The phases of Venus were first pointed out by Galileo; this being one of his earliest discoveries with the tele

scope.

Venus, like Mercury, being an inferior planet, cannot, of course, be at any time in opposition to the Sun: indeed, she never recedes further from him than 47°, which is her greatest elongation, or the angle which would be formed by two lines drawn to the Earth, one from the Sun and the other from the planet. The orbit of Venus being exterior to that of Mercury, the greatest elongation of Venus, specified by the angle mentioned above, is necessarily greater than that of Mercury; to which circumstance it is owing that Venus is sometimes visible above the horizon for more than three hours before the Sun rises, and upon other óccasions for as long a time after the Sun has set:-in the former case she is to the west of the Sun, and is called a morning star, and in the latter she is to the east and is designated an evening star*. The elongation of a planet refers, then, to that position in which the planet is seen at its greatest distance from the Sun; at which time the planet appears, as we just said, in the shape of a half-moon:-these phases, however, cannot be perceived without the aid of a telescope.

The surface of this planet is found to exhibit spots, similar to those of which we shall hereafter have to speak in the case of the Moon. By these spots not only the rotation of the planet on her axis has been deter

* This is the planet which, rising before the Sun, the old poets termed Phosphorus and Lucifer; both words meaning light-bearer. When setting after the Sun, in the evening, they termed it Hesperus or Vesper; which terms have relation to the evening.

mined, but the inclination of that axis to the axis of her orbit has been found to be as much as 75°. The inclination of the Earth's axis to the ecliptic, or path of the Earth round the Sun, is about 66°; and this inclination causes the diversity of seasons. How much greater then must be the diversity of seasons on the face of the planet Venus, than on the Earth! Some parts of her surface may enjoy the four seasons twice in the year. The light and heat which she receives from the Sun, is probably about twice as great as that received by the Earth.

We have now to speak of a train of observations, which were productive of important consequences, and in which the planet Venus rendered great service,—we mean the correct calculation of the Sun's parallax; and from that, his distance from the Earth, by means of a transit of Venus across his disk. We have stated that Mercury occasionally crosses the Sun's disk, as viewed from the Earth; and it may reasonably be expected that Venus, being, like Mercury, an inferior planet, would likewise cross the Sun's disk at certain times. Such is the case,—as was first observed by Horrox, a student of Cambridge, in the year 1639; but the transits of Venus occur with much less frequency than those of Mercury. The former happening alternately at intervals of eight and a hundred and thirteen years, nearly. The most celebrated of these transits occurred respectively in the years 1761 and 1769;-celebrated, because many of the European governments sent out scientific expeditions, in order that this phenomenon might be observed at different parts of the Earth, with the

greatest accuracy, and under the most favourable circumstances. At the time of the transit, Venus must,

of course, be at its nearest position in respect of the Earth, and its apparent diameter will be of the largest extent, which is 61", or five times that of Mercury. The mean apparent diameter of Venus is about 17".

The final object, which was more particularly held in view in making these observations was, to determine with greater precision than had been previously done, the distance of the Earth from the Sun; in order that the true magnitude and extent of the whole solar system might be from thence determined. The manner in which this was accomplished does not admit of a full explanation, without entering into more intricate details than are suitable to this work. We must, however, briefly explain the nature of parallax;-as it was through the medium of this phenomenon that the transit of Venus was rendered available for the object in view; and as the question of parallax is one of the fundamental principles, called into use, in our endeavours to appreciate the distances of the heavenly bodies.

The first step to the accomplishment of the main purpose was to ascertain the parallax of Venus; as a medium point, whereby the solar parallax might be more precisely obtained.

The term parallax signifies a change produced by passing by. Familiarly speaking, we have parallax constantly taking place; when an object is seen in relation to any other spot, owing to our changing our position. A parallax of the steeple in the following cut takes place, when the observer changes his station of view. When he is in the West, he sees the form of the steeple thrown towards the East: coming up to the foreground he sees it to the North; and, advancing on to the East, he sees the steeple Westward.

Now, astronomically speaking, parallax is defined to be the angular distance of any heavenly body between its true and apparent place; the former being its place as it would be seen from the centre of the Earth, and the latter as it actually appears from any part of the Earth's surface. As a heavenly body can only be viewed from the Earth's surface, its position is referred to, in calculations, by a necessary allowance, as seen from the centre of the Earth, which process is termed the reduction for the centre.

In the succeeding diagram this principle is illustrated; as also the following results: that a heavenly body, seen in the zenith, or point in the heavens just over our heads, can have no parallax, because it is seen in a straight line with the centre of the Earth; that the horizontal parallax is greatest of all; and that the parallactic angle diminishes in proportion as the celestial body reaches the zenith.

Let A B be the Earth, and c a part of the Earth's surface, from whence the heavenly bodies a b c d are viewed in the direction of the dotted lines; by which a b c d appear on the heavens at ei kl, respectively. Now if the Earth were transparent, a spectator placed at its centre, would see the four heavenly bodies a b c d at e f g h, respectively; which would be the true places. Hence the true place of a heavenly body is somewhat higher than its apparent place, excepting as was said before at the zenith; where the true and apparent places of objects coincide. The angle formed by the two lines at b, c, or d, is the parallactic angle.

Such then is the nature of parallax: and it will be seen that the horizontal parallax is nothing more than the angular dimensions of half the Earth's diameter, as seen from the planet. With such a planet as Venus, which approaches comparatively near to the Earth, the effect of parallax is considerable; but with respect to the Sun itself, such is not the case; for the Sun, being at the average distance of ninety-five millions of miles. from the Earth, the semi-diameter of the Earth must appear exceedingly small, when viewed from such a distance. This small quantity is, however, made more sensible by the transit of Venus over the face of the Sun; for an observer, situated eastward on the Earth's surface, sees Venus begin to pass over the disk of the Sun somewhat earlier than another observer, situated more to the west; and the chord described by the planet upon the solar disk will appear somewhat greater or smaller, according to the situation of the observers upon the Earth's surface. Hence the difference in the position of view gives a difference of time, taken up by Venus in her passage over the Sun, which furnishes, by