1904 - 5 .] Magnetic Quality in Molecular Assemblages . 1037 
Expanding, neglecting terms involving powers of a/p beyond the 
second, and writing P = aX + ftp. + y v, this reduces to 
210^ M -2-(A-a P )F( 2 p)-^. 
To this we have to add the second term in the expression for the 
transverse force (§ 6), which, on summation, reduces to 
3 5V2M _ q^ .( X _ a p) P 8( 2j) )-W . 
P 
The total components at the pole are therefore 
245 N /2Ma 2 ^ ( X _ ^ps^-t/s 
P 5 
and two cyclically related quantities. 
12. Modified Expressions for the Components of the Transverse 
Force . — For the purpose of separating magnetisation cosines from 
position cosines, we can put the above sums into the form 
^"X[a 3 A. 3 + 3aA(/3 2 p 2 + y 2 v 2 )] — a2*[a 4 A. 4 + /P/u. 4 + y 4 ^ 4 
+ 6 (a 2 /3 2 A 2 yU, 2 + p 2 y 2 p, 2 i/ 2 + y 2 a 2 i/ 2 A 2 )] , 
with the two other cyclically related quantities. Multiplying 
respectively by l , m, w, subject to the conditions 
at + Bm + yn = 0 , Z 2 + m 2 + n 2 = 1 , 
and adding, we get 
(a H + j$m + y %)2-(^ 4 - 3AV 2 )(2 V )~w 
= |-(a 3 Z + /3 B m + y 3 
N 
(2 P)~ m 
in which the sum is (§ 22) negative. 
The condition for this quantity vanishing is 
a 3 Z + + y 2 n = 0 ; 
whence l :m :n = /3Q3 2 - y 2 )y : y(y 2 - a 2 )a : a(a 2 - /3 2 )/3 . 
Now the transverse force is perpendicular to (a, /3, y) and also 
to (Z, m, n), as above conditioned. Therefore its direction cosines 
