An introduction to the mathematical theory of attraction ...

Charrges in terms of Potentials. 263
If we suppose each charge to receive a variation, the values
V, Vy2, &c., of the potential receive corresponding variations;
and we have from (5)
dW, dTVde dV
but
dWe ÎdJe V
VI = -, V = V -, &C.;
whence
d We
2VcYe = 2 e,
de
and therefore.zesV = ~ V.d W.
In this equation the variations Vy1, îV2, &c., may be
regarded as independent and arbitrary, and thus we get
ldW e dW &o (6)
6i dyT' e= d772'
Also, for any variations of the charges and the corresponding variations of the values of the potential, we have
V8e =2e V. (7)
Substituting for the differential coefficients in (6) their
values derived from (3) we have
e1 = q1 V1 + q122... + qin
e2 = q12 V + q V2.. + q + qn (8)
en qin Vi + q2n 2.. + qnn V
The quantities q11, q22, &c. are called coefficients of
capacity, and the quantities qj2, q23, &c. coefficients of
induction.