48 U. S. COAST AliJ"D GEODETIC SUEVEY. 



Because of this fact it is customary to treat these two terms as a 

 single component known as the Lj tide and having the speed of 

 (J.) 3, since this has the larger theoretical amplitude. 



Omitting for the present the general coefficient applying alike to 

 both terms, we have 



term U)3 = l/4 e cos* i /cos (2r+2/i,-s-p + 26-2y + 7r) (172) 



and term {A) ^g = 3/8 e sin^ /cos (2 7+ 2?^ - s + p - 2u) (173) 



Lete = 2r+2A-s-p + 2e-2j' + 7r (174) 



andP==2>-<? (175) 



Substituting (174) and (175) in (172) and (173) and combining the 

 latter we have 



1/4 e cos* \ I cosd + S/S e sin^ /cos (^ + 2p-2^-7r) 

 = 1/4 e cos* i / [cos 6-Q tan^ ^ / cos (6 + 2P)] 



= 1/4 e cos* i / [cos e-Q tan^ ^ I cos d cos 2P + 6 tan^ ^ / sin ^ sin 2P] 

 = 1/4 e cos* ^ / [(1 - 6 tan^ ^ / cos 2P) cos + 6 tan^ ^ I sin 2P sin 6] 

 = 1/4 e cos* i / [1 - 12 tan^* i / cos 2P + 36 tan* i /] i 



/^ ^ _. 6 tan^ i / sin 2P \ 



X cosi 6 — tan ^-z — ^— — , , j ^^^ ) 



V 1 — 6 tan^ ^ / cos 2P/ 



= 1/4 e^^^^cos {2T+2Ji-s-p + 7t + 2^-2u-B) (176) 



n which -^ = [1 - 12 tan^ h I cos 2P + 36 tan* i /] i (177) 



and 



P_, \ 6tanH/sin2P _^ sin 2P , . 



tc-tan i_6 tanH/cos2P~^^ 1/6 cot^ ^/-cos 2P ^^^^^ 



The values of log Pa and P corresponding to different values of / 

 and P will be found in Tables 7 and 8, respectively. 



Formula (176) represents the composite Lg tide. The V of the 

 argument is 2 T+ 2Ji — s — p + 'jr, with a speed identical with that of 

 (172). The inequality u of the argument is 2^ — 2v — R. 



For the mean value of the variable factors of the coefficient we have 



r^^^cos(2e-2^-P)] 



= [cos* 'i/j^^cos (26-2^;)+^^ sin (2^-2^)}! 



(179) 



From (177) and (178) 



cos R 



Pa 



sin R 

 substituting (180) and (181) to (179). 



= 1-6 tan2i/cos2P (180) 



= 6 tan='i/sin2P (181) 



