent the weight in the scale D, and Q that in E; then (supposing AB an inflexible straight line without weight), when AB becomes stable in the horizontal position, or when P balances Q, the condition of equilibrium is expressed by the equation

P×AC = Q× BC.

In order, therefore, that the two bodies P and Q may have precisely the same weight, or both exert the same force in turning the beam about its axis of motion, it is indispensable that the two points of suspension A and B be exactly equidistant from the fulcrum C.

When the two arms of the balance are not exactly of the same length, it is obvious that the two weights P and Q, which, in the case of equilibrium, are reciprocally as CA and CB, must also be unequal, in order that the foregoing equation may still be true. If, for example, AC is longer than CB, then a less weight in D will balance a greater in E; and it is on this principle that false balances are constructed. The fraud, however, may be easily detected by transferring the weights P and Q, to the opposite scales; for then the less weight P being attached to the shorter arm CB, the product P × CB will be smaller than Q × CA, and the equilibrium consequently destroyed.

It may be remarked, that the true weight of a body may easily be found by means of a false balance of this kind. It is only necessary to weigh the body first in the one scale and then in the other, and the true weight will be a mean proportional between the two weights thus indicated. To demonstrate this property, let w be the true weight of the body in grains, and suppose that when placed in the scale E it balances p grains in D, and that when transferred to D it balances q grains in E, and makes m = AC, η = BC; by the statical property of the lever we have the two equations, mp — mo i nq z= mlo; 1 m w m q whence — — —, — — —; η p n τo therefore — = — and w = √w∕ i p w 11 so that w is a mean proportional between p and q, and is consequently found by multiplying those numbers together, and extracting the square root of their product.

In what precedes, the beam has been regarded as an inflexible rod devoid of weight; but in order to investigate fully the properties of the instrument, and the conditions that must be fulfilled in order to render it practically useful, it is necessary to have regard to the weight of the beam, and the position of its centre of gravity in respect of the axis of motion. The great requisites of a good balance are sensibility and stability; that is to say, it ought to be such that a very small weight added to either scale disturbs the equilibrium, and causes the beam to deviate sensibly from the horizontal position; and also such, that when the equilibrium has been disturbed, it may return quickly to a state of rest. In order to discover the construction best adapted to confer these two properties, it is convenient to regard the beam as a bent lever. Let G (fig. 2) be the centre of gravity of the beam, 0 the middle point of the straight line joining the points of suspension A and B, H' H a horizontal straight line drawn through C, and GD, OE, BH, AH', perpendiculars to H'H. Make

W = weight of beam,

L = weight of scales with their load, P = the preponderating weight, <ρ =. COE = BOK = angle of inclination.

The condition of equilibrium is now

L.CE +W.CD = P.CH 5 whence, since CH = EH — EC = OK — EC, L.OC sin. φ + W.GC sin. p = P.OB cos. φ— P.OCsin. ß; therefore, εin. ţ> [(L + P) . OC + W.GC] = P.OBcos.¢; sin. φ _ P.OB

an tan. φ - c θ g ψ p) . OC + W . G( y

From this equation it appears that, for any given value of P, the tangent of the angle of inclination, which measures the sensibility of the balance, is directly as the length of the beam, inversely as the weights of the beam and load, and also inversely as the distances of G and 0 from the axis. The sensibility is therefore greatest when the quantity (L + P) . OC + W . CG is the least possible. On the other hand, when P = 0, the stability, or the force acting to restore the beam to the horizontal position, is sin. φ [L . OC -fW. CG], which will be diminished by diminishing the value of L . OC + W. CG.

In what precedes we have supposed the points G andθ both to fall below the centre of the motion C; but the balance may be constructed so that one or both of these points shall coincide with C, or fall above it. Suppose, in the first place, the arms to be bent upwards, so that 0 falls above the fulcrum, while G remains below it. In this case the measure of stability is sin. <ρ (W.CG — L.OC), whence it appears that a balance of this sort can only be used for small weights; for if the load is increased till L.OC becomes equal to W.CG, the balance has no restoring power, and is indifferent to any position. If L.OC exceeds W.CG, it would entirely upset by the slightest deviation from the horizontal position.

Suppose next that the centre of gravity G falls above the fulcrum, 0 remaining below it. The measure of stability now becomes sin. φ (L.OC — W.CG), and consequently the balance is only useful for heavy weights; for as L.OC is diminished, the stability is lessened, and when L.OC is equal to or less than W.CG, the balance is useless. Hence it appears that when either of the points G, 0, falls above C, the balance can only be employed in particular cases.

Let the point G coincide with C, and 0 fall below it. In this case CG vanishes, and the measure of stability becomes sin. φ L.OC, which, for any given value of p, increases with the load, or the weight of the substance to be weighed. A balance of this sort would be unfit for weighing small bodies on account of its want of stability, though it might be used in the estimation of great weights.

Lastly, let 0 coincide with C, while G falls below the axis. The three points of action A, C, B, are now arranged in a straight line, and the measure of stability is sin. ç W. CG, which is constant for a given value of φ. The restoring force is therefore independent of the load in the scales, so that a balance of this sort can be employed in all cases, whether the weights are great or small; and as it is easy, diminishing W and CG, to give it any required degree of sensibility, it is this form that ought to be adopted in every case where great precision and accuracy are necessary.

Another reason for this disposition of the three points of action in a straight line is, that unless C is in the same straight line with A and B, an equilibrium will subsist between two unequal weights when AB is not exactly horizontal. In fact, since the weights P, Q, suspended from A and B, act in the direction perpendicular to H'H, the moments[7:4:305] of these weights, or their energies in turning the beam round its axis, are respectively P × CH', and Q × CH; therefore, when BCH is a greater angle than ACH', and the line CH consequently less than CH', a smaller weight at A will balance a greater at B, and the beam remain at rest though loaded with unequal weights. It is hence important, in all accurate weighing, to make certain that when the equilibrium takes place, the line AB is exactly horizontal.

Having determined from theory the conditions that ouθ - ht to be observed in the construction of the balance, we shall now proceed to give a brief description of the instrument as it is constructed for assaying or other delicate purposes. In the first place, the beam ought to be as light as possible, consistently with its perfect inflexibility; for it is evident that the friction of the axis will be increased with its weight, and the sensibility proportionally diminished. To combine the qualities of lightness and inflexibility, it is found most advantageous to form the arms of the balance of two hollow cones of brass, very thin, but strengthened and inflexible by means of circular rings driven into them at proper intervals. In order to diminish as much as possible the extent of the surfaces in contact, the axis is formed of two sharp edges of tempered steel, lying in the same straight line, and supported on two planes of steel, agate, or crystal, finely polished, and placed with the greatest precision, in the same horizontal plane. In a balance made by the celebrated Troughton, the sharp edges are ground on the lower side of a cylinder of steel, which crosses the beam in the middle, and they extend over the agate planes about 2 j θth of an inch. The angle of the edges is about 30°. The suspension at the extremities of the beam ought also to be made by sharp, edges, crossing each other at right angles; and in order to obviate any risk of displacement, the edges may be concave, those formed in the beam being sharp upwards, and the others, to which the scales are attached, being sharp downwards. The horizontality of the beam is usually indicated by a slender pointed rod called the tongue of the balance, rising perpendicularly above the beam, and passing through the centres of gravity and motion. A divided ivory scale, placed contiguous to it, shows deviations of the tongue from the perpendicular, and renders sensible the slightest motion of the beam. In some balances the tongue is placed below the beam, pointing downwards, in order to diminish the volume of instrument. But the preferable method is to bring the arms themselves to terminate in sharp points, and place a divided scale behind each. By this means the tongue is rendered unnecessary, and any flexure of the beam immediately becomes evident. Care must be taken that the zeros of the two scales be placed exactly in the same level. The points of suspension at the extremities of the arms ought to be adjustable both horizontally and vertically; horizontally, for the purpose of giving the two arms exactly the same length; and vertically, in order to bring the three points of action into a straight line. A nut or bob, formed of some heavy substance, placed near the middle of the beam (in the interior of the cylinder if it be hollow), and capable of being raised or lowered by a screw, serves to increase or diminish the distance of the centre of gravity of the beam from the axis of motion, and consequently to accelerate or retard the oscillations at pleasure. Two supporters, the upper ends of,which are formed into angles, are placed under the b(⅛m. These, being raised by means of a screw, lift the beam from the supporting planes, and relieve the sharp edges when the balance is not in use. If the arms of the balance are hollow, this object may be accomplished with less risk by placing the supporters under the extremities of the cross steel bar on which the sharp edges are formed. Props should also be placed under the scales while loading or unloading them; and care taken to confine the oscillations within narrow limits, or prevent the beam from deviating much from the horizontal position, by which the points of action might be endangered. The sensibility, as we have seen, increases with the length of the beam; but the liability to flexure also increases in the same proportion: and the arms of a balance, such as has been described, cannot, perhaps, safely exceed nine or ten inches. When great delicacy is required, the apparatus must be protected from the disturbing influences of currents of air, by being inclosed within a glass case, having doors at the ends for the convenience of loading and unloading the scales.

Fig. 3, Plate CIII. represents a balance by Fortin, a celebrated mechanician of Paris. The beam is made of tempered steel, and the arms slightly bent, so that all the parts of action may be situated in the same plane, and the centre of gravity fall a little below the axis of motion, which is here under the beam. The planes of support are of steel, and highly polished. The suspension at the extremities of the arms is represented by fig. 4.

With a balance of great sensibility, weighing is not only a delicate, but also tedious operation. When the adjustments are all perfect, and the beam nearly poised, the oscillations should be extremely' slow and regular, and extend to equal distances on each side of the zero of the scale. In fact, it is by the equality of the excursions of the index from zero that the horizontality of the beam must be inferred; for a very long time would elapse before the oscillations entirely cease. The sensibility of a balance constructed with the requisite care, according to the principles above explained, is very great. Those of Fortin of Paris have been found to oscillate by the addition of a single milligramme, when loaded with a weight of 1000 grammes in each scale; so that the weight is indicated to the millionth part. A balance constructed by the late Mr Ramsden, for the Royal Society of London, is said to vibrate with the seven-millionth part of its load. In general, however, no such exactness can be hoped for; and even when the greatest precautions are taken, and the most delicate instruments employed, it would seldom be safe to vouch for the truth of any figure carried beyond the fourth decimal.

But notwithstanding the high state of perfection to which the mechanical arts have arrived, the mathematical equality of the length of the arms, and their symmetry in respect of the axis of motion, can never be practically attained; it is therefore desirable to have the means of obtaining results in as great a degree as possible independent of such extreme precision. The following method of weighing, ascribed by the French writers to Borda, gives results not affected by the inequality of the arms, or other imperfections to which the balance is principally subject, and ought to be practised whenever very great accuracy is necessary. Let the body to be weighed, which we shall call P, be placed in the scale A, and for a counterpoise put into the scale B, substances of any sort, for instance bits of copper, lead, wire, or even chips of paper, added in small quantities till the beam becomes perfectly horizontal, which is known by the index pointing to zero. This being done, remove gently the body P from A, and substitute for it known weights, as grains and fractions of a grain, till the equilibrium is restored, and the index again settles at zero. Now it is evident that the weights in A, having been placed exactly in the same circumstances with the body P, and producing equally with it an equilibrium with the loaded scale B, must be the exact equivalent or weight of P. In fact, the accuracy of this nrocess can only be affected by two circumstances; the [7:4:306]first is, the friction of the axis, or the want of sensibility in the balance; and the second is, a change of position in the point of suspension. Unless the points of suspension are identical in both operations, the weights which successively produce equilibrium with B will not be exactly equal; for even if no change takes place in the length of the arm, the friction developed at the new points of contact will have a different value, and consequently require a different force to overcome it. The chief objects to be attended to, therefore, in practising the method of double weighing, are, that the mode of contact may receive no change during the loading and unloading of the scales; and that the friction may be reduced to its least possible value by giving the finest polish to the edges, as well as the plane of support.

With regard to the weights that ought to be employed, it may be sufficient to state, that, in delicate weighing, and for philosophical purposes, they are usually reckoned by Troy grains. The geometrical series 1, 2, 4, 8, 16, &c. offers one considerable advantage, namely, that a smaller number of weights is required than when any other system is adopted; but it would, perhaps, be more convenient in practice to follow the decimal division, and use weights of the following values: 1, 2, 3, 4, &c.; 10, 20, 30, 40, &c.; 100, 200, 300, 400, &c.; 1000, 2000, 3000, 4000, &c., up to 9000; and ∙1, ∙2, ∙3, ∙4, &c.; ∙01, ∙02, ∙03, 0*4, &c.; ∙001, •002, Ό03, ∙004, &c. By this means the trouble of adding would be entirely avoided, and the number of weights in the scale would equal the digits in the number by which the grains are expressed. Thus a load of 735∙4 grains would be counterpoised by weights of 700 grains, 30 grains, 5 grains, and 4-10ths of a grain.

See Euler, Comment. Petrop. tom. x. p. 3. Phil. Trans. for 1766; Shuckburgh in ditto for 1798, part 2d; Prony, Annales de Chimie, tom. xxxvi. p. 3; Biot, Traité de Physique, tom. i. p. 9; Ure’s Dictionary of Chemistry; Leslie’s Elements of Natural Philosophy, vol. i∙ p. 185.

The Steelyard is a balance by which the weights of bodies are estimated by means of a single weight. This machine, which is represented by fig. 5, is likewise a lever of the first kind, having two unequal arms. The load L to be weighed is suspended from the extremity of the short arjn CA, and the counterpoise or constant weight P is movable along CB. Divisions traced on CB indicate the weight of L corresponding to each of the positions of P. In the East, where the steelyard is much in use, the standard weight P is generally made to resemble a pomegranate in shape; whence the instrument acquired the name of Pomman, and from this circumstance it has frequently but erroneously been denominated the Roman balance or Statera.

To find the points of division of the arm CB, let W be the weight of the bar AB, exclusive of L and P; and let p be the weight in pounds of the body L. Let CA = l, and x be the unknown distance of the centre of gravity of the beam from the fulcrum C. Then, carrying P along the arm CB till the beam is horizontal, let A 1 be the point at which P rests, and put CA 1 = X 1 . Now, the beam is kept in equilibrium by its own weight acting at the centre of gravity x, and by the weights p and P acting respectively at A and A 1 ; therefore the condition of equilibrium is expressed by the equation

Wa>+ y √+ PX 1 =0.

Let another weight p, equal to the former, be suspended from A, and let A 2 be the position of P when the equilibrium is restored. Make CA 2 = X 2 , and the above equation now becomes

Wae+ 2pld r PX 2 = 0.

In this manner, by the successive addition of equal weights p to A, the following system of equations is formed:

Wae÷ jnZ⅛PX 1 =0 Wx÷ 2τ√+ PX 2 = 0 Wae + 3, t√+ PX~ =0

W X + npl + PX w = 0.

By subtracting the first of these equations from the second, the second from the third, and so on, we have jt ,Z÷P(X 2 -X 1 ) = 0 pl+ P (X 3 -X 2 ) = 0 y>Z + P (X 4 — X 3 ) = 0

7 >Z+P(X w -X w - 1 ) = 0.

The successive differences X 2 — X 1 , X 3 — X 2 , &c. are therefore constant, each being equal to the constant quan- υl tity ψ-. The divisions of the arm CB may therefore be found as follows:

Having suspended the given weight p from the extremity of the shorter arm CA, find the point A 1 at which it is necessary to place P in order that the beam may be horizontal. Then, having removed ρ, substitute for it another weight, which is an exact multiple of p, as ηρ, and let P be moved toward C till the equilibrium is restored, A m being the point where P is now placed. Divide the distance A 1 A n into n — 1 equal parts, and the points of division will be respectively those at which P will balance the intermediate weights between p and np. If, therefore, each of those points is marked with the corresponding value of p, the weight of any body whatever suspended from A will be indicated by the number of the division at which P rests when the beam is horizontal. The distances A 1 A 2 , A 2 A 3 , &c. may be divided into tenths, or other fractional parts.

For weighing heavy loads the steelyard is a convenient instrument; but for small weights it is not susceptible of so much accuracy as the common balance. The pressure on the fulcrum, and consequently the friction, is greater, when the commodities to be weighed are less than the constant weight P, and the subdivision of the arm cannot be effected with the same precision as that of weights for the balance. It may be proper, however, to remark, that the instrument ought to be constructed so that the constant centres C and A may be in the same straight line with the divisions of the beam, and that the centre of gravity of the unloaded beam, when placed horizontally, shall be in the vertical passing through C, and a little below that point, as in the common balance. An index or tongue shows when the beam takes the horizontal situation.

The Chinese Balance is a sort of steelyard for weighing small commodities, formed of a slender tapering rod of wood or ivory, about a foot in length, perforated generally with four holes through which silk threads are passed, to serve as so many points of support. Four different sets of divisions are marked on the corresponding sides of the rod; and when any thing is to be weighed, the rod is held up by one of the strings, and a sliding weight of about 1∣ ounce Troy employed as a counterpoise to the substance, which is placed in a small scale suspended from the extremity of the shorter arm. The position of the standard weight indicates the weight of the substance, as in the ordinary steelyard.

The Danish or Swedish Balance, which is commonly employed in many parts of the north of Europe for weighing coarse commodities, is of a very simple construction. It consists usually of a batten of hard wood, having a heavy lump A (fig. 6) fixed at one end, and a swivel hook at the other. The goods to be weighed are fixed to the hook, and the whole is suspended in a loop of whipcord C, in which the rod is slid backward and forward [7:4:307]till the equilibrium is established. The weight of the ' load L is determined by the position of the loop on a scale of divisions, which may be formed in the following manner. .

Let 0 be the centre of gravity of the beam and the attached weight at A, W their weight, L the load to be weighed, and make BO == a, BC = x. The equation of 0 Wα

equilibrium is Lx = W (a — x), whence x = jyq—çŷ. Now, if we suppose a to be 30 inches, W = 2 lbs., and substitute for L the numbers 1, 2, 3, &c. successively, we shall have the following values of x:

When L = 1, x = 20 inches

L “2, X — 15 L — 3, X = 12 *

L = 4, X = 10

&c.

A balance constructed in this manner is obviously susceptible of very little accuracy.

The Bent Lever Balance, which is represented by fig. 7, is sometimes employed for expedition in the coarser processes of weighing. To one extremity of a bent lever ACB, is attached a constant weight B, which acts as a counterpoise to the load placed in the scale suspended from A. Through C, the point of support, draw the horizontal line DE, and through A and B the perpendiculars AD, BE, meeting DE in D and E. Now the equilibrium will take place when CE is to CD as the load at A to the constant weight B; and if the arms are bent so that the lines joining CA and CB are at right angles, then as B moves upward, its momentum increases in proportion to the sine of the arc it describes, while the momentum at B decreases in proportion to the cosine of a similar arc. The weight on A corresponding to any position of B, may therefore be expressed on a graduated circular scale placed behind the index at B. Theoretically considered, the range of this balance is very considerable; but the indications are little to be depended on when B approaches either the perpendicular or the horizontal line passing through C.

The Hydrostatic Balance is an instrument contrived for weighing bodies in water, and thereby determining their specific gravities.

It is constructed in various forms; but we shall content ourselves here with describing that which appears of all others the most accurate. VCG (fig. 8) is the stand or pillar of this hydrostatic balance, which is to be fixed in a table. From the top A hangs, by two silk strings, the horizontal bar BB, from which is suspended, by a ring i, the fine beam of a balance b, which is prevented from descending too low on either side by the gently springing piece txyz, fixed on the support M. The harness is an- ∏ulated at o, to show distinctly the perpendicular position of the examen, by the small pointed index fixed above it.

The strings by which the balance is suspended, passing over two pulleys, one on each side of the piece at A, go down to the bottom on the other side, and are hung over the hook at v; which hook, by means of a screw P, is movable about one inch and a quarter backward and forward, and therefore the balance may be raised or depressed so much. But if a greater elevation or depression be required, the sliding piece S, which carries the screw P, is readily moved to any part of the square brass rod VK, and fixed by means of a screw.

The motion of the balance being thus adjusted, the rest of the apparatus is as follows. HH is a small board, fixed upon the piece D, under the scales d and e, and is movable up and down in a low slit in the pillar above C, and fastened at any part by a screw behind. From the point in the middle of the bottom of each scale hangs, by a fine hook, a brass wire ad and ac. These pass throug⅛ two holes m, m, in the table. To the wire ad is suspended a cylindric wire rs, perforated at each end for that purpose. This wire rs is covered with paper, graduated by equal divisions, and is about five inches long.

In the corner of the board at E is fixed a brass tube, on which a round wire hl is so adapted as to move neither too tight nor too free, by its flat head I. Upon the lower part of this moves another tube Q, which has sufficient friction to make it remain in any position required. To this is fixed an index T, moving horizontally when the wire hl is turned about, and therefore may be easily set to the graduated wire rs. To the low er end of the wire rs hangs a weight L; and to that a wire pn, with a small brass ball g about one fourth of an inch diameter. On the other side, to the wire ac, hangs a large glass bubble R, by a horse hair.

Let us first suppose the weight L taken away, and the wire pn suspended from S; and, on the other side, let the bubble R be taken away, and the weight F suspended at c in its room. This weight F we suppose to be sufficient to keep the several parts hanging to the other scale in equilibrium; at the same time that the middle point of the wire pn is at the surface of the water in the vessel 0. The wire pn is to be of such a size that the length of one inch shall weigh four grains.

Now, it is evident, since brass is eight times heavier than water, that for every inch the wire sinks in the water it will become half a grain lighter, and half a grain heavier for every inch it rises out of the water: consequently, by sinking two inches below the middle point, or rising two inches above it, the wire will become one grain ' lighter or heavier. Therefore if, when the middle point is at the surface of the water in equilibrium, the index T be set to the middle point a of the graduated wire rs, and the distance on each side ar and as contains 100 equal parts; then, if in weighing bodies the weight is required to the hundredth part of a grain, it may be easily had by proceeding in the following manner.

Let the. body to be weighed be placed in the scale d. Put the weight X in the scale e; and let this be so determined, that one grain more shall be too much, and one grain less too little. Then, the balance being moved gently up or down by the screw P, till the equilibrium be nicely shown at o, if the index T be at the middle point a of the wire rs, it shows that the weights put into the scale e are just equal to the weight of the body. By this method we find the absolute weight of the body; the relative weight is found by weighing it hydrostatically in water, as follows.

Instead of putting the body into the scale e, as before, let it hang with the weight F at the hook c by a horse hair, as at R, supposing the vessel 0 of water were away. The equilibrium being then made, the index T standing between a and r at the 36 division, shows the weight of the body put in to be 1095∙36 grains. As it thus hangs, let it be immersed in the water of the vessel N, and it will become much lighter; the scale e will descend till the beam of the balance rest on the support z. Then, suppose 100 grains put into the scale d restore the equilibrium precisely, so that the index T stand at the 36 division above a, it is evident that the weight of an equal bulk of water would in this case be exactly 100 grains.

The Balance of Torsion is an instrument invented by Coulomb, for comparing the intensities of very small forces. It consists essentially of a metallic wire, suspended vertically from a fixed point, to the lower end of which a horizontal needle is attached, with a small weight for the purpose of keeping the wire stretched. The intensity of any small force made to act on the extremity of [7:4:308]the needle is measured by the arc which the needle passes over, reckoned from the point of repose. The force is thus balanced by the torsion of the wire, whence the name of the instrument.

To prevent any derangement from the agitation of the air, the apparatus must be covered by a glass cylinder, to which a circular scale is applied horizontally, for the purpose of measuring the amplitude of the arc traversed by the needle. A divided circle is also adapted to the top of the cylinder, and capable of being turned round on it, by means of which, and a fixed index attached horizontally to the hook from which the wire is suspended, the wire may be twisted any required number of degrees. This apparatus is represented by fig. 9. The length of the wire and the needle must be regulated by the object in view. If the forces to be measured are very small, and great sensibility is consequently required, the wire must be long and very fine; for the force of torsion is inversely proportional to the length of the wire, and directly as the fourth power of its diameter. It must also-be formed of a substance possessing considerable elasticity, and for this reason brass wire is greatly superior to iron. By experiments undertaken for the purpose, Coulomb found the elasticity of some wires so perfect, that on keeping them twisted through eight circumferences for thirty liours together, the centre of torsion was not displaced by a single degree. Their length was about a metre, or 39 inches.

The balance of torsion is used chiefly in experiments on electricity, magnetism, the adhesion of fluids, &c.; and it was by means of this instrument that Cavendish made his famous experiments on the attraction of lead balls, from which he deduced the mean density of the earth equal to about 5∙5, that of water being unit. (s,)