BALANCE, the name of a simple machine for ascertaining the weight of any body, or for finding a quantity of any substance equal to a given The balance has generally been arranged among the mechanical powers, but it is evidently only a particu lar species of the lever in which the two arms are equal, and in which there will be an equilibrium when the power and weight are equal.
The balance consists of a horizontal beam, which turns round an axis or centre of motion exactly in the middle of the beam. The two halves of the beam, on each side of the axis, are called the arms of the balance. From the two extremities of the beam, called the points of suspension, are hung two scales, in one of which is placed the substance to be weighed, and in the other are placed weights of a known magnitude. The equality of the weights in the two scales, or the perfect equilibrium of the ba lance, is known from the horizontal position of the beam. In the common balance, where the whole machine is suspended from the axis of motion, a slen der arm, called the tongue of the balance, rises per pzndieularly from the centre of the beam, and points to a particular part of the handle by which the whole is suspended when the beam is horizontal.
In balances where very great accuracy is required, the beam is not supported by suspension, but has a fine edge of steel for its axis, which rests upon steel planes. The horizontal position of the beam is in this case determined, by observing when the extremi ties of the arms point to the zero of two ivory scales fixed in the mahogany frame in which the instrument i3 placed, the line joining the two zeros having been previously placed in a horizontal position, by levels fixed in the mahogany frame. The beams of these delicate balances sometimes consists of a plain cylin drical rod, of a double cone, whose vertices form the points of suspension, or of a frame in the form of a rhombus.
In constructing an accurate balance, it is necessary, 1. That the two points of suspension, and the axis or centre of motion,, should be in the same straight line. energy of any weight in turning a lever round i its fulcrum is proportional to the perpendiculars let fall from the fulcrum upon a vertical line passing through the points of suspension. When the points of
suspension, therefore, and the centre of motion, are not in one line, the perpendiculars let fall upon the verti cal lines are equal only when the line joining the points of suspension is truly horizontal. In every other position, the perpendiculars will be unequal,' and there will not be an equilibrium between equal weights. When the points of suspension and the' centre of motion, however, lie in the same straight! line, the perpendiculars upon the vertical lines be equal, in every position of the beam, and there will always be an equilibrium between equal weights, the beam being supposed without weight. 2. The points of suspension must be precisely equidistant fronz the centre if motion, or, what is the same. thing, the arms of the balance must. be exactly the same length. It is obvious, that when the arms are unequal there cannot be an equilibrium between equal weights, as the one weight acts at the extre mity of a longer lever than the other. 3. The centre of gravity of the beam should be placed a little belotu the centre qf motion. If the centre of gravity of the beam coincides with the centre of motion, the beam will rest in any position in which it is placed, whether it is unloaded or loaded with equal weights. If the centre of gravity is above the centre of motion, the' beam will be overset by the slightest disturbance. But if the centre of gravity is below the centre of motion, the beam will not rest in any but a horizon talposition, and when disturbed will recover this po sition with a degree of facility proportioned to the distance between the centres of motion and gravity. The nearer, therefore, that the centre of gravity is to the centre of motion, the more easily will the equi librium be disturbed, and consequently the more de licate will be the balance. 4. The beam should be as light as possible, but at the same time so strong as not to change its form when the scales arc loaded to a maximum. It is evident, that the friction upon the centre of motion will be diminished by the lightness of the beam, and that the inertia of a light beam will be more easily overcome by a small weight than the inertia of a heavy one.