The Balance - General Considerations

The balance, as is well known, consists of a metal beam, supported so as to be free to turn in a vertical plane about an axis perpendicular to its length and vertically above its centre of gravity. At the extremities of this beam, pans are suspended in such a manner that they turn freely about axes, passing through the extremities of the beam, and parallel to its axis of rotation. The axes of rotation are formed by agate knife-edges bearing on agate plates. The beam is provided with three agate edges; the middle one, edge downwards, supporting the beam when it is placed upon the plates which are fixed to the pillar of the balance, and those at the extremities, edge upwards; on these are supported the agate plates to which the pans are attached.

The effect of hanging the pans from these edges is that wherever in the scale part the weights be placed, the vertical force which keeps them in equilibrium must pass through the knife-edge above, and so the effect upon the balance is independent of the position of the weights and the same as if the whole weight of the scale pan and included masses were collected at some point in the knife-edge from which the pan is suspended.

In order to define the position of the beam of the balance, a long metal pointer is fixed to it, its length being perpendicular to the line joining the extreme knife-edges. A small scale is fixed to the pillar of the balance, and the motion of the beam is observed by noting the motion of the pointer along this scale. When the balance is in good adjustment, the scale should be in such a position that the pointer is opposite the middle division when the scale beam is horizontal. The only method at our disposal for altering the relative position of the scale and pointer is by means of the levelling screws attached to the case. Levels should be placed in the case by the instrument-maker, which should show level when the scale is in its proper position.

In the investigation below we shall suppose the zero position of the balance to be that which is defined by the pointer being opposite the middle point of its scale, whether the scale is in its proper position, and the pointer properly placed or not.

The other conditions which must be satisfied if the balance is in perfect adjustment are:

• The arms must be of equal length.
• The scale pans must be of equal weight.
• The centre of gravity of the beam must be vertically under the axis of rotation when the beam is in its zero position. This can always be ensured by removing the scale pans altogether, and by turning the small flag of metal attached to the top of the beam until the latter comes to rest with the pointer opposite the middle of its scale. Then it is obvious from the equilibrium that the centre of gravity is vertically under the axis of support.