IONISATION, DIFFUSION, ROTATION 
277 
Thermal diffusion was predicted theoretically by S. Chapman and 
F. Enskog, and the phenomenon was satisfactorily verified experimentally 
by F. W. Footson*. Chapman has also considered its influence on the 
stratification of the elements in the starsf. He concluded that it was of minor 
importance compared with pressure diffusion; that it acted in the opposite 
direction, but could not reduce the general order of magnitude of the 
stratification. In reviewing Chapman’s conclusions in the light of recent 
knowledge I believe we must take the thermal diffusion to be in the same 
direction as pressure diffusion, i.e. tending to bring the heavy elements to 
the centre of the star. In Footson’s experiments the lighter gas became 
concentrated in the hotter region as was predicted for molecules resembling 
elastic spheres; but the theory indicates that thermal diffusion diminishes 
for “softer” models, and vanishes for a law of force varying as the inverse 
fifth power of the distance. Apparently it changes sign for a still lower 
force-index, so that with the inverse-square law of force between the 
atoms the concentration of the heavier atoms would be towards the hot 
regions. Evidently we have to do with the inverse-square law of repulsion 
between the charged ions in the interior of a star; owing to this repulsion 
the ions do not, as a rule, come to close quarters so that no other forces 
are invoked. It appears then that the effect of the temperature gradient 
will be to accentuate the tendency of heavy atoms to seek the centre of 
the star and the lighter atoms to go to the outsideJ. We may, however, 
probably accept Chapman’s judgment that the effect of thermal diffusion 
is unimportant and will not alter the order of magnitude of the con 
centration already indicated by other causes of diffusion. 
Rate of Diffusion of the Elements. 
195. According to the theory of gases the coefficient of diffusion of 
one gas into another is approximately § 
D = |AF (195-1), 
where A is the mean free path and V the velocity of the molecules. The 
average for the two gases is to be taken weighted in inverse ratio to the 
number of molecules of each. 
We shall attempt to estimate the order of magnitude of D in the stars. 
The ions whose diffusion we are studying will be deflected mainly by 
encounters with other ions, the deflections due to encounters with electrons 
being negligible. We may estimate that a deflection of 90° is a fair 
* Phil. Mag. March, 1917. f Monthly Notices, 77, p. 539 (1917). 
% Prof. Chapman confirms this inference. 
§ See for instance Jeans, Dynamical Theory of Gases, 2nd Ed., p. 326, equation 
(869).