1908] on Recent Researches in the Structure of the Universe. 311 



Mixture-Law. 



We are now able to derive at once the mixture law — i.e. the pro- 

 portions in which stars of different absohite magnitude are mixed in 

 the universe. For in one and the same shell (11th) we find two stars 

 of absolute magnitude - 1 ' 5, as against three of magnitude - • 5, 

 fifteen of absolute magnitude • 5, seventy-six of absolute magnitude 

 1 • 5, etc. 



That is, our results for the 11th shell furnish us with the proportion 

 in which stars of absolute magnitude - 1*5, -0'5, etc., to 4*5, are 

 mixed in space. The lOtli shell gives the proportions for all the abso- 

 lute magnitudes between -0*5 and 5 * 5, and so for the rest. All the 

 shells together give the proportions for the absolute magnitudes 

 - 1*5 to 14*5, that is for a range of not less than sixteen magni- 

 tudes. Not only that, but most of the proportions are determined 

 independently by the data of quite a number of shells. So, for 

 instance, the proportion of the stars of absolute magnitude 4* 5 to 

 those of absolute magnitude 5 '5. Each of the six shells from the 

 5th to the 10th furnishes a determination of this proportion. All of 

 them are not equally reliable. If we take this into account, we find 

 that the agreement of the several determinations is fairly satisfactory. 

 By a careful combination of all the results, a table representing the law 

 of the mixture of the stars of different absolute magnitude was finally 

 obtained. Kather than show you the direct result, however, I will 

 first replace the absolute magnitudes by luminosities expressed in the 

 total light of our sun as a unit. This will have the advantage of 

 presenting a more vivid image of the real meaning of our numbers. 



By photometric measures it was found that the sun, placed at a 

 distance of 826 Ught-years, would shine as a star of magnitude 10 '5. 

 In other words, the sun's absolute magnitude is 10*5. A star of 

 absolute magnitude 9 • 5 will, therefore, have 2 * 5 times the light- 

 power — that is, 2*5 times the luminosity of the sun. A star of 

 absolute magnitude 8*5 will again have a luminosity which is 2*5 

 times greater, and so on. 



Such results evidently enable us to transform our absolute magni- 

 tudes into luminosities. Thus translated, I found the results shown 

 in the following table. 



Luminosity Table. 



Within a sphere having a radius of 555 Ught-years, there must 

 exist : — 



1 star 10,000 to 100,000 times more luminous than the sun 



46 stars 1,000 „ 10,000 



1300 „ 100 „ 1,000 „ 



22,000 „ 10 „ 100 „ 



140,000 „ 1 „ 10 „ 



430,000 „ 0-1 „ 1 „ 



650,000 „ 0-01 „ 0-1 „ 



