Within a year of Halley's election as a Fellow of the Royal Society, he was chosen by the Society to represent them in a discussion which had arisen with Hevelius. The nature of this discussion, or rather the fact that any discussion should have been necessary, may seem strange to modern astronomers, for the point is one on which it would now seem impossible for there to be any difference of opinion. We must, however, remember that the days of Halley were, comparatively speaking, the days of infancy as regards the art of astronomical observation, and issues that now seem obvious were often, in those early times, the occasions of grave and anxious consideration. The particular question on which Halley had to represent the Royal Society may be simply stated. When Tycho Brahe made his memorable investigations into the places of the stars, he had no telescopes to help him. The famous instruments at Uraniborg were merely provided with sights, by which the telescope was pointed to a star on the same principle as a rifle is sighted for a target. Shortly after Tycho's time, Galileo invented the telescope. Of course every one admitted at once the extraordinary advantages which the telescope had to offer, so far as the mere question of the visibility of objects was concerned. But the bearing of Galileo's invention upon what we may describe as the measuring part of astronomy was not so immediately obvious. If a star be visible to the unaided eye, we can determine its place by such instruments as those which Tycho used, in which no telescope is employed. We can, however, also avail ourselves of an instrument in which we view the star not directly but through the intervention of the telescope. Can the place of the star be determined more accurately by the latter method than it can when the telescope is dispensed with? With our present knowledge, of course, there is no doubt about the answer; every one conversant with instruments knows that we can determine the place of a star far more accurately with the telescope than is possible by any mere sighting apparatus. In fact an observer would be as likely to make an error of a minute with the sighting apparatus in Tycho's instrument, as he would be to make an error of a second with the modern telescope, or, to express the matter somewhat differently, we may say, speaking quite generally, that the telescopic method of determining the places of the stars does not lead to errors more than one-sixtieth part as great as which are unavoidable when we make use of Tycho's method.