The coil of wire is first oriented in the magnetic north-south direction and the compass needle is acted on only by the horizontal component of the magnetic field of the earth.. The passage of the current sets up a magnetic field perpendicular to the coil, and the compass needle points in the direction of the total magnetic field. The coil is now rotated through an angle Ø until the plane of the coil coincides with the needle. Under these conditions, the two torques acting on the needle are due to (a) the magnetic field B of the coil, which is at right angles to the coil, and (b) the component of the earth's magnetic field perpendicular to the coil: B'sinØ. These two torques  just balance each other. Since the value of B is proportional to the current I setting up this field, I is proportional to sinØ. 

   The advantage of this apparatus is that the needle does not have to lie in a uniform magnetic field, and so the compass needle can be relatively large.

   This apparatus in the Garland Collection at Vanderbilt University was bought from Ruhmkorff of Paris about 1875.