1911-12.] The Molecular Theory of Magnetism in Solids. 221 
the direction cosines specifying the magnetisation with reference to the 
principal axes, 
cos 
6 = 
a\ +p/3/x + qyv 
\/A 2 + p 2 /x 2 + q 2 v 2 
Hence, by expression of (5), there results 
L' 0 = ^[A(3«2 - 1) + B(3/3 2 - 1) + C(3y 2 - 1)] 
( 6 ) 
where 
X 2 
(A 2 + p 2 fx 2 + q 2 v 2 f /2 
Bly,. 
pV 
(x 2 +i>V + ? V ! ) 5 ' !! 
. C =Z- 
q 2 v 2 
(A 2 +pV + ^ v 2)5/ 2 * 
The terms involving products of X, /x, v vanish by symmetry, since positive 
and negative values alike occur. 
Equation (6) indicates an ellipsoidal distribution of the parallel com- 
ponent of the internal field. 
The first term in the transverse component of the internal field is 
T'„ = 3M2 
sin 0 cos 0 
The component of this in the direction of the principal axis denoted by X is 
M 
= . [X - a(aX ■bpfSfA + qyv)](a\+ pftn + q-yv)(\ 2 + + q 2 v 2 )~ 5/2 , 
whence 
a T'o = ^a[A(l - a 2 ) - B/3 2 - Cy 2 ] , 
P 
M r 0 = ^/3[B( 1 -/3 2 )-Cy 2 -Aa| v .... (7) 
M 
,TV=^ 7 [C(l-r 2 )-Aa 2 -#]. 
8. The quantities B and C become respectively equal to A when 
p = q = l; they are equal to each other when p = q. The quantity A 
steadily decreases as either p or q increases. So also B and C steadily 
decrease as q and p respectively increase. When q differs little from 
unity, say q = 1 + e, with p = 1, we have, to the first order in e, 
c = yy .(a 2 +^+®-| £ s. ^(x 2 + /x 2 + 1 / 2 )- 7 ' 2 . 
O O 
But the latter term is less than e-^2 . r 2 (X 2 + /a 2 + r 2 ) _5/2 , so that dC/de is 
o o 
positive and greater than ^2 . (X 2 + /x 2 + i/ 2 )~ 3 ' 2 . Similarly, 
o 
