26 



NATURE 



[March 13, 1919 



against those of another. Each of the lines of astro- 

 physical evidence sketched below supports the exist- 

 ence of a long time-scale; taken altogether, I believe 

 they may be considered (in agreement with geological 

 results) as very strong evidence that the quantity of 

 energy radiated by the sun has not changed appreciably 

 during more than a thousand million years.* 



(a) Studies of globular clusters and of faint stars 

 now indicate a diameter of the known galactic system 

 of scarcely less than a half-million light-years".* 

 Average stellar velocities appear to be less than lo-* 

 times the velocity of light. Accordingly, a single 

 oscillation-period of a star, or of a group of stars, in 

 the galactic system is probably not less than lo" 

 years — nearly a thousand times longer than the interval 

 during which the Helmholtz-Kelvin contraction, ac- 

 cording to current interpretation, can sustain present 

 solar radiation — and one oscillation-period cannot be 

 taken to represent a very large part of the history 

 of a star's evolution.^ We have no evidence of 

 clusters the stars of which are all at the beginning or 

 end of their luminous careers; stars are not evolving 

 from invisibility continuously and in great numbers 

 in any part of the galactic system that we have 

 studied. In other words, the introduction of a vastly 

 greater linear scale into the sidereal system Indicates 

 the necessity for a corresponding increase in time. 



(b) Compared with the most distant globular clusters 

 known, the brighter ones are some 200,000 light-years 

 nearer the earth, and, therefore, in our records their 

 stars are 200,000 years older.* Such an interval of 

 time would more than suffice, on the basis of recog- 

 nised sources of energy, for the whole development 

 (through luminous stages) of a giant star, according 

 to calculations by Eddington.® There is, however, no 

 evidence of differences of age for near and distant 

 clusters, either in the numbers, colours, and dis- 

 tribution, or other properties of giant stars open to 

 investigation. Indeed, the distribution and motion of 

 globular clusters with respect to the galactic system, 

 their isolation in space, and the evidence of states of 

 internal equilibrium practically negative the possibility 

 of short life for their hundreds of giant stars. 



(c) The luminosity-period curve of Cepheid varia- 

 tion '^'^ uniquely relates the period of pulsation of a 

 giant Cepheid variable to its absolute brightness, the 

 individual deviations from the mean curve averaging 

 less than the observational uncertainties. The 

 shorter the period of a Cepheid, the less is its 

 absolute brightness. But for any given star this 

 brightness does not decrease during the giant stage, 

 according to theoretical results of Eddington ^^ and 

 Jeans ^^ ; apparently, therefore, the total life of the 

 variation of a Cepheid passes without appreciable 

 shortening of period.^' Since period oc density- i 

 according to the hypothesis that some type of pulsa- 

 tion is the cause of Cepheid phenomena, the variability 

 passes also without appreciable change In mean 

 density, and therefore gravitational contraction In these 

 giant stars makes no progress during the whole 

 interval of time that Cepheid variation Is effective. 

 This Interval of time, however, must be exceedingly 

 long ; no certain non-periodic diminution either In 

 amplitude or period has ever been detected In a typical 

 Cepheid. Disregarding both the period-luminosity 



S Cf. general discussion in Publ. Ast. Soc. Pac, vo!. xxx., p. 283 (1918). 

 B Mt. Wilson Cf-ntr., No. 157 (1918). 



7 Cf. Charlier, Observatory, vol. xl., p. 3Q0 (1917): Jeans, ibid., p. 406. 

 A m.ich smaller stellar system was considered by Charlier and Jeans than is 

 now under consideration. 



8 Publ. Ast. Soc. Pac, vol. xxx., p. 54 (1918); Mt. Wilson Contr., 

 No. 157, p. 14 (1918). 



9 Monthly Notices, vol. Ixxvu., pp. 610, 612 (1917). 



10 Mt. Wilson Contr., No. 151, p. 16(1917). 



11 Nature, vol. xcix., y. 30S (1917); Monthly Noticps, vol, Ixxvii., 

 pn. 16. soft (1016, ign). 



12 Mnnthlv Notic's. vol. Ixxviii., p. 36 (1917)- 



13 Mt. Wilson CoTiT.. N". Tcj. p. 6 r.oT-l. 



NO. 2576, VOL. 103] 



curve and the mathematical theory of a gaseous giant 

 star, we still have, as Eddington has also noticed," 

 an indication from individual Cepheids that the 

 time-scale is long. A study of 8 Cephei ^" for 125 

 years and of \ Geminorum for 75 years shows 

 no measurable change in period — no change, therefore, 

 either in mean density or in volume, and the observa- 

 tions are precise enough to justify the conclusion that 

 gravitational theory, as ordinarily interpreted, accounts 

 for less than a thousandth of the energy that is 

 radiated away. 



To the three groups of argument outlined above 

 may be added a number of quantitatively less definite 

 results. The clearest are : — (d) Evidence similar to (c) 

 from the study of the periods of eclipsing binaries, 

 and {e) the tidal development of our planetary system. 



None of these results goes farther numerically than 

 to indicate lower limits to the time-scale. The evi- 

 dence of contraction is essentially all negative, and 

 the duration of stellar radiation may be anything 

 greater than the lower limit. So far as we now know, 

 it is just as probably a million as a hundred times the 

 value provided by known sources of energy. 



(4) It should be remarked that the geological 

 evidence has become much stronger in recent years. 

 The exhaustive summarisation by Barrell ^* of methods 

 of measuring earth-age from the radio-activity of 

 rhythms in sedimentation and erosion, salinity of the 

 oceans, and biological evolution leaves little ground 

 for a short time-scale In geological history. The oldest 

 sedimentary rocks appear to be about 1,500,000,000 

 years old, and before their formation unknown ages 

 elapsed. Independently of the extrapolated results 

 from radio-activitv in terrestrial rocks, Schuchert ^' 

 derives from studies in historical geology an age of 

 some 800,000,000 years for the earliest Archaeozolc 

 formations. 



(5) In computing the total energy radiated by the 

 sun, the custom naturally has been to multiply the 

 amount measured for unit area at the earth's surface 

 by the total superficial area of the sphere the centre 

 of which is at the sun and the radius of which is 

 the earth's mean distance. It may be well to point 

 out, as a possible contribution to the solution of the 

 great discrepancy discussed above, that, however 

 natural the customary procedure may be, nevertheless 

 this integration over the whole sphere involves an 

 assumption that may be not only unnecessary, but 

 possibly even unwarranted in the present state of our 

 knowledge of the theories and phenomena of radia- 

 tion ; and if solar and stellar radiation is not uniformly 

 propagated in all directions— If In any way it Is facili- 

 tated by the presence of surrounding bodies — then the 

 controversy between the short and long time-scales 

 approaches a solution that does not violate the basic 

 results of either line of reasoning. 



If, following Sir J- J- Thomson,^' we actually 

 materialise the Faraday lines of electric force and 

 adopt a corpuscular theory of radiation, already we 

 may have good reason to question the assumed inde- 

 pendence of radiation and direction. The ordinary 

 undulatory theory, to be sure, requires a continuity 

 In the electromagnetic field, but continuity Is bv no 

 means a necessary postulate In the analysis of Max- 

 well's equations. 



k special and limiting condition, along the line^ of 

 the present suggestion, would require that the radiation 

 from an Isolated source should be wholly confined to 

 the solid angles subtended by surrounding matter. Dr. 



14 0(^,r^;T;a'ory, vol. xli., p. 379 (1918). 



15 Cf. analysis by Luizet, Annales de I'Universit^ de Lyon, N.S., i. 

 fascicule 33 (1912). 



IB Bull. Geol. Soc. of Amer., vol. xxviii., pp. 745-904 (1917). 

 1" " The Evolution of the Earth and its Inhabitants " (New Haven, 191 8), 

 chap. ii. 



18 " Electricity and Matter" (London 1904), and elsewhere. 



