26*2 Lord Rayleigh on Waves. 



the fluid will be less than before if the displacement be down- 

 wards, but will be increased if the displacement be upwards ; 

 so that the forces brought to bear on the envelope are in both 

 oases in the direction of displacement. The expression for the 

 variation of pressure at the envelope is 



P °A V A „ *J 



The Solitary Wave. 



This is the name given by Mr. Scott Russell to a peculiar 

 wave described by him in the British-Association Report for 

 1844. Since its length is about six or eight times the depth of 

 the canal, this wave is, to a rough approximation, included 

 under the theory of long waves ; but there are several circum- 

 stances observed by Mr. Russell which indicate that it has 

 a character distinct from that of other long waves. Among 

 these may be mentioned the very different behaviour of solitary 

 waves according as they are positive or negative, viz. accord- 

 ing as they consist of an elevation or a depression from the 

 undisturbed level. In the former case the wave has a remark- 

 able permanence, being propagated to great distances without 

 much loss ; but a negative wave is soon broken up and dissi- 

 pated. 



Airy, in his treatise on Tides and Waves, still probably the 

 best authority on the subject, appears not to recognize any 

 thing distinctive in the solitary wave. He says : — " We are 

 not disposed to recognize this wave as deserving the epithets 

 ' great ' or ' primary,' .... and we conceive that ever since it 

 was known that the theory of shallow waves of great length 



was contained in the equation -=-£- =gic -7-5 , . . . the theory of 



the solitary wave has been perfectly well known." And again, 

 " Some experiments were made by Mr. Russell on what he calls 

 a negative wave — that is, a wave which is in reality a progres- 

 sive hollow or depression. But (we know not why) he appears 

 not to have been satisfied with these experiments, and has 

 omitted them in his abstract. All the theories of our IVth 

 Section, without exception, apply to these as well as to positive 

 waves, the sign of the coefficient only being changed." 



On the other hand, Professor Stokes says* : — " It is the opinion 

 of Mr. Russell that the solitary wave is a phenomenon sui 

 generis, in no wise deriving its character from the circumstances 

 of the generation of the wave. His experiments seem to ren- 



* British-Association Report. 



