or point of rest of the balance does not coincide with the zero of the scale, the true zero must be determined by taking the mean of an even number of swings on one side, and an odd number on the other, and then their mean. The body is placed in one of the pans while both pans and beam are supported. In the other are placed the weights, the usual practice being to begin with the larger weights and work toward the smaller. The weights are of brass, platinum, or alu- minium, the smaller weights being in the form of pieces of sheet metal and 'riders' of fine wire. The pans and beams should always be supported while the weights are changed. After the ap- proximate weight of the body is ascertained, so that the addition of a centigram will cause the pointer to come to rest on the opposite side of the scale, the 'rider' is brought into play and adjusted at such a position that the pointer comes to rest at zero. A more rapid and usual method is that known as 'weighing by swings,' where points of rest when the weights differ by a certain small unit are obtained as described above. The amount to be added to the smaller amount of the weights will be such a fraction of the small units as will be obtained by taking as the denominator the number of scale divisions between the two rest-points, and as the numera- tor the distance of the true zero from the first point. It is often convenient with such a bal- ance to have a table of sensitiveness, from which one can tell at a glance the number of milligrams corresponding to a scale division for any given load. The experimenter can also find the ratio of the two arms of the balance and use it as a correction factor, as well as determine the errors of the set of weights in order to refine his meas- urement. He should, in addition, take into con- sideration the amount of air displaced by weights and the body being weighed, particularly if their densities differ considerably. An analytical or assay balance will have a sensitiveness of 1-.50 or even 1-400 of a milligram, and is used in chemi- cal analyses for the exact determination of the mass of various substances, though a sensitive- ness of one-half milligram suffices for many ordi- nary analytical purposes. In the use of the balance there are ninny methods, complex and exact, which are used by the physicist, and which will be found described in the more advanced treatises on experimental physics.
Probably the most accurate use of the balance is at the International Bureau of Weights and Measures at Sèvres, near Paris, where the standard kilograms constructed by the bureau are preserved and compared. Here the balances are of great sensitiveness, and are operated by an observer in an adjoining room, who uses a telescope to observe the deflections. There is automatic apparatus to change the weights from one pan to another, and the temperature is maintained constant.
Balances are constructed in many forms for various purposes where it is not at all necessary to employ such refinements as have been described. Those of the apothecary or grocer are familiar examples, while the balance for weighing bullion combines large capacity with considerable sensitiveness. In small balances use is sometimes made of the bent lever, especially in balances for weighing letters, chemicals, and other small objects. Here a constant weight is placed on the short or bent arm, and the body of unknown mass on the long arm. A pointer on a graduated scale indicates the weight of the body. The graduations are not even, as the angular displacement from a position of equilibrium does not increase proportionately with the increase of weight.
Bibliography. For a description of ancient balances, consult Gerland and Traumüller, Geschichte der physikalischen Experimentirkunst; and Sokeland, "Ancient Desemers or Steelyards," in the Smithsonian Annual Report for 1900 (Washington, 1901), translated from the Verhandlungen der Berliner Gesellschaft für Ethnologie (Berlin, 1900). For a description of the manipulation of a balance in fine measurements, the reader should consult Kohlrausch, Leitfaden der praktiscken Physik (Leipzig, 1896), or his more elementary Kleiner Leitfaden der praktischen Physik (Leipzig, 1900); Stewart and Gee, Lessons on Elementary Practical Physics, Vol. I. (London, 1889), and Glazebrook and Shaw, Practical Physics (London and New York, 1893), give excellent descriptions of the theory and manipulation of balances, which also will be found discussed at considerable length in the larger treatises on practical physics. The publications of the International Bureau of Weights and pleasures describe the method of testing standard kilograms and the balances used by the bureau.
BALANCE, and BALANCE-SPRING. The balance of a watch is a wheel finely poised on its axis; the pivot-holes in which it turns being frequently — in chronometers and clocks, as well as in watches — jeweled, or made of small rubies, diamonds, etc., for the sake of durability. The natural effect of an impulse given to such a wheel would be a complete rotation on its axis. This, however, is convertible, by the escapement (q.v.), and by the balance-spring, into a vibratory motion. The balance-spring is held to be a crowning invention in the mechanism of the watch; and the honor of its first suggestion has been claimed for no less than three very eminent men — Hooke, an Englishman; Abbé Hautefeuille, a Frenchman; and Huygens, the Dutch astronomer. The honor, however, is thought to belong to Hooke, who applied for a patent for the invention in 1658 or 1660.
The balance-spring consists of a coil of fine steel wire which determines the time of vibration of the balance. One of its extremities is fastened to a point independent of the balance, while the other is attached near its axis. When the balance is at rest, the spring is not under tension, its position being called the point of rest; but when an impulse is given to the balance by the crown-wheel of the escapement, the balance moves around just so far as the impulse given is able to overcome the elastic resistance of the spring. When that resistance becomes equal to the impulse given, the balance stops for a moment, and then is driven back by the elastic recoil of the spring, and continues thus to vibrate so long as the impulse is repeated or the watch is in motion. The subject of balances and balance-springs and their adjustment is treated at considerable length in Britten, Watch and Clockmakers' Handbook (London, 1896). For a general description of watchmaking and for illustration of the balance wheel, see Watch.
BALANCE OF POWER. An expression used in diplomacy, with reference especially to
