1892.] facilitating the Reduction of Tidal Observations. 353 



oscillation of sea level upon which the proposed analysis is performed 

 all those tides may be omitted from which ft is not very small, and 

 also all those whose frequencies are such that the period under con- 

 sideration 12nfi is nearly 180. 



Since the period under consideration will be a lunation, it follows 

 that, as far as is now material, the general expression for sea level 

 may be written as follows, t denoting mean solar hour angle equal to 



m. w., annual .......... A +H sa cos (hK Sa ) 



semi-annual ...... +S ssa cos (2h /c wa ) 



Solar tides, S lf S 2 ........ + H cos (t K^ + IT, cos (2 1 K S ) 



S 3 , S 4 ........ +JT M cos(4t-/c 25 )+.H w cos(6t K S 



Solar elliptic, T ........ + flicos (2t fc+p, ,) 



R ........ + H f C 



Luni-solar, K 2 .......... +i"H" cos 



Solar diurnal, P . . , ..... . +H P cos (t h + J TT Kp ) ......... (9). 



This includes all the tides whose initials are written at the head of 

 this section. 



It is now necessary to break up the year into 12 equidistant luna- 

 tions of 30 days. This can be done by the omission of 5 days in 

 ordinary years, and of 6 days in leap years. 



If the days of the year are numbered to 364 (365 in leap year), 

 the twelve months are as follows : 



0, 1 to 29 d ; 1, 30* to 59 d ; omit 60 d ; 2, 61 d to90 d ; 3, 91 d to 120 d ; 

 omit 121 d ; 4, 122 d to 151 a ; 5, 152 d to 181 d ; omit 182 d ; 6, 183 d to 

 212 d ; 7, 213 d to 242; 8, 243 d to 272 d ; omit 273 d ; 9, 274 d to 303 d ; 

 10, 304 d to 333 d ; omit 334 d ; 11, 335* to 364 d ; in leap year omit 

 365 d . 



The increments of sun's mean longitude from O d O h of month up 

 to O h of the day numbered of each group of days or month are as 

 follows : 



0, 0; 1, 30-0'431; 2, 60'124 ; 3, 90 -0-306; 4, 120'249; 

 5, 150-0-182; 6, 180'373; 7, 210-0'057; 8, 240-0 '488; 

 9, 270-068; 10, 300-0'364; 11, 330'191. 



Thus if fro be the sun's mean longitude at O d O h of month 0, the 

 sun's mean longitude at Qfi O h of month T is Ji + 30T, with sufficient 

 approximation. 



