ATMOSPHERE. 
condensed as they descend, and of tempe- 
rate warmth before they reach the fertile 
plains of Quito. 
Various attempts have been made to as- 
certain the height to which the atmosphere 
is extended all round the earth. These 
commenced soon after it was discovered by 
means of the Torricellian tube, that air is 
endued with weight and pressure. And 
had not the air an elastic power, but were 
it every where of the same density, from 
the surface of the earth to the extreme 
limit of the atmosphere, like water, which 
is equally dense at all depths, it would be a 
very easy matter to d9termine its height 
from its density and the column of mercury 
which it would counterbalance in the ba- 
rometer tube : for, it having been observed 
that the weight of the atmosphere is equi- 
valent to a column of 30 inches or 2~ feet of 
quicksilver, and the density of the former 
to that of the latter, as 1 to i 1040 ; there- 
fore the height of the uniform atmosphere 
would be 11040 times gi feet, that is 27600 
feet, or little more than 5 miles and a quar- 
ter. But the air, by its elastic quality, ex- 
pands and contracts ; and it being found by 
repeated experiments in most nations of 
Europe, that the spaces it occupies, when 
compressed by different weights, are reci- 
procally proportional to those weights them- 
selves ; or, that the more the air is pressed, 
so much the less space it takes up ; it fol- 
lows that the air in the upper regions of the 
atmosphere must grow continually more 
and more rare, as it ascends higher; and 
indeed that, according to that law, it must 
necessarily be extended to an indefinite 
height. Now, if we suppose the height of 
the whole divided into innumerable equal 
parts; the quantity of each part will be as 
its density ; and the weight of the whole 
incumbent atmosphere being also as its den- 
sity ; it follows, that the weight of the in- 
cumbent air is every where as the quantity 
contained in the subjacent part; which 
causes a difference between the weights of 
each two contiguous parts of air. But, by 
a theorem in arithmetic, when a magnitude 
is continually diminished by the like part 
of itself, and the remainders the same, these 
will be a series of continued quantities de- 
creasing in geometrical progression : there- 
fore if, according to tire supposition, the 
altitude of the air, by the addition of new 
parts into which it is divided, do continually 
increase in arithmetical progression, its 
density will be diminished, or, which is the 
same thing, its gravity decreased, in con- 
tinued geometrical proportion. And hence, 
again, it appears that, according to the hy- 
pothesis of the density being always pro- 
portional to the compressing force, the 
height of the atmosphere must necessarily 
be extended indefinitely. And, farther, as 
an arithmetical series adapted to a geome- 
trical one, is analogous to the logarithms of 
the said geometrical one ; it follows there- 
fore that the altitudes are proportional to 
the logarithms of the densities, or weights 
of air ; and that any height taken from the 
earth’s surface, which is the difference of 
two altitudes to the top of the atmosphere, 
is proportional to the difference of the loga- 
rithms of the two densities there, or to the 
logarithm of the ratio of those densities, or 
their corresponding compressing forces, as 
measured by the two heights of the baro- 
meter there. 
It is now easy, from the foregoing pro- 
perty, and two or three experiments, or 
barometrical observations, made at known 
altitudes, to deduce a general rule to de- 
termine the absolute height answering to 
any density, or the density answering to 
any given altitude above the earth. And 
accordingly, calculations were made upon 
this plan by many philosophers, particu- 
larly by the French; but it having been 
found that the barometrical observations 
did not correspond with the altitudes as 
measured in a geometrical manner, it was 
suspected that the upper parts of the atmos- 
pherical regions were not subject to the 
same laws with the lower ones, in regard 
to the density and elasticity. And indeed, 
when it is considered that the atmosphere 
is a heterogeneous mass of particles of all 
sorts of matter, some elastic, and others 
not, it is not improbable but this may be 
the case, at least in the regions very high 
in the atmosphere, which it is likely may 
more copiously abound with the electrical 
fluid. Be this however as it may, it has 
been discovered that the law above given, 
holds very well for all such altitudes as are 
within our reach, or as far as to the tops of 
the highest mountains on the earth, when a 
correction is made for the difference of 
the heat or temperature of the air only, as 
was fully evinced by M. De Luc, in a long 
series of observations, in which lie deter- 
mined the altitudes of hills both by the ba- 
rometer, and by geometrical measurement, 
from which he deduced a practical rule to 
allow for the difference of temperature. 
Similar rules have also been deduced from 
accurate experiments, by Sir George Shuck- 
