302 Professor Dr. J. C. Kapteyn [May 22, 



a certain time, which may be many centuries, they begin to thin 

 out, as a first warning of an approaching Hmit of the system ? Is 

 there really such a limit, which, once passed, leads us into abysses of 

 void space ? 



Herschel thought there was such a limit, and even imagined that 

 his big telescope penetrated to that limit ; that is, he assumed that 

 his telescope made even the remotest stars visible. On this supposi- 

 tion is based his celebrated disc theory of the system. 



Again, we may condense these questions in this single query : 

 How does the crowding of the stars, or the star-density^ that is the 

 number of stars in any determined volume (let us say in a cubic 

 light century) vary with the distance from our solar system ? 



But there is more. We supposed that our journey went straight 

 on in the direction of Cassiopeia, which is in the Milky-way. What 

 if our journey is directed to the Pleiades, which are at some distance 

 from that belt, or to the Northern Crown, which is still further, or 

 to the Hair of Berenice, which is furthest of all from the Milky- 

 way ? For different regions equally distant from the galaxy we 

 have seen that outward appearances are the same. We may admit, 

 with much probability, that in space, too, we would find little 

 difference. Summing up, the problem of the structure of the 

 stellar system in a first approximation comes to this : — 



Statement of Problem. 



To determine, separately for regions of different galactic latitude, in 



which way the star-density and the mixture vary with the distance 



from the solar system, 



I think that there is well founded hope that, even perhaps within 

 a few years, sufficient materials will be forthcoming which will allow 

 us to attack the problem to this degree of generality, with a fair 

 chance of success. At the present moment, however, our data are 

 yet too scanty for the purpose. Still, they will be sufficient 

 for the derivation of what must be in some sort average conditions 

 in the system. The method of treatment will not be essentially 

 different from that which will be applied later to the more general 

 problem, but we have provisionally to be content with introducing 

 the two following simplifications : — 



Restrictions. 



1. We will assume that the mixture is the same throughout the 

 whole of the system ; 



2. We will not treat the different galactic latitudes separately. 

 The consequence will be that the resulting variations of density 



to which our discussion leads, will not represent the actual variations 

 which we would find if we travelled in space in any determined fixed 

 direction, but a variation which will represent some average of what 



