430 Mr. T. H. Blakesley on the Differential 



therefore cos^=^/y ~, and /3 can have a real existence 



77" "D2 



when - 7T -<1; — the condition of Oscillatory Discharge. 



The complete period is t 2i and is obtained in the electrical 

 quantities thus ; — 



tan/3: 

 therefore 



27T^ 



2 _ (2tt)V _ (2?t)% 2 , 



2 ~tan 2 /3 ""sec^-l' 



and cos 2 fi=j- already obtained ; 



. 4ttVi 4tt 2 KL 



therefore £ 2 = ■ 



therefore 



1 *, Ul 



2ttVKL 



the form usually quoted if we neglect the second term of the 

 denominator. 



I purpose to show that in a discharge of the sort here con- 

 templated (which has been shown to be the result of the 

 ordinary premisses given at page 425) there will be no work 

 done by any electromotive force which lags at an angle j3 

 behind the current, provided the initial condition is one of 

 zero-current. And, further, that the source of E.M.F., which 

 is represented by the side of the isosceles triangle in advance 

 by the angle /3, of the effective E.M.F., does all the work of 

 heating the circuit and no more. It will thus be seen that 

 there is no provision in the theory for expenditure of power in 

 the field, and hence that the theory does not explain the well 

 recognized phenomenon of radiation into space. 



To establish the above-mentioned propositions, take the 

 product of the projections of two lines undergoing variations 

 corresponding to the two radii vectores of two equiangular 

 spirals of the same characteristic angle {3 and period, and 

 differing in phase by the angle 27. 



One of these quantities may be expressed by 



