65 



At any given origin of Greenwich time, the initial phase of the equihb- 

 rium component at Greenwich is, since S and L are both zero : 



Vo+u=n^(±180°)-\-n2ho^n,So+n,p,-^n,{p,)o+n,90°+u (79) 



while the initial phase of the actual tide at a station whose latitude 

 is i is : 



Vo+u-K=?h{-L±180°)+n2ho+nsSo+niPo+ns(p,)o,i-nSO°+u (80) 



The difference is : 



G=n,L-^K. (81) 



It may be observed that n-i is the same as the subscript of the com- 

 ponent. The formula for Greenwich epoch is usually written : 



G=pL-^K. (82) 



In which G is the Greenwich epoch, p the subscript of the component, 

 L the west longitude of the station and k the local epoch. 



The difference between the Greenwich epochs of a component of 

 the tide at any two stations is the constant difference between the 

 phases of the component at the two stations. 



121. Equilibrium arguments of overtides and compound tides. — The 

 equilibrium argument of an overtide is taken as the indicated mul- 

 tiple of that of the primary tide. The equilibrium arguments of com- 

 pound tides are the sums or differences of those of the components com- 

 pounded, 



122. Expression jor u of the Ki, K2, L2, and Mi components. — A 

 reference to equations (68) and (69) shows that the Ki component is 

 the resultant of a lunar component whose 

 equilibrium argument is T-\-h — v — 90° and a 

 solar component whose argument is 2"+^— 90°. 



The relation of the resultant to the components A 

 is graphically shown in figure 29, in which CPi 

 is the amplitude of the lunar component, CP2 

 the amplitude of the solar component, and CP3 

 the amplitude of the resultant. The angle 

 YCPi is T+h-90°-v, the angle YCP2 is 

 T+^- 90°, and the angle Pi CPs is v. Placing figure 29. 



the angle PzCP2=v' the equilibrium argument 

 of the resultant is T+/i— 90°— v'. If ^ is the foot of the perpendicular 

 drawn from P3 to CP2 produced, then 



sin /=AP3/CPs=P2P3smplCPs=CP,smvlCPs (83) 



cos /= {CP2+P^)/CPz= {CP2+CP1 cos v)ICPz. (84) 



