Electric Currents in Networks of Conductors. 245 



By the cycle equation, B?/-hB + S#=E : hence 



E-Bz/ 



#= 



B + S 



And if we write N for the factor (1 — e 



EBSN 



BO+GS + BQ- 



(B + S)L 



) j then 



E- 



#= 



BG+BS+SG 

 B+S 



_ E(BG+BS + SG-BSN) 



" (B + S)(BG + BS + SG) ; 



which gives the current through the shunt at any instant. 



§ 16. Consider now the combined resistance of the galva- 

 nometer and shunt at any instant. 



The self-induction of the galvanometer acts like a spurious 

 resistance during the commencement of the current and drags 

 out or prolongs the rise of current in the galvanometer-coils ; 

 accordingly, during this period the combined resistance is a 

 function of the time t from the commencement of the flow. 



To calculate the combined resistance of galvanometer and 

 shunt at any instant, we proceed as in the cases above exem- 

 plified. Form the cycle equations 



-S^ + (G+S + L|jy=0. 



Write down the determinant of these equations with the bat- 

 tery-circuit resistance put equal to zero, that is put B=0, and 

 the combined resistance R required is the quotient of this 

 determinant by its first minor, viz. 



s -s 



R= 



at 



G+S + L 



1 

 dt 



or 



S 







■S" G + L 



R= 



S + G + L 



_ s ( a+L jp 

 i s+ ( &+l s) 



