THE SUN.

5

of the Sun, so that the margins of the Sun and spot coincidedwith each other, forming the angle of contact.” * Crabtreewas also fortunate in obtaining a brief view of the transit, bywhich he confirmed the observations of Horrox.

The orbits and periodic times of the Earth and Venus aresuch that two transits of the latter occur at an interval of onlyeight years, after which considerably more than a centuryelapses, in which there is none. Then there' are two more, eightyears apart; then another long interval, and so on; every alter-nate two taking place in December and June respectively.f

The transit of December 1639 having been preceded by onewhich had passed unobserved in December 1631, the next twodid not take place until June 1761 and June 1769. In 1716Dr. Halley had explained the importance of an idea originallysuggested by James Gregory, in his Optica Promota, pub-lished in 1663, that these transits might be utilised for thedetermination of the Sun ’s distance. As the time approached,the English Government, as well as those of other countries,consequently made liberal arrangements for the necessaryobservations. In 1761 the observers were not very successful;but in 1769 they were much more fortunate, and a discussionof all the results which they obtained indicated that the Sun ’s

* Grant’s “ History of Astronomy,” p. 421. See also Horrox, “ Yenusin Sole visa,” translated in his Memoir by the Rev. A. B. Whatton.

t The plane of the orbit of Venus being very slightly inclined to thatof the Earth, and thirteen of its revolutions round the Sun occupyingonly one day less than eight of those of the Earth , the positions of thetwo relatively to the Sun are almost exactly reproduced after the lapseof eight years. There is, however, a slight residual difference of place, butso small that it permits the occurrence of two successive transits separatedby the above short interval. It is, however, sufficient to prevent the similaroccurrence of a third. And the very slowness with ■which the discrepancyof relative position increases, is at the same time the cause of the rapidsuccession of two transits, and of the long interval before another paircan take place. If we were to suppose two men to start at the same momentto run round and round two concentric circular courses, the one runningsteadily at 7 miles per hour, and the other at C miles per hour ; then, ifthe first course were 18 miles round, and the second 25 miles, it is evidentthat the first would take 33f hours to go thirteen times round his course, andthe second would take 33 J- hours to go eight times round his longer course