DYNAMOS. 719 



In other words, the real current I is equal to the excess of 

 the current Ij which is produced for the same velocity in a field 

 of maximum intensity, over the current I 2 , which would magnetise 

 the inductors to half the maximum. The current I x only depends 

 on the movable ring, while the current I 2 only depends on the 

 inductors ; the true current is thus expressed by two terms of very 

 different characters. 



1272. RESISTANCES OF THE INDUCTOR AND OF THE INDUCED 

 BODY. We may inquire what ratio should exist between the re- 

 sistances of the inductor and induced body so as to obtain the 

 greatest efficiency.* Suppose, first, that the two parts are not 

 traversed by the same current, and that we are given the volumes 

 occupied by the coiling of the wires. 



For an annular coil, let 



V be the total volume of the wire,- including the insulator, 



L the length of the wire, 



S the section, comprising the insulating material, 



the fraction of this section occupied by the conductor, 

 m 



a- the specific resistance of the metal, 

 a the total resistance, 

 I the current. 



If, in like manner, V, L', S', m\ </, b and I' are analogous 

 quantities for the inductor, we have 



V = SL 0--= 0--- 



"s ! "S2 ; 



putting K 2 = wo-V, we may write 



a 

 In like manner, putting K' 2 = wo-'V', we shall have 



*> ' 



* Sir W. THOMSON. Comptes rendus, Vol. XCIIL, p. 474. 1881, 



