Proceedings. 169 



disturbance always in the same phase as the disturbing 

 force. But if the disturbance has a period shorter than the 

 natural period, the system will oscillate in the same period 

 as the force, but in the opposite phase. Now, in the vessel 

 with oil and water three systems of oscillation, or wave 

 motions, are possible. If the vessel were completely full, so 

 that there were no free surface, and if there were no oil, no 

 oscillation would be possible except (1) the pendulous 

 motion. If half full of oil and filled up with water, then, if dis- 

 turbed and left, a wave motion (2) in its natural period would 

 be set up in the surface between the oil and water. In the 

 same way (3) if the vessel were half full of water without 

 oil. But in the latter case (3) the natural period would be 

 two or three times less than (2) between the oil and water. 

 Now, when the vessel contains oil and water, disturbances 

 (2) and (3) will both be set up, and might continue, till 

 destroyed by viscosity, in their natural periods if these 

 were the same, but the periods being different, the oscilla- 

 tions in the period (3) would cause periodic disturbance in 

 (2), and the natural period of (3J being much shorter 

 than that of (2), the oscillation so maintained in (2) would 

 be in opposite phase to (3), but, owing to viscosity, such 

 maintenance would be of short duration. If, however, the 

 natural period of the pendulous motion (1) of the vessel 

 were in magnitude between the periods 3 and 2, smaller 

 than (2) greater than (3), then it would maintain an oscilla- 

 tion in the same period as the pendulous motion in (3) and 

 also in (2), that in (3) having the same phase as the 

 pendulum, that in (2) having the opposite phase. So far 

 this explanation is only partial, as it is assumed that there 

 will be a disturbance in (2) in the same phase as in (3). 

 That this must be the case, however, becomes evident when it 

 is considered that the motion of the water cannot be that of 

 a solid, but must be irrational, and that the disturbance 

 arises from the non-spherical form of the surfaces of the 



