206 cosmos. 



(1836 and 1839), by Preuss and Otto Struve in Pulkowa 

 (since the catalogue of 1837), by Madler in Dorpat, and by 

 Mitchell in Cincinnati (Ohio), with a seventeen-feet Munich 

 refractor. How many of these 6000 stars, which appear to 

 the naked eye as if close together, may stand in an imme- 

 diate relation of attraction to each other T forming systems of 

 their own, and revolving in closed orbits — or, in other words, 

 how many are so-called physical {revolving) double stars — 

 is an important problem, and difficult of solution. More re- 

 volving companions are gradually but constantly being dis- 

 covered Extreme slowness of motion, or the direction of the 

 plane of the orbit as presented to the eye, being such as to 

 render the position of the revolving star unfavorable for ob- 

 servation, may long cause us to class physically double stars 

 among those which are only optically so ; that is, stars of 

 which the proximity is merely apparent. But a distinctly- 

 ascertained appreciable motion is not the only criterion. The 

 perfectly uniform motion in the realms of space (i. e., a com- 

 mon progressive movement, like that of our solar system, in- 

 cluding the earth and moon, Jupiter, Saturn, Uranus, and 

 Neptune, with their satellites), which in the case of a con- 

 siderable number of multiple stars has been proved by Arge- 

 lander and Bessel, bears evidence that the principal stars 

 and their . companions stand in undoubted relation to each 

 other in separate partial systems. Madler has made the in- 

 teresting remark, that whereas, previous to 1836, among 

 2640 double stars that had been catalogued, there were only 

 58 in which a difference of position had been observed with 

 certainty, and 105 in which it might be regarded as more 

 or less probable ; at present, the proportion of physically 

 double stars to optically double stars has changed so greatly 

 in favor of the former, that among the 6000 double stars, 

 according to a table published in 1849, 650 are known in 

 which a change of relative position can be incontestably 

 proved.^ The earliest comparison gave one sixteenth, the 



number of multiple stars in the northern hemisphere, discovered at 

 Pulkowa since 1837, at not less than 600. 



* The number of fixed stars in which proper motion has been un- 

 doubtedly discovered (though it may be conjectured in the case of all) 

 is slightly greater than the number of double stars in which change of 

 position has been observed. (Madler, Astr., s. 394, 490, and 520-540.) 

 Results obtained by the application of the Calculus of Probabilities, ac- 

 cording as the several reciprocal distances of the double stars are be- 

 tween 0" and 1", 2" and 8", or 16" and 32", are given by Struve, in his 

 Mens. Microm., p. xciv. Distances less than 0' -8 have been taken, and 



