4 
DTJ. G. H. BRYAN ON THE KINETIC THEORY 
speed to overcome the attraction of the Eartli, the Moon, Mars, or the Sun, as the 
case may l:»e. 
The wide difference in the numhers, due to the presence of the exjionential factor, 
is sufficient to account for the practical permanence of the atmospheres of certain 
planets and the non-existence of certain gases in the atmospheres of others. 
'fABLE of Average Numher of Molecules of Gas to every one whose Speed is suffi¬ 
ciently great to overcome the Attraction of the Corresponding Body. 
Hydrogen at 
TemjDeratnre. 
Oxygen at 
Temperature. 
Surface of 
Moon. 
Surface of 
Mars. 
Surface of 
Earth. 
Earth’s atmo¬ 
sphere at 
height of 80 
miles. 
At Earth’s 
distance 
from Sun. 
Ah.solute. 
Cent. 
Absolute. 
Cent. 
273“ 
0° 
4368 
4095“ 
3-6 
3920 
6-0 X 101-1 
2-3 X 1019 
2-7 X 10301 i 
68 
-205 
1092 
819 
610-0 
5-0 X 1015 
3-3 X 1081 
7-6 X 10™ 
6-6 X 101283 i 
17 
-246 
273 
0 
O 
X 
1-0 X 10'« 
2-3 X 10819 
5-7 X 1082-2 
2-0 X 101110 
4.1 
-269 
68 
-205 
6-9 X 10^1 
1-8 X 10'i63 
4-5 X 101821 
1-5 X 101298 
1-7 X 1019101 
4. Mr. Cook’s Method. 
Mr. Cook has enp^loyed a method almost identical with that explained above. 
He uses the formula (4), and proceeds to calculate the number of molecules crossing 
a unit of surface with velocity exceeding the critical velocity, which would just suffice 
to carry a molecide to infinity. For the Earth the number of molecides is computed 
under the following conditions :— 
(1) For a spherical sliell at the Earth’s surface at a mean temperature of 5° C. 
(2) For a spherical shell 200 kiloms. from the Earth’s surface at a temperature of 
-66° C. 
(3) For a spherical shell 20 kiloms. from the Earth’s surface at a temperature of 
-66° C. 
(4) For a spherical shell 50 kiloms. from the Earth’s surface at a temperature of 
180° C. 
Ajiart from the fact that no account was taken of axial rotation in either my earlier 
calculations or those of Mr. Cook, the assumption of the Boltzmann-Maxwell dis¬ 
tribution prevents us from drawing any hard and fast line between gases which can 
exist, and gases which cannot exist, at any given temperature on any planet. It seems 
natural to think that, mathematically speaking, the condition of jDermanence would 
be satisfied if the number of molecules out of which one would attain the critical 
velocity were greater than the total number of molecules in the planet’s atmosphere. 
But the loss of a good many cubic centimetres of air from our atmosphere in the 
course of a year might easily he taking place without producing any perceptible efiects 
on its practical permanence. 
