Deep Water Waves. 



393 



555 





The curve obtained from these numbers is shown in fig. 1. 

 It will be seen that the point of inflexion is very much 



nearer to the crest of the 

 wave than to the trough, 

 and that the greatest slope 

 of the wave is, as nearly as 

 can be measured, 30°. This 

 is just what it should be at 

 the crest of the highest 

 wave. 



There can be no doubt 

 that Stokes's series become, 

 as he supposed, divergent in 

 the neighbourhood of the 

 crest of the highest wave, 

 bat they evidently hold 

 right up to this point. 



I have also attempted to 

 determine whether the wave- 

 profile becomes unstable for 

 a ratio of amplitude to wave- 

 length less than that for 

 the highest wave, but as the 

 work is laborious, and the 

 Co conclusion arrived at is 

 c .° the merely negative one 

 ! that, so far as it is possible 

 fl to tell from the somewhat 

 j§ imperfect analysis, it does 

 ^ not become exponentially 

 % unstable until a exceeds the 

 ^ value corresponding to the 

 V highest wave for which 

 ►J Stokes's series converge, I 



have not included it. 

 % In attempting to deter- 



2 mine the stability of the 

 ° wave, we are compelled to 

 « consider only a small dis- 

 £ turbance of the progressive 

 wave profile, depending on a 

 time-factor of the form e~ k \ 

 where k may be complex. 

 We are also compelled, in 

 order to prevent the analysis 

 from becoming unmanage- 

 able, to assume that a 4 is 

 i i i i 



Phil Mag. S. 6. Vol. 27. No. 158. Feb. 1914. 2 D 



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