Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/352

them from the plane of the first is ${\sqrt {\frac {3}{7}}}C$. The number of windings on each of these coils is 49.

The value of $G_{1}$ is ${\frac {120}{C}}$.

This arrangement of coils is represented in Fig. 51.

Fig. 51.

Since in this three-coiled galvanometer the first term after $G_{1}$ which has a finite value is $G_{7}$, a large portion of the sphere on whose surface the coils lie forms a field of force sensibly uniform.

If we could wind the wire over the whole of a spherical surface, as described in Art. 627, we should obtain a field of perfectly uniform force. It is practically impossible, however, to distribute the windings on a spherical surface with sufficient accuracy, even if such a coil were not liable to the objection that it forms a closed surface, so that its interior is inaccessible.

By putting the middle coil out of the circuit, and making the current flow in opposite directions through the two side coils, we obtain a field of force which exerts a nearly uniform action in the direction of the axis on a magnet or coil suspended within it, with its axis coinciding with that of the coils; see Art. 673. For in this case all the coefficients of odd orders disappear, and since

Hence the expression for the magnetic potential near the centre of the coil becomes