LAWS OF THE TIDES FROM SHORT SERIES OF OBSERVATIONS. 243 



the occasional deviations in short series arising from the irregularity of the pheno- 

 mena, and from the imperfection of the other corrections. 



X. Does the declination correction of times vary as the square of the declination 9 

 The Bristol observations give 



1835. Total time correction from decl. 7°'3 to 18°-6 ; 81 parts 



from — 18°-6 to24°-4; 75 — 



The ratio of the squares is 81 to 69 ; the simple ratio is 81 to 41. 



1836. Total time correction from decl. 8° to 19°7 ; 7^ parts 



from — 19°-7 to 25 ; 46 — 

 The ratio of the squares is 76 to 56 ; the simple ratio is 7^ to 34. In both these 

 cases the actual result is in a ratio considerably higher than the simple ratio ; and the 

 mean approaches near to the ratio of the square. 



The Plymouth tides of 1835, 1836, 1837, were discussed in a different manner, the 

 declination corrections for each hour being kept separate. The effects due to decli- 

 nation being thrown into curves according to the degrees of declination, the form 

 of these curves from 2^^ to 6^ transit appeared to show very clearly, that at those 

 hours the correction is as the square of the declination ; while for the other hours of 

 transit the correction is small and irregular. It has already been shown that the 

 declination correction of times is of the form (sin^ ^ — sin^ A) (c + c? . *, 2 (p — 2 13), 

 and the form of the irregularity appears to indicate that |3 is smaller for the high 

 than for the low declinations. It may perhaps be possible hereafter to put this 

 correction in a form which shall escape this irregularity. 



XI. Can the laws of the corrections he deduced from a single year P 



Whether the observations of a single year, or of a few years, suffice for determi- 

 ning the tide corrections, is a question which the discussions just described enable us 

 to answer. For if the curves representing the laws of these corrections be regular for 

 each year and similar in successive years, we cannot doubt that the law is given with 

 some approximation by each, although the mean may be still more accurate. On 

 examining our curves with this view we find that most of the corrections are given 

 with tolerable precision, even by a single year's observations. The semimenstrual 

 inequality may be determined from that period, and gives a very regular curve if the 

 observations are good. It may be still improved by reducing each hour to the 

 parallax and declination which is the mean of the whole, as I shall further explain. 

 The parallax correction from a single year is less regular, as might be expected, the 

 observations for each hour of transit being further distributed to each minute of 

 parallax, so that each resulting number is the mean of a few observations only. Still 

 the general form of the parallax correction curve for one year exhibits the features 

 which belong to the mean ; namely, a maximum and minimum about 4^ and 8'' both 

 for time and height. And when the process is conducted with care, and the curves 

 which represent the corrections adjusted nearer and nearer to the observations, in 



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