148-151] 
Atomic Numbers 
163 
Stellar Temperatures. 
150. This last feature indicates that the orientation of our diagrams has 
been accurately arranged, and the only outstanding question is that of scale. 
Equation (149‘3) shews that the minima of ionisation of L, M and A-ring 
electrons ought to occur at temperatures which are approximately in the 
ratio of 
1 • 1 . I 
2- * 3 2 ’' 4 2 ’ 
or 36:16:9. Thus the central temperatures of stars on the extreme right- 
hand edges of the main sequence, the giant branch and the yet further branch 
ought to be in approximately this ratio. Calculated central temperatures seem 
to shew a rather greater range than this theoretical ratio would indicate, but 
the data for almost all stars except possibly those on the main sequence are so 
uncertain that we cannot attach much weight to the apparent discrepancy. 
Apart from this, our calculations have proceeded on the supposition that 
the ionisations of the separate rings of electrons do not overlap, so that one 
is completely ionised before the next begins to be ionised at all. A quite 
simple calculation shews that this is not a wholly legitimate assumption, so 
that inferences based on it are not likely to be fulfilled with high accuracy. 
Atomic Diameters. 
151. If it is granted that the two diagrams have been superposed in a 
legitimate way, one further test remains which the theory must survive if, it 
is to be considered at all tenable. This consists in estimating the actual 
diameters of atoms ionised down to their K, L and ilf-rings, and examining 
whether matter formed of such atoms and compressed to the densities which 
prevail at the centres of the stars would shew deviations from the gas-laws of 
amount adequate to ensue the stability ofithe star. 
This test is as difficult in practice as it is simple in principle. We have 
no means of calculating the effective diameters of these highly ionised atoms, 
and can only attempt an estimate from the known diameters of their outer 
most electronic orbits. According to Bohr’s theory the diameter of the 
hydrogen atom, in which only the K -ring exists, is 1*08 x 10 -8 cms., while the 
diameter of an atom of atomic number N ionised down to its K -ring is 
T08 x 10 ~ 8 /N, and that of the same atom ionised down to its Z-ring is four 
times this or 4*32 x 10~ 6 /N. 
Unfortunately these diameters give only the slightest indication of the 
spaces occupied by the atoms themselves. In liquid or solid helium each atom 
occupies a sphere of diameter 4 x 10 _8 cins., whereas the calculated diameter 
of the outermost ring of electrons in the helium atom is only 0'54 x 10 -8 cms. 
If theory provides no means of estimating even the effective diameter of the 
electrically neutral helium atom to better accuracy than this, it becomes