96 Mr. Ivory on the Theory of the Astronomical Refractions. 



the terms must next be expressed in seconds of a degree, 



which being done, the following final results will be obtained. 



r // log. ( /, log. 



T = sin ^ X ■[ e3 . 0-369, - 1 -5668, ^ = sin ^ x | e^ • 0-530, - 1-7340 



+^5 , 0-685, — 1-8356 -\-e^ . 1-113, 0-0465 



+e7 .0-712, —1-8526 +e7 . 1-350, 0-1306 



+<?9 .0-530, —1-7263 +e9. 1-207, 0-0817 



+e". 0-317, -1-5006 +e". 0-873, 1-9412 



+ei3 . 0-159, — 1-2013 +ei3 ^ 0.539^ _ 1.7313 



The values of T and h are added in separate columns of 

 the annexed table for altitudes less than 10°: for greater alti- 

 tudes they are omitted as of no account. The application for 

 finding the corrected refraction from the formula 



««+''-8« =TT7(!^) To -T(--^o)-*(30-i'). 



will best be explained by the examples afterwards given. 



14. The Theoretical Table of refractions which has been 

 computed by the foregoing formulas, and which is deduced 

 solely from die phaenomena of the atmosphere without arbi- 

 ti'ary assumptions, is next to be compared with the tables 

 most esteemed by astronomers. Two tables more eminently 

 deserve this character ; namely, Bessel's table with its supple- 

 ment in the Tabula; RegiomontancE, which may be considered 

 as the result of observations, and as beingnearly exactto 88° 

 or 8 8 1° from the zenith; and the table published annually 

 in the Coniiaissance des Temps. As all the tables are sup- 

 posed 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 9 in Bessel's table, the logarithm of the 

 refraction at the same zenith distance in the new table should 

 be equal to 



log a -f log tan 6 -{- -00507, 

 the number '00507 being the difference of the logarithms of 

 the refractions at the altitude 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 lo- 

 garithms in the new table. With regard to the refractions in 

 the Con?i. des Temps, it is more convenient to use the table 

 in the Tables Astronomiques, published by the French Board 

 of Longitude : for the logarithms in this table with the addi- 

 tion of 'OOll, should agree respectively with the logarithms 

 of the new table. According to these directions the follov^- 

 ing comparative view has been drawn up. 



A 



