436 Mr. J. H. Michell on the 



so that, since q 2 = 2gy, we have 



= 1-245, 

 and l + &i + & 2 + ... =1-0758, 



while h + bz + bs = -0511. 



Near the summit, the series for q 2 , every term having the 

 same sign, will not be well represented by the first three 

 terms. This is of little consequence since the sum of the 

 terms is known at the summit. Elsewhere the first three 

 terms give a good approximation, as appears below. 



Form of the Wave. 

 The coordinates of any point on the surface are got from 

 the two equations : — 



g = sin-^[cos(^-0-O4cos(20-lc/,+ ^) 



-•OO8cos^-J0+|)--OOlcos(60-J0 + ^l, 

 in-H[sing-^)-04sin(2^-^+|) 



The first terms do not integrate in convenient form and are 

 best calculated by means of the expansions 



sin-*(/> cosi(/> = 4>-i(l + -0008(£ 4 + . . .) 



sin"* <p sin 10 = 101(1 + -037 <£ 2 + '0023 4 4- . . .), 



The other terms integrate simply. 



The following table gives the values of x, y, and q 2 for the 

 specified values of </> : — 



dy 

 d$ 



:sm 



re 



0. 



X. 



y- 



Q 2 - 



fly- 



7T 



50 



•196 



•110 



174 



1-58 



7T 



20 



•366 



•197 



•318 



1-61 



To 



•591 



•298 



•489 



164 



7T 



•974 



•428 



•707 



1-65 



'Stt 

 10 



1-321 



•507 



•837 



1-65 



2tt 

 5 



1-654 



•552 



•912 



1-65 



7T 



~2 



1-979 



•567 



•936 



1-65 



