Page:Elementary Text-book of Physics (Anthony, 1897).djvu/93

§ 63] the load increases. As the angle $$\alpha$$ becomes less, the value of $$\beta$$ increases for a given load, and is less affected by cminges in the load, until, when $$A$$, $$O$$, and $$B$$ are in the same straight line, it depends only on $$\frac{pl}{Wd}$$, and is independent of the load. In this case $$\tan{\beta}$$ increases as $$d$$, the distance from the point of suspension to the centre of gravity of the beam, diminishes, and as the weight of the beam $$W$$ diminishes. To secure sensitiveness, therefore, the beam must be as long and as light as is consistent with stiffness, the points of suspension of the beam and of the scale-pans must be very nearly in the same line, and the distance of the centre of gravity from the point of suspension of the beam must be as small as possible. Great length of beam, and near coincidence of the centre of gravity with the axis, are, however, inconsistent with rapidity of action. The purpose for which the balance is to be used must determine the extent to which these conditions of sensitiveness shall be carried.

Accuracy is secured by making the arms of the beam of equal length, and so that they will perfectly balance, and by attaching scale-pans of equal weight at equal distances from the centre of the beam.

In the balances usually employed in physical and chemical investigations, various means of adjustment are provided, by means of which all the required conditions may be secured. The beam is poised on knife-edges; and the adjustment of its centre of gravity is made by changing the position of a nut which moves on a screw, placed vertically, directly above the point of suspension. Perfect equality in the moments of force due to the two arms of the beam is secured by a similar horizontal screw and nut placed at one end of the beam. The beam is a flat rhombus of brass, large portions of which are cut out so as to make it as light as possible. The knife-edge on which the beam rests, and those upon which the scale-pans hang, are arranged so that, with a medium load, they are all nearly in the same line. A long pointer attached to the beam moves before a scale, and serves to indicate the deviation of the