16 DE. G. H. BEY AX ON THE, KINETIC THEOEY 
(i.) The term A representing the gravitation potential at the planet’s surface, 
mass of planet , , 
melius —. (- 2 )- 
(ii.) The term B representing the jDotential of centrifugal force at the surface of the 
equator, 
/ radius of planet '\~ . . 
\ time of axial rotation /./• 
(iii.) The term C representing the combined ijotential of gravitation and centrifugal 
foi'ce over the critical surface, 
/ mass of planet _ 
\time of rotation/./• 
(iv.) It will also be convenient to notice that the equatorial mdius ot the closed 
[)art of tlie critical surface (which we have denoted by o) 
cc (mass)3 X (time of rotation)^.(25)- 
Employing the values for the radii, masses and times of rotation given in 
Dr. Stoxey’s paper, taking the Earth’s as unity, I obtain the following results :— 
Table of Logarithms of the Critical Density-ratio for Hydrogen for various 
Planets. 
100° absolute. 
200° absolute. 
300° absolute. 
Venus . 
40-6360 
20-3180 
13-5453 
Earth . . 
50-951 
25-475 
16-987 
Mars . . 
10-4690 
5-2345 
3-4896 
Jupiter. . 
Saturn . . 
711-94 
355 - 97 
237-31 
165-98 
82-99 
55-33 
The logarithm of the critical density-ratio being inversely proportional to the abso¬ 
lute temperature and directly proportional to the molecular weight of .the gas, it 
l)ecomes unnecessary to perform the calculations for othei' gases or other temperatures, 
as this is a mere matter of simple arithmetic. 
The high values for the logarithm of the critical density-ratio on Jupiter and 
Saturn leave little doubt as to the possibility of the lightest gases, such as hydrogen, 
remaining practically permanent in the atmospheres of these planets. When we 
apply the methods to helium (assuming its molecular weight twice that of hydrogen) 
on the Earth and watery vapour (molecular weight nine times that of hydrogen) on 
Mars, we have the following results :— 
