406 ASTROMETRY 



of the sixth magnitude, apparently, will thus also have absolute 

 magnitude six on the surface of the sphere separating the fifth and 

 the sixth shell of Fig. 2. 



To appear always as a star of the sixth magnitude, stars more 

 distant will have to be absolutely brighter, those at smaller distances 

 will be fainter. The apparent magnitude being known, they can be 

 easily computed, of course, for every distance. 



In the figure the mean absolute magnitude of the stars in any one 

 shell nas been inserted for the stars of the fourth, the fifth, and the 

 sixth apparent magnitude. 



Now, first, the numbers in the figure enable us to find out the mix- 

 ture-law, that is, the law which gives the proportion in which stars of 

 different absolute magnitude are mixed in nature. 



For we see from the figure, shell VII, that the proportion of the 

 number of stars of absolute magnitude 2.4 to that of the absolute 

 magnitudes 3.4 and 4.4 is as that of the numbers 



49, 211, 371 



Similarly in shell VI we find for the proportion of the number of 

 stars of absolute magnitude 3.4, 4.4, 5.4, the numbers 



65, 255, 901 



and so on. 



Therefore, if the mixture be the same at different distances from the 

 nun, then we have 



by shell VII, relat. frequ. of stars of abs. mag. 2.4, 3.4, 4.4 



by shell VI, relat. frequ. of stars of abs. mag. 3.4, 4.4, 5.4 



by shell V, relat. frequ. of stars of abs. mag. 4.4, 5.4, 6.4 



by shell I, relat. frequ. of stars of abs. mag. 8.4, 9.4, 10.4 

 so that, even if we had no other data than those represented in Fig. 2, 

 we should already get the mixture-law for a range of 8 magnitudes. 



As a matter of fact, it proves feasible to include not only a greater 

 number of apparent magnitudes, but also a greater number of shells, 

 in our computations. As a consequence we shall in reality find the 

 mixture-law for a range of not less than 18 or 19 magnitudes, though 

 it must be admitted that the uncertainty is much increased at the 

 extremes. 



We may go one step further and transform our absolute magni- 

 tudes into luminosities. By luminosity of a star we shall denote its 

 total quantity of light as compared to that of the sun. 



For as the stellar magnitude of our sun is at present known with 

 some degree of approximation, we can compute its absolute magni- 

 tude, for which I find the number 10.5. That is to say, the sun trans- 

 ferred to a distance corresponding to a yearly parallax 0"01 would 

 shine with the light of a star of the 10.5 magnitude. 



Absolute magnitude 10.5 thus corresponding with unity of lumin- 



