ON THE PROPER MOTIONS OF THE FIXED STARS. 



Bv W. r)OI?i:KrK, Pir.I).. f.r.a.s.. m.r.i.a. 



Halley found that some of the briglitest fixed stars 

 had changed their places since they had been observed 

 by the ancient Greeks, and such changes are so 

 obvious as to be recognised on ancient coins. Sir 

 \\'illiam Herschel. in 178 J, arrived at the conclusion 

 that a relative motion of the Sun among the fixed 

 stars in the direction of a point situated near X 

 Herculis would account for the greater part of these 

 proper motions : the motion of the sun towards the 

 " apex " must cause the fixed stars in half the sk\- to 

 apparenth" move awav from that point, and in the 

 other lialf of the sk\- to move towards the 

 diametrically opposite point, the '" anti-apex."' Since 

 then a great manv astronomers have determined the 

 situation of the " apex," but the results do not agree 

 very well, especially as regards the declination. 

 Bessel investigated the matter and declared him- 

 self dissatisfied with the evidence. When the 

 direction of the proper motion of a fixed star 

 has been ascertained, a great circle laid through 

 the positions of the star observed at two epochs is 

 thereby determined, and if the great circles belonging 

 to different stars intersect in a point (the apex), it is 

 easy to see that the poles of these great circles must 

 lie on another great circle, of which the apex is the 

 pole. Bessel found that the poles do not lie on or 

 near a great circle but are scattered over the skw 

 Kobold, the editor of the Astroiiomischc Xciclirichfen, 

 who some vears ago took up Bessel's in\'estigations. 

 proceeds as follows. He imagines the celestial 

 sphere inscribed in a cube which touches the 

 S{)here at the two poles and at four points 

 on the equator. He supposes the eye of the 

 observer situated in the centre of the sphere, and 

 any great circle on the sphere is then projected as 

 a straight line on one or more of the faces of the 

 cube. Kobold had already used maps made on this 

 principle in determining radiants of shooting stars, 

 and the writer had subsequently, in Hongkong, used 

 similar maps for the same purpose. Kobold projected 

 the poles of a great number of proper motions on 

 such maps. Those that correspond to proper 

 motions intersecting in the apex should lie on a 

 straight line corresponding to the great circle of 

 which the apex is the pole, but that is not clearly 

 shown on the maps. 



Kapte}-n, who has the merit of ha\'ing originated 

 man}- hypotheses that appear destined to aid greatly 

 in the astronomy of fixed stars, solves the difficulty by 

 accounting for a great number of proper motions on 

 the supposition that there are two distinct apices 

 both close to the galax)-. It had, indeed, in course 

 of years, become the general impression that the 

 galaxy is made up not of isolated heavenly bodies 

 but of a conglomerate of clusters of stars and 



nebulae. There was, therefore, nothing extra- 

 ordinary in the circumstance that the stars 

 belonging to two clusters did not move in the same 

 direction. Kapteyn's hypothesis has been examined 

 at the Greenw ich Observator}- and confirmed there 

 by the independent evidence of proper motions, 

 other than those used by Kapteyn. It has been 

 confirmed also at the Cape of Good Hope. It has 

 been to some extent confirmed by s[iectroscopic 

 evidence at the Cape Observatory and at tlie Lick 

 Observatorw 



The speed in miles with which a star is moving 

 towards or away from the earth can be measured in 

 the spectrum, the wave-length of the lines being 

 respectively shortened or lengthened, and it is found 

 that the stars on opposite sides of the sk\- indicate a 

 general drift or even two drifts, but the objects used 

 should be evenlv distributed over the \\hole sk\'. and 

 the spectra of only few faint stars are known with 

 sufficient accuracy- for this purpose. 



Meantime other radiants have been found. Boss, 

 editor of the 4s//-o/;o/n/c(T/ Jo»/7k7/, has shown that 

 the Hvades form a great cluster moving in parallel 

 lines towards a certain radiant point. .\nother 

 apparently- (but perhaps only apparentl}-) much larger 

 cluster, which has been investigated at the Potsdam 

 Observator\-, contains the stars in the Great Bear, 

 Sirius and other bright stars. 



As mentioned above, the spectroscope enables 

 astronomers to measure tiie motion of a heavenh- 

 body in the line of sight in miles per hour. The 

 proper motion, expressed in seconds of arc, shows 

 how much it is moving in the line perpendicular to 

 the line of sight. When the direction of motion in 

 space is known, then the parallax is at once obtained 

 from these two quantities, and that direction is given 

 by the radiant. Parallaxes of fixed stars are more 

 accurately determined in this wa\' than b\' an\- other 

 method. Numerous results have been obtained. 

 Thev show- that the magnitude of a star forms no 

 guide to its distance from us. Stars of different 

 intrinsic brightness are mixed in space. Therefore, 

 it would be no wonder if some of the small telesco[)ic 

 stars should turn out to be comparatively near the solar 

 system. Proper motions have hitherto been deter- 

 mined bv comparing positions recentl\- determined by 

 the meridian circle with older results. Burnham, at 

 the Yerkes Observatory, has of late years determined 

 a number of proper motions by aid of micrometric 

 measures compared with previous measures made 

 by Struve, Sir Robert Ball and others. In those 

 cases where his results differ from the result of 

 meridian work, the difference is probably caused 

 bv hitherto unsuspected proper motions of faint stars, 

 which it will be possible to determine by future 



