3.57 
in the relative. Situation of double Stars, &c. 
ratio of the velocities, therefore, and the directions of the motions, 
are equally given. But this will not be sufficient for the purpose : 
their distance from O must also be taken into consideration. 
It has been shown, that the two stars cannot be at an equal 
distance from us, without an evident connection ; it will there- 
fore be necessary for those who will not allow this connection, 
to place one of them nearer to us than the other. But, as the 
motions which have been assumed, when seen from . different 
distances, will subtend lines whose apparent magnitudes will be 
in the inverse ratio of the assumed distances, it is evident that 
this ratio, if the motions are given, must also be a given one ; 
or that, if the distances be assumed, the ratio of the motions 
must be compounded with the ratio of the distances. How 
then can it be expected that such precise conditions should be 
made good, by a concurrence of circumstances owing to mere 
chance ? Indeed, if we were inclined to pass by the difficulties 
we have considered, there is still a point left which cannot be 
set aside. The motion of the solar system, although its precise 
direction and velocity may still be unknown, can hardly admit 
of a doubt; we have therefore a third motion to add to the 
former two, which consequently will bring the case under the 
statement contained in our 7th number, and will be considered 
hereafter. 
(g) If we should intend to change our ground, and place the 
two motions in O and x , it will then be conceded, that the motion 
of a. is only an apparent one, which owes its existence to the 
real motion of the sun. By this, the effect of the solar parallax 
on any star at the same distance will be given ; and it cannot 
be difficult to assume a motion in x , which shall, with the effect 
of this given parallax, produce the apparent motion, in the 
MDCCCIIIo g A 
