284 Mr. K. H. M. Bosanquet on Self -regulating 



The equation E = $$vl then becomes 



B = knCvl 



E 



In main-circuit machines, C = ^ , , 



H-j-r 



9 1 knvl 



U + r' 



and v can only have one value for a given value of r 9 which 

 does not correspond with fact. 



The same difficulty applies to dynamo machines of all types. 

 The inference is that the assumption that the field-magnetism is 

 proportional to the number of current-turns is wrong. 



In fact, in the equation E = 5BvZ,if E is not to strike out on 

 both sides, 23 must be some other function of E than the 

 simple first power. The point is most easily dealt with by 

 assuming 33 proportional to a power 7 of the current-turns. 

 7 may not be an absolute constant; but its value can be easily 

 obtained in the different parts of the range of the machine. 



Then we get an equation of the form 



or 



for given resistance. 

 Dividing by (R + r) 1 ' 7 



E = K 1 E y t>, 

 E 1 " y =K 1 t7 



Put 



= x, or 1— 7=-, or 7 = 1 



1 — y x x 



then 



C = K 3 «* 



a relation which can be easily examined experimentally. 



I have examined this relation with my Gramme machine, 

 chiefly using the main circuit only. It is clear that the exci- 

 tation by a given number of current-turns cannot depend on 

 their supply by shunt or main circuit; so that it is sufficient to 

 examine the law in this simpler case. 



The result may be described by assigning approximate 

 values. I consider 5 to 20 amperes the practical range of my 

 machine. Without pretence to accuracy, I obtain 



