DIRECTIVE ACTIOIsr OF ONE QUARTZ CRYSTAL ON ANOTHER. 
247 
But if F is the amplitude of the couple 
ttL = [ F sin 0 d6 = 2F, 
J n 
and 
2F = (G - G') 
To seek for the directive action we have made use of the principle of forced 
oscillations, thereby obtaining to some extent a cumulative effect, and at the same 
time largely eliminating the errors due to accidental disturbances. 
Briehy the method was as follows :—A small quartz sphere, about 0'9 centim in 
diameter, was carried in a frame to which a light mirror was attached, and suspended 
by a quartz fibre inside a brass case, the position being determined by the reflection 
of a scale in the usual way. The complete time of torsional vibration was about 
120 seconds. 
Outside the case was a larger quartz sphere, about 6'6 centims. in diameter, its 
centre being level with that of the suspended sphere, and 5‘9 centims. from it. The 
larger sphere could be rotated about a vertical axis through its centre at any desired 
rate. The crystalline axes of both were horizontal, that of the smaller sphere being 
perpendicular to the line joining the centres. 
To test for the quadrantal couple, the larger sphere was rotated once in 
230 seconds—a period nearly double that of the smaller sphere. To test for the 
semicircular couple, the larger sphere was rotated once in 115 seconds, or nearly the 
period of the smaller sphere. 
Assuming that a couple exists, a continuous rotation of the larger sphere would 
set up a forced oscillation in the smaller sphere of the same period as the couple, and 
since the damping was very considerable, this forced oscillation would soon rise to 
approximately its full value. Meanwhile, any natural vibrations of the suspended 
system would be rapidly damped out. Though continually renewed by disturbances 
due to convection-currents and tremors, they would be irregularly distributed, and 
there was no reason to suspect that their maximum amplitude would recur at any 
particular phase of the period of the applied couple. To secure the distribution of 
successive maxima of natural vibrations of the smaller sphere over all phases of the 
forced period, the latter was made sensibly different from the natural period in the 
ratio 23:24; and though the cumulative effect of the forced oscillations was reduced 
by the largeness of this difference, we did not think it advisable to make the periods 
more nearly coincident, lest the distribution of the disturbances, which were some¬ 
times large, should not be sufficient. This conclusion was arrived at from the results 
of preliminary experiments with more nearly equal periods. 
During each complete period of the supposed applied couple, the position of the 
smaller sphere was I’ead ten times at equi-clistant intervals of time, and the scale- 
readings were entered in ten parallel columns, one horizontal line for each period. The 
