IONISATION, DIFFUSION, ROTATION 
275 
/ 
Neglecting thermal diffusion we apply (192-6) to a star. Then by (58-3) 
radiation pressure being neglected for the present since we have not taken 
account of it in (192-6). We have been reckoning p in grams but it is 
convenient at this stage to pass to the usual reckoning in terms of the 
hydrogen atom; accordingly 51 replaces E in (192-6). Then 
The ratio s x /s represents the abundance of the element at the place 
considered, since, apart from small changes of p, the number of free 
electrons is proportional to the mass. According to (192-8) very few 
elements will be distributed throughout the star; the heavy elements fall 
to the centre and the lighter elements rise to the surface. For suppose that 
p x — p 0 is no more than 0-05. Since this must refer to a mean element 
we can take Z x + 1 = 20, p = 2; the abundance then varies as T 2 . Even 
this difference is sufficient to give high concentration to the centre. Taking 
the molecular weights given in § 176 with p 0 = 2-3, the abundance varies 
as the following powers of T 
H He 0 A1 Ti Fe Ag Ba Sm Ta Pb 
-6 -5 -8 - 10 -8 -4 — + 24 + 36 + 60 + 70 
193. Radiation pressure greatly modifies these results since it has 
different effects on the different ions. Radiation pressure is allowed for 
by multiplying every mass by its own appropriate j8. The radiation 
pressure on the electrons is much smaller than on the ions; but we need 
not trouble about this as the minute masses of the electrons played only 
an ornamental part in the investigation of § 192, and apart from mathe 
matical elegance might just as well be dropped. Hence (192-8) is modified 
Here 1 — jS x is the ratio of radiation force to gravitation on the ion A x , 
and |S 0 , /3 are appropriately weighted means. There can be little doubt 
that the heavier ions perform the most absorption and experience the 
greatest radiation force, so that jS x diminishes as p x increases. 
This leads to an extraordinary behaviour of the elements. The dis 
tribution given at the end of § 192 refers to stars of very small mass in 
which radiation pressure is unimportant. As the mass increases the 
heavier elements abruptly leave the centre and come to the surface. The 
<f> = 4 iRT/p 
(192-7) 
dz 
Hence by integration 
log S j = 4 (Z x + 1) 
Pi - Po 
P 
log T + const (192-8). 
to 
log T + const (193-1).