IONISATION, DIFFUSION, ROTATION 
279 
Suppose that initially the element was uniformly distributed in the star 
We see from the left-hand side that for an element diffusing outwards 
t is the time in which the interior would be completely evacuated of atoms 
of the kind Z x if the initial rate of evacuation continued. 
For an element diffusing inwards the time t in which the exterior part 
would be completely drained at the initial rate of evacuation is given 
We have %{/G = 1-24.10 15 ; T ¡p is a minimum at the centre and cannot 
be much less than 10 7 ; D is of order unity; 477 (Z 1 + 1) (p x p x — p o Po) 
might perhaps in some cases amount to 300. Hence t is of order 10 20 
seconds or 10 13 years*. 
For an example we take in Capella the region containing the outermost 
6-6 per cent, of the mass and calculate how fast this is losing lead. By § 13 
T = 1-9.10 6 , p = -0012, M r /{M - M r ) = 14. 
We can take Z x + 1 = 70, p x — p 0 — 0-6, D = 0-3. 
For the moment we neglect radiation pressure which introduces the /3 
factors. Substituting in (196-5) 
The drain will become slower as it proceeds. 
If radiation pressure is taken into account p x j3 x — p o p o is less, and the 
drain is slower; or more probably it is reversed in Capella—the lead coming 
to the surface. 
* The very slow rate of diffusion was pointed out by Chapman (Monthly Notices, 
82, p. 292, 1922). His numerical illustrations treat the diffusion of hydrogen in 
detail. 
so that 
Then 
= 47) (Z, + 1) I log T (196-3) 
= 4 D (Z l + 1) 
by (193-1), the ratio of s x /s to p x /p being a constant. 
To interpret (196-3) we substitute 
Hence 
477r 2 Sil/ 1 
Mrpi/p 
4ttD (Z x + 1) (p 1 ß 1 - p 0 ß 0 ) Gp 
...(196-4) 
= 1 It. 
similarly by x ^ ^ ± ,> ( ^ Gp 
(196-5). 
t 
MT 
M - M r 
t — 9.10 20 secs. = 3.10 13 years. 
f