i6 



NATURE 



[September 2, 1920 



200; but to avoid controversy we shall be generous 

 and merely assume that the molecular weight is not 

 greater than— infinity. Here is the result : — 



For molecular weight 2, mass-coefficient of absorp- 



tion=io C.G.S. units. 

 For molecular weight co, mass-coefficient of ab- 

 sorption=i3o C.G.S. units. 

 The true value, then, must be between 10 and 130. 

 Partly from thermodynamical considerations, and 

 partly from further comparisons of astronomical 

 observation with theory, the most likely value seems 

 to be about 35 C.G.S. units, corresponding to mole- 

 cular weight 35. 



Now this is of the same order of magnitude as the 

 absorption of X-rays measured in the laboratory. 1 

 thinli the result is in itself of some interest, that in 

 such widely different investigations we should ap- 

 proach the same kind of value of the opacity of matter 

 to radiation. The penetrating power of the radiation 

 in the star is much like that of X-rays ; more than half 

 is absorbed in a path of 20 cm. at atmospheric den- 

 sity. Incidentally, this very high opacity explains why 

 a star is so nearly heat-tight, and can store vast 

 supplies of heat with comparatively little leakage. _ 

 So far this agrees with what might have been anti- 

 cipated; but there is another conclusion which physi- 

 cists would probably not have foreseen. The giant 

 series comprises stars differing widely in their densities 

 and temperatures, those at one end of the series being 

 on the average about ten times hotter throughout than 

 those at the other end. By the present investigation 

 we can compare directly the opacity of the hottest 

 stars with that of the coolest. The rather surpris- 

 ing result emerges that the opacity is the same for all ; 

 at any rate, there is no difference large enough for us 

 to detect. There seems no room for doubt that at 

 these high temperatures the absorption-coefficient _ is 

 approaching a limiting value, so that over a wide 

 range it remains practicallv constant. With regard to 

 this constancy, it is to be noted that the temperature 

 is concerned twice over : it determines the character 

 and wave-length of the radiation to be absorbed, as 

 well as the physical condition of the material which is 

 absorbing. From the experimental knowledge of X-rays 

 we should have expected the absorption to vary very 

 rapidly with the wave-length, and therefore with the 

 temperature. It is surprising, therefore, to find a 

 nearly constant value 



The result becomes a little less mysterious when we 

 consider more closely the nature of absorption. Ab- 

 sorption is not a continuous process, and after an atom 

 has absorbed its quantum it is put out of action for a 

 time until it can recover its original state. We know 

 very little of what determines the rate of recovery of 

 the' atom, but it seems clear that there is a limit to 

 the amount of absorption that can be performed by 

 an atom in a given time. When that limit is reached 

 no increase in the intensity of the incident radiation 

 will lead to anv more absorption. There is, in fact, a 

 saturation effect. In the laboratory experiments the 

 radiation used is extremely .weak ; the atom is practi- 

 cally never caught unprepared, and the absorption is 

 proportional to the incident radiation. But in the stars 

 the radiation is very intense and the saturation effect 



comes in. ... 



Even granting that the problem of absorption in the 

 stars involves this saturation effect, which does rot 

 affect laboratory experiments, it is not very easy to 

 understand theoretically how the various conditions 

 combine to give a constant absorption-coefficient inde- 

 pendent of temperature and wave-length. But the 

 astronomical results seem conclusive. Perhaps the 

 most hopeful suggestion is one made to me a few 

 years ago by CO. Barkla. He suggested that the 

 NO. 2653, VOL. 106] 



opacity of the stars may depend mainly on icailermg 

 rather than on true atomic absorption. In that case 

 the constancy has a simple explanation, for it is 

 known that the coefficient of scattering (unlike true 

 absorption) approaches a definite constant value for 

 radiation of short wave-length. The value, moreover, 

 is independent of the material. Further, scattering is 

 a continuous process, and there is no likelihood of any 

 saturation effect; thus for very intense streams of 

 radiation its value is maintained, whilst the true ab- 

 sorption may sink to comparative insignificance. The 

 difficulty in this suggestion is a numerical discrepancy 

 between the known theoretical scattering and the 

 values already given as deduced from the stars. 1 he 

 theoretical coefficient is only 02 compared with the 

 observed value 10 to 130. Barkla further pointed out 

 that the waves here concerned are not short enough to 

 give the ideal coefficient ; they would be scattered more 

 powerfully, because under their influence the electrons 

 in any atom would all vibrate in the same phase 

 instead of in haphazard phases. This might help to 

 bridge the gap, but not sufficiently. It must be re- 

 membered that many of the electrons have broken 

 loose from the atom and do not contribute to the 

 increase.' Making all allow-ances for uncertainties in 

 the data, it seems clear that the astronomical opacity 

 is definitely higher than the theoretical scattering. 

 Very recently, however, a new possibility has opened 

 up which may possibly effect a reconciliation. Later 

 in the address 1 shall refer to it again. 



Astronomers must watch with deep interest the 

 investigations of these short waves, which are being 

 pursued in the laboratory, as well as the study of the 

 conditions of ionisation by both experimental and 

 theoretical physics, and I am glad of this opportunity 

 of bringing before those who deal with these problems 

 the astronomical bearing of their work. 



I can allude onlv very briefly to the purely astro- 

 nomical results which follow from this investigation 

 (Monthly Notices, vol. l.xxvii., pp. 16, 596; vol. Ixxix., 

 p. 2); it is here that the best opportunity occurs for 

 checking the theory by comparison with observation, 

 and for finding out in what respects it may be defi- 

 cient. Unfortunately, the observational data are 

 generally not very precise, and the test is not so strin- 

 gent as we could wish. It tur;is out that (the opacity 

 being constant) the total radiation of a giant star 

 should be a function of its mass only, independent of 

 its temperature or state of diffusencss. The total 

 radiation (which is measured roughly by the lumin- 

 osity) of any one star thus remains constant during 

 the 'whole giant stage of its history. This agrees with 

 the fundamental feature, pointed out by Russell in 

 introducing the giant and dwarf hypothesis, that giant 

 stars of every spectral type have nearly the same 

 luminosity. From the range of luminosity of these 

 stars it is now possible to find their range of mass. 

 The masses are remarkably alike — a fact already sug- 

 gested by work on double stars. Limits of mass in the 

 ratio 3 :i would cover the great majority of the giant 

 stars. Somewhat tentatively we are able to extend 

 the investigation to dwarf stars, taking account of the 

 deviations of dense gas from the ideal laws and using 

 our own sun to supplv a determination of the unknown 

 constant involved. We can calculate the maximum 

 temperature reached bv different masses ; for example, 

 a star must have at least \ the mass of the sun in 

 order to reach the lowest spectral type, M ; and in 

 order to reach the hottest type, B, it must be at least 

 2\ times as massive as the sun. Happily for the 



I E.i: for iron non-ionised the theoretical scattering is 5-1, against an 



, astronomical value 170. If 16 electrons (2 ringsl are broVen o^ the 



theoretical coefficient is oq. against an astronomical value js. Yar different 



. assumptions as to ionisation the values chase one another, but cannot be 



I brought within reasonable range. 



