310 Stonry—Of Atmospheres upon Planets and Satellites. 
Cuapter Il.—Jnterpretation by the Kinetic Theory. 
In order to make these facts the starting-point for fresh advances, we must study 
their precise physical meaning when interpreted by the kinetic theory of gas. 
The velocity whose square is the mean of the squares of the velocities of the 
individual molecules of a gas—‘‘ the velocity of mean square” as it has been 
called—was determined* by Clausius to be 
AE 
wie 185 ory metres per second, 
where w is the velocity of mean square, 7’ the absolute temperature of the gas 
measured in Centigrade degrees, and o its specific gravity compared with air. 
We shall find it convenient to use p instead of o, where p is the density of the gas 
compared with hydrogen. Accordingly o = p/ 14:4, whereby Clausius’s formula 
becomes ae eA Vi (1) 
= 4) |= 
(uid), 
in metres per second. This formula gives a velocity of 1603 metres, nearly a 
mile a second as the “ velocity of mean square” in hydrogen at an absolute 
temperature of 207°, ze. at a temperature which is 66°C. below freezing point. 
This is the “ velocity of mean square” of the molecules of hydrogen in an 
atmosphere consisting either wholly or partly of hydrogen, at any situation in 
which the gas is at that low temperature. Similarly by putting p = 2 and 7'= 207, 
we find the velocity of mean square for helium at the same low temperature. It 
is about 1133 metres per second. ‘The actual velocities of the molecules are, of 
course, some of them considerably more and others considerably less than this 
mean, even if the hydrogen or helium be unmixed with other gases; and the 
divergences of some of the individual velocities from the mean will become 
exaggerated when the encounters to which the molecules of these lighter gases 
are subjected are sometimes with molecules many times more massive, and which 
may, when the encounter takes place, be moving with more than their average 
speed, as must often happen in our atmosphere. Under these circumstances we 
should be prepared to find that a velocity several times the foregoing mean is not 
unfrequently reached; and the evidence (see Chapter IV.) goes to show that a 
velocity which is between nine and ten times the velocity of mean square, a velocity which 
is able to carry molecules of either hydrogen or helium away from the Earth, is 
sufficiently often attained to make the escape of gas effectual. 
We are now in a position to aim at making our results so definite that they 
may be extended to other bodies in the Solar system. 
* Philosophical Magazine, vol. xtv. (1857), p. 124. 
