, Luna, <*>, one of the heavenly bodies, being a fatellite, or secondary planet to the earth, considered as a primary planet, about which she revolves in an elliptic orbit, or rather the earth and Moon revolve about a common centre of gravity, which is as much nearer to the earth's centre than to the Moon's, as the mass of the former exceeds that of the latter.

The mean time of a revolution of the Moon about the earth, from one new moon to another, when she overtakes the sun again, is 29d. 12h. 44m. 3s. 11th.; but she moves oncc round her own orbit in 27d. 7h. 43m. 8s. moving about 2290 miles every hour; and turns once round her axis exactly in the time that she goes round the earth, which is the reason that she shews always the same side towards us; and that her day and night taken together are just as long as our lunar month.

The mean distance of the Moon from the earth is 60 1/2 radii, or 30 1/4 diameters, of the earth; which is about 240,000 miles. The mean excentricity of her orbit is 55/1000, or 1/18th nearly of her mean distance, amounting to about 13,000 miles.

The Moon's diameter is to that of the earth, as 20 to 73, or nearly as 3 to 11, or 1 to 3 2/3; and therefore it is equal to 2180 miles: her mean apparent diameter is 31′ 16″ 1/2, that of the sun being 32′ 12″. The surface of the Moon is to the surface of the earth, as 1 to 13 1/4, or as 3 to 40; so that the earth reflects 13 times as much light upon the Moon, as she does upon the earth; and the solid content to that of the earth. as 3 to 146, or as 1 to 48 2/3. The density of the Moon's body is to that of the earth, as 5 to 4; and therefore her quantity of matter to that of the earth, as 1 to 39 very nearly: the force of gravity on her furface, is to that on the earth, as 100 to 293. The Moon has little or no difference of seasons; because her axis is almost perpendicular to the ecliptic.

Phenomena and Phases of the Moon. The Moon being a dark, opaque, spherical body, only shining with the light she receives from the sun, hence only that half turned towards him, at any instant, can be illuminated, the opposite half remaining in its native darkness: then as the face of the Moon visible on our earth, is that part of her body turned towards us; whence, according to the various positions of the Moon, with respect to the earth and sun, we perceive different degrees of illumination; sometimes a large and sometimes a less portion of the enlightened surface being visible: And hence the Moon appears sometimes increasing, then waning; sometimes horned, then half round; sometimes gibbous, then full and round. This may be easily illustrated by means of an ivory ball, which being before a candle in various positions, will present a greater or less portion of its illuminated hemisphere to the view of the observer, according to its situation in moving it round the candle.

The same phases may be otherwise exhibited thus: Let S represent the sun, T the earth, and ABCD &c the Moo<*>'s orbit. (Plate xv, fig. 3.) Now, when the Moon is at A, in conjunction with the sun S, her dark side being entirely turned towards the earth, she will be invisible, as at a, and is then called the new Moon. When she comes to her first octant at B, or has run through the 8th part of her orbit, a quarter of her enlightened hemisphere will be turned towards the earth, and she will then appear horned, as at b. When she has run through the quarter of her orbit, and arrived at C, she shews us the half of her enlightened hemisphere, as at c, when it is said she is one half full. At D she is in her 2d octant, and by shewing us more of her enlightened hemisphere than at C, she appears gibbous, as at d. At her opposition at E her whole enlightened side is turned towards the earth, when she appears round, as at e, and she is said to be full; having increased all the way round from A to E. On the other side she decreases again all the way from E to A: thus, in her 3d octant at F, part of her dark side being turned towards the earth, she again appears gibbous, as at f. At G she appears still farther decreased, shewing again just one half of her illuminated side, as at g. But when she comes to her 4th octant at H, she presents only a quarter of her enlightened hemisphere, and she again appears horned, as at h. And at A, having now completed her course, she again disappears, or becomes a new moon again, as at first. And the earth presents all the very same phases to a spectator in the Moon, as she does to us, but only in a contrary order, the one being full when the other changes, &c.

The Motions of the Moon are most of them very irregular, and very considerably so. The only equable motion she has, is her revolution on her own axis, in the space of a month, or time in which she moves round the earth; which is the reason that she always turns the same face towards us.

This exposure of the same face is not so uniformly so however, but that she turns sometimes a little more of the one side, and sometimes of the other, called the Moon's Libration; and also shews sometimes a little more towards one pole, and sometimes towards the other, by a motion like a kind of Wavering, or Vacillation. The former of these motions happens from this: the Moon's rotation on her axis is equable or uniform; while her motion in her orbit is unequal, being quickest when the Moon is in her perigee, and slowest when in the apogee, like all other planetary motions; which causes that sometimes more of one side is turned to the earth, and sometimes of the other. And the other irregularity arises from this: that the axis of the Moon is not perpendicular, but a little inclined to the plane of her orbit: and as this axis maintains its parallelism, in the Moon's motion round the earth; it must necessarily change its situation, in respect of an observer on the earth; whence it happens that sometimes the one, and sometimes the other pole of the Moon becomes visible.

The very orbit of the Moon is changeable, and does not always persevere in the same figure: for though her orbit be elliptical, or nearly so, having the earth in one focus, the excentricity of the ellipse is varied, being sometimes increased, and sometimes diminished; viz,| being greatest when the line of the apses coincides with that of the syzygies, and least when these lines are at right angles to each other.

Nor is the apogee of the Moon without an irregularity; being found to move forward, when it coincides with the line of the syzygies; and backward, when it cuts that line at right angles. Neither is this progress or regress uniform; for in the conjunction or opposition, it goes briskly forward; and in the quadratures, it either moves slowly forward, stands still, or goes backward.

The motion of the nodes is also variable; being quicker and slower in different positions.

The Physical Cause of the Moon's Motion, about the earth, is the same as that of all the primary planets about the sun, and of the satellites about their primaries, viz, the mutual attraction between the earth and Moon.

As for the particular irregularities in the Moon's motion, to which the earth and other planets are not subject, they arise from the sun which acts on, and disturbs her in her ordinary course through her orbit; and are all mechanically deducible from the same great law by which her general motion is directed, viz, the law of gravitation and attraction. The other secondary planets, as those of Jupiter, Saturn, &c, are also subject to the like irregularities with the Moon; as they are exposed to the same perturbating or disturbing force of the sun; but their distance secures them from being so greatly affected as the Moon is, and also from being so well observed by us.

For a familar idea of this matter, it must first be considered, that if the sun acted equally on the earth and Moon, and always in parallel lines, this action would serve only to restrain them in their annual motions round the sun, and no way affect their actions on each other, or their motions about their common centre of gravity. But because the Moon is nearer the sun, in one half of her orbit, than the earth is, but farther off in the other half of her orbit; and because the power of gravity is always less at a greater distance; it follows, that in one half of her orbit the Moon is more attracted than the earth towards the sun, and less attracted than the earth in the other half: and hence irregularities necessarily arise in the motions of the Moon; the excess of attraction in the first case, and the defect in the second, becoming a force that disturbs her motion: and besides, the action of the sun, on the earth and Moon, is not directed in parallel lines, but in lines that meet in the centre of the sun; which makes the effect of the disturbing force still the more complex and embarrassing. And hence, as well as from the various situations of the Moon, arise the numerous irregularities in her motions, and the equations, or corrections, employed in calculating her places, &c.

Newton, as well as others, has computed the quantities of these irregularities, from their causes. He finds that the force added to the gravity of the Moon in her quadratures, is to the gravity with which she would revolve in a circle about the earth, at her present mean distance, if the sun had no effect on her, as 1 to 178 29/40: he finds that the force subducted from her gravity in the conjunctions and oppositions, is double of this quantity; and that the area described in a given time in the quarters, is to the area described in the same time in the conjunctions and oppositions, as 10973 to 11073: and he finds that, in such an orbit, her distance from the earth in her quarters, would be to her distance in the conjunctions and oppositions, as 70 to 69. Upon these irregularities, see Maclaurin's Account of Newton's Discoveries, book 4, chap. 4; as also most books of astronomy. Other particulars relating to the Moon's motions, &c, have been stated as follow: The power of the Moon's influence, as to the tides, is to that of the sun, as 6 1/3 to 1, according to Sir I. Newton; but different according to others.

As to the figure of the Moon, supposing her at first to have been a fluid, like the sea, Newton calculates, that the earth's attraction would raise the water there near 90 feet high, as the attraction of the Moon raises our sea 12 feet: whence the figure of the Moon must be a spheroid, whose greatest diameter extended, will pass through the centre of the earth; and will be longer than the other diameter, perpendicular to it, by 180 feet; and hence it comes to pass, that we always see the same face of the Moon; for she cannot rest in any other position, but always endeavours to conform herself to this situation: Princip. lib. 3, prop. 38.

Newton estimates the mean apparent diameter of the Moon at 32′ 12″; as the sun is 31′ 27″.

The density of the Moon he concludes is to that of the earth, as 9 to 5 nearly; and that the mass, or quantity of matter, in the Moon, is to that of the earth, as 1 to 26 nearly.

The plane of the Moon's orbit is inclined to that of the ecliptic, and makes with it an angle of about 5 degrees: but this inclination varies, being greatest when she is in the quarters, and least when in her syzygies.

As to the inequality of the Moon's motion, she moves swifter, and by the radius drawn from her to the earth describes a greater area in proportion to the time, also has an orbit less curved, and by that means comes nearer to the earth, in her syzygies or conjunctions, than in the quadratures, unless the motion of her eccentricity hinders it: which eccentricity is the greatest when the Moon's apogee falls in the conjunction, but least when this falls in the quadratures: her motion is also swifter in the earth's aphelion, than in its perihelion. The apogee also goes forward swifter in the conjunction, and goes slower at the quadratures: but her nodes are at rest in the conjunctions, and recede swiftest of all in the quadratures.

The Moon also perpetually changes the figure of her orbit, or the species of the ellipse she moves in.

There are also some other inequalities in the motion of this planet, which it is very difficult to reduce to any certain rule: as the velocities or horary motions of the apogee and nodes, and their equations, with the difference between the greatest eccentricity in the conjunctions, and the least in the quadratures; and that inequality which is called the Variation of the Moon. All these do increase and decrease annually, in a triplicate ratio of the apparent diameter of the sun: and this variation is increased and diminished in a duplicate ratio of the time between the quadratures; as is proved by Newton in many parts of his Principia.|

He also found that the apogees in the Moon's syzygies, go forward in respect of the fixed stars, at the rate of 23′ each day; and backwards in the quadratures 16′ 1/3 per day: and therefore the mean annual motions he estimates at 40 degrees.

The gravity of the Moon towards the earth, is increased by the action of the sun, when the Moon is in the quadratures, and diminished in the syzygies: and, from the syzygies to the quadrature, the gravity of the Moon towards the earth is continually increased, and she is continually retarded in her motion: but from the quadrature to the syzygy, the Moon's motion is perpetually diminished, and the motion in her orbit is accelerated.

The Moon is less distant from the earth at the syzygies, and more at the quadratures.

As radius is to <*> of the sine of double the Moon's distance from the syzygy, so is the addition of gravity in the quadratures, to the force which accelerates or retards the Moon in her orbit.

And as radius is to the sum or difference of 1/2 the radius and 3/2 the cosine of double the distance of the Moon from the syzygy, so is the addition of gravity in the quadratures, to the decrease or increase of the gravity of the Moon at that distance.

The apses of the Moon go forward when she is in the syzygies, and backward in the quadratures. But, in a whole revolution of the Moon, the progress exceeds the regress.

In a whole revolution, the apses go forward the fastest of all when the line of the apses is in the nodes; and in the same case they go back the slowest of all in the same revolution.

When the line of the apses is in the quadratures, the apses are carried in consequentia, the least of all in the syzygies; but they return the swiftest in the quadratures; and in this case the regress exceeds the progress, in one entire revolution of the Moon.

The eccentricity of the orbit undergoes various changes every revolution. It is the greatest of all when the line of the apses is in the syzygies, and the least when that line is in the quadratures.

Considering one entire revolution of the Moon, cæteris paribus, the nodes move in antecedentia swiftest of all when she is in the syzygies; then slower and flower, till they are at rest, when she is in the quadratures.

The line of nodes acquires successively all possible situations in respect of the sun; and every year it goes twice through the syzygies, and twice through the quadratures.

In one whole revolution of the Moon, the nodes go back very fast when they are in the quadratures; then slower till they come to rest, when the line of nodes is in the syzygies.

The inclination of the plane of the orbit is changed by the same force with which the nodes are moved; being increased as the Moon recedes from the node, and diminished as she approaches it.

The inclination of the orbit is the least of all when the nodes are come to the syzygies. For in the motion of the nodes from the syzygies to the quadratures, and in one entire revolution of the Moon, the force which increases the inclination exceeds that which di- minishes it; therefore the inclination is increased; and it is the greatest of all when the nodes are in the quadratures.

The Moon's motion being considered in general: her gravity towards the earth is diminished coming near the sun, and the periodical time is the greatest; as also the distance of the Moon, cæteris paribus, the greatest when the earth is in the perihelion.

All the errors in the Moon's motion are something greater in the conjunction than in the opposition.

All the disturbing forces are inversely as the cube of the distance of the sun from the earth; which when it remains the same, they are as the distance of the Moon from the earth. Considering all the disturbing forces together, the diminution of gravity prevails.

The figure of the Moon's path, about the earth, is, as has been said, nearly an ellipse; but her path, in moving, together with the earth about the sun, is made up of a series or repetition of epicycloids, and is in every point concave towards the earth. See Maclaurin's Account of Newton's Discov. pa. 336, 4to. Ferguson's Astron. pa. 129, &c; and Rowe's Flux. pa. 225, edit. 2.

Astronomy of the Moon.

To determine the Periodical and Synodical Months; or the period of the Moon's revolution about the earth, and the period between one opposition or conjunction and another.

In the middle of a lunar eclipse, the Moon is in opposition to the sun: compute therefore the time between two such eclipses, at some considerable distance of time from each other; and divide this by the number of lunations that have passed in the mean time; so shall the quotient be the quantity of the synodical month. Compute also the sun's mean motion during the time of this synodical month, which add to 360°. Then, as the sum is to 360°, so is the synodical to the periodical month.

For example, Copernicus observed two eclipses of the Moon, the one at Rome on November 6, 1500, at 12 at night, and the other at Cracow on August 1, 1523, at 4h. 25 min. the dif. of meridians being oh. 29 min.: hence the quantity of the synodical month is thus determined:

2d Observ.1523y237d4h25<*>
1st Observ.1500 310 029
Difference22 292 356
Add intercalary days
Exact interval22 297 356
which divided by 282, the number of lunations in that time, gives the synodical month 29d 12h 41m.

From two other observations of eclipses, the one at Cracow, the other at Babylon, the same author determines more accurately the quantity of the synodical month to be 29d 12h 43m &c; and from other observations, probably more accurate still, the same is fixed at 29d 12h 44m.

The sun's mean motion in that time 29° 6′ 24″ 18‴, added to 360°, gives the Moon's motion 389 6 24 18; Therefore the periodical month is 27d 7h 43m 5<*>.|

According to the observations of Kepler, the mean synodical month is 29d 12h 44m 3s 2th, and the mean periodical month 27 7 43 8

Hence, 1, the quantity of the periodical month being given, by the rule of three are found the Moon's diurnal or horary motion, &c: and thus may tables of the mean motion of the Moon be constructed.

2. If the mean diurnal motion of the sun be subtracted from that of the Moon, the remainder will give the Moon's diurnal motion from the sun: and thus may a table of this motion be constructed.

3. Since the Moon is in the node at the time of a total eclipse, if the sun's place be found for that time, and 6 signs be added to the same, the sum will give the place of that node.

4. By comparing the ancient observations with the modern, it appears, that the nodes have a motion, and that they proceed in antecedentia, or backwards from Taurus to Aries, from Aries to Pisces, &c. Therefore if the diurnal motion of the nodes be added to the Moon's diurnal motion, the sum will be the motion of the Moon from the node; and thence by the rule of three, may be found in what time the Moon goes 360° from the dragon's head, or ascending node, or in what time she goes from, and returns to it; that is, the quantity of the Dracontic Month.

5. If the motion of the apogee be subtracted from the mean motion of the Moon, the remainder will be the Moon's mean motion from the apogee; and hence, by the rule of three, the quantity of the Anomalistic Month is determined.

Thus, according to Kepler's observations,

The mean synodical month is29d12h44m3s2th
The periodical month "277438
The place of the apogee for the}11s57′ 1″
 year 1700 Jan. 1 old style, was
The place of the ascending node4273917
Mean diurnal motion of the Moon.131035
Diurnal motion of the apogee..641
Diurnal motion of the nodes..311
Theref. diurnal mot. from the latter.131346
And the diurnal motion from}.13354
 the apogee
Lastly, the eccentricity is 4362, of such parts as the semidiameter of the eccentric is 100,000.
To find nearly the Moon's Age or Change.

To the epact add the number and day of the month; their sum, abating 30 if it be above, is the Moon's age; and her age taken from 30, shews the day of the change.

The numbers of the months, or monthly epacts, are the Moon's age at the beginning of each month, when the solar and lunar years begin together; and are thus: 0 2 1 2 3 4 5 6 8 8 10 10 Jan. Feb. Mar. Ap. M<*>. Jun. Jul. Aug. Sep. Oct. Nov. Dec.

For Ex. To find the Moon's age the 14th of Oct. 1783.

Here, the epact is26
Number of the month8
Day of the month14
The sum is48
Subtract or abate30
Leaves Moon's age18
Taken from30
Days till the change12
Answering to Oct.26

To find nearly the Moon's Southing, or coming to the Meridian.

Take 4/5 or 8/10 of her age, for her southing nearly; after noon, if it be less than 12 hours; but if greater, the excess is the time after last midnight. For Ex. Oct. 14, 1783; The Moon's age is 18 days

8/10 of which is 14.4 or14h24m
Rem. Moon's fouthing 224in the morning.

Mr. Ferguson, in his Select Exercises, pa. 135 &c, has given very easy tables and rules for finding the new and full Moons near enough the truth for any common almanac. But the Nautical Almanac, which is now always published for several years before hand, in a great measure supersedes the necessity of these and other such contrivances.

Of the Spots and Mountains &c in the Moon.

The face of the Moon is greatly diversified with inequalities, and parts of different colours, some brighter and some darker than the other parts of her disc. When viewed through a telescope, her face is evidently diversified with hills and valleys: and the same is also shewn by the edge or border of the Moon appearing jagged, when so viewed, especially about the consines of the illuminated part when the Moon is either horned or gibbous.

The astronomers Florenti, Langreni, Hevelius, Grimaldi, Riccioli, Cassini, and De la Hire, &c, have drawn the face of the Moon as viewed through telescopes; noting all the more shining parts, and, for the better distinction, marking them with some proper name; some of these authors calling them after the names of philosophers, astronomers, and other eminent men; while others denominate them from the known names of the different countries, islands, and seas on the earth. The names adopted by Riccioli however are mostly followed, as the names of Hipparchus, Tycho, Copernicus, &c. Fig. 4, plate xv, is a pretty exact representation of the full Moon in her mean libration, with the numbers to the principal spots according to Riccioli, Cassini, Mayer, &c, which denote the names as in the following List of them: also the asterisk refers to one of the volcanoes observed by Herschel.

 * Herschel's Volcano12 Helicon
 1 Grimaldi13 Capuanus
 2 Galileo14 Bulliald
 3 Aristarchus15 Eratosthenes
 4 Kepler16 Timocharis
 5 Gassendi17 Plato
 6 Schikard18 Archimedes
 7 Harpalus19 Insula Sinus Medii
 8 Heraclides20 Pitatus
 9 Lansberg21 Tycho
10 Reinhold22 Eudoxus
11 Copernicus23 Aristotle
24 Manilius36 Cleomedes
25 Menelaus37 Snell and Furner
26 Hermes38 Petavius
27 Possidonius39 Langrenus
28 Dionysius40 Taruntius
29 PlinyA Mare Humorum
30 { Catharina Cyrillus, TheophilusB Mare Nubium
C Mare Imbrium
31 FracastorD Mare Nectaris
32 { Promontorium acutum, CensorinusE Mare Tranquilitatis
F Mare Serenitatis
33 MessalaG Mare Fœcunditatis
34 Promontorium SomniiH Mare Crisium
35 Proclus

That the spots in the Moon, which are taken for mountains and valleys, are really such, is evident from their shadows. For in all situations of the Moon, the elevated parts are constantly found to cast a triangular shadow in a direction from the sun; and, on the contrary, the cavities are always dark on the side next the sun, and illuminated on the opposite one; which is exactly conformable to what we observe of hills and valleys on the earth. And as the tops of these mountains ave considerably elevated above the other parts of the surface; they are often illuminated when they are at a considerable distance from the confines of the enlightened hemisphere, and by this means afford us a method of determining their heights.

Thus, let ED be the Moon's diameter, ECD the boundary of light and darkness; and A the top of a hill in the dark part beginning to be illuminated; with a telescope take the proportion of AE to the diameter ED: then there are given the two sides AE, EC of a right angled triangle ACE, the squares of which being added together give the square of the third side AC, and the root extracted is that side itself; from which subtracting the radius BC, leaves AB the height of the mountain. In this way, Riccioli observed the top of the hill called St. Catherine, on the 4th day after the new moon, to be illuminated when it was distant from the confines of the enlightened hemisphere about one 16th part of the Moon's diameter; and thence found its height must be near 9 miles.

It is probable however that this determination is too much. Indeed, Galileo makes AE to be only one 20th of ED, and Hevelius makes it only one 26th of ED; the former of these would give 5 1/2 miles, and the latter only 3 1/4 miles, for AB, the height of the mountain: and probably it should be still less than either of these.

Accordingly, they are greatly reduced by the observations of Herschel, whose method of measuring them may be seen in the Philos. Trans. an. 1780, pa. 507. This gentleman measured the height of many of the lunar prominences, and draws at last the following conclusions:—“From these observations I believe it is evident, that the height of the lunar mountains in general is greatly over-rated; and that, when we have excepted a few, the generality do not exceed half a mile in their perpendicular elevation.” And this is confirmed by the measurement of several mountains, as may be seen in the place above quoted.

As the Moon has on her surface mountains and valleys in common with the earth, some modern astronomers have discovered a still greater similarity, viz, that some of these are really volcanoes, emitting fire as those on the earth do. An appearance of this kind was discovered some few years ago by Don Ulloa in an eclipse of the sun. It was a small bright spot like a star near the margin of the Moon, and which he at that time supposed to be a hole or valley with the sun's light shining through it. Succeeding observations, however, have induced astronomers to attribute appearances of this kind to the eruption of volcanic sire; and Mr. Herschel has particularly observed several eruptions of the lunar volcanos, the last of which he gives an account of in the Philos. Trans. for 1787. April 19, 10h. 36m. sidereal time, I perceived, says he, three volcanos in different places of the dark part of the new Moon. Two of them are either already nearly extinct, or otherwise in a state of going to break out; which perhaps may be decided next lunation. The third shews an actual eruption of fire or luminous matter: its light is much brighter than the nucleus of the comet which M. Mechain discovered at Paris the 10th of this month.” The following night he found it burnt with greater violence; and by measurement he found that the shining or burning matter must be more than 3 miles in diameter; being of an irregular round figure, and very sharply defined on the edges. The other two volcanos resembled large faint nebulæ, that are gradually much brighter in the middle; but no well-desined luminous spot was discovered in them. He adds, “the appearance of what I have called the actual fire, or eruption of a volcano, exactly resembled a small piece of burning charcoal when it is covered by a very thin coat of white ashes, which frequently adhere to it when it has been some time ignited; and it had a degree of brightness about as strong as that with which a coal would be seen to glow in faint day-light.

It has been disputed whether the Moon has any atmosphere or not. The following arguments have been urged by those who deny it.

1. The Moon, say they, constantly appears with the same brightness when our atmosphere is clear; which could not be the case if she were surrounded with an atmosphere like ours, so variable in its density, and so often obscured by clouds and vapours. 2. In an appulse of the Moon to a star, when she comes so near it that a part of her atmosphere comes between our eye and the star, refraction would cause the latter to seem to change its place, so that the Moon would appear to touch it later than by her own motion she would do. 3. Some philosophers are of opinion, that because there are no seas or lakes in the Moon, there is therefore no atmosphere, as there is no water to be raised up in vapours.

But all these arguments have been answered by other astronomers in the following manner. It is denied that the Moon appears always with the same brightness, even when our atmosphere appears equally clear. Hevelius relates, that he has several times found in| skies perfectly clear, when even stars of the 6th and 7th magnitude were visible, that at the same altitude of the Moon with the same elongation from the sun, and with the same telescope, the Moon and her maculæ do not appear equally lucid, clear, and conspicuous at all times; but are much brighter and more distinct at some times than at others. And hence it is inferred that the cause of this phenomenon is neither in our air, in the tube, in the Moon, nor in the spectator's eye; but must be looked for in something existing about the Moon. An additional argument is drawn from the different appearances of the Moon in total eclipses, which it is supposed are owing to the different constitutions of the lunar at mosphere.

To the 2d argument Dr. Long replies, that Newton has shewn (Princip. prop. 37, cor. 5), that the weight of any body upon the Moon is but a third part of what the weight of the same would be upon the earth: now the expansion of the air is reciprocally as the weight that compresses it; therefore the air surrounding the Moon, being pressed together by a weight of one-third, or being attracted towards the centre of the Moon by a force equal only to one-third of that which attracts our air towards the centre of the earth, it thence follows, that the lunar atmosphere is only onethird as dense as that of the earth, which is too little to produce any sensible refraction of the star's light. Other astronomers have contended, that such refraction was sometimes very apparent. Mr. Cassini says, that he often observed that Saturn, Jupiter, and the fixed stars, had their eircular figures changed into an elliptical one, when they approached either to the Moon's dark or illuminated limb, though they own that, in other occultations, no such change could be observed. And, with regard to the fixed stars, it has been urged that, granting the Moon to have an atmosphere of the same nature and quantity as ours, no such effect as a gradual diminution of light ought to take place; at least none that we could be capable of perceiving. At the height of 44 miles, our atmosphere is so rare as to be incapable of refracting the rays of light: this height is the 180th part of the earth's diameter; but since clouds are never observed higher than 4 miles, it appears that the vapourous or obscure part is only the 1980th part. The mean apparent diameter of the Moon is 31′ 29″, or 1889″: therefore the obscure parts of her atmosphere, when viewed from the earth, must subtend an angle of less than one second; which space is passed over by the Moon in less than two seconds of time. It can therefore hardly be expected that observation should generally determine whether the supposed obscuration takes place or not.

As to the 3d argument, it concludes nothing, because it is not known that there is no water in the Moon; nor, though this could be proved, would it follow that the lunar atmosphere answers no other purpose than the raising of water into vapour. There is however a strong argument in favour of the existence of a lunar atmosphere, taken from the appearance of a luminous circle round the Moon in the time of total solar eclipses; a circumstance that has been observed by many astronomers; especially in the total eclipse of the sun which happened May 1, 1706.

Of the Harvest Moon. It is remarkable that the Moon, during the week in which she is full about the time of harvest, rises sooner after sun-setting, than she does in any other full-moon week in the year. By this means she affords an immediate supply of light after sun-set, which is very benesicial for the harvest and gathering in the fruits of the earth: and hence this full Moon is distinguished from all the others in the year, by calling it the Harvest-Moon.

To conceive the reason of this phenomenon; it may first be considered, that the Moon is always opposite to the sun when she is full; that she is full in the signs Pisces and Aries in our harvest months, those being the signs opposite to Virgo and Libra, the signs occupied by the sun about the same season; and because those parts of the ecliptic rise in a shorter space of time than others, as may easily be shewn and illustrated by the celestial globe: consequently, when the Moon is about her full in harvest, she rises with less difference of time, or more immediately after sun-set, than when she is full at other seasons of the year.

In our winter, the Moon is in Pisces and Aries about the time of her first quarter, when she rises about noon; but her rising is not then noticed, because the sun is above the horizon.

In spring, the Moon is in Pisces and Aries about the time of her change; at which time, as she gives no light, and rises with the sun, her rising cannot be perceived.

In summer, the Moon is in Pisces and Aries about the time of her last quarter; and then, as she is on the decrease, and rises not till midnight, her rising usually passes unobserved.

But in autumn, the Moon is in Pisces and Aries at the time of her full, and rises soon after sun-set for several evenings successively; which makes her regular rising very conspicuous at that time of the year.

And this would always be the case, if the Moon's orbit lay in the plane of the ecliptic. But as her orbit makes an angle of 5° 18′ with the ecliptic, and crosses it only in the two opposite points called the nodes, her rising when in Pisces and Aries will sometimes not differ above 1 h. and 40 min. through the whole of 7 days; and at other times, in the same two signs she will differ 3 hours and a half in the time of her rising in a week, according to the different positions of the nodes with respect to these signs; which positions are constantly changing, because the nodes go backward through the whole ecliptic in 18 years 225 days.

This revolution of the nodes will cause the Harvest Moons to go through a whole course of the most and least beneficial states, with respect to the harvest, every 19 years. The following Table shews in what years the Harvest Moons are least beneficial as to the times of their rising, and in what years they are most beneficial, from the year 1790 to 1861; the column of years under the letter L, are those in which the Harvest-Moons are least of all beneficial, because they fall about the descending node; and those under the letter M are the most of all beneficial, because they fall about the ascending node.|

Harvest Moons.

As to the Influence of the Moon, on the changes of the weather, and the constitution of the human body, it may be observed, that the vulgar doctrine concerning it is very ancient, and has also gained much credit among the Learned, though perhaps without sufficient examination. The common opinion is, that the Lunar Influence is chiefly exerted about the time of the full and change, but more especially the latter; and it would seem that long experience has in some degree established the fact: hence, persons observed at those times to be a little deranged in their intellects, are called Lunatics; and hence many persons anxiously look for the new Moon to bring a change in the weather. The Moon's Influence on the sea, in producing tides, being agreed upon on all hands, it is argued that she must also produce similar changes in the atmosphere, but in a much higher degree; which changes and commotions there, must, it is inferred, have a considerable influence on the weather, and on the human body.

Beside the observations of the Ancients, which tend to establish this doctrine, several among the Modern Philosophers have defended the same opinion, and that upon the strength of experience and observation; while others as strenuously deny the fact. The celebrated Dr. Mead was a believer in the Influence of the Sun and Moon on the human body, and published a book to this purpose, intitled, De Imperio Solis ac Lunæ in Corpore Humano. The existence of such influence is however opposed by Dr. Horsley, the present bishop of Rochester, in a learned paper upon this subject in the Philos. Trans. for the year 1775; where he gives a specimen of arranging tables of meteorological observations, so as to deduce from them facts, that may either confirm or refute this popular opinion; recommending it to the Learned, to collect a large series of such observations, as no conclusions can be drawn from one or two only. On the other hand professor Toaldo, and some French philosophers, take the opposite side of the question; and, from the authority of a long series of observations, pronounce decidedly in favour of the Lunar Influence.

Acceleration of the Moon. See Acceleration.

Moon-Dial. See Dial.

Horizontal Moon. See Apparent Magnitude.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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MOORE (Sir Jonas)