278 
IONISATION, DIFFUSION, ROTATION 
equivalent to the termination of a free path. For two equal ions the radius 
of the apparent target giving a 90° deflection is found to be 
which in different parts of the star, and for stars of the same mass, varies 
as T~^. Hence the coefficient of diffusion is not much different in different 
parts of the star. For iron (with two K electrons) at the centre of Capella 
the numerical results are 
Results for other elements will be of the same order of magnitude. 
It will be seen from a consideration of physical dimensions that it will 
take an extremely long time to establish a steady state when D is of order 
unity in c.G.S. units. For the time of relaxation of an unevenness of 
distribution of wave-length x centimetres will be of order x 2 /D seconds 
(this combination having the dimensions of time). To reach a steady state 
it is necessary to fill up unevennesses of extent comparable to the radius 
of the star, say x = 10 11 cm. ; the time required is of order 10 22 secs., or 
greater than the largest estimates of the life of a star. 
This is scarcely sufficient to prove that no important stratification of 
the elements occurs in reasonable time; for many elements the steady 
state involves such an extreme concentration that a relatively small 
advance towards it would be significant. 196 
196. When the distribution in a star has not reached a steady state 
there will be a net flow of ions of one kind through a surface perpendicular 
to r. The coefficient of diffusion D signifies that the mass of molecules of 
kind 1 passing in this way through 1 sq. cm. per sec. is 
where the bracketed expression is the difference between the density 
gradient actually present and the density gradient for a steady state*. 
The formula is equivalent to 
* The steady state is supposed here to be attained by changing dp x \dr without 
changing at the point considered. 
Z 2 e 2 Z 2 e 2 
a 4 V 2 Ah Ï2RT ' 
Hence the mean free path is 
(195-2). 
It follows that 
À V oc /xT^/p 
(195-3), 
A = 1-66.10- 7 cm., 
V = 5-20.10 6 cm./sec. 
Hence 
D = 0-29 cm. 2 /sec. 
(195-4). 
(196-2).