Sronry—Of Atmospheres upon Planets and Satellites. 327 
at the freezing temperature. Itis got by putting 7’=273 and p=1 into Clausius’s 
formula, page 810. We thus find w = 1:841 km./sec. This multiplied by 9°27 
(see page 314) gives us a velocity v, which the molecules of hydrogen could, at 
this temperature, get up sufficiently frequently, for the purposes of escape. And 
if multiplied by 18 (see page 320), it furnishes a velocity 7, which hydrogen is 
unable to get up sufficiently frequently for effective escape. We thus find 
®, = 17 kan. / sec. v, = 33:14 km. /sec. 
We have next to find how large the Sun should be in order that one or other 
of these velocities should be that which is just sufficient for the escape of a 
molecule. For that, 7, and r, being the corresponding radii, the potentials must 
amount to 9 ; 2 
ee ad se (SEMA) axing 
(ey) o Up) 2 
But at the distance of the Earth we found m/r = 900. Therefore 
ie SOOO) 2) ye UE es 
ayaa reaNegns a 
That is, the surface of the Sun would need to have been about 6} times farther 
from the Sun than the Earth now is, in order that hydrogen at 0°C. should 
escape from it as freely as helium does from the Earth at — 66°C. And it 
would need to have been 1:64 times farther than the Earth to imprison the 
hydrogen as firmly as water is held by Venus. 
Hence, the greatest size which the Sun can have had since it became a sphere, 
consistently with its not allowing hydrogen at 0° C. to escape, is an immense 
globe extending to some situation intermediate between the orbits of Mars and 
Jupiter. From some such vast size it may have been ever since slowly contracting. 
Cuaprer XV.—Of Motions in a Gas. 
In carrying on an inquiry such as that of the present Memoir, we should keep 
in mind that the encounters between molecules have not the same effect on their 
subsequent motions as mere collisions between elastic or partially elastic solids 
would have. Let us, for simplicity, picture to ourselves two molecules which 
approach one another along a straight line, and after an encounter, which is in 
fact a complex struggle, recede from one another along the same line. 
If they were solid particles with elasticity e, the equations of their motion 
would be 
MU, + My = MV, + MyWV2, 
Wh — Uy + € (¥; — 2%) ul) 
where 2,2, are the velocities before, and wu, the velocities after, the collision, 
