The problem which Bradley set himself was to examine whether any star could be seen to have in the course of the year a slight motion relative to others or relative to fixed points on the celestial sphere such as the pole. It was known that such a motion, if it existed, must be very small, and it was therefore evident that extreme delicacy in instrumental adjustments and the greatest care in observation would have to be employed. Bradley worked at first in conjunction with his friend _Samuel Molyneux_ (1689-1728), who had erected a telescope at Kew. In accordance with the method adopted in a similar investigation by Hooke, whose results it was desired to test, the telescope was fixed in a nearly vertical position, so chosen that a particular star in the Dragon (γ Draconis) would be visible through it when it crossed the meridian, and the telescope was mounted with great care so as to maintain an invariable position throughout the year. If then the star in question were to undergo any motion which altered its distance from the pole, there would be a corresponding alteration in the position in which it would be seen in the field of view of the telescope. The first observations were taken on December 14th, 1725 (N.S.), and by December 28th Bradley believed that he had already noticed a slight displacement of the star towards the south. This motion was clearly verified on January 1st, and was then observed to continue; in the following March the star reached its extreme southern position, and then began to move northwards again. In September it once more altered its direction of motion, and by the end of the year had completed the cycle of its changes and returned to its original position, the greatest change in position amounting to nearly 40′. The star was thus observed to go through _some_ annual motion. It was, however, at once evident to Bradley that this motion was not the parallactic motion of which he was in search, for the position of the star was such that parallax would have made it appear farthest south in December and farthest north in June, or in each case three months earlier than was the case in the actual observations. Another explanation which suggested itself was that the earth’s axis might have a to-and-fro oscillatory motion or nutation which would alter the position of the celestial pole and hence produce a corresponding alteration in the position of the star. Such a motion of the celestial pole would evidently produce opposite effects on two stars situated on opposite sides of it, as any motion which brought the pole nearer to one star of such a pair would necessarily move it away from the other. Within a fortnight of the decisive observation made on January 1st a star[116] had already been selected for the application of this test, with the result which can best be given in Bradley’s own words:—