64 



As has been stated, the values of h, s, p, pi, and A^, at hour Green- 

 wich mean civil time on January 1 of each calendar year are given in 

 tables contained in manuals for the harmonic analysis of tides, to- 

 gether with the differences to be added successively to give these values 

 on the first day of each month, on each day of the month, and at 

 each hour of the day, Greenwich time. The values of ho, Sq, po, and 

 (Pi)q are the values of h, s, p, and pi, at Greenwich time of hour on 

 the initial date of the observations. The value of N, the longitude of 

 the moon's node, is similarly taken off for the middle of the period of 

 observations, and from it the values of ^, and v, taken from the table 

 showing the value of these angles for each degree of A^. Entering these 

 values in equation (78), the value of Vq-^-u is immediately determined. 

 This value, added (algebraically) to the value of f found from the 

 observations, gives the value of k. The value of k so derived is, it 

 may be observed, independent of the meridian on which the times of 

 the observations are based. 



If the observations are made on local time, instead of standard 

 time, S=L, and the angle S—L becomes zero. 



119. Example. — The computation in paragraph 95 shows that for 

 the Ms component of Sitka, Alaska, long. 135°20' W.,for the 29-day 

 period beginning at hour, mean local time, July 1, 1893, f =61° .6. 

 The Greenwich time of the beginning of the period is then 9.02h, 

 July 1. The equilibrium argument for the M2 component is from 

 equation (68): 



V+u=2T+2h-2s+2^-2v. 



Since the observations are on mean local time, 2T=0. The values 

 of h and s, at 9.02^, July 1, 1893, Greenwich time, found from the 

 tables, are: 



ho=99°M So=308°.03 



and the value of A^ for 9.02^ July 15, 1893, is 24°. 17. The corre- 

 sponding tabular values of vi and ^1 are: 



vi=4°.45 ^i=4°.01. 



Then 



yo+w=0 + 199°.28-256°.06 + 8°.02-8°.90=-57°.66 = 302°.34 

 K = 61°.6 + 302°.3-360° = 3°.9. 



The value of k derived from observations for a year is 3°. (Table 

 V, par. 134.) 



120. Greenwich epochs. — The Greenwich epoch of a component at a 

 station is the difference between the phases of the equilibrium com- 

 ponent at Greenwich and of the actual component at the station. 



