222 
Proceedings of the Royal Society of Edinburgh. [Sess. 
B-2- 
/X 2 
0B 
0€ 
(A 2 + /x 2 + v 2 ) 5/2 
-»2- 
1 -5e 
A 2 + 
/X 2 !/ 2 
(A 2 + /X 2 + v 2 ) 7/2 
So that 0B/3e is negative, and this result is independent of the value of p. 
Results of this kind, along with considerations of symmetry, enable 
us to obtain general information regarding the magnetic action of a 
homogeneous crystalline arrangement (referable to rectangular axes) of 
magnets, without actual evaluation of the constants A, B, C. It should be 
noted also that, in the application to solids, M may be a function of the 
temperature. In the absence of knowledge ^regarding the constitution of 
a magnetic molecule, it may possibly have to be regarded as a function of 
the resultant magnetic field intensity. 
From (6) we get the principal values of the internal field in the directions 
in which A, /ul, v are taken : 
,L' 0 = p[2A-B-C], 
Hence 
L' _Mr 
L'-Mr 
A + 2B - C] , 
A - B + 2C 
aL 0 ”1“ juR o jR o 0 j 
( 8 ) 
(9) 
which shows that the internal force must have a demagnetising effect when 
the magnetisation is along one principal axis at least. 
From (6) and (7) we see that there is zero internal field when p = q = l, 
i.e. when A = B = C. This is the case of a cubic crystalline arrangement. 
Hence we perceive the possibility of metals which crystallise on the cubic 
system having strong magnetic properties. (It must be remembered that 
this zero field is due to co-orientation of all the magnets.) 
If p — 1, q>p, A and B remain equal, while C increases ; hence aR' 0 and 
L' become negative, while v \' 0 becomes positive. Provided that q is 
sufficiently greater than p, the same condition holds even if p> 1. Thus, 
in a crystal containing magnetic molecules in ortho-rhombic arrangement 
subject to the above limitations, the axis along which the spacing is widest 
is a Direction of Easy Magnetisation , while magnetisation is difficult in 
directions lying in the perpendicular plane. Experimental exemplification 
of this condition is still wanting. 
If ^ > 1 , provided that the excess of q over p be not too great, we 
may have V L' 0 and M L' 0 both positive, while aL'o is negative. Thus, in a 
costal containing magnetic molecules in ortho-rhombic arrangement 
