398 ASTROMETRY 



studied. They will furnish us in time, not generally with individual 

 masses, but with a thorough knowledge, both of the mean masses 

 and of the frequencies of determined deviations from these means, 

 at least for the stars of this class. 



The remaining elements are: 



The three coordinates and the three components of the velocity. 



Of the coordinates two are known for a great number of stars, and 

 there is nothing in the way of a more complete knowledge where such 

 may be wanted. 



Of the third coordinate, the distance, we know exceedingly little. 



Of the three components of the velocity we know, or may soon 

 hope to know, for great numbers of stars: 



By spectroscopic observation, the absolute value of one of the 

 components; 



By the classical astronomical observations ancient and modern, 

 the two others expressed in arc. 



Here, too, our data, to be complete, require the knowledge of the 

 distances. So at the bottom of all lies the difficulty of the determina- 

 tion of the distances. 



This has long been felt, and endeavors have not been wanting to 

 remedy the defect. 



By these endeavors it has become evident that, save in exceptional 

 cases, these determinations are beyond our power. 



Astronomers looked out, therefore, for such exceptional cases, and 

 nearly exclusively concentrated their effort on these. There will be, 

 however, little to encourage us to go on in this way, as soon as the 

 parallaxes of a few hundreds of the most promising objects (stars of 

 excessive brightness or proper motion) shall have been satisfactorily 

 determined. Not only will the most exceptional arid really promis- 

 ing objects be exhausted to a great extent, but we must not forget, 

 moreover, that the knowledge of the distance of such selected objects 

 will directly but little further our insight into the general structure 

 of the system. Just because they are selected objects they will not 

 be representative of the whole. What other way remains open? 



The difficulty depends evidently on the smallness of the parallaxes, 

 in other words, on the smallness of the diameter of the earth's orbit 

 as a base. We are thus necessarily driven to employ the only greater 

 base available, viz. the path traversed by the solar system in its motion 

 through space. 



The distance traversed by the sun since Bradley 's time is already 

 well over 300 times the diameter of the earth's orbit. The parallactic 

 motion corresponding thereto, where not foreshortened, must amount 

 to over 7" for the mean of the stars of the sixth magnitude, to about 

 2* for those of the ninth. 



