NOTES ON MAGNETISM. 167 



through the axis of one of the magnets while the other passes 

 through that of the other. 



Let the axis of the magnet, whose action on the other is to 

 be calculated, be taken as axis of x, the centre of the magnet 

 being the origin of co-ordinates. Let x, y, z be the co-ordinates 

 of any point in the other magnet. Then, if r*= 



and sin cos fl 



r z 



Again, let a, b, c be the co-ordinates of the centre of the second 

 magnet, a, /?, 7 the cos angles its axis makes with the co-ordi- 

 nate axes, p the distance of any element dp from the centre, 

 X, Yj Z the forces on dp parallel to the .axes of co-ordinates, 

 m the intensity of dp. Then 



7 



Z = 5 xzaa. 



r 



Let @, H, K be the moments of these forces about lines drawn 

 through the centre of the second magnet parallel to the axes of 

 co-ordinates, 



~ . . . ., , 



G = - x {y(z-c]-z(y-V}} dp, 



(x-a)- (Zx* - r z ) (z-c}\ dp, 



K^~{(^~ O (y - 1} - Say (x - a)} dp. 



Now x = a + ap, y = b + @p, z 



Hence, neglecting the square, &c. of p, 



3Mm ( , . 



G = ^- a (by -c/3) pdp, 



H= ~ }3aca - (3a 2 - R*) 7) pdp, 



pdp, 

 where 2 = a 2 + 



