January 1, 1895.] 



KNOWLEDGE. 



9 



indifferently ill all directions, and that consequently, taking 

 an average of all the motions of the stars composing the 

 group, the effects due to the real motions will destroy each 

 other, and there will remain as the most reliable criterion 

 the effect due to the sun's motion in space. If, however, 

 we compare the proper motions of groups situated in 

 (liriifent parts of the sky, there is a consideration which to a 

 great extent vitiates this conclusion. For, near the point 

 of the heavens towards which the sun and earth are 

 moving known as the ope.v of the solar way, and situated 

 about seven degrees south of the bright star Vega, as 

 indicated by recent researches, and near the point fmni 

 which the sun is monng — known as the <nit-ape.i-, about 

 fifteen degrees south of Sirius — there will be no apparent 

 displacement due to the solar motion through space, as 

 this motion takes place in the line of sight with reference 

 to these points of the sky. The observed proper motion at 

 these points will, therefore, be solely due to the real 

 motion of the stars in those regions. In other parts of 

 the heavens, however, the total proper motion will be a 

 combination of the apparent and real motions of the stars, 

 and for stars in difircnt parts of the heavens it will not 

 follow that stars having equal proper motions are necessarily 

 at the same distance from the earth. To make this point 

 clearer, let us assume that there are two stars at absolutely 

 the same distance from our eye, one situated at or near the 

 solar apes and the other at a point ninety degrees from 

 the apex, and let us suppose that both are moving through 

 space with exactly the same velocity, and in the same 

 direction, say at right angles to the direction of the solar 

 motion. Then, in the case of the star near the apex, the 

 observed " proper motion " will be solely due to the star's 

 )Vfl/ motion, and in the star ninety degrees distant from the 

 apex the "proper motion" will be solely due to the solar 

 motion. Now, unless the stellar motion and the solar 

 motion happen to be equal, the observed " proper motions '' 

 vn\\ not be equal, although both stars are at the same 

 distance from the earth. If both stars are really at rest, 

 the star at the aptx will have no proper motion, while the 

 star ninety degrees distant will have an apparent proper 

 motion due to the sun's motion. To overcome this source 

 of error in estimating the distance of a star from its proper 

 motion. Prof. Kapteyn made use of another measure which 

 is independent of the solar motion. This is the component 

 of the proper motion measured at right angles to a great 

 circle of the sphere passing through a star and the solar 

 apex. The amount of motion iu this direction will evidently 

 not be affected by the sun's motion, and fi-om a discussion 

 of the stars contained in the Draper Catalogue of Stellar 

 Spectra, which were observed by Bradley (and of which the 

 proper motions are consequently now known with accuracy), 

 Prof. Kapteyn tiuds that this motion is " nearly inversely 

 proportional to the distance," that is, the greater the 

 motion the less the distance of the stars, and the smaller 

 the motion the greater the distance. Excluding stars with 

 proper motions greater than half a second of arc per annum, 

 Prof. Kapteyn found that for stars at various distances from 

 the Milky Way this component of the " proper motion " 

 forms a good measure of distance. 



As the result of his investigations on this interesting 

 question, Prof. Kapteyn arrives at the following con- 

 clusions. 



Neglecting stars with small or imperceptible proper 

 motions, we have a group of stars which no longer show 

 any condensation in a plane. Stars with very small or 

 no proper motions show a condensation towards the plane 

 of the Milky Way. This applies to stars of the second or 

 solar type as well as to those of the first or Siriau type of 

 spectrum, and evidently indicates that the stars composing 



the Milky Way lie at a great distance from the earth. The 

 extreme faintuess of the majority of the stars composing 

 the Galaxy seems to confirm this conclusion. The con- 

 densation of stars of the first type is more marked than 

 those of the second, and this agrees with the fact which 

 has been noticed by Prof. Pickering, that the majority of 

 the brighter stars of the Milky Way .show spectra of the 

 first or Sirian type, and, judging from the ease with which 

 { the fainter stars of the Galaxy can be photographed, he 

 concludes that most of these fainter stars are bluish, and 

 probably have spectra of the first type, like Sirius and 

 Vega, which are bluish-white stars. From an enumera- 

 tion of the stars included in the Dorpat Catalogue, 

 I find that sixty-three per cent, of the stars of the 

 Milky Way, as drawn by Heis, have spectra of the 

 Sirian type. 



Prof. Kapteyn finds that this condensation of stars with 

 small proper motions is very perceptible even for the stars 

 visible to the naked eye, and is as well marked in those 

 stars which have spectra of the second type as for all the 

 stars of the ninth magnitude, but for stars of the first type 

 the condensation is still more marked. He considers that 

 this condensation is either partly real or that there is a 

 real thinning out of stars near the pole of the Milky Way. 

 As I have shown elsewhere, M. Celoria's observations with 

 a small telescope, compared with Sir William Herscbel's 

 observations with a large telescope, indicate clearly that 

 there is a real thinning out of stars at the poles of the 

 Milky Way. 



Prof. Kapteyn concludes that the arrangement of 

 the stars suggested by Struve has no real existence. 

 He attributes the fallacy in Struve's hypothesis to 

 the fact that the mean distance of stars of a given 

 magnitude in the Milky Way, and outside it, is not 

 the same. 



Prof. Kapteyn finds that the vicinity of the sun is 

 almost exclusively occupied by stars of the second or solar 

 type, a conclusion which reminds us of Dr. Gould's " solar 

 cluster." He finds that the number of Sirian type stars 

 increases gradually with the distance, and that beyond a 

 distance corresponding to a proper motion of about one- 

 fourteenth of a second per annum the Sirian stars largely 

 predominate. 



In the group of stars known as the Hyades, however, 

 the components of which have a common proper motion 

 both in amount and direction, stars of tbe first and second 

 types appear to be mixed, and Prof. Kapteyn assumes 

 that the two types represent different phases of evolu- 

 tion, and that as the brightest stars of the group are 

 chiefly of the solar type, these stars must be the largest 

 of the group. From this fact he concludes that the 

 solar type stars are in a less advanced stage of evolution 

 than those of the Sirian type. This does not agree with 

 the generally accepted view. Thus Prof. Vogel considers 

 the Sirian stars to represent the earlier stage of stellar 

 evolution. Mr. Proctor held the same opinion, and in 

 Prof. Lockyer's hypothes's of increasing and decreasing 

 tetnperatures in stars of various types he places the Sirian 

 stars at the summit of the curve, and the sun and solar 

 just below them on the descending branch of the curve 

 (" The Meteoritic Theory," pp. 3S0, 381). These hypotheses 

 are in conformity also with tbe current opinion that the 

 sftn^is^au_caolrQ'g body. This discrepancy may perhaps be 

 explained by ^supposing that the hrii/liter stars of the 

 Hyades form a connected group, and that some, at least, 

 of the fainter stars do not belong to the group, but are 

 situated at a great distance behind it. In the case of the 

 Pleiades, which form a much more evident cluster, I find 

 from the Draper Catalogue that the great majority of the 



