103. As the ellipse which the moon describes about the sun, is subject to a variation, the periodic time of the moon about the earth will also vary; in winter, the moon's orbit is dilated, and the periodic time is increased; and in summer, her orbit is contracted, and her periodic time is diminished. The periodic time of the moon increases whilst the sun is moving from his apogee to his perigee, and decreases whilst he moves from his perigee to his apogee; and the greatest difference of the periodic times is found to be about 22 121 minutes.

104. The mean periodic time of the moon is 27d. 7h. 43′. 11",5; this is called her sidereal revolution, being the mean time from her leaving any fixed star, till her return to it again. Now it is found by observation, that the mean time from her leaving her apogee till she returns to it, is 27d. 13h. 18'. 4"; hence, the moon is longer in returning to her apogee than she is in making a revolution in her orbit, and therefore her apogee must move forward. The mean time from her leaving her node till she returns to it again, is 27d. 5h. 5'. 35",6, and this being less than her mean periodic time, it follows that she returns to her node before she has completed her revolution, and therefore her nodes must have a retrograde motion.

105. The time between two mean conjunctions of the sun and moon, or from new moon to new moon, supposing their motions had both been uniform, is found by the rule in article 101; taking therefore the mean periodic time of the moon and sun as already stated, we get the mean time from conjunction to conjunction to be 29d. 12h. 44′. 2′′ ,8, and this is called her synodic revolution. The true time from new to new moon will be sometimes greater and sometimes less than this. The causes of all these irregularities we will briefly explain.

106. The apparent diameter of the moon is found continually to

vary; now the apparent diameter of any very distant body, varies inversely as its distance. Hence, as the apparent diameter of the moon increases, she must approach the earth; and when it decreases, she must recede from the earth. This variation of her apparent diameter agrees exactly with what ought to be the case, if the moon moved in an ellipse about the earth in one of its foci; we conclude therefore that the moon moves in an ellipse about the earth situated in one of its foci, as no other supposition will agree with the observed variation of the moon's diameter. From the variation of the sun's diameter, it appears in like manner, that the earth must revolve in an ellipse about the sun, having the sun in one of the foci.

107. The earth moving in an ellipse about the sun in its focus, the nearer the earth comes to the sun, the more it is attracted by him, and this attraction increases in the same ratio as the square of the distance diminishes; and on the contrary, it decreases as the square of the distance increases. As therefore the earth approaches the sun all the time it moves from the aphelion to the perihelion, the attraction increases, and conspiring partly with the earth's motion, it accele rates the motion of the earth; and when the earth moves from perihelion to aphelion, the attraction acts partly against the earth's motion, and diminishes its motion. Thus, the velocity of the earth increases whilst it moves from the aphelion to perihelion, and decreases as much whilst it moves from perihelion to aphelion. As the moon moves in an ellipse about the earth in its focus, she must, in like manner by the earth's attraction, have her velocity increased from her apogee to perige, and decreased as much from her perigee to apogee. These are the principal causes of the variation of the velocities of the earth and moon. But as the sun attracts the moon, as well as the earth attracts it, the attraction of

the sun will cause another variation of the moon's velocity. Thus the moon being attracted both by the sun and earth, they will cause great irregularities in her motion; and hence it is very difficult to coinpute the place of the moon. After finding the mean place of the moon, that is, the place where she would have been if her motion had been uniform, it requires not less than 20 corrections, in order to get the true place to a sufficient degree of accuracy. Sir I. NEWTON was the first person who pointed out the sources of these irregularities; but they are of a nature too difficult to admit of a popular illustration.

108. When we view the moon with a telescope, we find that her surface is very rough with mountains and cavities; this appears from the very jagged boundary of the light and dark parts. Also, certain parts are found to project shadows always opposite to the sun; and when the sun becomes vertical to any of them, they are observed to have no shadow; these therefore must be mountains. Other parts are always dark on that side next the sun, and illuminated on the opposite side; these therefore must be cavities. Hence, the appearance of the moon constantly varies, from its altering its situation in respect to the sun. The tops of the mountains on the dark part of the moon, are frequently seen enlightened at a distance from the confines of the illuminated part. The dark parts have, by some, been thought seas; and by others, to be only a great number of caverns and pits, the dark sides of which next to the sun, would cause those places to appear darker than the rest. The great irregularity of the line bounding the light and dark parts, on every part of the surface, proves that there can be no very large tracts of water, as such a regular surface would necessarily produce a line, terminating the bright part, perfectly free from all irregularity. Also, if there was much water upon its surface, and an atmosphere, as

conjectured by some astronomers, the clouds and vapours might easily be discovered by our telescopes, but no such phenomena have ever been observed.

109. On April 9, 1787, Dr. HERSCHEL discovered three volcanos in the dark part of the moon; two of them seemed to be almost extinct, but the third showed an actual eruption of fire, or luminous matter, resembling a small piece of burning charcoal covered by a thin coat of white ashes; it had a degree of brightness about it, as strong as that with which such a coal would be scen to glow in faint day light. The adjacent parts of the volcanic mountain seemed faintly illuminated by the eruption. A similar eruption appeared on May 4, 1783. On March 7, 1794, a few minutes before 8

o'clock in the evening, Mr. WILKINS of Norwich, an eminent architect, observed, with the naked eye, a very bright spot upon the dark part of the moon; it was there when he first looked at the moon; and the whole time he saw it, which was about 5 minutes, it was a fixed, steady light, except the moment before it disappeared, when its brightness increased. The same phenomenon was also observed by Mr. T. STRETTON, in St. John'ssquare, Clerkenwell, London. On April 13, 1793, M. PIAZZI, Astronomer-Royal, at Palermo, observed a bright spot on the dark part of the moon; and several other astronomers have observed the same phenomenon.

110. It has been a doubt amongst astronomers, whether the moon has any atmosphere; some suspecting that at an occulation of a fixed star by the moon, the star did not vanish suddenly, but lost its light gradually, and thence concluded, that the moon has an atmosphere. M. SCHROLTER of Lilianthan in the Dutchy of Bremen, has endeavoured to establish the existence of an atmos phere, from the following observations. 1. He observed the moon when 21 days old, in the evening soon after sun set, before the dark

part was visible; and continued to observe it till it became visible. Two cusps appeared tapering in a very sharp, faint, prolongation, each exhibiting its farthest extremity faintly illuminated by the solar rays, before any part of the dark hemisphere was visible; soon after, the whole dark limb appeared illuminated. This prolongation of the cusps beyond the semicircle, he thinks must arise from the sun's rays being refracted by the moon's atmosphere. He computes also the height of the atmosphere, which refracts light enough into the dark hemisphere to produce a twilight, more luminous than the light reflected from the earth when the moon is about 32° from the new, to be 1556 Paris feet; and that the greatest height capable of refracting the solar rays is 5376 feet. 2dly. At an occulation of jupiter's satellites, the third disappeared, after having been 1" or 2" of time indistinct; the fourth became indiscernible near the limb; this was not observed of the other two. See the Phil. Trans. 1792.

111. Many astronomers have given maps of the moon; but the most celebrated are those of HEVELIUS in his Selenographia; in which he has represented the appearance of the moon in its dificrent states from the new to the full, and from the full to the new; these figures MAYER prefers. LANGRENUS and RICCIOLUS denoted the spots upon the surface, by the names of philosophers, mathematicians, and other celebrated men; giving the names of the most celebrated characters, to the largest spots. HEVELIUS marked them with the geographical names of places upon the earth. The former distinction is now generally used.

112. Very nearly the same face of the moon is always turned to wards the earth, it being subject to only a small change within certain limits, those spots which lie near the edge appearing and disappearing by turns; this is called its Libration. The moon turns about

its axis in the same direction in which it revolves in its orbit. Now the angular velocity about its axis is uniform, and it turns about its axis in the same time in which it makes a complete revolution in its orbit; if therefore the angular motion about the earth were also uniform, the same face of the moon would always be turned towards the earth. For if the moon had no rotation on her axis, when she is on opposite sides of the earth she would show different faces; but if, after she has made half a revolu tion in her orbit, she has also turned half round her axis, then the face which would otherwise have been shown, will be turned behind, and the same face will appear. And thus if the moon's angular velocity about her axis were always equal to her angular velocity in her orbit about the earth, the same side of the moon would be always towards the earth. But as the moon's angular velocity about her axis is uniform, and her angular velocity in her orbit is not uniform, their angular velocities cannot continue always equal, and therefore the moon will sometimes show a little more of her eastern parts, and sometimes a little more of her western parts; this is called a libration in longitude. Also, the moon's axis is not perpendicular to the plane of her orbit, and therefore at opposite points of her orbit, her opposite poles are turned towards the earth; therefore her poles appear, and disappear, by turns; this is called a libration in latitude.

113. Hence, nearly one half of the moon is never visible at the earth, and therefore nearly one half of its inhabitants (if it have any) never saw the earth, and nearly the other half never lose sight of it. Also, the time of its rotation about its axis being a month, the length of the lunar days and nights will be about a fortnight each.

114. It is a very extraordinary circumstance, that the time of the moon's revolution about her axis should be equal to that in her orbit.

Sir I. NEWTON, from the altitude of the tides upon the earth, has computed the altitude of the tides on the moon's surface to be 93 feet, and therefore the diamater of the moon perpendicular to a line joining the earth and moon, is less than the diameter directed to the earth, by 186 feet. Hence, says he, the same face must always be towards the earth, except a small oscillation; for if the longest diameter should get a little out of that direction, it would be brought into it again, by the earth's attraction. The supposition of D. DE MAIRAN is, that the hemisphere of the moon next the earth is more dense than the opposite one, and hence, the same face would be kept towards the earth, upon the same principle as before.

115. When the moon is in conjunction with the sun, she is then said to be new, and her dark side being next to the earth, she is then invisible. As she recedes from the sun, we first discover some of her bright part, and she appears horned till she gets 90° from the sun, when she appears half enlightened, or dichotomised; from thence till she comes into opposition, she appears above half enlightened, or gibbous; and at opposition she appears full orbed, the same face being then turned towards the earth which is towards the sun, and she is then said to be at her full. And from oppoşition to conjunction, her apparent bright part decreases as it before increased.

116. When the moon is about three days from the new, the dark part is very visible, by the light reflected from the earth, which is moon-light to the lunarians, considering our earth as a moon to them; and in the most favourable state, some of the spots may be then seen. But when the moon gets into quadratures, its great light prevents the dark part from being seen. According to Dr. SMITH, the strength of moon-light at the full moon, is 90 thousand times less than the light of the sun; but from experiments made by M.BOUGUER, he conclud

ed it to be 300,000 times less. The light of the moon, condensed by the best mirrors, produces no sensible effect upon the thermometer. Our earth, in the course of a month, shows the same phases to the lunarians, as the moon does to us; the earth is at the full, at the time of the new moon, and at new, at the time of the full moon. The surface of the earth being about 13 times greater than that of the moon, it affords 13 times more light to the moon, than the moon does to us.

117. Dr. HERSCHEL has measured the height of a great many of the lunar mountains, and finds that, a few excepted, they generally do not much exceed half a mile. Before he measured them, they were reckoned much higher, being generally overrated. He observes, that it should be examined whether the mountain stands on level ground, which is necessary, that the measurement may be exact.

118. As the spectator is carried by the earth's rotation, his horizon will continually change its situation, and therefore it will continually cut the moon's orbit at different points till it has gone through the whole orbit; and the inclination of the orbit to the horizon will be continually changed. Now the difference between the times of the rising of the moon on two successive nights, will depend upon the angle which the moon's orbit makes with the horizon; the less the angle is, the less the moon will have descended below the horizon, at the time when the horizon is brought into the same situation it was 24 hours before; therefore when the angle which the moon's orbit makes with the horizon is the least, there will be the least difference of the times of her rising. Now, that angle is the least, when the first point of aries rises, at which time, in the latitude of London, there is only about 17 minutes difference of the moon's rising on two successive nights. Now, about the 22d of September, the first point of aries rises at the time the