222 The Evolution of Star-Clusters [CH. x 



Some evidence can be obtained from the masses of the stars and their 

 distribution, but, except for our own sun there is no means of determining the 

 mass of a star except when it happens to be a binary. Eddington* has given 

 a list of all the stars whose masses he believes to be really well determined. 

 They are only seven in number, their masses in terms of that of our sun 

 being 07, TO, T3, 1*8, 1*9, 2'5 and 3'4. Including our sun, this gives eight 

 stars, all of fairly equal mass, the average of these masses being 1*7 times that 

 of our sun, or 10 83 ' 53 gms. The circumstance that the masses of the stars are 

 fairly uniform is not unfavourable to our hypothesis as to their origin ; we 

 should expect the condensations in the nebular arms, if formed in the way we 

 have imagined, to be all about equal in mass. 



On equating the average mass of the stars to the mass of a nebular con- 

 densation, as given by formula (543), we can determine the density of the 

 primitive nebular arms. The equation is 



(7 3 7~V~ i = 10 33 ' 53 (544). 



Unfortunately the value of p depends largely on the unknown molecular 

 velocity C, varying as C s . On taking G = T6 x 10 we find p = 4 x 10~ 17 . For 

 cold gas, or gas mixed with solid dust particles the value of C might perhaps 

 be only a quarter of that just used, and the calculated value of p would then 

 be only one four-thousandth part of that calculated, say p = 10~ 20 . 



If I is the mean distance of the condensations in the primitive nebular arms, 

 each member of equation (544) is equal to pi 3 , so that 1 = p~% x 10 11 ' 18 cms. 

 Taking p = 4 x 10~ 17 , we find I = 10 16 ' 64 cms. = ^ parsec. Taking p = 1Q- 20 , 

 we find I = 10 17 ' 84 cms. = 1 parsec. 



Compare these figures with the present density and distances in our galactic 

 universe. Eddington f estimates that there are probably between 30 and 40 

 stars within a distance of 5 parsecs of our sun. The higher estimate gives 

 a stellar density of one star per 13 cubic parsecs, or per 10 56 ' 54 cubic cms., 

 and an average stellar distance of (13)* or 2*3 parsecs. Introducing our 

 former estimate of 10 33 ' 53 for the average stellar mass, this gives an average 

 density of matter of about 10" 23 in the neighbourhood of our sun. 



It is more difficult to estimate the mean-density in the universe as a 

 whole. At a rough guess, our universe may be supposed to be a lens- 

 shaped figure of equatorial radius 2000 parsecs and transverse radius 

 600 parsecs. The volume of such a figure is 4 x 10 9 cubic parsecs or 

 10 65 cubic cms. Thus a total mass of 5 x 10 42 grammes would require a mean 

 density of 5 x 10~ 23 , or five times the density just estimated for the neigh- 

 bourhood of the sun. 



Both these estimates evaluate the density of the matter in the bright 

 stars only; the dark stars, of which it is impossible even to guess at the 



* Stellar Movements, p. 22. t I.e. p. 15. 



