TIDAL OBSERVATIONS. 371 



It P X V ■ /I or 2MS 



(r) (7-2.7) (y-2,) (y-^ff+^w-^) (y-|(r-itir4-'j) (7-^2(7+.;) 



Rj O'zoyo 0-3008 o'oyjo 



"1 ioo°75 99°'34 262°-58 ...... 



E., o'4279 0-1785 o'3526 0-2639 



H i°°-SS i69°-97 3i8°'0S 83°-79 



26. In the determination of the long-period tides the mean height of 

 the tide for each solar day, i. e. the mean of the twenty-four hourly heights 

 as originally taken from the diagram-sheets, must be taken. This will give 

 365 means in an ordinary year ; in IcajT year the last mean must be disre- 

 garded, the subsequent equations being adapted for only 365 means. It 

 will be necessary to clear the means thus obtained of all undue lunar in- 

 fluence, inasmuch as the periods of the lunar tides are not commensurable 

 with the solar twenty-four hours. In practice the tide-components evaluated 

 from the series named, for brevity, M, N, and are generally found to be 

 the only ones which have any sensible effect. The necessary correction to 

 be applied to these means, on account of the semidiurnal tides of M and N, is 



R„ sin \2n .^ , . 



^. X ■ ^ X cos (2ni-e,), 

 24 sm hn 



and for the diurnal tide of 



E, sin 12)1 , , , 



-^X^-^ X cos(ni!-e,), 

 24 sm gH - 



where nt is the hour-angle of the ideal star at the time corresponding to the 

 mean of the times for which the heights have been given. If the observa- 

 tions of the tide-heights have been commenced at noon, then the mean of the 

 times for the first day will correspond to 11| hours of that day. The values 

 of (nt—e) for each ideal star (M, N, and 0) having been fovind for 11| hours 

 of the first day, then the values for succeeding days will be found from those 

 of the first day by addition of the respective daily A'ariations of nt. The 

 first part of the formula will form a constant for each tide, and the correc- 

 tions are found by multiplying these constants into the cosines of the re- 

 spective values of {nt — e). The mean height, minus the sum of these correc- 

 tions, -will give the purified mean for each day. The next step is to take 

 the mean of the 365 purified daily means, and to subtract the purified daily 

 mean of each day from the mean height thus found. This will give 365 small 

 differences (termed hereafter ch), and it is on these differences that the cal- 

 culation for the long-period tides is based. 



27. The value of Ih for each day is assumed equal to the following 

 formula : — • 



lli= Acos(<T— ro)i -f B sin (cr— sr)* 



+ Ccos2(Ti! -|-Dsin2ff< 



+ C cos 2(a— ;/)<+D' sin 2(ff— 7;)« 



-\- E cos }ji + F sin rit 



-f-Gcos2?;< +Hsin2/jf, 



in which 



A and B express the coefficients of the lunar monthly elliptic tide, 

 C „ D ,, „ lunar fortnightly declinational tide, 



C „ D' „ „ lunisolar synodic fortnightly tide, 



E ,, F „ „ solar annual elliptic tide, 



G „ H „ „ solar semiannual declinational tide. 



2c2 



