September 2, 1920] 



NATURE 



17 



thtory, no star has yet been found with a mass less 

 than \ of the sun's; and it is a well-known fact, dis- 

 covered from the study oT spectroscopic binaries, 

 that the masses of the B stars are large compared 

 with those of other types. Again, it is possible to 

 calculate the difference of brightness of the giant and 

 dwarf stars of type M, i.e. at the beginning and end 

 of their career ; the result agrees closely w'ith the 

 observed difference. In the case of a class of variable 

 stars in which the light changes seem to depend on a 

 mechanical pulsation of the star, the knowledge we 

 have obtaintnl of the internal conditions enables us to 

 predict the period of pulsation within narrow limits. 

 Kor example, for i Cephei, the best-known star of this 

 kind, the theoretical period is between four and ten 

 days, and the actual period is 5J days. Corresponding 

 agreement is found in all the other cases tested. 



Our observational knowledge of the things here 

 discussed is chiefly of a rather vague kind, and wc can 

 scarcely claim more than a general agreement of 

 theory and observation. What we have been able to 

 do in the way of tests is to offer the theory a con- 

 siderable number of opportunities to "make a fool of 

 itself," and so far it has not fallen into our traps. 

 When the theory tells us that a star having the mass 

 of the sun will at one stage in its career reach a maxi- 

 mum effective temperature of 9000° (the sun's effective 

 temperature being 6000°) we cannot do much in the 

 way of checking it ; but an erroneous theory might 

 Weil have said that the maximum temperature was 

 jo,ooo° (hotter than any known star), in which case we 

 should have detected its error. If we cannot feel con- 

 fident that the answers of the theory are true, it must 

 be admitted that it has shown some discretion in lying 

 without being found out. 



It would not be surprising if individual stars occa- 

 sionally depart considerably from the calculated 

 results, because at present no serious attempt has been 

 made to take into account rotation, which may modify 

 the conditions when sufficiently rapid. That appears 

 to be the next step needed for a more exact study of 

 the question. 



Probably the greatest need of stellar astronomy at 

 the present day, in order to make sure that our theo- 

 retical deductions are starting on the right lines, is 

 some means of measuring the apparent angular dia- 

 meters of stars. .Xt present we can calculate them 

 approximately from theory, but there is no observa- 

 tional check. We believe we know with fair accuracy 

 the apparent surface brightness corresponding to each 

 spectral type ; then all that is necessary is to divide the 

 tot.il apparent brightness by this surface brightness, 

 ind the result is the angular area subtended bv the 

 -far. The unknown distance is not involved, because 

 surface brightness is independent of distance. Thus 

 the estimation of the angular diameter of any star 

 -••ems to be a very simple matter. For instance, the 

 -tar with the greatest apparent diameter is almost 

 certainly Betrlgeuse. diameter 0051'. Next to it 

 comes ,^^tares, 0043'. Other examples are .Mdebaran 

 11022', Arrturus 0020'. Pollux o-on'. Siriiis comes 

 rather low down with diameter 0007*. The following 

 fable may be of interest as showing the angular dia. 

 meters expected for stars of various types and visual 

 magnitudes : — 



Probable Angular Diameters of Stnrs. 

 vii. M>K. A r r, K M 



However confidently we may bel'ieve in these values, 

 it would be an immense advantage to have this first 



NO. 2653, VOL. 106] 



step in our deductions placed beyond doubt. If the 

 direct measurement of these diameters could be made 

 with any accuracy it would make a wonderfully rapid 

 advance' in our knowledge. The prospects of accom- 

 plishing some part of this task are now quite hopeful. 

 \Ve have learnt with great interest this )ear that work 

 is being carried out by interferometer methods with 

 the loo-in. reflector at Mount Wilson, and the results 

 are most promising. At present the method has been 

 applied only to measuring the separation of close 

 double stars, but there seems to be no doubt that an 

 angular diameter of 005' is well within reach. Al- 

 though the great mirror is used for convenience, the 

 interferometer method does not in principle require 

 great apertures, but rather two small apertures widely 

 separated, as in a range-finder. Prof. Hale has stated, 

 moreover, that successful results were obtained on 

 nights of poor seeing. Perhaps it would be unsafe to 

 assume that "'poor seeing" at Mount Wilson means 

 quite the same thing as it does for us, and 1 anticipate 

 that atmospheric disturbance will ultimately set the 

 limit to what can be accomplished. But even if we 

 have to send special expeditions to the top of one of 

 the highest mountains in the world, the attack on this 

 far-reaching problem must not be allowed to languish. 

 I spoke earlier of the radiation-pressure exerted by 

 the outflowing heat, which has an important effect 

 on the equilibrium of a star. It is quite easy to calcu- 

 late what proportion of the weight of the material is 

 supported in this way ; it depends on neither the den- 

 sity nor the opacity, but solely oh the star's total mass 

 and on the molecular weight. No astronomical data 

 are needed ; the calculation involves only fundamental 

 physical constants found by laboratory researches. 

 Here are the figures, first for average mofecular weight 

 3-0:— 



For mass Jxsun, fraction of weight supported by 



radiation-pressure = 0-044. 

 For mass sxsun, fraction of weight supported by 



radiation-pressure = 0-457. 



For molecular weight 5-0 the corresponding fractions 

 are 0-182 and 0-645. 



The molecular weight can scarcely go beyond this 

 range,' and for the conclusions I am about to draw it 

 does not much matter which limit we take. Probably 

 90 per cent, of the giant stars have masses between 

 i and 5 times the sun's, and we see that this is just 

 the range in which radiation-pressure rises from unim- 

 portance to importance. It seems clear that a globe 

 of gas of larger mass, in which radiation-pressure and 

 gravitation are nearly balancing, would be likely to 

 1)C unstable. The condition may not be strictly un- 

 stable in itself, but a small rotation or perturbation 

 would make it so. It may therefore be conjectured 

 that, if nebulous material began lo concentrate into 

 a mass much greater than five times the sun's, it 

 would probably break up, and continue to redivide 

 until more stable masses resulted. .Above the upper 

 limit the chances of survival arc small ; when the lower 

 limit is approached the danger has practically disap- 

 peared, and there is little likelihocxl of any further 

 breaking-up. Thus the final masses are left distri- 

 buted almost entirely helw<"en the limits given. To fiut 

 the matter slightly differently, we are able to predict 

 from general principles Ih.'it the material of the stellar 

 universe will ageregate primarily into masses chiefly 

 lying between 10" and ro" grams; and this is just the 



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 Srvnk nw^v the Atremiie ttiol'-ctiUr w^iRht iit ) ; if t6 break away the ntole- 

 1 ' .'• « 1. Kgg'n {I'hyt. /.tilt., t9i«, p )7a) hat lUKCMed tiy 



t' aI reaftininc that in moM ra*Cft the two nnl*r ringt (16 



r. M break away in iht ttark. Tb« cnmpar iton of thaorr af*d 



i>K.rr>.iii.'n ><>r iht dwarf >ian alto pointt lo a iMiiaailar waighi a litlt* 

 fraaler than > 



