The transits of Mercury and Venus were first predict ed by the celebrated Kepler. He announced a transit of Mercury for 1631, and two of Venus for 1631 and 1761. The transit of Mercury was observed by Gassendi ; but as the transit of Venus in the same year must have been over before the rising of the sun, Gassendi, who had made preparations to observe it, could not fail to be dis appointed. Another transit of Venus, which Kepler had not predicted, was observed at Hool, near Liverpool, in 1639, by our countryman Mr Horrox, the first person who had the singular felicity of observing Venus upon the disc of the sun.
It will appear by examining the tables of transits at the end of this article, that these phenomena return at stated periods. If a transit happens at any given time at either of the nodes of Mercury or Venus, it is obvious that before another transit can happen, the earth must perform a certain number of revolutions round the sun, in the same time that the planet performs a greater num ber of revolutions in its orbit. The number of revolu tions performed by the earth and the inferior planet, must be such, that they are brought into nearly the same re lative position to the sun which they had at the first tran sit, and will evidently be in the inverse ratio of the pe riodic times of the earth and the planet. In order to determine their periods, therefore, we must find whole numbers for Mercury in the ratio of 87.969 :365.256. These numbers are 7 : 29 ; 13 :54; 33 :137;46:191; 217:901, 26: 1092 ; consequently in seven years Mer cury will have performed nearly twenty-nine revoluttons, and so on with the rest. The periods are more accurate ly thus : The whole numbers expressing the periods of Venus' transits being in the ratio of 224.701 to 365.256, are 8 : 13 ; 235: 382; 243:395; 713 : 1159. The following are the periods in more accurate numbers.
The transits of Venus over the sun's disc are among the most interesting phenomena in astronomy, not only from the rarity of their occurrence, but from the import ant determinations to which they lead. Dr Halley point ed out the advantages which astronomers would receive from accurate observations of the transits of Venus, in enabling them to determine the distance of the sun from the earth ; and, accordingly, the transits in 1761 and 1769 were observed with the utmost perseverance and zeal in every quarter of the globe.
In order to explain the method of finding the distance of the sun from the earth by means of the transits of Venus, it will be necessary to consider shortly the sub ject of parallax, or the difference in the position of a pla net as seen from the centre and from the surface of the earth. Let AB, Plate XXXVIII. Fig. 6, be the earth, C its centre, H the horizon, Z the zenith of the place A, and E, F, G, H the different positions of any planet. When the planet is at E, he will appear It the horizon at H to a spectator at the earth's centre C ; but to a spectator on the surface at A, the planet E will appear at h below the horizon, H being the true place, and h the apparent place of the planet. The parallax of the
planet E will therefore be measured by the arch Hh, or by the angle HEh=AEC. When the planet is above the horizon at F, its parallax will be Pit; when it is at G, its parallax will be Rr ; and when it is at H, its paral lax will vanish, and its true and apparent place will coin cide. The parallax is obviously greatest at the horizon H, and diminishes as the altitude of the body increases. The angle AEC is called the horizontal parallax, and is manifestly equal to the angle subtended by the earth's semidiameter at the planet. Hence the effect of parallax is to diminish the altitude of the celestial body, or to make it appear nearer the horizon, and therefore it is called the parallax of altitude. As it must change, how ever, the longitude, latitude, right ascension, and decli nation of the body, we shall have also a parallax in longi tude, a parallax in latitude, a parallax in right ascension, and a parallax in declination. By observing the relative position of a planet to a given fixed star, at two places on the earth nearly under the same meridian, the paral lax of the planet may be easily found ; but in the case of the sun, the parallax is so small that it can only be de termined with *curacy from the transits of Venu$.
The method of finding the sun's parallax will be un derstood from Plate XXXVIII. Fig 7. where ABC is the earth, C its centre, V Venus moving in her orbit in tne direction RVT, S the sun. As the earth's motion on its axis in the direction BDA is contrary to the motion of Venus in her orbit RVT, the motion of Venus across the sun's disc in the path v, v', v", will be accelerated in consequence of the observer being carried in the direc tion BDA, and therefore the duration or the transit will be shorter than if it were observed from the earth's cen tre, or from any point of the earth at rest. If Venus were even to stand still, and the earth to have no other motion but that of its daily rotation, the planet Venus would ap pear to move upon the sun's disc. When the observer is at B, Venus will appear like a black spot at v; when the observer has arrived at D, Venus will appear at ; and when he has reached A, Venus will be seen at v". But Venus' own motion in the direction RT will cause her to move across the sun's disc in the path v, v', v", and therefore that motion must be considerably accelerat ed by the diurnal motion of the earth. The contraction of the transit, arising from this cause, evidently increases with the proximity of Venus to the earth, and is there fore proportional to her horizontal parallax. By observ ing, therefore, at proper places on the earth, how much the duration of the transit is shortened, or by finding the difference between the observed time of the transit and the calculated time of the transit as seen from the earth's centre, we shall be able to determine the parallax of Ve nus, and that of the sun.