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BALANCE. A simple machine, in which the lever is employed to determine the equality or difference of two given weights. Balances are of various kinds, differing in their form, and in the perfection of their construction, according to the nature of the objects for which they are employed. The common balance or scales are well known to consist of a lever or beam a b, turning on its axis in a ver tical plane, and having two dishes or scale pans d e suspended at its two ends. The distances between the centre of the beam and the extremities a and b are made as nearly equal as possible : hence it is clear, from the nature of the lever, that the weights placed in the two scales will be equal to each other when the beam rests in a horizontal position. Although, theoreti cally speaking, the balance is exceedingly simple, consisting merely of a right line turning on its centre, yet in practice it becomes a matter of considerable difficulty to approximate its construction to that perfection which theory points out, and which the nicer operations of philosophical research demand. Although it is not necessary on all occasions to use a balance capable of detecting differences in weight equivalent to the of a grain, yet the more perfect our model is, and the nearer we approach to it, the greater chance there is of obtaining the object of our search, viz. an exact indication of the weight of any given sub stance. In the mast perfect balances, one of which is represented in the annexed engraving, the beam L L is a bar of tempered steel, so strong as not sensibly to bend with the weights usually placed in it. If G is the centre of gravity of the beam, the arms G L G L should be of precisely the same length. At the extremities, silk cords of the same length and weight support the scale-pans A A, which are also equal. That the slightest motion of the beam may be distin guished, an index S C is attached to the beam exactly perpendicular to it, and in the same plane with the centre of gravity. The whole is sustained on an axis perpendicular to the beam at C; and in order that the line around which the beam turns may not change its place, and thus vary the lengths of the arms, the axis is formed below into a sharp knife edge of hardened steel, and moves on planes of polished crystal, agate, or other hard substance. Now if a equality were established between the parts of the balance on each centre G, an equilibrium would naturally occur when the beam L Lc was in a horizontal position ; for the centre of gravity of the whole would then be in the same vertical line as the point C ; hence if weights were placed in the scale, and the beam retained its horizontal position, we might infer their equality. But an experiment of this kind may be possible or not, according to the posi tion in the vertical line of the points C and G. If the centre of gravity G coincided with the centre of motion C, the beam would rest in any position into which it might be thrown. Or if the centre G were above the centre C, the beam would remain horizontal when placed so, but its equilibrium would be unstable, and the least additional weight to either side would cause that side to descend indefinitely. But if the centre of gravity be below the centre of support, then, if the horizontality of the beam be deranged, it will be recovered after a succession of oscillations of continually diminishing amplitude. The delicacy, or stability, of the beam, will depend, in a at measure, on the dis tance between these two points. Thus, if G be much below C, a considerable weight will be required to turn the beam, but it will soon regain its state of rest. On the other hand, if the point G be only a short distance below C, a slight additional weight will cause the arm to descend, but it will be longer in regaining its quiescent position. The sensibility is increased by lengthening the arms, diminishing the distance between the centre of support and centre of gravity, and lessening the weight of the beam, and the quantity of matter to be weighed. The stability also increases with the weight, and the distance between the two centres. As another step towards the perfection of the balance, we must be careful that the centre C and the knife edges that support the scale pans at L L, be in the same right line. If this be neglected, the beam becomes a bent lever, and the weight of the body will appear to vary with the position of the beam. The great difficulty of attaining an exact equality in the length of the arms of a balance, renders it almost hopeless to attempt to obtain the exact weight of any mass of matter by this means. It is fortunate, therefore, that there is a method of weighing which will enable us to dispense with one of these, and not the least difficult of attainment. The method of double weigh ing, introduced by Borda, renders the equality in the length of the arms a matter of indifference. To ascertain the weight of a body by his method, we place the body in one scale, as A, for example, then exactly counterbalance it by small shot, sand, &c. placed in the other scale A, till the index points to 0 on the scale at the foot of the pillar supporting the beam. The body is next carefully removed from the scale A, and its place supplied by known weights, until the beam again stands horizontal. The weights then in the scale will indi cate the weight of the body. As the weights, and the body to be weighed, have both been placed in the same scale, and, consequently, at the same distance from the centre, it is manifest, whatever may be the length of the arms, or their weight, that the true weight of the body has been ascertained. That this method may be completely efficient, only two conditions are required to be fulfilled. The one is, that the distances between the centre C, and the points L L, con tinue the same during the operation of weighing; and the second is, that the balance be exceedingly sensible, i. e. that it turn with the smallest possible quantity of matter. The first of these conditions is fulfilled by making the points L and L', of hardened steel, and sharpened to a knife edge, like the point C, as, in this case, the motion of the beam will not sensibly change the points of support, and, consequently, the distance between C and L will be accurately preserved. The second condition is to make the balance sufficiently

sensible, which is accomplished by attention to the centre C, diminishing its friction as much as possible. For this purpose, the planes that support the knife-edge are highly polished; and, in order that they may be preserved in their original state, the beam is not suffered to rest upon its centre but when in actual use. To sustain it when not in use, the two forks, F F are employed, which raise it from its support, and preserve it in a horizontal position. These forks are movable by means of the handle N. When the balance is to be used, the forks are lowered, and the beam set at liberty ; and, as soon as the obser vation is completed, the forks are raised, and the beam elevated from its sup ports till again required. To preserve the balance from the motions that would result from currents of air, it is sometimes inclosed in a glass case, having aper tures in it large enough to admit the substance to be weighed to be put into the pans. When the instrument is not in use, it is recommended to place within the case a small saucer filled with muriate of lime, or some other substance of strong hygrometric power, to absorb the moisture that would otherwise settle on the instrument, and destroy its polish by oxidation. In order to ascertain the value of a balance, the scales may be removed from the beam, to see whether the beam balances without them. They may then be put on again in opposite sides, and tried. Equal weights should then be placed in each scale, and after wards changed to the opposite one; and if the beam maintains its horizontal position during all these trials, it may be considered as accurate. The utility of gond balances for weighing different substances, is not limited to the accu rate performance of delicate experiments, but applies also to the saving of much time in weighing, when a smaller degree of accuracy is required. If a pair of scales, loaded with a certain weight, be barely sensible to one-tenth of a grain, it will require a considerable time to ascertain the weight to that degree of accuracy, because the turn is small, and must be observed several times over ; but, if a balance were used that would turn with the hundredth part of a grain, and the weight was not required to any greater accuracy than the tenths of grains, a single tenth of a grain, more or less, would make so great a differ ence in the position of the beam, that it would be seen immediately. If a balance be found to turn with a certain additional weight, and is not moved by any smaller weight, a greater sensibility may be given to it by producing a vibratory, or tremulous motion, in its parts. If the edge of a blunt saw, file, or similar instrument, be drawn along any part of the case, or support, of a balance, it will produce a jarring which will diminish the friction on the moving parts so much, that the balance will turn with a third or fourth of the addition that would otherwise be required. In this way, a beam that would barely turn with one-tenth of a grain, may be made to turn with a thirtieth or fortieth of that quantity. The improvement in the balance has progressed with the general advance of the mechanic art, to such an extent, that it would seem impossible to attain a higher degree of perfection than that which has been attained in the construction of some modern balances. Mr. Read's balance, described in the sixty-sixth volume of the Philosophical Transactions, readily turned with one pennyweight, when loaded with fifty-five pounds, but distinctly turned with four grains, when tried more patiently. This is about „4, part of the weight. In the same volume, a balance, by Mr. Whitehurst, is described, which weighed one pennyweight, and turned with of a grain, or of its weight. Ramaden's balance, turning on points instead of edges, is described in the seventy-fifth volume of the Philosophical Transactions. With a load of four cr five ounces, a difference of one division in the index was made by of a grain. This is of the weight, and, consequently, this beam will ascertain the weight correctly to five decimal places. The Royal Society's balance, which was recently constructed by Ramsden, turns on steel edges upon planes of polished crystal. Dr. Ure states, " I was assured that it ascertained a weight to the seven millionth part. I was not present at this trial, which must have required great care and patience, as the point of suspension could not have moved over much more than the two hundredth of an inch in the first half minute ; but from some trial, which I saw, I think it probable that it may be used in general practice, to determine weights to five places and better. The assay balance is of a similar kind to that which is here described in detail, but small, and extremely delicate. It is used in docimastical operations, to deter mine exactly the weight of minute bodies. The beam should be made of the best steel, and of the hardest kind, as this metal is less apt to be spoiled with rust than iron, and it more easily takes a perfect polish, which, at the game time, prevents the rust. The longer the beam is, of course, the more exactly may the weight be determined ; but, in general, ten or twelve inches is con sidered a sufficient length. The thickness of it should be so small, that two drachms might hardly be hung at either end without its bending , for the largest weight put upon it seldom exceeds one drachm. The whole surface of the beam should be without ornament, as these only collect dust, and render the balance inaccurate. The whole apparatus is, when used for nice experiments, enclosed in a case with glass faces, and which are opened only so far as may be neces sary to introduce the weights and the body to be weighed.

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