1911-12.] The Molecular Theory of Magnetism in Solids. 217 
arrangement, but randomly oriented on the whole, would possess residual 
magnetisation of the magnitude observed in iron. 
2. Very valuable experimental development of the subject has been made 
by Weiss, who showed that crystals of magnetite, which crystallises in 
forms belonging to the cubic system, exhibit magnetic quality having cubic 
symmetry. It is by no means necessary that the magnetic and the 
structural symmetries of a magnetic crystal should be identical when non- 
magnetic constituents are also present ; and it is of interest to note in this 
connection that Weiss finds that the magnetic quality of pyrrho tine does 
not present true hexagonal symmetry. 
Weiss has also developed the theory of molecular magnetism in its 
application to crystalline structures, on the assumption that the internal 
field acting on any one magnet is uniform, and has ' successfully explained 
the observed phenomena. In particular, he has explained the existence of 
the “ magnetic plane ” observed in pyrrhotine as the result of an internal 
demagnetising field in the direction normal to that plane. 
3. In two former papers ( Proc . R.S.E., 1905 and 1907) I have worked 
out and evaluated expressions for the internal fields acting on the poles of 
co-directed molecular magnets in a cubic arrangement, and have compared 
the results with Weiss’s observations on magnetite. In particular it 
appears that the cubic arrangement of most open order cannot, while that 
of the homogeneous closest-packed order can, give results in agreement 
with the observed facts. 
It is very desirable that a general development of the theory should be 
given, in order that those general results, which hold, with mere modifica- 
tions of detail, in many particular cases, should appear. The object of this 
paper is to furnish such a discussion, and to apply its results specially to 
the cases of magnetite and pyrrhotine and to the general question of the 
dependence of magnetic quality upon molecular configuration. 
4. Consider an ideal magnet of semi-length a and pole-strength m. 
The centre of this magnet being at the origin, the force F at the point (r, 0), 
0 being measured from the south to north direction of the axis, has a radial 
component 
F cos cfj = ^1 - - cos 0^1 + - 2 cos 0 
and a transverse component 
i ma sin 0 
Fsm 4> = |__ 
By expansion we find 
- 3/2 
m , 
- — 1 + - cos 0 1 + 
r l \ r J\ r\r 
a a 
+ 2 cos 0 
a a 
1 + £1^.-2 cos fl)) "" + q +^-2- + 2 cos0 XX 
-i CL ( CL ^ 
1 + — ( — — 2 cos 0 
- 3/2 
1 ( _ ) 1> |2(?» -p) + 1 cos" 
* On d 
| n — p \n — 2p I p 
