STRUCTURE OP THE UNIVERSE KAPTEYN. 303 



If SO, how many of them are brighter than our sun, how many 

 fainter? Or, to be more particular, how many per cent of the stars 

 are 10, 100, 1,000, etc., times more hnninous than our sun? How 

 many are equal to the sun, or 10, 100 times fainter? Or in two 

 words: What is the nature of the mixture? Or, lastly, what is the 

 mixture law of the system of the stars? 



And furthermore, in traveling on shall we find the stars in reality 

 equally thickly or rather thinly crowded everywhere? Or shall we 

 find that after a certain time, which may be many centuries, they 

 begin to thin out as a first warning of an approaching limit of the 

 system? Is there really such a limit, which, once passed, leads us 

 into ab3^sses 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 disk 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 cen- 

 tury) 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. Wliat 

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

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

 to the Hair of Berenice, which is farthest 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 differ- 

 ence. Summing up, the problem of the structure of the stellar system 

 in a first approximation comes to this : 



Statement or 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 : 



