304 ASTRONOMY.

than the rest of the surface, so that the light of the Sun may reachthem. Astronomers have endeavoured to measure (he height olthese lunar mountains, in the following manner. Let L G D,(Plate XX. Fig. 8,) be the hemisphere of the Moon illuminated bythe Sun , E C D the diameter of the circle bounding light and dark-ness, and A the top of a hill within the dark part when it first be-gins to be illuminated. Observe with a telescope the proportionof the right line A E, or the distance of the point A from the lucidsurface to the diameter of the Moon E D ; and because in this casethe ravof light ES touches the globe of the Moon , A E C will bea right angle, and therefore in the triangle AE C, having the twos'des A E and E C, we can find out the third side A C ; from whichsubducting 15 C or EC, there will remain A 15, the height of themountain. I5v this mode of measuring, which would be just if theline A E could be taken accurately, the height of St. Catherinewould be nearlv 8 j-miles, if according to Riccioli its top wasabout a sixteenth part of the Moon ’s diameter distant from theconfines of the lucid surface. But by the more accurate observa-tions and just calculations of Ilerschel this disproportionate heightappears to be ill-founded, and the generality of the lunar moun-tains do not exceed half a mile in perpendicular elevation. Thushe calculates their heights: Let S L M, or ? I m, (fig. 9,) be a linedrawn from the Sun to the mountain, touching the Moon at L orl, and the mountain at M or m. Then to an observer at E or e,the lines L M, l m, will not appear of the same length, though themountain should be of an equal height; for L M will be pro-jected into o n, and Im into OX. But these are the quantitiesthat are taken by the micrometer when we observe a mountain toproject from the line of illumination. From the observed quan-tity o n, when the Moon is not in her quadrature, to find L M, wehave the following analogy. The triangles oO L, r M L, are si-

1, () x on

milar; therefore Lo : LO : : Lr : LM ; or —;-—=

’ L o

L M : but L O is the radius of the Moon , and L r or o rt is the ob-served distance of the mountain’s projection ; and L « is the sineof the angle R O L —o LS ; which we may take to be the distanceof the Sun from the Moon without any material error, and whichtherefore we may find at any given time from an ephemeris.

(150.) Modern astronomers have discovered that some of thelunar mountains are really volcanoes, and emit fire, as ours do.An appearance of this kind was discovered some years ago byUlloa, in an eclipse of the Sun . It was a small bright spot like astar near the margin of the Moon . By the assistance of a tele-scope such pluenomena are frequently seen on the unenlightenedparts of theMoon’ssurface. Dr. Ilerschel has particularly observedseveral eruptions of the lunar volcanoes, which he has described inthe Philosophical Transactions . It is the opinion of astronomersthat some of the spots on the lunar surface are shallows on whichthe shadows of the elevated parts fall, and that some of them are wa-ter. It is also now generally concluded tjiat the Moon is surroundedbv an atmosphere. She always keeps the same side towards us;hence it is evident that she turns round her axis exactly in thetime that she goes round the Earth , and that her day ail’d nighttaken together is as long as our lunar month.

(151.) d'he Moon is an opaque globe like the Earth , and shinesonly by reflecting the light of the Sun : therefore, whilst that half ofher which is towards the Sun is enlightened, the other half must bedark and invisible. Hence she disappears when she comes betweenus and the Sun ; because her dark side is then towards us. Whenshe is gone a little way forward, we see a little of her enlightenedside: which increases to our view as she advances, until she comesto be opposite to the Sun ; when her whole enlightened side is to-wards the Earth , and she appears a round illuminated orb, whichwe call the Full Moon ; her dark side being then turned awayfrom the Earth . From the full she seems to decrease gradually asshe goes through the other half of her course ; shewing us "lessand less of her enlightened side every day, till her next change orconjunction with the Sun , when she disappears as before. TheMoon has scarcely any difference of seasons ; her axis being almostperpendicular to the ecliptic. What is very singular, one-half ofler has no darkness at all; the Earth constantly affording it a stronglight in the Sun ’s absence; while the other half has a fortnight’sdarkness and a fortnight’s light by turns.

(15-\) Our Earth appears as a moon to the inhabitants of theMoon ; waxing and waning regularly, but appearing 13 times asbig, and affording them 13 times as much light, as she docs to us.—

When she changes to us, the Earth appears full toiler; and when sleis in her first quarter to us, the Earth is in its third quarter to her;and vice versa. But from one-half of the Moon the Earth is n.evi rseen at all: from the middle of the other half, it is always seenover head; turning round almost 28 times as quick as the Mocadoes. From the circle which limits our view’ of the Moon , onlyone-half of the Earth ’s side next her is seen ; the other half beinghid below the horizon of all places on that circle. To her inha-bitants the Earth appears the biggest body in the universe; for itappears 13 times as big as she does to us. While the Earth turnsround its axis, the several continents, seas, and islands, appear tothe Moon 's inhabitants like so many spots of different forms andbrightness, moving over its surface; but much fainter at sometimes than others, according as our clouds cover them. By thesespots the Lunarians can determine the time of the Earth ’s diurnalmotion, just as we do the motion of the Sun : and they may mea-sure their time by the motion of (he Earth ’s spots,' for they cannothave a more true dial. The inhabitants of the Moon on the sidenext the Earth , may find the longitude of their places as easily aswe can find the latitude of ours. l*'or the Earth keeping constantly,or very nearly so, over one meridian of the Moon , the east or westdistances of places from that meridian are as easily found as we canfind our distance from the equator by the altitudeof our celestial poles.

(153.) The Moon being an opaque spherical body (for her'hillstake off no more from her roundness, than the inequalities on thesurface of an orange take off from its roundness,) we can only seethat part of the enlightened half, which is towards the Earth . Andtherefore, when the Moon is at A, (Plate XXIV. fig, 3,) in con-junction with the Sun S, her dark half is towards the Earth , andshe disappears, as at a, there being no light on that half to renderit visible. When site conies to her first octant at 13, or has gotn»an eighth part of her orbit from her conjunction, a quarter of herenlightened side is towards the Earth , and she appears horned, asat' b. W hen she has gone a quarter of Iter orbit from between tin*Earth and Sun to C, she shews us one-half of her enlightened side,as at c, and we say ( she is a quarter old. At D, she is in her se-cond octant; and by shewing us more of her enlightened side, slutappears gibbous, as at tl. At E, her whole enlightened side is to-wards the Earth ; and therefore she appears round, as at c, when wesay it is Full Moon . In her third octant at F, part of her dark sidebeing towards the Earth , she again appears gibbous, and is on thedecrease, as at f. At G, we see just one-half of her enlightenedside ; and she appears half decreased, or in her third quarter, as a8g. At II, we only see a quarter of her enlightened side, being inIter fourth octant; where she appears horned, as at h. And at A,having completed her course from the Sun to the Sun again, shedisappears; and we say it is New Moon . Tints, in going front Ato E, the Moon seems continually to increase, and in goingfrom E to A, to decrease in the same proportion; havingIke phases at equal distances front A lo E, but as seen fromthe Sun S she is always full. ’Flic Moon does not appear perfectlyround, when she is full in the highest or lowest part of her orbit,because we have not a full view of her enlightened,side at thattime. When full in the highest part of her orbit, a small defici-ency appears on her lower edge; and the contrary when full in thelowest part of her orbit. From the figure, it is evident, that whenthe Moon changes to the Earth, the Earth appears full to the Moon ;and vice versa. For when the Moon is at A, new to the Earth ,the whole enlightened side of the Earth is towards the Moon ; andwhen the Moon is at E, full to the Earth , its dark side is towardsher. Hence a New Moon answers to a Full Earth, and a Full Moon to a New Earth . The quarters are also reversed to each other.

I be position of the Moon ’s cusps, or a right line touching thepoints of her horns, is very differently inclined to (he horizon, atdifferent hours of the same days of her age. Sometimes shestands, as it were, upright on her lower horn, and then such a lineis perpendicular to the horizon: when this happens, she is inwhat the astronomers call the nonagesimal degree; which is thehighest point of the ecliptic above the horizon at that time, and ii90 degrees from both sides of the horizon, where it is then cut hrthe ecliptic. But this never happens when the Moon is on themeridian, except when she is at the very beginning of Cancer orCapricorn. It is easy to demonstrate, that the Moon turns roundIter axis in the time that she goes round her orbit ; for, a specta*tor at rest, without the periphery of the Moon ’s .orbit, would seeall her side; turned regularly towards him in that time. She (ur;,»round her axis from any star to the same star again in 27 davs 7F!-J

"hours: