68 



KNOWLEDGE. 



[April 1, 1893. 



group, which, it may be remarked, has Httle or nothing in 

 common with " Gould's chister." This is projected in the 

 form of a belt, and is largely made np of Sirian stars 

 with slight or iuappi-eeiable proper motions ; while 

 Prof. Kapteyn's collection shows no preference for the 

 galactic, or any other plane, and includes only a slight 

 sprinkhng of " white stars," such as Vega, Sirius, Altair, 

 and Regulus, admitted because of the vicinity implied by 

 their motions. 



Beyond a certain Umit of distance (estimated by proper 

 motion), both Sirian and solar stars exhibit marked con- 

 densation towards the plane of the Milky Way. The 

 former, indeed, much more than the latter ; yet even solar 

 stars, when remote enough to be sensibly stationary,'" obey 

 the law of galactic attraction to an equal extent with the 

 whole body of stars down to the ninth magnitude. The 

 distribution, accordingly, of second type stars is apparently 

 regulated by two distinct principles ; and the first, that of 

 globular aggregation about the sun, acts altogether inde- 

 pendently of the second, that of galactic thronging. But 

 how the sphere and the stratum resulting severally from 

 the two kinds of influence are related, whether they are 

 contiguous or widely separated, we have no means of 

 determining. 



Stars of the tirst type are more equably distributed. They 

 are at least exempt from the tendency of their correlatives 

 to concentration in the neighbourhood of the sun. On 

 the other hand, they are drawn more strongly towards the 

 llilky Way. They accumulate mainly into a disc, or 

 possibly into a series of rings. The proportion of their 

 numbers to those of second type objects grows rapidly with 

 increase of distance. Outside a sphere, of which the 

 radius corresponds to an annual proper motion of ()-07", 

 they are in a minority smaller and smaller as its centre is 

 approached ; outside of that sphere they claim about a two- 

 fold numerical superiority. But is the superiority real or 

 fictitious? We seem obliged to adopt the latter alter- 

 native. The disparity can, at any rate, be amply accounted 

 for by the systematic diflerence in real brightness between 

 the two great stellar orders. 



Prof. Kapteyn holds that there is no satisfactory 

 evidence of their differing systematically in real swiftness. 

 He has investigated the matter with a negative upshot. 

 At equal distances, he finds Sirian and solar stars to be 

 pretty equally displaced. The balance, that is to say, does 

 not so far incUne decisively either way. But at equal 

 distances Sirian stars appear brighter by more than two 

 magnitudes than solar stars of similar mass. To send us 

 the same quantity of light, they must then be 2-7 times 

 more remote. Hence, obviously, an indiscriminate collection 

 of stars exceeding a given magnitude represents the 

 contents of a far larger ^olume of space as regards the 

 first than as regards the second stellar order. | If the 

 latter be included in a sphere of mean radius=l, the 

 former must be diffused through a sphere of radius = 2-7. 

 The true proportion of their numbers, as compared with 

 solar stars, would accordingly be increased in such a 

 collection not far from twenty times ! And the chief part 

 of these adventitious stars, if they may be called so, 

 would naturally fall into the ranks of immobile objects. 

 To their presence, then, the excess of first type spectra 

 among the Bradley-Draper stars with evanescent proper 

 motions may safely be attributed. 



The leading results of Prof. Kapteyn's able and ex- 

 haustive discussion may be recapitulated in the two 

 following propositions : — 



1. Stars with appreciable proper motions belong mainly 

 to the solar spectral class, and gather round a point 

 adjacent to the sun, in total disregard to the position of 

 the Milky Way. 



2. Stars sensibly fixed, Sirian and solar alike, although 

 not to the same extent, collect towards the galactic plane. 

 Both types can hence be inferred to obey the same 

 organic laws, and to be united into a coherent whole. 



An imexpected peculiarity of distribution, indicated by 

 this investigation, if not convincingly proved by it, is that 

 stars of determinate magnitude of either type are on the 

 whole more remote when situated in or near the Milky 

 Way. It can only be explained as due to a greater 

 prevalence of larger or more luminous bodies in that 

 region than in other parts of the sky. 



The general shape of the stellar universe is compared 

 by Prof. Kapteyn to that of the Andromeda nebula, as 

 depicted in Mr. Roberts's photographs. The globular 

 nucleus represents the solar cluster, the far-spreading 

 rings or whorls the compressed layers of stars enclosed 

 by the ring of the remote Galaxy. 



* With iji'oper luotiou, that is to say, smaller than 0-04". 

 t Xliis luoUe of ivasouiug has been anticiijatcil by Mr. Monck. 



[Prof. Kapteyn's conclusion that Sirian stars appear 

 brighter by more than two magnitudes than solar stars of 

 similar mass is very interesting in connection with the 

 evidence we already possess as to the relative density of 

 Sirian and solar binary stars. The tables given on pages 

 796-7 of " The Old and New Astronomy " give 0-3094 as 

 the mean density of the binary stars of known period 

 whose spectrum is of the solar type, and 0-021 as the 

 mean density of the binaries of known period whose spec- 

 trum is of the Sirian type — that is, solar binaries are 

 on the average about fifteen times as dense as Sirian 

 binaries. 



So that, if Sirian stars and solar stars have photospheres 

 of equal brightness, the Sirian stars will have on the 

 average a diameter nearly two and a half (2-406) times as 

 great as the diameter of solar stars of the same mass, and 

 they would appear equally bright to us if situated at 2-466 

 times the distance of similar solar stars. In other words, 

 the evidence derived from binary stars shows that Sirian 

 stars appear to us nearly two magnitudes brighter than 

 solar stars of similar mass. 



Prof. Kapteyn's general result seems to me to be involved 

 in his assumption that proper motions are to be taken as 

 the criterion of distance. This seems to me to involve 

 the assumption that all types of stars are moving with 

 the same average velocity, an assumption which is not 

 self-evident, but which seems, on the contrary, improbable 

 in view of what we know as to certain types of stars being 

 associated in clusters. Such clusters evidently form 

 systems, and the individual stars cannot therefore have 

 large proper motions relatively to one another, for such 

 motions could not be controlled by the mutual gravity 

 of the stars forming the system. 



A solar cluster of swift-moving stars, such as Prof. 

 Kapteyn supposes, could not form a permanent system. 

 The vast velocity which we know that our sun and other 

 stars having large proper motions are endowed with would 

 carry them away from the centre of gravity of such a 

 system, if it was composed only of the swift-moving 

 bright stars we see. Their swift motions cannot be con- 

 trolled by one or more dark stars of enormous mass, for 

 the places of such dark attracting masses would be indi- 

 cated by the symmetry of the motion of the bright bodies 

 about them ; and it is evident that such a solar cluster 

 could not be held together by the attraction of rings of 

 matter outside it. — A. C. Ranyard.t 



