66 

 whence 



tan v'^'CPi sin vjiCPi+CPi cos j')=sin v/(cos v+'CP./CPi) (85) 



The amplitude CP2 is, from equation (69), after substituting the 

 numerical value of the general factor of this equation (par. 112): 



0.8091(1/4+3/8 e\) sin 2co sin 2X, 



and the amplitude CPi is, from equation (68) : 



1.7527(1/4+3/8 e^) sin 27 sin 2X 



The substitution of these values in equation (85) gives, after 

 applying the numerical values of e, ei and co 



y^^f^-n-i ^^^ ^ sin 2/ (86) 



cos V sin 27+0.3357 



The equilibrium argument for the K2 component may similarly be 

 shown to be: y+^=2r+2A— 2j^", where 



g,//_Hn-i sin2vsin^7 (87) 



zu -tan cos 2vsin2 7+0.0728 



Since v and 7 are both functions N, the longitude of the moon's 

 node, v' and 2v'^ are also functions of N. The values of v' and 2i/" 

 for each degree of A^^ are included in the tables showing the values of v 

 and ^ (par. 114). 



The equilibrium arguments for the L2 and Mi components are taken 

 from special tables, contained in Manuals for the Harmonic Analysis 

 of Tides. These components are not important, and the derivation 

 and application of these tables is here omitted. 



MEAN VALUES 



123. Equilibrium components. — Each component of the lunar 

 equilibrium tide developed in equation (68) is in the form: 



y=Jcos{V+u) (88) 



in which J is made up of factors formed by astronomical constants ; a 

 factor formed of a trigonometric function of X, the latitude of the 

 tidal station, which is constant at any given station; and a factor 

 formed of a trigonometric function of 7, the inclination of the moon's 

 orbit to the Equator, which slowly changes with the longitude of the 

 moon's node. If this last factor is represented by ^ (7), then 



J=C 0(7) (89) 



