258 Prof. Thomson, A Method of Comparing the [Feb. 11, 



The following Communications were made to the Society: 



(1)* A Method of Comparing the Conductivities of Badly Con- 

 ducting Substances for rapidly Alternating Currents. By Professor 

 J. J. Thomson. 



The method employed in the following experiments consists in 

 making a secondary circuit of standard form made of the substance 

 whose conductivity is to be investigated, and observing the effect 

 produced by its presence on the alternating currents in a primary 

 circuit. 



Before proceeding to consider the results of the experiments it 

 will be convenient to discuss some points connected with the 

 theory of the reaction of the secondary circuit on the primary. 

 The first case we shall consider is that of the ordinary transformer 

 when the electromotive force acting on the piimary circuit is given. 

 If this electromotive force is E cos pt, and if L, M, N are re- 

 spectively the coefficient of self-induction of the primary, the 

 coefficient of mutual induction between the primary and secondary 

 and the coefficient of self-induction of the secondary ; R the 

 resistance of the primary, 8 that of the secondary, x the current 

 through the primary, y that through the secondary : then we have 



L^ + M ~ + Raj=E cos pt, 

 dt dt 



Solving these equations we find 



_ E cos {pt — a) 



where 



•(1), 



L' = L- 



R' = R + 

 tana = 



S' + N-y 



M^-Sp^ 



S' + Ny 



L'p 

 'R' 



Substituting these values of Z' and R' in (1) we get 



_ E cos (pt — a) 



|xy + R^ + s^TNY ^^ ^^ - ^^^^' - ^'^ P'^f 



* The chair was taken by Professor Sir G. G. Stokes, Vice President, whilst 

 Professor Thomson read his paper. 



