1052 Proceedings of Royal Society of Edinburgh. [sess. 
Thus, apart from the action of terms of different order from those 
now under consideration, the resultant magnetisation would he 
determined mainly by the internal part. 
But it is impossible to leave out of account in this connection 
the effects of the first terms in the expressions for the components 
of force (§ 6). These terms, being independent of the ratio a/r 9 
are the terms which give rise to the action at distant external 
points, and also to the self-demagnetising action of the so-called 
surface magnetisation. 
The term 2 x /2M/p 3 ^-(3 cos 2 0 - l)(2p)~ 3/2 becomes 2^2M/p 3 -S- 
[3v 2 - N(2p)](2p) _5/2 , if we put y=l, so that the magnetisation is 
along a quaternary axis. Now, in the evaluation of these sums from 
the data in § 22, the convergence of terms is not nearly so rapid 
as it was in the case of the expressions which involved the ratio 
a 2 Ip 2 ; so that the approximations to the values of the sums are 
not so exact as in the former cases. As a test, we may note that 
the sum of those terms in ^ which involve v 2 should be equal to 
the sum of the terms which do not involve v when the summation 
is carried to infinite values of v. When it is carried to the values 
v— ± 10, as in § 22, the value of the former sum is 19 '75 and the 
value of the latter is 14-54. The difference is not so excessive as 
to make it likely that results deduced from the limited summation 
would be reversed when the summation was extended farther. 
When the limited summation is taken for zero and positive 
values of v only, the whole term is found to be positive, its 
value being T39 M/p 3 . And a similar treatment of the term 
fi^/lM/p 3 -^- sin 0 cos Q( 2jp)~ 3/2 shows that this transverse component 
of force is practically zero so long as the angular displacement of 
the direction of magnetisation from the quaternary axis is so small 
that its square can be neglected. It therefore seems certain that 
magnetisation along a quaternary axis which is normal to a 
boundary possesses a fair amount of stability. 
It is needless to give a more full discussion of self-demagnetisa- 
tion relative to this orientation of the boundary alone. Full 
treatment would be somewhat lengthy, and may be deferred mean- 
while. But in support of the conclusion just reached, it should 
be noted that Weiss observed an obliquity between the external 
field and the direction of magnetisation, which, on allowance for 
