Coefficients of Self-induction and Mutual Induction. 237 

 T=M'z (b-y), 

 F = i(G- . l^u + S . u~^v 4-Ri^y 



+ R'.w-^ + 

 The equations are of the form 



ax + G.as — u + . . . =— L 



#o> 



-g.^- 



■u+S.u-v + R'. u—y + ... = 0. 

 — S . u— v + Rx- v— y + . . . = — Mi , 

 -Ri . v—y—W. u—y + . . . = Mi . 

 The third of these equations gives 



(R 1 + S)v = R, 1 y + Su-Mz , 

 which reduces the second and fourth respectively to 



SR, \ . „ S 



-G>x-u + (n f + ^-~)u-y + ...= 



-( R ' + S>"^ + - = 



M 



M 



Ri + S' 



S 

 Ri + S' 



^o> 



*0« 



These are exactly what we should have got by supposing 

 the resistance of R^ affected in the usual way, and M dimi- 

 nished in the ratio S : Ri + S. 



§ 6. To express a Coefficient of Mutual Induction in Terms of 

 the Capacity of a Condenser. 



It is evident that a condenser and resistance placed in AD 

 instead of an electromagnet will balance the current of mutual 

 induction. The conditions for this may be easily inferred 

 from what precedes ; but they may be independently deduced 

 by the general method. 



With the first figure of § 5, ex- 

 cept that a condenser whose poles 

 are at A, P occupies the place of 

 the coil L, we have a 



T: 



2» 



X) 



m.i 



u~y, 



H = 1t; 2 /C. 

 The first equation is 



X(>--t') + 0-X)j: + ... = 



■], 



