8 
DR. G. H. BRYAN ON THE KINETIC THEORY 
The Hb(jve distribution, if it exist at any instant, will be permanent in the absence 
of encounters, and will lie unaffected by encounters between the molecules ; moreover, 
if the molecules form the atmosphere of a planet or other body rotating with angular 
velocity O, the distribution will clearly be unaffected by the molecules colliding with 
obstacles on the surface of the planet, while this could not be said of other distribu¬ 
tions that might be assumed. 
7. Conditions for the above Law of Distribution. 
Let iis now examine how far the conditions necessary for establishing this distri- 
biition are fulfilled in the atmosphere of a planet. 
In the denser regions of the atmosphere where collisions are frequent, the effect 
of these collisions must be to distribute the velocities of the molecules, occurring j^er 
unit volume in the neighl^ourhood of a point, according to Maxwell’s law, the 
rate of progress towards the stationary state being calculable by the methods of 
Boltzmanx, Watson, Burbury, and Tait. The tendency to equalisation of the 
value of F in different regions of the atmos})here is determinable ])y the known 
metliods of investigating diffusion, thermal conductivity, &c. 
As we ascend in the planet’s atmosphere, collisions l)etween the molecules will 
become more and more infrequent, and at last we shall reacli a region where practically 
all the molecules are descril^ing free })aths. These molecules will be those which are 
projected frt)ni the lower regions, and those which do not escape will frequently 
return to these lower regions. And since the pro230sed law of distribution remains 
permanent in the absence of interniolecular encounters, it follows that the molecules in 
question will remain distril)uted according to the same law, and this distribution will 
be brought about by the collisions which these molecules undergo in the less rarefied 
portions of the atmosphere. 
At still greater distances from the planet we may have to deal with cases in which 
instead of there being a large number of molecules in a unit volume, the presence of 
a single molecule in, say, a cuiiic kilom., is an event of rare occurrence, owing to the 
smallness of But as the Boltzmann-Maxwell distribution is generally 
accepted to be a theorem in probability, we may still apply the present distribution 
to determine the probability that a molecule may reach these regions. It has been 
ol jected that the error law cannot be applied to calculate the probability of events of 
exceptional occurrence ; but it appears to l^e the generally accepted view that such 
cases should, if anything, Ije excluded. Practically, it is immaterial which course we 
take. If theory proves that the escape of a molecule is of such exceptional occurrence 
as will be found in some of the subsequent calculations, it will make no difference to 
the permanence of the atmosphere whether we assume the escaping molecule to exist 
or not. 
’fhe chief objection to the distribution is that it is an isothermal one, whereas in 
