252 Dr. J. A. Fleming on the Distribution of 



Having now the value of the quantity of electricity left in 

 the condenser at any instant, we can find easily, from the 

 cycle equation (i.), the value of the current through the 

 galvanometer. For 



or 



dt+JjV CL' 



,-p J 3 



and the constant C is determined by the condition y=0 when 



t=0. 



Substituting the value of q above, we have 



G 

 a= 2L' 



y = «-** { a + 1 -^ j>* (/3 cos 0t + a sin j3t) J 

 {c' + ^^sin^}; 



but c=o, 



and since 



^ = TO e " a<Sin/3 ' 5 



/G+S 

 a= _ an d ^=y -Jjjr-jip 



Q 



f 



/ /G + S G 2 \ 

 "/G + S nT CPC* 2L ' Sm W WJ-iL^' 



which gives the value of the instantaneous current in the 

 galvanometer-circuit at any instant t after starting a discharge 

 from a condenser of capacity C and original quantity Q through 

 a shunted galvanometer, the shunt being wound without self- 

 induction, and the galvanometer having a coefficient of self- 

 induction Lj. 



§ 19. Two concluding examples of this method of treating 

 network problems will now be given, which are in Professor 

 Clerk Maxwell's own words*. 



* In the May term 1870, Professor Clerk Maxwell lectured at Cam- 

 bridge on Electromagnetisin, and in the two last lectures of the Course he 



