Ponder omotive and Electromotive Forces* 265 



In a similar manner we will treat the expression of r given 

 in equation (5); but at the same time we will besides trans- 

 form the first term separately. We can, namely , put 



BV) =2 9i-|i +2) , a ! 





and simultaneously we get from r 2 =%(x — a/) 2 



From the combination of these two equations results 

 ydx "bx r _ _ ^' B^ _ "d 2 r d y/ _ r\'d± 



diW~ TtW~ rz &W B7 ^ * ; a*' 



The algebraic sum standing here on the right-hand side we 



d v n v 

 will insert in equation (5) for ^g— ^-y. At the same time 



Ctt (jS 



we will reverse all the signs of this equation, so that, after 



i 



division by k, it will determine the quantity — 7, in the follow 



ing manner : — 



6 7 8 



r_ ,, a i -a'' B?'^' ., x — x' ~d 2 r _.,x—x' "b ^/ _ r\do/ 



9 10 ll 12 



The twelve terms occurring in these two expressions form 



together the expression of —r — J an d now it requires to be 



brought into a form as simple as possible and suitable for the 

 further calculations ; this can be done by suitable grouping of 

 the terms. We obtain, namely, if we indicate the terms briefly 

 by their numbers : — 



Herewith all the terms except the 11th, which will have to 

 Phil. Mag. S. 5. Vol. 10. No. 62. Oct. 1880. U 



