306 Prof. G. H. Darwin. [June 19, 



To find V,. 



No table is necessary for the conversion of time into angle at 30 

 per hour to find V,, or 2(7 1/), since we multiply the hours by 30, 

 and add half the number of minutes. This rule is the same for every 

 day. 



B. The tides S 9 and K 9 . 



& & 



It is required to compute U and from 

 ZJcos = n + X,,f" cos w, 



?7sin = \ n i" sin w, 

 where ta = 2h 2v" 



/sun's parx. mean parxA 



and n = l + 3(- -), 



\ mean parx. / 



the sun's parallax referred to being its value at the middle of the 

 period under reduction. 



If, for example, February 14 is the middle of the period, II is 

 found thus : 



Sun's parx. Feb. 14 = 8"'95, mean parx. = 8"'85, diff. = + 0"'10. 

 Then n = 1 + ~ = 1-034. 



O'OD 



The period under reduction consists in this case of an exact number 

 of semi-lunations. The following table gives X and , according to 

 the number of semi-lunations : 



No. of semi- 

 lunations. 1. 2. 3. 4. 5. 6. 



log X* 9-4300 9-4159 9-3920 9'3575 9-3113 9-2517 

 * 14-28 28-82 43-36 57-90 72-43 86-97 



h is the sun's mean longitude at epoch, found from Kaut. Al. ; and 

 2v", f" are found from Baird's Manual in. the tables applicable to the 

 tide K 2 . 



C. The Tides N and L. 



Summations are carried out over quarter-lunar-anomalistic periods, 

 numbered i, ii, iii, &c. Grand totals are then made in two different 

 ways, viz. : 



+ [2(v+vij 2(vii+viii)] + &c., to find S, 

 and [2(ii + iii) 2(iv + v)]-f [2(vi + vii) 2(iv + v) 



+ [2(vi + vii) 2(viii + ix)] + &c., to find S**, 



