1911-12.] The Molecular Theory of Magnetism in Solids. 227 
It is of importance to note the symmetry of the expressions for the 
transverse component when the magnetisation is in any one of the three 
principal planes. The symmetry is identical with regard to either principal 
axis in one plane, and is therefore not influenced by difference of scale of 
the space-lattice in the three principal rectangular directions. 
11. In the hexagonal system we shall consider the v - axis to be the 
normal to the plane of the hexagonal arrangement, and the X-axis to be 
along a line of closest grouping in the hexagonal plane (fig. 4). Here we 
have r 2 = p 2 (X 2 + 3/x 2 + gr 2 ), so thaty>= J 3 and p is half of the least distance 
between centres of magnets in the hexagonal arrangement. Using the 
same notation as before, we have equations (6), (8), (9), and (10) holding 
with respect to the parallel component of force, and the structural sym- 
metries will determine relations amongst A, B, and C. Thus the condition 
of identity of arrangement in the primary plane relatively to the X-axis or 
a line inclined to it at 60° makes (6) take the same value with a = l, /3 = 0, 
y = 0 as with a = 1/2, /3= JS/2, y = 0; from which at once 
A = B 
independently of the value of C. Hence, by (12), we have Q = 0, 
•>. \r 
P = — (C - A) sin </> cos . 
P 6 
The axis of hexagonal symmetry is therefore a direction of stable or un- 
stable magnetisation according as C is > or < A. 
12. To deal with the cases in which the space-lattice belongs to the 
monoclinic or triclinic groupings, it is convenient to refer the system of 
magnets to the (in general) oblique X, /x, v axes. Here, as before, x = p\, 
V — pVV-i z — pqv’ anc f l > wi, n being now direction ratios , we have x = lr, 
y — mr, z — nr ^ along with 
1(1 + mZ + nY) + m(?n + nX + IZ) + n(n + IY + raX) = 1 , 
