On atmospherical Refraction. 345 
as has already been shown: at the temperature ¢, it becomes 
a x (1-++ md). 
On the whole, therefore, by the changes of the barometer and 
thermometer, the factor = which enters into the expression 
21 , 
of the horizontal refraction, will become 
p 1 b. 
Se ee 
A 2i (1+ mt) B 
and this proves incontestably the justness of Mayer's rule in the 
hypothesis of Cassini. The series into which —— is multiplied, 
Zt 
will likewise produce some change in the horizontal refraction 5 
but the variation arising from this cause is not very consider- 
able; it is peculiar to the particular hypothesis; and it is not 
now the subject of consideration. 
The hypothesis of Cassini, on account of its simplicity, is well 
calculated to elucidate the variations in refraction produced by 
barometrical and thermometrical changes. As is apt to be the 
case in some more complicated suppositions, the attention is not 
here so absorbed by intricate combinations of the quantities con- 
certied, as to overlook the manner in which the phenomenon is 
produced by its real causes, which are the alterations in the re- 
fracting power of the medium and in the extent of the homo- 
geneous atmosphere. But if we attend to the analysis of this 
problem, given in this Magazine for September last, it will ap- 
ear that the same factor es which enters into the expression 
P = Pp 
u 
of the horizontal refraction in the hypothesis of Cassini, is 
equally a part of the same quantity in every hypothesis. We 
must, therefore, conclude that the rule of Mayer is true, not 
ouly i in the hypothesis of Cassini, or in that of Mayer whatever 
it was, but absolutely in every supposition that can possibly be 
formed with regard to the eonstitution of the atmosphere. 
It follows from the nature of the differential expression of the 
refraction that, so long as the zenith distance is not too great; 
or so long as cos* A is considerably greater than 7; we may de- 
velop the refraction in a series of terms multiplied by the small 
coefficients, 8; 67,78; &c., the quantity 7 never entering into 
a denominator. Now the term multiplied by 78 varies only with 
the barometer ; for heat produces equal and opposite changes 
in 7 and £, which compensate another: and, on the whole, so 
far as this mode of computation can be followed, the variation in 
refraction is very nearly proportional to 6, that is to the density 
of the air, according to the usual practice of astronomers, But 
when the zenith distance is. great; or when’ cos? A is less than 
Vol. 58, No. 283, Nov, 1821. Aske +S i; 
