2900.] on Recent Studies in Gravitation. 289 



each other. Remove one to a very great distance, doing work 

 against their mutual attractions. Then, when it is quite out of 

 range of appreciable action, turn it round till its axis is parallel to 

 that of the fixed crystal. This absorbs no work if done slowly. 

 Then let it return. The force on the return journey at every point 

 is greater than the force on the outgoing journey, and more work will 

 be got out than was put in. When the sphere is in its first position, 

 turn it round till the axes are again at right angles. Then work 

 must be done on turning it through this right angle to supply the 

 difference between the outgoing and incoming works. For if no work 

 were done in the turning, we could go through cycle after cycle, 

 always getting a balance of energy over, and this would, I think, 

 imply either a cooling of the crystals or a diminution in their weight, 

 neither supposition being admissible. We are led, then, to say that 

 if the attraction with parallel axes exceeds that with crossed axes, 

 there must be a directive action resisting the turn from the crossed 

 to the parallel positions. And conversely, a directive action implies 

 axial variation in gravitation. 



The straightforward mode of testing the existence of this direc- 

 tive action would consist in hanging up one sphere by a wire or 

 thread, and turning the other round into various positions, and 

 observing whether the hanging sphere tended to twist out of posi- 

 tion. But the action, if it exists, is so minute, and the disturbances 

 due to air currents are so great, that it would be extremely difficult 

 to observe its effect directly. It occurred to us that we might call 

 in the aid of the principle of forced oscillations, by turning one 

 sphere round and round at a constant rate, so that the couple would 

 act first in one direction and then in the other, alternately, and so 

 set the hanging sphere vibrating to and fro. The nearer the com- 

 plete time of vibration of the applied couple to the natural time of 

 vibration of the hanging sphere, the greater would be the vibration 

 set up. This is well illustrated by moving the point of suspension 

 of a pendulum to and fro in gradually decreasing periods, when the 

 swing gets longer and longer, till the period is that of the pendulum, 

 and then decreases again. Or by the experiment of varying the 

 length of a jar resounding to a given fork, when the sound suddenly 

 swells out as the length becomes that which would naturally give 

 the same note as the fork. Now, in looking for the couple between 

 the crystals, there are two possible cases. The most likely is that 

 in which the couple acts in one way while the turning sphere is 

 moving from parallel to crossed, and in the opposite way during the 

 next quarter turn from crossed to parallel. That is, the couple 

 vanishes four times during the revolution, and this we may term a 

 quadrantal couple. But it is just possible that a quartz crystal has 

 two ends like a magnet, and that like poles tend to like directions. 

 Then the couple will vanish only twice in a revolution, and may be 

 termed a semicircular couple. We looked for both, but it is enough 

 now to consider the possibility of the quadrantal couple only. 



