55 o SCIENCE PROGRESS 



condensation by the ratio of the number of stars in a belt of 

 20° on either side of the galactic plane to the number in a 

 spherical cap of 50 radius around the galactic plane, Kapteyn 

 obtained condensations of r8 at 5 m , 2' 6 at io m , and 10*4 

 at i6 m . Chapman and Melotte obtained 2*1 at 5*, and 

 3*1 at i6 m , a very different rate of progression; it did not 

 seem possible to reconcile the two results by taking into con- 

 sideration that Kapteyn 's scale was not an absolute one and 

 that one result was based on visual and the other on photo- 

 graphic magnitudes. 



Dr. van Rhijn's results are based upon counts of 65 Northern 

 Durchmusterung plates of the Selected Areas of Kapteyn, 

 taken at Harvard Observatory. Prof. Seares has used the 

 counts made by Prof. Turner of the number of stars of different 

 magnitudes in various zones of the Astragraphic Catalogue ; 

 these counts refer to definite but unknown limits of magnitude, 

 the limits being transferred to a numerical scale by comparison 

 with Kapteyn 's tables. He has also made counts on 88 plates 

 taken at Mt. Wilson of the Selected Areas, of which only a 

 preliminary account has so far been published (Proc. Nat. Acad. 

 Sci. 3, 217, 191 7). These results are in close accord with 

 Kapteyn 's, particularly when the magnitude scale used by 

 Kapteyn is reduced to an absolute scale. Thus at i6 m , van 

 Rhijn obtains a condensation of 5*5, Kapteyn (revised) of 6*3; 

 at i7 m .6, Seares obtains 10*2, Kapteyn iro. At the same 

 time, van Rhijn has pointed out an error in the method of 

 reduction used by Chapman and Melotte, the harmonic mean 

 of the star densities actually being obtained by the method 

 adopted, instead of the arithmetic mean ; Dr. Chapman has 

 admitted this error, and in the paper referred to above revises 

 his results accordingly ; the corrected values agree closely 

 with those obtained in the other investigations. We have 

 therefore now three determinations, all based upon photographic 

 magnitudes, which agree closely, so that the galactic conden- 

 sation and progression with magnitude may be said to be well 

 determined. 



By extrapolation from the counts, the total number of stars 

 in our stellar universe can be estimated, assuming that there 

 is no scattering of light in interstellar space. This number 

 is found to be alout 3,000 millions, of which one-half are brighter 

 and one-half fainter than 2 5™. 5. 



