GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
251 
must of course be from the surface, but the probability of any particular magnitude 
and direction of the velocity will be the same as in a gas at rest with respect to the 
surface. 
The distribution of velocity among the molecules which are leaving the surface will 
therefore be the same as if, instead of the solid, there were a portion of gas at rest, 
having the temperature of the solid, and a density such that the number of molecules 
which pass from it through the surface in a given time is equal to the number of mole¬ 
cules of the real gas outside which strike the surface. 
To distinguish the molecules, which, after being entangled in the stratum of spheres, 
afterwards return into the surrounding gas, we shall call them, collectively, the 
absorbed and evaporated gas. 
If the spheres are so near together that a considerable part of the surface of each 
sphere of the outer layer is shielded from the direct impact of the incident molecules 
by the spheres which lie next to it, then if we call that point of each sphere which 
lies furthest from the solid the pole of the sphere, a greater proportion of molecules 
will strike any one of the outer layer of spheres near its pole than near its equator, 
and the greater the obliquity of incidence of the molecule, the greater will be the 
probability that it will strike a sphere near its pole. 
The direction of the rebounding molecule will no longer be with equal probability in 
all directions, but there will be a greater probability of the tangential part of its 
velocity being in the direction of the motion before impact, and of its normal part 
being opposite to the normal part before impact. 
The condition of the molecules which leave the surface will therefore be intermediate 
between that of evaporated gas and that of reflected gas, approaching most nearly to 
evaporated gas at normal incidence and most nearly to reflected gas at grazing 
incidence. 
If the spheres, instead of being hard elastic bodies, are supposed to act on the mole¬ 
cules at finite, though small distances, and if they are so close together that their 
spheres of action intersect, then the gas which leaves the surface will be still more like 
reflected gas, and less like evaporated gas. 
We might also consider a surface on which there are a great number of minute 
asperities of any given form, but since in this case there is considerable difficulty 
in calculating the effect when the direction of rebound from the first impact is such as 
to lead to a second or third impact, I have preferred to treat the surface as some¬ 
thing intermediate between a perfectly reflecting and a perfectly absorbing surface, 
and, in particular, to suppose that of every unit of area a portion f absorbs all the 
incident molecules, and afterwards allows them to evaporate with velocities corres¬ 
ponding to those in still gas at the temperature of the solid, while a portion 1 —f 
perfectly reflects all the molecules incident upon it. 
We shall begin by supposing that the surface is the plane y z, and that the gas is 
on that side of it for which x is positive. 
2 K 2 
