432 Mr. T. H. Blakesley on the Differential 



or 



cos 27 = cos P cos /3 + 20 1? 



showing that the condition that no work shall be done in the 

 electric problem depends on the initial circumstances, i. e. 6 l 

 is involved. If 27=/? the condition of no work becomes 



cos £ + 20, = 1, 

 which is satisfied when 



01—2- 



Hence if the initial condition be that of no current, the line 

 bisecting the angle between the line of effective E.M.F. and that 



of the self-induced E.M.F. makes — ^ with the line 0=0, and 



it is thus proved that on the whole no work 

 is done in the field. 



If, on the other hand, we make 



<?!-+ 2 > 



and start from a point where the current 



is zero, we have in the above expression, 



when proper substitutions are made for a and b, the value of 



the work done on the circuit by the discharging condenser. 



The integral between infinity and 6 X becomes, when X = - and 



ab . t 2 



87T 



{1— cos 2/S} sin/3.e tan/3 



or 



ab . t 2 . . _ - _i_ 

 —; — sm 6 3e tan/s. 

 4tt 



In this case b= ^5 and ae "t^sin^is the potential difference 



between the plates of the condenser at starting =V 1? say, 

 = Vsin/3. Hence the expression becomes 



E t 2 • 3 o TT 



(E and V being now the full sides of the triangle, properly 

 interpreted), and ^-y =cos /3 by the geometry of the triangle, 

 and further, 



