14 G,. Jonystons Sronry on the Penetration of Heat across Layers of Gas. 
fully formed. The Crookes’s layer in this case will obviously consist of a flat 
stratum of the gas in contact with the hot surface of A: and within this stratum the 
temperature will gradually decrease from within outwards, from 6,, the temperature 
of A, down to 6,, the temperature of the surrounding gas. This gradual falling off 
of the temperature implies a corresponding gradual augmentation of the density, 
since we have supposed the gas to be everywhere subjected to the same pressure. 
If the gas could* admit of the formation of a complete Crookes’s layer, then we 
know from the familiar experiments which show gases to be bad conductors of 
heat, that, after the brief interval of adjustment, a permanent state would ensue, in 
which there would be no further change of density, or motion of heat except by 
radiation. Accordingly, if an isothermal surface be now drawn within the layer 
(which, in the simple case we have supposed, will be a plane parallel to A), there 
will fly the same number of molecules per second in both directions, across an 
element 6S of this surface, the momentum of the two processions which pass 
through 6S in a second will be the same, and their kinetic energy also will be the 
same. Their number will be the same, for otherwise the density would be still 
undergoing change, and we have supposed that the period of adjustment is over ; 
their momentum will be the same, because the pressure is everywhere constant ; 
and their kinetic energy is the same because there is no transfer of heat across S. 
4. Hence, the change of temperature and density in passing along 6x, an 
element of the normal to 6S, must be such as to secure these three conditions. 
In investigating the law of this variation, we have to take into account— 
P, the pressure everywhere through the gas ; 
g, the temperature measured from absolute zero, on the isothermal surface S ; 
p, the density of the gas on the isothermal surface S: 
x, the distance of S from A; and 
G, a quantity which changes from one gas to another, but is almost constant 
in each gas, within a wide range of temperature and pressure. 
When the gas and its tension are given, G and P are constants ; and » is a known 
function. of G, P, and @; hence only two of the foregoing quantities are independent, 
d: 
suppose @ and «; instead of which we may use “4 and 6. It is easy to see, by 
taking particular instances, that = and 0 will remain independent of one another, 
if only two of the conditions in §. 3 need to be fulfilled, but if all three have to be 
fulfilled, we find by experiment, that a definite Crookes’s layer is formed, and that, 
dz . ae 
therefore, n each gas and at each pressure 7 is a definite function of 6. In 
other words— 
da 
aaah (0) GaP ys. ae Pana ()) 
* See next page, the last paragraph of section 4. 
