If now an electric charge is imparted to the two balls by touching the connecting wire of the fixed ball with a charged body, the beam is deflected, and the deflecting force can be calculated from the angular position at which the beam comes to rest. By twisting the torsion head the balls can be brought nearer, and a new position of equilibrium obtained. Observations of the deflection, with different amounts of twist of the torsion head, are taken, and from these it is possible to calibrate the balance, that is, mark out the scale, and then use the calibration for the exact measurement of the repulsive forces acting between the balls. Coulomb was thus able, by means of his torsion balance, to establish the law of electric action at a distance.
We may look on the torsion balance as the practical way of making the experiment described in Chapter I. There is, however, this difference. The purely experimental part of the work with the torsion balance is quite simple, and free from external disturbing influences, but the mathematical investigation of the experimental results is complicated. On the other hand, the mathematics of the experiment described in Chapter I are quite simple and elementary, but the practical carry-
