1904 - 5 .] Magnetic Quality in Molecular Assemblages . 1039 
It is necessary now to discriminate the directions of stable and 
unstable equilibrium. 
When in the quantities a [a 4 + /3 4 + y 4 - a 2 ], /3 [a 4 + /3 4 + y 4 - yS 2 ], 
y[a 4 + / 2 4 + y 4 - y 2 ], we make a nearly equal to unity, f3 and y 
small, we find that the transverse force acts oppositely to and 
more strongly than the parallel force so as to increase displace- 
ments from the quaternary axes, which are therefore directions 
of unstable equilibrium. Similarly, putting a, /3, y, each nearly 
equal to 1/ J 3, we find that the ternary axes are directions of 
stable equilibrium. Lastly, putting a and /3 nearly equal to 
1 / J 2, with y small, we find that the components of displacements 
from a binary axis in the direction of a ternary axis are aided, 
while displacements in the direction of a quaternary axis are 
resisted, by the transverse force ; and the opposite effect of the 
parallel force is overcome in the former case. 
Thus we find that, for molecules subject to random displace- 
ments, the direction of a ternary axis is the only direction of 
stable equilibrium. This result is of vital importance in any 
discussion of magnetic quality in a random aggregate of crystals. 
14. Transverse Force under Magnetisation in Principal Planes. 
— Since the component of the transverse force in the direction 
(l, m, n) is proportional to a H + fPm -f y s n, we can find the trans- 
verse force when the magnetisation is in a face plane of the cubic 
arrangement, say the (a, /3) plane, by putting y = 0 , at + fim = 0 , 
n = 0. Writing a = cos0, we get as the value of the force 
where B (§ 9) is proportional to the magnetic moment per unit 
volume. 
Similarly, taking (a, /3 , y) and (l, m, n) in the plane perpen- 
where cos 6 = y, as the value of the force in a diagonal plane of 
the cubic arrangement. 
These values are plotted respectively in figs. 5 and 6. In fig. 5 
JB sin 40, 
, so that a + j3 = 0 , l + m= 0 , 2a l + yn — 0 , 
we find 
JB sin 20(3 cos 2 0-1), 
