OF PLANETARY ATMOSPHERES. 
15 
ixlim . the term due to centrifugal force at the Earth’s surface = '1130. 
Call this term B. 
IxhmV^ the term due to the total potential at the critical surface = 14'880. 
Call this term C. 
Tlie logarithm of the critical density ratio is equal to A + B — C. 
Hence we obtain the following results :— 
Table of Logarithms of the Critical Density-ratio for Hydrogen relative to 
the Earth. 
Absolute temp. 
Centigrade temp. 
Log. crit. dens, ratio. 
100° 
-173° 
50-951 
200 
- 73 
25-475 
300 
+ 27 
16-987 
To make the meaning of these figures perfectly clear we notice, as remarked by Dr. 
Stoney, that at the bottom of our atmosphere the number of molecules in each cub. 
centini. of air is about 10~b Supposing now that the earth was invested with an 
atmosphere of hydrogen containing 10^^ molecules per cub. centim. at the surface 
of the earth. Then at a temperature of 27° C. there would he i(j;n-iG-087^ 
roughly 10"*^ or 10,000 molecules in every cul), centim. at the critical surface; at 
— 73° C. there would be on an average one molecule to every or roughly 
lOLUo Qj. 30,000 cub. centims. at the critical surface; at —173° there would only be 
one molecule per or 10®*^ cub. centims. at the critical surface. 
In the first case a considerable escape of gas would take place thinugh molecules 
passing beyond the critical surface. In the second case it will be noticed that there 
would be about 33 molecules per culjic metre up at the critical surface, so that 
molecules would escape fairly frequently, though the rate of loss of the atmosphere 
Avould of course be very slow. In interpreting the third case it will be convenient to 
observe that the equatorial radius of the critical surface is about 4'225 X 10^ centims., 
and the volume of a sphere having this radius, and therefore enclosing the whole of 
the Earth’s atmosjDhere, is about 3'162 X 10"*^ cub. centims. The calculated result 
for the frequency of distribution at the critical surface represents an average of about 
one-third of a molecule per volume equal to this vast enclosing sphere. 
11. Calculation Jor other Planets. 
In performing the calculations of the logarithm of the critical density-ratio for 
other planets, the data for the Earth may be taken as a starting-point, it being 
observed (as may be easily proved) that 
