STELLAR ASTRONOMY 409 



of the constancy of the mixture for different distances from the sun, 

 and this being the case, the change in the density from shell to shell 

 found for the stars of any determined absolute magnitude must at the 

 same time represent the change in the total star-density. We thus see 

 that the law of the total densities for various distances from the sun 

 can be found, although, as long so our data do not embrace the whole 

 range of the absolute magnitudes existing in nature, we cannot tell 

 the total number of stars pro unit of volume, that is, we can only find 

 the relative densities, not the absolute ones. 



Taking the mean of the two determinations in the preceding 

 example, we may thus assume: 



Total star-density in shell VII 



J _ =0.79 



Total star-density in shell VI 



From the whole of the available data was derived the number 0.76. 

 In this way I find, taking as unity of density the density in the 

 neighborhood of the sun: 



f Corresp. dist. Star-density 



0*00118 8.5 0.162 



.00187 5.3 .292 



.00296 3.4 .465 



.00469 2.1 .684 



.00743 1.35 .852 



.0118 0.85 .945 



.0187 0.53 .984 



.0296 to oo 0.34 to 0. 1.000 



This determination is quite provisional because some data have 

 been neglected in its derivation, which must have considerable in- 

 fluence. Still, always granting the validity of our premises, there can 

 be no doubt of the general course of these numbers. 



In the mean of the whole sky we find a regular thinning out of the 

 stars as we recede further and further from the sun. The thinning 

 out is hardly perceptible as long as the parallax is upward of 0"01. 



We might now look at another face of the question. The use of 

 the method just now explained is not necessarily confined to the sky 

 as a whole, but is applicable as well to separate parts of it. 



So, for instance, we may derive the laws of the mixture and that of 

 the densities separately for stars in the Milky Way and for those at 

 considerable distance away from that belt. A few years ago I car- 

 ried out such an investigation, but for the same reason that then made 

 me refrain from publication, I shall not now communicate results. 

 The reason is that some difficulties became apparent which make 

 the results seem doubtful. It may be sufficient here to have directed 

 the attention to the fact that, granting our fundamental hypothesis, 



