358 Dr. Herschei/s Account of the Changes that have happened 
direction of a chord from the first to the last angle of position 
pointed out by my observations ; taking care, however, not to 
place the stars a and x at the same distance from us ; and using 
the inverse ratio of the solar parallax as a multiple in the assigned 
motion. For instance, let the sun have a motion of the velocity 
expressed as before by 3", 51, and in a direction which makes an 
angle of 53 0 31' south following with the parallel of a. Gemi- 
norum ; and let the small star x have a real motion in an angle 
of 18 0 40' south preceding from the parallel of its situation, and 
with a real velocity which, were it at the distance of a, would 
carry it through i", 8 c). Then, if the distance of the small star 
be to that of the large one as 3 to 2, the effect of the solar 
parallax upon it will be j of its effect upon u ; that is, while 
which is at rest, appears to move over a space of 3", 51, in an 
angle of 53 0 31' north preceding, the parallactic change of place 
in x will be 2", 34 in the same direction. This, though only 
an apparent motion, will be compounded with the real motion 
we have assigned to it, but which, at the distance of u , will only 
appear as i", 26; and the joint effect of both will bring the star 
from the place in which it was seen 23!- years ago, to that 
where now we find it situated. «, in the same time, will appear 
to have had an annual proper motion of — o ,/ ,io5 in right 
ascension, and o'', 12 in declination towards the north ; and thus 
all phenomena will be explained. 
From this statement, we may draw a consequence of consi- 
derable importance. If we succeed, in this manner, in account- 
ing for the changes observed in the relative situation of the two 
stars of a double starve shall fail in proving them to form a 
binary system ; but, in lieu of it, we shall gain two other points, 
of equal value to astronomers. For, as u Geminorum, according 
