Fig. 41.—A simple equatorial mounting.Fig. 41.—A simple equatorial mounting.
80.The equatorial mounting.—Telescopes are of all sizes, from the modest opera glass which may be carried in the pocket and which requires no other support than the hand, to the giant which must have a special roof to shelter it and elaborate machinery to support and direct it toward the sky. But for even the largest telescopes this machinery consists of the following parts, which are illustrated, with exception of the last one, in the small equatorial telescopeshown inFig. 41. It is not customary to place a driving clock on so small a telescope as this:
(a) A supporting pier or tripod.
(b) An axis placed parallel to the axis of the earth.
(c) Another axis at right angles toband capable of revolving uponbas an axle.
(d) The telescope tube attached tocand capable of revolving aboutc.
(e) Graduated circles attached tocandbto measure the amount by which the telescope is turned on these axes.
(f) A driving clock so connected withbas to makec(andd) revolve aboutbwith an angular velocity equal and opposite to that with which the earth turns upon its axis.
Such a support is called an equatorial mounting, and the student should note from the figure that the circles,e, measure the hour angle and declination of any star toward which the telescope is directed, and conversely if the telescope be so set that these circles indicate the hour angle and declination of any given star, the telescope will then point toward that star. In this way it is easy to find with the telescope any moderately bright star, even in broad daylight, although it is thenabsolutely invisible to the naked eye. The rotation of the earth about its axis will speedily carry the telescope away from the star, but if the driving clock be started, its effect is to turn the telescope toward the west just as fast as the earth's rotation carries it toward the east, and by these compensating motions to keep it directed toward the star. InFig. 42, which represents the largest and one of the most perfect refracting telescopes ever built, let the student pick out and identify the several parts of the mounting above described. A part of the driving clock may be seen within the head of the pier. InFig. 43trace out the corresponding parts in the mounting of a reflecting telescope.
Fig. 42.—Equatorial mounting of the great telescope of the Yerkes Observatory.Fig. 42.—Equatorial mounting of the great telescope of the Yerkes Observatory.
Fig. 43.—The reflecting telescope of the Paris Observatory.Fig. 43.—The reflecting telescope of the Paris Observatory.
A telescope is often only a subordinate part of some instrument or apparatus, and then its style of mounting is determined by the requirements of the special case; but when the telescope is the chief thing, and the remainder of the apparatus is subordinate to it, the equatorial mounting is almost always adopted, although sometimes the arrangement of the parts is very different in appearance from any of those shown above. Beware of the popular error that an object held close in front of a telescope can be seen by anobserver at the eyepiece. The numerous stories of astronomers who saw spiders crawling over the objective of their telescope, and imagined they were beholding strange objects in the sky, are all fictitious, since nothing on or near the objective could possibly be seen through the telescope.
81.Photography.—A photographic camera consists of a lens and a device for holding at its focus a specially prepared plate or film. This plate carries a chemical deposit which is very sensitive to the action of light, and which may be made to preserve the imprint of any picture which the lens forms upon it. If such a sensitive plate is placed at the focus of a reflecting telescope, the combination becomes a camera available for astronomical photography, and at the present time the tendency is strong in nearly every branch of astronomical research to substitute the sensitive plate in place of the observer at a telescope. A refracting telescope may also be used for astronomical photography, and is very much used, but some complications occur here on account of the resolution of the light into its constituent colors in passing through the objective.Fig. 44shows such a telescope, or rather two telescopes, one photographic, the other visual, supported side by side upon the same equatorial mounting.
Fig. 44.—Photographic telescope of the Paris Observatory.Fig. 44.—Photographic telescope of the Paris Observatory.
One of the great advantages of photography is found in connection with what is called—
82.Personal equation.—It is a remarkable fact, first investigated by the German astronomer Bessel, three quarters of a century ago, that where extreme accuracy is required the human senses can not be implicitly relied upon. The most skillful observers will not agree exactly in their measurement of an angle or in estimating the exact instant at which a star crossed the meridian; the most skillful artists can not draw identical pictures of the same object, etc.
These minor deceptions of the senses are included in the termpersonal equation, which is a famous phrase in astronomy, denoting that the observations of any given person require to be corrected by means of some equation involving his personality.
General health, digestion, nerves, fatigue, all influence the personal equation, and it was in reference to such matters that one of the most eminent of living astronomers has given this description of his habits of observing:
"In order to avoid every physiological disturbance, I have adopted the rule to abstain for one or two hours before commencing observations from every laborious occupation; never to go to the telescope with stomach loaded with food; to abstain from everything which could affect the nervous system, from narcotics and alcohol, and especially from the abuse of coffee, which I have found to be exceedingly prejudicial to the accuracy of observation."[C]A regimen suggestive of preparation for an athletic contest rather than for the more quiet labors of an astronomer.
83.Visual and photographic work.—The photographic plate has no stomach and no nerves, and is thus free from many of the sources of error which inhere in visual observations, and in special classes of work it possesses othermarked advantages, such as rapidity when many stars are to be dealt with simultaneously, permanence of record, and owing to the cumulative effect of long exposure of the plate it is possible to photograph with a given telescope stars far too faint to be seen through it. On the other hand, the eye has the advantage in some respects, such as studying the minute details of a fairly bright object—e. g., the surface of a planet, or the sun's corona and, for the present at least, neither method of observing can exclude the other. For a remarkable case of discordance between the results of photographic and visual observations compare the pictures of the great nebula in the constellation Andromeda, which are given inChapter XIV. A partial explanation of these discordances and other similar ones is that the eye is most strongly affected by greenish-yellow light, while the photographic plate responds most strongly to violet light; the photograph, therefore, represents things which the eye has little capacity for seeing, andvice versa.
84.The spectroscope.—In some respects the spectroscope is the exact counterpart of the telescope. The latter condenses radiant energy and the former disperses it. As a measuring instrument the telescope is mainly concerned with the direction from which light comes, and the different colors of which that light is composed affect it only as an obstacle to be overcome in its construction. On the other hand, with the spectroscope the direction from which the radiant energy comes is of minor consequence, and the all-important consideration is the intrinsic character of that radiation. What colors are present in the light and in what proportions? What can these colors be made to tell about the nature and condition of the body from which they come, be it sun, or star, or some terrestrial source of light, such as an arc lamp, a candle flame, or a furnace in blast? These are some of the characteristic questions of the spectrum analysis, and, as the name implies, they are solved by analyzing the radiant energy into its componentparts, setting down the blue light in one place, the yellow in another, the red in still another, etc., and interpreting this array of colors by means of principles which we shall have to consider. Something of this process of color analysis may be seen in the brilliant hues shown by a soap bubble, or reflected from a piece of mother-of-pearl, and still more strikingly exhibited in the rainbow, produced by raindrops which break up the sunlight into its component colors and arrange them each in its appropriate place. Any of these natural methods of decomposing light might be employed in the construction of a spectroscope, but in spectroscopes which are used for analyzing the light from feeble sources, such as a star, or a candle flame, a glass prism of triangular cross section is usually employed to resolve the light into its component colors, which it does by refracting it as shown at the edges of the lens inFig. 38.
Fig. 45.—Resolution of light into its component colors.Fig. 45.—Resolution of light into its component colors.
The course of a beam of light in passing through such a prism is shown inFig. 45. Note that the bending of the light from its original course into a new one, which is here shown as produced by the prism, is quite similar to the bending shown at the edges of a lens and comes from thesame cause, the slower velocity of light in glass than in air. It takes the light-waves as long to move over the pathA Bin glass as over the longer path1,2,3,4, of which only the middle section lies in the glass.
Not only does the prism bend the beam of light transmitted by it, but it bends in different degree light of different colors, as is shown in the figure, where the beam at the left of the prism is supposed to be made up of a mixture of blue and red light, while at the right of the prism the greater deviation imparted to the blue quite separates the colors, so that they fall at different places on the screen,S S. The compound light has been analyzed into its constituents, and in the same way every other color would be put down at its appropriate place on the screen, and a beam of white light falling upon the prism would be resolved by it into a sequence of colors, falling upon the screen in the order red, orange, yellow, green, blue, indigo, violet. The initial letters of these names make the wordRoygbiv, and by means of it their order is easily remembered.
Fig. 46.—Principal parts of a spectroscope.Fig. 46.—Principal parts of a spectroscope.
If the light which is to be examined comes from a star the analysis made by the prism is complete, and when viewed through a telescope the image of the star is seen to be drawn out into a band of light, which is called aspectrum, and is red at one end and violet or blue at the other, with all the colors of the rainbow intervening in proper order between these extremes. Such a prism placed in front of the objective of a telescope is called an objective prism, and has been used for stellar work with marked success at the Harvard College Observatory. But if the light to be analyzed comes from an object having an appreciable extent of surface, such as the sun or a planet, the objective prism can not be successfully employed, since each point of the surface will produce its own spectrum, and these will appear in theview telescopesuperposed and confused one with another in a very objectionable manner. To avoid this difficulty there is placedbetween the prism and the source of light an opaque screen,S, with a very narrow slit cut in it, through which all the light to be analyzed must pass and must also go through a lens,A, placed between the slit and the prism, as shown inFig. 46. The slit and lens, together with the tube in which they are usually supported, are called acollimator. By this device a very limited amount of light is permitted to pass from the object through the slit and lens to the prism and is there resolved into a spectrum, which is in effect a series of images of the slit in light of different colors, placed side by side so close as to make practically a continuous ribbon of light whose width is the length of each individual picture of the slit. The length of the ribbon (dispersion) depends mainly upon the shape of the prism and the kind of glass of which it is made, and it may be very greatly increased and the efficiency of the spectroscope enhanced by putting two, three, or more prisms in place of the single one above described. When the amount of light is very great, as in the case of the sun or an electric arc lamp, it is advantageous to alter slightly the arrangement of the spectroscope and to substitute in place of the prism a grating—i. e., a metallic mirror with a great number of fine parallel lines ruled upon its surface at equal intervals, one from another. It is by virtue of such a system of fine parallel grooves that mother-of-pearl displaysits beautiful color effects, and a brilliant spectrum of great purity and high dispersion is furnished by a grating ruled with from 10,000 to 20,000 lines to the inch.Fig. 47represents, rather crudely, a part of the spectrum of an arc light furnished by such a grating, or rather it shows three different spectra arranged side by side, and looking something like a rude ladder. The sides of the ladder are the spectra furnished by the incandescent carbons of the lamp, and the cross pieces are the spectrum of the electric arc filling the space between the carbons.Fig. 48shows a continuation of the same spectra into a region where the radiant energy is invisible to the eye, but is capable of being photographed.
Fig. 47.—Green and blue part of the spectrum of an electric arc light.Fig. 47.—Green and blue part of the spectrum of an electric arc light.
It is only when a lens is placed between the lamp and the slit of the spectroscope that the three spectra are shown distinct from each other as in the figure. The purpose of the lens is to make a picture of the lamp upon the slit, so that all the radiant energy from any one point of the arc may be brought to one part of the slit, and thus appear in the resulting spectrum separated from the energy which comes from every other part of the arc. Such an instrument is called ananalyzing spectroscopewhile one without the lens is called anintegrating spectroscope, since it furnishes to each point of the slit a sample of the radiant energy coming from every part of the source of light, and thus produces only an average spectrum of that source without distinction of its parts. When a spectroscope is attached to a telescope, as is oftendone (seeFig. 49), the eyepiece is removed to make way for it, and the telescope objective takes the part of the analyzing lens. A camera is frequently combined with such an apparatus to photograph the spectra it furnishes, and the whole instrument is then called aspectrograph.
Fig. 48.—Violet and ultraviolet parts of spectrum of an arc lamp.Fig. 48.—Violet and ultraviolet parts of spectrum of an arc lamp.
85.Spectrum analysis.—Having seen the mechanism of the spectroscope by which the light incident upon it is resolved into its constituent parts and drawn out into a series of colors arranged in the order of their wave lengths, we have now to consider the interpretation which is to be placed upon the various kinds of spectra which may be seen, and here we rely upon the experience of physicists and chemists, from whom we learn as follows:
Fig. 49.—A spectroscope attached to the Yerkes telescope.Fig. 49.—A spectroscope attached to the Yerkes telescope.
The radiant energy which is analyzed by the spectroscope has its source in the atoms and molecules which make up the luminous body from which the energy is radiated, and these atoms and molecules are able to impress upon the ether their own peculiarities in the shape of waves of different length and amplitude. We have seen that by varying the conditions of the experiment different kinds of waves may be produced in a bucket of water; and as a study of these waves might furnish an index to the conditions which produced them, so the study of the waves peculiar to the light which comes from any source may be made to give information about the molecules which make up that source. Thus the molecules of iron produce a system of waves peculiar to themselves and which can be duplicated by nothing else, and every other substance gives off its own peculiar type of energy, presenting alimited and definite number of wave lengths dependent upon the nature and condition of its molecules. If these molecules are free to behave in their own characteristic fashion without disturbance or crowding, they emit light of these wave lengths only, and we find in the spectrum a series of bright lines, pictures of the slit produced by light of these particular wave lengths, while between these bright lines lie dark spaces showing the absence from the radiant energy of light of intermediate wave lengths. Such a spectrum is shown in the central portion ofFig. 47, which, as we have already seen, is produced by the space between the carbons of the arc lamp. On the other hand, if the molecules are closely packed together under pressure they so interfere with each other as to give off a jumble of energy of all wave lengths, and this is translated by the spectroscope into a continuous ribbon of light with no dark spaces intervening, as in the upper and lower parts of Figs.47and48, produced by the incandescent solid carbons of the lamp. These two types are known as the continuous and discontinuous spectrum, and we may lay down the following principle regarding them:
A discontinuous spectrum, or bright-line spectrum as it is familiarly called, indicates that the molecules of the source of light are not crowded together, and therefore the light must come from an incandescent gas. A continuous spectrum shows only that the molecules are crowded together, or are so numerous that the body to which they belong is not transparent and gives no further information. The body may be solid, liquid, or gaseous, but in the latter case the gas must be under considerable pressure or of great extent.
A second principle is: The lines which appear in a spectrum are characteristic of the source from which the light came—e. g., the double line in the yellow part of the spectrum at the extreme left inFig. 47is produced by sodium vapor in and around the electric arc and is never produced by anything but sodium. When by laboratory experiments we have learned the particular set of lines corresponding to iron, we may treat the presence of these lines in another spectrum as proof that iron is present in the source from which the light came, whether that source be a white-hot poker in the next room or a star immeasurably distant. The evidence that iron is present lies in the nature of the light, and there is no reason to suppose that nature to be altered on the way from star to earth. It may, however, be altered by something happening to the source from which it comes—e. g., changing temperature or pressure may affect, and does affect, the spectrum which such a substance as iron emits, and we must be prepared to find the same substance presenting different spectra under different conditions, only these conditions must be greatly altered in order to produce radical changes in the spectrum.
Fig. 50.—The chief lines in the spectrum of sunlight.—Herschel.Fig. 50.—The chief lines in the spectrum of sunlight.—Herschel.
86.Wave lengths.—To identify a line as belonging to and produced by iron or any other substance, its position in the spectrum—i. e., its wave length—must be very accurately determined, and for the identification of a substance by means of its spectrum it is often necessary to determine accurately the wave lengths of many lines. A complicated spectrum may consist of hundreds or thousands of lines, due to the presence of many different substances in the source of light, and unless great care is taken in assigning the exact position of these lines in the spectrum, confusion and wrong identifications are sure to result. For the measurement of the required wave length a tenth meter (§ 75) is the unit employed, and a scale of wave lengths expressed in this unit is presented inFig. 50. The accuracy with which some of these wave lengths are determined is truly astounding; a ten-billionth of an inch! These numerical wave lengths save all necessity for referring to the color of any part of the spectrum, and pictures of spectra for scientific use are not usually printed in colors.
87.Absorption spectra.—There is another kind of spectrum, ofgreater importance than either of those above considered, which is well illustrated by the spectrum of sunlight (Fig. 50). This is a nearly continuous spectrum crossed by numerousdarklines due to absorption of radiant energy in a comparatively cool gas through which it passes on its way to the spectroscope. Fraunhofer, who made the first careful study of spectra, designated some of the more conspicuous of these lines by letters of the alphabet which are shown in the plate, and which are still in common use as names for the lines, not only in the spectrum of sunlight but wherever they occur in other spectra. Thus the double line markedD, wave length 5893, falls at precisely the same place in the spectrum as does the double (sodium) line which we have already seen in the yellow part of the arc-light spectrum, which line is also calledDand bears a very intimate relation to the darkDline of the solar spectrum.
The student who has access to colored crayons should color one edge ofFig. 50in accordance with the lettering there given and, so far as possible, he should make the transition from one color to the next a gradual one, as it is in the rainbow.
Fig. 50is far from being a complete representation of the spectrum of sunlight. Not only does this spectrum extend both to the right and to the left into regions invisible to the human eye, but within the limits of the figure, instead of the seventy-five lines there shown, there are literally thousands upon thousands of lines, of which only the most conspicuous can be shown in such a cut as this.
The dark lines which appear in the spectrum of sunlight can, under proper conditions, be made to appear in the spectrum of an arc light, andFig. 51shows a magnified representation of a small part of such a spectrum adjacent to theD(sodium) lines. Down the middle of each of these lines runs a black streak whose position (wave length) is precisely that of theDlines in the spectrum of sunlight, and whose presence is explained as follows:
The very hot sodium vapor at the center of the arc gives off its characteristic light, which, shining through the outer and cooler layers of sodium vapor, is partially absorbed by these, resulting in a fine dark line corresponding exactly in position and wave length to the bright lines, and seen against these as a background, since the higher temperature at the center of the arc tends to broaden the bright lines and make them diffuse. Similarly the dark lines in the spectrum of the sun (Fig. 50) point to the existence of a surrounding envelope of relatively cool gases, which absorb from the sunlight precisely those kinds of radiant energy which they would themselves emit if incandescent. The resulting dark lines in the spectrum are to be interpreted by the same set of principles which we have above applied to the bright lines of a discontinuous spectrum, and they may be used to determine the chemical composition of the sun, just as the bright lines serve to determine the chemical elements present in the electric arc. With reference to the mode of their formation, bright-line and dark-line spectra are sometimes called respectivelyemissionandabsorptionspectra.
Fig. 51.—The lines reversed.Fig. 51.—The lines reversed.
88.Types of spectrum.—The sun presents by far the most complex spectrum known, andFig. 50shows only a small number of the more conspicuous lines which appearin it. Spectra of stars,per contra, appear relatively simple, since their feeble light is insufficient to bring out faint details. In ChaptersXIIIandXIVthere are shown types of the different kinds of spectra given by starlight, and these are to be interpreted by the principles above established. Thus the spectrum of the bright star β Aurigæ shows a continuous spectrum crossed by a few heavy absorption lines which are known from laboratory experiments to be produced only by hydrogen. There must therefore be an atmosphere of relatively cool hydrogen surrounding this star. The spectrum of Pollux is quite similar to that of the sun and is to be interpreted as showing a physical condition similar to that of the sun, while the spectrum of α Herculis is quite different from either of the others. In subsequent chapters we shall have occasion to consider more fully these different types of spectrum.
89.The Doppler principle.—This important principle of the spectrum analysis is most readily appreciated through the following experiment:
Listen to the whistle of a locomotive rapidly approaching, and observe how the pitch changes and the note becomes more grave as the locomotive passes by and commences to recede. During the approach of the whistle each successive sound wave has a shorter distance to travel in coming to the ear of the listener than had its predecessor, and in consequence the waves appear to come in quicker succession, producing a higher note with a correspondingly shorter wave length than would be heard if the same whistle were blown with the locomotive at rest. On the other hand, the wave length is increased and the pitch of the note lowered by the receding motion of the whistle. A similar effect is produced upon the wave length of light by a rapid change of distance between the source from which it comes and the instrument which receives it, so that a diminishing distance diminishes very slightly the wave length of every line in the spectrum produced by thelight, and an increasing distance increases these wave lengths, and this holds true whether the change of distance is produced by motion of the source of light or by motion of the instrument which receives it.
This change of wave length is sometimes described by saying that when a body is rapidly approaching, the lines of its spectrum are all displaced toward the violet end of the spectrum, and are correspondingly displaced toward the red end by a receding motion. The amount of this shifting, when it can be measured, measures the velocity of the body along the line of sight, but the observations are exceedingly delicate, and it is only in recent years that it has been found possible to make them with precision. For this purpose there is made to pass through the spectroscope light from an artificial source which contains one or more chemical elements known to be present in the star which is to be observed, and the corresponding lines in the spectrum of this light and in the spectrum of the star are examined to determine whether they exactly match in position, or show, as they sometimes do, a slight displacement, as if one spectrum had been slipped past the other. The difficulty of the observations lies in the extremely small amount of this slipping, which rarely if ever in the case of a moving star amounts to one sixth part of the interval between the close parallel lines markedDinFig. 50. The spectral lines furnished by the headlight of a locomotive running at the rate of a hundred miles per hour would be displaced by this motion less than one six-thousandth part of the space between theDlines, an amount absolutely imperceptible in the most powerful spectroscope yet constructed. But many of the celestial bodies have velocities so much greater than a hundred miles per hour that these may be detected and measured by means of the Doppler principle.
90.Other instruments.—Other instruments of importance to the astronomer, but of which only casual mentioncan here be made, are the meridian-circle; the transit, one form of which is shown inFig. 52, and the zenith telescope, which furnish refined methods for making observations similar in kind to those which the student has already learned to make with plumb line and protractor; the sextant, which is pre-eminently the sailor's instrument for finding the latitude and longitude at sea, by measuring the altitudes of sun and stars above the sea horizon; the heliometer, which serves for the very accurate measurement of small angles, such as the angular distance between two stars not more than one or two degrees apart; and the photometer, which is used for measuring the amount of light received from the celestial bodies.
Fig. 52.—A combined transit instrument and zenith telescope.Fig. 52.—A combined transit instrument and zenith telescope.
91.Results of observation with the unaided eye.—The student who has made the observations of the moon which are indicated inChapter IIIhas in hand data from which much may be learned about the earth's satellite. Perhaps the most striking feature brought out by them is the motion of the moon among the stars, always from west toward east, accompanied by that endless series of changes in shape and brightness—new moon, first quarter, full moon, etc.—whose successive stages we represent by the words, the phase of the moon. From his own observation the student should be able to verify, at least approximately, the following statements, although the degree of numerical precision contained in some of them can be reached only by more elaborate apparatus and longer study than he has given to the subject:
A. The phase of the moon depends upon the distance apart of sun and moon in the sky, new moon coming when they are together, and full moon when they are as far apart as possible.
THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph made at the Paris Observatory.THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph made at the Paris Observatory.
B. The moon is essentially a round, dark body, giving off no light of its own, but shining solely by reflected sunlight. The proof of this is that whenever we see a part of the moon which is turned away from the sun it looks dark—e. g., at new moon, sun and moon are in nearly the same direction from us and we see little or nothing of the moon, since the side upon which the sun shines is turned away from us. At full moon the earth is in line between sunand moon, and we see, round and bright, the face upon which the sun shines. At other phases, such as the quarters, the moon turns toward the earth a part of its night hemisphere and a part of its day hemisphere, but in general only that part which belongs to the day side of the moon is visible and the peculiar curved line which forms the boundary—the "ragged edge," orterminator, as it is called, is the dividing line between day and night upon the moon.
A partial exception to what precedes is found for a few days after new moon when the moon and sun are not very far apart in the sky, for then the whole round disk of the moon may often be seen, a small part of it brightly illuminated by the sun and the larger part feebly illuminated by sunlight which fell first upon the earth and was by it reflected back to the moon, giving the pleasing effect which is sometimes called the old moon in the new moon's arms. The new moon—i. e., the part illumined by the sun—usually appears to belong to a sphere of larger radius than the old moon, but this is purely a trick played by the eyes of the observer, and the effect disappears altogether in a telescope. Is there any similar effect in the few days before new moon?
C. The moon makes the circuit of the sky from a given star around to the same star again in a little more than 27 days (27.32166), but the interval between successive new moons—i. e., from the sun around to the sun again—is more than 29 days (29.53059). This last interval, which is called a lunar month orsynodicalmonth, indicates what we have learned before—that the sun has changed its place among the stars during the month, so that it takes the moon an extra two days to overtake him after having made the circuit of the sky, just as it takes the minute hand of a clock an extra 5 minutes to catch up with the hour hand after having made a complete circuit of the dial.
D. Wherever the moon may be in the sky, it turns always the same face toward the earth, as is shown by the fact that the dark markings which appear on its surface stand always upon (nearly) the same part of its disk. It does not always turn the same face toward the sun, for the boundary line between the illumined and unillumined parts of the moon shifts from one side to the other as the phase changes, dividing at each moment day from night upon the moon and illustrating by its slow progress that upon the moon the day and the month are of equal length (29.5 terrestrial days), instead of being time units of different lengths as with us.
Fig. 53.—Motion of moon and earth relative to the sun.Fig. 53.—Motion of moon and earth relative to the sun.
92.The moon's motion.—The student should compare the results of his own observations, as well as the preceding section, withFig. 53, in which the lines with dates printed on them are all supposed to radiate from the sun and to represent the direction from the sun of earth and moon upon the given dates which are arbitrarily assumed for the sake of illustration, any other set would do equally well. The black dots, small and large, represent the moon revolving about the earth, but having the circular path shown inFig. 34(ellipse) transformed by the earth's forward motion into the peculiar sinuous line here shown. With respect to both earth and sun, the moon's orbit deviates but little from a circle, since the sinuous curve ofFig. 53follows very closely the earth's orbit around the sun and is almost identical with it. For clearness of representation the distance between earth and moon in the figure has been made ten times too great, and to get a proper idea of the moon's orbit with reference to the sun, we must suppose the moon moved up toward the earth until its distance from the line of the earth's orbit is only a tenth part of what it is in the figure. When this is done, the moon's path becomes almost indistinguishable from that of the earth, as may be seen in the figure, where the attempt has been made to show both lines, and itis to be especially noted that this real orbit of the moon is everywhere concave toward the sun.
The phase presented by the moon at different parts of its path is indicated by the row of circles at the right, and the student should show why a new moon is associated with June 30th and a full moon with July 15th, etc. What was the date of first quarter? Third quarter?
We may find inFig. 53another effect of the same kind as that noted above in C. Between noon, June 30th, and noon, July 3d, the earth makes upon its axis three complete revolutions with respect to the sun, but the meridian which points toward the moon at noon on June 30th will not point toward it at noon on July 3d, since the moon has moved into a new position and is now 37° away from the meridian. Verify this statement by measuring, inFig. 53, with the protractor, the moon's angular distance from the meridian at noon on July 3d. When will the meridian overtake the moon?
93.Harvest moon.—The interval between two successive transits of the meridian past the moon is called a lunar day, and the student should show from the figure that on the average a lunar day is 51 minutes longer than a solar day—i. e., upon the average each day the moon comes to the meridian 51 minutes of solar time later than on the day before. It is also true that on the average the moon rises and sets 51 minutes later each day than on the day before. But there is a good deal of irregularity in the retardation of the time of moonrise and moonset, since the time of rising depends largely upon the particular point of the horizon at which the moon appears, and between two days this point may change so much on account of the moon's orbital motion as to make the retardation considerably greater or less than its average value. In northern latitudes this effect is particularly marked in the month of September, when the eastern horizon is nearly parallel with the moon's apparent path in the sky, and nearthe time of full moon in that month the moon rises on several successive nights at nearly the same hour, and in less degree the same is true for October. This highly convenient arrangement of moonlight has caused the full moons of these two months to be christened respectively the Harvest Moon and the Hunter's Moon.
94.Size and mass of the moon.—It has been shown inChapter Ihow the distance of the moon from the earth may be measured and its diameter determined by means of angles, and without enlarging upon the details of these observations, we note as their result that the moon is a globe 2,163 miles in diameter, and distant from the earth on the average about 240,000 miles. But, as we have seen inChapter VII, this distance changes to the extent of a few thousand miles, sometimes less, sometimes greater, mainly on account of the elliptic shape of the moon's orbit about the earth, but also in part from the disturbing influence of other bodies, such as the sun, which pull the moon to and fro, backward and forward, to quite an appreciable extent.
From the known diameter of the moon it is a matter of elementary geometry to derive in miles the area of its surface and its volume or solid contents. Leaving this as an exercise for the student, we adopt the earth as the standard of comparison and find that the diameter of the moon is rather more than a quarter, 4/15, that of the earth, the area of its surface is a trifle more than 1/14 that of the earth, and its volume a little more than 1/49 of the earth's. So much is pure geometry, but we may combine with it some mechanical principles which enable us to go a step farther and to "weigh" the moon—i. e., determine its mass and the average density of the material of which it is made.
We have seen that the moon moves around the sun in a path differing but little from the smooth curve shown inFig. 53, with arrows indicating the direction of motion, and it would follow absolutely such a smooth path were it not for the attraction of the earth, and in less degreeof some of the other planets, which swing it about first to one side then to the other. But action and reaction are equal; the moon pulls as strongly upon the earth as does the earth upon the moon, and if earth and moon were of equal mass, the deviation of the earth from the smooth curve in the figure would be just as large as that of the moon. It is shown in the figure that the moon does displace the earth from this curve, and we have only to measure the amount of this displacement of the earth and compare it with the displacement suffered by the moon to find how much the mass of the one exceeds that of the other. It may be seen from the figure that at first quarter, about July 7th, the earth is thrust ahead in the direction of its orbital motion, while at the third quarter, July 22d, it is pulled back by the action of the moon, and at all times it is more or less displaced by this action, so that, in order to be strictly correct, we must amend our former statement about the moon moving around the earth and make it read, Both earth and moon revolve around a point on line between their centers. This point is called theircenter of gravity, and the earth and the moon both move in ellipses having this center of gravity at their common focus. Compare this with Kepler's First Law. These ellipses are similarly shaped, but of very different size, corresponding to Newton's third law of motion (Chapter IV), so that the action of the earth in causing the small moon to move around a large orbit is just equal to the reaction of the moon in causing the larger earth to move in the smaller orbit. This is equivalent to saying that the dimensions of the two orbits are inversely proportional to the masses of the earth and the moon.
By observing throughout the month the direction from the earth to the sun or to a near planet, such as Mars or Venus, astronomers have determined that the diameter of the ellipse in which the earth moves is about 5,850 miles, so that the distance of the earth from the center of gravityis 2,925 miles, and the distance of the moon from it is 240,000 - 2,925 = 237,075. We may now write in the form of a proportion—
Mass of earth : Mass of moon :: 237,075 : 2,925,
and find from it that the mass of the earth is 81 times as great as the mass of the moon—i. e., leaving kind and quality out of account, there is enough material in the earth to make 81 moons. We may note in this connection that the diameter of the earth, 7,926 miles, is greater than the diameter of the monthly orbit in which the moon causes it to move, and therefore the center of gravity of earth and moon always lies inside the body of the earth, about 1,000 miles below the surface.
95.Density of the moon.—It is believed that in a general way the moon is made of much the same kind of material which goes to make up the earth—metals, minerals, rocks, etc.—and a part of the evidence upon which this belief is based lies in the density of the moon. By density of a substance we mean the amount of it which is contained in a given volume—i. e., the weight of a bushel or a cubic centimeter of the stuff. The density of chalk is twice as great as the density of water, because a cubic centimeter of chalk weighs twice as much as an equal volume of water, and similarly in other cases the density is found by dividing the mass or weight of the body by the mass or weight of an equal volume of water.
We know the mass of the earth (§ 45), and knowing the mass of a cubic foot of water, it is easy, although a trifle tedious, to compute what would be the mass of a volume of water equal in size to the earth. The quotient obtained by dividing one of these masses by the other (mass of earth ÷ mass of water) is the average density of the material composing the earth, and we find numerically that this is 5.6—i. e., it would take 5.6 water earths to attract as strongly as does the real one. From direct experiment weknow that the average density of the principal rocks which make up the crust of the earth is only about half of this, showing that the deep-lying central parts of the earth are denser than the surface parts, as we should expect them to be, because they have to bear the weight of all that lies above them and are compressed by it.
Turning now to the moon, we find in the same way as for the earth that its average density is 3.4 as great as that of water.
96.Force of gravity upon the moon.—This number, 3.4, compared with the 5.6 which we found for the earth, shows that on the whole the moon is made of lighter stuff than is the body of the earth, and this again is much what we should expect to find, for weight, the force which tends to compress the substance of the moon, is less there than here. The weight of a cubic yard of rock at the surface of either earth or moon is the force with which the earth or moon attracts it, and this by the law of gravitation is for the earth—
W=k· (mm')/(3963)2;
and for the moon—
w=k· {m(m'/81)}/(1081)2;
from which we find by division—
w= (W/81) (3963/1081)2=W/6 (approximately).
The cubic yard of rock, which upon the earth weighs two tons, would, if transported to the moon, weigh only one third of a ton, and would have only one sixth as much influence in compressing the rocks below it as it had upon the earth. Note that this rock when transported to the moon would be still attracted by the earth and would have weight toward the earth, but it is not this of which we arespeaking; by its weight in the moon we mean the force with which the moon attracts it. Making due allowance for the difference in compression produced by weight, we may say that in general, so far as density goes, the moon is very like a piece of the earth of equal mass set off by itself alone.
97.Albedo.—In another respect the lunar stuff is like that of which the earth is made: it reflects the sunlight in much the same way and to the same amount. The contrast of light and dark areas on the moon's surface shows, as we shall see in another section, the presence of different substances upon the moon which reflect the sunlight in different degrees. This capacity for reflecting a greater or less percentage of the incident sunlight is calledalbedo(Latin, whiteness), and the brilliancy of the full moon might lead one to suppose that its albedo is very great, like that of snow or those masses of summer cloud which we call thunderheads. But this is only an effect of contrast with the dark background of the sky. The same moon by day looks pale, and its albedo is, in fact, not very different from that of our common rocks—weather-beaten sandstone according to Sir John Herschel—so that it would be possible to build an artificial moon of rock or brick which would shine in the sunlight much as does the real moon.
The effect produced by the differences of albedo upon the moon's face is commonly called the "man in the moon," but, like the images presented by glowing coals, the face in the moon is anything which we choose to make it. Among the Chinese it is said to be a monkey pounding rice; in India, a rabbit; in Persia, the earth reflected as in a mirror, etc.
98.Librations.—We have already learned that the moon turns always the same face toward the earth, and we have now to modify this statement and to find that here, as in so many other cases, the thing we learn first is only approximately true and needs to be limited or added to ormodified in some way. In general, Nature is too complex to be completely understood at first sight or to be perfectly represented by a simple statement. InFig. 55we have two photographs of the moon, taken nearly three years apart, the right-hand one a little after first quarter and the left-hand one a little before third quarter. They therefore represent different parts of the moon's surface, but along the ragged edge the same region is shown on both photographs, and features common to both pictures may readily be found—e. g., the three rings which form a right-angled triangle about one third of the way down from the top of the cut, and the curved mountain chain just below these. If the moon turned exactly the same face toward us in the two pictures, the distance of any one of these markings from any part of the moon's edge must be the same in both pictures; but careful measurement will show that this is not the case, and that in the left-hand picture the upper edge of the moon is tipped toward us and the lower edge away from us, as if the whole moon had been rotated slightly about a horizontal line and must be turned back a little (about 7°) in order to match perfectly the other part of the picture.
This turning is called alibration, and it should be borne in mind that the moon librates not only in the direction above measured, north and south, but also at right angles to this, east and west, so that we are able to see a little farther around every part of the moon's edge than would be possible if it turned toward us at all times exactly the same face. But in spite of the librations there remains on the farther side of the moon an area of 6,000,000 square miles which is forever hidden from us, and of whose character we have no direct knowledge, although there is no reason to suppose it very different from that which is visible, despite the fact that some of the books contain quaint speculations to the contrary. The continent of South America is just about equal in extent to this unknown region,while North America is a fair equivalent for all the rest of the moon's surface, both those central parts which are constantly visible, and the zone around the edge whose parts sometimes come into sight and are sometimes hidden.
An interesting consequence of the peculiar rotation of the moon is that from our side of it the earth is always visible. Sun, stars, and planets rise and set there as well as here, but to an observer on the moon the earth swings always overhead, shifting its position a few degrees one way or the other on account of the libration but running through its succession of phases, new earth, first quarter, etc., without ever going below the horizon, provided the observer is anywhere near the center of the moon's disk.