The distance and apparent size of the moon being known, her real diameter is found by means of a triangle formed as shown in Fig. 105. C represents the centre of the moon, CB the distance of the moon from the earth, and CA the radius of the moon. BAC is a triangle, right-angled at A. The angle ABC is half the apparent diameter of the moon. With the angles A and B, and the side CB known, it is easy to find the length of AC by trigonometrical computation. Twice AC will be the diameter of the moon.
The volume of the moon is about one-fiftieth of that of the earth.
90. Apparent Size of the Moon on the Horizon and in the Zenith..—The moon is nearly four thousand miles farther from the observer when she is on the horizon than when she is in the zenith. This is evident from Fig. 106. C is the centre of the earth, M the moon on the horizon, M' the moon in the zenith, and O the point of observation. OM is the distance of the moon when she is on the horizon, and OM' the distance of the moon from the observer when she is in the zenith. CM is equal to CM', and OM is about the length of CM; but OM' is about four thousand miles shorter than CM': hence OM' is about four thousand miles shorter than OM.
Fig. 106.
Notwithstanding the moon is much nearer when at the zenith than at the horizon, it seems to us much larger at the horizon.
This is a pure illusion, as we become convinced when we measure the disc with accurate instruments, so as to make the result independent of our ordinary way of judging. When the moon is near the horizon, it seems placed beyond all the objects on the surface of the earth in that direction, and therefore farther off than at the zenith, where no intervening objects enable us to judge of its distance. In any case, an object which keeps the same apparent magnitude seems to us, through the instinctive habits of the eye, the larger in proportion as we judge it to be more distant.
91. The Apparent Size of the Moon increased by Irradiation.—In the case of the moon, the word apparent means much more than it does in the case of other celestial bodies. Indeed, its brightness causes our eyes to play us false. As is well known, the crescent of the new moon seems part of a much larger sphere than that which it has been said, time out of mind, to "hold in its arms." The bright portion of the moon as seen with our measuring instruments, as well as when seen with the naked eye, covers a larger space in the field of the telescope than it would if it were not so bright. This effect of irradiation, as it is called, must be allowed for in exact measurements of the diameter of the moon.
Fig. 107.
92. Apparent Size of the Moon in Different Parts of her Orbit.—Owing to the eccentricity of the moon's orbit, her distance from the earth varies somewhat from time to time. This variation causes a corresponding variation in her apparent size, which is illustrated in Fig. 107.
93. The Mass of the Moon.—The moon is considerably less dense than the earth, its mass being only about one-eightieth of that of the earth; that is, while it would take only about fifty moons to make the bulk of the earth, it would take about eighty to make the mass of the earth.
One method of finding the mass of the moon is to compare her effect in producing the tides with that of the sun. We first calculate what would be the moon's effect in producing the tides, were she as far off as the sun. We then form the following proportion: as the sun's effect in producing the tides is to the moon's effect at the same distance, so is the mass of the sun to the mass of the moon.
The method of finding the mass of the sun will be given farther on.
94. The Orbital Motion of the Moon.—If we watch the moon from night to night, we see that she moves eastward quite rapidly among the stars. When the new moon is first visible, it appears near the horizon in the west, just after sunset. A week later the moon will be on the meridian at the same hour, and about a week later still on the eastern horizon. The moon completes the circuit of the heavens in a period of about thirty days, moving eastward at the rate of about twelve degrees a day. This eastward motion of the moon is due to the fact that she is revolving around the earth from west to east.
Fig. 108.
95. The Aspects of the Moon.—As the moon revolves around the earth, she comes into different positions with reference to the earth and sun. These different positions of the moon are called the aspects of the moon. The four chief aspects of the moon are shown in Fig. 108. When the moon is at M, she appears in the opposite part of the heavens to the sun, and is said to be in opposition; when at M' and at M''', she appears ninety degrees away from the sun, and is said to be in quadrature; when at M'', she appears in the same part of the heavens as the sun, and is said to be in conjunction.
96. The Sidereal and Synodical Periods of the Moon.—The sidereal period of the moon is the time it takes her to pass around from a star to that star again, or the time it takes her to make a complete revolution around the earth. This is a period of about twenty-seven days and a third. It is sometimes called the sidereal month.
The synodical period of the moon is the time that it takes the moon to pass from one aspect around to the same aspect again. This is a period of about twenty-nine days and a half, and it is sometimes called the synodical month.
Fig. 109.
The reason why the synodical period is longer than the sidereal period will appear from Fig. 109. S represents the position of the sun, E that of the earth, and the small circle the orbit of the moon around the earth. The arrow in the small circle represents the direction the moon is revolving around the earth, and the arrow in the arc between E and E' indicates the direction of the earth's motion in its orbit. When the moon is at M1, she is in conjunction. As the moon revolves around the earth, the earth moves forward in its orbit. When the moon has come round to m1, so that m3m1 is parallel with M3M1, she will have made a complete or sidereal revolution around the earth; but she will not be in conjunction again till she has come round to M, so as again to be between the earth and sun. That is to say, the moon must make more than a complete revolution in a synodical period.
Fig. 110.
The greater length of the synodical period is also evident from Fig. 110. T represents the earth, and L the moon. The arrows indicate the direction in which each is moving. When the earth is at T, and the moon at L, the latter is in conjunction. When the earth has reached T', and the moon L', the latter has made a sidereal revolution; but she will not be in conjunction again till the earth has reached T'', and the moon L''.
97. The Phases of the Moon.—When the new moon appears in the west, it has the form of a crescent, with its convex side towards the sun, and its horns towards the east. As the moon advances towards quadrature, the crescent grows thicker and thicker, till it becomes a half-circle at first quarter. When it passes quadrature, it begins to become convex also on the side away from the sun, or gibbous in form. As it approaches opposition, it becomes more and more nearly circular, until at opposition it is a full circle. From full moon to last quarter it is again gibbous, and at last quarter a half-circle. From last quarter to new moon it is again crescent; but the horns of the crescent are now turned towards the west. The successive phases of the moon are shown in Fig. 111.
Fig. 111.
98. Cause of the Phases of the Moon.—Take a globe, half of which is colored white and the other half black in such a way that the line which separates the white and black portions shall be a great circle which passes through the poles of the globe, and rotate the globe slowly, so as to bring the white half gradually into view. When the white part first comes into view, the line of separation between it and the black part, which we may call the terminator, appears concave, and its projection on a plane perpendicular to the line of vision is a concave line. As more and more of the white portion comes into view, the projection of the terminator becomes less and less concave. When half of the white portion comes into view, the terminator is projected as a straight line. When more than half of the white portion comes into view, the terminator begins to appear as a convex line, and this line becomes more and more convex till the whole of the white half comes into view, when the terminator becomes circular.
Fig. 112.
The moon is of itself a dark, opaque globe; but the half that is towards the sun is always bright, as shown in Fig. 112. This bright half of the moon corresponds to the white half of the globe in the preceding illustration. As the moon revolves around the earth, different portions of this illumined half are turned towards the earth. At new moon, when the moon is in conjunction, the bright half is turned entirely away from the earth, and the disc of the moon is black and invisible. Between new moon and first quarter, less than half of the illumined side is turned towards the earth, and we see this illumined portion projected as a crescent. At first quarter, just half of the illumined side is turned towards the earth, and we see this half projected as a half-circle. Between first quarter and full, more than half of the illumined side is turned towards the earth, and we see it as gibbous. At full, the whole of the illumined side is turned towards us, and we see it as a full circle. From full to new moon again, the phases occur in the reverse order.
99. The Form of the Moon's Orbit.—The orbit of the moon around the earth is an ellipse of slight eccentricity. The form of this ellipse is shown in Fig. 113. C is the centre of the ellipse, and E the position of the earth at one of its foci. The eccentricity of the ellipse is only about one-eighteenth. It is impossible for the eye to distinguish such an ellipse from a circle.
Fig. 113.
100. The Inclination of the Moon's Orbit.—The plane of the moon's orbit is inclined to the ecliptic by an angle of about five degrees. The two points where the moon's orbit cuts the ecliptic are called her nodes. The moon's nodes have a westward motion corresponding to that of the equinoxes, but much more rapid. They complete the circuit of the ecliptic in about nineteen years.
The moon's latitude ranges from 5° north to 5° south; and since, owing to the motion of her nodes, the moon is, during a period of nineteen years, 5° north and 5° south of every part of the ecliptic, her declination will range from 23-1/2° + 5° = 28-1/2° north to 23-1/2° + 5° = 28-1/2° south.
101. The Meridian Altitude of the Moon.—The meridian altitude of any body is its altitude when on the meridian. In our latitude, the meridian altitude of any point on the equinoctial is forty-nine degrees. The meridian altitude of the summer solstice is 49° + 23-1/2° = 72-1/2°, and that of the winter solstice is 49° - 23-1/2° = 25-1/2°. The greatest meridian altitude of the moon is 72-1/2° + 5° = 77-1/2°, and its least meridian altitude, 25-1/2° - 5° = 20-1/2°.
When the moon's meridian altitude is greater than the elevation of the equinoctial, it is said to run high, and when less, to run low. The full moon runs high when the sun is south of the equinoctial, and low when the sun is north of the equinoctial. This is because the full moon is always in the opposite part of the heavens to the sun.
102. Wet and Dry Moon.—At the time of new moon, the cusps of the crescent sometimes lie in a line which is nearly perpendicular with the horizon, and sometimes in a line which is nearly parallel with the horizon. In the former case the moon is popularly described as a wet moon, and in the latter case as a dry moon.
Fig. 114.
The great circle which passes through the centre of the sun and moon will pass through the centre of the crescent, and be perpendicular to the line joining the cusps. Now the ecliptic makes the least angle with the horizon when the vernal equinox is on the eastern horizon and the autumnal equinox is on the western. In our latitude, as we have seen, this angle is 25-1/2°: hence in our latitude, if the moon were at new on the ecliptic when the sun is at the autumnal equinox, as shown at M3 (Fig. 114), the great circle passing through the centre of the sun and moon would be the ecliptic, and at New York would be inclined to the horizon at an angle of 25-1/2°. If the moon happened to be 5° south of the ecliptic at this time, as at M4, the great circle passing through the centre of the sun and moon would make an angle of only 20-1/2° with the horizon. In either of these cases the line joining the cusps would be nearly perpendicular to the horizon.
Fig. 115.
If the moon were at new on the ecliptic when the sun is near the vernal equinox, as shown at M1 (Fig. 115), the great circle passing through the centres of the sun and moon would make an angle of 72-1/2° with the horizon at New York; and were the moon 5° north of the ecliptic at that time, as shown at M2, this great circle would make an angle of 77-1/2° with the horizon. In either of these cases, the line joining the cusps would be nearly parallel with the horizon.
At different times, the line joining the cusps may have every possible inclination to the horizon between the extreme cases shown in Figs. 114 and 115.
103. Daily Retardation of the Moon's Rising.—The moon rises, on the average, about fifty minutes later each day. This is owing to her eastward motion. As the moon makes a complete revolution around the earth in about twenty-seven days, she moves eastward at the rate of about thirteen degrees a day, or about twelve degrees a day faster than the sun. Were the moon, therefore, on the horizon at any hour to-day, she would be some twelve degrees below the horizon at the same hour to-morrow. Now, as the horizon moves at the rate of one degree in four minutes, it would take it some fifty minutes to come up to the moon so as to bring her upon the horizon. Hence the daily retardation of the moon's rising is about fifty minutes; but it varies considerably in different parts of her orbit.
There are two reasons for this variation in the daily retardation:—
(1) The moon moves at a varying rate in her orbit; her speed being greatest at perigee, and least at apogee: hence, other things being equal, the retardation is greatest when the moon is at perigee, and least when she is at apogee.
Fig. 116.
Fig. 117.
(2) The moon moves at a varying angle to the horizon. The moon moves nearly in the plane of the ecliptic, and of course she passes both equinoxes every lunation. When she is near the autumnal equinox, her path makes the greatest angle with the eastern horizon, and when she is near the vernal equinox, the least angle: hence the moon moves away from the horizon fastest when she is near the autumnal equinox, and slowest when she is near the vernal equinox. This will be evident from Figs. 116 and 117. In each figure, SN represents a portion of the eastern horizon, and Ec, E'c', a portion of the ecliptic. AE, in Fig. 116, represents the autumnal equinox, and AEM the daily motion of the moon. VE, in Fig. 117, represents the vernal equinox, and VEM' the motion of the moon for one day. In the first case this motion would carry the moon away from the horizon the distance AM, and in the second case the distance A'M'. Now, it is evident that AM is greater than A'M': hence, other things being equal, the greatest retardation of the moon's rising will be when the moon is near the autumnal equinox, and the least retardation when the moon is near the vernal equinox.
The least retardation at New York is twenty-three minutes, and the greatest an hour and seventeen minutes. The greatest and least retardations vary somewhat from month to month; since they depend not only upon the position of the moon in her orbit with reference to the equinoxes, but also upon the latitude of the moon, and upon her nearness to the earth.
Fig. 118.
The direction of the moon's motion with reference to the ecliptic is shown in Fig. 118, which shows the moon's motion for one day in July, 1876.
104. The Harvest Moon—The long and short retardations in the rising of the moon, though they occur every month, are not likely to attract attention unless they occur at the time of full moon. The long retardations for full moon occur when the moon is near the autumnal equinox at full. As the full moon is always opposite to the sun, the sun must in this case be near the vernal equinox: hence the long retardations for full moon occur in the spring, the greatest retardation being in March.
The least retardations for full moon occur when the moon is near the vernal equinox at full: the sun must then be near the autumnal equinox. Hence the least retardations for full moon occur in the months of August, September, and October. The retardation is, of course, least for September; and the full moon of this month rises night after night less than half an hour later than the previous night. The full moon of September is called the "Harvest Moon," and that of October the "Hunter's Moon."
105. The Rotation of the Moon.—A careful examination of the spots on the disc of the moon reveals the fact that she always presents the same side to the earth. In order to do this, she must rotate on her axis while making a revolution around the earth, or in about twenty-seven days.
106. Librations of the Moon.—The moon appears to rock slowly to and fro, so as to allow us to see alternately a little farther around to the right and the left, or above and below, than we otherwise could. This apparent rocking of the moon is called libration. The moon has three librations:—
(1) Libration in Latitude.—This libration enables us to see alternately a little way around on the northern and southern limbs of the moon.
This libration is due to the fact that the axis of the moon is not quite perpendicular to the plane of her orbit. The deviation from the perpendicular is six degrees and a half. As the axis of the moon, like that of the earth, maintains the same direction, the poles of the moon will be turned alternately six degrees and a half toward and from the earth.
(2) Libration in Longitude.—This libration enables us to see alternately a little farther around on the eastern and western limbs of the moon.
It is due to the fact that the moon's axial motion is uniform, while her orbital motion is not. At perigee her orbital motion will be in advance of her axial motion, while at apogee the axial motion will be in advance of the orbital. In Fig. 119, E represents the earth, M the moon, the large arrow the direction of the moon's motion in her orbit, and the small arrow the direction of her motion of rotation. When the moon is at M, the line AB, drawn perpendicular to EM, represents the circle which divides the visible from the invisible portion of the moon. While the moon is passing from M to M', the moon performs less than a quarter of a rotation, so that AB is no longer perpendicular to EM'. An observer on the earth can now see somewhat beyond A on the western limb of the moon, and not quite up to B on the eastern limb. While the moon is passing from M' to M'', her axial motion again overtakes her orbital motion, so that the line AB again becomes perpendicular to the line joining the centre of the moon to the centre of the earth. Exactly the same side is now turned towards the earth as when the moon was at M. While the moon passes from M'' to M''', her axial motion gets in advance of her orbital motion, so that AB is again inclined to the line joining the centres of the earth and moon. A portion of the eastern limb of the moon beyond B is now brought into view to the earth, and a portion of the western limb at A is carried out of view. While the moon is passing from M''' to M, the orbital motion again overtakes the axial motion, and AB is again perpendicular to ME.
(3) Parallactic Libration.—While an observer at the centre of the earth would get the same view of the moon, whether she were on the eastern horizon, in the zenith, or on the western horizon, an observer on the surface of the earth does not get exactly the same view in these three cases. When the moon is on the eastern horizon, an observer on the surface of the earth would see a little farther around on the western limb of the moon than when she is in the zenith, and not quite so far around on the eastern limb. On the contrary, when the moon is on the western horizon, an observer on the surface of the earth sees a little farther around on the eastern limb of the moon than when she is in the zenith, and not quite so far around on her western limb.
Fig. 120.
This will be evident from Fig. 120. E is the centre of the earth, and O a point on its surface. AB is a line drawn through the centre of the moon, perpendicular to a line joining the centres of the moon and the earth. This line marks off the part of the moon turned towards the centre of the earth, and remains essentially the same during the day. CD is a line drawn through the centre of the moon perpendicular to a line joining the centre of the moon and the point of observation. This line marks off the part of the moon turned towards O. When the moon is in the zenith, CD coincides with AB; but, when the moon is on the horizon, CD is inclined to AB. When the moon is on the eastern horizon, an observer at O sees a little beyond B, and not quite to A; and, when she is on the western horizon, he sees a little beyond A, and not quite to B. B is on the western limb of the moon, and A on her eastern limb.
Since this libration is due to the point from which the moon is viewed, it is called parallactic libration; and, since it occurs daily, it is called diurnal libration.
Fig. 121.
107. Portion of the Lunar Surface brought into View by Libration.—The area brought into view by the first two librations is between one-twelfth and one-thirteenth of the whole lunar surface, or nearly one-sixth of the hemisphere of the moon which is turned away from the earth when the moon is at her state of mean libration. Of course a precisely equal portion of the hemisphere turned towards us during mean libration is carried out of view by the lunar librations.
If we add to each of these areas a fringe about one degree wide, due to the diurnal libration, and which we may call the parallactic fringe, we shall find that the total area brought into view is almost exactly one-eleventh part of the whole surface of the moon. A similar area is carried out of view; so that the whole region thus swayed out of and into view amounts to two-elevenths of the moon's surface. This area is shown in Fig. 121, which is a side view of the moon.
108. The Moon's Path through Space.—Were the earth stationary, the moon would describe an ellipse around it similar to that of Fig. 113; but, as the earth moves forward in her orbit at the same time that the moon revolves around it, the moon is made to describe a sinuous path, as shown by the continuous line in Fig. 122. This feature of the moon's path is greatly exaggerated in the upper portion of the diagram. The form of her path is given with a greater degree of accuracy in the lower part of the figure (the broken line represents the path of the earth); but even here there is considerable exaggeration. The complete serpentine path of the moon around the sun is shown, greatly exaggerated, in Fig. 123, the broken line being the path of the earth.
Fig. 123.
The path described by the moon through space is much the same as that described by a point on the circumference of a wheel which is rolled over another wheel. If we place a circular disk against the wall, and carefully roll along its edge another circular disk (to which a piece of lead pencil has been fastened so as to mark upon the wall), the curve described will somewhat resemble that described by the moon. This curve is called an epicycloid, and it will be seen that at every point it is concave towards the centre of the larger disk. In the same way the moon's orbit is at every point concave towards the sun.
Fig. 124.
The exaggeration of the sinuosity in Fig. 123 will be more evident when it is stated, that, on the scale of Fig. 124, the whole of the serpentine curve would lie within the breadth of the fine circular line MM'.
109. The Lunar Day.—The lunar day is twenty-nine times and a half as long as the terrestrial day. Near the moon's equator the sun shines without intermission nearly fifteen of our days, and is absent for the same length of time. Consequently, the vicissitudes of temperature to which the surface is exposed must be very great. During the long lunar night the temperature of a body on the moon's surface would probably fall lower than is ever known on the earth, while during the day it must rise higher than anywhere on our planet.
Fig. 125.
It might seem, that, since the moon rotates on her axis in about twenty-seven days, the lunar day ought to be twenty-seven days long, instead of twenty-nine. There is, however, a solar, as well as a sidereal, day at the moon, as on the earth; and the solar day at the moon is longer than the sidereal day, for the same reason as on the earth. During the solar day the moon must make both a synodical rotation and a synodical revolution. This will be evident from Fig. 125, in which is shown the path of the moon during one complete lunation. E, E', E'', etc., are the successive positions of the earth; and 1, 2, 3, 4, 5, the successive positions of the moon. The small arrows indicate the direction of the moon's rotation. The moon is full at 1 and 5. At 1, A, at the centre of the moon's disk, will have the sun, which lies in the direction AS, upon the meridian. Before A will again have the sun on the meridian, the moon must have made a synodical revolution; and, as will be seen by the dotted lines, she must have made more than a complete rotation. The rotation which brings the point A into the same relation to the earth and sun is called a synodical rotation.
It will also be evident from this diagram that the moon must make a synodical rotation during a synodical revolution, in order always to present the same side to the earth.
110. The Earth as seen from the Moon.—To an observer on the moon, the earth would be an immense moon, going through the same phases that the moon does to us; but, instead of rising and setting, it would only oscillate to and fro through a few degrees. On the other side of the moon it would never be seen at all. The peculiarities of the moon's motions which cause the librations, and make a spot on the moon's disk seem to an observer on the earth to oscillate to and fro, would cause the earth as a whole to appear to a lunar observer to oscillate to and fro in the heavens in a similar manner.
It is a well-known fact, that, at the time of new moon, the dark part of the moon's surface is partially illumined, so that it becomes visible to the naked eye. This must be due to the light reflected to the moon from the earth. Since at new moon the moon is between the earth and sun, it follows, that, when it is new moon at the earth, it must be full earth at the moon: hence, while the bright crescent is enjoying full sunlight, the dark part of its surface is enjoying the light of the full earth. Fig. 126 represents the full earth as seen from the moon.
Fig. 126.
111. The Moon has no Appreciable Atmosphere.—There are several reasons for believing that the moon has little or no atmosphere.
(1) Had the moon an atmosphere, it would be indicated at the time of a solar eclipse, when the moon passes over the disk of the sun. If the atmosphere were of any considerable density, it would absorb a part of the sun's rays, so as to produce a dusky border in front of the moon's disk, as shown in Fig. 127. In reality no such dusky border is ever seen; but the limb of the moon appears sharp, and clearly defined, as in Fig. 128.
Fig. 127.
Fig. 128.
If the atmosphere were not dense enough to produce this dusky border, its refraction would be sufficient to distort the delicate cusps of the sun's crescent in the manner shown at the top of Fig. 125; but no such distortion is ever observed. The cusps always appear clear and sharp, as shown at the bottom of the figure: hence it would seem that there can be no atmosphere of appreciable density at the moon.
(2) The absence of an atmosphere from the moon is also shown by the absence of twilight and of diffused daylight.
Upon the earth, twilight continues until the sun is eighteen degrees below the horizon; that is, day and night are separated by a belt twelve hundred miles in breadth, in which the transition from light to darkness is gradual. We have seen (66) that this twilight results from the refraction and reflection of light by our atmosphere; and, if the moon had an atmosphere, we should notice a similar gradual transition from the bright to the dark portions of her surface. Such, however, is not the case. The boundary between the light and darkness, though irregular, is sharply defined. Close to this boundary the unillumined portion of the moon appears just as dark as at any distance from it.
The shadows on the moon are also pitchy black, without a trace of diffused daylight.
Fig. 129.
(3) The absence of an atmosphere is also proved by the absence of refraction when the moon passes between us and the stars. Let AB (Fig. 129) represent the disk of the moon, and CD an atmosphere supposed to surround it. Let SAE represent a straight line from the earth, touching the moon at A, and let S be a star situated in the direction of this line. If the moon had no atmosphere, this star would appear to touch the edge of the moon at A; but, if the moon had an atmosphere, a star behind the edge of the moon, at S', would be visible at the earth; for the ray S'A would be bent by the atmosphere into the direction AE'. So, also, on the opposite side of the moon, a star might be seen at the earth, although really behind the edge of the moon: hence, if the moon had an atmosphere, the time during which a star would be concealed by the moon would be less than if it had no atmosphere, and the amount of this effect must be proportional to the density of the atmosphere.
The moon, in her orbital course across the heavens, is continually passing before, or occulting, some of the stars that so thickly stud her apparent path; and when we see a star thus pass behind the lunar disk on one side, and come out again on the other side, we are virtually observing the setting and rising of that star upon the moon. The moon's apparent diameter has been measured over and over again, and is known with great accuracy; the rate of her motion across the sky is also known with perfect accuracy: hence it is easy to calculate how long the moon will take to travel across a part of the sky exactly equal in length to her own diameter. Supposing, then, that we observe a star pass behind the moon, and out again, it is clear, that, if there is no atmosphere, the interval of time during which it remains occulted ought to be exactly equal to the computed time which the moon would take to pass over the star. If, however, from the existence of a lunar atmosphere, the star disappears too late, and re-appears too soon, as we have seen it would, these two intervals will not agree; the computed time will be greater than the observed time, and the difference will represent the amount of refraction the star's light has sustained or suffered, and hence the extent of atmosphere it has had to pass through.
Comparisons of these two intervals of time have been repeatedly made, the most extensive being executed under the direction of the Astronomer Royal of England, several years ago, and based upon no less than two hundred and ninety-six occultation observations. In this determination the measured or telescopic diameter of the moon was compared with the diameter deduced from the occultations; and it was found that the telescopic diameter was greater than the occultation diameter by two seconds of angular measurement, or by about a thousandth part of the whole diameter of the moon. This discrepancy is probably due, in part at least, to irradiation (91), which augments the apparent size of the moon, as seen in the telescope as well as with the naked eye; but, if the whole two seconds were caused by atmospheric refraction, this would imply a horizontal refraction of one second, which is only one two-thousandth of the earth's horizontal refraction. It is possible that an atmosphere competent to produce this refraction would not make itself visible in any other way.
But an atmosphere two thousand times rarer than our air can scarcely be regarded as an atmosphere at all. The contents of an air-pump receiver can seldom be rarefied to a greater extent than to about a thousandth of the density of air at the earth's surface; and the lunar atmosphere, if it exists at all, is thus proved to be twice as attenuated as what we commonly call a vacuum.
Fig. 130.
112. Dusky Patches on the Disk of the Moon.—With the naked eye, large dusky patches are seen on the moon, in which popular fancy has detected a resemblance to a human face. With a telescope of low power, these dark patches appear as smooth as water, and they were once supposed to be seas. This theory was the origin of the name mare (Latin for sea), which is still applied to the larger of these plains; but, if there were water on the surface of the moon, it could not fail to manifest its presence by its vapor, which would form an appreciable atmosphere. Moreover, with a high telescopic power, these plains present a more or less uneven surface; and, as the elevations and depressions are found to be permanent, they cannot, of course, belong to the surface of water.
The chief of these plains are shown in Fig. 130. They are Mare Crisium, Mare Foecunditatis, Mare Nectaris, Mare Tranquillitatis, Mare Serenitatis, Mare Imbrium, Mare Frigoris, and Oceanus Procellarum. All these plains can easily be recognized on the surface of the full moon with the unaided eye.
113. The Terminator of the Moon.—The terminator of the moon is the line which separates the bright and dark portions of its disk. When viewed with a telescope of even moderate power, the terminator is seen to be very irregular and uneven. Many bright points are seen just outside of the terminator in the dark portion of the disk, while all along in the neighborhood of the terminator are bright patches and dense shadows. These appearances are shown in Figs. 131 and 132, which represent the moon near the first and last quarters. They indicate that the surface of the moon is very rough and uneven.
Fig. 131.
Fig. 132.
As it is always either sunrise or sunset along the terminator, the bright spots outside of it are clearly the tops of mountains, which catch the rays of the sun while their bases are in the shade. The bright patches in the neighborhood of the terminator are the sides of hills and mountains which are receiving the full light of the sun, while the dense shadows near by are cast by these elevations.
114. Height of the Lunar Mountains.—There are two methods of finding the height of lunar mountains:—
(1) We may measure the length of the shadows, and then calculate the height of the mountains that would cast such shadows with the sun at the required height above the horizon.
The length of a shadow may be obtained by the following method: the longitudinal wire of the micrometer (19) is adjusted so as to pass through the shadow whose length is to be measured, and the transverse wires are placed one at each end of the shadow, as shown in Fig. 133. The micrometer screw is then turned till the wires are brought together, so as to ascertain the length of the arc between them. We may then form the proportion: the number of seconds in the semi-diameter of the moon is to the number of seconds in the length of the shadow, as the length of the moon's radius in miles to the length of the shadow in miles.
Fig. 133.
The height of the sun above the horizon is ascertained by measuring the angular distance of the mountain from the terminator.
(2) We may measure the distance of a bright point from the terminator, and then construct a right-angled triangle, as shown in Fig. 134. A solution of this triangle will enable us to ascertain the height of the mountain whose top is just catching the level rays of the sun.
Fig. 134.
B is the centre of the moon, M the top of the mountain, and SAM a ray of sunlight which just grazes the terminator at A, and then strikes the top of the mountain at M. The triangle BAM is right-angled at A. BA is the radius of the moon, and AM is known by measurement; BM, the hypothenuse, may then be found by computation. BM is evidently equal to the radius of the moon plus the height of the mountain.
By one or the other of these methods, the heights of the lunar mountains have been found with a great degree of accuracy. It is claimed that the heights of the lunar mountains are more accurately known than those of the mountains on the earth. Compared with the size of the moon, lunar mountains attain a greater height than those on the earth.
115. General Aspect of the Lunar Surface.—A cursory examination of the moon with a low power is sufficient to show the prevalence of crater-like inequalities and the general tendency to circular shape which is apparent in nearly all the surface markings; for even the large "seas" and the smaller patches of the same character repeat in their outlines the round form of the craters. It is along the terminator that we see these crater-like spots to the best advantage; as it is there that the rising or setting sun casts long shadows over the lunar landscape, and brings elevations into bold relief. They vary greatly in size; some being so large as to bear a sensible proportion to the moon's diameter, while the smallest are so minute as to need the most powerful telescopes and the finest conditions of atmosphere to perceive them.
Fig. 135.
The prevalence of ring-shaped mountains and plains will be evident from Fig. 135, which is from a photograph of a model of the moon constructed by Nasmyth.
This same feature is nearly as marked in Figs. 131 and 132, which are copies of Rutherfurd's photographs of the moon.
116. Lunar Craters.—The smaller saucer-shaped formations on the surface of the moon are called craters. They are of all sizes, from a mile to a hundred and fifty miles in diameter; and they are supposed to be of volcanic origin. A high telescopic power shows that these craters vary remarkably, not only in size, but also in structure and arrangement. Some are considerably elevated above the surrounding surface, others are basins hollowed out of that surface, and with low surrounding ramparts; some are like walled plains, while the majority have their lowest depression considerably below the surrounding surface; some are isolated upon the plains, others are thickly crowded together, overlapping and intruding upon each other; some have elevated peaks or cones in their centres, and some are without these central cones, while others, again, contain several minute craters instead; some have their ramparts whole and perfect, others have them broken or deformed, and many have them divided into terraces, especially on their inner sides.
A typical lunar crater is shown in Fig. 136.