206 MEASUREMENT OF CURRENTS. 



If the length of the needle is considerable in respect of the 

 dimensions of the coil and the value G holds for the centre of the 

 needle, the moment may be put in the form 



(1) IMG(i + 7) sin ft = IMGj sin ft, 



the factor G 1 being a mean value of the action of the coil in the 

 space occupied by the needle. The term of correction y which 

 enables us to express G l as a function of G depends on the dimen- 

 sions of the needle and on the angle which it makes with the mean 

 plane of the coil. The factor G l may also be regarded as constant 

 when the needle in the various experiments occupies the same 

 position in respect of the coil, or is very little displaced from its 

 mean position. 



If the coil is one of revolution, the force G is parallel to the 

 axis of the frame for all points of the axis or of the mean plane. 

 We shall say that the needle is in a principal position when its centre 

 occupies one of these points. If 8 is the angle which the direction 

 of the needle makes with the plane of the coil, we have, apart from 

 the term of correction y, 



(2) IMG sin /3 = IMG cos 8. 



This couple is a maximum when the needle is parallel to the 

 coil. We know further that if the coil is symmetrical with respect 

 of its mean plane, the factor G is a maximum at the centre relative 

 to points on the axis. 



The various methods differ in respect of the way in which the 

 couple IMG sin/3 is measured to obtain from it the intensity of the 

 current in relative or absolute values. 



We shall see that in galvanometers properly so called, we estimate 

 the moment of the current as a function of the couple MH, which 

 an external field of intensity H exerts on the needle. If the field is 

 uniform, or the needle so small that the term of correction may be 

 neglected, the magnetic moment M of the needle drops out as a 

 factor common to the two actions. The indications of the gal- 

 vanometer are then independent of the magnetisation and of the 

 shape of the needle. 



830. METHOD OF TORSION. We may counterbalance the action 

 of the current by that of a torsion couple. Suppose the needle sus- 

 pended to a metal wire and in equilibrium in the magnetic meridian, 

 the torsion is then zero. If & is the angle through which the wire 

 must be turned to keep the needle in this position notwithstanding 



