330 



REPORT — 1844. 



To render the results of all these experiments still more appreciable, they 

 ai"e graphically laid down in Plate XLVIIL, the stars representing the indi- 

 vidual experiments, and the line the formula. The coincidence is satisfactory. 



Table IV. Table V. 



Velocity of larger Waves. Velocity of smaller Waves. 



Wave of the First Order not formerly described. — Although many distin- 

 guished philosophers from the time of Sir Isaac Newton have devoted 

 themselves to the study of the theory of waves, I have not been able to 

 discover in their works anything like the prediction of a phaenomenon such 

 as the wave of translation or the solitary wave of the first order. The waves 

 of the second order, or gregarious oscillations, which make their appearance 

 in successive groups, or long and recurring series, such oscillations of the 

 surface of the water as we notice on the sea, or are excited when the quies- 

 cent surface of a lake is disturbed by dropping a stone, and which diffuse 

 themselves in concentric circles around the centre of derangement ; these 

 have long been familiar to naturalists, and have been studied, though with 

 comparatively little success, by philosophers. But I have not found the phas- 

 nomenon, which I have called the wave of the first order, or the great solitary 

 wave of translation, described in any observations, nor predicted in any theory 

 of hydrodynamics. 



Unquestionably the means of making such a prediction must have existed 

 in any sound theory. It is, I think, pretty generally admitted that Lagrange 

 was quite successful in stating the general equations of fluid motion ; so that 

 it was only necessary to obtain complete solutions of these equations to ex- 

 hibit the formulae of all motion consistent with the maintenance of continuity 

 of the fluid and obedience to the laws of motion and pressure. After find- 



i 



