TIDAL OBSERVATIONS. 129 



This year's results were incorporated with the previous three years and 

 new tables, using average values, formed, and the heights recomputed and 

 again compared with a similar although somewhat improved result to what 

 had before been obtained. 



61. It appearing probable that a closer approximation to the movement of 

 the moon than what is given by a moan motion, including the motion of her 

 perigee, would give a closer agreement between the actual and the calculated 

 heights, it was thought advisable to extend the schedule of arguments (§ 2). 

 Accordingly the terms depending on the two next largest perturbations of the 

 moon (the evectlon and variation corrections) have been included. The argu- 

 ments of the components for the evection semidiurnal tide are2(y — g<r-t- 4nr— jj) 

 and 2(y — fi— |ra- + ;j), and for the variation semidiurnal tides 2(y— ry) and 

 2(y—2ir + r]). One of the components of the variation tide, having the 

 same period as the solar semidiurnal, is necessarily included in the results of 

 the analysis which we have performed for the latter. Our new terms are 

 therefore reduced to three. Series of hour-angles of these arguments (named 

 for brevity \, y, and n) have been formed and added to our Table. The 

 period chosen for the \ and f series was 349"* 22'', and for the /j. series 

 369'^ S"", each period eliminating in the summation of each the effect of the 

 lunar semidiurnal tide. The results of the four years' analyses of these tides 

 are : — 



62. Tables of these components have been formed, and the heights due to 

 eash added to the height of the sum of the original nine tide-factors, A^— SR 

 having been corrected, and the differences again taken. These differences 

 showed clearly four distinct maxima and minima for each day ; and it ap- 

 peared highly probable that the (Helmholtz) compound luni-solar tide of 

 period 2(2y— o- — rj) mentioned in § 24 was of considerable value for Liver- 

 pool. The differences having been grouped according to hours of this length 

 (hereafter termed M S), its existence was placed beyond doubt. The four 

 years' observations have been analyzed for its estimation with the following 

 results : — 



MS. 



1857-58. 1858-59. 1859-60. 1866-67. 



Ej 0-4379 0-3488 0-3879 o"4fi35 



6^ 270°-68 265°-86 270^-49 269°-45 



There was a sensible value for A^, B, in each of the above series. The 

 comparative largeness of A^, B^ of Series L for Ramsgate, § 23, and for Liver- 

 pool, § 37, is probably due to this luni-solar quarter-diurnal tide, the period 



1870. K 



