MOVABLE COILS. 237 



These two equations give separately the intensity I and the 

 component H : 



C 



12= tan S tan 3', 



S' tan 8 



The magnetic field is not in general identical for both instru- 

 ments. The ratio of the intensities H and H' of the two fields 

 should then be determined ; for instance, by the oscillations of the 

 same needle. 



. 858. Sir W. Thomson has proposed* to combine the experiment 

 so as to obtain two deflections 8 and 8' by the same instrument. 

 This double galvanometer is made of a rather large frame with a 

 small needle at the centre, as in the tangent compass ; both frame 

 and needle, however, being movable. Both being parallel to the 

 magnetic meridian in the original position of equilibrium, the de- 

 flections 8 and 8' are observed which the needle and the coil expe- 

 rience in opposite directions during the passage of the current. 



The equilibrium of the needle is defined by equation 



the action of the needle on the coil being equal to that of the coil on 

 the needle, we have, on the other hand, for the equilibrium of the 

 needle with a bifilar suspension 



(26) HIS cos 8' + IMG cos (8 + 8') = C sin 8'. 



From these two equations it follows that 



C tan 8' C tan 8' 



1 = 



(27) HS MGcos(S + ff) HS MsinS* 



+ H^ cos 8' + I 



To deduce from these equations the values of I and of H, it is 



necessary to know one of the ratios - - or ; but as the needle 



Ho lo 



MAXWELL. Electricity and Magnetism, Vol. u., p. 337. 



