392 Mr. J. K. Wilton on 



For a = 1/^/10, I find:— 



A 8 =-U2, 



~A 3 =-060, 



A 4 =«037, 



2 ^ = <S6, 



-A 5 = -026, 

 A 6 =-019, 



-A 7 =*-013, 

 A 8 = -010, 



\/A=7'3, 



- A 9 = -00G, 

 A 10 = -004, 



-A u = -003, 

 A 12 = -002, 



— 1-2 



where A is the amplitude of the wave. Comparison of these 

 figures with those obtained by Michell * for the corresponding- 

 quantities in the case of the highest wave show that the 

 wave for which a = l/\/10 is not far short of the highest. 

 Michell's figures are 



X/A = 7-04, ^V-=l-20. 



From the above values of the coefficients I find the 

 following table of values of ct — x and y on the free surface, 

 whose equation, given by putting ^r = cy in the expression 

 for 7] as a function of f and then equating real and imaginary 

 parts, is found to be that resulting from the elimination of f 



between 



and 



Z7T 



(<rf— ^) = f4-A 1 sinf + A 2 sin2f+ . 



27n; 



A 1 cosf + A 2 cos2f+ . 



?_ 



£(--*). 



2?r 



e. 



0° 







•24 



360° 



45° 



•64 



•20 



315° 



eo° 



1-30 



•09 



270° 



135° 



2-01 



-13 



OOr,o 



150° 



2' 28 



-•26 



210° 



105° 



2-60 



-•42 



195° 



170° 



275 



-•53 



190° 



175° 



2-93 



-•59 



185° 



180° 



3-14 



-•62 



180° 



Phil. Ma"-.. November 1893. 



