By examining the table it will be seen that, prior to the discovery of the new planets, there was an abrupt increase from Mars to Jupiter. This break in the series of distances, led some astronomers to suppose there must be a planet occupying an intermediate position. Kepler had broached a similar opinion in one of his earliest publications, though it was not until after the discovery of Uranus, which seemed to strengthen the idea of a harmony in the planetary distances, that astronomers thought of searching for the body needed to complete the series. In the year 1800 an association of practical observers was established for the purpose of finding, if possible, this concealed planet, each member undertaking to examine minutely all the telescopic stars in a certain portion of the zodiac; and, on the first day of the present century, Piazzi, one of their number, discovered the planet Ceres, the first of thirteen small bodies discovered within the last half century, revolving around the sun at distances varying from 22 to 32. The average of the distances of the Asteroids is about 26 as inserted in the table. It was supposed that, if a planet existed exterior to Uranus, its distance would be about 388, but, unfortunately for Bode's Law, the distance of Neptune is only about 300.

CHAPTER XV.

INFERIOR PLANETS, MERCURY AND VENUS.

TRANSITS. SUN'S

PARALLAX.

291. Greatest elongations of Mercury and Venus. Mercury and Venus have their orbits so far within that of the earth, that their elongations are never great. They seem to accompany the sun, being seen in the west soon after sunset, or in the east a while before sunrise.

Let S, Fig. 50, be the place of the sun, ABC the orbit of Mercury, which we will here suppose to coincide with the plane of the ecliptic, FG a part of the earth's orbit, and A and a corresponding positions of the planet and earth, when the former is at its greatest elongation, at which time the angle aAS is a right angle. As the distances of the planet and earth from the sun both vary, the greatest elongation must also vary. Its value will evidently be greatest when SA is greatest, and at the same time Sa least, that is, when, at the time of greatest elongation, Mercury is at the aphelion of his orbit and the earth in perihelion; and least, when the positions are reversed. With the least value of SA and greatest of Sa, we find the least value of Mercury's greatest elongation to be about 1710, 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 formula (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; and is much less than the earth. His apparent diameter varies from 5" to 12". He 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 the horizon when he is below it, and that principally during the twilight, telescopic observations of his appearance are difficult and considerably uncertain.

295. Period, Distance from sun, &c. Mercury revolves round the sun in a little less than three months, at a distance of 37 millions of miles. His diameter is about 3000 miles, and his volume or bulk about that of the earth. According to the observations of some astronomers, he revolves on his axis in 24h. 5m.; the axis making a large angle, with a perpendicular to the plane of the ecliptic.

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296. Visibility of Mercury. In high latitudes, Mercury is seldom visible to the naked eye, in consequence of the increased

* 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.

duration of twilight (182). But, in latitudes not higher than those of the United States, he may, under favourable circumstances, be seen in the evening or morning, for a number of days about the period of his greatest east or west elongation. Supposing the atmosphere clear, the other circumstances that favour his visibility are, that the greatest elongation should occur during the period of shorter twilight, that he should then be near the aphelion of his orbit, or, at least, not very remote from it, and that his 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, 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.

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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 Calculus, in which the circumstances that influence the intensity of her light are noticed, it has been found that she gives the greatest light in 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 mid-day, especially if at the time she has considerable north declination so as to rise far above the horizon.

301. Mountains of Venus. Some astronomers have 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.

*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.