376 On the Minimum Velocity of Waves in Sea- water, 



a vessel moving at a speed of not more than two or three knots* 

 through very smooth water, the surface of the water is marked 

 with an exquisitely fine and regular fringe of ripples, in which 

 several scores of ridges and hollows may be distinguished (and 

 probably counted, with a little practice) in a space extending 20 

 or 30 centimetres in advance of the solid. Right astern of either 

 a steamer or sailing vessel moving at any speed above four or 

 five knots, waves may generally be seen following the vessel at 

 exactly its own speed, and appearing of such lengths as to verify 

 as nearly as can be judged the ordinary formula 



_ 2irw* 



9 

 for the length of waves advancing with velocity w, in deep 

 water. In the well-known theory of such waves, gravity is as- 

 sumed as the sole origin of the motive forces. When cohesion 

 was thought of at all (as, for instance, by Mr. Froude in his im- 

 portant nautical experiments on models towed through water, or 

 set to oscillate to test qualities with respect to the rolling of ships 

 at sea), it was justly judged to be not sensibly influential in 

 waves exceeding 5 or 10 centimetres in length. Now it becomes 

 apparent that for waves of any length less than 5 or 10 centi- 

 metres cohesion contributes sensibly to the motive system, and 

 that, when the length is a small fraction of a centimetre, cohesion 

 is much more influential than gravity as " motive " for the vi- 

 brations. 



The following extract from part of a letter to Mr. Froude, 

 forming part of a communication to ' Nature ; (to appear on the 

 26th of this month), describes observations for an experimental 

 determination of the minimum velocity of waves in sea-water : — 



"About three weeks later, being becalmed in the Sound of 

 " Mull, I had an excellent opportunity, with the assistance of 

 " Professor Helmholtz, and my brother from Belfast, of deter- 

 " mining by observation the minimum wave-velocity with some 

 " approach to accuracy. The fishing-line was hung at a distance 

 " of two or three feet from the vessel's side, so as to cut the 

 " water at a point not sensibly disturbed by the motion of the 

 " vessel. The speed was determined by throwing into the sea 

 " pieces of paper previously wetted, and observing their times of 

 " transit across parallel planes, at a distance of 912 centimetres 

 " asunder, fixed relatively to the vessel by marks on the deck 

 " and gunwale. By watching carefully the pattern of ripples 

 " and waves which connected the ripples in front with the waves 

 " in rear, I had seen that it included a set of parallel waves 



* The speed " one knot " is a velocity of one nautical mile per hour, or 

 51*5 centimetres per second. 



