118 
Proceedings of the Royal Society 
Again, if 
S.8p<l 
Sap 
V 
, either is equal to 
-S.8p<^Pby(ll), 
Here a particular case is 
cT'= which {Quarterly Math. Journal, vol. hi. 
p. 338) is the vector-force exerted by an element a of a current 
upon a particle of magnetism at p. 
and the same paper shows 
that this is the vector-foroe exerted by a small plane current at the 
origin (its plane being perpendicular to a) upon a magnetic particle, 
or pole of a solenoid, at p. This expression, being a pure vector, 
denotes an elementary rotation caused by the distortion of the 
solid, and it is evident that the above value of <r- satisfies the equa- 
tions (16)^, (17), and the distortion is therefore producible by 
external forces. Thus the efi*ect of an element of a current on a 
magnetic particle is expressed directly by the displacement, while 
that of a small closed current or magnet is represented by the 
vector-axis of the rotation caused by the displacement. 
Again, let 
SSp<| ‘^0^=8 7^3 . 
It is evident that cn satisfies (16)^, and that the right-hand side of 
the above equation may be written 
-S.8p<3^. 
Hence a particular case is 
<1 and this satisfies (17) also. 
Ip 
Hence the corresponding displacement is producible by external 
forces, and <i cr> is the rotation axis of the element at p, and is 
seen as before to represent the vector-force exerted on a particle of 
magnetism at p by an element a of a current at the origin. 
