202. Halley also rendered good service to astronomy by calling attention to the importance of the expected transits of Venus across the sun in 1761 and 1769 as a means of ascertaining the distance of the sun. The method had been suggested rather vaguely by Kepler, and more definitely by James Gregory in his _Optics_ published in 1663. The idea was first suggested to Halley by his observation of the transit of Mercury in 1677. In three papers published by the Royal Society he spoke warmly of the advantages of the method, and discussed in some detail the places and means most suitable for observing the transit of 1761. He pointed out that the desired result could be deduced from a comparison of the durations of the transit of Venus, as seen from different stations on the earth, _i.e._ of the intervals between the first appearance of Venus on the sun’s disc and the final disappearance, as seen at two or more different stations. He estimated, moreover, that this interval of time, which would be several hours in length, could be measured with an error of only about two seconds, and that in consequence the method might be relied upon to give the distance of the sun to within about 1∕500 part of its true value. As the current estimates of the sun’s distance differed among one another by 20 or 30 per cent., the new method, expounded with Halley’s customary lucidity and enthusiasm, not unnaturally stimulated astronomers to take great trouble to carry out Halley’s recommendations. The results, as we shall see (§ 227), were, however, by no means equal to Halley’s expectations. 203. In 1718 Halley called attention to the fact that three well-known stars, Sirius, Procyon, and Arcturus, had changed their angular distances from the ecliptic since Greek times, and that Sirius had even changed its position perceptibly since the time of Tycho Brahe. Moreover comparison of the places of other stars shewed that the changes could not satisfactorily be attributed to any motion of the ecliptic, and although he was well aware that the possible errors of observation were such as to introduce a considerable uncertainty into the amounts involved, he felt sure that such errors could not wholly account for the discrepancies noticed, but that the stars in question must have really shifted their positions in relation to the rest; and he naturally inferred that it would be possible to detect similar =proper motions= (as they are now called) in other so-called “fixed” stars.