314 Sroney— Of Atmospheres upon Planets and Satellites. 
Let us now turn to what happens in gas. By Clausius’s formula, p. 310, 
; : [ey 
w (the velocity of mean square in a gas) = (111°4) | : m. / sec., 
which, at 66° below zero (which we regard as the temperature at station L’) gives 
w = (111-4) |e: 
P 
= 1603 /Jp m./sec., (12) 
where w means the velocity of mean square in a gas at the temperature — 66°C. 
If in this we put p = 1, we find 
w = 1603 m./ sec. in hydrogen. 
This is nearly a mile a second. Similarly putting p = 2, we find 
w = 1133 m./sec., mm helium, 
which is somewhat more than a kilometre per second. And, finally, if we put 
p = 9, we find 
w = 534 m./sec., in the vapour of water, 
which is somewhat more than half a kilometre per second. 
Now, we found above that, in order that any gas may cease to be imprisoned 
by the Earth, its molecules must now and then be able to attain at least a speed of 
10-5 kilometres per second: see equation 11. Whenever this happens to a molecule 
favourably circumstanced it escapes. Hence, since hydrogen succeeds in leaking 
away from the Earth, its molecules must in sufficient numbers attain this speed, 
which is 6°55 times the velocity of mean square in that gas at a temperature 66° 
below zero; and since helium can escape, its molecules must sufficiently often 
reach a speed equal to or exceeding 9°27 times what we have found to be the 
velocity of mean square in helium at a temperature of — 66°C. 
On the other hand, in order that a molecule of water may escape from the 
Earth, it has to get up a speed of 19°66, nearly twenty times the velocity of mean 
square in that vapour at the above temperature: and the fact that water does not 
drain away from the Earth in sensible quantities shows that this seldom happens. 
We are now ina position to make a very important deduction in Molecular 
Physics from these facts, which is that i a gas a molecular speed of 9°27 times the 
velocity of mean square is reached sufficiently often to have a marked effect upon the 
progress of events in nature; while on the other hand a molecular speed of 20 times 
the velocity of mean square is an event which occurs so seldom that it exercises 
no appreciable influence over the cosmical phenomena which we have been con- 
sidering. We must remember, however, that there are other events in nature— 
