1892.] facilitating the Reduction of Tidal Observations. 355 



sin 



TT COS 



= 



With the meaning of the term month in the present context, the 

 sun has a mean motion of 30 per month, and each of the first five 

 gl's and Jj'8 is a function with a constant part and with annual and 

 semi-annual inequalities^ 



When T has successively the 12 values 0, 1, . . . ., 11, we have 12 

 equidistant values of the gi's and JJ's. These may be harmonically 

 analysed for annual and semi-annual inequalities. 



Suppose that the several coefficients to be determined by harmonic 

 analysis are defined by the following equations : 



2U (T) = A Q + A l cos 30T + #! sin 30T + A z cos 60T + B z sin 60T ; 



sin 30T+ 



e 2 



Then on comparing (12) with (11) we see that: 



Q = A ; 



>cos60T + Vsin60T 



= B. . . (12). 



C 



COS 



S} = t 



COS 

 



sm 



