46 REPORT — 1886. 



department of the Survey of India. An error of 2° in the value of (Cn, 

 corresponds to an error of only 4™ in the time of high and low water. 

 The concordance between the two affords evidence of the utility of even 

 so short a series of observations as during a fortnight. 



§ 4. Computation of a Tide-table. Semidiurnal Tides. 



The computation of a tide-table from tidal constants which do not 

 contain the elliptic tides N and L presents some difficulty, because the 

 total neglect of these tides would make the results very considerably in 

 eiTor. On this account it was found necessary to use the moon's hour- 

 angle, declination, and parallax in making the computations. 



We shall begin by considering only the semidiurnal tide. 



In the Tidal Report of 1885 it was shown how the expression for this 

 tide in the harmonic notation may be transformed so as to involve hour- 

 angles, declinations and parallaxes, instead of mean longitudes and eccen- 

 tricities of orbits. 



The formula (27) of the Report of 1885 for the total semidiurnal 

 tide, when written in the notation of § 2 is 



cos^ A 



^2=^^^2-^^m cos (2^/ — /C„)-f-H, cos (2vi/, — /.-,) 



cos^o' — cos^ A 



+ r-2-r 683H" cos (2xL-k") 



sm''A/ ^ ^ ' 



coB^a-cos^A, ^^^^,^^ 



sm"' A^ V T/ / 



sinScosacZa/ •683H" ^ , ^. ^ 



^ — jT r"77 r — Hm tan- A, Ism (2\L — »,■ ") 



<7Sin-A, at \cos (^■" — /.-,„) '" 'J ^ ^ '"'' 



cos^A H„co3i.-„— HiCos)>-i 



-i ^-r-(F' —I)- cos (2li— £) 



cos'' A/ ■' ecose ^ ^ ■' 



-f(P,-l)5^.-cos(24.,-.,) 



col^dFldf^r ^g^^_ E„ sec (.-.-.-J + H, sec ('-i-'--.) V-^ .2^_^. . .g 

 cos^A; <7—'st\ e J "' ^ 



We shall now proceed to simplify this. 



In the first place, the terms depending on dl\dt and dY\dt are 

 certainly small, and may be neglected. 

 Then let 



cos^ A cos^ c' — cos^ A 



'cos2 A, ""■•' sin2 A, 



cos^ A H„coBx„— Hicoan i 



c^s^^^-cos^ ,in (.-_.J 



" ™ sm^ A^ ^ ' 



cos2 A H„ cos >■„— Hi cos k^ . 



cos^ A/ ^ ^ e cos£ ^ ™''' 



M,=H,-f- g.^2-^^^ 317H +(P_1)— ^, 



\^,=<. (9) 



M=^^y^ H.-H - X.r -essH" cos a-"-o 



