18/6.] L. Schwendler — On the General Theory of Duplex Telegraphy. 15 



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 bridsre method. 



A 



ofi> V o 



Physical meaning of 



It has been proved that balance in each station is to be established by 

 adjusting resistance and not by a movement of the coils or their armatures. 

 Hence it will be practical and convenient to coil the two helices above each 

 other, and have them acting on one and the same iron core. 



r /I . 



Further as d = - = *./ ^ it follows that the magnetic action of the 

 q V 2 ° 



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 resistance a (in 

 Siemens units) can be expressed as follows : 



/ AX 



m = s \/a ** c I 



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

 of the coil) expressed in [] m m - 



X the absolute conductivity of the wire material ( H g = 1 at 0° G) 



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 



m a = s' \/ a ,J — TtT = q \/c 

 for the b coil 



, ,- I A" X" /- 



= s s/ b . / — — — — = rVb 



* V n" J," 



Dividing mi by m a> and remembering that by condition a = b, and that 

 X' = A", c' = c" by necessity, we have : 



q s V j> i" 



