on Waves in water supposed frictionless. 371 



(17) 



/ i -°" 





9=S \ + <r' 



T 



T' — 



~l + <r 



* * ' 



and 



(0- = •00122), you always see an exquisite pattern of ripples in 

 front of any solid cutting the surface of water and moving hori- 

 zontally at any speed, fast or slow. The ripple-length is the 

 smaller root of the equation 



T T ' + kv'= w2 > ( 18) 



where w is the velocity of the solid. The latter may be a sailing- 

 vessel or a row-boat, a pole held vertically and carried hori- 

 zontally, an ivory pencil-case, a penknife- blade either edge or 

 flat side foremost, or (best) a fishing-line kept approximately 

 vertical by a lead weight hanging down below water, while car- 

 ried along at about half a mile per hour by a becalmed vessel. 

 The fishing-line shows both roots admirably ; ripples in front, 

 and waves of same velocity (\ the greater root of same equation) 

 in rear. If so fortunate as to be becalmed again, I shall try 

 to get a drawing of the whole pattern, showing the transition 

 at the sides from ripples to waves. When the speed with which 

 the fishing-line is dragged is diminished towards the critical 



Telo6it * v*7W, 



which is the minimum velocity of a wave, being [see Part V. 



below] for pure water 23 centims. per second (or of a nau- 



tical mile per hour), the ripples in front elongate and become 

 less curved, and the waves in rear become shorter, till at the 

 critical velocity waves and ripples seem nearly equal, and with 

 ridges nearly in straight lines perpendicular to the line of motion. 

 (This is observation.) It seems that the critical velocity may 

 be determined with some accuracy by experiment thus [see 

 Part V. below] :— 



Remark that the shorter the ripple-length the greater is the 

 velocity of propagation, and that the moving force of the ripple- 

 motion is partly gravity, but chiefly cohesion ; and with very 

 short ripple-length it is almost altogether cohesion, i. e. the same 

 force as that which makes a dew drop tremble. The least velo- 

 city of frictionless air that can raise a ripple on rigorously 

 quiescent frictionless water is [(16) above] 



-i . 660 centimetres per second 



^oeing , x m i n i mum wave- velocity) 



= 12*8 nautical miles per hour. 

 2B 2 



