70 The Right Hon. Lord Rayleigh [March 20, 



WEEKLY EYENIXG MEbiTING, 



Friday, March 20, 1914. 



Alexander Siemens, Esq.. M.Inst.C.E. M.I.E.E., Secretary 

 and Vice-President, in the Chair. 



The Right Hon. Lord RayleiCxH, O.M. P.O. LL.D. D.Sc. F.R.S. 



M.R.L, Honorary Professor of Natural Philosophy, 



Royal Institution. 



Fluid Motions. 



The subject of this lecture has received the attention of several 

 generations of mathematicians and experimenters. Over a part of 

 the field their labours have been rewarded with a considerable degree 

 of success. Li all that concerns small vibrations, whether of air, 

 as in sound, or of water, as in waves and tides, we have a large body 

 of systematized knowledge, though in the case of the tides the question 

 is seriously complicated by the fact that the rotation of the globe is 

 actual and not merely relative to the sun and moon, as well as by 

 the irregular outlines and depths of the various oceans. And even 

 when the disturbance constituting the vibration is not small, some 

 progress has been made, as in the theory of sound waves in one 

 dimension, and of the tidal hores, which are such a remarkable 

 feature of certain estuaries and rivers. 



The general equations of fluid motions, when friction or viscosity 

 is neglected, were laid down in quite early days by Euler and 

 Lagrange, and in a sense they should contain the whole theory. But, 

 as Wliewell remarked, it soon appeared that these equations by 

 themselves take us a surprisingly little way, and much mathematical 

 and physical talent had to be expended before the truths hidden in 

 them could be brought to light and exhibited in a practical shape. 

 What was still more disconcerting, some of the general propositions so 

 arrived at were found to be in flagrant contradiction with observa- 

 tion, even in cases where at first sight it would not seem that viscosity 

 was likely to be important. Thus a solid body, submerged to a 

 sufficient depth, should experience no resistance to its motion through 

 water. On this principle the screw of a submerged boat would be 

 useless, but, on the other band, its services would not be needed. It 

 is little wonder that practical men should declare that theoretical 

 hydrodynamics has nothing at all to do with real fluids. Later we 

 will return to some of these difliculties, not yet fully surmounted, but 



