A T R 
162 
A T M 
A UrM 
elastic quality, expands and contracts, and it 
being found by repeated experiments in most 
countries of Europe, that the spaces it occu- 
pies, when compressed by different weights, 
are reciprocally proportional to those weights 
themselves; or that the more the air is press- 
ed, so much the less space it occupies; it 
follows that the air in the upper regions of 
the atmosphere must grow continually more 
and more rare, as it ascends higher ; and in- 
deed that, according to that law, it must ne- 
cessarily be extended to an indefinite height. 
Now, if we suppose the height ot the whole 
divided into innumerable equal parts, the 
quantity of each part will be as its density : 
and the w eight of the whole incumbent at- 
mosphere being also as its density ; it follows, 
that the weight of the incumbent air is every 
where as the quantity contained in the sub- 
jacent part ; which causes a difference be- 
tween 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 tiie remainders 
the same, these will be a series of continued 
quantities decreasing in geometrical progres- 
sion; therefore if, according to the supposi- 
tion, the altitude of the air, by the addition 
of new parts into which it is divided, con- 
tinually increases 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 propor- 
tional to the compressing force, the height of 
the atmosphere must necessarily be extended 
indefinitely. And farther, as an arithmetical 
series adapted to a geometrical one, is analo- 
gous to the logarithms of the geometrical 
one; it follows therefore that the altitudes 
are proportional to the logarithms ot 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. dif- 
ference of the logarithms 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 barometer there. This law was first ob- 
served and demonstrated by Dr. Halley, 
from the nature of the hyberbola; and after- 
wards by Dr. Gregory, by means ot the lo- 
garithmic curve. see Philos. Trans. N° 181, 
or Abridg. vol. 2. p. 13, and Greg. Astron. 
lib. v. prop. 3. 
It is now easy, from the foregoing proper- 
ty, and two or three experiments, or baro- 
metrical observations, made at known alti- 
tudes, to deduce a general rule to determine 
the absolute height answering to any density, 
or the density answering to any given alti- 
tude above the earth. And accordingly cal- 
culations were made upon this plan by many 
philosophers, particularly by the French ; but 
ft having been found that ' the barometrical 
observations did not correspond with the al- 
titudes as measured in a geometrical manner, 
it was suspected that the upper parts of the 
atmospherical regions were not subject to 
the same laws with the lower ones, in regard 
to- the density and elasticity. It has, how- 
ever, 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 
q { the highest mountains on the earth, when 
a correction is made for the difference of tire 
heat or temperature of the air only ; as was 
fully evinced by M. DeLuc, in along senes 
of observations, in which he determined the 
altitudes of hills both by the barometer and by 
geometrical measurement, from which he de- 
duced a practical rule to allow for the differ- 
ence of temperature. See his r I reatise on the 
Modifications of the Atmosphere. Similar 
rules have also been deduced from accurate 
experiments, by sir George Shuckburgh and 
general Roy, both concurring to shew that 
such a rule for the altitudes and densities, 
holds true for all heights that are accessible 
to us, when the elasticity ot the air is correct- 
ed on account of its density; and the result 
of their experiments shewed, that the differ- 
ence of the logarithms ot the heights ot the 
mercury in t lie barometer, at two stations, 
when multiplied by 10000, is equal to the al- 
titude in English fathoms, of the one place 
above the other; that is, when the tempera- 
ture ot the air is about 31 or 32 degrees of 
Fahrenheit’s thermometer, and a certain 
quantity, more or less, according as the ac- 
tual temperature is different from that de- 
gree. 
But it may here be shewn, that the same rule 
may be deduced independent of such a train of 
experiments as those above, merely by the den- 
sity of the air at the surface of the earth alone. 
Thus, let D denote the density of the air at cue 
place, and d the density at the other ; both 
measured by the column of mercury in the ba- 
rometrical tube : then the difference of altitude 
between the two places will be proportional to 
the log. of D — the log. of d, or to the log. 
But as this formula expresses only the 
10592 to 10000, because the difference 5.02 is 
the 18th part of the whole factor 10552, and 
because 18 is the 24th part of 435 ; therefore 
the change of temperature, answering to the 
change of the factor h, is ?4°; which reduces the 
M 
55° to 31°. So that, a — 10000 X log. of — 
fathoms, is the easiest expression for the alti- 
tude, and answers to the temperature of 31®, 
or very nearly the freezing point : and for every 
degree above that, the result must be increased 
by so many times its 435 th part, and diminished 
when below it. 
From this theorem it follows, that, at the 
height of 3-j miles, the density of the atmo- 
sphere is nearly twice rarer than it is ai the 
surface of the earth ; at the height of 7 miles, 4 
times rarer ; and so on, according to the fol- 
lowing table : 
Height in miles. 
H 
7 
14 
21 
28 
35 
42 
49 
56 
C3 
• 70 
Number of times rarer. 
4 
16 
64 
256 
1024 
4096 
16384 
65536 
262144 
104S576 
of 
relation between different altitudes, and not the 
absolute quantity of them, assume some indeter- 
minate, but constant quantity b, which multi- 
plying the expression log. — may be equal to 
the real difference of altitude a ; that is, a — h 
X log. of ~ j. Then, to determine the value of 
the general quantity h, let us take a case in which 
wc know the altitude a, which corresponds to a 
known density d ; as for instance, taking a = 1 
foot, or 1 inch, or some such small altitude: 
then, because the density D may be measured 
by the pressure of the whole atmosphere, or the 
uniform column of 27600 feet, when the tem- 
perature is 55°; therefore 27600 feet will denote 
the density D at the lower place, and 27599 the 
less density d at 1 foot above it ; consequently 
, „ 27600 , . . . 
1 = b X log. of — — , winch, by the nature 
27599 
.43429448 
of logarithms, is nearly = l X — 27600 — ’ 
1 
63551 
nearly ; and hence we find h — 63551 
feet ; which gives us this formula for any alti- 
D 
tude a in general, viz. a — 63551 X log of — , 
M 
or a — 63551 X log. of — feet, or 10592 X 
771 
log. of — fathoms ; where M denotes the co- 
lumn of mercury in the tube at the lower place, 
and m that at the upper. This formula is 
adapted to the mean temperature of the air 55°: 
but it has been found, by the experiments of 
sir Geo. Shuckburgh and general Roy, that for 
every degree of the thermometer, different from 
55°, the altitude a will vary by its 435th part ; 
hence, if wc- would change the factor h from 
And, by pursuing the calculations in this 
table, it might be easily shewn, that a cubic 
inch of the air we breathe would be so much 
rarefied at the height of 500 miles, that it would 
fill a sphere equal in diameter to the orbit of 
Saturn. 
AT OM, in philosophy, a particle of mat- 
ter, so minute as to admit of no division. 
ATONIA, or Atony, in medicine, a 
word that signifies want of firmness, or 
strength, in the muscular hbre. Th.s condi- . 
tion takes place in most forms of chronic dis- 
eases, and in the convalescent period of acute 
diseases. 
ATONICS, in grammar, words not ac- 
cented. 
AIR A bilis, the black bile, one of the 
humours of the antient. physicians ; which 
the moderns call melancholy. See Medi- 
cine. 
ATRACTYLIS, in botany, a genus of the 
syngenesia polygamia class of plants. 1 he 
corolla is radiated; and each of the little 
corolla; of the radius has 2 teeth. There are 3 
species. 
1. Atractylis cancellata, or small cnicus, 
is an annual' plant, rising about eight or nine 
inches high, with a slender stem ; at the top 
of the branches are sent out two or three, 
slender stalks, each terminated by a head of 
flowers, like those of the thistle, and of a 
purplish colour. 
2. Atractylis gummifera, or prickly gum- 
bearing cnicus, known among physicians by 
the name of carline thistle, is a perennial 
plant. It has many florets inclosed in a 
prickly empalement. Those on the border 
are white ; but such as compose the disk, 
are of a yellowish colour. It flowers in July, 
but never perfects seeds in Britain. Its roots 
were formerly used as a warm diaphoretic 
and alexipharmic ; but the present practice 
has entirely rejected them. 
3. Atractylis humilis, or purple prickly 
cnicus, rises about a foot high, with purple 
flowers. All these plants are natives of tin 
warm parts of Europe ; as Spain, Sicily, aiwj 
the Archipelago islands. 
