orbit of the planet, and one million and a-half of miles due to the excentricity of the orbit of the earth.

312. Greatest elongation.-Owing to the ellipticity of the planet's orbit, the greatest elongation of Mercury is subject to some variation. Its mean amount is 22°.5.

313. Scale of the orbit relatively to that of the earth.— The orbit of Mercury and a part of that of the earth are exhibited on their proper scale in fig. 55, where s E is the earth's distance from the sun, and m m' m the orbit of the planet. The lines E m" drawn from the earth touching the orbit of the planet determine the positions of the planet when its elongation is greatest east and west of the sun. The points m are the positions of the planet at inferior and superior conjunction.

=

314. Apparent motion of the planet. The effects of the combination of the orbital motions of the planet and the earth upon the apparent place of the planet will now be easily comprehended. Since the mean value of the greatest elongation m" Es=22°. the arc mm" 67° and therefore m" mm"=671° x 2=135°. The times of the greatest elongations east and west therefore divide the whole synodic period into two unequal parts, in one of which, that from the greatest elongation east through inferior conjunction to the greatest elongation west, the planet gains upon the earth 135°; and in the other, that from the greatest elongation west, through superior conjunction to the greatest elongation east, it gains 360°-135°=225°. Since the parts into which the synodic period is thus divided are proportional to these angles, they will be (taking the synodic period in round numbers as 116 days),

And since the former interval is divided equally by the epoch of inferior, and the latter by the epoch of superior, conjunction, it follows, that the intervals between inferior conjunction and greatest

elongation are 21 days, and the intervals between superior conjunction and greatest elongation are 36 days.

The interval between the times at which the planet is stationary, before and after inferior conjunction, is subject to some variation, owing to the excentricities of the orbits both of the planet and the earth, but chiefly to that of the planet's orbit, which is considerable. If its mean value be taken at 22 days, the angle gained by the planet on the earth in that interval being 68 4, the angular distances of the points at which the planet is stationary from inferior conjunction as seen from the sun would be 34°2, which would correspond to an elongation of about 21°, as seen from the earth. This result, however, is subject to very great variation, owing to the excentricity of the planet's orbit and other causes.

315. Conditions which favour the observation of an inferior planet. -These conditions are threefold: 1. The magnitude of that portion of the enlightened hemisphere which is presented to the earth. 2. The elongation. 3. The proximity of the planet to the earth.

Since it happens that the positions which render some of these conditions most favourable render others less so, the determination of the position of greatest apparent brightness is somewhat complicated. When the planet is nearest to the earth its dark hemisphere is presented towards us; besides which, being in inferior conjunction, it rises and sets with the sun, and is only present in the day time. At small elongations in the inferior part of the orbit its distance from the earth is not much augmented, but it is still overpowered by the sun's light, and would only appear as a thin crescent when it would be possible to see it. At the greatest elongation, when it is halved, it is most removed from the interference of the sun, but is brightest at a less elongation, even though it moves to a greater distance from the earth, since it gains more by the increase of its phase than it loses by increased distance and diminished elongation.

Owing to the very limited elongation of Mercury, that planet, even when its apparent distance from the sun is greatest, sets in the evening long before the end of twilight; and when it rises before the sun, the latter luminary rises so soon after it that it is never free from the presence of so much solar light, which renders it extremely difficult to see the planet with the naked eye.

In these latitudes Mercury is therefore only occasionally seen with the naked eye. It is said that Copernicus himself never saw this planet, a circumstance which, however, may have been owing, in a great degree, to the unfavourable climate in which he resided. In lower latitudes, where the diurnal parallels are more nearly vertical and the atmosphere less clouded, it is more frequently

visible, and there it is more conspicuous, owing to the short duration of twilight.

316. Apparent diameter

- Owing to the variation of the planet's distance from the earth, its apparent diameter is subject to a corresponding change. At its greatest distance its apparent diameter is 4", and at its least distance 11", its value at the mean distance being 61".

The apparent diameter of the moon being familiar to every eye supplies a convenient and instructive comparison by which the apparent magnitudes of other objects may be indicated, and we shall refer to it frequently for that purpose. The disk of the full moon subtends an angle of 1800" to the eye. It follows, therefore, that the apparent diameter of Mercury when it appears as a thin crescent near inferior conjunction is about the 150th part, near the greatest elongation it is the 280th part, and near superior conjunction the 400th part of the apparent diameter of the moon.

317. Real diameter. The real diameter has been assumed, from some recent measures, to be about 3058 miles.

318. Volume.—Assuming that the diameter of Mercury equals 3058 miles, it follows that its volume would amount to about the 19th part of that of the earth.

M

The relative volumes are represented by м and E, fig. 56.

319. Mass and density. --Some uncertainty has hitherto attended the calculation of the density and mass of this planet, owing to the absence of a satellite. The disturbances produced by it upon the motion of Encke's comet (a body which will be described in another chapter) have, however, supplied the means of a closer approximation to it. By this means it has been found that if M' express the mass of the planet, and м that of the earth, we shall have

Fig. 56.

so that the mass is 15 times less than that of the earth.

The density of the planet relatively to that of the earth, determined from the above, would equal 1.20. Other estimates make it 112. So that it may be inferred that the density of Mercury exceeds that of the earth by an eighth to a fifth; this result is, however, problematical.

320. Solar light and heat.—The apparent magnitude of the sun is greater than upon the earth, in the same ratio as the distance is less; and owing to the considerable ellipticity of Mercury's orbit,