we find the least value of Mercury's greatest elongation to be about 170, and with the greatest value of SA and least of Sa, we find the greatest value to be about 281°. In a similar manner, we find the greatest elongation of Venus to vary from about 45° to nearly 48°.

292. Synodic Revolutions of Mercury and Venus. From the formulæ (272 cor.), the synodic revolution of Mercury is found to be about 116 days, and that of Venus, 584 days.

293. Phases of Mercury and Venus. Regarding the planets as opaque globular bodies, which shine by reflecting the light of the sun, Mercury and Venus must assume the various phases of the moon. Referring to Fig. 50, let A and a, B and b, &c., be corresponding positions of one of these planets and the earth. Then, it is obvious that while the planet is passing from its greatest eastern elongation at A to its greatest western at C, the enlightened disc must have the crescent form, like the moon from third quarter to first; and while passing from C to the following greatest eastern elongation at E, it must have the gibbous form, like the moon from first quarter to third; excepting however, the positions of inferior and superior conjunction at B and D, at the former of which, the enlightened surface is turned wholly from the earth, and at the latter, entirely towards it, like the moon at new and full moon. When viewed with a telescope of sufficient power, both Mercury and Venus exhibit these phases. We have thus another confirmation of the truth of the Copernican System.*

MERCURY.

294. General Remarks. Mercury is the least of the planets, with the exception of the four lately discovered;

* It was objected to the system of Copernicus, that if it were true, Venus should sometimes appear horned like the moon. He admitted the conclusion, adding, that should we ever be able to see the actual shape, it would appear so.

and is much less than the earth. Her apparent diameter varies from 5" to 12". She shines with a steady white light, appearing as a luminous point above the western or eastern part of the horizon. Being always near the sun and, therefore, but for a short interval above the horizon when he is below it, and that principally during the twilight, telescopic observations of her appearance are difficult and considerably uncertain.

295. Period, Distance from sun, &c. Mercury revolves round the sun in a little less than 3 months, at a distance of 37 millions of miles. Her diameter is about 3000 miles, and her volume or bulk about that of the earth. According to the observations of some astronomers, she revolves on her axis in 23h. 5m.; the axis making a large angle, with a perpendicular, to the plane of the ecliptic.

296. Visibility of Mercury. In high latitudes, Mercury is seldom visible to the naked eye, in consequence of the increased duration of twilight (182). But, in latitudes not higher than those of the United States, she may under favourable circumstances be seen in the evening or morning, for a number of days about the period of her greatest east or west elongation. Supposing the atmosphere clear, the other circumstances that favour her visibility are, that the greatest elongation should occur during the period of shorter twilight, that she should then be near the aphelion of her orbit, or at least, not very remote from it, and that her polar distance should be some degrees less than that of the sun.*

VENUS.

297. General Remarks. Venus, the most brilliant of the planets, is frequently called the morning and evening star,

In December of last year (1841), Mercury was visible each clear morning for eight or ten days. Being contiguous to Venus, her mild, steady radiance contrasted finely with the glittering splendour of the latter body.

as she is in general conspicuously visible, at one or the other of these times. In remote periods, this planet was regarded as two different bodies; the morning star being called Lucifer, and the evening, Hesperus. The discovery that they were the same body is ascribed to Pythagoras.

The size of Venus is nearly the same as that of the earth, though a little less. Her apparent diameter varies from 10" to 61".

298. Period, Distance, &c. Venus revolves round the sun in about 7 months, at a distance of 69 millions of miles. Her diameter is about 7600 miles, and her volume that of the earth.

From observations of the motions of spots seen on the surface, it has been inferred that Venus revolves on her axis in 23h. 21m.; the axis making an angle of 75° with a perpendicular to the plane of the ecliptic, and 72° with a perpendicular to the plane of the orbit.

299. Day and night and Seasons at Venus. As the axis of Venus makes so large an angle with the axis of the orbit, it is evident that she must be subject to great and rapid changes in the lengths of her day and night, and correspondingly great vicissitudes in her seasons. The circles corresponding to our tropics must be within 18° of her poles, and those corresponding to our polar circles, within the same distance of her equator. It can, therefore, only be within a zone extending 18° on each side of her equator, that each rotation on her axis will throughout the year, bring a return of day and night. In other parts there may in the course of a year be at the same place, alternate day and night for each rotation of the planet; a day lasting during many rotations; and a night of like duration. In the two zones of 54° breadth, extending from the polar circles to the tropics, the sun will sometimes ascend to the zenith, and at others scarcely rise above the horizon, or not rise at all, for many consecutive days.

300. Venus sometimes visible during the full light of day. In consequence of the changes in the extent of the enlightened part of the disc and the varying distance of Venus from the earth, the intensity of her light is subject to considerable variation. By a simple investigation in Differential Calcules, in which the circumstances that influence the intensity of her light are noticed, it has been found that she gives the greatest light about 36 days before and after inferior conjunction; her elongation being then about 40°, and the enlightened part of the disc not much over a third of the whole. At these periods the light is so great, that objects illuminated by it, cast perceptible shadows. She may also, then, be very distinctly seen by the naked eye during the full light of day, even at midday, especially if at the time she has considerable north declination so as to rise far above the horizon.

Some astronomers have

301. Mountains of Venus. thought that they had detected evidences of high mountains on Venus, and have computed the heights of some of them to be over 20 miles. But, as the intense light of this planet dazzles the sight and exaggerates the imperfections of the telescope, thereby, rendering observations difficult, and some of them quite uncertain, the existence of these mountains is not to be regarded as established.

TRANSITS OF MERCURY AND VENUS.

302. Definition. When either Mercury or Venus at the time of inferior conjunction is near to either node of her orbit, or which amounts to the same, when the longitudes of the sun and node are at that time nearly equal, she must pass between the sun and earth, appearing as a well-defined black spot traversing the disc. This phenomenon is called a Transit of the planet.

* This is quite observable when the object is placed in an open window of a room and the shadow is received on the opposite wall or on a white screen.

303. Transits of Mercury. The longitudes of Mercury's nodes are about 46° and 226°, and these longitudes vary but little more than a degree in a century. In the present age, therefore, transits of Mercury can only occur in the months of May and November, for it is only in these months that the sun can have the same longitude as the nodes.

When a transit has occurred at one node, there cannot be another at the same node, till the lapse of a period of time composed of whole synodic revolutions, and also, of whole years or nearly so. For they occur only at inferior conjunction, and those at the same node, nearly at the same time in the year. Hence, taking s to represent a synodic revolution of Mercury, p the periodic revolution of the earth or sidereal year, if m and n be two whole numbers such that ns = mp nearly, or

n

m

=

P

S

nearly, then, will m be the number of the years in the period between two consecutive transits at the same node. Different values for m and n, less or more exact, may be obtained by the method of continued fractions.* It is thus found that transits at the same node occur at intervals of 6 or 7 years, 13 years, 33 years. &c.

A transit at one node is generally preceded or followed, at an interval of 3 years, by one at the other node.

The next two transits of Mercury, both of which will be visible in this country, will occur in May 1845, and November, 1848.†

304. Transits of Venus. The longitudes of the nodes of Venus are about 75° and 255°, and the sun has these longitudes in June and December. Hence, it is only in June and December that transits of Venus occur.

* This method is frequently given in treatises on Algebra. A practical rule is given in Lewis's Arithmetic.

+ Other transits that will occur during the present century, will happen November, 1861, November 1868, May 1878, November 1881, May 1891, and November 1894. Of these the third and last will be visible in this country.