188 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
The variation of relative density in the atmosphere due to the temperature 
gradient (which is about 7° C. per kilometre) is still smaller, and in the opposite 
direction. Thus, taking v x : v 2 for oxygen and nitrogen as 1 : 3 roughly, and T as 
280° C. approximately, the equation giving the variation of v 1 : v 2 near the earth’s 
surface (independently of the effect of the difference in mass) is 
d_U\ _ _ 1_ , J_3T 
dx\J~ X 2 3 T T0x' 
0'008, X 2 = f, while if we adopt one kilometre as the unit of 
0T v 
280 and — as —7, the change in — per unit length is found 
ox v 2 
—. 0'008 . 7 = 0-00035, 
9 280 
or per cent, per kilometre. This variation is of one-sixth the magnitude of the 
gravity variation, which it tends to neutralise, since the heavier gas tends to rise 
owing to the temperature gradient. These changes are masked, however, by the 
effects of convection currents ; it has been found that the proportions of nitrogen and 
oxygen in our atmosphere are the same for all altitudes up to 10 kilometres, 
and, indeed, above this height, right into the isothermal layer or stratosphere. 
As another instance of the phenomenon of a concentration gradient due to 
temperature, we may consider the case of a mixture of equal parts (by volume) of 
oxygen and hydrogen, or argon and helium, placed between two plates which are 
maintained at freezing and boiling points respectively. Neglecting the small 
variation in vjv 2 , as far as the integration with respect to x is concerned, in the 
equation 
A/fi\ _ __L ic a Io g T 
a x\J x 2 2 T ax ’ 
we may conclude that, independently of the distance between the plates,* the change 
in the value of vjvo is 
-4 .0-130. log, f-ff- - 0'161, 
where we have taken k T = 0'130 (cf. Table VI.), which is approximately the case 
either for Ar-He or O-H. Thus near the hot plate there will be approximately 
48 per cent, of the heavier gas to 52 per cent, of the lighter, and vice versd near 
the cool plate. This remarkable result is independent of the pressure of the gas, 
assuming this to be uniform between the two plates, as will be the case in the 
* To the order of accuracy according to which k T may be regarded as constant. 
By Table VI., Jc T = 
length, writing T = 
to be 
