DIMENSIONS OF MACHINES. 723 



at two homologous points. The field of the inductors is then the 

 same in the two machines. 



The surface traversed by the windings of the ring being /x 2 times 

 greater, and the field being the same, the flow of force cut at each 

 turn, or the characteristic function, becomes /A 2 times greater that 

 is to say, /x. 2 </>(I). The electromotive force of the second machine 



E' = n V < (I) = /*< (I) = fiE 



is then //, times greater than that of the first. 



Finally, the resistance of the inducing wire, being proportional to 

 its length and inversely as its section, is inversely as //. ; as the same 

 ratio holds for the induced wire, the total resistance a' + b' of the 



second machine is equal to - . 



* 

 The energy lost by heating 



is then proportional to the ratio of the similitude. The heat lost by 

 radiation is, for the same rise of temperature, proportional to its 

 surface that is, to ft 2 . The heating will then be much less for the 

 larger machine. 



The ratio of the energies expended is then 



W 

 the useful work is 



and the efficiency 



RI 



" 



This efficiency increases with the dimensions. The fictive re- 

 sistance which is equivalent to the effects of self-induction does not 

 change, since the coefficient / for each ring is proportional to its 

 dimensions that is to say, to //., and we have 



mn'l' = mnl=a. 



But as the resistance of the machine is diminished, the relative im- 

 portance of the effects of self-induction increases with the dimensions. 



A AA 2 



