Analogue for the sEther. 657. 



Michelson and Morley experiment and other experiments of 

 the same type. The fluid analogue also fulfils the conditions 

 to he fulfilled by a fluid aether in this other important detail — 

 namely in that a very small degree of viscosity in the fluid 

 has a practically insensible effect in tending to extinguish 

 waves o£ any length exceeding the critical wave-length,, 

 while its influence is sensible in the case of the very short 

 waves *. 



Very few, if any, theoretical investigations have been made 

 of the fluid motion which is produced by bodies moving uni- 

 formly on the surface of a fluid, at speeds increasing up to,. 

 but not actually attaining to, the minimum wave-speed in 

 the fluid f. Nevertheless the general nature of the effects 

 to be observed can readily be inferred from experience and. 

 from the theoretical results obtained for the sphere and other 

 solids in uniform motion in an infinite liquid. As no vvave- 

 motion is possible within the fluid so long as the speed of the 

 solid does not exceed the minimum wave-speed, the main 

 disturbance within the fluid will clearly be a steady., or nearly 

 steady, motion confined to the immediate neighbourhood of 

 the moving solid. There is according, 1y no difficulty in 

 recognizing that the action of the total fluid pressure upon a 

 solid moving within it, or on its surface, would be equivalent 

 in effect to an increase in the inertia of the solid. If the 

 velocity of any solid be continuously increased from very 

 small values, it is clear that the apparent inertia of the 

 solid would also continuously increase, as the mass of fluid 

 set in motion by the solid became greater and greater. 



AY hen we come to consider the fluid motion arising from 

 the motion of a solid on the surface of a fluid at a speed 

 exactly equal to the minimum wave-speed in the fluid, we 

 have, however., the theoretical guidance we require in the 

 investigation by the late Lord Kay leigh just referred to. The 

 result obtained is that, in the entire absence of friction 

 within the fluid, the amplitude of the resulting fluid motion 

 is infinite ; and when only a small retarding force pro- 

 portional to the velocity, (av), acts at each point of the 

 fluid, the amplitude of the fluid motion arising from 

 the uniform motion of the solid is proportional to (l/\/ a), 

 an exceedingly large quantity. If a solid in steady motion 

 at a speed equal to the minimum wave-speed were suddenly 

 brought to rest by an obstacle, a fluid pulse of large 

 amplitude would be reflected from the obstacle into the 



* Lamb's ' Hydrodynamics/ 3rd ed. § 331. 



f See, however/' Standing- Waves on the Surface of Running Water,"' 

 Proc. Lond. Math. Soc. vol. xv. no. 219. 



