as the sun or on the diametrically opposite point, the annual parallax is zero, but the aberration is a maximum. The displacement due to parallax takes place towards the sun, and that due to aberration towards a point on the ecliptic 90° behind the sun.

111. The aberration of a planet differs somewhat from that of a star, being due to two causes-(1) That due to the velocity of the earth, and (2) to the velocity of the planet. If the planet's motion were equal to that of the earth, and in the same direction, there would be no aberration. In general, it is easy to calculate the aberration due to these two causes separately.

As the velocity of the moon about the earth is very small compared with the velocity of light, we may regard the aberration due to this velocity as zero. Neither is there any aberration on account of the earth's orbital motion round the sun, for this motion is shared in by the moon. We may, therefore, regard the moon as having practically no aberration.

Discovery of Aberration.—Bradley was first led to the discovery of aberration while attempting to find the annual parallax of y Draconis. Observing that the latitude of this star was subject to small annual variations for which he could not account by attributing them to any known cause, he was eventually led to adopt the above explanation.

112. Diurnal Aberration.-Owing to the earth's rotation on its axis, a point on the equator turns through 25,000 miles in 23h 56m. This is at the rate of th of a mile per second, or th of the velocity of the earth in its orbit. Any other point on the earth not on the equator will have, of course, a less velocity than this.

The aberration due to this motion is called diurnal aberration. It is, however, as we can easily see by comparing the above velocity of rotation with that of light, so small as to be almost inappreciable.

CHAPTER IX.

THE MOON.

113. Next to the sun the moon is to us the most important of all the heavenly bodies. Besides its diurnal motion from east to west, which is imparted to it in common with all the other heavenly bodies in consequence of the rotation of the earth on its axis, it has, like the sun, a motion among the fixed stars in the opposite direction, making a complete revolution of the heavens in about 27d 7h 43m. As the sun appears to make a complete revolution of the ecliptic in one year, we see that the moon's motion among the fixed stars is about thirteen times faster than that of the sun. So rapid is this motion, that its change of position with respect to bright stars in its neighbourhood can be easily seen, even after as short an interval as two or three hours.

The moon's path, on being mapped out on a celestial globe, is found to be represented by a great circle, cutting the ecliptic at an angle of 5° 9', from which it follows that, like the planets, it is always to be found near the ecliptic, its north or south latitude never exceeding 5° 9′.

The moon's motion among the fixed stars is due to an orbital motion round the earth. In fact, the moon is the earth's satellite. We must not, however, suppose that its orbit round the earth is a circle, because the projection of this orbit on the celestial sphere, on being traced out, is represented by a great circle. No, for just as in the case of the sun, we find that the moon's distance from the earth is not constant. We are led to this conclusion by the fact

that its angular diameter, on being measured at different times by means of a micrometer, is found to undergo periodic changes, which shows that its distance from the earth must be changing also, being least when the apparent diameter is greatest. Its greatest angular diameter is 33; least 291', and the mean 31, or a little more than half a degree. These changes in the apparent angular diameter lead us to the conclusion—(1) that the moon's orbit round the earth is approximately elliptic with the centre of the earth situated in one of the foci, (2) the radius vector joining the centres of the earth and moon sweeps out equal areas in equal times.

From this we might infer that the moon's motion among the fixed stars is not uniform. In fact, it varies from a maximum of 33′ 40′′ per hour to a minimum of 27', its mean hourly velocity being 32′ 56′′. So that we may say that the moon in its motion among the fixed stars moves through an arc equal to its own diameter in one hour.

The mean distance of the moon from the earth is 238,000 miles, or about 60 times the earth's radius. As this distance is much less than the radius of the sun, which is 110 times the radius of the earth (Art. 44), we see that if the sun were placed with its centre at the centre of the earth its mass would extend considerably beyond the moon, a consideration which will perhaps enable the mind to form some idea of the magnitude of the body which forms the centre of our system.

The Moon's Phases

114. One of the most interesting phenomena to be seen in the heavens is the series of changes which the visible portion of the moon's illuminated surface presents during its orbital motion about the earth. These appearances are called its phases. They prove that the moon is an opaque spherical body deriving its light from the sun. As only one

hemisphere of the moon can be illuminated at once, viz. that half which is turned towards the sun, an observer will therefore see a variable amount of this bright surface depending on the relative positions of the sun, moon, and earth.

Let ACMD (fig. 62) represent the orbit of the moon, E the earth, and S the direction of the sun. In the eight positions of the moon, which we have here depicted, the line mn, which is perpendicular to the direction of the sun,

3

FIG 62.

separates the illuminated half of the moon from the unilluminated half, and all the positions of mn are drawn as if parallel to one another, the sun being so far distant. The line ab may be taken as separating the half of the moon which is turned towards the observer from that which is turned away from him.

When the moon is in conjunction at A, its dark hemisphere is turned towards the earth, and no portion is visible to the observer. It is then said to be new moon.

Some four or five days afterwards, when the moon is at B, the observer will see a small portion of the illuminated surface which will appear as a thin crescent in the sky, seen in the west after sunset.

When the moon is at C, 90° from the sun; that is, in quadrature, it will appear in the sky as a bright semicircle. This is said to be first quarter, and the moon is then said to be dichotomized.

At D it is gibbous, and when in opposition at M, which occurs at about 15 days after conjunction, the whole of the illuminated hemisphere is turned towards the observer. The moon will then present a complete circular disc in the sky. This is said to be full moon.

After full moon, these phases are repeated in reverse order, the moon being again in quadrature at G, which is called third quarter, and finally, conjunction is once more reached at A.

When in conjunction and opposition, the moon is said to be in syzygy. Its elongation from the sun is then 0° and 180°, respectively.

When in quadrature at first quarter its

elongation is 90°, and at third quarter 270°.

Definitions.

(1). The time taken by the moon to make a complete revolution with reference to the fixed stars is called its periodic time or sidereal period. This period is 27d 7h 43m.

(2). The interval between two successive conjunctions or oppositions, or, in other words, the time taken to make a complete revolution with reference to the sun is called the synodic period or a lunation. This period is 29 days, or, more accurately, 29-5305887 days.

It is obvious that if the sun had no apparent motion in the ecliptic, the synodic and sidereal periods would be exactly the same, so that the full moons would follow one another at intervals of 274 7h, instead of 29 days. But while the