416 Mr. Ivory on the astronomical refractions. 
as to the actual height of the finite atmosphere. Gay Lussac 
ascended in a balloon to the altitude of 3816 English fathoms, 
or nearly miles above the level of the Seine at Paris ; the 
proportion of the heights of the barometer in the balloon and 
at the surface of the earth being 0.467 nearly, which is 
therefore the relative elasticity of the air. The temperatures, 
as observed at the extremities of the elevation, were 3o°.8, 
and — 9 0 . 5 on the centigrade scale ; and if we increase 0.467 
to what it would have been, had the temperature remained 
unchanged during the ascent, we shall find 0.500, which is 
the density of the air at the height ascended in parts of the 
density at the surface of the earth. Thus, in the decreasing 
scale of elasticities, the diminution is from 1 to 0.467 ; but, 
in the decreasing scale of densities, it is only from 1 to 0.500. 
The quantities of the one scale continually fall behind those 
of the other at a rate that must bring them to zero, whatever 
be the gradation of the latter. If we divide 3816 fathoms, 
the whole height ascended, by 40°.3, the difference of tempe- 
rature, the elevation for depressing the thermometer one de- 
gree will come out equal to 95 fathoms : and if we suppose 
that the same rate prevails in all parts of the atmosphere, the 
whole height will be 2 66 x 95 fathoms, or nearly 29 miles. 
The observations of the twilight show that this is less than 
the true altitude ; and hence we must infer, that the ther- 
mometer falls at a slower rate in the higher, than in the lower, 
parts of the atmosphere. But, taking the observed rate of 
95 fathoms for the first 40 degrees, and allowing, on an ave- 
rage, a double, or even a triple, elevation for the remaining 
226°, we shall still find that the atmosphere will extend only 
to a moderate height above the earth's surface. 
