182 MR. S. S. HOUGH ON THE APPLICATION OF HARMONIC 



17. Solar Semi-diurnal Tides in an Ocean of Variable Depth. 



To evaluate the tides when the depth is a function of the latitude we must make 

 use of the formulae of 4. The method will be sufficiently illustrated by the 

 computation of the solar semi-diurnal tide for the case where 



8 a 8 = - 2 Jg- + & sin 8 *, 

 or, where 



A = (14,520 + 9680 sin 2 0) feet, 



6 denoting the co-latitude. 



Putting Ig/4:co 2 a 2 = $, and making use of the numerical values found in 15 for 



*'?!> 2/L A> we obtain from (41) 



log = 3-63907 log ft = ft 3-06261 



log f; = 3-12901 log f| = n 3'4369 



log rj'r, = 2-17040 log 17; = n 3'957G7 



loo- rj\ n 375301 log yl = n 3'9962 



while, when - - = -A-, we obtain 

 4o)-~ 



%., = + 0-0207G5 IU = - 0-05787 



Hj = - 0-039717 1- = - 0-0606 



ILii = - 0-052592. 



From these we deduce in succession, on neglecting Hjo, 



log Itf - n 4-651 log Hi = 4-1 632 



log m s - = n 4-26 1 2 log W, = 3'2089 1 



and 



log H = 3-49214. 



But the first two of equations (40) give 



- KQ + ,10; = [^ + 8 JMJ ,5 = [Jt + 8 ^ A;; ] . , 



which, on solution, yield 



- ^ -- 



4V - mi-It! " '4o,V 



j^_ ., ] m| @i 



4 A2 J ^ %| - J 



' 



