1046 Proceedings of Royal Society of Edinburgh. [sess. 
We shall therefore assume that this formula gives the value of 
I, at constant H, over the range corresponding to all possible 
directions. 
But it should be noted that any necessity for this particular 
interpretation of the meaning of I 0 may disappear when an accurate 
expression for the magnetisation, in terms of force, is obtained. 
Under the conditions now postulated we have to take B = 2 b 
(I - 1 0 ), and the extremity of the line representing the external 
force lies on the quartic at all values of the force and the induction 
within the limits considered. Hence the component of magnetisa- 
tion, I - I 0 , parallel to the external force is 
H a 4 + /I 4 + y 4 
b a 6 + /3 6 + y 6 ’ 
and the component perpendicular to it is 
H Ja 6 + /3 6 + y 6 — Q 2 
b a 6 + /3 6 + y 6 
the direction cosines of the force being a = a z /Ja 6 + + y 6 , etc. 
In a plane parallel to a face of the cubic arrangement, these 
expressions become 
H 1 - 2a 2 (l - a 2 ) H aj\ - a 2 (2a 2 - 1 ) 
b 1 — 3a 2 (l — a 2 ) ’ b 1 — 3a 2 (l — a 2 ) ’ 
a =2a 3 / x /l-3a 2 (l-a 2 ). 
In a plane parallel to a diagonal plane of the cubic arrangement, 
they are 
0 H 1 — 2a 2 + 3a 4 
b 1 — 3a 2 (l — a 2 — a 4 ) * 
aj\ — a 2 (3a 2 — 1) 
1 — 3a 2 (l — a 2 — a 4 )’ 
a =2a 3 /Vl-3a 2 ( 1 -a 2 -“ 4 )- 
The corresponding curves are shown in fig. 7, the full lines 
referring to the face plane and the dotted lines to the diagonal 
plane, the radii being proportional to I - I 0 . 
The flatness of the loops, which represent the transverse effect, 
on the sides remote from axes of maximum induction in a plane 
is apparent. In this respect Weiss’s experimental results are 
reproduced. The curve representing the longitudinal component 
in the face plane is very similar to Weiss’s curve of the effect in 
