86 
MR. GALLOWAY ON THE PROPER 
the question proposed by Sir W. Herschel was simply to determine the point 
towards which the sun must be supposed to move, in order that, after deducting the 
parallactic effect, the amount of the residual motions might be the least possible. 
Burkhardt’s memoir was published in the Connaissance des Temps for 1809. It 
contains formulae for the solution of the problem, with their application to several of 
the stars in Maskelyne’s catalogue ; but he found little accordance among the results, 
and concluded that we are not yet in possession of a sufficient number of facts to 
decide on the direction of the sun’s motion. 
Biot, in the Additions to his Astronomie Physique, also considered the question 
of the translation of the planetary system, and gave formulae for determining the 
right ascension and declination of the solar apex. He computed the intersections of 
the great circles containing the arcs described by eight stars, viz. Aldebaran, Capella, 
Sirius, Procyon, Pollux, Arcturus, a Lyrae, and a Aquilae, the proper motions of which 
were given by Zach from a comparison of Bradley’s places with those of Maske- 
lyne, and also of the catalogues of Mayer and Piazzi. If the apparent motions 
depended solely on the displacement of our system, the intersections would, of course, 
all be found at the same two points of the sphere; but he found the discrepancies to 
be so great that he considered them to be irreconcileable with the supposition of their 
dependence on any systematic motion or common cause. “ The examination,” he 
remarks, “ of all these irregularities shows that the stellar motions hitherto observed 
are not subject to any law, and that it would be in vain to attempt to reconcile them 
by supposing them all to be directed towards the same pole. Hence it becomes in- 
finitely probable that such of these motions as are well determined are due, in part, 
to a real displacement of the stars themselves, and not to that of our system. With 
respect to those whose proper motions are less certain, not only does their want of 
precision prevent us from concluding from them the direction of the motion of our 
own system, but their comparison does not even afford any indication which can lead 
to the inference that it is in motion at all.” 
In the 12th section of his Fundamenta Astronomic, Bessel has given an elabo- 
rate investigation of this question, founded on a much larger number of proper 
motions (and probably better determined) than had previously been brought to bear 
on the inquiry. On comparing the catalogue deduced from Bradley’s observations 
with that of Piazzi, he found seventy-one stars having a proper motion of not less 
than 0"’5 annually in the arc of a great circle, and computed the positions of the great 
circles in which the apparent motions are contained. But even from this large 
number he obtained no satisfactory or conclusive result. The investigation, he 
remarks, did not confirm Herschel’s supposition of the sun’s motion towards the 
constellation Hercules, since many points on the sphere, very remote from each other, 
and even diametrically opposite, may be assigned which are situated in the direction 
of the motion of many stars ; but whatever point may be taken, there will always 
be found so many proper motions evidently receding from it, that no sufficient reason 
