A. — MATHEMATICS AND PHYSICS. 37 



familiar hot bodies the second form exists only in insignificant quanti- 

 ties. In the giant stars the two forms are present in more or less equal 

 proportions. That is the new feature of the problem. 



On account of this new aspect of the problem the first attempts to 

 penetrate the interior of a star are now seen to need correction. In 

 saying this we do not depreciate the great importance of the early 

 researches of Lane, Eitter, Emden, and others, which not only pointed 

 the way for us to follow, but achieved conclusions of permanent value. 

 One of the first questions they had to consider was by what means the 

 heat radiated into space was brought up to the surface from the low 

 level where it was stored. They imagined a bodily transfer of the hot 

 material to the isurface by currents of convection, as in our own 

 atmosphere. But actually the problem is, not how the heat can be 

 brought to the surface, but how the heat in the interior can be held 

 back sufficiently — how it can be ban'ed in and the leakage reduced to the 

 comparatively small radiation emitted by the stars. Smaller bodies 

 have to manufacture the radiant heat which they emit, living from 

 hand to mouth; the giant stars merely leak radiant heat from their 

 store. I have put that much too crudely ; but perhaps it suggests the 

 general idea. 



The recognition of ethereal energy necessitates a twofold modifi- 

 cation in the calculations. In the first place, it abolishes the supposed 

 convection currents; and the type of equilibrium is that known as 

 radiative instead of convective. This change was first suggested by 

 R. A. Sampson so long ago as 1894. The detailed theory of radiative 

 equilibrium is particularly associated with K. Schwarzschild, who 

 applied it to the Sun's atmosphere. It is perhaps still uncertain whether 

 it holds strictly for the atmospheric layers, but the arguments for its 

 validity in the interior of a star are far more cogent. Secondly, the 

 outflowing stream of ethereal energy is powerful enough to exert a 

 direct mechanical effect on the equilibrium of a star. It is as though 

 a strong wind were rushing outwards. In fact we may fairly say that 

 the stream of radiant energy is a. wind ; for though ether waves are not 

 usually classed as material, tHey have the chief mechanical properties 

 of matter, viz. mass and momentum. This wind distends the star 

 and relieves the pressure on the inner parts. The pressure on the gas 

 in the interior is not the full weight of the superincumbent columns, 

 because that weight is partially borne by the force of the escaping 

 ether waves beating their way out. This force of radiation-pressure, 

 as it is called, makes an important difference in the formulation of the 

 conditions for equilibrium of a star. 



Having revised the theoretical investigations in accordance with 

 these considerations,^ we are in a position to deduce some definite 

 numerical results. On the observational side we have fairly satis- 

 factory knowledge of the masses and densities of the stai*s and of the 

 total radiation emitted by them ; this knowledge is partly individiaal and 

 partly statistical. The theoretical analysis connects these observational 

 data on the one hand with the physical properties of the material inside 



- Astrophysical Journal, vol. 48, p. 205. 



