~*~ 
calculating the atmospherical Refraction. 167 
of the first terms of the series, or even a considerable number 
of them, are not sufficient for computing the refractions with the 
requisite exactness. It appears therefore that no great improve- 
ment of the theory of refraction is to be expected from the new 
way of considering the subject. 
For greater illustration we may apply the foregoing method to 
the actual caleulation of the horizontal refraction, taking the 
data as they are given in the Mécanique Céleste; that is, the 
mean pressure of the atmosphere being 0:76 metres, and the 
temperature at the earth’s surface, that of melting ice. Then, 
B = -000293876 
i = -00125254 
= °234625 
B 
7 
C = -0:382625 
E = :0:0318906 
G = :0:0059446 
&c. 
and we have this equation for finding g, viz. 
1 = 382625 g* + -0318906 04 + -0059446 05; 
the solution of which is g?= 210117; and g= 1-44964. Hence 
r= aa x g ='0120365, or 41’ 22”; which is 88” too much, 
u 
the true quantity being 2394"-6 according to the calculation of 
Laplace. This great excess arises from the terms of the series 
that are left out; and, although the error would be lessened, yet, 
on account of the slow convergency, it would by no means be 
quite corrected by taking in two or three more terms. There 
can be no doubt that the calculations, § vii. pp. 357 and 359, 
likewise bring out results considerably above the truth. 
The observations that have been made ‘relate only to Dr. 
Young’s Theory, and do not bear at all upon the Table of Re- 
fractions published in the Nautical Almanac 1822. In the ex- 
planation annexed to the Table, we are told indeed that it is con- 
structed upon principles explained by Dr. Young in the Philoso- 
phical Transactions; but the truth is, that the formula and the 
Table have very little reference to any theoretical principles, and 
must both be considered as entirely empirical. The real autho- 
rity of the Table, or the ground on which its estimation with 
astronomers must rest, is the manner in which the coefficients 
have been determined; and upon this point we have very little 
satisfactory information. 
We may suppose that the author of the Table employed two 
ways for finding the numeral coefficients of his formula, He 
: may 
