374 Sir W. Thomson on Waves under motive power 



" The second condition of wave motion is to be observed when 

 " the velocity of the wind acting on the smooth water has in- 

 " creased to two miles an hour. Small waves then begin to rise 

 " uniformly over the whole surface of the water; these are waves 

 " of the second order, and cover the water with considerable re- 

 " gularity. Capillary waves disappear from the ridges of these 

 " waves, but are to be found sheltered in the hollows between 

 " them, and on the anterior slopes of these waves. The regu- 

 " larity of the distribution of these secondary waves over the 

 " surface is remarkable ; they begin with about an inch of am- 

 " plitude, and a couple of inches long ; they enlarge as the ve- 

 " locity or duration of the wave increases ; by and by contermi- 

 " nal waves unite ; the ridges increase, and if the wind increase 

 " the waves become cusped, and are regular waves of the second 

 " order. They continue enlarging their dimensions ; and the 

 " depth to which they produce the agitation increasing simulta- 

 " neously with their magnitude, the surface becomes extensively 

 " covered with waves of nearly uniform magnitude." 



The " Capillary waves " or " waves of the third order " re- 

 ferred to by Russell are what I, in ignorance of his observations 

 on this branch of his subject, had called "ripples." The velocity 

 of 8^ inches (21^- centimetres) per second is precisely the velo- 

 city he had chosen (as indicated by his observations) for the 

 velocity of propagation of the straight-ridged waves streaming 

 obliquely from the two sides of the path of a small body moving 

 at speeds of from 12 to 36 inches per second; and it agrees re- 

 markably with my theoretical and experimental determination of 

 the absolute minimum wave-velocity (23 centimetres per second; 

 see Part V.). Russell has not explicitly pointed out that his 

 critical velocity of 8^ inches per second was an absolute mini- 

 mum velocity of propagation. But the idea of a minimum velo- 

 city of waves can scarcely have been far from his mind when he 

 fixed upon 8j inches per second as the minimum of wind that 

 can sustain ripples. In an article to appear in c Nature ' on the 

 26th of this month, I have given extracts from Russell's Report 

 (including part of a quotation which he gives from Poncelet and 

 Lesbros in the memoirs of the French Institute) for 1829, show- 

 ing how far my observations on ripples had been anticipated. 

 I need say no more here than that these anticipations do not 

 include any indication of the dynamical theory which I have 

 given, and that the subject was new to me when Parts III., 

 IV., and V. of the present communication were written. 



Part V. Waves under motive power of Gravity and Cohesion 



jointly, without wind. 

 Leaving the question of wind, consider (13), and introduce 



