BALANCE (Lat. bilanx, having two scales, from his, twice + lame, plate). An instrument used for the comparison of two masses, or, speak ing less technically, for ascertaining the weight of a body. The balance in its essence is simply a lever (q.v.) or beam poised or suspended so as to move freely about an axis transverse to its length. The force acting on one arm of the lever is produced by the action of gravity on the body whose weight is to he determined, and is equal to its mass In multiplied by g, the accelera tion due to gravity. (See AlEcitAxics.) If the lever is in equilibrium, or the beam at a horizon tal position, there must be a force equal, but opposite in direction, acting on the other arm at an equal distance, and as the acceleration due to gravity is a constant for any one point on the earth's surface, and as the inns• of the lever are equal by construction, the mass of known mag nitude upon which gravity acts must be equal to the mass of the unknown body. if the arms of the balance are unequal in length, it follows, from the law of the lever, that the masses are inversely as the length of the arms. The bal ance, accordingly, enables us to learn the actual mass of a body by direct comparison with a standard of mass. The spring balance (q.v.), on the other hand, measures the weight or attrac tion exerted by the earth on a body. and as the force of gravity varies from point to point, the force acting on the spring must vary with the place. The mass of the body which is being weighed is constant, so that the amount that the spring is stretched depends upon the acceleration due to gravity.
From the foregoing considerations it will read ily be seen that there are two methods which may be followed in the construction of a balance: Either to make the arms equal in length, and then find the number of weights of known value which will produce equilibrium, as in the case of the ordinary balance; or by having a known constant weight whose position, and consequently the effective length of the arm on which it is suspended, can he varied at will, as in the case of the steelyard. These facts were early known, and the balance is one of the first instruments to be used for measurements, having been em ployed by the ancient Egyptians, as the accom panying illustration testifies, and by other na tions of antiquity. The steelyard played an important part in the ordinary coin me r c ia 1 trans actions of the Ro mans, and interest ing specimens of these balances and their weights have survived which show few if any important varia tions from the or dinary steelyard of the present.
Considering the simple balance, it is found that its first essential is that the arms should be equal, so that iv h e n once there is equilib rium the known and unknown weights may be interchanged out disturbing this condition. Otherwise the ance is false, and the weight obtained is not correct, being too great if the standard or known weights are placed in the short pan, and vice versa. Then, as it is necessary that the beam should move freely, there must be a proper mounting or suspension where friction is re duced to a minimmn, and as the force of gravity acts vertically, both known and uhknown weights must be carried in suitably suspended pans.
The balance is instrument whose use is sus ceptible of great accuracy, and this is attained in the balances used by physicists and chemists in their measurements of precision. While the
theoretical considerations involved are of course applicable to all forms of balances, they become of greater significance in discussing these finer instruments where extreme accuracy is desired. In such a balance the beam is of metal and car ries at its middle point, transverse to its length, a steel or agate knife-edge which rests on sur faces of similar material. The line of contact between the knife-edge and tint plane is the axis around which the beam revolves; and when the beam is at rest a vertical line through the centre of gravity would include this knife-edge. Con nected with the beam, as shown in the illustra tint, Fig. 3, is a fine pointer, which passes over a graduated scale at the base of the supporting pillar, while at or near its extremities arc placed, at equal distances from the central knife-edge, knife-edges upon whose sharp edges, turned up ward, are placed the bearing surfaces of the metallic pieces from which the pans are sus pended. In order that a Mini mu m of wear should come upon these sharp edges, mechanism is provided to support the beam and pans when ever there is no actual weighing, and the devices to accomplish this vary in different forms of bal ances. The beam is graduated into 10 equal divisions, which in turn are similarly subdivided, and a hook on a movable rod is provided, by means of which a fine loop or rider of wire can be placed and removed at any desired point on the beam. Such is a general description of a balance, though there are, of course, numerous mechanical modifications and refinements to in sure facility of operation and accuracy of meas urement. The underlying principles will per haps better be understood by referring to the diagram, Fig. 4. Let AC'B represent the beam of a balance, and let the points where the knife edges intersect a vertical plane through the beam be located on the line :lei?, though this condi tion in practice is not always realized, and the knife-edges at the end of the beam may be either higher or lower than the centre knife-edge. The point of support is at (', consequently the centre of gravity is situated at On a vertical line passing through this knife-edge. The location of the centre of gravity of the beam is an impor tant consideration. If it were above the point of support the beam would be in unstable equi librium, and would seek a more stable pfisition, and in so doing would overturn. If the centre of gravity coincided with the axis of revolution, the beam would rest in any position indiffer ently, while the stability increases with the dis tance of the centre of gravity below the point of support. With an increase in the stability of the beam, the less the sensitiveness of the balance and the quicker the time in which it will cease from oscillating and take up a position of The sensitiveness also depends on the length of the arms, increasing with the length, and the case, or lack of friction resulting from skillful construction, with which the beam oscillates. The more sensitive, the balance the larger the period of oscillation of the beam, though it is necessary to consider the time necessary in mak ing a weighing, and not adjust an ordinary bal ance to too high a degree of sensitiveness. An ordinary fine balance, as used by the physicist or chemist, is constructed and adjusted to have a period of vibration of between ten and fifteen seconds.