THE TWO GREAT SOLITARY WAVES OF RUSSELL. 



341 



effect upon the wave itself, and an indirect effect in keeping the surface of the fJuid in a state 

 of agitation till the return of the wave after reflection at the end of the canal ; by which the 

 difficulty of accurately observing the exact time of transit would be greatly increased. Without 

 the aid of some supposition of this kind, I cannot account for the manifest irregularities 

 exhibited in Mr. Russell's table of the observed velocities of negative waves. {Eeport, page 349). 



An inspection of the fifth column will at once acquaint the reader, that the errors here are 

 far larger than in case of the positive wave. Instances however might have been selected from 

 Mr. Russell's table which would have exhibited a much closer agreement between theory and 

 observation. It is not necessary to repeat the remarks before made respecting the discontinuity 

 of the pressure, and the consequent destruction of the wave. 



I will now conclude this paper with a few general remarks. 



Mr. Russell states, " that the positive and negative waves do not stand to each other in the 

 relation of companion phaenomena. They cannot be considered in any case as the positive and 

 negative portions of the same pha;nomena." This is completely borne out by the foregoing 

 theory ; which shews that the two waves are distinguished in our investigations by a circumstance 

 which prevents their coexistence ; a certain constant being positive for one, and negative 

 for the other, thereby making it impossible for p to be the same for both at the junction of the 

 two parts, supposing them to be portions of one wave. 



If it were possible for both waves to coexist at the same place, by meeting each other, or 

 by one overtaking the other, then we should have for the vertical motion of a particle in the 

 compound wave, 



ot'y = (n^ - n')y- 



This is obtained by uniting equations (9) and (9'). Hence if n' be greater than n, the result 

 would be a negative wave ; but if m be less than n, the result would be a postive wave ; and if 

 n = w the result would be that y would be constant, or there would be no wave at all. 



This explains the following phaenomena observed by Mr. Russell. 



" If a positive and negative wave of equal volume meet in opposite directions, they neutralize 

 each other and botii cease to exist." 



" If a positive wave overtake a negative wave of equal volume, they also neutralize each other 

 and cease to exist." 



" If either bo larger, the remainder is propagated as a wave of the larger class." {Report, p. 351). 



S. EARNSHAW. 



