292 Mr. E. H. M. Bosanquet on Self-regulating 



Then —^ becomes negative in itself, and ~ — ^ is always 



dv to J dv dv J 



positive, so that the motion is stable. 

 The governing relation is therefore 



1 

 E 2 / E— 1 \ 

 P = Jpn-Wv\ n -- V + X'! 



(ixvy- 1 



The practical deductions are as follows : — The ratio of 

 shunt and main coils is subject to a condition in order that 

 the required governing relation for constant E.M.F. may be 

 stable. This condition may be put in the form 



R n 

 < 



R + /> ^ v 



This tells us therefore that the ratio of the number of main 

 coils to shunt must be greater than that of armature resistance 

 to sum of armature and shunt resistance. 



A suitable value of R//o might be 1/100. Then, suppose 

 there are 10,000 coils in the shunt, there must be more than 

 101 coils of the main circuit. 



Under these circumstances it would appear that there is 



another condition to be fulfilled in order that the expression 



for the power may be positive, viz. 



i 



v—n E*" 1 

 < -• 



(l\vf- 



"FT 



But, remembering that ., y = ~F X ~ , this condition becomes 



n-\--r 

 ■n p 



< 



p R + rs 



and it can be shown that this reduces to the same condition as 

 that found above, viz. 



R/ U \ n 

 — (or t^ I < -. 



sp\ K-\-p/ v 



So that it is only necessary to satisfy this one condition. 

 This being so, the governing function assumes the form 



a B 



