192 194] DIELECTRICS AND MAGNETIZABLE BODIES. 371 



to turn it about the axis perpendicular to this plane. Suppose 

 the force is in the XY- plane, and makes an angle 6 with the Z-axis. 



Then 



Xo = ^ cos0, Y = F sm0, Z 9 = Q t 



and the couple about the ^-axis acting on the whole ellipsoid of 

 volume 4?ra&c/3, 



*L) 



The values of L, M, N are by 113, 



I 



Jo 



, 



(q 2 + u) V(a 2 + u) (b" + u) (c 2 + u) 



where L, M, N are obtained by putting a, b, c respectively for q. 

 Accordingly L, M, N are in the reverse order of magnitude from 

 a, b, c. Consequently if a > b and 6 < 7r/2 the couple is positive, 

 or from X to F, that is, the ellipsoid tends to turn its longer axis 

 parallel to the field, whether K is positive or negative. This is in 

 contradiction to a statement frequently made, that diamagnetic 

 bodies tend to set their longest dimension across the field. They 

 do not do so if the field is uniform. If an ellipsoid be suspended 

 by a torsion fibre in a magnetic field, the field will cause it to 

 vibrate more rapidly when its long axis is parallel to the field, and 

 more slowly when it is across the field, than it would do in the 

 absence of the field. It is however extremely difficutoi|tf .not 

 impossible, to obtain a magnetic field nearly enough uniform to 

 show these phenomena in diamagnetic bodies, on accounl^F the 

 extreme smallness of /c 2 . 



194. Polarization of Sphere. In the case of a sphere for 

 inside points we have by 80, 



# 2 - 3 

 so that 

 (2) L=M = N=^, 



which is the self-demagnetizing factor. 



Accordingly the force is in the direction of the original field, 

 rr_ ff> _ -ff> 3^ 



" *' 



242 



