VOL. LXXIII.] PHILOSOPHICAL TRANSACTIONS. 403 



proper motion of the stars, let us first consider what will be the consequence of a 

 proper motion in the sun ; and let it move in a direction from a towards b, and 

 suppose it now arrived at c. Here, by a mere inspection of the figure, it will be 

 evident, that the stars s, s, s, which were before seen at a, a, a, will now, by the 

 motion of the sun from s to c, appear to have gone in a contrary direction, and 

 be seen at b, b, b ; that is, every star will appear more or less to have receded from 

 the point b, in the order of the letters ab, ab, ab. The converse of this pro- 

 position is equally true; for if the stars should all appear to have had a retrograde 

 motion, with respect to the point b, it is plain, on a supposition of their being 

 at rest, that the sun must have a direct motion towards the point b, to occasion 

 all these appearances. From a due consideration of what has been said, we may 

 draw the following inferences. 



1. The greatest or total systematical parallax of the fixed stars, fig. 9, will fall 

 on those that are in the line de, at rectangles to the direction ab of the sun's 

 motion. 2. The partial systematical parallax of every other star, s, s, s, not in the 

 line de, will be to the total parallax, as the sine of the angle Bsa, (being the stars 

 distance from that point towards which the sun moves,) to radius. 3. The 

 parallax of stars at different distances will be inversely as those distances ; that is, 

 one half at double the distance, one 3d at 3 times, and so on ; for the subtense 

 sc remaining the same, and the parallactic angle being very small, we may admit 

 the angle ssc, to be inversely as the side ss, which is the star's distance. — 

 4. Every star at rest, to a system in motion, will appear to move in a direction 

 contrary to that in which the system is moving. 



Hence it follows, that if the solar system be carried towards any star situated 

 in the ecliptic : ever}- star, whose angular distance in antecedentia (reckoned on 

 the ecliptic from the star towards which the system moves) is less than ] 80 de- 

 grees, will decrease in longitude. And that, on the contrary, every star, whose 

 distance from the same star (reckoned upon the ecliptic but in consequentia) is 

 less than 180 degrees, will increase in longitude, in both cases without alteration 

 of latitude. 



The immense regions of the fixed stars may be considered as an infinitely ex- 

 panded globe, having the solar system for its centre. With this idea it will 

 occur to us, that no method can be so proper for finding out the direction of the 

 motion of the sun, as to divide our observations on the systematical parallax of 

 the fixed stars into 3 principal zones. These, for the convenience of fixed in- 

 struments, may be assumed so as to let them pass around the equator and the 

 equinoctial and solstitial colures, every one being at rectangles to the other two, 

 'according to the 3 dimensions of solids. And since no observations can be so 

 conveniently made to ascertain small relative proper motions among the fixed stars 

 as those on double stars, Mr. H. continued his researches in that line with great 



3 p 1 



