480 
ATMOSPHERE. 
bola; and afterwards by Dr. Gregory, by means of the lo¬ 
garithmic curve. See Phil.Tranf. No.clxxxi. or Abridg. 
vol.ii. p. 13, and Greg. Aftron. lib. v. prop. 3.. 
It is now eafy, from the foregoing property, and two or 
three experiments, or barometrical obfervations, made at 
known altitudes, to deduce a general rule to determine 
the abfolute height anfwering to any denfity, or the denfi- 
ty anfwering to any given altitude above the earth. And 
accordingly, calculations were made upon this plan by ma¬ 
ny philofophers, particularly by the French; but, it hav¬ 
ing been fou*d that the barometrical obfervations did not 
correfpond with the altitudes as meafured in a geometri¬ 
cal manner, it was fufpeded, that the upper parts of the 
atmofpherical regions were not fubjeCt to the fame laws 
with the lower ones, in regard to the denfity and elafticity. 
And indeed, when it is confidered that the atmofphere is 
a heterogeneous mafs of particles of all forts of matter, 
fome elaffic, and others not, it is not improbable but this 
may be the cafe, at leaft in the regions very high in the at- 
piofphere, which it is likely may more copioufly abound 
with the electrical fluid. Be this however as it may, it 
has lately been difeovered, that the law above given holds 
very well for all fuch altitudes as are within our reach, or 
as far as to the tops of the higheft 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 feries of obfervations, in which he de¬ 
termined the altitudes of hills both by the barometer, and 
by geometrical meafurement, from which he deduced a 
practical rule to allow for the difference of temperature. 
See his Treatife on the Modifications of the Atmofphere. 
Similar rules have alio been deduced from accurate expe¬ 
riments, by Sir George Shuckburgh and general Roy, both 
concurring to (hew, that fuch a rule for the altitudes and 
denfities holds true for all heights that are acceffible to us, 
when the elafticity of the air is corrected on account of its 
denfity: and the refult of their experiments (hewed, that 
the difference of the logarithms of the heights of the mer¬ 
cury in the barometer, at two (fations, when multiplied by 
xoooo, is equal to the altitude in Englifh fathoms, of the 
one place above the other; that is, when the temperature 
of the air is about 31 0 or 32 0 of Fahrenheit’s thermome¬ 
ter ; and a certain quantity more or lefs, according as the 
aCtual temperature is different from that degree. 
But it may here be fhewn, that the fame rule may be 
deduced independent of fuch a train of experiments as 
thofe above, merely by the denfity of the air at the fur- 
face of the earth alone. Thus, let D denote the denfity 
of the air at one place, and d the denfity at the other; 
both meafured by the column of mercury in the barome¬ 
trical tube : then the difference of the altitude between 
the two places will be proportional to the log. of D — the 
log. of d, or to the log. of —. But, as this formula ex- 
a 
prefles only the relation between different altitudes, and 
not the abfolute quantity of them, affume fome indeter¬ 
minate, but conftant, quantity k, which multiplying the 
e-xpreflion log. —, may be equal to the real difference of 
altitude a\ that is, a-h-y log. of 
D 
Then, to deter¬ 
mine the value of the general quantity k t let us take a 
rafe in which we know the altitude a which correfponds to 
a known denfity d ; as, for inffance, taking a— 1 foot, or 1 
inch, or fome fuch fmall altitude : then, becaufe the den¬ 
fity D may be meafured by the prelfure of the whole at¬ 
mofphere, or the uniform column of 27600 feet, when the 
temperature is 55 0 ; therefore, 27600 feet will denotd the 
denfity D at the lower place, and 27599 the lefs denfity d 
at 1 foot above it; confequently, i=^x log. of f-f | -§ A t 
which, by the nature of logarithms, is nearly — k x 
'" '2^60 0 ' ’ ° r war ^ nd hence we find ^=63551 
feet ; which gives 11s this formula for any altitude a in 
D 
general, viz. a~6 3551 x log. of—, or 0=6355* x log. of 
M M 
feet, or 10592x log. of — fathoms; where M denote# 
m 
the column of mercury in the tube at the lower place, and 
n that at the upper. This formula is adapted to the mean 
temperature of the air 55 0 : but it has been found, by the 
experiments of Sir George Shuckburgh and general Roy, 
that, for every degree of the thermometer different from 
55 0 , the altitude a will vary by its 435th part; hence, ir 
we would change the faftoi /: from 10592 to 10000, be¬ 
caufe the difference 592 is the 18th part of the whole fac¬ 
tor 10592, and becaufe 18 is the 24th part of 435 ; there¬ 
fore the change of temperature, anfwering to the change 
of the factor/:, is 24°, which reduces the 55 0 to 31°. So 
M 
that, <z=ioooox log. of — fathoms, is the eafieff expref- 
7)1 * 
fion for the altitude, and anfwers for the temperature of 
31 0 , or very nearly the freezing point: and for every de¬ 
gree above that, the refult muff be increafed by fo many 
times its 435th part, and diminifhed when below it. 
From this theorem it follows, that, at the height of 3J: 
miles, the denfity of the atmofphere is nearly 2 times ra¬ 
rer than it is at the furface of the earth; at the height of 
7 miles, 4 times rarer ; and fo on, according to the follow¬ 
ing table : 
it in miles. 
Number o£ times 
3 § 
2 
7 
4 
14 
1 6 
21 
64 
28 
256 
35 
1024 
42 
4 ° 9 & 
49 
16384 
56 
6 553 <> 
63 
262144 
70 
1048576 
And, by purfuing the calculations in this table, it might 
be eafily fhewn, that a cubic inch of the air we breathe 
would be fo much rarefied at the height of 500 miles, that 
it would fill a fphere equal, in diameter to the orbit of Sa¬ 
turn. Hence we may perceive how very foon the air be¬ 
comes fo extremely rare and light, as to be utterly imper¬ 
ceptible to all experience; and that hence, if all the pla¬ 
nets have fuch atmofpheres as our earth, they wilf, at the 
difiances of the planets from one another, be fo extremely 
attenuated, as to give no fenfible refiftance to the planets 
in their motion round the fun for many, perhaps hundreds 
or thoufands of ages to come. Even at the height of 
about fifty miles, it is fo rare as to have no fenfible effect 
on the rays of light: for it was found by Kepler, and De 
la Hire after him, who computed the height of the fenfible 
atmofphere from the duration of twilight, and from the 
magnitude of the terrefirial fhadow in lunar eclipfes, that 
the efteft of the atmofphere to refleCt and intercept the 
light of the fun is only fenfible to the altitude of between 
forty and fifty miles: and at that altitude we may eolleCt, 
from what has been already faid, that the aiF is above 
10,000 times rarer than at the furface of the earth. It is 
well known, that the twilight begins and ends when the 
centre of the fun is about 18 0 below the horizon, or only 
17 0 27', by fubtraCting 33' for refraction, which raifes the 
fun fo much higher than he would be. And a ray coming 
from the fun in that pofition, and entering the earth’s at¬ 
mofphere, is refraCted and bent into a curve-line in paffing 
through it to the eye. 
M. de la Hire took great pains to demonftrate, that, 
fuppofing the denfity of the atmofphere proportional to its 
weight, this curve is a cycloid : he alfo fays, that, if the 
ray be a tangent to the atmofphere, the diameter of its ge¬ 
nerating circle will be the height of the atmofphere; and 
that 
