334 Prof. G. H. Darwin. [June 19 % 



We have already shown in B the way of computing IT, and 

 n = 1-034* 



In C and D we have shown how to compute j, t, I, andj 1 = + 6'46, 

 i = + 6-52, I = - 0-97. 



By the formula in B, with = 86'97 for 6 semi-lunations, 



w 2h 2i>" + u" +at n 

 - 299-97 = -60-03. 



By the formula in D, with f} H = 87'52 for XIII quarter- lunar periods. 



= 294-ll = -65-89. 

 By the formula in B, viz. : 



U cos = n + ^f " cos w, 

 Z7sin = Xf" sin w. 



With log \ n = 9'2517 for6 semi-lunations, and with the above values 

 of II, f", w : 



= _6-40, ( + ) log U = 0-0464. 



By the formula in D, viz : 



T cos Y' = f ' p n cos 9, 

 T sin YT = p n sin 9, 



with log- p n = 9'4618 for XIII quarter-lunar periods, and with the 

 above values of f ' and 6 : 



YT = - 18 -35, ( + ) log T = 9-9241. 



(r.) Final Evaluation of M 2 . 

 From (j) B, = +38'47, A m = -30' 58, tan m = ^-- 



-"-m 



B,, ( is + and A m is , so that f m lies in second quadrant; whence 

 m = 7r-51-51 = 128-49. 



Then H, . B a cosec % m ; 



* As the Indian tide predicting instrument takes no account of solar parallax, I 

 should in reality hare done better to take n as unity. But of course this considera- 

 tion does not apply to real observations. 



