Manchester Memoirs, Vol. I. (1906), No. 8- 



VIII. On the Range of Progressive Waves of Finite 

 Amplitude in Deep Water. 



By R. F. Gwyther, M.A. 



(Communicated by Professor H. Lamb, LL.D., D.Sc, F.R.S.) 



Received and Read February 2jt]i, igo6. 



The waves considered in this paper are those first, 

 and very fully, discussed by Stokes,* in his paper on the 

 " Theory of Oscillatory Waves," and in the " Supplement " 

 to that paper. 



The object of the investigation is to confirm the 

 hypothesis that this class of wave is mathematically 

 capable of propagation with uniform velocity and without 

 change of form, and to determine the limit of the range 

 of such waves in height, and as far as possible, the change 

 in shape of the profile oi the wave as the ratio of the 

 height to the wave length is increased. 



The method which I employ is that of tracing the 

 paths of the fluid particles. It is not supposed that the 

 knowledge of these paths is of interest ; but there seems 

 no more complete method of testing whether the motion 

 assumed can actually take place than one which shews 

 how the motions of the particles are to be coordinated 

 in order to adapt themselves to the circumstances of the 

 case. Since this investigation shews that the motions of 

 the individual particles can, within a certain range, be 

 traced to any desirable degree of accuracy, it follows 

 that this is a form of wave of finite amplitude which 

 represents an actually possible phenomenon. 



* Mathematical and Physical Papers, vol I., p. 196, and Sitpplement, p. 314. 



J!i[ay 31st, igo6. 



