40) Prof. A. Anderson on the Force on a 
PQQ’P’.. We have, easily, 
H — dH =4A7w, 
p dn 
where w is the current density per unit area. 
Let PX (fig. 3) making an angle ¢ with the normal PO 
to the line of force at P, be the direction in w hich the mag- 
netic intensity increases most rapidly, and PR, making an 
angle @ with Pp: the direction of he force on a mag 
particle at dee Also, let the angle XPR=a. 
Then 
fae an H 
ds/ p 
and te dHH | dH | 
: Ors ae ie 
from which it follows that - 
Ampw sin d cos b 
tan a= 
H—4rpw sin? 6 
If d=0, a=0, which is the case for a particle outside a 
straight wire carrying a current. 
If ¢=7, a=, which is the case for a particle inside a 
wire carrying a current. 
To solve the general case, let u, v, w be the components of 
current density aha any point, a, 8, y the components of mag- 
netic intensity, r, H, v the direction cosines of the direction in 
which the magnetic intensity increases most rapidly, and 
rN, pw’, v' the dir ection cosines of the force on the particle. | 
