268 Mr. Louis Schwendler on Differential Galvanometers. 



blished when using shunts must be multiplied by the multiplying- 

 power of their respective shunts before they are to be substituted 

 in the equations (a), (b), (c), and (d). 



Mechanical Arrangement designed by p. — The condition which 

 must be fulfilled in the construction of any differential galvano- 

 meter to make a simultaneous maximum sensitiveness possible 

 was expressed by 



f— — , (c) 



m 7V 

 while p= : and it will be now instructive to inquire what 



■* mn 



special physical meaning equation (c) has. 



By m was understood the magnetic effect of an average con- 

 volution (i. e. one of average size and mean distance from the 

 magnet acted upon when the latter is parallel to 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 dif- 

 ferential coil of resistance g ! . 



Further, n and n' were quantities expressed by 



U =n Vg, 

 and 



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

 and g ! respectively. 



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

 the coil normal to the direction of the convolutions), which 

 section, as the wire is to be supposed uniformly coiled, must 

 be uniform throughout. 

 Thus we have generally 



c(q + 8) 



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 supposing 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 practically of equal thickness throughout 

 the coil.) 



q is the metallic section of the wire, and h the non-metallic 

 section due to the necessary insulating covering of the wire. 



