( 626 ) 



Astronomy. — "On f/ie incan star-denaity at different distances 

 from the solar si/steni." Hy .1. C. Kapteyn. 



(Communicated in the mceiing of February 20, 1908). 



In the meeting of April 20, 1901, I derived not only the so-called 

 luminosity-curve bnt also the law according- to which tlie star-density, 

 i. e. the nnniber of stars per nnit of vohime, diminishes with increas- 

 ing distance from tlie solar system^). I assnmed, and the assumption 

 will again be made in the present paper, that there is no absorption 

 of Might in space. 1 then pointed ont that the Inminosity-cnrve is 

 not veryTappreciably modified if we change, within admissable limits 

 the data from which it was derived. On the otlier hand it was 

 expressly stated that the determination of the change of density was 

 only qnite provisional. Its discnssion was deferred to a snbsequent 

 communication, in which, along with the data then used, other ele- 

 ments might be taken into account. (I.e. p. 731). 



These other elements are mainly; the total numbers of stars of 

 ditferent magnitude and their mean parallaxes. As to the first, the 

 numbers: a short time ago I treated all the materials accessible to 

 me (see Publications of the Astr. Lab. at Groningen N". 18) 

 and I think that I obtained very reliable results for the stars brighter 

 than 11.5, fairly reliable ones down to the 15"^^' magnitude. Now, 

 though the mean parallaxes are still wanting, we are already able, 

 by the numbers alone, to arrive at a considerable improvement in 

 the distribution of the densities, at least for the larger distances. 

 Such a derivation will be given in what follows. 



As formerly a separate treatment of the regions of ditferent galactic 

 latitude was not yet attempted, because I think that it will be desirable 

 that in carrying out such a separate treatment we investigate at the 

 same time whether it be admissable or not to assume the same 

 luminosity curve (mixture-law) for the ditferent parts of the system. 



Already I have collected fairly extensive materials for this purpose, 

 but still some time will have to elapse before the investigation can 

 be carried out with advantage. 



In the main my purpose, in making the following determinatiou, 

 was simply to get first notions about the star-density at still greater 

 distances than could ^be reached in our former investigation. The 

 determination embraces also the smaller distances but it remains to 

 be seen whether for these the correction found is or is not an 

 improvement. 



In the Astron. Jou.rn. N". 566 I derived analytical expressions, 



^) See also: Publications of the Astr. Lab. at Groningen No. IL 



