DIRECTIVE ACTION OF ONE QUARTZ CRYSTAL ON ANOTHER. 
251 
In combining the results it appeared useless to attempt to weight them according 
to the number of periods taken, since no accurate conclusion could be expected. It 
will be seen that in each case thei'e is an outstanding periodicity, but the amplitude 
is less when the disturbances (as indicated by the greatest range during a period) are 
less, and it diminishes when the results are combined so as to lessen the effect of want 
of symmetry. 
In the “ quadrantal ” observations (Series C, D), where the effect of want of 
symmetry of the apparatus should almost be eliminated, since it is ajqDroximately 
semicircular, the mean range is much smaller than in Series A and B. 
For these reasons we do not think that our observations can be taken as indicating 
the existence of a couple of the kind sought, but only as giving a superior limit to its 
value, should it exist. 
We now proceed to the Calculation of Superior Limit of Couple. 
Equatio7i of Motion of the Smaller Sphere. 
Let I be the moment of inertia of sphere and cage. 
„ p ,, torsion couple per radian, 
,, X ,, damping couple per unit angular velocity. 
,, F cos pt be the supposed couple due to the larger sphere, having period 27r/p. 
Then 
Id -{■ \d p6 — Y cos pjt. 
Putting 
K = X/I; n" = p/l ; E = F/I 
we have 
9 k9 71^9 = E cos pt . ..(1). 
The solution of this is 
9 = 
E sin 
27 K 
COS {pt — e) + Ae cos t — a], . . . (2) 
where tan e = and A, a are constants. 
71- — 
The first term in the value of 9 in (2) gives the forced, and the second term the 
natural vibrations, the period of the latter being 
Stt ^ 
-p—, -= 1, say. 
^{ 71 - - |/c-) 
The value of T was always very near to 120 secs., and the mean of various 
determinations during the observations gave 
T = 
iTT 
^( 71 ^ - f/C'b 
2 K 2 
= 120’8 secs. 
(3). 
