357 
in the relative Situation of double Stars. 
the motions of the stars, or at whatsoever different distances we 
may place them, the effect which is to arise from these combined 
circumstances is positively determined; for the star a. must 
appear to move at the rate of 3", 123 of an arch of a great circle 
in 234- years, and in the direction of 17 0 31' south-preceding its 
parallel ; while the star x, in the same time, must seem to move 
over an arch of 4", 179, in a direction of 32 0 52' south-preceding 
the same parallel. When these quantities, resulting from the 
proper motions of our new Tables, are substituted for those 
which have been used in the paragraph (/) of my former Paper, 
the arguments which it contains will remain in full force, and 
need not be here repeated. 
( g ) The same argument which has been used in the first 
Paper, when the sun and the small star only were supposed to 
be in motion, will perfectly apply to the proper motion of Castor, 
as given in the new Tables. For, as this motion is now to be 
accounted for by the motion of the sun, we have only to sub- 
stitute the velocity of 3", 12 3, in a direction which makes an 
angle of 17 0 30' 56" north-following with the parallel of « 
Geminorum, for the quantity of the solar motion before used; and 
to assign a proper motion to the small star, having a direction 
of 68° io' south- preceding the parallel of a, Geminorum, with a 
velocity which, if the star was at the distance of a from us, 
would carry it in 23^ years through i",4303. 
( 5 ) When the sun and Castor only are supposed to be in 
motion, the former statement of the case will in every respect 
remain conclusive. 
Motion of the three Bodies. 
(z) It remains now only to be shown, that the arguments 
which are contained in my first Paper, against the probability of 
