[Ill.u.s.tration: FIG. 48.--Violet and ultraviolet parts of spectrum of an arc lamp.]

[Ill.u.s.tration: FIG. 49.--A spectroscope attached to the Yerkes telescope.]

85. SPECTRUM a.n.a.lYSIS.--Having seen the mechanism of the spectroscope by which the light incident upon it is resolved into its const.i.tuent 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:

The radiant energy which is a.n.a.lyzed 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 a limited 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 s.p.a.ces showing the absence from the radiant energy of light of intermediate wave lengths. Such a spectrum is shown in the central portion of Fig. 47, which, as we have already seen, is produced by the s.p.a.ce 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 s.p.a.ces intervening, as in the upper and lower parts of Figs. 47 and 48, 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 in Fig. 47 is 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.

[Ill.u.s.tration: 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 a.s.signing 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 in Fig. 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, of greater importance than either of those above considered, which is well ill.u.s.trated by the spectrum of sunlight (Fig. 50). This is a nearly continuous spectrum crossed by numerous _dark_ lines due to absorption of radiant energy in a comparatively cool gas through which it pa.s.ses 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 marked _D_, 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 called _D_ and bears a very intimate relation to the dark _D_ line of the solar spectrum.

The student who has access to colored crayons should color one edge of Fig. 50 in 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. 50 is 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, and Fig. 51 shows a magnified representation of a small part of such a spectrum adjacent to the _D_ (sodium) lines. Down the middle of each of these lines runs a black streak whose position (wave length) is precisely that of the _D_ lines 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 respectively _emission_ and _absorption_ spectra.

[Ill.u.s.tration: FIG. 51.--The lines reversed.]

88. TYPES OF SPECTRUM.--The sun presents by far the most complex spectrum known, and Fig. 50 shows only a small number of the more conspicuous lines which appear in it. Spectra of stars, _per contra_, appear relatively simple, since their feeble light is insufficient to bring out faint details. In Chapters XIII and XIV there 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 Aurigae 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 a 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 a.n.a.lysis 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 pa.s.ses 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 the light, 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 pa.s.s 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 marked _D_ in Fig. 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 s.p.a.ce between the _D_ lines, 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 mention can here be made, are the meridian-circle; the transit, one form of which is shown in Fig. 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 s.e.xtant, which is pre-eminently the sailor's instrument for finding the lat.i.tude and longitude at sea, by measuring the alt.i.tudes 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.

[Ill.u.s.tration: FIG. 52.--A combined transit instrument and zenith telescope.]

CHAPTER IX

THE MOON

91. RESULTS OF OBSERVATION WITH THE UNAIDED EYE.--The student who has made the observations of the moon which are indicated in Chapter III has 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.

[Ill.u.s.tration: 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 sun and 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," or _terminator_, 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 or _synodical_ month, 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 ill.u.s.trating 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.

[Ill.u.s.tration: 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, with Fig. 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 a.s.sumed for the sake of ill.u.s.tration, 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 in Fig. 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...o...b..t deviates but little from a circle, since the sinuous curve of Fig. 53 follows very closely the earth's...o...b..t 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...o...b..t 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...o...b..t 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 it is 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 a.s.sociated with June 30th and a full moon with July 15th, etc. What was the date of first quarter? Third quarter?

We may find in Fig. 53 another 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, in Fig. 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 r.e.t.a.r.dation 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...o...b..tal motion as to make the r.e.t.a.r.dation considerably greater or less than its average value. In northern lat.i.tudes 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 near the 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 Ma.s.s OF THE MOON.--It has been shown in Chapter I how 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 in Chapter 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...o...b..t 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 ma.s.s 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 in Fig. 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 degree of 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 ma.s.s, 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 ma.s.s 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...o...b..tal 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 their _center 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 ma.s.ses 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 gravity is 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--

Ma.s.s of earth : Ma.s.s of moon :: 237,075 : 2,925,

and find from it that the ma.s.s of the earth is 81 times as great as the ma.s.s 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 ma.s.s or weight of the body by the ma.s.s or weight of an equal volume of water.

We know the ma.s.s of the earth (-- 45), and knowing the ma.s.s of a cubic foot of water, it is easy, although a trifle tedious, to compute what would be the ma.s.s of a volume of water equal in size to the earth. The quotient obtained by dividing one of these ma.s.ses by the other (ma.s.s of earth ma.s.s 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 we know that the average density of the princ.i.p.al 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 (m m') / (3963)^{2};

and for the moon--