180 MR. R. S. HOUGH OX THE APPLICATION- OF HARMONIC 



rather greater than 12 hours, when p/<r = the corresponding period will be less 

 than 12 hours 



16. Lunar Semi-diurnal Tides. 



A similar method to that of the last section may be used to evaluate the lunar 

 semi-diurnal tides for which we take X/2w = 0"96350. The arithmetical work is, 

 however, more severe, in consequence of the fact that the quantities a?*, y",, A* must 

 be evaluated from the formula? (29), (30) which do not assume the simple forms 

 obtained in the last section. Substituting in these formulae the value of X/2w 

 quoted above we deduce 



Aj = 0-075603 AJ O = 0-00,1845 



A; = 0-019864 Af, = 0'002750 



A|j 0-009856 A? 4 = 0'002028 



A^ = 0-005834 Ai e = 0-001968 ; 



log x-. = 376026 log xi c = 3'1566 



log .rj = 3~-63756 log x\. 2 = 3'0362 



log xl = 3-45530 log x^ = 4'9299 ; 

 loo- yfi = 3-29488 



log yr, = 2-68108 log 7/f = 3'3867 



log y\ = 2-14687 log y\ = 3'2313 



\og-yl = 3-81592 log ?/j, = 3"'0994. 

 log y- 3-57549 



Our procedure is now exactly similar to that of the last section. Thus, if the 

 height of the equilibrium tide be 



W V (/*), 



we find, when %/4w s 2 = ^ and p/<r = 0'18093, 



{ = 03 [0-1039S Pi + 0-57998 Pj - 0'19273 P^ + 0'03054 Pi 



- 0-002960 P?o + 0-000196 Pf, - O'OOOOIO P? 4 + ] 



Similarly, when hg/^a* = -$, 



=0S[- 1 -0647 P: + 0-24038 Pj- 0'02774 P^ + 0'001867 Pi 



- 0-000082' Pio 4- 0-000003 Pf, -...]; 



when h ft/la)" a~ = -f^, 



C = 05 [9-1 1 81 P^ - 0-71533 P; + 0-03621 P^ 



- 0-001136 PI -f 0-000024 Pjo ...]; 



