1 68 Proceedings. 



the paradox becomes even more pronounced when the 

 vessel is, by suspension or otherwise, subject to regular 

 harmonic motion in one plane, and compared with a vessel 

 in all respects and similarly situated, except that it contains 

 one fluid only. For while the upper surface of the oil 

 appears to follow the motion of the vessel, remaining very 

 nearly perpendicular to the line of suspension, as it would 

 if the whole mass were a solid, the free surface of the water 

 in the vessel without oil has a decidedly greater amplitude 

 than that of the line of suspension, though the oscillations 

 are exactly in the same phase and the amplitude is still 

 small. On the other hand the surface separating the oil 

 and water has an oscillatory motion about the line of suspen- 

 sion much greater in magnitude than that of the surface of the 

 water in the vessel without oil and in exactly the same or 

 the opposite phase. Another very striking fact is that all the 

 surfaces appear to remain plane surfaces when the motion 

 is within certain considerable limits. These motions, how- 

 ever, do depend on the relations between the length of the 

 pendulum, the size of the vessel, and the depths of the 

 fluids, the phase of the separating surface changing from 

 the same to the phase opposite to that of the line of 

 suspension as the pendulum is shortened. The solution 

 of the problem presented by this paradox, although not 

 altogether confirmed or fully worked out, appears to be 

 indicated by the fact that the oscillations of all the surfaces 

 are steady, and in the same or opposite phase with the line 

 of suspension, that is, in the same or opposite phase with 

 the disturbance, together with the fact that the free surfaces 

 of the fluids remain nearly plane. For if any material 

 system is, when disturbed, capable of oscillating in a particular 

 period (its natural period), and such oscillation is subject to 

 a viscous resistance, then if subject to a very gradually 

 increasing disturbance, having a period longer than the 

 natural period, the system will oscillate in the period of 



