406 PHILOSOPHICAL TRANSACTIONS. [ANNO 1783. 



tions, which this hypothesis will not account for. And these exceptions must be 

 resolved into the real proper motion of the stars. 



There are also some very striking circumstances in the quantities of these mo- 

 tions that deserve our notice. First, Arcturus and Sirius being the largest of 

 the stars, and therefore probably the nearest, ought to have the most apparent 

 motion, both in right ascension and declination ; which is agreeable to observa- 

 tion, as we find by the table. Next, in regard to the right ascension only, Arc- 

 turus being better situated to show its motion, by theorem 2, ought to have it 

 much larger, which we find it has. Aldebaran, both badly situated and consi- 

 derably smaller than the two former, by the same theorem ought to show but 

 little motion. Procyon, better situated than Sirius, though not quite so large, 

 should have almost as much motion; for by the 3d theorem, on supposing it 

 farther off because it appears smaller, the effect of the sun's motion will be les- 

 sened on it; whereas, on the other hand, by the 2d theorem, its better situation 

 will partly compensate for its greater distance. This again is conformable to the 

 table, i Cygni very favourably situated, though but a small star, should show 

 it considerably, as well as «. Aquilae; whereas |3 Cygni should have but little mo- 

 tion ; and y Piscium, best situated of all, should have a great increase of right 

 ascension; and these deductions also agree with the table. 



In the last place, a very striking agreement with the hypothesis is displayed in 

 Castor and Pollux. They are both pretty well situated, and we accordingly find 

 that Pollux, for the size of the star, shows as much motion in right ascension as 

 we could expect; but it is remarkable, and seemingly contrary to our hypothesis, 

 that Castor, equally well placed, shows by the table no more than half the mo- 

 tion of Pollux. Now, if we recollect that the former is a double star, consisting 

 of 2 stars not much different in size, we can allow but about half the light to 

 each of them, which affords a strong presumption of their being at a greater 

 distance, and therefore their partial systematical parallax, by the 3d theorem, 

 ought to be so much less than that of Pollux; which agrees wonderfully with 

 observation. Not to mention the great difficulty in which we should be involved, 

 were we to suppose the motion of Castor to be really in the star; for how extra- 

 ordinary must appear the concurrence, that two stars, namely, those that make 

 up this apparently single star, should both have a proper motion so exactly alike, 

 that in all our observations hitherto they have not been found to disagree a single 

 second, either in right ascension or declination, for 50 years together! Does 

 not this seem strongly to point out the common cause, the motion of the solar 

 system ? With respect to the change of declination, I would observe, that the 

 point of A Herculis, which in fig. 1 1 is assumed as the apex of the solar motion, 

 is not perhaps the best selected. A somewhat more northern situation may agree 



