Analogue for the JEthev. 653 



in shallow water a medium which transmits waves whose 

 length exceeds the critical wave-length at an almost constant 

 velocity and also transmits a certain stress between solid 

 bodies floating on its surface. 



According to the analogy suggested above, long waves in 

 shallow water correspond to luminous or electromagnetic 

 waves in aether, and the forces of attraction exhibited 

 between bodies floating on the surface of water correspond 

 to the forces of gravity propagated through the aether. 

 From the standpoint of this analogy, it is significant that, 

 though gravity and surface tension are both concerned in 

 the propagation of waves, the influence of surface tension 

 practically disappears in the case of the longer waves, while 

 its influence predominates in the case of the shorter waves. 

 The suggestion this contains with respect to aether waves is 

 that the agencies which give rise to gravitational attraction 

 between bodies in aether are also concerned in the pro- 

 pagation of luminous and electromagnetic waves, though 

 they may play only a subordinate part in their propagation. 

 The actual law of speed for different wave-lengths given 

 in (1) may be taken as illustrating only certain possibilities 

 of the case for aether gravitational waves. If, however, w r e 

 adhere closely to the analogy betw r een aether gravitational 

 waves and waves in water for which the motive influence 

 governing the wave-motion is mainly surface tension, we 

 would then expect to find waves in aether governed mainly 

 by the agencies which give rise to gravitational attraction. 

 These weaves would be shorter than any hitherto observed, 

 and -the law of velocity of propagation of the waves would 

 be — velocity inversely proportional to square-root of wave- 

 length. 



The comparison of the mode of action of gravitation with 

 that of surface tension leads us on to an interesting similarity 

 between the two systems compared. In the immediate neigh- 

 bourhood of any body at rest or in motion on the surface of a 

 shallow fluid, there is owing to surface tension a region within 

 which the depth of the fluid is sensibly different from the 

 uniform depth obtaining at some distance from any solid 

 body- Any portion of a plane wave, in passing close to the 

 edge of a solid body, would therefore be subjected to an 

 alteration in its speed of propagation corresponding to the 

 alteration in depth of the fluid. Thus the waves would 

 suffer a certain amount of deviation from a rectilineal path. 

 This effect produced by the presence of solid bodies upon 

 waves in water is evidently analogous to the bending of 

 luminous waves from their path in a strong gravitational 



