the reading of this screw
would show the change. Now, before setting out on the observations, the
observers knew what to expect if the star had a real parallax; that is to
say, they knew that the star would seem to be farthest south in December,
farthest north in June, and at intermediate positions in March and
September; though they did not know _how much_ farther south it would
appear in December than in June--this was exactly the point to be decided.

[Illustration: FIG. 2.]

[Sidenote: Unexpected results.]

The reason of this will be clear from Fig. 2. [Remark, however, that this
figure and the corresponding figure 4 do not represent the case of
Bradley's star, [gamma] Draconis: another star has been chosen which
simplifies the diagram, though the principle is essentially the same.] Let
A B C D represent the earth's orbit, the earth being at A in June, at B in
September, and so on, and let K represent the position of the star on the
line D B. Then in March and September it will be seen from the earth in
the same direction, namely, D B K; but the directions in which it is seen
in June and December, viz. A K and C K, are inclined in opposite ways to
this line. The farther away the star is, the less will this inclination or
"parallax" be; and the star is actually so far away that the inclination
can only be detected with the utmost difficulty: the lines C K and A K are
sensibly parallel to D B K. But Bradley did not know this; it was just
this point which he was to examine, and he expected the greatest
inclination in one direction to be in December. Accordingly when a few
observations had been made on December 3, 5, 11, and 12 it was thought
that the star had been caught at its most southerly apparent position, and
might be expected thereafter to move northwards, if at all. But when
Bradley repeated the observation on December 17, he found to his great
surprise that the star was still moving southwards. Here was something
quite new and unexpected, and such a keen observer as Bradley was at once
on the alert. He soon found that the changes in the position of the star
were of a totally unexpected character. Instead of the extreme positions
being occupied in June and December, they were occupied in March and
September, just midway between these. And the range in position was quite
large, about 40"--not a quantity which could have been detected in the
days before telescopes, but one which was unmistakable with an instrum