Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/375

744.] If the coefficient of torsion of the suspension fibre is $$\tau MH$$ (see Art. 452), we must use the corrected formula Rh

743.] In some galvanometers the number of windings of the coil through which the current flows can be altered at pleasure. In others a known fraction of the current can be diverted from the galvanometer by a conductor called a Shunt. In either case the value of $$G$$, the effect of a unit-current on the magnet, is made to vary.

Let us determine the value of $$G$$, for which a given error in the observation of the deflexion corresponds to the smallest error of the deduced value of the strength of the current.

Differentiating equation (1), we find RhRh

This is a maximum for a given value of $$\gamma$$ when the deflexion is 45°. The value of $$G$$ should therefore be adjusted till $$G\gamma$$ is as nearly equal to $$H$$ as is possible; so that for strong currents it is better not to use too sensitive a galvanometer.

744.] When the observer is able, by means of a key, to make or break the connexions of the circuit at any instant, it is advisable to operate with the key in such a way as to make the magnet arrive at its position of equilibrium with the least possible velocity. The following method was devised by Gauss for this purpose.

Suppose that the magnet is in its position of equilibrium, and that there is no current. The observer now makes contact for a short time, so that the magnet is set in motion towards its new position of equilibrium. He then breaks contact. The force is now towards the original position of equilibrium, and the motion is retarded. If this is so managed that the magnet comes to rest exactly at the new position of equilibrium, and if the observer again makes contact at that instant and maintains the contact, the magnet will remain at rest in its new position.