Stonry— Of Atmospheres upon Planets and Satellites. 315 
in Chemistry, and especially in Biology—which may be, and probably are, 
determined by conditions that occur far more rarely. 
The separation of the swiftest moving molecules from the boundary of our 
atmosphere is of necessity accompanied by a lowering pro danto of the temperature 
of the atmosphere left behind. It is one of the many operations carried on by 
nature to which the Second Law of Thermodynamics does not apply. We must 
remember that this law is only a law of molecular averages, and therefore is not a 
law of nature where, as in this case, nature separates one class of molecules (those 
moving fastest) from the rest. 
Cuaprter V.—Lxtension of the Inquiry to other Bodies. 
In order to extend our inquiry to the atmospheres upon other bodies of the 
Solar system, we have to determine the potential of gravitation upon them. 
We can do this where 7, the radius of the new body B, and m/M the ratio of 
its mass to the mass of the Earth, are known. For then 
k (the potential at the surface of B) = - 
m R+h M 
eee: Son moors 13 
M r RE (ce) 
of which the last factor is the A’ which is given in a numerical form in equation (9) 
Combining this with the dynamical equation (see p. 311) 
Uy lei Sei) (14) 
we can calculate v, which would be the minimum velocity of escape from B, if B 
were at rest. In general B rotates, and then the minimum velocity of escape is 
y= oy, (15) 
where uw, the velocity at the equator of B due to its rotation, is easily found, if we 
know from observation the period of rotation. 
Having calculated vo’, we can determine what density a gas must have to 
escape from B with the same facility with which helium leaves the Earth. For 
this purpose, let w, be its velocity of mean square. Then, in accordance with 
what is stated on p. 314, w, may be as large as 
U 
w= aon (16) 
where w, and v’ are to be expressed in metres per second: and then Clausius’s 
equation, viz. # 
w, = aus |? m. /sec., (17) 
enables us to calculate p,/7Z, 7.e. the density of that gas which, at a specified 
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