60 Mr. W. Gr. Rhodes on a Theory 



and, corresponding to c = 0, we have 



<? = ±E. 

 Now, solving equation (5) as a quadratic in c we get 



°= + §± pV^(PE 2 -RV), .... (6) 



and, as c is real, we must have 



I 2 E 2 >RV 

 or IE >Re ; 



therefore the maximum value of e is given by 



IE 

 ± R 



and the corresponding current is 



e$ 

 F 



C = + T2 



__ SE 

 The equation 



= + Rr 



* 2 -2S*? + I 2 c 2 = E 2 



is the characteristic curve of the motor running light. It 

 may be written 



* 2 -2Sce + SV + RV=E 2 



or (*-Sc) 2 +RV=E 2 , 



or (e— Sc) 2 c 2 __ 



E 2 + E 2- ' 

 R 2 



which is the equation to an ellipse having as conjugate 

 diameters the lines 



e — Sc = and c=0. 



Similarly, the equation 



* 2 + 2Sc<> + IV=E 2 , 



which refers to the generator, may be written 



(<?+Sc) 2 _c*_ 

 E 2 E 3 '" ' 



R 2 



