MOTION OF THE SOLAR SYSTEM. 
85 
The intersections thus found, although lying in the same quarter of the heavens, 
were not confined within a very narrow space, and in order to obtain a precise 
result, he proceeds as follows. Confining his attention to the six stars above named, 
he found the sum of their annual apparent motions in space to be 5" - 353 7- Now, 
assuming the star X Herculis (as determined in his first paper) to be the point 
towards which the sun is moving, he computes the angle included between the great 
circle of the sphere which passes through this point and the star, and the great circle 
in which the star’s motion takes place according to the comparison of the catalogues ; 
he then multiplies the apparent quantity of the annual proper motion of the star by 
the cosine and sine respectively of this angle, whereby the apparent proper motion is 
resolved into two parts, — one in the direction in which the star would appear to 
move in consequence of the hypothetical motion of the sun, and the other at right 
angles to that direction. The first of these may be ascribed to the motion of the 
sun ; the second must be regarded as due to the true proper motion of the star. 
Adding, therefore, into one sum the former of these resolved parts for each of the six 
stars, and deducting the sum from the sum of the observed annual motions, the latter 
sum was reduced from 5"’3 537 to 2" - 2249. By assuming another point in the same 
constellation as the apex of the sun’s motion, the sum of the annual proper motions 
of the six stars, in the direction perpendicular to that resulting from the hypothesis, 
was further reduced to 1"‘4594 ; and after some other trials, he ultimately fixed upon 
the point (near 34 Herculis) whose right ascension was 245° 52' 30", and north declina- 
tion 49° 38', by which the sum of the true annual proper motions of the six stars was 
reduced to 0"'9559. He concluded that this point must be very near the truth, 
inasmuch as “ the alteration of a few minutes in right ascension or north polar 
distance, either way, would immediately increase the required real motion of our 
stars.” 
This determination of the position of the solar apex differs from that which was 
given in Sir W. Herschel’s former paper by about 1 1° of right ascension, and 24° 38' 
of declination. It rests, however, on the proper motions of only six stars, and, there- 
fore, notwithstanding the greater probable accuracy of the observations, and the 
more elaborate process of calculation by which it was arrived at, it is probably not 
of greater intrinsic value than the first. The principle on which it is based, namely, 
the supposition that the sum of the true proper motions of the stars is a minimum, 
and consequently that the direction to be assigned to the sun’s motion must be that 
which will account for the greatest amount possible of the observed motions, was 
objected to by Burkhardt, on the ground that there is no more reason for supposing 
the sum of the true proper motions to be a minimum than a maximum, excepting on 
the hypothesis that the stars are more inclined to rest than to motion. But this 
objection seems to imply some misapprehension of the problem under consideration. 
No hypothesis respecting the disposition of the stars to rest or to motion is involved. 
The apparent proper motions are the results of the comparison of the catalogues, and 
