18 
DR. G. H. BRYAN ON THE KINETIC THEORY 
free trajectories, the formula gives a superior limit to the rate at which the pla.net is 
losing its atmosphere. To obtain an estimate of the time which must elapse before 
the loss in question would have an appreciable effect on the amount of the gas 
present in the atmosphere, let us calculate the time in which the loss would represent 
an amount of gas equivalent to the removal of a layer I centim. thick from the 
surface of the planet. If q he measured in centims. per sec., and if L represent the 
critical density-ratio, then the recpiired time 
__ 144 m L 
“ 25 iF q 
Putting this equal to L 'E years, we have 
_ 365-25 X 24 X 60 X 60 X 25 RY/ ^ ^ 
E = -—- —.(27). 
144 a~ ' ' 
Calculating the value of log E from this formula for hydrogen at temperature 100° 
absolute, we have the following results :— 
Hydrogen at - 173° C. = 100’ absolute. 
Log E. 
The Earth .. 
14•40133 
Venus. 
14-35456 
Mars. 
14-35149 
Jupiter. 
13-47129 
Saturn . 
13-27377 
For other gases at other temperatures, the value of log E is easily deduced. 
For E varies as q, which varies as tlie square root of the absolute temperature 
divided by the square root of the molecular weight. Thus for hydrogen at 200° 
absolute, the temperature is doubled, E is increased in the ratio ^'1 ; 1, and log E 
has to be increased by ^ log 2. For oxygen, the molecular weight is 16 times as 
great as for hydrogen, E is decreased in the ratio of 4:1, and log E has to be 
decreased by log 4 ; similarly for other cases. It will be seen, however, that log E 
is, roughly, somewhere about 14 for the majority of gases at ordinary temperatures 
relative to tlie Earth, Venus, or Mars, and rather less (namely, about 13) for the larger 
planets. 
It follows that if the logarithm of the critical density-ratio for a given gas at a 
given temperature relative to a given planet is equal to about 14, the total rate of 
effusion of that gas across the critical surface woidd he equivalent to the removal of 
the amount of that gas present in a layer 1 centim. thick over the surface of the planet 
in a period of time comparable with a year. 
If the logarithm of the critical density-ratio is 20, the corresponding period of time 
would he comparable with a million years; if 26, ivith a billion years, and so on. 
