GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 
249 
Appendix. 
(Added May, 1879.) 
In the paper as sent in to the Royal Society, I made no attempt to express the 
conditions which must be satisfied by a gas in contact with a solid body, for 1 thought 
it very unlikely that any equations I could write down would be a satisfactory repre¬ 
sentation of the actual conditions, especially as it is almost certain that the stratum of 
gas nearest to a solid body is in a very different condition from the rest of the gas. 
One of the referees, however, pointed out that it was desirable to make the attempt, 
and indicated several hypothetical forms of surfaces which might be tried. I have 
therefore added the following calculations, which are carried to the same degree of 
approximation as those for the interior of the gas. 
It will be seen that the equations I have arrived at express both the fact that 
the gas may slide over the surface with a finite velocity, the previous investigations 
of which have been already mentioned p' and the fact that this velocity and the corres¬ 
ponding tangential stress are affected by inequalities of temperature at the surface of 
the solid, which give rise to a force tending to make the gas slide along the surface 
from colder to hotter places. 
This phenomenon, to which Professor Osborne Reynolds has given the name of 
Thermal Transpiration, was discovered entirely by him. He was the first to point out 
that a phenomenon of this kind was a necessary consequence of the Kinetic Theory of 
Gases, and he also subjected certain actual phenomena, of a somewhat different kind, 
indeed, to measurement, and reduced his measurements by a method admirably 
adapted to throw light on the relations between gases and solids. 
It was not till after I had read Professor Reynolds’ paper that I began to recon¬ 
sider the surface conditions of a gas, so that what I have done is simply to extend to 
the surface phenomena the method which I think most suitable for treating the interior 
of the gas. I think that this method is, in some respects, better than that adopted 
by Professor Reynolds, while I admit that his method is sufficient to establish the 
existence of the phenomena, though not to afford an estimate of their amount. 
The method which I have adopted throughout is a purely statistical one. It con¬ 
siders the mean values of certain functions of the velocities within a given element of 
the medium, but it never attempts to trace the motion of a molecule, not even so far 
as to estimate the length of its mean path. Hence all the equations are expressed in 
the forms of the differential calculus, in which the phenomena at a given place are 
connected with the space variations of certain quantities at that place, but in which 
no quantity appears which explicitly involves the condition of things at a finite 
distance from that place. 
The particular functions of the velocities which are here considered are those of one, 
two, and three dimensions. These are sufficient to determine approximately the prin- 
* Sect. 12 of introduction. 
2 K 
MDCCCLXXJ X. 
