in terms of the Coefficients of Electrostatic Induction. 385 



We can now write down the capacity of [0], i.e. of [1] and [2] 

 " in parallel," by the aid of (9). Thus 



A' A' 



tf 1+2 =a,=-£-=-F- (20). 



H 00 **11, 22 



The determinant A' can easily be expressed in terms of the four 

 minors A u , A 12 , A 21 and A 22 of the original determinant A. Writing 

 A' as the sum of two determinants, we have 



A' = 



or 



A u + A 21 . 



In a similar way the second determinant on the right may 

 be written 



A 12 + A 22 . 



Hence A' = A u + A 12 + A 21 + A 22 . 



Substituting this value of A' in (20), we obtain 



A X1 + A 12 + A„ + A 22 



C 1-1-2 — 



A 11)22 



.(21). 



.(22). 



The result obtained in § 8 was 



A„ + A 12 + A 21 + A 22 

 0l+3 ~ A A n A 22 -A 12 A 21 



Comparing (21) with (22), we obtain the known formula 



AA lli22 = A u A 22 -A 12 A 21 , 

 which was the result employed in § 7. 



§11. When all the conductors except [1] and [2] are kept at 

 zero potential, we find from (22) 



C1+2 = qu + qi-2 + q,i + q™, 



as might have been inferred from (17). 



