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



TT" 



Again, if we put 7 = ^-, we have 



-0.* 



R" = f'H" = f'^H,. 



Also since the argument of the K 2 tide is 2i + i 2h2v" K ", where 

 2v" is a certain function of the longitude of the moon's node (tabu- 

 lated by Baird), and since t = 0, h = h at epoch, it follows that 



Now, when the means of the equations (17) are taken forw + 1 



successive tides, the latter terms become R" . ' (^ng ""), where 



cy sin 



\ . . Sin ^( re + U9 r n&\ 



"n 7 f~ v /' 



Also, if we write 



n = J 



A s = 7^2/1 COS TP 



J 



our equations become 



AS = nH^cos *Tj+f"XHj cos (w K '), 



B s = IlHs sin K S i."\nS. s sin (u> *c"). 



It may be observed that n is the mean value of P during the interval 

 embraced by the + l tides. 



In reducing a short series of observations we have to assume what 

 is usually nearly true, viz., that K" = K S and 7 = 0'272, as would be 

 the case in the equilibrium theory of tides. 



With this hypothesis, put 



U cos = n -f Xf " cos w, 

 U sin = Xf " sin w, 



from which to find U and 0, Then 



AS = H,Z7COS (K S 0), 



B s = H,Z7sin (K S 0), 

 from which to find H$ and K S . 

 Lastly, K" = * s , H" = 7 H, = O272 H,. 



