322 



NATURE 



[August i, 1907 



in considerable detail. But I have not there made adequate 

 reference to the labours of Dr. Gould and Dr. Thome at 

 Cordoba. To their labours, combined with the work done 

 under Stone at the Cape, we owe the fact that for the 

 epoch 1875 the meridian sidereal astronomy of the southern 

 hemisphere is nearly as well provided for as that of the 

 northern. The point I wish to make is that the facts of 

 exact sidereal astronomy in the southern hemisphere may 

 be regarded as dating nearly a hundred years behind those 

 of the northern hemisphere. 



The Constitution of the Universe. 



It was not until 1718, when Edmund Hatley, afterwards 

 Astronomer Royal of England, read a paper before the 

 Royal Society,' entitled " Considerations on the Change 

 of the Latitudes of Some of the Principal Fixt Stars," 

 that any definite facts were known about the constitution 

 of the universe. In that paper llalley, who had been 

 investigating the precession of the equinoxes, says : " But 

 •while I was upon this enquiry I was surprized to find 

 the Latitudes of three of the principal Stars in heaven 

 directly to contradict the supposed greater obliquity of the 

 Ecliptick, which seems confirmed by the Latitudes of most 

 of the rest." 



This is the first mention in history of an observed 

 change in the relative position of the so-called fixed stars 

 — the first recognition of what we now call " proper 

 motion." 



Tobias Mayer, in 1760, seems to have been the first to 

 recognise that if our Sun, like other stars, has motion in 

 space, that motion must produce apparent motion amongst 

 the surrounding stars; for in a paper to the Gottingen 

 Academy of Sciences he writes : " If the Sun, and with 

 it the planets and the Earth which we inhabit, tended to 

 move directly towards some point in the heavens, all the 

 stars scattered in that region would seem to gradually move 

 apart from each other, whilst those in the opposite quarter 

 would mutually approach each other. In the same manner 

 one who walks in the forest sees the trees which are before 

 liim separate, and those that he leaves behind approach 

 each other." No statement of the matter could be more 

 clear; but Mayer, with the meagre data at his disposal, 

 came to the conclusion that " the motions of the stars are 

 not governed by the above or any other common law, but 

 belong to the stars themselves." 



Sir William Herschel, in 1783, made the first attempt 

 to apply, with any measure of success, Mayer's principle 

 to a determination of the direction and amount of the solar 

 motion in space.- He derived, as well as he could from 

 existing data, the proper motions of fourteen stars, and 

 arrived by estimation at the conclusion that the Sun's 

 motion in space is nearly in the direction of the star 

 \ Herculis, and that 80 per cent, of the apparent motions 

 of the fourteen stars in question could be assigned to this 

 common origin. 



This conclusion rests in reality upon a very slight basis, 

 but the researches of subsequent astronomers show that it 

 was an amazing accidental approach to truth — indeed, a 

 closer approximation than Herschel 's subsequent determin- 

 ations of 1805 and 1806, which rested on wider and better 

 data.' 



Consider for a moment the conditions of the problem. 

 If all the stars except our Sun were at rest in space, then, 

 in accordance with Mayer's statement, just quoted, all the 

 stars would have apoarent motions on great circles of the 

 sphere away from the apex and towards the antapex of 

 the solar motion. That is to say, if the position of each 

 star of which the apparent motion is known was plottec" 

 on the surface of a sphere and a line with an arrow-head 

 drawn through each star showing the direction of its motion 

 on the sphere, then it should be possible to find a point 

 on_ the sphere such that a great circle drawn from thir 

 point through any star would coincide with the line of 

 direction of that star's proper motion. The arrow-head: 

 would all point to that intersection of the great circlr- 

 which isthe antapex of the solar motion, and the other 

 point of intersection of the great circles would be the apex 



1 Phil. Trans., 1718, p. 738. 



2 //wW., 1783, p. 247. 



3 /I'ii/., 1805, p. 233 ; i8c6, p. J05. 



NO. 1970. VOL. 76] 



that is to say, the direction of the Sun's motion in 

 space. 



But as the apparent stellar motions are small and only 

 determinable with a considerable percentage of error, it 

 would be impossible to find any point on the sphere such 

 that every great circle passing through it and any par- 

 ticular star, w-ould in every case be coincident with the 

 observed direction of motion of that star. 



Such discordances would, on our original assumption, 

 be due to errors of observation, but in reality much larger 

 discordances will occur, which are due to the fact that 

 the other stars (or suns) have independent motions of their 

 own in space. This at once creates a new difficulty, viz., 

 that of defining an absolute locus in space. The human 

 mind may exhaust itself in the effort, but it can never 

 solve the problem. We can imagine, for example, the 

 position of the Sun at any moment to be defined with 

 reference to any number of surrounding stars, but by no 

 effort of imagination can we devise means of defining the 

 absolute position of a body in space without reference to 

 surrounding material objects. If, therefore, the referring 

 objects have unknown motions of their own, the rigour of 

 the definition is lost. 



What we call the observed proper motion of a star has 

 three possible sources of origin : — 



(i) The parallactic motion, or the effect of our Sun's 

 motion through space, whereby our point of view of 

 surrounding celestial objects is changed. 



(2) The peculiar or particular motion of the stac, i.e., its 

 own absolute motion in space. 



(3) That part of the observed or tabular motion which 

 is due to inevitable error of observation. 



In all discussions of the solar motion in space, from that 

 of Herschel down till a recent date, it has been assumed 

 that the peculiar motions of the stars are arranged at 

 random, and may therefore be considered zero in the mean 

 of a considerable number of them. It is then possible to 

 find such a value for the Precession, and such a common 

 apex for the solar motion as shall leave the residual 

 peculiar motions of the stars under discussion to be' in the 

 mean = zero. That is to say, we refer the motion of the 

 Sun in space to the centre of gravity of all the stars con- 

 sidered in the discussion, and regard that centre of gravity 

 as immovable in space. 



In order to proceed rigorously, and especially to deter- 

 mine the amount as well as the direction of the Sun's 

 motion in space, we ought to know the parallax of every 

 sta'r employed in the discussion, as well as its proper 

 motion. In the absence of such data it has been usual 

 to start from some such assumption as the following : the 

 stars of a particular magnitude arc roughly at the same 

 distance; those of different classes of magnitude may be 

 derived from the hypothesis that on the average they have 

 all equal absolute luminosity. 



The assumption is not a legitimate one — 



(i) Because of the extreme difference in the absolute 

 luminosity of stars. 



(2) Because it implies that the average absolute 

 luminosity of stars is the same in all regions of space. 



The investigation has been carried out bv many successive 

 astronomers on these lines with fairly accordant results as 

 to the position of the solar apex, but with very unsatis- 

 factory results as to the distances of the fixed stars.' In 

 order to jildge how far the magnitude (or brightness) of 

 a star is an index of its probable distance, we must have 

 evidence from direct determinations of stellar parallax. 



Stellar Parallax. 



To extend exact measurement from our own solar system 



to that of other suns and other systems may be regarded 



as the supreme achievement of practical astronomy. So 



great are the difficulties of the problem, so minute the 



1 Krat^^iXiAfrc^ M?m. />yi'scniis al'Arad. hup ih's Sciences St. PiHershoitr^^ 

 tome iii. : l.und.ihl, Astron. Natltrichten. ^q8, 20Q ; Argelander, .,4j^rf7«. 

 Nachrkhh-H. 398 110 ; Olto Slruvc, Mhii. Ara.l. drs .Stiriicc.'! SI. P/ler.<- 

 I'oiirg.vi'^ S^rie. Math, et Phys., tome iii., p. 17; Galloway, Phil. Tran-:., 

 1847. p 7g ; M.idler, Dorpat Observations, vol. xiv., and Ast. Nach., 566. 

 213: Airy, Mem R.A S., vol. xxviii.. p. 143: Dunliin. Mem. R A.S .vol. 

 xxsii-, p. 19; Stone, Monthly Notices R.A.S., vol. xxiv.. p. 36; De Ball, 

 Inaugural tlis<ertation, Bonn, 1877; Rancken, .Aslrm. Nnclirichtiu,-!i%l. 

 149: Bischoff, Inaugural nis>ert.ation. Bonn. 1884; Ludwig Struve, .!/«« 

 Acad. St. Pflerstcu.g, vii'-' s^rie, tome xxxv.. No. 3. 



