286 Mr. R. H. M. Bosanquet on Self-regulating 



nished in ratio 7. So that the next increment of E, developed 

 by the motion in the increased field, is defined by 



d 2 E _ dv 



E7~ 7 V 



Similarly each successive term is derived from the preceding 

 by multiplication by 7. Whence 



1 dv 



1 — 7 v 



or, if we now write <£E for AE, since the total change is com- 

 parable with dv, 



oTE_ 1 dv 



m ~~i— 7 v' 



Integrating, 



log e v = (l—y) log E + constant, 

 or 



# = E 1-y x constant; 

 which is the form of equation above assumed. 



We will now consider the general case of a machine having 

 the magnets wound both with main and shunt coils. 



Number of Coils. 

 n main-magnet coils. v shunt coils. 



Resistances. 



R armature, r external and magnets, p shunt coils. 

 r resultant of r and p in parallel circuit. 



Ui + i- 



r r p 



It is required to simplify ^ 



1 



r = 



r p 



r 



1+ 1 - 

 p 



