28. Summary. 



Any character of a star varying in apparent intensity with the distance can 

 be used for studying the constitution of the Milky Way. Such characters are the 

 brightness and the proper motions of the stars and tlie distances between the com- 

 ponents of double stars. 



The relation between the absolute intensity {E) of the character and the 

 apparent intensity (e) is supposed to be known. 



For each character we obtain two relations (fundamental equations) involving 

 four functions: 



1) a(e) = number of stars having the apparent intensity e± y 2 de; 



2) D{r) — density = number of stars per cub. siriometer at the distance r ; 



3) 's{E) = frequency function for the absolute intensity of the character in 



question ; 



4) Me{r) = mean distance of stars having the apparent intensity e ± '^k de. 



If two of these functions are known the two others can be found from the 

 fundamental equations. 



Owing to the imperfect state of the observations no character of the stars is, 

 as yet, known with sufficiant accuracy for determining any two of these functions. 

 Through a combination of two or more characters we are, however, able now to get 

 an approximate, though vague, conception of the construction of the Milky Way. 



The character best known from the observations, especially through the efforts 

 of the Harvard Observatory in America, is the brightness of the stars. The func- 

 tion a[e) — for e — the apparent magnitude {in) — may be considered as compara- 

 tively well known for a great part of the sky, though our knowledge even of this 

 function is very incomplete. 



The corresponding frequency function f{M) for the absolute magnitudes {M) 

 could be determined, if the parallaxes of a sufficiently large number of stars were 

 known. For the present our knowledge in this respect is too incomplete. It must 

 expecially be noted that the spectral type of the stars here plays a predominant rôle. 



As to D{r) this function is a priori fully unknown. It may be that theoretical 

 considerations will at some future time put us in the position to predict the form 



