24G 
DR. J. H. ROTATING AND MR. P. L. GRAY lY SEARCH OF A 
M' to an infinite distance, in a line perpendicular to the parallel axes, is GMM'/r. 
Now turn M' through 90° to cross the axes, and bring it back to the original position, 
but with the axes crossed. 
Fig, 1. 
The force will do work G'MM'/r Then turn M' through 90° into its original 
orientation. Assuming that the forces are conservative, th.e total work vanishes, so 
that there must be a couple acting during the last rotation, which does v\mrk equal to 
the difterence between the works done on withdrawal and approach. 
If we take the average value of the couple as .L, then 
TT 
2 
L = (G - G') 
MM' 
Our suppositions as to the law of force are doubtless arbitraiy, but they serve to 
show the probability of the existence of a directive couple accompanying any axial 
difference in the gravitative field. 
In the absence of any distinction between the ends of an axis we may assume 
that the couple is “ quadrantal,” that is, that it goes through its range of values 
with the rotation of the sphere through 180° and vanishing in every quadrant, and 
we shall suppose that it is zero when the crystals are in the positions shown in 
fig. 1 («), and fig. 1 (b). 
Taking the couple as a sine function of amplitude F, we have 
“F sin 29 (16 = F, 
0 
(G - G') ■ 
v'hence 
TT 
L r.:r 
F = 
But it is conceivable that the two ends of an axis are different, having polarlt}’ of 
the magnetic type. The couple would then be “ semicircular,” going through its 
range of values once and vanishing twice in the revolution. We shall suppose that 
the couple is zero when the axes are parallel. We should now have G and G' 
constants for the axes parallel, the one when like ends are in the same direction, 
the other when they are in opposite directions, and we have 
ttL r=(G 
G') 
]\IM' 
