208 



SCIENCE 



[N.li. Vol. XXVI. No. 659 



same proportion in space, it will be evident 

 that the comparative ricliness of stars in 

 any part of the system will be the same 

 as the comparative richness of the same 

 part of the system in stars of a particular 

 luminosity. Therefore, as we have already 

 found the arrangement in space of the 

 stars of different degrees of luminosity, 

 and consequently their number at different 

 distances from the sun, we must also be 

 able to determine their relative density for 

 these different distances. 



Kapteyn finds in this way that, starting 

 from the sun, the star-density {i. e., the 

 number of stars per unit volume of space) 

 is pretty constant till we reach a distance 

 of some 200 light-years. Thence the 

 density gradually diminishes till, at about 

 2,500 light-years, it is only about one fifth 

 of the density in the neighborhood of the 

 sun.^* This conclusion must, however, be 

 regarded as uncertain until we have by in- 

 dependent means been enabled to estimate 

 the absorption of light in its course through 

 interstellar space, and obtained proof that 

 the ratio of intrinsically faint to bright 

 stars is constant throughout the universe. 



Thus far Kapteyn 's researches deal with 

 the stellar universe as a whole ; the results, 

 therefore, represent only the mean condi- 

 tions of the system. The further develop- 

 ment of our knowledge demands a like 

 study applied to the several portions of the 

 universe separately. This will require 

 much more extensive material than we at 

 present possess. 



As a firet further approximation the in- 

 vestigation will have to be applied sepa- 

 rately to the Milky Way and the parts of 

 the sky of higher galactic latitude. The 

 velocity and direction of the sun's motion 

 in space may certainly be treated as con- 

 stants for many centuries to come, and 

 these constants may be separately deter- 



^ Ptihlications Astron. Lab. Groningen, No. 11. 



mined from groups of stars of various 

 regions, various magnitudes, various proper 

 motions, and various spectral types. If 

 these constants as thus separately deter- 

 mined are different, the differences which 

 are not attributable to errors of observa- 

 tion must be due to a common velocity or 

 direction of motion of the group or class 

 of star to which the sun's velocity or 

 direction is referred. Thus, for example, 

 the sun's velocity as determined by spec- 

 troscopic observations of motion in the line 

 of sight, appears to be sensibly smaller 

 than that derived from fainter stars. The 

 explanation appears to be that certain of 

 the brighter stars form part of a cluster or 

 group of which the sun is a member, and 

 these stars tend to some extent to travel 

 together. For these researches the exist- 

 ing material, especially that of the deter- 

 mination of velocities in the line of sight, is 

 far too scanty. 



Kapteyn has found that stars whose 

 proper motions exceed 0".05 are not more 

 numerous in the Milky Way than in other 

 parts of the sky;-° in other words, if only 

 the stars having proper motions of 0".05 

 or upwards were mapped there would be 

 no aggregation of stars showing the exist- 

 ence of a Milky Way. 



The proper motions of stars of the second 

 spectral type are, as a rule, considerably 

 larger than those of the first type; but 

 Kapteyn comes to the conclusion that this 

 difference does not mean a real difference 

 of velocity, but only that the second- type 

 stars have a smaller luminosity, the mean 

 difference between the two types amount- 

 ing to 2-| magnitudes.-" 



THE FUTURE COURSE OF RESEARCH 



In the last address delivered from this 

 chair on an astronomical subject. Sir Wil- 



^ Verl. Kn. Ahad. Amsterdam, January, 1893. 

 ■''Ihid., April, 1892. 



