Haughton — On the Effects of Lunar and Solar Tides, 8fc. 611 

 Substituting k - , and reducing, we find 



I'^co sin 2^Sif 



or, 



8T= + 



6,023,000 «2 ' 

 Q65-25 T^w eon sin. 2cli 



6,023,000 a"" 



or 



Sr= + 638-57 eo?^ sin 2<^. (Z) 



Comparing this with the rate of retardation caused by the residual 

 tidal current, we find the ratio of the rates of retardation to be, after 

 the same number of years, 



638-57 sin2<^^ 



3,561,000 Co ' 



or 



sin 2<;i 



5577 €o ' 

 1 



or, since 



16,500,000' 



ratio of rates of retardation = 2959 sin 2<5f). 



"With any sensible value of ^, this retardation will greatly exceed 

 that caused by the residual tidal current. 



Substituting for cq its value, equation (Z) becomes 



n sin 2<^ rri-\ 



We have also, if x be the acceleration of tidal phase, 



/ = 2co X tan 2x ; 

 or, 



/=^ tan 2a;; 



or 



tan 2x 

 •'^ 6875-5' 



R. I. A. PEOC, SER. II. VOL. III. — SCIENCK. 3 H 



