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



We then proceed to count these 1's and f's just as was done 

 with the number of entries in the sorting of ^V OT , and to operate on 

 them in the same way. 



The results are 



S cos (V-V,) =--0078, S sin (-,) =--0060, 



S* cos (fcV- V.) = + -0280, S*- sin (%V m - V,) = + "0078, 



S cos (|V m +V.) =+-1244, S sin(iV+V,) =+'0094, 



S*- cos (V + V,) = + '0147, SI- sin (V tt + V,) = + '0834. 



(p). Evaluation of F w ( >, G w <>, <>, g m ( ">, FJW, G w <*->, !<*->, g->, 



F,>, G,<>, ,<>, g, (o) , F/H G,->, ,->, g,<*->. 



These 16 coefficients are required to correct the four sums 



S"h jjVm, Si^/i . ^V m , for the influence of the tides M 2 and S 2 . 

 sin sin 



I call Sh cos jjV m + corrn., W, Sh sin ^V,+ corrn., X, and the 

 other two Y and Z. 



The correction to be applied to S^ cos ^V m to get W is 



and the correction to be applied to S7i sin ^V m to get X is 



and the two other corrections are given by symmetrical formulae 

 with (^TT) in place of (o). 



These coefficients are computed from S and Si* of 



' 





and of (^V m + Vs),as given in (m) (n) (o). It must be especially 



noticed that we have above in (m) computed S and S of sin^V OT ; 

 but iV m V w = ^V m , so that the signs of our previous results must 

 be changed in these two cases. 



If we remark that k m and k s are constants found by theoretical con- 

 siderations, that A m , B m , A s , B,, are already found, and that in the 

 first column we are compelled to omit the affixes to the letters S, k, 

 and the F's and G's, because they indicate various sorts of S's and 's 

 and F's and G's in the different columns, the computations in the 

 following table are easily followed : 



