478 Mr. Ivory on the astronomical refractions. 
perfect agreement between the two tables : first, on account 
of the difference in the hypotheses respecting the constitu- 
tion of the atmosphere ; secondly, because the tables are 
differently constructed. 
The French refractions at low altitudes are computed by 
a formula which the sagacity of Laplace deduced from a 
hypothesis respecting density, that must be a near approach 
to the law that actually obtains in nature. The formula is so 
constructed as to give the horizontal refraction adopted by 
astronomers ; but we may still judge, in some measure, of 
the accuracy of the hypothesis, by comparing the rate of the 
decrease of heat at the earth’s surface with the result of 
actual observation. Now, in the hypothesis of Laplace, I 
have found 
(making s — o) =0.7159 ; 
which is a near approach to 0.8, the quantity assumed in 
this Paper. But the difference, although it seem very little, 
has nevertheless a great influence on the constitution of the 
atmosphere, as will be obvious if, by means of the equation 
— (5 = 0 ) = 1 — - , 
as ^ ' f/. 
we compute the value of y resulting from the preceding value 
of -f- It will be found that p, = 59 \ ; which is the eleva- 
tion in fathoms that in this hypothesis will depress the cen- 
tigrade thermometer one degree ; and it is no more than about 
j of the true quantity. It follows, therefore, that the theory 
of Laplace does not strictly accord with the actual condition 
of the atmosphere, which must affect the accuracy of the re- 
fractions near the horizon. 
