BALANCE (of doubtful derivation), an instrument for ascertaining the weight of bodies in grains, ounces, pounds, or any other units of weight. The ordinary B. con sists of a lever called a beam, whose point of support is in• the middle of its length, mind having dishes or scales suspended from either extremity. As it is of importance that time beam should move easily round its point of support, it rests on polished agate or steel planes, by means of knife-edges of tempered steel, which project trans versely from its sides, and serve as the axis of rotation. By this arrangement, the surface of contact is reduced to a mere line, and the friction of the axis of the beam on its support almost entirely obviated. The scales are hung by means of chains attached to steel hooks, which rest also on knife-edges, but turned upwards instead of down wards, as in the first case. The essential requirements of a B. of this description are 1st, That the beam shall remain in a horizontal position.when no weights are in either scale; and 2d, That the beam shall be a lever of equal arms, or have the distances between the central knife-edge and those at either end exactly the same. To insure. the first of these conditions, it is necessary that the center of gravity of the beam lie vertically below the point of support, when the beam is horizontal. When such is. the case, the center of gravity at which the weight of the beam may be considered to act, oscillates as in a pendulum round the point of support, and always comes to rest • right under that point, thus restoring to the beam its horizontal position when it has been tilted out of it. If the center of gravity were above. the joint of support, the beam would topple over; and if it coincided with that point, there being no restoring force, the beam would occupy indifferently any position into which it was thrown, the B. in both cases being useless. That a 11 possesses the second of the above conditions, is ascertained by putting weights Into the scales winch keep the beam horizontal, and then transposing them, when, if it still remain so, the lengths of the arms are equal. Should the arms be of different lengths, a less weight at the end of the longer arm will balance a larger weight at the end of the shorter arm (see LEVER); but when transposed, the larger weight having the longer arm, and the smaller weight the shorter, the beam can DO longer remain horizontal, hut will incline towards the larger weight. A balance with unequal arms is called a false B., as distinguished from an equal-armed or just balance. When weighing with a false B., it is usual to weigh a body in both scales, and take the arithmetical mean—that is, half the sum of the apparent weights for the true weight. This is'near enough to the truth when the apparent weights differ little from each other; but when it is otherwise, the geometrical mean (q.v.) must be taken, which gives the exact weight in all cases.
Although the preceding conditions are of essential importance, they do not supply all that we look for in a good balance. It is necessary, in addition, that the beam should turn visibly from its horizontal position when there is a slight excess of weight in the one scale as compared with the other. This tendency is termedwititibllity, and depends upon the weight of the beam, the position of its center of gravity, and the length of its arms. Let MID (fig. 1) represent the beam of a balance, C the point of suspension,
the center of gravity, and ACB the straight line joining the knife-edges, which may be taken as the skeleton lever of the balance. We shall here confine our attention to that construction where the three knife-edges are in a line, because it is the most simple and at the same time the most desirable. We may, without filtering the principles of librium, consider the beam reduced to the lever AB, and embody its weight in a heavy point or small ball at the center of gray ay, G, connected with U by the rigid arm CG. The scales (represented small in the fig. for the sake of space), with the equal weights in them being at an equal distance from C, have their center of gravity in that point; and their com bined pressure acting there, is met directly by the supporting plane, so that they have no influence in deter mining any particular position of the beam. If a small weight, p, therefore, be put into the scale at B, the position of the beam is determined by its rotating tendency (moment) round C, and the counter rotating tendency of the weight of the beam, W, acting at G. The question of sensibil ity is thus reduced to the action of the crooked lever GCB, with p acting at one end, and W at the other. The relations of the arms and forces of a crooked lever will be found under LEVEIt. It is only necessary here to state that. the moment of the weight acting at the end of a crooked lever increases with its size, the length of its arm, and the small ness of 'the angle which that arm makes with the horizontal line passing through the ful crum. Let us suppose that, under the effect of the opposing moments, the beam. as represented by the line AB, takes up the position marked by the dotted lines. If, now we were to lengthen CB', and keep CG' as it is, CG' would rise nearer to the horizontal line, and CB' fall further from it, before equilibrium would be restored; and the inclina tion of CB', or the beam to the horizontal line, thus being greater, the sensibility of the balance would be increased. Consequently, the longer the arms of a B. are, all other things being the same, the greater will oe its sensibility. But the same object would be reached by keeping CB its original length, and shortening CG', or bringing the center of gravity of the beam nearer to the point of support. The weight of the balance then having a shorter arm, the point Gy, for the same reason as before, would need to rise higher, and IV sink lower, before A'B' would find its position of rest. Here, also, the nearer the center of gravity of the beam is to the point of support, the greater will be the sensi bility the balance. If now, however, we keep the length of the arms CG', CB' constant, but diminish the weight acting at 0', while p acting at B' remains the same, it is mani fest that to make up the deficiency in the weight W, the two arms will turn to the left, as in the preceding cases, so as to give W a longer and p a shorter ereetice arm. The snuffler, therefore, the weight acting at 0, or the smaller the weight of the beam, the greater will be the Rensihility of the balance.