Mr. Ivory on the Theory of the Astronomical IXefr actions, 93 
f X sin a X X Qs =/' X sin 9 X -Te’ X 35-324, l'?4807 
+ X 51-529, 1-71205 
32-476, 1-51156 
+ e^^x 1-809, 0-25755 
-^i^x 16-205, 1-20965 
— 18-588, 1-26925 
X 13-334, 1-12498 
-e"^^ X 7-427, 0*87080 
-e^x 3-480, 0-54158 
The amount of this expression at the horizon, or when ^ = 1," 
is/'x62''-l, almost the same with y'' x 62"-4, which, as is 
shown in § 9, is the limit of the integral when it is extended 
from jr = 0 to ^ = cvD. It is thus proved that the error of 
the series is of no account. This part of the refraction can- 
not be computed because f' is unknown. But although the 
precise value of f' is uncertain, it is probably very consider- 
2 
ably less than f or — \ so that the effect on the refraction 
cannot exceed a few seconds even at the horizon. We shall 
be better able to form a just notion with respect to this point, 
when the Theoretical Table in this paper is compared with 
observations. 
13. It remains to investigate the corrections that must be 
made in the practical application for the deviations indicated 
by the meteorological instruments from the mean constants 
used in constructing the table. 
For this purpose we have 
V 5 i 
S = Qo + A Qi — y^Q2 5 
5 i _ e 
cos 0 ” 1 — c® ’ 
X 
a. 
l 
The quantities e and A depend only upon a and i\ a varies 
both with the barometer and thermometer, and f, with the 
thermometer only : the quantity f does not seem liable to 
change in our climate. Admitting that the prefix d refers 
only to variations of the barometer and thermometer, we 
shall have 
