i8 



NATURE 



[September 2, 1920 



magnitude of the masses of the stars according to 

 astronomical observation.^ 



This study of the radiation and internal conditions 

 of a star brings forward very pressingly a problem 

 often debated in this Section : \Vhat is the source of 

 the heat which the sun and stars are continually 

 squandering? The answer given is almost unanimous 

 — that it is obtained from the gravitational energy con- 

 verted as the star steadily contracts. But almost as 

 unanimously this answer is ignored in its practical 

 consequences. Lord Kelvin showed that this hypo- 

 thesis, due to Helmholtz, necessarily dates the birth 

 of the sun about 20,000,000 years ago; and he made 

 strenuous efforts to induce geologists and biologists to 

 accommodate their demands to this time-scale. 1 do 

 not think they proved altogether tractable. But it is 

 among his own colleagues, physicists and astronomers, 

 that the most outrageous violations of this limit have 

 prevailed. 1 need only refer to Sir George Darwin's 

 theory of the earth-moon system, to the present Lord 

 Rayleigh's determination of the age of terrestrial rocks 

 from occluded helium, and to all modern discussions 

 of the statistical equilibrium of the stellar system. No 

 one seems to have any hesitation, if it suits him, in 

 carrying back the history of the earth long before the 

 supposed date of formation of the solar system ; and, 

 in some cases at least, this appears to be justified by 

 experimental evidence which it is difficult to dispute. 

 Lord Kelvin's date of the creation of the sun is treated 

 with no more respect than Archbishop Ussher's. 



The serious consequences of this contraction hypo- 

 thesis are particularly prominent in the case of giant 

 stars, for the giants are prodigal with their heat and 

 radiate at least a hundred times as fast as the sun. 

 The supply of energy which suffices to maintain the 

 sun for 10,000,000 years would be squandered by a 

 giant star in less than 100,000 years. The whole evo- 

 lution in the giant stage would have to be very rapid. 

 In 18,000 years at the most a typical star must pass 

 from the initial M stage to type G. In 80,000 years 

 it has reached type A,_ near the top of the scale, ar:d 

 is about to start on the downward path. Even these 

 figures are probably very much over-estimated.* Most 

 of the naked-eye stars are still in the giant stage. 

 Dare we believe that they were all formed within the 

 last 80,000 years? The telescope reveals to us objects 

 remote not only in distance, but also in time. We 

 can turn it on a globular cluster and behold what was 

 passing 20,000, 50,000, even 200,000 years ago un- 

 fortunately not all in the same cluster, but in different 

 clusters representing different epochs of the past. As 

 Shapley has pointed out, the verdict appears to fce 

 "no change." This is perhaps not conclusive, because 

 it does not follow that individual stars have suffered no 

 change in the interval ; but it is difficult to resist the 

 impression that tlie evolution of the stellar universe 

 proceeds at a slow, majestic pace, with respect to 

 which these periods of time are insignificant. 



There is another line of astronomical evidence which 

 appears to show more definitely that the evolution of 

 the stars proceeds far more slowlv than the contraction 

 hypothesis allows ; and perhaps it may ultimately 

 enable us to measure the true rate of progress. There 

 are certain stars, known as Cepheid variables, which 

 undergo a regular fluctuation of light of a characteristic 



* By admitting plausible assumptions closer limits could be drawn. 

 Taking the molecular weight as 3*5. and a.ssiiming that the most critical 

 condition is when J of gravitation is coiinterhaI.inced (by analogy with the 

 case of rotating spheroids, in which centrifugal force opposes cravitation 

 and creates instability), we find that the crit'cal mass is just twice that of 

 the sun, and stellar masses may be expected to cluster closely round this 

 value, 



* '_ have tiken the ratio of specific heats at the extreme possible value. \ ; 

 that is tosay. no al'owancc has been made fnr the energy needed for iontsa- 

 tion and internal vibrations of the atoms, which makes a further call on the 

 scanty supply available. 



NO. 2653, VOL. 106] 



kind, generally with a period of a few days. This light 

 change is not due to eclipse. Moreover, the colour 

 quality of the light changes between maximum and 

 minimum, evidently pointing to a periodic change in 

 the physical condition of tne star. .Although these 

 objects were formerly thought to be double stars, it 

 now seems clear that this was a misinterpretation of 

 the spectroscopic evidence. There is, in fact, no room 

 for the hypothetical companion star; the orbit is so 

 small that we should have to place it inside the prin- 

 cipal star. Everything points to the period of the light 

 pulsation being something intrinsic in the star ; and 

 the hypothesis advocated by Shapley, that it represents 

 a mechanical pulsation of the star, seems to be the 

 most plausible. I have already mentioned that the 

 observed period does, in fact, agree with the calculated 

 period of mechanical pulsation, so that the pulsation 

 explanation survives one fairly stringent test. But 

 whatever the cause of the variability, whether pulsa- 

 tion or rotation, provided only that it is intrinsic in the 

 star, and not forced from outside, the density must be 

 the leading factor in determining the period. If the 

 star is contracting so that its density changes appre- 

 ciably, the period cannot remain constant. Now, on 

 the contraction hypothesis the change of density must 

 amount to at least i per cent, in forty years. (I give 

 the figures for 8 Cephei, the best-known variable of 

 this class.) The corresponding change of period should 

 be very easily detectable. For 8 Cephei the period 

 ought to decrease 40 seconds annually. 



Now S Cephei has been under careful observation 

 since 1785, and it is known that the change of period, 

 if any, must be very small. S. Chandler found a 

 decrease of period of ^^ second per annum, and in a 

 recent investigation E. Hertzsprung has found a 

 decrease of ^ second per annum. The evidence tl.at 

 there is any decrease at all rests almost entirelv on 

 the earliest observations made before 1800, so that it is 

 not very certain; but in any case the evolution is pro- 

 ceeding at not more than jjjj of the rate required by 

 the contraction hypothesis. There must at this rlage 

 of the evolution of the star be some other source of 

 energy which prolongs the life of the star 400-fold. 

 The time-scale so enlarged would suffice for practically 

 all reasonable demands. 



I hope the dilemma is plain. Either we must admit 

 that whilst the density changes i per cent, a certain 

 period intrinsic in the star can change no more than 

 hJxt °f ' P^r cent., or we must give up the contraction 

 hypothesis. 



If the contraction theory were proposed to-day as a 

 novel hypothesis I do not think it would stand the 

 smallest chance of acceptance. From all sides — bio- 

 'ogyi geology, physics, astronomy — it would be 

 objected that the suggested source of energv was hope- 

 lessly inadequate to provide the heat spent during the 

 necessary time of evolution ; and, so far as it is pos- 

 sible to interpret observational evidence confidently, the 

 theory would be held to be negatived definitely. Only 

 the inertia of tradition keeps the contraction hypothesis 

 alive — or, rather, not alive, but an unburied corpse. 

 But if we decide to inter the corpse, let us frankly 

 recognise the position in which we are left. A star is 

 drawing on some vast reservoir of energv bv means 

 unknown to us. This reservoir can scarcely be other 

 than the sub-atomic energv w'hich, it is known, exists 

 abundantly -in all matter; we sometimes dream that 

 man will one day learn how to release it and use it 

 for his service. The store is well-nigh inexhaustible, 

 if only it could be tapped. There is sufficient in the 

 sun to maintain its output of heat for 15 billion years. 



Certain physical investigations in the past vear, 

 which I hope we may hear about at this meeting, 

 make it probable to my mind that some portion of this 



