STELLAR ASTRONOMY 397 



even now data, no doubt extremely incomplete but still by no means 

 contemptible, is the recognition of the general character of the dis- 

 tribution of these elements, from which we may get an insight into 

 the general plan of the system, and in due time some glimpses of its 

 history past and future. 



Just as the physicist investigating the small world of the molecules 

 of a gas cannot hope to follow any one particular molecule in its 

 motion, but is still enabled to draw important conclusions as soon 

 as he has determined the mean of the velocities of all the molecules 

 and the frequency of determined deviations of the individual veloc- 

 ities from this mean, so in the greater world of the stars our main 

 hope will be in the determination of means and of frequencies. 



What is the mean mass of the stars? 



How many of them have double, treble - - half, a third - - that 

 mean mass; in other words, what is the frequency of a given mass? 



Are this mean and this frequency the same for the different por- 

 tions of the stellar world? If not, how do they vary? 



In the same way: 



What is the mean luminosity of the stars? What the frequency 

 of given multiples of that mean? How do these quantities vary with 

 the position in space? 



And again: 



What is the mean distance of determined groups of stars and 

 what the frequency of distances different from this mean? Knowing 

 which elements, we shall know the number of stars per unit of vol- 

 ume, that is, the star-density for this group. 



Is this density the same at different distances from the sun? Is it 

 the same in and out of the Milky Way? 



And once more: 



What is the mean velocity of the stars; what the frequency of a 

 determined amount of velocity, and how do these quantities vary 

 with the position? 



The knowledge of all these elements will not only give us a general 

 insight into the structure of the stellar system, but also of its change 

 in a relatively short time. Even if, in the course of time, our know- 

 ledge becomes sufficiently complete, it will yield a notion about the 

 attractive forces at work in the system, from which again a conclusion 

 will be possible in regard to its more remote past and future. 



Looking more closely at the difficulties of the problem, we find that, 

 as far as the masses are concerned, they lie in the fact that, up to the 

 present, but very few traces of a mutual attraction of the stars have 

 been found. But already spectroscopy has made a splendid begin- 

 ning. It has brought to light the fact that a large proportion of the 

 stars are binaries. Campbell estimates the proportion at no less than 

 a fifth of the whole. Of these the motions in the visual line can be 



