PRESIDENT’S ADDRESS. 13 
This conclusion rests in reality upon a very slight basis, but the 
researches of subsequent astronomers show that it was an amazing acci- 
dental approach to truth—indeed, a closer approximation than Herschel’s 
subsequent determinations 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 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 position 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 direc- 
tion 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 inter- 
section 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 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 particular star, would 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 :— 
1. 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 star, 7.¢., its own absolute 
motion in space. 
3. That part of the observed or tabular motion which is due to inevi- 
table error of observation. 
Phil. Trans., 1805, p. 233 ; 1806, p. 205, 
