Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/383

751.] numerical determination, and should be reserved for obtaining evidence of the existence or non-existence of currents too small to be observed directly.

In all experiments in which transient currents are made to act on the moving magnet of the galvanometer, it is essential that the whole current should pass while the distance of the magnet from the zero point remains a small fraction of the total elongation. The time of vibration should therefore be large compared with the time required to produce the current, and the operator should have his eye on the motion of the magnet, so as to regulate the instant of passage of the current by the instant of passage of the magnet through its point of equilibrium.

To estimate the error introduced by a failure of the operator to produce the current at the proper instant, we observe that the effect of a force in increasing the elongation varies as and that this is a maximum when $$\phi = 0$$. Hence the error arising from a mistiming of the current will always lead to an underestimation of its value, and the amount of the error may be estimated by comparing the cosine of the phase of the vibration at the time of the passage of the current with unity.