610 



SCIENCE 



[N. S. Vol. XXV. No. 642 



of increase is decidedly less than fourfold, 

 while a very simple analysis shows that if 

 the stars are strewn with some rough uni- 

 formity of distribution throughout a re- 

 gion of indefinite extent, the average star ' 

 ratio should be very approximately a four- 

 fold increase per magnitude. The dis- 

 parity between this theoretical ratio and 

 that found actually to obtain, throws dis- 

 credit upon the hypothesis above made with 

 respect to the distribation of the stars, and 

 there has been reared upon it the current 

 concept which represents the stellar sys- 

 tem as of finite and measurable extent, 

 broader in the galaxy because here the star 

 ratio is relatively large, smaller at right 

 angles to the Milky Way because here the 

 star ratio diminishes. The idea is that the 

 faint stars are faint because of their 

 greater distance and are more numerous 

 because the volume of space in which they 

 may be distributed increases with the cube 

 of the distance. But if the stellar system 

 reaches out only to a certain limit and the 

 space beyond is void, it can contribute 

 nothing to the number of stars and the star 

 ratio, while everywhere below the value 

 that would obtain for an infinite system 

 ought to diminish very rapidly as we ap- 

 proach the confines and deal with stars 

 fainter than any that have been hitherto 

 enumerated, although Professor Pickering 

 holds that even within the range of magni- 

 tudes covered by his investigations, such a 

 diminution in the value of the ratio is 

 distinctly shown. 



The present paper controverts the views 

 above outlined and shows that the sup- 

 posed fourfold ratio that constitutes their 

 theoretical basis has been erroneously de- 

 rived through ignoring an essential factor 

 of the problem. The faint stars appear 

 faint not only because of their greater dis- 

 tance, but because they actually emit less 

 light than do the brighter ones, and be- 

 cause of this inferior luminosity they are 



nearer than has been assumed. This 

 diminished distance is shown by observa- 

 tion of their proper motions and because of 

 it we have a diminished space available for 

 the faint stars, they are less numerous and 

 the star ratio smaller than is required by 

 the erroneous theory above considered. 

 When the diminishing intrinsic brightness 

 of the fainter stars is properly taken into 

 account the author finds from a discussion 

 of the star ratio for galactic stars down 

 to the faintest yet enumerated (the Her- 

 schel gauges), that there is here no indica- 

 tion of a limit to the stellar system. 



Outside the galaxy the conditions are 

 different, the values of the star ratio are 

 progressively smaller and suggest some one 

 of the following alternative conditions or 

 possibly a combination of them : 



(a) At right angles to the galaxy the 

 limits of the stellar system fall within the 

 range of vision, as indicated above. 



(&) The stars remote from the plane of 

 the galaxy are on the average progressively 

 less luminous than those in the galaxy. 



(c) The transmission of light through 

 the extra-galactic spaces is impeded by 

 some absorbing medium which serves to 

 diminish the brilliancy of the stars in 

 larger measure than is the case in the 

 galaxy. 



Any of these alternatives will serve in 

 explanation of the observed facts and it is 

 not now feasible to make definitive choice 

 among them. 



Preliminary Wwve-lengths from Plash 

 Spectra taken in Spain, 1905: S. A. 

 Mitchell. 



The flash spectra were photographed by 

 means of a Rowland four-inch grating 

 ruled on a parabolic surface. The grating 

 was used without a slit, so that the spectro- 

 graph consisted merely of grating and 

 photographic plate. The spectra, which 

 show wonderfully fine definition, extend 



