1911-12.] The Molecular Theory of Magnetism in Solids. 225 
cipal axes, the principal components of the transverse force when the 
magnetisation is in the direction of that radius- vector. 
But it is more useful to analyse the transverse force into its two 
components P and Q respectively in, and perpendicular to, a plane contain- 
ing the direction of magnetisation and the y-axis, i.e. the y-axis. Let S 
indicate the trace of this plane on the (a, /3) plane, the trace making an 
angle 0 with the a-axis. Writing the expressions of type (11) in the 
forms 3M/yo 3 . [(A — B)/3 2 + (A — C)y 2 ]a, etc., we have 
Q = 3^[ - {( A - B)/3 2 + (A - C)y 2 }a sin 6 + {(B - C)y 2 + (B - A)a 2 }/3 cos 6 } , 
R = 3^.[{(A - B)/3 2 + ( A - C)y 2 }a cos 6 + { (B - C)y 2 + (B - A)a 2 }/3 sin 0] , 
where R is the component along S. With the conditions y = cos (p, 
a = sin (fy cos 6, f3 = sin 0 sin 0, and noting that the component parallel 
to y is ^L'o^SM/p^C — A)ot 2 + (C — B)/3 2 ]y, so that P = V L' 0 sin 0 — R cos <f>, 
we find 
P = — [(C - A) cos 2 0 + (C - B) sin 2 #] sin <f> cos , 
Q M 
Q = — - (B - A)(l + cos 2 cf>) sin <f> cos 0 sin 0 . 
r 
( 12 ) 
These formulae show that the component of the internal field trans- 
verse to the direction of magnetisation vanishes, as the parallel component 
(§ 8) does, when A = B = C; so that the magnets, when in the cubic or 
isometric arrangement, are absolutely free from mutual control so far as 
VOL. XXXII. 15 
