63 



tide differs from that of the corresponding equilibrium component by 

 a fixed angle, which is designated as its epoch, and is conventionally 

 represented by the symbol k. If then the equation of the equilibrium 

 component is (equation (73)) : 



y=Ai cos [at+(Vo+u)] 



the equation of the component of the actual tide is: 



y=A cos [af + (Vo+u-k)] (74) 



Comparing this equation with the equation for a component of the 

 actual tide in the form given in equation (29) : 



y=A cos (ai— f), (75) 



it is evident that : 



Vo+u-K=-^, (76) 



whence : 



K^Vo+u+t (77) 



The computation of f from a series of tidal observations was shown 

 in paragraphs 94 and 95, the origin of time being taken at the beginning 

 of the series. To determine the value of k, the value of Vq at the same 

 origin of time must be computed. Since u is regarded as constant 

 during the period of the observations, its value is taken as that at the 

 middle of the period. 



118. Computation of Vo-\~u. — For simplicity, the hourly tidal 

 heights from which the components of the actual tide are computed 

 begin at hour (midnight). The time is usually the standard time 

 at a time meridian, whose longitude, S, differs from the longitude, L, 

 of the tidal station. Taking longitude west of Greenwich as positive, 

 and east as negative, the Greenwich time of the beginning of the 

 observations is then the S/15th hour of the initial date. The expres- 

 sion for Vq-{-u for each component is in the form: 



Vo-\-u=niTo+n2ho-^niSo-\-niPo+n5ipi)o+nfi90° + Ji:^i-{-nsVi (78) 



in which To, ho, So, Po, and (pi)o are the values of the respective angles 

 at hour on the initial date of the observations, and ^i, and Pi are the 

 values of ^ and v at the middle of the period. 



Since T, the hour angle of the mean sun, is zero at noon, mean 

 local time of the tidal station, it is ±180° at midnight (0 hour) mean 

 local time, and (♦S'— i)±180° at midnight, standard time. For 

 dirunal components, ni=l, and niTo=S—L±180°; for semidiurnal 

 components n,=2, and nrTo=2iS-L)±3Q,0° = 2{S-L). 



