August i, 1907] 



NA TURE 



323 



angles involved, that it is but in comparatively recent 

 years that any approximate estimate could be formed of 

 the true parallax of any fixed star. Bradley felt sure that 

 if the star 7 Draconis had a parallax of i" he would 

 have detected it. Henderson by " the minute sifting of 

 the numerical results " of his own meridian observations 

 of o Centauri, made at the Cape of Good Hope in 1832-3, 

 first obtained certain evidence of the measurable parallax 

 of any fixed star. He was favoured in this discovery by 

 the fact that the object he selected happened to be, so far 

 as we yet know, the nearest sun to our own. Shortly 

 afterwards Struve obtained evidence of a measurable 

 parallax for a Lyrse and Bessel for bi Cygni. Astronomers 

 hailed with delight this bursting of the constraints which 

 our imperfect means imposed on research. But for the 

 great purposes of cosmical astronomy what we are chiefly 

 concerned to know is not what is the parallax of this or 

 that particular star, but rather what is the average parallax 

 of a star having a particular magnitude and proper motion. 

 The prospect of even an ulliniate approximate attainment 

 of this knowledge seemed remote. The star a Lyrse is one 

 of the brightest in the heavens ; the star 61 Cygni one 

 that had the largest proper motion known at the time ; 

 whilst a, Centauri is not only a very bright star, but it 

 has also a large proper motion. The paralla.xes of these 

 stars must therefore in all probability be large compared 

 with the parallax of the average star ; but yet to deter- 

 mine them with approximate accuracy long series of observ- 

 ations by the greatest astronomers and with the finest 

 instruments of the day seemed necessary. 



Subsequently various astronomers investigated the 

 parallaxes of other stars having large proper motions, but 

 it was only in 1881, at the Cape of Good Hope, that general 

 research on stellar parallax was instituted.' Subsequently 

 at Yale and at the Cape of Good Hope the work was con- 

 tinued on cosmical lines with larger and improved helio- 

 meters." By the introduction of the reversing prism and 

 by other practical refinements the possibilities of systematic 

 error were eliminated, and the accidental errors of observ- 

 ation reduced within very small limits. 



These researches brought to light the immense diversity 

 in the absolute luminosity and velocity of motion of 

 different stars. Take the following by way of example : — 



Our nearest neighbour amongst the stars, a, Centauri, 

 has a parallax of o"-76, or is distant about 4j light-years. 

 Its mass is independently known to be almost exactly 

 equal to that of our Sun ; and its spectrum being also 

 identical with that of our Sun, we may reasonably assume 

 that it appears to us of the same magnitude as would our 

 Sun if removed to the distance of a, Centauri. 



But the average star of llie same apparent magnitude 

 as a, Centauri was found to have a parallax of only o".io, 

 so that either a, Centauri or our Sun, if removed to a 

 distance equal to that of the average fixed star of the 

 first magnitude, would appear to us but little brighter than 

 a star of the fifth magnitude. 



.'\gain, there is a star of only 8J magnitude^ which has 

 the remarkable annual proper motion of nearly 8f seconds 

 of arc — one of those so-called runaway stars — which moves 

 with a velocity of 80 miles per second at right angles to 

 the line of sight (we do not know with what velocity in 

 the line of sight). It is at about the same distance from 

 us as Sirius, but it emits but one ten-thousandth part of 

 the light energy of that brilliant star. Sirius I'tself emits 

 about thirty times the light-energy of our Sun, but it in 

 turn sinks into insignificance when compared with the 

 giant Canopus, which emits at least 10,000 times the light- 

 energy of our Sun. 



Truly " one star differs from another star in glory." 

 Proper motion rather than apparent brightness is the truer 

 indication of a star's probable proximity to the Sun. 

 Every star of considerable proper motion yet examined has 

 proved to have a measurable parallax. 



This fact at once suggests the idea. Why should not the 

 apparent parallactic motions of the stars, as produced by 

 the Sun's motion in space, be utilised as a means of deter- 

 mining stellar parallax? 



1 Mem. R..A.«., vol. xlviii. 



- Annals of ihe C.-ine Ob'ervatnry. vol. viii., part ii., and Trans. Astion. 

 Ohservaterv of Val- Tlniversity, vol.' i. 

 " Gould's Zones, Vh 24:) 



Secular Parallactic Motion of Stars. 

 The strength of such determinations, unlike those made 

 by the method of annual parallax, would grow with time. 

 It is true that the process cannot be applied to the deter- 

 mination of the parallax of individual stars, because the 

 peculiar inotion of a particular star cannot be separated 

 from that part of its apparent motion which is due to 

 parallactic displacement. But what we specially want is 

 not to ascertain the parallax of the individual star, but 

 the mean parallax of a particular group or class of stars, 

 and for this research the method is specially applicable, 

 provided we may assume that the peculiar motions are 

 distributed at random, so that they have no systematic 

 tendency in any direction ; in other words, that the centre 

 of gravity of any extensive group of stars will remain fixed 

 in space. 



This assumption is, of course, but a working hypothesis, 

 and one which from the paper on star-streaming com- 

 municated by Prof. Kapteyn of Groningen to the Johannes- 

 burg ineeting of the Association two years ago we already 

 know to be inexact.' Kapteyn 's results were quite recently 

 confirmed in a remarkable way by Eddington,° using in- 

 dependent material discussed by a new and elegant method. 

 Both results showed that, at least for extensive parts of 

 space, there are a nearly equal number of stars moving in 

 exactly opposite directions. The assumption, then, that the 

 mean of the peculiar motions is zero may, at least for 

 Jhese parts of space, be still regarded as a good working 

 hypothesis. 



.\dopting an approximate position of the apex of the 

 solar motion, Kapteyn resolved the observed proper motions 

 of the Bradley stars into two components, viz., one in the 

 plane of the great circle passing through the star and the 

 apex, the other at right angles to that plane." The former 

 component obviously includes the whole of the parallactic 

 motion ; the latter is independent of it, and is due entirely 

 to the real motions of the stars themselves. From the 

 former the mean parallactic motion of the group is derived, 

 and from the combination of the two components, the 

 relation of velocity of the Sun's motion to that of the 

 mean velocity of the stars of the group. 



.\s the distance, of any group of stars found by the 

 parallactic inotion is expressed as a unit in terms of the 

 Sun's yearly motion through space, the velocity of this 

 motion is one of the fundamental quantities to be deter- 

 mined. If the mean parallax of any sufl'iciently extensive 

 group or class of stars was known we should have at 

 once means for a direct determination of the velocity of 

 the Sun's motion in space; or if, on the other hand, we 

 can by independent methods determine the Sun's velocity, 

 then the mean parallax of any group of stars can be 

 determined. 



Determination of Stellar Motion in the Line of Sight. 



Science owes to Sir William Hoggins the application of 

 Doppler's principle to the determination of the velocity 

 of star-motion in the line of light. The method is now 

 so well known, and such an admirable account of its theory 

 and practical development was given by its distinguished 

 inventor from this Chair at the Cardiff meeting in 1891, 

 that further mention of that part of the matter seems un- 

 necessary. 



The Velocity of the Sun's Motion in Space. 



If by this method the velocities in the line of sight of 

 a sufficient number of stars situated near the apex and 

 antapex of the solar motion could be determined, so that 

 in the mean it could be assumed that their peculiar motions 

 would disappear, we have at once a direct determination 

 of the required velocity of the Sun's motion. 



The material for' this determination is gradually 

 accumulating, and indeed much of it, already accumulated, 

 is not yet published. But even with the compai^atively 

 scant material available, it now seems almost certain that 

 the true value of the Sun's velocity lies between 18 and 20- 

 kilometres per second ; ' or, if we adopt the mean value. 

 It) kilometres per second, this would correspond almost 



1 Rep. Brit. Assrc, idos, p. 257. 

 ■.: Monthly Notices R.A.S.. vo'. IxviL, p 34- 

 " Publications Astron. Lahoralory, Gronineen, No'. 7 and o. 

 J Kapteyn, /Isl. Nadu, No. 3487, p. 108; and Campbell, Astrofltys. 

 Jourtt., x'ii., p. 80. 



NO. 1970, VOL. 76] 



