440 



SCIENCE 



[N. S. Vol. XLII. No. 1083 



of the orbital motions of stars in the neigh- 

 borhood. An attempted explanation on 

 these lines, as on Professor Turner's, im- 

 plies that the sun is some distance from the 

 center of the stellar system. 



A discovery of an entirely different char- 

 acter was made by Professor Boss in 1908. 

 He spent many years in constructing a 

 great catalogue giving the most accurate 

 positions and motions of 6,200 stars obtain- 

 able from all existing observations. This 

 catalogue, which was published by the Car- 

 negie Institution, was intended as a prelim- 

 inary to a still larger one which would give 

 the accurate positions and motions of all 

 the stars down to the seventh magnitude. 

 SEn the course of this work Professor Boss 

 ifound that forty or fifty stars scattered 

 toyer a considerable region of the sky near 

 t3ie constellation Taurus were all moving 

 towards the same point in the sky and with 

 nearly the saiae angular velocity. He in- 

 ferred that these stars were all moving in 

 parallel directions with an equal linear 

 velocity, and the supposition was verified, 

 in the case of several of them, by the deter- 

 mination of their radial velocities. Prom 

 these data he was able to derive the distance 

 of each star and thus its position in space. 

 The existence of a large group of stars, 

 separated from one another by great dis- 

 tances, and all having the same motion in 

 space, is a very remarkable phenomenon. 

 It shows, as was pointed out by Professor 

 Eddington, how small is the gravitational 

 action of one star on another, and that the 

 movement of each star is determiaed by the 

 total attraction of the whole mass of the 

 stars. Several other interesting moving 

 clusters have been found since. For all the 

 stars belonging to these clusters, the dis- 

 tances have been found, and from them lu- 

 minosities and velocities of individual stars, 

 particulars which are generally only ob- 

 tainable for stars much nearer to us. 



Proper motions are the main source of 

 our knowledge of the distances of stars 

 which are beyond the reach of determina- 

 tion by annual parallax. If a star were 

 known to be at rest its distance could be 

 calculated from the shift of its apparent 

 position caused by the translation of the 

 solar motion. As the solar system moves 

 410 times the distance of the earth from the 

 sun iu a century, this gives a displacement 

 of 1" for a star at the distance of 500 

 parsecs. This method has been applied by 

 Kapteyn to determine the distances of the 

 helium stars, as their velocities are suffi- 

 ciently small to be neglected in comparison 

 with that of the solar system. But gen- 

 erally it is only possible to find the mean 

 distances of groups of stars of such size 

 that it may be assumed that the peculiar 

 motions neutralize one another ia the mean. 

 For example, the average distance of stars 

 of type A, or stars of the fifth magnitude, 

 or any other group desired may be found. 

 In this way Kapteyn has found from the 

 Bradley stars that the mean parallax of 

 stars of magnitude m is given by the 

 formula 



log. 7rOT=— 1.108 — 0.125 m. 



In conjunction with another observa- 

 tional law which expresses the number of 

 stars as a function of the magnitude, this 

 leads to a determination of the density of 

 stars in space at different distances from us, ' 

 and also of the ' ' luminosity law, ' ' i. e., the 

 percentage of stars of different absolute 

 brightness. Professors Seeliger and Kapteyn 

 have shown in this way that there is a con- 

 siderable falling off of star-density as we 

 go further from the solar system. It seems 

 to me very necessary that this should be 

 investigated in greater detail for different 

 parts of the sky separately. A general 

 mathematical solution of general questions 

 which arise in the treatment of astronom- 



