IONISATION, DIFFUSION, ROTATION 
255 
178. With these results before us we can consider two questions which 
have been reserved from our earlier work for discussion here. 
(1) How far are we justified in adopting a constant molecular weight 
for all stars ? 
(2) Is the opacity appreciably reduced by the “guillotine” (§ 160) so 
as to fall below that given by the approximate law k oc p/T used in our 
discussions ? 
The molecular weight depends on the degree of ionisation and therefore 
mainly on A 1} although some attention should be paid to i ¡s x \RT which 
determines the cleanness of the ionisation. We are chiefly interested in 
those stars for which a comparison of theory and observation has been 
made in Pig. 2, so that the more extreme values of in Table 31 do not 
concern us. For all comparison stars A x falls within the range 0-8-4*0 A, 
whilst the most accurate comparisons are covered by the range 1-3 A. 
For elements of atomic number about 50-60 the L ionisation falls in 
this range and, for example, iodine (Z = 53, A — 127) might perhaps lose 
the eight L electrons in passing from Capella to Sirius, thereby reducing 
its molecular weight from 2*89 to 2*44. A long series of elements below 
50 will be unaffected, and then we come to a few elements in the neighbour 
hood of titanium {Z = 22, A = 48) which lose their two K electrons; the 
molecular weight for titanium will change from 2*28 to 2*08 between Capella 
and Sirius. The lighter elements will be fully ionised in both stars. Since 
the change amounts to 0*2-0*4 for a few of the elements only, and is much 
smaller for the majority, it seems clear that the difference of molecular 
weight between the various stars used in our comparisons is unlikely to 
exceed 0*1. 
The effect of a change A/x in the adopted molecular weight on the pre 
dicted bolometric magnitude m of a star can be calculated from (84*4) and 
(99*2). We find 
— Am = 
9/3 + 8 
log! 
A/x 
4 — 3/3 — /x 
Table 32 gives the increase of brightness (— Am) for an increase of 0*1 in 
the molecular weight— 
Table 32. 
Effect of Increase of 0*1 in the Molecular Weight . 
1-/3 
Mass 
- Am 
1-/8 
Mass 
— Am 
0-0 
0*0 
m 
0*35 
0*3 
4*5 
m 
0*16 
0*05 
1*0 
0*30 
0*4 
7*1 
0*13 
0*1 
1*6 
0*25 
0*6 
19*6 
0*09 
0*2 
2-8 
0*20 
0-8 
90*6 
0*06