As the full moons always happen when the moon is directly opposite to the sun, all the full moons in our winter, happen when the moon is on the north side of the equinoctial. The moon, while she passes from Aries to Libra, will be visible at the north pole, and invisible during her progress from Libra to Aries; consequently, at the north pole, there is a fortnight's moonlight and a fortnight's darkness by turns. The same phenomena will happen at the south pole during the sun's absence, in our summer. If the earth, the moon, and the sun were all in the same plane, there would be an eclipse of the sun at every new moon (for then the moon is betwen the earth and the sun), and there would be an eclipse of the moon at every full moon, at which time the earth is between the sun and the moon. But as the orbit of the moon crosses the orbit of the earth or the ecliptic in two opposite points, called the nodes; it is evident that the moon is never in the ecliptic except when she is in one of these nodes; an eclipse, therefore can never happen unless the moon be in or near one of these nodes, at all other times she is either above or below the orbit of the earth; and though the moon crosses each of these nodes every month, yet if there should not be a new or full moon, at or near that time, there will be no eclipse. (See more of this subject in a succeeding chapter). The influence of the moon upon the waters of the ocean has already been explained; and the nature of the harvest-moon will be shewn amongst the problems on the globes. The moon's greatest horizontal parallax is 61' 32′′, the least 54' 4", consequently the mean horizontal parallax is * 57' 48" ; and her mean distance from the earth 236847 miles. The apparent diameter of the moon ; *Dr. Hutton's mathematical Dict. word Parallax. As in the note page 61. Sine of angle PSO 57′ 48′′ Is to semi-diam. of the earth PO 8.2256335 0.0000000 So is radius sine of 90° - sine OPS 10.0000000 To 59.47938 semi-diameters 1.7743665 Hence 59.47938 x 3882 236846.89 miles, distance of the moon from the earth. is variable according to her distance from the earth; her mean apparent diameter is stated to be 31' 7";* hence, her real diameter is 2144 miles,† and her magnitude about of the magnitude of the earth. The moon performs her revolution round the earth in 27 days 7 hours 43 minutes 5 seconds, as has been observed before, consequently she travels at the rate of +2270 miles per hour round the earth, besides attending the earth in its annual journey round the sun. The surface of the moon is greatly diversified with inequalities, which through a telescope have the appearance of hills and valleys. Astronomers have drawn the face of the moon as viewed through a telescope, distinguishing the dark and shining parts by their proper shades and figures. Each of the spots on the moon has been marked by a numerical figure, serving as a reference to the proper name of the particular spot which it represents; as,*, Herschel's volcano ; 1, Grimaldi ; 2, Galileo, &c.; so that the several spots are named from the most noted astronomers, philosophers, and mathematicians. The best and most complete picture of the moon is that drawn on Mr. Russel's lunar globe. * Vince's Astronomy. :: As in the preceding notes say, inversely, as 59.47938 semidiam.: 31' 7": 23882.84 sem.: 4" .6497, the apparent diameter of the moon at a distance from the earth equal to that of the sun; hence, 32′ 2′′: 886149: :4" .6497: 2143.8 miles, the diameter of the moon. Or, by trigonometry, the angle m On, (Plate IV. Fig. 3.) 180°-31'7" 31' 7", hence Omn=2 89° 59′ 44′′ 26"" = = 2 1 (sine of 90 extremely 10.0000000 1.7743665 7.9567310 1.7310975 To .53839 semi-diameters of the earth And.55839 x 3982 2143.86, &c. miles, the diameter of the moon ; See the note pages 127, 128. If the cube of the earth's diameter be divided by the cube of the moon's diameter, the quotient will be 51.2; hence, the magnitude of the earth is upwards of 50 times that of the moon. For, by the note page 129, as 113: 355 : : 236846.9 × 2: 1488 153.09 miles, circumference of the moon's orbit; then 27 d. 7 h. 43 m. 5 sec. 1488153.09 m. : : 1h: 2269.5 miles. T Dr. Herschel informs us, that on the 19th of April 1787, he discovered three volcanoes in the dark part of the moon; two of them appeared nearly extinct, the third exhibited an actual eruption of fire, or luminous matter. On the subsequent night it appeared to burn with greater violence, and might be computed to be about three miles in diameter. The eruption resembled a piece of burning charcoal, covered by a thin coat of white ashes; all the adjacent parts of the volcanic mountain were faintly illuminated by the eruption, and were gradually more obscure at a greater distance from the crater. That the surface of the moon is indented with mountains and caverns, is evident from the irregularity of that part of her surface which is turned from the sun; for, if there were no parts of the moon higher than the rest, the light and dark parts of her disc at the time of the quadratures would be terminated by a perfectly straight line; and at all other times the termination would be an elliptical line, convex towards the enlightened part of the moon in the first and fourth quarters, and concave in the second and third: but, instead of these lines being regular and well defined when the moon is viewed through a telescope, they appear notched and broken in innumerable places. It is rather singular that the edge of the moon, which is always turned towards the sun, is regular and well defined, and at the time of full moon no notches or indented parts are seen on her surface. In all situations of the moon, the elevated parts are constantly found to cast a triangular shadow with its vertex turned from the sun; and, orf the contrary, the cavities are always dark on the side next the sun, and illuminated on the opposite side: these appearances are exactly conformable to what we observe of hills and valleys on the earth: and even in the dark part of the moon's disc, near the borders of the lucid surface, some minute specks have been seen, apparently enlightened by the sun's rays: these shining spots are supposed to be the summits of high mountains, which are illuminated by the sun, while the ad * * Supposing this to be the fact, astronomers have determined the height of some of the lunar mountains. The method made use of jacent valleys nearer the enlightened part of the moon are entirely dark. Whether the moon has an atmosphere or not, is a question that has long been controverted by various astronomers; some endeavour to prove that the moon has neither an atmosphere, seas, nor lakes; while others contend that she has all these in common with our earth, though her atmosphere is not so dense as ours. It can not be expected in an intoductory treatise, where generally received truths only ought to be admitted, that we should enter into the discussion of a controverted question; however, it may be proper to inform the student, that the advocates for an atmosphere, if we may be allowed to reason from analogy, have the advantage over those who contend that there is none. It is admitted on all hands, that the moon has mountains and by Riccioli (though it gives the true result only at the time of the quadratures) is here explained, because it is much more simple than the general method given by Dr. Herschel, in the Philosophical Transactions for 1780. Let ADB (Plate IV. Fig. 7.) be the disc or face of the moon at the time of the quadratures, ACB the boundary of light and darkness; MO a mountain in the dark part, the summit M of which is just beginning to be enlightened, by a ray of light SAM from the sun. Now, by means of a micrometer, the ratio of MA to AB may be determined; and as AC is the half of AB, and MAC a right angled triangle, by Euclid 1 and 47th AC+AM miles. CM from which take COAC, and the remainder MO, is the height of the mountain. Riccioli observed the illuminated part of the mountain St. Catharine, on the fourth day after the new moon, to be distant from the illuminated part of the moon about one sixteenth part of the moon's diameter, viz. MA 1-sixteenth of AB, or =1-eighth of AC; now, if we take the moon's diameter 2144 miles, as we have before determined, the height of this mountain will be 83 miles! Galileo makes MA = 1.20th of AB; and He. velius makes MA 1-26th of AB; the former of these will give the height of the mountain 5 miles, and the latter 3 Dr. Herschel thinks, "That the height of the lunar mountains is in general greatly over rated, and that the generality of them do not exceed half a mile in their perpendicular elevation." On the contrary, M. Schroeter, a learned astronomer of Lilienthal, in the duchy of Bremen, says, that there are mountains in the moon much higher than any on the earth; and mentions one above a thousand toises higher than Chimboraco in South America. The same author has likewise lately published a new work on the height of the mountains of Venus, some of which he makes upwards of twenty-three thousand toises in height, which is above seven times the height of Chim, boraco! valleys, like the earth, and appears nearly the same with respect to shape and the nature of her motions; may we not, then, fairly infer that she is similar to the earth in other respects?y V. OF MARS . Mars appears of a dusky red colour, and though he is sometimes apparently as large as Venus, he never shines with so brilliant a light. From the dulness and ruddy appearance of this planet, it is conjectured that he is encompassed with a thick cloudy atmosphere, through which the red rays of light penetrate more easily than the other rays. This being the first planet without the orbit of the earth, he exhibits to the spectator appearances different from Mercury and Venus. He is sometimes in conjunction with the sun, like Mercury and Venus, but was never known to transit the sun's disc. Sometimes he is directly opposite the sun, that is, he comes to the meridian at midnight, or rises when the sun sets, and sets when the sun rises; at this time he shines with the greatest lustre, being nearest to the earth. Mars, when viewed through a telescope, appears sometimes full and round, at others gibbous, but never horned. The foregoing appearances clearly show, that Mars moves in an orbit more distant from the sun than that of the earth. The apparent motion of this planet, like that of Mercury and Venus, is sometimes direct, or from east to west; at others retrograde, or from west to east; and sometimes he appears stationary. Sometimes he rises before the sun, and is seen in the morning; at others he sets after the sun, and of course is seen in the evening. Mars revolves on its axis in 24 hours 39 minutes 22 seconds; and its polar diameter is to its equatorial diameter as 15 to 16, according to Dr. Herschel; but Dr. Maskelyne, who carefully observed this planet at the time of opposition, could perceive no difference between its axis. The inclination of the orbit of Mars to the place of the ecliptic is 1° 51'; the plane of his ascending node about 18o |