353 
i?i the relative Situation of double Stars, &c. 
Glasgow;* and has, since the publication of my paper, been 
taken up by several astronomers,/ who agree that such a motion 
exists. In consequence of this, let us now, according to No. 3, 
assign to the sun a motion in space, of a certain velocity and 
direction. Admitting therefore a and x to be at rest, let the 
angle PaO be 90 degrees ; then, by the 1st case of No. 3, we 
find that none of the observed changes of the angles of position 
will admit of an explanation. There is moreover an evident 
concession of the point in question, in the very supposition of 
the above angle of 90 degrees ; for, if x be at the same distance 
as a from the sun, and no more than 5" from that star, its 
real distance, compared to that of the sun from the star, will be 
known ; and, since that must be less than the 40 thousandth 
part of our distance from Castor, these two stars must necessarily 
be within the reach of each other’s attraction, and form a binary 
system. 
(d) Let us now take the advantage held out by the sd case 
of No. 3, which allows us to place x far behind a, ; in which 
situation, the angle P^O will be more than 90 degrees. The 
star x being less than a, renders this hypothesis the more 
plausible. Now, as a motion of Castor, be it real or apparent, 
has actually been ascertained, we cannot set it aside ; the real 
motion of O, therefore, in order to account for the apparent one 
of oc, must be of equal velocity, and in a contrary direction ; that 
is, when decomposed, 0^,105 towards/, and o",is, towards s. 
The effect of the sun’s moving from O towards / according to 
* See my note in Phil. Trans. Vol. LXXIII. page 283. 
t See Aslronomhbes Jahrbucb fur das Jabr 178 6 y seite 259. Uber die fortriickung 
■unseres Sonnen- Systems, von Herrn Professor Prevost. Und fiir das Jabr 1805 ; 
seite 1 1.3,. 
