Electric Currents in Networks of Conductors. 249 



and 



L 2^^— y + $x— y = Q> (»•) 



we get 



and 



= (L 1 + L 2 )^-L 1 S^ + (L 1 S-L 2 G)y. . (iii.) 



Differentiate this last equation with regard to t and eliminate 

 -^ by the help of the equation above it, and we arrive at 



L X L 2 _ 2 = - Ll S ^+ Li ^- Qy). 



Eliminating y between the last and equation (iii.) and re- 

 ducing, we arrive at 



L X L 2 ^+(L 1 S + L,G)g + GS«=(G+S) g; 

 but now cc= — -^. Making this substitution we have 



L 1 L 2 C§ + C(L 1 S + L 2 G)g + CGsg + (G + S) 2 =0, (in) 



an interesting equation, the solution of which gives us 

 the quantity of electricity in the condenser at any instant, £, 

 after starting the discharge. According to the equation above 



This equation gives us a value of y or the current through 

 the galvanometer at any instant when we know q, or the 

 quantity left in the condenser at that instant. The above 

 may be written 



and the final equation (iv.) may be written 



J*(inW?y+'(^s+i^)(?|i+ciw|+cKo+s))"oi 



