September 2, 1920] 



NATURE 



J5 



that in the stars, particularly in the giant stars, the 

 sethereal portion rises to an importance which quite 

 transcends our ordinary experience, so that we are con- 

 fronted with a new type of problem. In a red-hot mass 

 of iron the ajthereal energy constitutes less than a bil- 

 lionth part of the whole ; but in the tussle between 

 matter and aether the a;ther gains a larger and larger 

 proportion of the energy a» the temperature rises. 

 This change in proportion is rapid, the aethereal energy 

 increasing rigorously as the fourth power of the tem- 

 perature, and the material energy roughly as the first 

 power. But even at the temperature of some millions 

 of degrees attained inside the stars there would still 

 remain a great disproportion ; and it is the low density 

 of material, and accordingly the reduced material energy 

 per unit volume in the giant stars, which wipes out the 

 last few powers of lo. In all the giant stars known 

 to us, widely as they differ from one another, the 

 conditions are just reached at which tliese two varieties 

 of heat-energy have attained a rough equality ; at any 

 rate, one cannot be neglected compared with the other 

 Theoretically there could be conditions in which the 

 disproportion was reversed and the aethereal far out- 

 weighed the material energy ; but we do not find them 

 in the stars. It is as though the stars had been 

 measured out — that their sizes had been determined — 

 with a view to this balance of power ; and one cannot 

 refrain from attributing to this condition a deep signi- 

 ficance in the evolution of the cosmos into separate 

 stars. 



To recapitulate. We are acquainted with heat in 

 two forms — the energy of motion of material atoms 

 and the energy of asther waves. In familiar hot bodies 

 the second form exists only in insignificant quantities. 

 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, Ritter, Emden, and others, which not only 

 jxiinted the way for us to follow, but also achieved con- 

 clusions 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 surface 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 he held back sufficiently — how it can be barred 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 recopnition of aethereal energy necessitates a 

 twofold modification In the calculations. In the first 

 place, it abolishes the supposed convection currents ; 

 and the tvpe of equilibrium is that known as radiative 

 instead of ronvective. This change was first suggested 

 bv R. A. Sampson so lone ago as 1804. The detailed 

 theorv of radiative equilibrium is particularly asso- 

 ciated with K. Schwarzsrhild, who applied it to the 

 sun's atmosphere. It is perhaps still uncertain whether 

 it holds strictly for the atmospheric layers, but the 

 .nrguments for its vnliditv in the interior of a star are 

 far more cogent. Secondly, the outflowing stream of 

 .Tther»>.'il enorfv is powerful enottgh to exert a direct 

 nwchnniral effect on the equilibrium of a star. It is 

 as though a strong wind were rushing outward*. In 



NO. 2653, VOL. 106] 



fact, we may fairly say that the stream of radiant 

 energy '-s a wind ; for though aether waves are not 

 usually classed as material, they have the chief mech- 

 anical 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 supenncumbent 

 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 {Astropliysical 

 Journal, vol. xlviii., p. 205), we are in a position to 

 deduce some definite numerical results. On the obser- 

 vational side we have fairly satisfactory knowledge of 

 the masses and densities of the stars and of the total 

 radiation emitted by them ; this knowledge is partly 

 individual and partly statistical. The theoretical 

 analysis connects these observational data on the one 

 hand with the physical properties of the material inside 

 the star on the other. We can thus find certain 

 information as to the inner material, as though we had 

 actually bored a hole. So far as can be judged, there 

 are only two physical properties of the material which 

 can concern us — always provided that it is sufficiently 

 rarefied to behave as a perfect gas- — viz. the average 

 molecular weight and the transparency or permeability 

 to radiant energy. In connecting these two unknowns 

 with the quantities given directly by astronomical ob- 

 servation we depend entirely on the well-tried prin- 

 ciples of conservation of momentum and the second 

 law of thermodynamics. If any element of speculation 

 remains in this method of investigation, I think it is 

 no more than is inseparable from every kind of theo- 

 retical advance. 



We have, then, on one side the mass, density, 

 and output of heat, quantities as to which we have 

 observational knowledge ; on the other side, molecular 

 weight and transparency, quantities which we want to 

 discover. 



To find the transparency of stellar material to the 

 radiation traversing it is of particular interest, because 

 it links on this astronomical inquiry to physical inves- 

 tigations now being carried on in the laboratory, and 

 to some extent it extends those investigations to condi- 

 tions unattainable on the earth. At high temperatures 

 the Kther waves are mainly of very short wave-length, 

 and in the stars we arc dealing mainly with radiation 

 of wave-length 3 to 30 Angstrom units, which might 

 be described as very soft X-rays. It is interesting, 

 therefore, to compare the results with the absorption 

 of the harder X-rays dealt with by physicists. To 

 obtain an exact measure of this absorption in the stars 

 we have to assume a value of the molecular weight; 

 but fortunately the extreme range possible for the 

 molecular weight gives fairlv narrow limits for the 

 absorption. The average weight of the ultimate inde- 

 pendent particles in a star is probably rather low, 

 because in the conditions prevailing there the atoms 

 would be strongly ionised ; that is to say, many of the 

 outer electrons of the system of the atom would be 

 broken off ; and as each of these free electrons counts 

 as an independent molecule for present purposes, 

 this brings down the average weight. In the extreme 

 case (probably not reached in a star) when the whole 

 of the electrons outside the nucleus are detached the 

 average weight comes down to about 2, whatever the 

 material, because the number of electrons is about half 

 the atomic weight for all the elements (except hydro- 

 gen). We may, then, safely take 2 as the extreme 

 lower limit. For an upper limit we might perhaps take 



