93-95] Atomic Weight of Stellar Matter 105 
Thus our assumed value of jjl = 2 5 is too small to be consistent with the 
calculated values of N 2 /A. Before we can accept these values we must amend 
our model by increasing the value of /a very substantially. The values of 
N*/A must now be recalculated for this increased value of /a and since, as we 
have already seen, these values vary approximately as ft 8 ' 8 , the new values of 
N 2 ¡A will be far greater than the old. This increase in the values of N 3 /A 
demands a still further increase in /a and so on indefinitely. We know nothing 
about the relation between /a, N and A for our hypothetical heavy atoms, so 
that it is impossible to say whether or not the race will ever stop; it may be 
it is impossible to find values of N 2 ¡A and /a which are consistent with one 
another and with the observed stopping-power of the stars for X-radiation on 
the model we have under discussion. What is abundantly clear is that if ever 
the race does stop, we shall by then have reached values of N 2 /A far higher 
than those shewn in Table XIII, and shall be contemplating atoms of which 
the atomic weight is many thousands. 
While no absolutely convincing reason can be assigned why such atoms 
should not exist in the stars, it will be generally felt that it is improbable that 
they do. If their existence is found to be a necessary consequence of our 
having assumed a special model for stellar structure, then it behoves us to 
look for other models which entail less improbable consequences. 
95. Eddington, who found himself confronted with a similar difficulty in 
discussing his model of a star (§ 76), examined whether the difficulty could 
be avoided by concentrating the star’s generation of energy near its centre*. 
If this is done, all the radiation has to pass through the whole radius of the 
star; on the model we have just been discussing, in which energy is generated 
uniformly throughout the star’s interior, the radiation has, on the average, 
only to pass through about half of the star’s radius before emerging into space. 
Eddington’s plan, in effect, sets twice as many atoms at work to stop the 
radiation, so that each atom need only have half the stopping power it would 
otherwise require. 
His actual calculation shews that in the extreme case in which the whole 
generation of energy is localised at the centre of the star, the observed facts 
can be explained by assuming a coefficient of opacity less by a factor of about 
2*5 than would otherwise be required. Some later calculations of my ownf 
confirm the general accuracy of this result, but apart from such detailed 
calculations it is in any case obvious, on the general grounds explained above, 
that the factor of reduction cannot be very far from 2. 
Thus if we change our model and suppose its whole generation of energy 
to be localised at its centre, the values of N*fA shewn in Table XIII may be 
divided by a factor of from 2 to 2 - 5. But when this is done the values of 
N*/A are still of the order of 150, and such values correspond to atomic 
* M.N. lxxxv. (1925), p. 408. 
t M.N. lxxxvi. (1926), p. 561.