‘On atmospherical Refraction. 347 
or, if we make 
2B 
ea JV ti—2B 
These expressions take place at the standard temperature and 
mean pressure; but, according to what has been shown, and 
neglecting in the radical quantity the variation of 28 which is 
inconsiderable when compared with the variation of 47, they will 
becoitie, at the temperature ¢, and the pressure J, 
x sin A tan 3 y. 
Tan y = (1 4+-mt)? x Las 3E, 
5 cos 
i 6 2p ; 
fe eM a pe K sin A tan 5 ¥. 
(l+mt)z af 4i—28 
The horizontal refraction, when ¢ = 0, and b = B, is 
— 26 . 
 eaeeaee. 
which agrees with the determination in the Mécanique Céleste, 
vol. iv. p. 260, the symbols only being different. Using the values 
of i and 6 given by Laplace *, this quantity falls greatly short of 
observation. But the expressions that have now been investigated 
are perfectly similar to the formule of Mayer ; and it is reasonable 
to suppose that that astronomer followed the usual practice, and 
determined the two coefficients so as to represent the refractions 
observed at the horizon, and at the altitude of 45”. 
When the zenith distance is not too great, the factor depend- 
ing on leat in the value of tan y, very nearly compensatess the 
equal divisor in the expression of the refraction ; and in such 
cases Mayer’s formula coincides with the usual practice of astro- 
nomers in making the refraction vary in proportion to the den- 
sity of the air. At the horizon the compensation ceases to take 
place, and the correction for heat, according to Mayer, is quite 
different from the common rule. But the formula of the cele- 
brated astronomer of Gottingen has the merit of being, in both 
circumstances, consonant to general principles, and independent 
of arbitrary assumptions. Its imperfection arises from the phy- 
sical hypothesis employed; for the law of a uniform decrease of 
density cannot be that of nature; because it leads to a determi- 
nation of the horizontal refraction much too small ; and because 
it limits the atmosphere to the third or fourth part of its real 
extent. 
Sept. 5, 1821, J. Ivory. 
* Magazine for September, p. 167. 
Xx 2 LXXIV. dc- 
