PROBLEMS OF ASTROPHYSICS 465 



they cast upon the construction of other systems than ours. When 

 we look at the sky on a clear night, we may be sure that at least one 

 star in six or seven is attended by an invisible companion, comparable 

 in mass with the primary body, the two revolving around their 

 common centre in periods varying from two or three days in many 

 cases, up to three or more years in others. For the triple system of 

 Polaris l the long period perhaps exceeds fifteen or twenty years. As 

 the shortest-period visual binary now known, that of d Equulei, is 

 only 5.8 years, 2 the gap between visual and spectroscopic binaries has 

 been definitely closed. 



The companions of binaries discovered by means of the spectro- 

 graph have not been observed visually in our powerful telescopes, 

 although they have been carefully searched for. They may be so close 

 to the principal star that, viewed from our distance, the two images 

 cannot be resolved. The separation of the components is probably less 

 than one hundredth of a second of arc for most of the binaries thus 

 far announced. Again, for very few of the systems are the spectra 

 of both components recorded. This does not establish that the com- 

 panion is a dark body, but only that it is at least one or two photo- 

 graphic magnitudes fainter than the primary. The fourth-magnitude 

 companion of a second-magnitude star would scarcely be able to im- 

 press its lines upon the primary's spectrum. The invisible components 

 in many spectroscopic binaries might be conspicuous stars, if they 

 stood alone. 



Only those systems have been detected whose periods are relatively 

 short, and for which the variations of radial speed are considerable. 

 The smallest observed variation is that of Polaris six kilometers per 

 second. Had the variation for Polaris been only one kilometer, it 

 would no doubt have escaped detection. Such a variation could be 

 measured by present instruments and methods ; but this range would 

 not have excited the observer's suspicion, and the discovery would 

 have remained for the future. It is probable that there are more 

 systems with variations of speed under six kilometers than there are 

 with larger ones; and all such are awaiting discovery. The velocity 

 of our sun through space varies slightly, because it is attended by 

 companions very minute ones compared with the invisible bodies 

 discovered in spectroscopic binaries. It is revolving around the centre 

 of mass of itself and its planets and their moons. Its orbit around 

 this centre is small, and the orbital speed very slight. The total 

 range of speed is but three one-hundredths of a kilometer per second. 

 An observer favorably situated in another system, provided with 

 instruments enabling him to measure speeds with absolute accuracy, 

 could detect this variation, and in time say that our sun is attended 



1 Astrophysical Journal, xiv, 60. 



2 Lick Observatory Bulletin, no. 84. 



