earth; all known quantities. Selecting then a similar triangle; viz., L'S'E', and regarding L'E' as one mile long, we find that according to the table the length of L'S' is four hundred and fifty-six hundred thousandths of a mile (00456ths.) We then make this proportion; to wit, (L'E') 1: (S'L') .00456:: (LE) 238,613 1088. Half the diameter of the moon therefore measures 1088 miles, and the entire diameter is 2176 miles, which is nearly its true length. When the calculation is carried out with the greatest exactness, and every refined correction made, the moon's diameter according to Prof. Mädler is found to be 2,160 miles long; an extent a little greater than one fourth of the earth's diameter. The relative sizes of the earth and moon are shown in Fig. 53, where E represents the earth and M the moon. What is the extent of the diameter ? MOON'S PHASES. 266. The moon has no light of her own, but shines by the reflected light of the sun, the hemisphere presented to the sun being illumined with his rays while that which is turned from him is shrouded in darkness. The relative positions of the sun, moon, and earth are not always the same, and hence arise those periodical fluctuations in the lunar light which are termed the phases' of the moon. FROM NEW MOON TO THE FIRST QUARTER. 267. At new moon the centres of the sun, moon, and earth, are situated in nearly the same straight line, the moon being in the middle, at which time she is said to be in conjunction. In this position the unenlightened part of the moon is turned towards the earth, and the orb is lost to our view. In a short time it advances so far to the east of the sun as to become visible in the west soon after his setting. Its bright portion then appears of a crescent form, on that side of the disk which is nearest to the sun, while the remaining dark part of the disk is just discerned, being faintly illumined by the earth-light." In this position the convex part of the moon's crescent is towards the sun, and the line which separates the illumined from the unillumined part, called the terminator, is concave. 268. Each succeeding night the moon is found farther eastward of the sun, and the bright crescent occupies more and more of her disk, the terminator gradually growing less curved, until when the moon is 90° distant from the sun, half the disk is illuminated and the terminator becomes a straight line; the moon is then in her 1. Phases from the Greek word phasis, meaning an appearance. 2. Earth-light. Some of the light which falls upon the earth from the sun is reflected to the moon, and a portion of this is reflected back again from the moon's surface to the earth. This is the earth-light. The amount thus reflected from the lunar surface must necessarily be very small, but it is sufficient to enable us faintly to discern the outlines of the moon. Does the moon shine by her own light? What is the cause of the periodical fluctuations in the lunar light? What name is given to these fluctuations? Describe the phases of the moon from new moon to the first quarter ? FROM THIRD QUARTER TO NEW MOON. 147 FIRST QUARTER. The extremities of the moon's crescent are called cusps,' and from the time of new moon to the first quarter the moon is said to be horned. FROM THE FIRST QUARTER TO FULL MOON. 269. As the moon advances beyond her first quarter, the terminator becomes concave toward the sun and more than half the lunar disk is illuminated, when the moon is said to be gibbous. At length in her easterly progress, she reaches her second quarter, and the sun, earth, and moon are again in nearly the same straight line; the earth however being in the middle. The moon is now in opposition, 180° from the sun, rising in the east at about sunset; and as her whole enlightened disk is turned toward the earth, she is now at the FULL. FROM FULL MOON TO THE THIRD QUARTER. 270. After opposition the enlighted part of the moon again becomes gibbous as she returns toward the sun; and she rises later and later every night. When she has arrived within 90° of the sun, she is then in her THIRD QUARTER, the terminator is once more a straight line, and the bright portion of the orb again fills up one half of the disk. FROM THIRD QUARTER TO NEW MOON. 271. After passing her third quarter the moon resumes her crescent shape, rising early in the morning before the sun. As her time of rising approaches nearer and nearer to that of the sun, the glittering crescent contracts in breadth, until at length the moon arriving again at CONJUNCTION its light entirely disappears. The positions of the moon where she is midway between any two adjacent quarters are termed her octants." 1. Cusps, from the Latin word cuspis, meaning the point of a spear. 2. Gibbous from the Latin word gibbus, meaning swelled out. 3. Octant, derived from the Latin word octo, eight; an octant being distant from its adjacent quarters, one eight part of the moon's orbit, or 450. From the First Quarter to the Full? From the Full to the Third Quarter? From the Third Quarter to New Moon? What are the octants ? 5 This subject is further illustrated by Fig. 54, where S8, S1, and all lines parallel to these indicate the direction in which the sunbeams come, and E represents the earth. The circles 1, 2, 3, 4, 5, 6, 7 and 8, show the places of the moon in her orbit; at conjunction (1,) the first octant (2,) the first quarter (3,) the second octant (4,) at opposition (5,) the third octant (6,) the third quarter (7) and at the fourth octant (8;) while the white portions of the circles 1', 2', 31, 4', 5', 61, 7' and 8', exhibit the phases of the moon in all the preceding positions. Thus when the moon is at the first octant (2,) the phase corresponding to this place is displayed in circle 21, that of the first quarter (3,) in circle 3'; and so of all the other positions. 272. The points in the moon's orbit where she is in conjunction and opposition are called the syzygies', and those where she is 90° from the sun the quadratures. Fig. 55, exhibits the appearance presented by |