270 Mr. Louis Schwendler on Differential Galvanometers, 



magnet acted upon, and that therefore the magnetic action of 

 each coil is dependent on the number of convolutions only. 

 In this case we have evidently 



m = m', 



b = V, 

 J 



and as 



we have, finally, 



i- A' 



n' m r 



p= > 



n m 



A' w f ,. 



A=^ ' ■•- « 



Equation (e) shows at once that under the supposed conditions 

 (i. e, when the average convolutions in each coil are of equal size 

 and shape) the wire used in either coil is of the same absolute 

 conductivity, and that the thickness of the insulating material 

 can be neglected against the diameter of the wire : — 



The wire used for filling each coil must be invariably of the 

 same diameter ; otherwise a maximum sensitiveness is impossible. 



How the above simple law expressed by equation (e) would 

 be altered when the given suppositions were not fulfilled must 

 be found by further calculation ; but as the latter is intricate 

 and a more general result is not required in practice, I shall 

 dispense at present with this labour. 



Special Differential Galvanometers. — Here shall be given the 

 special expressions to which the general equations (a), (b), (c) } 

 and (d) are reduced when certain conditions are presupposed. 



1st case. — When w and w' } the two resistances at which ba- 

 lance is arrived at, are so large that/, the resistance of the testing 

 battery, can be neglected against either of them without percep- 

 tible error. Substituting therefore /=0 in equations (a) and (b) } 

 we get 



g=§> ....... . (a) 



£=3-; ( b ) 



and the other two remain as they are, namely 



f=^, (c) 



r w v ' 



6-£' ....... (d) 



W V ' 



