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. 
{^3. 0-369, 
- 1-5668, 
5 = sin 1^3- 0-530, 
—1-7240 
+^5 .0-685, 
1-8356 
.1-113, 
0-0465 
+e7 .0-712, 
— 1-8526 
+«?? . 1-350, 
0-1306 
+e^ .0-530, 
— 1-7263 
-\-e^ .1-207, 
0-0817 
. 0-317, 
— 1-5006 
. 0-873, 
1-9412 
+^1^0-159, 
— 1-2013 
, 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 
+ -T(,-S0)-i(30-rt 
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 the phaenomena of the atmosphere without arbi- 
trary 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 Tahulce llegiomontancBy which may be considered 
as the result of observations, and as being nearly exact to 88° 
or 88 from the zenith ; and the table published annually 
in the Connaissance 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 + log tan 9 *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 Conn, des Temps^ it is more convenient to use the table 
in the Tables Astronomiques, published by the French Board 
of Loiiijitude : for the lof^arithms in this table with the addi- 
lion of *001 1, should agree respectively with the logarithms 
of the new table. According to these directions the follow- 
ing comparative view has been drawn up. 
