Self- Excitation in a Dynamo Machine. 471 



such as electric and magnetic leakage, being the only point 

 assumed. 



It is known that the electromotive force of a dynamo may 

 be written 



E = nCN; (1) 



where E is the electromotive force (in absolute C.G.S. units); 

 n the number of revolutions of the armature per second ; 

 C the number of conductors counted round the periphery of 

 the armature, and closed in series ; N the whole number of 

 magnetic lines (in C.G.S. units) that traverse the armature. 



So, writing XR for the sum of the electric resistances (in 

 C.G.S. units) of the circuit in which the electromotive force 

 operates, the current flowing in the circuit may be written as 



i- 7 ^ (2) 



Again, it is known that the number of magnetic lines in the 

 armature may be calculated by dividing the line-integral of the 

 magnetizing forces by the sum of the magnetic resistances of the 

 " magnetic circuit " of the dynamo. If the machine is joined 

 up with its exciting coil of S convolutions in series with the 

 main circuit, the line-integral of the magnetizing forces will 

 be written as 47rS/. Then, writing 2p as the sum of all the 

 magnetic resistances in the magnetic circuit, we shall have 



N-^' (3) 



From (2) we get 



N 2K' w 



and, from (3), 



N 4ttS W 



Equating (4) and (5), we have 



47rSnC = ^.SR (G) 



It will be noticed that this equation contains neither N nor i, 

 and its truth is independent of the relation between i and N. 

 It is true that *lp, which is a factor of the expression on the 

 right-hand side, depends on N, and, in general, increases when 

 N is increased. But the truth of the equation is not affected 

 by the form of the relation between 2p and N ; in brief, it is 

 true independently of any assumptions as to the form of the 

 law of magnetization. 



On examining the expression on the left hand of the equa- 

 2 K2 



