94 
MR. GALLOWAY ON THE PROPER 
Q and perpendicular to the equator, the effect of the sun’s motion towards Q would 
be to increase the right ascensions of all the stars in one of the hemispheres, and to 
diminish the right ascensions of all those in the other. Now, out of the whole of the 
stars compared, thirty-five are situated in the hemisphere in which the right ascen- 
sions should increase according to the hypothesis, and of these there are twenty-three 
whose right ascensions have actually increased, and twelve whose right ascensions 
have diminished; that is to say, there are twenty-three instances favourable to the 
hypothesis, and twelve unfavourable. In the other hemisphere there are forty-six 
stars ; and of these the number whose right ascensions have diminished, agreeably to 
the hypothesis, is thirty-nine, and the number whose right ascensions have increased, 
contrary to the hypothesis, is seven. Hence it appears that in respect of the eighty- 
one stars included in the inquiry the observed motions in right ascension are favour- 
able to the hypothesis in sixty-two -instances, and unfavourable in nineteen. Allowing 
the same weight to each instance, the wager is therefore sixty-two to nineteen, or 
somewhat more than three to one in favour of the hypothesis of a common tendency 
towards a determinate region. 
Secondly, with respect to the observed variations of declination. In all cases in 
which the angle %//' is less than 90°, or greater than 270°, the effect of the sun’s mo- 
tion in the direction of the assumed point Q, is to bring the apparent place of the 
star towards the north, so that its declination (which is south in all cases) should ap- 
pear, on comparison of the catalogues, to have diminished ; and in all cases in which 
is greater than 90° and less than 270°, the variation in the place of the star should 
be towards the south, and the declination should increase. Now, in the first case 
there are fifteen stars, and of these ten have advanced towards the north, agreeably to 
the hypothesis, and five towards the south, contrary to the hypothesis. In the second 
case there are sixty-six stars ; and of these the observed motion of fifty-three is 
towards the south, agreeing with the hypothesis, and of thirteen towards the north, 
contrary to the hypothesis. On the whole, therefore, in respect of declination, there 
are sixty-three instances favourable to the hypothesis and eighteen unfavourable ; and 
the wager is seven to two in favour of the hypothesis. It may be added that there 
are only three stars out of the whole number (Nos. 18, 34 and 36 in the subjoined 
table) whose observed proper motions are contrary to the hypothesis both in right 
ascension and declination. 
Another inference may be drawn from the comparison of the angles ^ and . If 
the observed changes of position were wholly independent of the sun, all directions 
would be equally probable, and it would be an even wager that the difference be- 
tween 4 1 and 4 1 ' would be less or greater than 90° in any case, since all possible values 
of that difference lie between 0 and 180°. But there are only ten instances, out of 
eighty-one, in which the difference exceeds 90°. 
From this general agreement of the hypothetical and observed motions, a strong- 
presumption is raised in favour of the hypothesis ; for it can scarcely be supposed 
