G. Jounstone Stoney on the Penetration of Heat across Layers of Gas. 15 
in which G and P are constants. This furnishes by integration an equation of the 
form— 
o—oomina (@; Cle) 5 a (By 
which represents the law by which the temperature must change across the layer. 
What we learn from this investigation is, that besides the uniform distribution of 
a gas with the same temperature everywhere, there is one other permanent 
distribution possible (except at the limits), and perhaps only one; that in it there 
is, for each gas and at each tension, a definite gradient of temperature, with its 
accompanying equally definite gradient of density in the opposite direction. 
These results might have been arrived at in another way, viz., by a consideration 
of the effects of the inter-molecular encounters. 
Another case in which the three conditions will be fulfilled is the familiar one of 
a uniform medium, in which case— 
do 
pan 00h 9—const, (7): 
But if there is a transition from one of these solutions to the other, as there must 
be where the Crookes’s layer is in contact with the rest of the gas, there will be 
an interval of compromise, in which the three conditions are not strictly fulfilled. 
Similarly, they cannot be fulfilled where the Crookes’s layer adjoins the hot body 
A. Hence there must, in the cases that really arise, be some escape of heat, which 
may be small, but cannot vanish, because discontinuity is impossible, since the 
length of the mean path of a molecule between its encounters with other molecules 
is finite. Hence, also, the values of the temperature at different depths within the 
Crookes’s layer will differ by small amounts from those assigned to it by equation 
(8). It will appear, however, from the next paragraph, that the rate of cooling 
arising from these imperfections will be very slow,* and although the heat that 
passes would doubtless accumulate and ultimately become considerable if there 
were no gravity, its presence will be inappreciable in most of the experiments we 
can make, where the portion of gas in which the Crookes’s layer is formed is being 
constantly renewed by convection currents. 
5. We have hitherto supposed that the atmosphere of gas was of sufficient 
extent to allow the whole of the Crookes’s layer to come into existence ; but we 
shall have entirely new conditions if a body Bat temperature 0,, which for simplicity 
we may suppose to have a large flat surface, is placed parallel to A at a distance less 
than the thickness of an unrestricted Crookes’s layer. In this case a compressed + 
Crookes’s layer will come into existence, in which, as explained in §. 16 of my 
former papers, the density of the gas must be everywhere greater than at the same 
distances from A in the complete Crookes’s layer, to preserve the lateral pressure 
* For, the Crookes’s layer being in this case almost complete, the values of AQ, and A@, (see §. 5) will 
be exceedingly small. 
_ +2.¢., a Crookes’s layer confined between: the heater and cooler, against which the layer of gas expends 
its Crookes’s stress. In withstanding this stress the heater and cooler compress the layer. 
iD) 
