[B89] 
III. On the Force on a Magnetic Particle in a Magnetic Field. 
By Prof. A. AnpErson, W.A., LL.D." 
A SMALL particle of soft iron, or a small magnet, when 
placed in a magnetic field is acted on by a force in the 
direction in which the intensity of the field increases most 
rapidly. This is, in general, only true when the field is 
conservative. 
Consider a magnetic particle, P (fig. 1), whose axis of 
magnetization is along a line of force, PQ. It is easy to 
show that the forces acting along the tangent and normal are, 
respectively, 
ee and es 
ds p 
where M is the moment of the particle, H the intensity of 
the field, and p the radius of curvature of the line of force 
at P. 
If the particle be of small susceptibility, these expressions 
may be written 
2 
bree and ight 
ds p 
v denoting the volume, and k the susceptibility. 
Let the resultant, R, of these forces make an angle @ with 
the normal. Then, if this direction is that along which the 
intensity of the magnetic field increases most rapidly, the rate 
of increase perpendicular to R is zero, or 
dH cos 6 -- dH sin @=0. 
ds dn 
_ And hence 
Bl vi dB 
piel ada 
* Communicated by the Author. 
