August 16, 1907] 



SCIENCE 



201 



greater obliquity of the Eeliptick, 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 recogni- 

 tion of what we now call "proper motion." 



Tobias Mayer, in 1760, seems to have 

 been the first to recognize 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 Sci- 

 ences 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 op- 

 posite quarter would mutually approach each 

 other. In the same manner one who walks in the 

 forest sees the trees which are before him sepa- 

 rate, and those that he leaves behind approach 

 each other. 



No statement of the matter could be 

 more clear; but Mayer, with the meager 

 data at his disposal, came to the conclusion 

 that "the motions of the stars are not 

 governed by the above or any other com- 

 mon law, but belong to the stars them- 

 selves. ' ' 



Sir William Herschel, in 1783, made the 

 first attempt to apply, with any measure of 

 success, Mayer's principle to a determina- 

 tion 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 A 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 sub- 

 'Phil. Trans., 1783, p. 247. 



sequent astronomers show that it was an 

 amazing accidental approach to truth — in- 

 deed, a closer approximation than Her- 

 schel 's subsequent detei-minations of 1805 

 and 1806, which rested on wider and better 

 data.i" 



Consider for a moment the conditions of 

 the problem. If all the stars except our 

 sun were at rest in space, then, in accord- 

 ance with Mayer's statement, just quoted, 

 all the stars would have apparent 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 posi- 

 tion of each star of which the apparent 

 motion is known was plotted 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 

 this point through any star would coincide 

 with the line of direction of that star's 

 proper motion. The arrow-heads would 

 all point to that intersection of the great 

 circles which is the antapex of the solar 

 motion, and the other point of intersection 

 of the great circles would be the apex, 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 con- 

 siderable percentage of error, it would be 

 impossible to find any point on the sphere 

 such that every great circle passing through 

 it and any particular star, would in every 

 case be coincident with the observed direc- 

 tion of motion of that star. 



Such discordances would, on our origi- 

 nal assumption, be due to errors of observa- 

 tion, but in reality much larger discord- 

 ances will occur, which are due to the fad: 

 that the other stars (or suns) have inde- 

 pendent motions of their own in space. 



"Pfea. Trans., 1805, p. 233; 180G, p. 205. 



