DIRECTIVE ACTION OP ONE QUARTZ CRYSTAL ON ANOTHER. 
253 
E sin e 5N 
j)K ~ 2 X 35800’ 
whence 
F = El = 0-8293N x 10'®, 
using the values already found for e, k, I. 
Taking the limiting values of the amplitudes as half the mean ranges given in 
Table III., the vibration due to the quadrantal couple has amplitude not greater than 
0'033 div., and that due to the semicircular couple, amplitude not greater than 
0'095 div. Whence 
F (quadrantal) is not greater than 2’737 X 10“^°, 
and 
F (semicircular) is not greater than 7'878 X 
Perhaps some idea of these values may be obtained by noticing that the times of 
vibration of the small sphere under couple F per radian would be respectively 
32 hours and 25 hours. But it is probably best to interpret the value in terms of 
the assumptions we made as to the force in the introduction. We found for the 
quadrantal couple 
F = (G - G') MM'/r, 
G - G' GMM' 
~ G ■ r ’ 
where MM' are the masses of the spheres, r the distance between their centres, GG' 
the parallel and crossed gravitation constants. 
Now M, the mass of the larger sphere, is 399'9, say 400 grams, 
M „ „ smaller „ 1’004 grams, 
r is 5‘9 centims., 
G and G' are exceedingly near 6'66 X 10“ 
whence 
G - G' _ Er 1 
G ~ G.MM'~ 
On the assumed law of force this implies that the attractions between the two 
spheres, with distance 5’9 centims. between their centres, do not differ in the parallel 
and crossed positions by as much as xFsoo whole attraction. 
We may compare this result with PtUDBERG’s values of the refractive indices of 
quartz for the mean D line 
P'0 
1-05328 - 1-544 8 
1-54418 
= yto iibout. 
For the semicircular couple 
GMM' 
whence 
__ _L_ 
— 2 8 5 0 • 
