MOTION OF THE SOLAR SYSTEM. 
87 
will remain for preferring one point to another. And he concluded that a very long 
time must elapse before any proficiency would be made in the theory of the proper 
motions of the stars. 
The opinion of Bessel, now quoted, appears to be that which, until lately at least, 
has been generally entertained by astronomers ; but on attentively considering the 
nature of the question, it will soon be seen that none of the methods of investigation 
yet alluded to can be considered as capable of leading to an entirely satisfactory 
conclusion. They are all founded essentially on the principle of determining the 
apex of the sun’s motion from the apparent motions of single pairs of stars ; and, 
with the exception of Bessel’s, all the results which had been given were deduced 
from a very small number of proper motions. Now, it is a very improbable supposi- 
tion that the stars are subject to no variations but such as depend on the motion of the 
sun. We must suppose them to have true proper motions, producing apparent effects 
at least equal in amount to those which are supposed to be produced by the sun’s 
displacement. Assuming, then, that the stars themselves are in motion as well as 
the sun, and that they move in all directions, the appearances will necessarily be 
of a very complicated nature. The proper motions of some stars will conspire with 
that of the sun, and increase the apparent change of position. In other cases they 
will be contrary to that of the sun, and the apparent effect will be that which is due 
to the difference of two real motions. In general the directions of the true and paral- 
lactic motions will be inclined to each other ; but in all cases the difference given by 
the comparison of the catalogues will be compounded of the effect of the real motion 
of the star and the effect of the sun’s displacement. Hence it is manifest that the 
fact of proper motions being observed to take place in all directions, is in no way in- 
consistent or incompatible with an apparent general drifting of the stars towards 
one particular region ; and the problem to be solved is to separate, if possible, the 
general effect produced by the sun’s displacement from the complicated effects caused 
by the motions of stars in every direction with which it is entangled and mixed up. 
Now it is easy to see that a question of this kind cannot be solved by taking account 
of only a small number of proper motions. A very considerable number must be 
employed ; and, indeed, in order that the solution may be satisfactory, regard must 
be had to every star without exception of which the proper motion has been deter- 
mined with sufficient certainty. It is also necessary that the investigation be con- 
ducted in such a manner that every observed displacement shall contribute, accord- 
ing to its weight, to the general result ; and the probable error of the result must 
likewise be determined in order that the relative probabilities of results obtained from 
different hypotheses respecting the direction of the sun’s motion, may be submitted 
to exact comparison. In this manner it will be seen whether, as Bessel and others 
inferred from particular cases, numerous points may be assumed towards any one of 
which the sun may be supposed with equal probability to be advancing, or whether 
there is so great a preponderance of observed motions towards one particular region 
