September 9, 1915] 



NATURE 



45 



parallelism is mainly confined to them, and indicates 

 the genera! directions of the orbital motions of stars 

 in the neighbourhood. An attempted explanation on 

 these lines, as on Prof. Turner's, implies that the sun 

 is some distance from the centre of the stellar system. 



A discovery of an entirely different character was 

 made by Prof. Boss in 1908. He spent many years in 

 constructing a great catalogue giving the most accu- 

 rate positions and motions of 6200 stars obtainable 

 from all existing observations. This catalogue, which 

 was published by the Carnegie Institute, was intended 

 as a preliminary to a still larger one which would give 

 the accurate positions and motions of all the stars 

 down to the seventh magnitude. In the course of this 

 work Prof. Boss found that forty or fifty stars scat- 

 tered over a considerable region of the sky near the 

 constellation Taurus were all moving towards the 

 same point in the sky and with nearly the same 

 angular velocity. He inferred 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 determination of their radial 

 velocities. From 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 distances, and all having the 

 same motion in space, is a very remarkable pheno- 

 menon. It shows, as was pointed out by Prof. Edding- 

 ton, how small is the gravitational action of one 

 star on another, and that the movement of each star 

 is determined 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 distances have been 

 found, and from them luminosities and velocities of 

 individual stars, particulars which are generally only 

 obtainable for stars much nearer to us. 



Proper motions are the main source of our know- 

 ledge of the distances of stars which are beyond the 

 reach of determination by annual parallax. If a star 

 were known to be at rest its distance could be calcu- 

 lated 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 in a century, this gives a displacement of i" 

 for a star at the distance of 500 parsecs. This method 

 has been applied by Kapteyn to determine the dis- 

 tances of the helium stars, as their velocities are 

 sufficiently small to be neglected in comparison with 

 that_ of the solar system. But generally 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 neutralise one another in 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. ;r„j= - i-io8— 0-125 *"• 



In conjunction with another observational 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. Profs. Seeliger 

 and Kapteyn have shown in this way that there is a 

 considerable 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 mathe- 

 matical solution of general questions which arise in 

 the treatment of astronomical statistics has been given 

 by Prof. Schwarzschild. His investigations are of the 

 NO. 2393, VOL. 96] 



greatest value in showing the exact dependence of 

 the density, luminosity, and velocity laws on the statis- 

 tical facts which can be collected from observation. 

 The many interesting statistical studies which have 

 been made are liable to be rather bewildering without 

 the guidance furnis.hed by a general mathematical 

 survey of the whole position. 



When the proper motions are considered in relation 

 to the spectral types of the stars, the small average 

 velocities of the hydrogen stars and still smaller ones 

 of the helium stars found from line-of-sight observa- 

 tions are confirmed. If stars up to a definite limit 

 of apparent magnitude, say, to 6-om., or between 

 certain limits, say 80m. and 90m., are considered, 

 then the solar stars are found to be much nearier than 

 either the red or the blue stars. Thus both red and 

 blue stars must be of greater intrinsic luminosity than 

 the solar stars. As regards blue stars, this agrees 

 with results given by parallax observations. But the 

 red stars appear to consist of two classes, one of great 

 and one of feeble luminosity, and it does not seem that 

 a sufficient explanation is given by the fact that a 

 selection of stars brighter than any given apparent 

 magnitude will include the very luminous stars which 

 are at a great distance, but only such stars of feeble 

 luminosity as are very near. 



The significance of these facts was pointed out by 

 Prof. Hertzsprung and Prof. Russell. They have a 

 very important bearing on the question of stellar 

 evolution, a subject for discussion at a later meeting 

 this week. From the geometrical point of view of my 

 address these facts are of importance in that they help 

 to classify the extraordinarily large range found in the 

 luminosities of stars. Putting the matter somewhat 

 broadly, the A stars, or hydrogen stars, are on the 

 average intrinsically 5 magnitudes brighter than the 

 sun, whilst the range in their magnitudes is such that 

 half of them are within \ magnitude of the mean 

 value. The stars of type M, very red stars, are of two 

 classes. Some of them are as luminous as the A stars, 

 and have a similar range about a mean value 5 mag- 

 nitudes brighter than the sun. Others, on the con- 

 trary, have a mean intrinsic brightness 5 magnitudes 

 fainter than the sun and with the same probable 

 deviation of | magnitude. Between the types M and 

 A there are two classes the distance apart of which 

 diminishes as the stars become bluer. The facts in 

 support of this contention are very forcibly presented 

 by Prof.^ Russell in Nature in May, 19 14. If this 

 hypothesis is true, and it seems to me there is much 

 to be said in its favour, then the apparent magnitude 

 combined with the type of spectrum will give a very 

 fair approximation to the distances of stars which are 

 too far away for their proper motions to be determin- 

 able with accuracy. 



In dealing with the proper motions of the brighter 

 stars, the sky has been considered as a whole. Now 

 that the direction and amount of the solar motion are 

 known, we may hope that, as more proper motions 

 become available, the different parts of the sky will 

 be studied separately. In this way we shall obtain 

 more detailed knowledge of the streaming, and also 

 of the mean distances of stars of different n^agnitudes 

 in all parts of the sky, leading to a determination of 

 how the density of stars in space changes in different 

 directions. A second line of research which may be 

 expected to give important results is in the relation- 

 ship of proper motions to spectral type. There is in 

 preparation at Harvard College by Miss Cannon, under 

 Prof. Pickering's direction, a catalogue giving the 

 type of spectrum of every star brighter than the ninth 

 magnitude. It would be very desirable to determine 

 the proper motions of all these stars. If all the mate- 

 rial available is examined it should be possible to do 

 this to a very large extent. 



