1892.] facilitating the Reduction of Tidal Observations. 351 



"We will now find the p th harmonic constituents A^, Bp. By the 

 ordinary rules 



Ap I _ 



Now 



2 15|rf cos 



Sill 



COS 



sin 



2-p)-/) -r- 12/3 (-i)] ; 



and T V of the sum of the 24 values corresponding to t = 0, 1, . . . . , 23 is 



+ the same with sign of p changed 



This expression admits of simplification, because 12x15 = 180 ; 

 making this simplification, and introducing the result into (3), we 

 obtain 



1 . /7sl*+(l2-i)/3 + V 



~ 24n 



am L- 



.... (4). 



In the particular case where jp = q, we have 



sin (15 q - 



I 1 



(5). 



