ON WAVES. 



311 



Report on Waves. By J. Scott Russell, Esg., M.A., F.R, S. Edin., 

 made to the Meetings in 1842 and 1843. 

 ,, , ,„ .^ rSir John RoBisoN*, -S'ec, i?.xS'.£'rfm. 

 Mentbers of Committee | j^ g^^^,^ Russell, F.R.S. Edin. 



A Provisional Report, on this subject was presented to the IMeeting held at 

 Liverpool in 1838, and is printed in the Sixth Volume of the Transactions. 

 That report was a partial one. It states that " the extent and multifarious 

 nature of the subjects of inquiry have rendered it impossible to terminate the 

 examination of all of them in so short a time ; but it is their duty to report 

 the progress which they have made, and the partial results they have already 

 obtained, leaving to the reports of future years such portions of the inquiries 

 as they have not yet undertaken." 



The first of these subjects of inquiry is stated to have been " to determine 

 the varieties, phaenomena and laws of waves, and the conditions which aflFect 

 their genesis and propagation." 



It is this branch of the duty of the Committee which forms the subject of 

 the present report. Ever since the date of that report, it has happened that 

 the author of this has been so fully pre-occupied by inevitable duty, that it 

 was not in his power to indulge much in the pleasures of scientific inquiry ; 

 and as the active part of the investigation necessarily devolved upon him, 

 it was not practicable to continue the series of researches on the ample and 

 systematic scale originally designed, so soon as he had anticipated, so that 

 the former report has necessarily been left in a fragmentary state till now. 



But I have never ceased to avail myself of such opportunities as I could 

 contrive to apply to the furtherance of this interesting investigation. I have 

 now fully discussed the experiments which the former report only registered. 

 I have repeated the former experiments where their value seemed doubtful, I 

 have supplemented them in those places where examples were wanting. I 

 have extended them to higher ranges, and where necessary to a much larger 

 scale. In so far as the experiments have been repeated and more fully dis- 

 cussed, they have tended to confirm the conclusions given in the former re- 

 port, as well as to extend their application. 



The results here alluded to are those which concern especially the velocity 

 and characteristic properties of the solitarj' wave, that class of wave which 

 the writer has called the great wave of translation, and which he regards 

 as the primary wave of the first order. The former experiments related 

 chiefly to the mode of genesis, and velocity of propagation of this wave. 

 They led to this expression for the velocity in all circumstances, 



v^ Vff (Ji + k), 

 k being the height of the crest of the wave above the plane of repose of the 

 fluid, h the depth throughout the fluid in repose, and g the measure of gra- 

 vity. Later discussions of the experiments not only confirm this result, but 

 are themselves established by such further experiments as have been recently 

 instituted, so that this formerly obtained velocity may now be regarded as the 

 phsenomenon characteristic of the wave of the first order. 



The former series of experiments also contained several points of research 

 not published in the former report, because not suflSciently extended to be of 



* I cannot allow these pages to leave my hands without expressing my deep regret that 

 the death of Sir John Robison has suddenly deprived the Association of a zealous and di- 

 stinguished office-bearer, and myself of a kind friend. In all these researches the responsible 

 duties were mine, and I alone am accountable for them ; but in forwarding the objects of the 

 investigation I always found him a valuable counsellor and a respected and cordial cooperator. 



