182 W. E. Ayrton— Quantitative Method [No. 2, 



If the testing battery he reversed so that the earth current tends 

 to. oppose the testing current we have — 



C',A-C' 2 B =o \ 



G\ W" — 0' r = e (IX) 



(C, + C' a ) F + C' a (B + r) = E — e ) 



From equations (VIII) by eliminating 2 we obtain. 

 1 B a e 



(c, + c 1 A.)F + o 1 A( B - fl .) 



E + e 

 A 



-r-W 

 or; ;-t T-, : = 9 (X) 



Similarly from equations (IX) we obtain — 



W—i, 



(« + 4)» + 4<»*') T-' 



(XI) 



E 



Eliminating — from equations (X) and (XI) we obtain, 

 e 



BF(A + B)(W+ W") + B 2 { A (W + W") +2W W" | 

 A B (W + W") + 2AF (A + B) + 2 A 2 B 



(Appendix II.) 



First let W and W" be very nearly equal, that is, 

 let W" = W + dW 

 then 2 W W = 2 W (W + dW) 



= W' 2 + (W + dW') 2 — dW'"1 



2 



a 



... 2 W W = (W + W") 2 - 2 W W" - dW'l 



or 2 W W » ^ ^ J 



in which the square of a differential only is neglected. Substitut- 

 ing this value for 2 W W" in equation (III) we obtain \ 



