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XX\l.—On the Theory of Waves. Part I. By The Rev. P. Kelland, M.A., 

 F.R.SS.L.SfE.,F.C.P.S., late Fellom of Queens' College, Canibridge; Pro- 

 fessor of Mathematics, S^-c. in the University of Edinburgh. 



(Read April 1. 1839.) 



It is my intention to undertake a series of Memoirs on that branch of Hydro- 

 dynamics which treats of the transmission of reciprocating motion. It may ap- 

 pear superfluous at first, that any fm-ther investigation should he bestowed on 

 the general problem, when it is remembered that two of the most able mathe- 

 maticians of the present age, M. Poisson and M. Cauchy, have devoted so much 

 of their talents and attention to the subject. Yet, when advances are rapidly 

 making in our experimental knowledge, we generally find that the complex and 

 apparently general results, deduced by those who have paid the greatest attention 

 to the science as it presented itself to their view, are in reality only pai-ticular 

 cases, when they have to be applied to experiments in their actual form. This 

 circumstance detracts greatly from the value of almost all general investigations ; 

 and in this instance it does so in a remarkable degree. The prosecution of the 

 research has been extended in one direction — the prosecution of experimental 

 knowledge has taken another ; and thus, in order to meet the challenge of ex- 

 perimenters to keep pace with them, it behoves the theorist frequently to return 

 on his path, and cross over to the line of their march. 



I doubt much, however, whether such men as Laplace and Lagrange would 

 have been induced, with the expectation of joining experiment on her lower and 

 more trodden fields, to reconsider and remodel their investigations ; nor have I 

 any reason to hope, that such men as Poisson and Cauchy will quit the delectable 

 atmosphere in which they are involved, of abstruse analysis, for the more humble, 

 but not less important task of endeavouring to treat the simpler problems in a 

 manner not made general arbitrarily to lead to the most elegant formulae, but 

 general to that extent, and in that mode, in which the problem in nature is so. 

 It may seem strange, but I confess it appears to me, that this problem has hitherto 

 fallen into the hands of men too distinguished, — of men who had attaiaed such 

 an elevation, that the labours of ordinary men, the trivial difficulties which im- 

 pede the progi-ess of less gigantic minds, do not form part either of their actual 

 research, or of that which the world expects at their hands. Hence their inves- 



VOL. XIV. PART II. 4 N 



