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MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS, 



the table published annually in the Connaissance des Temps. As all the tables are 

 supposed to contain the same series of refractions, the numbers corresponding to the 

 same altitude should have constantly the same proportion : so that taking the number 

 a which answers to the zenith-distance & in Bessel's table, the logarithm of the re- 

 \fraction at the same zenith distance in the New Table should be equal to 



log a + log tan d + -00507, 



the number -00507 being the difference of the logarithms of the refractions at the alti- 

 tude of 45° in the two tables : but, in the supplemental table, which contains the 

 logarithms of the refractions, it is sufficient to add "00507 to obtain the logarithms in 

 the New Table. With regard to the refractions in the Conn, des Temps, it is more 

 convenient to use the Table in the T'ahles Astronomiques published by the French 

 Board of Longitude: for the logarithms in this table with the addition of '0011, 

 should agree respectively with the logarithms of the New Table. According to these 

 directions the following comparative view has been drawn up. 



From this view it appears that the three Tables agree within less than 1" as far as 80* 

 from the zenith ; the New Table is in accordance with Bessel's, with slight discre- 

 pancies, to 88° or 88^° from the zenith ; from 80° to 88° of zenith distance the num- 

 bers in the French Table exceed those in Bessel's, the excess being 2" at 84°, and 4" 

 at 88°. But when the distance from the zenith is greater than 80°, the accuracy of 



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