414 Mr. Ivory on the astronomical refractions. 
and therefore, by the operation of this cause, as we ascend in 
the atmosphere, the expansive force of a given volume of air 
is constantly diminished and brought nearer to an equality 
with its weight. To estimate this effect with greater pre- 
cision, let p' , zf, t', denote the barometric pressure, the density, 
and the temperature by the centigrade thermometer, at the 
earth’s surface ; and let the same letters, without the accent, 
denote the same things at any height x ; then, if j0 = gT,the 
expansion for one centigrade degree, the known laws that 
obtain in the expansion of elastic fluids, will lead to this 
formula, viz. 
p i + (3t z 
p i + @ 1' * z 
Now here T is the measure of the elastic force at the height 
x in parts of the same force at the surface ; and we see that 
it depends on the temperature as well as on the relative 
density ~ • At the earth’s surface the quantity is equal 
to unit, but it continually decreases as the temperature be- 
comes less in ascending. We cannot conceive that it will 
become negative, nor can we set any bounds to its approach 
to zero. But when - -f . ^ t is evanescent, or when t = — 2 66 °, 
the elastic force of the air will cease, and gravity will stop 
the farther dilatation of the atmosphere. This reasoning is 
independent of the law of the densities ; and it proves both 
that the atmosphere may be finite in its extent, and that it 
may have a finite density at its upper surface. But it may 
be objected, that the effect of temperature on the air’s elas- 
ticity has been verified only to a certain extent ; and that in 
the case of air of great rarity, and subjected to extreme 
