312 
THE SOURCE OF STELLAR ENERGY 
5 < 
(most massive) stars are in the earliest diffuse stages. The uniformity 
appears to indicate evolutionary progress. But it has always been difficult 
to understand why the smaller mass should evolve more rapidly than the 
greater; every circumstance seems to be against it. Although it does not 
radiate away its source of energy so fast, yet after the same lapse of 
time it has reached higher temperature and density as though it were 
endeavouring to stimulate a failing supply. 
Table 42 exhibits Shajn’s results. In the column “Difference of 
Spectrum” OT represents one-tenth of a type. 
219. The effect of radiation of mass on the orbits of binary stars has 
been discussed by J. H. Jeans and W. M. Smart*. For simplicity, consider 
two equal masses. A star does not receive any kick from its own radiation f ; 
consequently the orbit is the same as that of a star of constant mass under 
the attraction of a centre of force of gradually diminishing strength. The 
equation of the orbit is thus 
d 2 u ix 
_L 7 / =s 1 
dd 2 ^ h 2 
where h is constant and ¡x diminishes with the time according to the same 
law as the masses. Since 7 , 
h 2 = ¡xa (1 — e 2 ), 
where a and e are the elements of the instantaneous ellipse, we have 
Ma (1 — e 2 ) = const. 
The latus rectum of the orbit increases in proportion as the mass diminishes. 
In studying binary stars it is difficult to resist the impression that there 
is an evolution of wide pairs from close pairs. The relations of type, 
separation and eccentricity suggest that the components recede from one 
another in the course of time. But no cause is known which can increase 
the separation to more than a limited extent. Radiation of mass does not 
help very much. The latus rectum of a system with masses now equal to 
the sun cannot have increased more than tenfold unless the masses were 
originally more than 10 times the sun’s mass—a very rare occurrence. 
Since a tenfold increase by no means meets requirements, the discussion 
affords no particular support for the theory of radiation of mass. 
Jeans further points out that the law that the separation of the stars 
increases in proportion as the masses diminish, is roughly true of more 
complicated systems, e.g. clusters. If the stellar system consisted wholly 
of dwarf stars we could argue that its linear dimensions must have ex 
panded, say fivefold, since these were first formed as giants. The presence 
* Monthly Notices, 85, pp. 2, 423. 
f Note that angular momentum is lost by the system. Each component can be 
compared to a ship firing guns equally fore and aft; the velocity is unaffected, but 
momentum is reduced by the loss of the shells.