HARMONIC ANALYSIS AND PREDICTION OF TIDES. 5T 



The lunar K^ term {A)^^ o^ (100) i^iay then be written 



C^A, cos iT+Ji-v-T/2) . (226) 



and the solar K^ term (5)42 of (215) 



C,B, cos (T+h- t/2) (227) 



Taking the smn of (226) and (227) we have 



Lunisolar K^^ C^iA^ cos {T+h-v- 7r/2) + 5, cos {T+'h- 7r/2)] 



= C^ [A^ cos V cos (r+^-7r/2) +^1 sin v sin (T +71- -Tr/2) 

 + B, cos iT-\-h-T/2)] 



= C^ [{A^ cos v + B,) cos {T+'h-T/2) 

 + Ai sin V sin {T+h-Tl2)] 



= 0^ {A^^ + B i^ + 2 A,B, cos v)i cos iT+Ji-irl2-v') 



= C sin 2X [A^ sin2 21 +B^ sin^ 2w 



+2AB sin 2/ sin 2co cos I'j^ cos iT+h-Trl2- v') 



in which 



, , , ^1 sin v 



I' = tan-^ -i — ^^ -p- 



^1 cos v + i>i 



sin V 

 = tan-^ — 



(228> 



2 + 3e2 6^sin2w 



cos v + - 



2 + Se^ sin 2/ 



, , sin 1/ sin 2/ /ooov 



= tan-i : — 07 I n ooc-T (229; 



cos V sm 2/+ 0.3357 



the values for the constants in (229) being obtained from Table 2. 

 Similarly, for the semidurnal component from ^17 of (100) and 5„. 

 of (215), using the abbreviations of (216) to (225), we have 



Lunisolar K. = C^ {A^^ + B.^ + 2A.B. cos 2v) i cos (2 T+ 2h - 2v' ') 



in which 



C cos^ X \A} sin* 7+^2 sin* co (230> 



^2AB sin2 / sin^ w cos 2?/]* cos (2 7+2/^-2/0 



_ „ , , J., sin 2i' 

 2j''' = tan-^ -i — ^ 



= tan" 



A^ cos 21^ + 52 



sin 2 J- 



^ , 2+3e.2 6^sin2a) 

 cos 2i' H 



2 + 3e, sin^ 7 



sin 2v sin^ 7 

 2^^ sin2 7+0.( 



Values of v' and 2v" for each degree of N are given in Table 6. 



^^"^ cos 2. sin^' 7+0.0728 ^^^^^ 



