OF PLANETARY ATiyrOSPIIFRES. 
17 
100° absolute. 
200° absolute. 
.300° absolute. 
Terrestrial helium . 
101-90 
50-95 
33-97 
Water on i\Iars . 
94-22 
47-11 
31-41 
The values of the logarithm of the critical density-ratio at 200° absolute—a point 
sufficiently near the temperature — 66°C. assumed in Dr, Johnstonj] Stoney’s paper— 
appear far too great to be consistent with any appreciable loss taking place from the 
planets at those temperatures. Even at 300° absolute or 27° C,, the figures repre¬ 
sent averages of 100 and 30,000 molecules per cub, kilom. at the critical surface for 
every 10^^ molecules per cub. centim. at the surface of the planet. While the figures 
show that the conditions for water on Mars are less favourable tlian for terrestrial 
helium, they appear distinctly favourable to both these elements at the temperatures 
ordinarily assumed for planetary atmospheres. To examine this point more fully it is 
important to calculate limits for the rate at which a planet would lose its atmosphere 
for the supposed values of the critical density-ratio, and for the time in which this 
loss would become appreciable. 
12. Rate of Flow across Critical Surface. 
The total rate of eftusion across the closed portion of the critical surface may he 
calculated from the fornnda 
i-zpS.■ . . . ( 26 ). 
where q is tlie mean translational speed of the molecules, p the density, and S the area 
of the critical surface. 
Without entering into the matliematical prol)lem of the quadrature of the surface 
In question l)y actual Integration, Its area can be found sufficiently closely for our 
purpose by noticing that the closed portion In question consists of two caps cutting 
their common base at 60°, and whose lieights are f of the radius of the base. Now, 
if we take two spherical caps the radius of whose common base is o, and whose 
lieights are each | «, the area of the closed surface formed by them = -^-Tra®; while 
if we take two spherical caps on the same base and cutting that base at an angle of 
60° the area = -^ira^. As the closed part of the critical surface lies between the first 
and second pair of spherical caps, we know that its superficial ai’ea is -g-Tra^, correct 
to within ffi 4 per cent., and this value we shall adopt. 
For the Eartli a = 6'625 R, where 11 = Earth’s radius; 
a — 4'225 X 10° centims. 
If we Imagine all the molecules which cross the surface in question to leave tlie 
planet’s atmosphere, and leave out of count all those which return after describing 
VOL, CXCVI. —A. D 
