38 Mr MeConnel, On the Mechanical Force acting [Nov. 22, 
dp 
= Ae Te Ae +02 +00 — wh, Sepa ie aan (1) 
and a couple one of whose components is 
. dis By — CB a esgic eee (2) 
These expressions are obtained by combining the forces on the 
two poles of the element. 
The notation is that used by Maxwell. 
Nowhere in his book does he give any complete proof of this 
result, and the object of the following paper is to supply one. 
It is easy to show that, if a magnetised element, the com- 
ponents of whose magnetisation are A, B, C, be placed in a field 
of magnetic force whose undisturbed values are a, 8, y, it is subject 
to a force of translation of which one component is 
OS at ae Dates leek eke (3) 
and a couple of which one component is 
Le = By SOB kbd ate tse one aeaeene seer (4) 
Next consider an element which forms part of a finite magnet. 
The magnetic force can now be no longer defined as the force 
on an unit magnetic pole, but requires a special definition. We 
shall take that used by Maxwell, which may be thus stated :— 
It is zero at an infinite distance from the system of magnets 
and currents, and satisfies the following equations at every point 
dy dB _ 
(§ 607) 5 dy — ae = Aru nvcllaleletevetetelatelelcletatarctetelstetate (5) 
with two at ones, 
dB. dy CA TAB a ) 
and (§ 403) Tat dy * den = Aer tlhe tae ie (6). 
There is only one value of § which can satisfy these conditions. 
¥% is given by the definition 
B= H + 4c. 
At present we suppose that there is no current through the 
element. 
Let the element be spherical. We may consider its magneti- 
sation to be uniform and equal to that at its centre without error; 
for the forces on it, depending on the outstanding irregularities 
of magnetisation, must be indefinitely small relatively to those 
depending on the uniform eae The § at any point 
may be divided into two parts, , due to the element, and $, 
due to the rest of the magnet and all external magnets and 
