DE. G. H. BRYAN ON THE KINETIC THEORY 
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Again, the molecules which at the surface of the ^^lanet happen to be moving with 
velocity greater than the critical velocity, so far from leaving its atmosphere, will 
only collide with other molecules, provided the atmosphere is of sufficient density to 
possess the attrilDutes of ordinary gases, he., is of density comparable with that of 
our atmosphere. It is only in media of extreme tenuity, possessing the properties ot 
high vacua, where the mean free path of the molecules is very great, that there is 
practically any chance of a molecule, Avhich possesses sufficient speed, escaping with¬ 
out coming: into collision witli other molecules. In the case of the Earth this circum- 
stance is taken into account hy Dr. Stoxey, where he calculates the critical velocity- 
ratio at a certain distance from the Earth’s surface, this distance being assumed to 
represent the limit of height of the atmosj^here. But this bring us to the question 
as to what is to he regarded as the limit of a planet’s atmosphere, and we are thus 
brought to consider the problem of the law of stationary distribution of the molecules 
in the atmosphere of a rotating planet. 
The original object of the present investigation was to clear up a number of obscure 
points such as those mentioned above, and at the same time to replace considerations of 
the critical velocity-ratio by results of a more statistical character. But the calculations 
have led to the residt that certain gases believed by many physicists to escape from 
our atmosphere either do not so escape, or, if they do, that their escape takes place 
under different conditions as to tenq)erature, &c., to those commonly assumed, or is a 
result of causes lying outside the principles of the Kinetic Theory of Gases. 
6. The Laio of Molecular Distribution in the Atmosphere of a Rotating Planet. 
d’he modification of “ Maxwell’s Law ” for the case of a gas in a field of external 
force has been discussed by several writers, the proofs given by Watsox being- 
simple and neat."^' The case of a rotating gas was discussed by Maxwell, but his 
treatment is hardly lucid. We now proceed to investigate the modifications which 
must be made in the Boltzmaxx-Maxwell distribution in order to take account of 
axial rotation. We assume the field of force due to the planet’s attraction to be 
symmetrical about the axis of rotation. 
Let F^, Fo be the functions determining the frequencies of given distributions of 
co-ordinates and momenta of two molecules. These satisfy the following con¬ 
ditions :— 
(i.) In the absence of encounters, Fj and Eg are constant. 
(ii.) When an encounter occurs, the values before and after the encounter are con¬ 
nected by the relation 
FiF,= F/Fb.(5). 
Condition (i.) is satisfied if and F^ are functions of any of the integrals of the 
* ‘Treatise oa the Kinetic Theory of Gases,’ § 11. 
