315 
of the plane of polarization by solutions. 
where P, Q, R are the moments of the forces around the axes of 
x', y , z respectively, solving these equations, we get 
do) x 
dt 
fjl = v p + q Q + xR, 
— pP + vQ + pR, 
•(4), 
^ = ^P + XQ + rR, 
where p, q, r, \, p, v are quantities depending on the masses and 
positions of the electrified bodies, but not upon their electrical 
charges. 
If Xf Yf Z, are the components of the electric force at the 
points xf yf zf where the charge of electricity is e„ then 
P = 2(Z'y'-Y'z')e 1 . 
If (l„ m 1 , ni), (l 2i m 2 , n 2 ), ( l 3 , m 3 , n 3 ) are the direction-cosines of 
the axes x', y', z with reference to fixed axes x, y, z and X lt Y„ Z 1 , 
the components of (X/, 7/, Zf) along x, y, z, then 
X/ = l,X, + m 1 Y l + n,Z,, 
7/ = IX, + m 2 Y, + n 2 Z„ 
Z-[ — l 3 X i + m 3 Y,+ n 3 Z 
If X 0 , F 0 , Z 0 are the values of X, 7, £ at the origin of the 
x , y', z axes, then, retaining only the first powers of x', y , z , 
t\ / / /\ o 
Xj = X„ + (fxi + kyi + l 3 z') + (myf + m 2 y, + m 3 z, ) 
+ n,x / + n 2 y( + n 3 zf) ^ 
dY 0 
7j = 7 0 + (l,xi + lyji + l 3 zf) + (niyif + myj, + m 3 z, ) 
.,xdY 0 
dy 
/ / / > /\ d Y 0 
+ (n,x, + n 2 y, + n 3 z, ) , 
(IF dZ 
Z , = X, + (fxi + l 2 y' + l 3 z') ( -X£ + {m,xf + m 2 yi + m 3 z') 
+ (n,x-[ + n 2 y / + n 3 z,') ~ . 
Substituting these values of Z\ Y' in P and remembering that 
= ’%e l x l , z- i ' = 'Zeyjiz-^ = 0, we see that as far as terms in 
dY ,dZ A 
— and -j— are concerned, 
dz dy 
