540 Mr. L. Schwendler on the General Theory 



with respect to regularity of working, as close to the different 



tial method as is possible for us to do ; for the disturbance of 

 balance in the sending-station by the steady decrease of the 

 internal resistance of the two batteries has now been probably 

 eliminated, which defect is excluded from the other two me- 

 thods by their own nature. There are then remaining only 

 those variations of the battery-resistance which do not follow 

 the law of steady decrease, but which are more accidental, and 

 make therefore the compensation method still inferior to either 

 the differential or bridge method. 



Physical meaning of v = a /_. 



It has been proved that balance in each station is to be estab- 

 lished by adjusting resistance, and not by a movement of the 

 coils or their armatures. Hence it will be practical and con- 

 venient to coil the two helices above each other and have them 

 acting on one and the same iron core. 



Further, as v = - = a/ it follows that the magnetic action 



of the a coil must be made greater than that of the b coil. 

 Therefore it will be best to coil the helix b on the top of the 

 helix a. 



Further, the magnetic action of a cylindrical coil of resist- 

 ance a (in Siemens units) can be expressed as follows — 



= W "V 7T 



where A is half the cross section of the coil (cut by a plane 

 through the axis of the coil) expressed in square millimetres ; 



X the absolute conductivitv of the wire material (BL=1 at 

 0° C); 



I the length of an average convolution expressed in metres ; 



s the magnetic force exerted by an average convolution of 

 the coil when the unit of current passes ; 



c a coefficient representing the manner of coiling. 



Hence for the a coil we have 



for the b coil 



m a =s f s/a \/ —jy- = q */a, 



— / A! f \ f/ 



Dividing m b by m a , and remembering that by condition 

 a = 6, and that X / = X // , c' = c f/ by necessity, we have 



l== r_£L' A A"* 7 



q s'V Ml"' 



