in the relative Situation of double Stars, &c. 353 
to the foregoing hypothesis, is a star that has no real motion, 
its apparent motion will give us the velocity and direction of the 
motion of the solar system ; and, this being obtained, we shall 
also have the relative parallax of every star, not having a proper 
motion, which is affected by the solar motion. Astronomical 
observations on the proper motion of many different stars, 
however, will not allow us to account for the motion of a Ge- 
minorum in the manner which the foregoing instance requires; 
the hypothesis, therefore, of its being at rest, must be rejected. 
( h ) If we place our two motions in O and «, we shall be 
led to the same conclusion as in the last hypothesis. The 
known proper motion of «, and the situations of the small star 
in 1779 and 1803, given by my observations, will ascertain the 
apparent motion, of x, now supposed to be at rest. Then, since 
the change in the place of x must be intirely owing to the effect 
of parallax, it will consequently give us, in the same manner as 
before, the quantity and direction of the motion of the solar 
system, and the relative distances of all such stars as are af- 
fected by it. But, here again, the solar motion required for the 
purpose is such as cannot be admitted; and the hypothesis is 
not maintainable. 
Motion of the three Bodies. 
(i) There is now but one case more to consider, which is, 
according to No. 5, to assign real motions to all our three 
bodies ; and this may be done as follows. Suppose the sun to 
move towards a Herculis, with the annual velocity 1 . 
Let the apparent motion of a Geminorum be as it is stated 
in the astronomical tables before mentioned ; but suppose it to 
arise from a composition of its real motion with the effect of the 
3 A 2 
