Dynamo-electric Machines 285 



Current. 



amperes. x. y. 



5 3 § 



10 2 i 



15 

 20 



> average 1*25 ^ 



#=1, <y = correspond to the condition of saturation 



Theoretical Basis. 



I will now examine the effect of a small change of velocity 

 civ in a dynamo, first on the ordinary theory, and then accord- 

 ing to the hypothesis above indicated. 



Let the equation of development of E be 



E d =KNT? = K'E«;, (1) 



and suppose that initially E d = E = E , 

 v becomes v + alv. 

 An increase takes place in the E developed ; 



d 1 E = K'E Q dv, 

 or, dividing by (1), 



diE _ dv , 9 . 



E^"V ^ 



This increase develops in time an increase of magnetism, so 

 that E on the right of (1) becomes 



= E + d 1 E. 



The increased magnetism develops in turn on the left an 

 increase of E, = cZ 2 E; and the amount of the change is the 

 same as in the first case; and so on. 



Hence there are an infinite number of equal increments of 

 E.M.F. developed by a single change dv; and the total change 

 may be expressed, 



AE dv 



-E =QO T 



This being contrary to experience, we will introduce the 

 hypothesis that the change of magnetism falls short of the 

 change of exciting current in a ratio 7, which is less than unity. 

 We arrive as above at equation (2), 



djE _ dv 



An increase of magnetism is next developed; but by hypo- 

 thesis, instead of being the fnll increase due to ^E, it is dimi- 



