370 Sir W. Thomson on the Influence of Wind 



(1) When Tr . 71-fo- 



the values of « are positive and negative ; that is to say, waves 

 can travel with or against the wind. The positive value is 

 always greater; that is to say, waves travel faster with than 

 against the wind. The velocity of waves travelling against the 

 wind is always less than w, the velocity without wind. 



(2) When 



V<2w, 



the velocity of waves travelling with the wind is greater than w. 

 When 



V=2w, 



the velocity of the waves with the wind is undisturbed by the 

 wind ; a result obvious without analysis. When 



V>2w, 



the velocity of waves travelling with the wind is less than the 

 velocity of the same waves without wind. 



(3) When 



y>w \/^r' 



waves of such length that w would be their velocity without wind, 

 cannot travel against the wind. 



(4) When 



\>w— r -> 

 V<r 



there cannot be waves of so small length as that for which the 



undisturbed velocity is w, and the equilibrium of the water is 



essentially unstable. And (13) shows that the minimum value 



of w is 



WmEA. ..... (i6) 



l + o- 



Hence the water with a plane level surface is unstable if the ve- 

 locity of the wind exceeds 



Wr(i-o- 2 ) 



^ 



^ 



W. T. 



Part IV. {Letter to Professor Tait, of date August 23, 1871.) 

 Defining a ripple as any wave on water whose length 



/T' 



< 2tt a/ — *, where 



* Which for pure water = 17 centira. (see Part V.). 



