the earth's surface. An idea of the comparative proximity of the moon to the earth may be obtained, by imagining the earth's centre to coincide with that of the sun; if this were so, not only might the moon's orbit be included within the body of the sun, but this would be the case were its diameter nearly double what it is: or, again, let us suppose a spectator at the sun to be able to trace the moon's orbit in the heavens, the plane of which, for the purpose, must be imagined to be at right angles to the earth's orbit, the diameter of the circle described by her would be only a little larger than one half of the diameter of the sun's disk, or 18'. The form of the moon's orbit may be readily deduced from measurements of her diameter, which is found to vary from day to day to the extent of several seconds. As we are aware that an object increases in size as it draws near, and as it recedes diminishes, we conclude that she varies her distance from the earth, appearing of a less diameter when farther off-of the greatest, at her nearest approach. In the Nautical Almanac her semi-diameter is given for every twelve hours. If we take out the values for every day for a month, and at the same time the moon's longitude, with these data we can show the character of her orbit; as, however, this orbit is inclined to the ecliptic at an angle of 5° 9'-not quite coincident with it-this method will be slightly incorrect. SEMI-DIAMETER OF THE MOON IN SECONDS, AND LONGITUDE AT NOON. New Moon, Jan. 28, 5h. 11m. Full Moon, Feb. 12, 14h. 56m. Above are the requisite data for the month of February; since it is clear that the distances will be inversely as the measures of the semi-diameter, we must take the mean of all the semi-diameters given as the mean semidiameter of the moon for the month: with this quantity, taken from a scale of equal parts, describe a circle, the centre of which shall represent the position of the earth; on this circle set off the longitude of the moon for the noon of each day; draw lines from the centre through the points thus obtained, which produce somewhat beyond the circle. Take the difference between the mean semi-diameter and that for each day, and if the semidiameter be greater than the mean, set off from the same scale the difference on the line of longitude towards the centre, seeing that the moon on that day is so much nearer than her mean distance; but if the semidiameter for the day be less than the mean, set the difference off on the line of longitude outside the circle, or farther than the mean distance : having done this for the month, join the points thus obtained, and the orbit of the moon will be delineated. It will be found to be elliptical, with the earth not in the centre, but in one of the foci; but it will not be possible to describe an ellipse which shall pass through all the points, seeing that the moon is subject to many disturbances, productive of irregularities in her course; the sun especially operates on her through gravitating attraction, elongating her orbit when the moon is between him and the earth, and flattening it when the earth is between the other two bodies, because then the lines of attractive force of the sun and the earth chance to coincide. Another complexity is introduced by the fact, that while the moon is revolving round the earth, she is herself carried forward with the earth around the sun; so that her orbit never returns into itself, but describes a succession of wavy curves. An entire revolution of the moon is completed in 27 days, 7 hours, 44 minutes, which falls far short of a month, or complete lunation, the time of which is 29 days, 12 hours, 14 minutes; this will be distinctly seen by remarking the orbit delineated from the above data: a complete circuit round the earth will have been completed between January 28 and February 24, but the new moon will not occur till the 26th of that month. To understand how this happens, let us suppose that at the time of full moon the moon is in conjunction with some well-known star; when she has arrived again at that star, a revolution round the earth will have been completed, but she will not have arrived opposite the sun, or be full, seeing that the earth has advanced in her orbit during that time, taking the moon with her, which will have to describe an arc equal to that passed through by the earth before she is in the same position as regards the sun; hence, between two successive full moons, or new moons, 29 days and a half will elapse, which period is termed a synodic revolution, and constitutes what is ordinarily termed a month. During this time the moon will pass through all her changes, from new to full, and onwards to new moon again. The regularity of the moon's orbit is constantly disturbed on account of her different distances from the earth's equator. The earth, as was shown in the last paper of this series, is not a sphere but a spheroid, having a great redundance of matter accumulated at the equatorial regions. Now the tendency of this portion of the earth will be ever to draw the moon towards it, or to prevent her attaining so high a declination as she would if it were absent. Indeed, so nicely has her place been determined that the amount of attraction due to the spheroidal figure of the earth has been calculated by noting its perturbing effect on the moon, and thence has been deduced the proportion between the accumulated matter at the equator and the entire earth. Some of the planets draw aside, impel, or delay, the moon in her course. In short, there exist no less than sixty sources of irregularity, nearly all of which must be taken into account before the moon's predicted place will be found to agree with the observed. Some of these are so delicate as to be scarcely appreciable, others are easily detected. The discovery of some has been the result of observation, others have been reasoned out from theory; the two methods always advancing hand in hand to perfect that wondrous result of mathematical skill," the Lunar Theory." Since the moon completes a revolution round the earth in 27 days 7 hours, at a known distance, by calculating the circumference of her orbit and dividing the result by the number of seconds in that time, we ar rive at 1.15 mile as the rate at which she is carried forward in her orbit per second. Now, although the telescope has disclosed to us every portion of her surface within certain limits, yet it would appear that, both in consequence of this rapid motion and also of the diurnal motion of the earth, unless we can attain to greater stability of mounting very large telescopes, and can communicate a movement equal in regularity and steadiness to that of the earth on its axis, we shall never see objects much smaller than a mile in diameter. To perceive an object of one second in diameter requires an immense amount of optical power; but, as the power increases, so does the apparent rapidity of motion, and small objects would pass the field of view with such rapidity as to prevent our acquiring an accurate knowledge of their nature or their form. The angular advance of the moon from west to east, is a quantity about equal to her own diameter in one hour; and on this very appreciable quantity is founded the method of lunar observations for the purpose of obtaining the longitude at sea; the principle of which, as well as eclipses and tides, in which the moon is a party concerned, must be passed by for the present, as not consistent with the object the writer has proposed to himself. He will therefore proceed to describe the telescopic appearance and the physical constitution of our satellite as far as scientific research has developed it. Placed at a comparatively short distance from the earth, the moon has been a favourite object of telescopic observation. Many of her peculiar features are easily made out with very inferior optical aid; but the minuter details demand high powers and superior instruments. Two German astronomers, Beer and Madler, have published a map of the entire surface of the moon, in which every feature is so accurately laid down, that future observers will be able most readily to mark any change. Every mountain, crater, valley, and peak has been plotted from accurate measurements with the micrometer; hence many have affirmed that, for accuracy and minuteness, it is far superior to any map we possess of the surface of the globe which we inhabit. What are the physical conditions of the lunar hemisphere? What are those blendings of light and shadow attractive even to unassisted vision? What resemblance does our nearest celestial neighbour bear to her primary? Questions, these, of the highest interest, and such as we are able only in part to answer satisfactorily. The smallest astronomical telescope ever constructed will enable an observer at once to satisfy himself that the similarity between the formations on the surface of the moon to those of the earth is very slight; indications will at once be perceived of another geological era, and traces of the operation of forces which have long slumbered in our globe. He will perceive that one half of her surface is covered with circular pits or hollows, of all sizes, but of a singular uniformity of outline. If he increases his optical power by the use of superior instruments, a far greater number will be successively developed, all of the same type, varying in size from one quarter of a mile to 150 miles in diameter. These cup-shaped hollows are surrounded by precipitous ridges, and, in the centre of many of them, rise conical peaks, perpendicularly and suddenly, in some cases to an amazing height. The nearest approach to a resemblance with these formations which can be met with on our earth are in the craters of Hecla, Vesuvius, Etna, and Puy de Dome. By the eruption of Vesuvius in October, 1822, the contents of the crater were all ejected, and replaced by a gulf or chasm three miles in circumference, three-quarters of a mile in its longest diameter, and 2000 feet in depth. Such a chasm, viewed from the moon, would present an appearance not unlike those which cover her surface, but wanting the complete circular form which is one of their characteristics. The finer telescopes show deep fissures and rocks in wild confusion, dreary and sublime scenery, perhaps unequalled here. A passage in Madame Pfeiffer's journey to Iceland does, however, describe scenery so exactly similar to what we might imagine a lunar landscape would present, that it may be quoted in illustration of that which the finest telescopes reveal to patient investigators :-"Suddenly," says she, "I found myself standing on the brink of a chasm, into which I could scarcely look without a shudder-colossal blocks of stone hang loosely in the form of pyramids and broken columns from the lofty walls of lava which encircle the whole long ravine in the form of a gallery. Speechless, and in anxious suspense, we descend a part of this chasm, hardly daring to look up, much less to give utterance to a single sound, lest the vibration should bring down one of those avalanches of stone to the terrific force of which the rocky fragments scattered around bear ample testimony. The entire length of the ravine is about a mile, but a small portion only can be traversed; the rest is blocked up by masses of lava, heaped one upon another. I could have fancied that I wandered through the depths of a crater which had itself raised these stupendous barriers during a mighty eruption in times long gone by." To these various crater-like formations on the moon the early observers gave the names of men famous in ancient or contemporary history. By these the principal are still distinguished. Flat and extensive plains, which occur on the surface of the moon, ranging from 200 to 300 miles in diameter, were thought to be seas, and called "mare serenitatis," "mare imbrium," &c. More perfect telescopes have shown that these plains are spread over with blocks or masses of matter, and that their surface is not smooth or flat, but rugged and uneven, as shadows falling on them clearly indicate; the names, however, are retained for convenience of reference, though originally applied on an assumption contrary to truth. A description of Theophilus, one of the most striking of the craters, may enable us to compare, or rather contrast, lunar with terrestrial scenery. Around it, on every side, rises a mighty wall of broken and precipitous rocks, forming a circle sixty-five miles across; the character of the summits, as we learn from the shadows thrown on the plains below, resembles the rugged and broken form of Alpine ridges, and they rise 18,000 feet above the level of the enclosed valley, from which spring several conical peaks to the height of a mile. The irregularities of the outer ridge indicate distinctly that it has resulted from successive eruptions at different epochs, which may be traced in formations overlying others previously originated; in some portions, a new crater appears formed on the edge of a more ancient, of which only a portion has remained unaltered. As the observer traces these objects through the telescope, he recals that feeling of awe experienced in wandering over the region of the Alps; and the recollection enables him, in some degree, to realize the sublimity of the scenery as he passes from crater to crater-each one a mighty record of violent rupture and energetic operation of disturbing force. The conical peaks which occupy, either singly or in groups of three or four, the centre of most of the craters may find a terrestrial representative in the Peter Botte mountain of the Mauritius, or in the peaks not infre quent in the islands of the Atlantic to the west of Southern Europe and Africa. When the moon is only partially enlightened, the rays of the sun, falling on them and the mountainous ridges, bring them out in strong relief, their brilliancy contrasting with the deep shadows of the valleys beneath a contrast far more striking than that between the summits of the Alps and the lower land at sun-set, though both appearances arise from identical causes. Ranges of mountains are not wanting in the moon; the Apennines, so called, form a curved line of 600 miles in extent, and rise to an elevation, in parts, of 14,000 and 18,000 feet; the escarpment on one side is fearfully precipitous. The whole are composed of sharp and jagged rocks, whose outline is shadowed on the plain beneath. It is by the length of the shadows that the heights of the lunar mountains are determined; if we know the angle of elevation of the sun above the plain on which the mountain rests, and then by micrometrical measurement ascertain the proportion between the length of the shadow and the moon's diameter, also known, we have sufficient data to calculate the height of any elevation required. In this way Beer and Madler have determined the heights of many lunar elevations, and from them have been derived the measurements given in this paper. From several craters, but most extensively from Tycho, proceed concentric rays to an enormous distance, reminding the observer of solidified streams of lava, which at former epochs may have been supplied from the central source by repeated energetic eruptions. It would not be philosophical, however, to arrive immediately at such a conclusion; their great extentfor they cover nearly the entire south-western quadrant of the moon's diskthrows doubt upon the supposition of Sir William Herschel of their being lava streams. Uncertainty hangs over the cause of this peculiar feature, and no satisfactory solution of the phenomenon has yet been suggested. Madler imagines that the ring mountains may have been amongst the first lunar formations, and, consequently, the points to which all the gases evolved in the formation of our satellite would have been attracted; these emanations produced effects, such as vitrification or oxidation, which modified the reflective powers of the surface. On this ingenious conjecture the writer would not pretend to express an opinion. A question far more readily settled is, Has the moon been provided with an atmosphere? The result of observation compels us to answer in the negative; no traces of clouds have ever been observed to obscure any part of her surface, no phenomenon resembling twilight on our globe has been detected. The shadows of her mountains are sharp and definite, not shaded off gradually; for the deep black of the valley stands in striking and immediate contrast with the brilliantly-illumined summit. Were the moon surrounded by a gaseous envelope, endued with refractive powers at all resembling our atmosphere, it would affect the position of a star seen through it at the time of an occultation-its light would begin gradually to fade before it was covered by the body of the moon passing over it; but this has never been found to happen, although stars have been selected and watched by different observers for the purpose of determining the point. The star vanishes instantaneously, so that the fraction of the second of the occurrence can be easily noted and compared with the time given in the Nautical Almanac, an observation on which is founded a method of obtaining the longitude of a place. Nor has any atmospheric effect been observed when the moon has been passing over the sun's disk at the time of a solar eclipse. Observations have tended to show that if there were an |