OF PLANETARY ATIMOSPHERES. 
5 
5. Dr. Stoxey’s Method. 
If V be the critical velocity which would enable a particle to overcome the attrac¬ 
tion of a planet, so that = p/a, and u he the velocity of translation at the planet’s 
equator due to axial rotation, it is clear that a particle moving in the proper direction 
with relative velocity v — u would escape. If this relative velocity be a large 
multiple of the mean molecular velocity of the gas, then the escape of molecules will 
he of rare occurrence; if it be a comparatively small multiple, the gas cannot remain 
permanently on the planet. Dr. Stoney, in his paper of 1897, calculates the corre¬ 
sponding critical relative velocity v' — u' at the top of the atmosphere of the planet; 
then, if ?(; be the velocity of mean square in the gas, his condition of permanence is 
/ / 
, . . V — 
that the velocity-ratio -must be CTeat, 
J yj o 
The limiting value of this ratio consistent with permanence might for convenience 
he called the critical velocity-ratio. 
There being no well-defined fheorefical limit to this velocity-ratio. Dr. Stoxey has 
adopted the plan of judging the unknown from the known. Assuming that free 
hydrogen and helium could not exist in our atmosphere, while watery vapour does 
actually so exist, it is inferred that a velocity-ratio of 20 is consistent with perma¬ 
nence, while a velocity-ratio of 9‘27 is incompatible with permanence. Applying 
these criteria to the case of other members of the Solar System, Dr. Stoxey investi¬ 
gates the possibility of the existence of different gases in the atmospheres of the 
other members of the Solar System. Those for which the velocity-ratio falls between 
the two above limits are uncertain as constituents of the corresponding atmospheres, 
and any observations as to their actual existence or non-existence will enable closer 
limits to be fixed for the velocity-ratio. In making these calculations. Dr. Stox'EY 
assumes a temperature of —6G° C. 
Now there are many circumstances which render a furtlier investigation of the 
ocnditions of permanence of planetary atmospheres desirable. It is not obvious that 
inferences drawn from the value of the velocity-ratio in different planets are neces¬ 
sarily conclusive. Thus, for example, the relative velocity v' — u might be the same 
for two planets—one rotating very slowly and having the smaller gravitation poten¬ 
tial, and the other rotating very rapidly and having the greater gravitation potential. 
The above velocity only determines the j^Toportion of molecules at the ]olctnef s equator 
moving in the direction of rotation which would fly off But it is clear that in the 
planet with the smaller potential and slower rotation a greater proportion of molecules 
at other points or moving in other directions woidd leave. For a non-rotating body, 
the velocity-ratio determines the proportion of all the molecules that would fly olf, 
provided that they were moving away from the planet. A planet would get rid of 
its atmospliere much more quickly if the molecules flew off to infinity in all directions 
from all parts of its surface than if they were only whirled off near its equator. 
