Magnetic Particle in a Magnetic Field. 41 
Then 
Xr oe be af v 
Mee). dy. da, “dB. dy da dB. dy 
* dit de ot) te Sara a eee 
and 
xr’ po’ yp’ 
da da da. dB 
dy 
These equations, with the relations 
dy dg da dy _ dB _ da 
ed, ae 5 Aar Gane Rep Arrw ee dy 
are sufficient to find the angle between the force on a mag- 
netic particle and the direction in which the magnetic intensity 
increases most rapidly, the field being due to permanent 
magnets, and to a given distribution of currents. 
_ It can easily be seen that the relation 
bits ree Bw—ryv | =() 
aye MW, -Yyu—aw | 
peor Vv, au — Bu | 
holds between the components of magnetic intensity and 
current and the two directions considered. Hence if a line 
be drawn perpendicular to both the current and magnetic 
intensity, a magnetic particle will be urged in a direction 
lying in a plane through this line and the “direction in which 
the magnetic intensity increases most rapidly. 
Queen’s College, Galway. 
March 30, 1904. 
Postscript. 
The complete solution may be put < as follows :— 
Let A, w, v be the direction cosines of the direction of 
greatest increase of the magnetic intensity H, X’, p’, v’ those 
of the force F on the magnetic particle ; then : 
1 dH? ld? tiab: 
Pr=5 Sr ae ae . dy’ aaa ae 
N= oa + 4mr(vy~wB), 
OU = a +4r(uB—va). 
