PROPERTIES OF MATTER IN THE GASEOUS STATE. 
787 
in the mean component velocities of the molecules arriving from one direction 
we have a very different tiling from the mean component velocities of the gas. How- 
ever, ignoring this caution, the most obvious supposition appears to be that as an 
approximation towards the condition of the molecules as they arrive at A, we may 
suppose them to come from a uniform gas having the density, mean pressure and com¬ 
ponent velocities of the gas at a point distant 5 from A in the direction from which 
they arrive. Such an assumption can be worked out, and the results compared with 
known experimental results. But we need go no farther than the case of gas at equal 
pressure and varying temperature. As applied to this case, our supposition leads to 
the inevitable conclusion that, unless 5 is zero, such a gas must be in motion from the 
colder to the hoter part with a velocity greater than its actual velocity, whatever this 
may be, which is absurd. This brings us back to the caution already mentioned respect¬ 
ing the difference between the component velocities of the group of molecules approach¬ 
ing A, and the component velocities of the gas. Without attempting to investigate 
this difference from first principles, we may follow the obvious course of attributing 
certain arbitrary mean component velocities to the uniform gas as from which the mole¬ 
cules are supposed to arrive at A. 
We now suppose the molecules to arrive at A as from a uniform gas having the 
mean pressure and density at a distance s as before, but having arbitrary component 
velocities U, V, W (where U, V, W are so small that their squares may be neglected). 
This gets over the difficulty in the case mentioned above, for U, Y, W being arbitrary 
can be so determined that the gas resulting from all the groups arriving at A shall 
have any mean velocity, and hence the mean velocity of the gas. It is only one such 
case, however, that we can meet in this way; for having once determined U, Y, W, 
they are no longer arbitrary, and hence if the calculated results fit, to the same degree 
of approximation, all other cases, it must be that the approximation is a true one. 
This test, however, can only be partially applied. As worked out in the subsequent 
sections of this paper, it was found that the supposition explained the phenomena of 
the radiometer and suggested the laws of transpiration and thermal transpiration 
exactly as they were afterwards realised. And in so far as they can be compared 
there is a complete agreement between the theoretical and experimental results. 
Under these circumstances, the course which I first adopted in drawing up this 
paper was to found the theoretical investigation on such an assumption as has just 
been discussed. 
The only other course was to look to first principles for the evidence wanting to 
establish the truth of the assumption. This I had attempted. 
Obviously the first step in this direction was to examine the values of U, Y, W as 
determined by the case of gas at varying temperature and uniform pressure. This 
showed that if a plane be supposed to be moving through the gas with velocities U, V, W, 
then, measured with respect to the moving plane, the aggregate momenta carried from 
opposite sides across the plane are equal. 
