October 15, 1891] 



NA TURE 



573 



I be further granted that light travels faster with than 

 against such a current, then indeed it becomes specula- 

 tively possible, through slight alternate accelerations and 

 retardations of eclipses taking place respectively ahead 

 of and in the wake of the sun, to determine his absolute 

 path in space as projected upon the ecliptic. That is to 

 say, the longitude of the apex could be deduced together 

 with the resolved part of the solar velocity ; the latitude 

 of the apex, as well as the component of velocity perpen- 

 dicular to the plane of the ecliptic, remaining, however, 

 unknown. 



The beaten track, meanwhile, has conducted two recent 

 inquirers to results of some interest. The chief aim of 

 each was the detection of systematic peculiarities in the 

 motions of stellar assemblages after the subtraction from 

 them of their common perspective element. By varying 

 the materials and method of analysis, Prof. Lewis Boss, 

 Director of the Albany Observatory, hopes that correspond- 

 ing variations in the upshot may betray a significant 

 char.icter. Thus, if stars selected on different principles 

 give notably and consistently different results, the cause 

 of the difference may with some show of reason be sup- 

 posed to reside in specialities of movement appertaining 

 to the several groups. Prof Boss broke ground in this 

 direction by investigating 284 proper motions, few of 

 which had been similarly employed htiore {As/r. Jour., 

 No. 213). They were all taken from an equatorial zone 

 4° 20' in breadth, with a mean declination of -|-3°, ob- 

 served at Albany for the catalogue of the Astronomische 

 Gesellschaft, and furnished data accordingly for a virtually 

 independent research of a somewhat distinctive kind. It 

 was carried out to three separate conclusions. Setting 

 aside five stars with secular movements ranging above 

 100", Prof Boss divided the 279 left available into two 

 sets— one of 135 stars brighter, the other of 144 stars 

 fainter, than the eighth magnitude. The first collection 

 gave for the goal of solar translation a point about 4^ 

 north of a Lyrte, in R.A. 280°, Decl. + 43° ; the second, 

 one some thirty-seven minutes of time to the west of 

 8 Cygni, in R.A. 286°, Decl. -j- 45°. For a third and final 

 solution, twenty-six stars moving 4o"-ioo" were rejected, 

 and the remaining 253 classed in a single series. The 

 upshot of their discussion was to shift the apex of move- 

 ment to R.A. 289°, Decl. -f 51°. So far as the difference 

 from the previous pair of results is capable of interpreta- 

 tion, it would seem to imply a predominant set towards 

 the north-east of the twenty-six swifter motions subse- 

 quently dismissed as prejudicial, but in truth the data 

 employed were not accurate enough to warrant so definite 

 an inference. The Albany proper motions, as Prof Boss 

 was careful to explain, depend for the most part upon the 

 right ascensions of Bessel's and Lalande's zones, and are 

 hence subject to large errors. Their study must be 

 regarded as suggestive rather than decisive. 



A better quality and a larger quantity of material was 

 disposed of by the latest and perhaps the most laborious 

 investigator of this intricate problem. M. Oscar 

 Stumpe, of Bonn {Astr. Nach., Nos. 2999, 3000) took his 

 stars, to the number of 1054, from various quarters, if 

 chiefly from Auwers's and Argelander's lists, critically 

 testing, however, the movement attributed to each of not 

 less than 16" a century. This he fixed as the limit of 

 secure determination, unless for stars observed with ex- 

 ceptional constancy and care. His discussion of them is 

 instructive in more ways than one. Adopting, the addi- 

 tional computative burden imposed by it notwithstanding, 

 Schonfeld's modification of Airy's formulae, he introduced 

 into his equations a fifth unknown quantity expressive of 

 a possible stellar drift in galactic longitude. A negative 

 result was obtained. No symptom came to light of 

 " rotation " in the plane of the Milky Way. 



M. Stumpe's intrepid industry was further shown in his 

 disregard of customarj' "scamping" subterfuges. Ex- 

 pedients for abbreviation vainly spread their allurements ; 



NO. I 146, VOL. 44] 



every one of his 2108 equations was separately and reso- 

 lutely solved. A more important innovation was his sub- 

 stitution of proper motion for magnitude as a criterion of 

 remoteness. Dividing his stars on this principle into 

 four groups, he obtained an apex for the sun's translation 

 corresponding to each as follows : — 



r..^,,^ Number of 

 ^""P- included stars. 



I ... 55r .. 

 IL ... 340 ... 



in. ... los ... 



IV. ... 58 ... 



Proper motion. 



Apex. 



o-i6 to 0-32 ... R.A. 287 '4 Decl. -I- 42 

 0-32 to 0-64 ... ,, 2797 ,, 405 

 0-6410 1-28 ... ,, 287*9 >» 321 

 I '28 and upwards ,, 285*2 ,, 30*4 



Here, again, we find a marked and progressive descent 

 of the apex towards the equator with the increasing 

 swiftness of the objects serving for its determination, 

 leading to the suspicion that the most northerly may be 

 the most genuine position, because the one least affected 

 by stellar individualities of movement. By nearly all 

 recent investigations, moreover, the solar point de mire 

 has been placed considerably further to the east and 

 nearer to the Milky Way, than seemed admissible to 

 their predecessors ; so that the constellation Lyra may 

 now be said to have a stronger claim than Hercules to 

 include it ; and the necessity has almost disappeared for 

 attributing to the solar orbit a high inclination to the 

 medial galactic plane. 



From both the Albany and the Bonn discussions, there 

 emerged with singular clearness a highly significant re- 

 lation. The mean magnitudes of the two groups into 

 which Prof Boss divided his 279 stars, were respectively 

 66 and 86, the corresponding mean proper motions 21 "'Q 

 and 20" '9. In other words, a set of stars on the whole 

 six times brighter than another set owned a scarcely 

 larger sum-total of apparent displacement. And that this 

 approximate equality of movement really denoted approxi- 

 mate equaHty of mean distance was made manifest by 

 the further circumstance that the secular journey of the 

 sun proved to subtend nearly the same angle whichever 

 of the groups was made the standpoint for its survey. 

 Indeed, the fainter collection actually gave the larger 

 angle (i3"73 as against I2""39), and so far an indication 

 that the stars composing it were, on an average, nearer 

 to the earth than the much brighter ones considered 

 apart. 



A result similar in character was reached by M. 

 Stumpe. Between the mobility of his star groups, and 

 the values derived from them for the angular movement 

 of the sun, the conformity proved so close as materially 

 to strengthen the inference that apparent movement 

 measures real distance. The mean brilliancy of his 

 classified stars seemed, on the contrary, quite inde- 

 pendent of their mobihty. Indeed, its changes tended 

 in an opposite direction. The mean magnitude of the 

 slowest group was 6"o, of the swiftest 6"5, of the inter- 

 mediate pair 67 and 6-i. And these are not isolated 

 facts. Comparisons of the same kind, and leading to 

 identical conclusions, were made by Prof. Eastman at 

 Washington in 1889 (Phil. Society Bulletin, vol. xi. p. 143; 

 Proceedings Araer. Association, 1889, p. 71). 



What meaning can we attribute to them .? Uncritically 

 considered, they seem to assert two things, one reason- 

 able, the other palpably absurd. The first — that the 

 average angular velocity of the stars varies inversely 

 with their distance from ourselves — few will be disposed 

 to doubt ; the second — that their average apparent lustre 

 has nothing to do with greater or less remoteness— few 

 will be disposed to admit. But, in order to interpret 

 truly, well-ascertained if unexpected relationships, we 

 must remember that the sensibly moving stars used 

 to determine the solar translation are chosen from 

 a multitude sensibly fixed ; and that the proportion of 

 stationary to travelling stars rises rapidly with de- 

 scent down the scale of magnitude. Hence a mean 



