1911-12.] The Molecular Theory of Magnetism in Solids. 223 
subject to these conditions, the axis along which the spacing is closest is 
a direction of difficult magnetisation, while the plane perpendicular to it 
is a Plane of Easy Magnetisation. Extension of experimental evidence 
on this point is desirable, but the existence of a magnetic plane has been 
shown by Weiss in the case of pyrrhotine, and has been explained by him 
as the result of an internal demagnetising field. 
9. By means of (8), it is easy to deduce 
L'o — aL' 0 (X 2 + jaL'o/3 2 + „L 0 y 2 , (10) 
which gives the parallel component of the internal field in the direction 
(a, (3, y) in terms of the principal parallel components. From this equation 
it follows that (9) is invariant relative to any set of rectangular axes suiting 
the crystalline symmetry, and that the conditions A = B = C, or A = B 
provided that the new X, /m axes lie in the plane of the old X, /ul axes, etc., 
are also invariant. But the condition of correspondence to crystalline 
symmetry is very restrictive. Thus, if we take y = 0, a 2 = (3 2 = J, we get 
L'o = |>L' 0 for both 45° lines, and therefore A = B necessarily for these two 
lines as axes ; so that the invariance is restricted to pairs of axes relatively 
to which the crystalline symmetry is identical. 
The special case in which 2B = A + C is of interest. Here ,J/ 0 = 0, 
A L' 0 = — „L' 0 , so that there is no internal field in the direction of the /ul axis, 
while magnetising and demagnetising forces respectively exist along the 
X and /UL axes. The surface represented by (10) encloses, in the plane (3 = 0 , 
an area whose boundary is r — A L' 0 cos 20, alternate lobes having opposite 
signs. In the plane y = 0, the trace is r = A L' 0 cos 2 d. 
Equations (10) and (9) show that the lines a 2 = /3 2 = y 2 are lines of zero 
parallel component. The surface represented by (10) has three lobes 
situated in the spaces marked out by these lines. The elliptic cone, given 
by equating the left-hand side of (10) to zero, passes through the lines and 
separates the lobes. 
In fig. 1 sections of (10), with the values A L' = — 2, ,JL' 0 = — 1, V L' 0 = +3, 
the y-axis being a magnetic line, are given. The curves represent one 
quadrant of the section by the planes y = 0 and a = 0. L'o is negative in 
the former case ; in the latter case, in the loop next the */-axis, it is positive. 
If we took a L' 0 = — 3, j^L'o —— 1 , l/ L / 0 = 2, the signs of L' 0 in the respective 
regions would be reversed, and the plane perpendicular to the X-axis would 
be a magnetic plane. 
10. From (2) we find 
r, - 2 • M Sin OP' = 3M V ■ sin<?cos<? , 
