68 



RECORD AND REDUCTION OF THE TIDES. 



The mean establishment resulting from the observed times of 480 high waters 

 at Van Rensselaer Harbor is therefore 11'' 43.3"", referred to the moon's transit 

 immediately preceding and corresponding to a mean horizontal parallax of the 

 moon and sun, and to the moon's and sun's declination of 16° nearlj'. The mean 

 interval corresponds to the moon's transit of ()'' 21" nearly, indicating that the 

 epoch would have come out 0'' 0™ if transit E (see An Elementary Treatise on the 

 Tides, by J. W. Lubback, Esq., London, 1839) or that immediately preceding 

 transit F had been used. 



In like manner we obtain the following table from the observed times of 485 

 loiv icaters at Van Kensselaer Harbor : — 



The mean establishment r(^sultiiig from the observed times of 485 low waters is 

 17'' 48.0"', referred to the moon's transit immediately preceding low water, and the 

 same to which the preceding high water has been referred ; the difference between 

 the two mean intervals is 6'' 04.7"". 



To obtain a numerical expression for the half-monthly inequality in time, the 

 value for a should be determined so as to furnish, in jjurticular, good results for 



