in the relative Situation of double Stars, &c. g 6 i 
place, at the annual rate of o",io 5 in right ascension, and o",i2 
in declination towards the north. 
In this manner, we may certainly account for the phenomena 
of the changes which have taken place with the two stars of « 
Geminorum. But the complicated requisites of the motions 
which have been exposed to our view, must surely compel 
every one who considers them to acknowledge, that such a 
combination of circumstances involves the highest degree of 
improbability in the accomplishment of its conditions. On the 
other hand, when a most simple and satisfactory explanation 
of the same phenomena may be had by the effects of mutual 
attraction, which will support the moving bodies in a permanent 
system of revolution round a common centre of gravity, while 
at the same time they follow the direction of a proper motion 
which this centre may have in space, it will hardly be possible 
to entertain a doubt to which hypothesis we ought to give the 
preference. 
As I have now allowed, and even shown, the possibility that 
the phenomena of the double star Castor may be explained by 
proper motions, it will appear that, notwithstanding my foregoing 
arguments in favour of binary systems, it was necessary, on a 
former occasion, to express myself in a conditional manner,* 
when, after having announced the contents of this Paper, I added, 
“ should these observations be found sufficiently conclusive for, if 
there should be astronomers who would rather explain the phe- 
nomena of a small star appearing to revolve round Castor by the 
hypothesis we have last examined, they may certainly claim the 
right of assenting to what appears to them most probable. 
I shall now enter into a more detailed examination of the 
• See Phil. Trans, for 1802, page 486. 
