ON THE HARMONIC ANAXTSIS OF TIDAL OBSERVATIONS. 



45' 



to '58385, or 1 to 3, and the tides having nearly the same speed, we may 



assume iCp^/^',. Hence : 



^i=H{'f cos (t + h—i''-^—K')—^cos [t + h—7''—y—K' — {2h—p')]} 

 =R' cos (t + h—r'—h7r—iy + (}>), 



where tan^^ 



sin(2/i— ^') 



Sf'-cos(2h-.') 

 3f'-cos(2/i— .')' 3cos^ ^ 



(6) 



If, therefore, the harmonic analysis for diurnal tides has given the two 

 components Ai, B^ which are to define R', ^' by the equations 



A, =R' cos 4', Bi =R' sin C' ; 



and if we write V=Ao — ''' — h^j where h^ is the sun's mean longitude at 

 the beginning of the observations, and if we put for the value of the 

 sun's mean longitude at the middle of the fortnight or month, we get 



Scosd) , , „ 



H' 



where tan f 



~3f'— cos(2©— I'O' 

 _ sin (2©—.') 



and Hp=iH', *.-=».' . 



• (7) 



3f'-cos (2©-)'') 



In the article in the ' Admiralty Manual ' these rules are applied to 

 a series of observations at Port Blair, Andaman Islands, commencing 

 0'^ April 19, 1880, and extending over a fortnight. The observations are 

 taken from a tide-curve registered by a gauge, and were supplied to me 

 by Major Baird.' 



The result of the reduction is as follows : — 



Kesulxs of Hakmonic Analysis or 15 days' hourly observations at 

 Port Blair, commencing 0^, April 19, 1880. 



Mean of Three Tears' 

 Hourly Observation. 



A„ = 4-74 ft 4740 ft. 



H,,= 2-19 ft 2-022 ft. 



M 



S 



K 



K 



fH„=2-19 

 Un, =280° 

 r H, = 0-71 ft. 

 \ ,.'3 = 314° 

 r H"= 0-19 ft. 

 2 1 k" = 314° 

 / H' = 0-46 ft. 

 1 (/ = 327° 



p f Hp = 0-15 ft. 



^ Up =327° 



^ .■H„=0-14ft. 



^ 1 ,.•„ = 299° 



278° 



0-968 ft. 

 315° 



0-282 ft. 

 311° 



0-397 ft. 

 327° 



0-134 ft. 

 326° 



0-160 ft. 

 302° 



The second column is inserted for the sake of comparison, and gives 

 the results of three years of continuous hourly observation by the tidal 



' Only one place of decimals of a foot was used. In the Indian tidal operations 

 the heights are measured to two places. The second place of decimals was at one 

 time given up, but the computers having got used to the two decimal figures, it was 

 found that there was actually some loss of time in giving up the second place. 



