RECORD AND REDUCTION OF THE TIDES. 



73 



observations, while they give reliable value for the half-monthly inequality, cannot 

 be expected to give more than an approximation to its variations. For any one 

 station, and any one inequality or correction to it, special examinations require to 

 be made to ascertain that transit of the moon, best suited for the purpose; this has 

 hardly been done for any standard station, and it suffices to state here that, by 

 referring to an anterior transit, the whole half-monthly inequality is moved back- 

 ward through nearly twenty-four minutes for every transit preceding. Upon the 

 inequality itself, the effect is but of a differential character. Thus to refer our 

 table to transit E, deduct 24'" from eacli value. 



To concentrate as many values as possible to a mean, the changes of declination 

 and parallax were grouped for three values. The separate parcels for declination 

 are for declination to 13°, 13° to 21°, and 21° to 27°.5, irrespective of sign. The 

 parallax groups are: 54' to 56', 56' to 58', and 58' to 6r.4. 



The differences of interval for the high and low waters were made out separatelv, 

 and, in general, agreed tolerably well. I obtained tlie following results : — 



TABLE SHOWING THE CORRECTION (IN MINUTES) TO THE MEAN HOURLY INTERVAL, FOR A CHANGE IN THE 



moon's DECLINATION AND PARALLAX. 



Mean declination 10°. n. 



Mean parallax 57'.0. 



The above table of declination corrections exhibits systematic values for the 

 periodical part of the lunar effect, or for the term D sin. 2 (<^ — y). Between 0° 

 and 13° of declination, the correction is positive for transits between l*" and 1^, for 

 other hours negative; for declinations between 13° and 21° it is positive, between 

 the hours of 4 and 10 ; for remaining hours it is negative, and for declinations 21° 

 to 27°. 5, the correction is positive, for hours 7 to 1, and negative for remainino- 

 hours of transit. The quantity D is accordingly about 14 minutes, and y equals 

 15°, 60°, and 105° respectively. 



The variation in the inequality due to the changes of the moon's declination 

 appears large when comparetl with its value at other places, but is in conformity 

 with the large value of the half-monthly inequality itself. 



The periodical part of the parallax correction is of the same form as given above. 

 10 



