1911 — 12 .] The Molecular Theory of Magnetism in Solids. 233 
Similarly, the expression for A T' 2 reduces to 
a T'„ L 2^!(D - <3-)[a 2 /3 2 - j8f- y3 2 ]a=0, . . . (22) 
P 
so that the component of the internal field transverse to the direction of 
magnetisation is absolutely zero. 
15. The expression for the next order term in the parallel component 
of the internal field is 
L' 4 = <^(ffZ • C 2 +fV + 2 V)- w 16P, , 
231 JC - 315-2— + 105'^a— 5- 
yi3/2 f 11/2 ' * y9/2 y’7/2 
where g = a\ +p/3/u + gyr, /= X 2 + j9 2 /x 2 + g'V. On expansion the sum is 
231 { + 
+ 15 
+ fZ$%) + rfz^ + « 2 2^) 
-^\^Zm+P l Z%+y l Z%+s WZ^X+WZ 
X 4 . %> 4 a 4 . a C 4 ^ 4 . „T o ™ ^ p 2 X 2 /x, 2 ,n 2 2 V p 2 q 2 p 2 v 2 
i yn/2 
/i 1/2 
yu/2 
++I 
gVX 2 ' 
y n/2 
105 
h 2 2 ^^ 2 Z 0 2 + r 2 Z?}-^-^- 
■ (23) 
y »/2 ■ i- y 9/2 
In the special case of the cubic system this becomes 
231 {(a 6 + /3 6 + y 6 ) A] + 15[a 4 (/3 2 + y 2 ) ,+ /3 4 (y 2 + « 2 ) + 7 V + d 2 )]B' 3 + 6a 2 /l 2 y 2 E' 3 } 
- 315{(a 4 + /3 4 + y 4 )C' 3 + 6 (a 2 /! 2 + /l 2 y 2 + y 2 a 2 )D' 3 } + 30R' 0 , 
where 
A' - V p' _ x>X 4 /x 2 , _ y ^ 4 tv _ v A V E ' _ V X 2 /x 2 r 2 pp _ v 1 
3 zLyi 3 / 2 ’ -°3 ^ yi 3/2 ’ 3 ^Zyi/2’ x 3 Z-J yfflg’ 3 ^ yii /2 ’ 3 Z-jyi/2 ■ 
In the case of magnetisation parallel to a principal plane (y = 0) we 
get, by means of the conditions a 4 + /3 4 + 2a 2 /d 2 = 1 — a 6 -f-/3 6 + 3a 2 /3 2 , the 
result 
^[3(«« + j8*)(A', 
5B' 3 ) - (A' 3 - 15B' 3 )] - 315[(a 4 + /? 4 )(C' 3 - 3D' S ) + 3D 8 ] + 30R/ 3 . 
Now, by expression respectively of the quantities (X 2 + /x 2 + r 2 )X 4 , 
'(X 2 + ,a 2 + r 2 )XV 2 , and (X 2 + //, 2 + y 2 ), each divided by the proper power of /, 
we obtain 
C' 3 = 2B' 3 + A' 3 , 
D'g = 2B' 3 + E'g , 
B'g = 3C' 3 + 6E' 3 ; 
