80 
MR. GALLOWAY ON THE PROPER 
accounted for by theory, mix themselves up with the determination of the precession 
and other fundamental elements ; and the first step towards acquiring any knowledge 
of their laws, quantities, or directions, is obviously to distinguish between what is 
real and what is only apparent, and to separate from the whole observed displace- 
ment the effect due to the motion of our own system. 
Before proceeding to describe the data and results of the present investigation, it 
will be desirable, perhaps, to give a brief notice of the principal inquiries that have 
heretofore been undertaken with reference to the same subject. 
In the Philosophical Transactions for 1713, Halley first called attention to the 
circumstance that a comparison of the ancient with modern observations showed 
that three of the principal stars, Sirius, a Tauri and Aldebaran, had changed their 
positions relatively to the fixed circles of the sphere, and advanced considerably 
towards the south. Until this time the notion had universally prevailed that the 
places of the stars are subject to no relative change ; but no sooner was the notion 
called in question than instances of such change were multiplied ; and the proper 
motions of stars being once admitted, it was naturally suggested that the sun itself 
partakes of a similar motion. Bradley, in the memorable paper in which he an- 
nounced the discovery of the nutation, published in the Philosophical Transactions 
for 1748, described the appearances which would result from a change of the position 
of the solar system in absolute space, but he made no attempt to explain the observed 
phenomena on this hypothesis, and remarked that the alterations in the relative po- 
sitions of the stars might arise from so great a variety of causes, that many centuries, 
perhaps, would be required to discover their laws. 
Tobias Mayer, in a memoir presented to the Gottingen Society in 1760, and pub- 
lished among his Opera Jnedita in 1776? gave a list of eighty stars which had been 
observed by Rcemer in 1706, and compared their places as given by Roemer with 
those deduced from his own observations (1756) and those of Lacaille (1750). Out 
of the eighty stars about fifteen or twenty were found in respect of which the differ- 
ence of position, either in right ascension or declination, exceeded 15", a quantity 
which he considered would be at least equal to the error of observation. In the cases, 
therefore, in which the difference did not much exceed 15", he thought a proper mo- 
tion was not improbable; but in some cases, as those of Arcturus, Sirius, Procyon, 
a Aquilse, Piscis Austrinus, and a few others, the difference was so great that there 
could be no question about the existence of such motion. Mayer also made the re- 
mark, that the stars which appear to change their places are not confined to those 
of the first or second order of magnitude, which, by reason of their greater brilliancy, 
might be presumed to be the nearest to the earth ; and that among the brighter there 
are some which appear to be altogether at rest. And he further remarked, that 
although it is by no means improbable that the sun as well as the stars may have a 
motion of its own, yet, as the observed changes of position do not follow the law they 
would observe if caused by the motion of our solar system towards a given point in 
