in terms of the Coefficients of Electrostatic Induction. 381 



These equations suffice to determine the potentials of the 

 to insulated conductors [1], [2], ... [m] in terms of e^ When these 

 potentials have been found in terms of e lt the remaining n — m 

 equations, of which the first is 



^im+Di^i + O l i m+ i) 2 V 2 + . . . + q(m+i)mVm = #m+i (5)> 



give the charges upon the uninsulated conductors [to + 1], ... [n] 

 in terms of e x . In the present problem, however, we are not con- 

 cerned with the values of these charges. 



Let A denote the determinant of m rows formed from the 

 coefficients in equations (4), so that 



A = 



In 



#21 



?12 



q*m 



.(6). 



2W (Zm-2 • • • Qlmi 



In (6) no suffix higher than m appears, but it must be remem- 

 bered that every coefficient appearing in (6) is a function of the 

 forms and positions not only of the conductors [1], [2], ... [to], but 

 also of the conductors [to + 1], ... \n\. 



Let A n denote the determinant formed by deleting the row 

 and the column which contain q u , so that 



A u 



(?22 ^23 • • ■ q^m 



q$2 qs3 • • • q$m 



.(7). 



q>n2 qim • •• qmm 

 Thus A n is the minor of A which is complementary to q n . 

 Solving equations (4) for v l , we at once obtain 



v 1 A = e 1 & 11 (8). 



Hence, if G ± be the capacity of [1] under the specified condi- 

 tions, we have, by Definition A, G±v x — e x and thus 



.(9). 



It must be remembered that A is a determinant of to rows 

 and not of n rows. Coefficients with suffixes referring to one or 

 more of the conductors, which are kept at zero potential, do not 

 appear in A. 



