Mr. Ivory on the astronomical refractions. 423 
In order to simplify, I shall now write P for the relative 
pressure^-, and likewise put s = - ^ then, observ- 
ing that y = 1 — w, what has now been investigated will be 
expressed by these equations, viz. 
P = / — ds ( 1 — to ) 
p _ 1 + ftr 
x + 
X 
C 1 — ") 
K A ) 
x 
S — (i+W 
The quantity 
1 + 
I + &T 
> is equal to the proportion of the relative 
elasticity of the air to its relative density ; and it may depend 
upon the moisture diffused in the atmosphere, as well as 
upon the temperature. Whatever be the true form of this 
function, it must be evanescent at the boundary of the atmos- 
phere. The reason of this will readily appear, if we consider 
first, that, at the surface of the earth, the elasticity of a given 
volume of air is incomparably greater than its weight ; and, 
secondly, that in a finite atmosphere, there must be an equa- 
lity between the same two forces at the upper surface. With 
regard to the density, we may form two suppositions ; it may 
either be evanescent at the top of the atmosphere, or it may 
have some very small finite value. But in reality we know 
that, in ascending, the density of the air decreases with con- 
siderable rapidity ; so that if it do not decrease so as to be 
absolutely evanescent, it must finally become so small, that 
we may safely consider it as equal to zero. 
To the equations already investigated we must add ano- 
ther, which is requisite to the solution of this Problem, al- 
though it has been universally neglected. By equating the 
