STELLAR ASTRONOMY 411 



assume a value about 200 or 300 times higher in the theory which 

 assumes absorption than we should in the theory which neglects it. 



For shells at a smaller distance the difference of the density in the 

 two theories becomes rapidly smaller, to vanish altogether in the 

 immediate vicinity of the sun. 



On the other hand, this difference increases with enormous rapidity 

 for greater distances. For a distance of 10 units we are already led 

 to a density of over 20,000,000,000 times that which would be found 

 for a transparent universe. 



I think that we are justified in rejecting a value of the absorption 

 leading to such results. With an amount of absorption ten times 

 smaller, however, we find, for distance 10, a star-density nearly equal 

 to that in the vicinity of the sun, a state of things against which 

 there can be no a priori objection. 



From considerations like the preceding it must be evident that we 

 cannot hope to get a thorough insight into the real structure of the 

 universe without attacking this problem of the absorption of light 

 in space. Not to argue in a vicious circle, the determination of its 

 amount has to be independent of the star-density at different dis- 

 tances from the sun. 



I shall not stop to consider a method for this determination, which 

 I have explained elsewhere. 1 It may suffice to say that, here again, 

 we can only arrive at a satisfactory solution when we have at our 

 disposal the necessary data for the proper motions of very faint 

 stars. 



In what precedes we have considered how we may hope to find: 

 (1) the arrangement of the stars in space; (2) the frequency of differ- 

 ent degrees of luminosity. We thall hardly succeed in deriving in the 

 same way what we may call the law of the velocities, that is, we shall 

 not be able to find the frequency with which determined velocities 

 occur in the stellar world. 



This law, however, is readily obtainable by spectroscopic observa- 

 tion. If from the directly observed radial velocities we subtract 

 that part which is due to the motion of the solar system, and which, 

 since Campbell's observations, is known with very respectable pre- 

 cision, we obtain at once the real velocity of the stars in the line of 

 sight. Simple countings will thus furnish us immediately with the 

 frequency of different values of this component. Hence, adopting 

 our fundamental hypothesis, we may readily derive the frequency of 

 the total velocities themselves, by considerations founded on the 

 theory of probabilities. 2 The following table shows what I derived, 

 in a somewhat indirect way, from the results published by Campbell; 3 



1 See Astronomical Journal, no. 566. 



2 Publications of the Astronomical Laboratory at Groningen, no. 5, pp. 11, 12. 



3 Astronomical Journal, xvm, p. 80. 



