314 ANNUAL, EEPORT SMITHSONIAN INSTITUTION, 1908. 



tance of 326 light years. The choice of just this number is simply a 

 matter of convenience, and need not be explained here. 



As a consequence, the stars at a distance of 326 years, which to 

 us appear as stars of the fifth magnitude, will have also the absolute 

 magnitude 5. Those of the same apparent magnitude, but at a dis- 

 tance of 517 light years — that is, just one shell farther — must have 

 the absolute magnitude -i in order to show us the same brightness, 

 notwithstanding the greater distance. Now, our eighth shell lies just 

 between these limits of distance. In the middle of this shell, there- 

 fore, the stars of apparent magnitude 5 must have absolute magni- 

 tude 4.5. In the box, therefore, belonging to the fifth apparent mag- 

 nitude, eighth shell, all the stars are of absolute magnitude 4.5. In 

 the ninth shell a star must already have the absolute magnitude 3.5 in 

 order to shine as a fifth apparent magnitude at this greater distance, 

 and so on. In this way the absolute magnitudes were found which 

 in our figure have been inscribed on the lids of the boxes. 



MIXTURE LAW. 



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

 portions in which stars of different absolute magnitude are mixed 

 in the universe. For in one and the same shell (eleventh) we find 

 two stars of absolute magnitude — 1.5, as against three of magnitude 

 — 0.5, fifteen of absolute magnitude 0.5, seventy-six of absolute 

 magnitude 1.5, etc. 



That is, our results for the eleventh shell furnish us with the pro- 

 portion in which stars of absolute magnitude — 1.5, — 0.5, etc., to 4.5, 

 are mixed in space. The tenth shell gives the proportions for all the 

 absolute 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 magnitudes. 

 Not only that, but most of the proportions are determined inde- 

 pendently 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 shells from the fifth to the tenth 

 furnishes a determination of this proportion. All of them are not 

 equally reliable. If we take this into account, we find that the agree- 

 ment of the several determinations is fairly satisfactory. By a care- 

 ful combination of all the results, a table representing the law of the- 

 mixture of the stars of different absolute magnitude was finally 

 obtained. Rather than show j^ou 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 326 light years, would shine as a star of magnitude 10.5, 



