Dynamo-electric Machines. 291 



Eliminating r, 



E 2 _ 

 pR-E 2 _ Y~ PS 

 KR-n ~ v 



whence 



P 



V [y ~ sn ) = — (y-n-K P ). 



The condition ^ = — makes the coefficient of p vanish: so 

 ±v ps L 



that the power supplied mast be independent of the velocity. 

 We have seen that in a similar case the equilibrium of the 

 motion is neutral, and the arrangement is not likely to be 

 of use. 



The value of v in this case will depend on E and on x, and 

 is determined by the condition 



v— n — Kp = 0. 



(3) It remains to examine the stability. Writing for K 

 its yalue, the governing relation becomes 



/Rv \ E 2 / E^ 31 \ 



(l\v)x-i 



If we assume — > T=othe motion will not generally be stable. 

 sp W & J 



For, using the general value of the power absorbed, 



dp / - \ 2 *-l/ ,. \2(a:-l) 



dv 



and 



-wfe) K-ro-3 



i 

 dp, _ E 2 x E*" 1 



efe _ 7Rv \' x-1 JL 



i 



dp dp 



Both terms of -=-2 ~ are therefore positive in themselves. 



dv dv 



As x comes to differ little from 1 the second term increases 



indefinitely ; therefore anywhere near the point of saturation 



of the magnets the motion would be unstable. 



We must therefore have 



v n 

 — < t>- 



SO IX 



