6 Louis Schwendler — On Differential Galvanometers. [No. 1, 



By m was understood the magnetic effect of an average convolution 

 (i. e, one of average size and mean distance from the magnet acted upon, 

 when the latter is parallel with the plane of the convolutions) in the 

 differential coil of resistance g, when a current of unit strength passes 

 through it. Similarly m' was the magnetic effect of an average convolution 

 in the other differential coil of resistance g'. 



Further n and n' were quantities expressed by 

 U = w A^g 

 and U' = n' ^g' 



U and U' being the number of convolutions in the two coils g and g' respec- 

 tively. 



Now we will call A half the cross section of the coil g (cut through 

 the coil normal to the direction of the convolutions) and which section, as 

 the wire is to be supposed uniformly coiled, must be miiform throughout. 



Thus we have generally 



^ =u 



<1 + S) 

 wherever the normal cut through the coil is taken. 



c is a constant indicating the manner of coiling, either by dividing the 

 cross-section A into squares, hexagons or in any other way, but always sup- 

 posing that however the coiling of the wire may have been done, it has been 

 done uniformly throughout the coil. (This supposition is quite sufficiently 

 nearly fulfilled in practice because the coiling should always be executed 

 with the greatest possible care, and further the wire can be supposed practi- 

 cally of equal thickness throughout the coil). 



q^ is the metallic section of the wire, and 8 the non-metallic section due 

 to the necessary insulating covering of the wire. 



Further we have 



y = U — ■ where h is the length of an average convolution and \ the 



absolute conductivity of the wire material supposed to be a constant for the 

 coil. 



Now, for brevity's sake, we will suppose that 8, the cross-section of the 

 insulating covering, can be neglected against ^ the metallic cross-section of 

 the wire. 



Consequently we have 



— = U (approximately) 

 and o' = U -T- 



/ax / 



