1873.] Louis Schwendler^— 0;^ Differential Galvanometers. 



or 



similarly 



w 

 "n " V AX h'c' 

 But using wire of the same conductivity in both the differential coils, 

 which should be as high as is possible to procure it, and fui'ther supposing 

 the manner of coiling to be identical in both coils, we have 



c = c' 





Further we know that if the shape and dimensions of each coil are 

 given, and in addition also their distance from the magnet acted upon, it 

 will be always possible to calculate m and m', though it may often present 

 mathematical difficulties, especially if the forms of the two coils differ from 

 each other and are also not circular. This latter condition is generally 

 necessitated in order to obtain the greatest absolute magnetic action of each 

 coil in as small a space as possible. 



However it is clear that we may assume generally that the two coils 

 have each an average convolution of identical shape and of the same length, 

 placed at an equal distance from the 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 

 on =^ m' 



n' __ Ik! 

 n'~~^ k. 



T n' on' 



and as « == — • — 

 n m 



we have finally 



A w 



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 diame- 

 ter of the wire : 



