1 042 Proceedings of Royal Society of Edinburgh. [sess. 
Weiss does not give, in his abstract at least, any investigation 
of the transverse magnetisation along a ternary axis when the 
external force lies in a plane perpendicular to that ternary axis. 
The case is one of considerable interest. If we presume, con- 
versely, that the magnetisation lies in that plane, the condition is 
a 4- (3 + y = 0, from which we find a 4 + /3 4 + y 4 = 1/2. Hence (§ 9) 
the component of internal force in the direction of magnetisation 
is constant in amount. Also the factors a (Q - a 2 ), /3 (Q - /3 2 ), 
y(Q - y 2 ), in the expressions for the cosines of the transverse 
component of the internal force, become each equal to — a/3y. 
Therefore the transverse component is entirely along the ternary 
axis. Its magnitude is - 4^/3 B a/3y. Transforming to co- 
ordinates in the plane of magnetisation, this becomes 
where 0 is measured from a binary axis counter-clockwise when 
we look inwards along the ternary axis. Hence, as the direction 
of magnetisation revolves in the plane, the transverse force 
alternates along the ternary axis, changing sign at intervals of 
60° as the direction of magnetisation passes through a binary 
axis. It is positive in the three sextants which contain the 
planes passing through the ternary axis and the three conter- 
minous edges of the cubic arrangement. This is simply a result 
of the fact that the direction of magnetisation tends to approxi- 
mate to the nearest ternary axis. The graph is shown in fig. 8, 
in which the radial scale is less than that used in figs. 5, 6, and 7, 
in the ratio ^2/4^3. In all cases in these figures the diagram 
scales must be used, for the absolute scales have been altered in 
the process of reproduction by photography. 
On Wallerant’s view, the above expression should represent the 
component of magnetisation along the ternary axis when the 
external force is perpendicular to it. 
15. The Magnetisation Quartic . — The quartic surface cc 4 + y^ + z* 
= 1 is of fundamental importance in the geometrical representation 
of the magnetic properties of the cubic arrangement of molecular 
magnets here considered. Its form is roughly that of a cube with 
