Electric Currents in Networks of Conductors. 255 



then x is the current through the galvanometer, and y is the 

 current through the battery. When the arrangement is made 

 as in the diagram, and the fork set vibrating, the vibrating 

 fork and the condenser act together like a resistance, and let 

 through so much electricity per second. 



Now, as the condenser gets its charge by electricity flowing 

 into it, it builds up an opposing electromotive force in the z 



circuit which at any instant is equal to the value of J * c , where 



K 

 K is the capacity of the jar, the integral being integrated from 

 the instant when the charging commences up to the instant 

 considered. Now, if the fork makes n vibrations a second 

 when the steady state is set up, the current z which flows into 



the jar has a mean value z; and therefore -^ is the opposing 



electromotive force in that branch. 



Accordingly, the condenser and associated commutator 

 behave like a voltameter inserted in the branch a/3, or like a 

 resistance with a counter electromotive force in it. Only such 

 a combined jar and fork differs from an ordinary metallic 

 resistance in this, that its apparent resistance is not constant, 

 but depends on two things, the speed of commutation or 

 charge and recharge, and the capacity of the condenser; whilst 

 the counter electromotive force depends on the current z, and, 



being represented by -^, is dependent not only on n and K, 



but also on the values of all the other resistances in the branches. 

 In the first place, we require an expression for the electro- 

 motive force charging the condenser. Let the difference of 

 potential between a and b be called e. Then consider the net- 

 work formed by the five conductors R, S, Q, Gr, and B with 

 the electromotive force in the branch B; write down the net- 

 work equations for this z mesh network. 



■(B + R+S)y-S(* + *) = E, 



-Sy+(Q+S+G)(^+^)==Q, 



Hence 

 and 



_E(Q + S + G) 



y- i ; 



_ES 



where 8= the determinant 



i B + R + S, -S 



! -S, Q + S + G 



T2 



