in the relative Situation of double Stars, &c. 355 
too large. This shows, that no distance, beyond Castor, at which 
we can place the star, will explain the given observations, 
(e) The last remaining trial we have to examine, is to sup- 
pose x to be nearer than a; the angle PaO, will then be less 
than go degrees ; and the effect of a motion of O towards/, by 
the 2d Table in No. 3, will be an increase of the distance of the 
two stars, and a diminution of their angle of position. But the 
motion Os, which is also to be considered, will add to the in- 
crease of the distance, and counteract the diminution of the 
angle. It is therefore to be examined, whether such an increase 
of distance as we can allow to have escaped observation, will 
explain the change which we know to have happened in the 
angle, during the last 23!- years. By the same method of com- 
pounding the two motions as before, it immediately appears, 
than we cannot place the small star more than about l-tenth of 
the distance Ok on this side of Castor, without occasioning 
such an increase of the apparent distance of the two stars as 
cannot possibly be admitted ; and that, even then, the angle of 
position, instead of being less, will be a few degrees larger, 
at the end of 23^ years, than it was at the beginning. This 
hypothesis, therefore, like all the foregoing ones, must also be 
given up, as inconsistent with my observations. 
It is moreover evident, that the observations of astronomers 
on the proper motion of the stars in general, will not permit us 
to assume the solar motion at pleasure, merely for the sake of 
accounting for the changes which have happened in the ap- 
pearances of a double star. The proper motion of Castor, 
therefore, cannot be intirely ascribed to a contrary motion of 
the sun. For we can assign no reason why the proper motion 
of this star alone, in preference, for instance, to that of Arcturus, 
