The conditions now determined from theory must be the guide of the artist in the construction of a good balance. It is of importance that the beam be as light as possible, consistent with inflexibility ; for not only the inertia, but also the fne tion, is increased in proportion to the weight, and the sensibility consequently diminished. In order to Five lightness and strength at the same time, the beam should be formed of two hollow cones of brass, joined together at the broad ends.
A cylinder of steel, passing through the middle of the beam at right angles, forms the axis; and its extremities,. ground into sharp edges on the lower side, serve as the points of support. The two edges must be accurately in the same straight line, and turn on smooth planes of agate or polished steel carefully levelled. The scales should likewise be suspended from the extremities of the beam on knife edges, crossing each other at right an gles; those in the beam being sharp up wards, and those to which the scales are attached sharp downwards. A needle, or tongue, is usually attached to the beam, pointing directly upwards or down wards when the beam is for the purpose of indicating the deviations of the beam from the horizontal position on a graduated scale. It is better, how ever, to bring the arms to terminate in sharp points, and to place a scale behind each ; in this way the slightest flexure of the beam will be rendered evident, if the zeros of the scales are placed exactly in the same level. The scale is indis pensably necessary, because the balance, if very sensible, would require a long time to come to rest ; but it is known to be poised, when the excursions of the needle on both sides of the zero of the scale are equal. In order to preserve the knife edges, the beam, when not in use, is supported on rests. Props should also be placed under the scales while loading or unloading the balance. The whole apparatus must be placed under a glass case, to protect it from the disturbing in fluence of currents of air.
The sensibility of a balance constructed with due according to the princi ples now explained, may be carried to an almost inconceivable extent. There is one in the possession of the Royal So ciety, made by Ramsden, which weighs ten pounds, and is said to turn with the ten millionth part of that load, or the thousandth part of a grain. Neverthe less, whatever skill may be employed in the construction, it is plain that the con ditions necessary to mathematical accu racy can never be entirely fulfilled. It is impossible to make the two arms of the beam exactly similar, or exactly equal in length. Absolute precision is unattain
able in practice. This difficulty, how ever, may be overcome by the following simple method, imagined by Borda, by which accurate results are obtained in dependently of extreme precision in the construction of the balance : it is only necessary that it be very sensible. Let P, the substance to be weighed, be placed in the scale A ; instead of placing known weights in the scale B, put into it some other substance, for instance bits of iron, chips of wire, or sand, added in minute quantities till the substance P is exactly counterpoised, or the beam becomes ex actly horizontal. This being done, let the substance P begently removed out of the scale A, and let known weights, as grains, be put into it till the substance in the scale B is again exactly counter poised. It is now of no consequence whether the balance was accurate or not, or whether the body P was exactly equal in weight to the substance against which it was weighed in B. The weight of P must be precisely equal to that of the grain weights ; because, under exactly the seine circumstances, they both form ed a counterpoise to the substance placed in B.
Chinese Balance. This is formed of a slender tapering rod of wood or ivory, about a foot in length. A silk thread passed through a hole perforated nearer one of its extremities than the other, serves as the point of suspension. The balance has thus two unequal arms. From the extremity of the shorter a small scale is suspended to hold the sub stance to be weighed. A sliding weight passes along the other arm, on which divisions are marked • and when the counterpoise is made, the distance of the standard weight from the fulcrum indi cates the weight of the substance. In order to procure a greater range, the rod has generally four holes or points of sup port, at different distances from the ex tremity, and a corresponding set of divi sions is marked on each of its four sides. The principle of this machine is exactly the same as that of the common steel yard.
The Danish Balance, much used in the north of Europe for weighing coarse com modities, is usually formed of an iron bar or a batten of hard wood, having a lump of lead at one of its extremities. The goods are fixed on a hook in the other end ; and the whole is suspended through a loop of cord, which is passed backwards and forwards under the rod till equilibrium is obtained. The weight of the goods is then to the weight of the lead reciprocally as their respective dis tances from the loop.
Boman Balance or Steelyard. (See