316 
Prof. Thomson, On the theory of the rotation 
■( 5 ), 
P = ( Bm 2 n 3 — Cm 3 n 2 ) ^ — (On 3 m 2 — Bn 2 m 3 ) } 
d 7 (tY 
Q = (Cm x n 3 — Am 3 n^ —(Am x n 3 — Cn x m 3 ) , y 
r71 r 
R = Bn x m n ) . (Bn 2 m x — A m x m 2 ) , 
ay dz / 
where A = %e x xf, B = ^e x yf, G='%ez" 2 and may be called the 
electrical moments of inertia. 
The convection current parallel to x is equal to 
te^ = 2e^ t (W + kl' + te')- 
Now, since l x , l 2 , l 3 are the direction-cosines of a line fixed in 
space with reference to the axes x, y' , z , 
df 
dt 
dl 2 
dt 
dl 3 
dt 
— tof oof, 
— oof tolls, 
= 00 x l 2 — oof. 
Hence u, the x component of the convection current, is equal to 
2 [e x x x (oof — oof) + e x y x (oof — oof) + e x z (oof — oof)), 
and neglecting the squares of oo x , an, oo 3 , we have 
du 
dt 
2 ^e x x x 
doo 2 j doo- 
dt 2 dt 
, , , doo 3 , doo x \ 
substituting for -j- 
CLL 
dco, doy 2 d(o ?> 
dt 9 dt 
+ e x z x ^1. 2 
doo, . doo s 
dt 1 dt 
from equations (1) 
§ = (pP + pQ + y-R) (42e A - lAy t ) 
+ (vP + qQ + \R) (ZaSe^i — l x %e x z x ) 
+ QiP + \Q + rR) (l x Xe x y x - LXe x x x ). 
Now 
l x = m 3 n 2 — m 2 n 3 , l 2 = m x n 3 — m 3 n x , l 3 = m 2 n x — m x ii 2 . 
Substituting for P, Q, R the values just found and averaging for 
all the molecules in unit volume, the axes of these molecules 
being supposed uniformly distributed, we get 
