Highest Waves in Water, 435 



Solving, we find as sufficiently close values : 



£=8-25, 

 b 1 = -0397, 



6 2 = -0094, 

 Z> 3 = '002; 



and thus, as a close approximation to the value of— , 



— = (-/sin wf e ¥w (l + -0397^ + -0094* 4 * + -002J**). 



The Depth of the Wave. 

 Since 



18 \/3.?/7r = & = 8-25, 



2^=1-66. 



Now at <f> = — , 



f=(i-b l+ b 2 -b,+ ... y 



= (-9677) 2 . 



The depth of the wave is <? 2 /2^, and therefore the ratio of 

 depth to length is 



h _ (-9677)* 

 L 1-66x3-96 



so that the height of the wave is very nearly one seventh of 

 its length. 



As was to be expected, actual record of high waves does 

 not come within some distance of this : Abercromby, for 

 example, measured waves 46 feet high and 765 long (Phil. 

 Mag. xxv. 1888). 



I At the Summit. 



Near the summit $ = we have 

 ^=^cos|-2sin|j(l + & i f5 2 + ...), 

 and therefore 

 and 

 * = §£l(cos~ +e'sin^J /(l+fc 1 + fc | + .. .), 

 2 G2 



