422 Mr. T. H. Blakesley on the Differential 



ample evidence. Therefore an equation will not meet such 

 cases in which the induced electromotive force is taken as 

 entirely in quadrature with the current, or when F is wholly 



of the form — L-77. 

 at 



Hence, in the geometrical representation it is clear that 



the induced electromotive-force line must 



not be exactly at right angles with that of 



the effective electromotive-force line ; i. e. 



the angle B C A is not exactly a right angle; 



and it is easy to see that it must be greater 



than a right angle, for B C may be resolved 



into BD.DC, where B D is a right 



angle and A C D is one straight line. For 



then the w T hole work done is equal to 



The work done in heating 



2R 



conductor is - — ' \ and the d 



AC . DC 



ence, or the work done in the field, is 



Hence, if D lies on the side of C nearer to A , A D would 

 be less than A C, and the work done by the discharge would 

 be less than that required to heat the conductor : in other 

 words, energy would have to be received from space. 



Hence the induced electromotive forces may be represented 

 by two components — one A D in quadrature with the current, 

 and one D in opposition to it, 



where X may or may not be a constant, but is in kind a 

 resistance. 



The equation among the electromotive forces may be 



written 



L~-\C = RC. 

 at 



Multiplying through by Cdt and integrating through a 

 complete period, 



fvOfc-L fe^=K(W+ (\C 2 dt. 



The second term on the left vanishes as before, the first 

 term representing ihe whole work done. On the right the 



