332 REPORT — 1844. 



suits obtained by M. Poisson in his ' Theory of Waves,' any result that repre- 

 sents the phaenomena of this wave, although he shows that the solution of 

 Lagrange cannot either mathematically or physically be applied to consider- 

 able depths. Nearly all of them seem to apply only to the phaenomena of the 

 fluid in the vicinity of the initial disturbance. The supposed method of 

 genesis is one also which precludes the existence of the wave of the first order. 

 The greater part of the investigations of M. Poisson and of M. Cauchy 

 under the name of wave theory, are rather to be regarded as mathematical 

 exercises than as physical investigations ; but an account of what has been 

 accomplislied in this way by them, and by M. Laplace, may be found in the 

 excellent Reports of Mr. Challis in the Transactions of the British Association, 

 and in the treatise of MM. Weber*. 



* I think it right in tliis place to mention, with such distinction as I am able to bestow, a very 

 valuable treatise on waves, which was published nearly twenty years ago in Leipsic, by the 

 brothers Ernest H. AVcbcr and William Weber, entitled ' Wellenlehre auf Expcriniente ge- 

 griindet, oder iiber die Wellen tropfbarcr Fliissigkeiten niit Anwendung auf" die Schall- und 

 Licht-Wellen, von den Briidern Ernst Heinrich Weber, Professor in Leipzig und Wilhelm 

 Weber in Halle. Mit 18 Kupfertafeln. Leipzig, bei Gerhard Fleischer, 1825.' The work is 

 distinguished by more than the usual characteristics of German industry in the collection of 

 materials, and contains nearly all that has ever been written on waves since Ihe time of 

 Newton, and as a book of reference alone is a valuable history of wave research. To this 

 synopsis of the labours of others is appended a valuable series of experiments by the Messrs. 

 Webers themselves, contrived with much ingenuity, and conducted with apparently a high 

 degree of accuracy, designed to illustrate, extend, contradict or confirm the various theories 

 that have been advanced. 1 have been disposed to regret that this excellent book did not reach 

 me till long after my own researches had advanced far towards completion. But if it had done 

 so, it might have diverted me from my own trains of research. As the subject now stands, it 

 so happens that their labours and mine do not in the least degree supersede or interfere with 

 each other. Our respective works may be rather reckoned as suppleinentary the one to the 

 other, inasmuch as a great part of what they have done I have not attempted, and the most 

 part of what I have done will not be found in any part of their work. Of the existence of my 

 great solitary wave of the first order they were not aware, and although I am now able to re- 

 cognise hi influence on their results, yet owing to the nature of their experiments, it was not 

 likely they should recognise its existence, much less could they examine its phsenomena. 



The following passages serve to show that the Messrs. Weber had never recognised the ex- 

 istence of my solitary wave of the first order. They say in Abschnitt IV. Art. 87, — 



" Waves make their appearance as heights and hollows upon the surface of the liquid, one 

 part being raised above the level surface, and another part sunk below it ; hence the height 

 may be called the wave-ridge, and the depression the wave-hollow. These wave-ridges and 

 wave-hollows never come singly, but always connected with one another. This is the reason 

 why we do not call the wave-ridge by itself alone a tvave, nor the wave-hollow by itself alone 

 a wave, but simply the two conjoined." Art. 89. "The sum of the breadths of one wave- 

 ridge and of its companion wave-hollow, is called the breadth of a wave." Art. 101. " But 

 never in nature appears a wave-ridge unconnected with a wave-hollow, nor in like manner 

 any wave-hollow without its companion wave-ridge. Also from this reason it follows that we 

 can never have, during wave-motion, u particle of the fluid moved forward in its path without 

 immediately before or after having a contrary uiction also ; nor backwards, without also its 

 path being reversed." 



Their observations on the larger class of waves are ingeniously contrived, carefully observed, 

 and faithfully recorded, but lose much of the value as the basis of calculation and of general 

 laws from the following circumstances : — 1st, the narrowness of the channel ; tliat in which the 

 greater number of observations was made, being only 6'7 lines wide ; from this cause so great 

 an influence was produced by the adhesion of the sides as seriously to interfere with the phae- 

 nomena, which ought not therefore to be considered as the phmomenaof perfectly free fluids; 

 2, the shortness of the channels ; the longest having a depth of 2 feet and only 6 feet of length ; 

 in this case an observation of the wave of the first order was impossible ; and when we add that 

 the wave genesis was in general produced by the descent of a water column of great height, it » as 

 impossible that in the short period of wave transit the phaenomena could attain a condition of 

 uniformity favourable to accurate observation, one second and a fraction of a second being the 

 whole period of an observation, and it being necessary to observe accurately to at least one- 

 twentieth of a second, the results possess little value as measures of the phaenomena. In my 

 experiments we found that the first observations immediately after the wave genesis were the 



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