312 REPORT 1844. 



the desired value. Among these were a series of observations on the actual 

 motion of translation of particles of the fluid during wave transmission ; these 

 have since been completed and extended, and the results of the whole are now 

 given. 



The former report was inevitably a fragment. I have endeavoured to give 

 to the present report a somewhat greater degree of completeness. For this 

 purpose I have now incorporated under one general form all those results of 

 the present as well as of all my former researches, which could contribute to 

 the unity and completeness of the view of a subject so interesting and im- 

 portant. I have re-discussed my former experiments, combined them with the 

 more recent observations, and thus, from a wider basis of induction, obtained 

 results of greater generality. Until the date of these observations, there had 

 been confounded together in an indefinite notion of waves and wave motion, 

 phaenomena essentially different, — different in their genesis, laws of propagation, 

 and other characteristics. I have endeavoured, by a rigid course of examina- 

 tion, to distinguish these different classes of phaenomena from each other. 1 

 have determined certain tests, by which these confused phaenomena have 

 been made to divide themselves into certain classes, distinguished by certain 

 great characteristics. Contradictions and anomalies have in this process gra- 

 dually disappeared ; and I now find that all the waves which I have observed 

 may be distinguished into four great orders, and that the waves of each order 

 differ essentially from each other in the circumstances of their origin, are 

 transmitted by different forces, exist in different conditions, and are governed 

 by different laws. It is now therefore easy to understand how much has been 

 hitherto added to the difficulty of this difficult subject, by confounding together 

 phaenomena so different. The characteristics, phaenomena, and laws of these 

 great orders I have attempted in the present report to determine and define. 



The knowledge I have thus endeavoured to obtain and herein to set forth 

 concerning these beautiful and interesting wave phaenomena, is designed to 

 form a contribution to the advancement of hydrodynamics, a branch of phj^sical 

 science hitherto much in arrear. But besides this their immediate design, 

 these investigations of wave motion are fertile in important applications, not 

 only to illustrate and extend other departments of science, but to subserve 

 the purposes and uses of the practical arts. I have ascertained that what I 

 have called the great wave of translation, my wave of the first order, furnishes 

 a type of that great oceanic wave which twice a day brings to our shores 

 the waters of the tide. This type enabled us to understand and explain by 

 analogy many of the phaenomena of fluvial and littoral tides, formerly ano- 

 malous" (see Proceedings R.S. Ed., 1838) ; and thus do these wave researches 

 contribute to the advancement of the theory of the tides, a branch of physical 

 astronomy long stationary, but which has recently made rapid strides towards 

 the same high perfection which other branches of predictive astronomy have 

 long enjoyed, a perfection which we owe chiefly to Sir John W. Lubbock, 

 to Mr. Whewell, and the co-operation of the British Association. It is the 

 •wave of the first order enumerated in this report which furnishes to us the 

 model of a terrestrial mechanism, by means of which the forces primarily 

 imparted by the sun and moon are taken up and employed in the transport 

 of tidal waters to distant shores (see previous Reports of Brit. Ass.), and 

 their distribution in remote seas and rivers, which they continue in succession 

 to agitate long after the forces employed in the genesis of the wave have 

 ceased to exist (see Report on Tides). This apjilication of the phaenomena 

 of waves to explain the tides is not their only application to the advancement 

 of other branches of science. The phaenomena of resistance of jiuids I have 

 found to be intimately connected with those waves (see Phil. Trans. Edin. 



