D. Whatever may have been the mode of their formation, the craters can not have been produced by scooping out material from the center and piling it up to make the wall, for in three cases out of four the volume of the excavation is greater than the volume of material contained in the wall.

106. MOON AND EARTH.--We have gone far enough now to appreciate both the likeness and the unlikeness of the moon and earth. They may fairly enough be likened to offspring of the same parent who have followed very different careers, and in the fullness of time find themselves in very different circ.u.mstances. The most serious point of difference in these circ.u.mstances is the atmosphere, which gives to the earth a wealth of phenomena altogether lacking in the moon. Clouds, wind, rain, snow, dew, frost, and hail are all dependent upon the atmosphere and can not be found where it is not. There can be nothing upon the moon at all like that great group of changes which we call weather, and the unruffled aspect of the moon's face contrasts sharply with the succession of cloud and sunshine which the earth would present if seen from the moon.

The atmosphere is the chief agent in the propagation of sound, and without it the moon must be wrapped in silence more absolute than can be found upon the surface of the earth. So, too, the absence of an atmosphere shows that there can be no water or other liquid upon the moon, for if so it would immediately evaporate and produce a gaseous envelope which we have seen does not exist. With air and water absent there can be of course no vegetation or life of any kind upon the moon, and we are compelled to regard it as an arid desert, utterly waste.

107. TEMPERATURE OF THE MOON.--A characteristic feature of terrestrial deserts, which is possessed in exaggerated degree by the moon, is the great extremes of temperature to which they and it are subject. Owing to its slow rotation about its axis, a point on the moon receives the solar radiation uninterruptedly for more than a fortnight, and that too unmitigated by any cloud or vaporous covering. Then for a like period it is turned away from the sun and allowed to cool off, radiating into interplanetary s.p.a.ce without hindrance its acc.u.mulated store of heat. It is easy to see that the range of temperature between day and night must be much greater under these circ.u.mstances than it is with us where shorter days and clouded skies render day and night more nearly alike, to say nothing of the ocean whose waters serve as a great balance wheel for equalizing temperatures. Just how hot or how cold the moon becomes is hard to determine, and very different estimates are to be found in the books. Perhaps the most reliable of these are furnished by the recent researches of Professor Very, whose experiments lead him to conclude that "its rocky surface at midday, in lat.i.tudes where the sun is high, is probably hotter than boiling water and only the most terrible of earth's deserts, where the burning sands blister the skin, and men, beasts, and birds drop dead, can approach a noontide on the cloudless surface of our satellite. Only the extreme polar lat.i.tudes of the moon can have an endurable temperature by day, to say nothing of the night, when we should have to become troglodytes to preserve ourselves from such intense cold."

While the night temperature of the moon, even very soon after sunset, sinks to something like 200 below zero on the centigrade scale, or 320 below zero on the Fahrenheit scale, the lowest known temperature upon the earth, according to General Greely, is 90 Fahr. below zero, recorded in Siberia in January, 1885.

Winter and summer are not markedly different upon the moon, since its rotation axis is nearly perpendicular to the plane of the earth's...o...b..t about the sun, and the sun never goes far north or south of the moon's equator. The month is the one cycle within which all seasonal changes in its physical condition appear to run their complete course.

108. CHANGES IN THE MOON.--It is evidently idle to look for any such changes in the condition of the moon's surface as with us mark the progress of the seasons or the spread of civilization over the wilderness. But minor changes there may be, and it would seem that the violent oscillations of temperature from day to night ought to have some effect in breaking down and crumbling the sharp peaks and crags which are there so common and so p.r.o.nounced. For a century past astronomers have searched carefully for changes of this kind--the filling up of some crater or the fall of a mountain peak; but while some things of this kind have been reported from time to time, the evidence in their behalf has not been altogether conclusive. At the present time it is an open question whether changes of this sort large enough to be seen from the earth are in progress. A crater much less than a mile wide can be seen in the telescope, but it is not easy to tell whether so minute an object has changed in size or shape during a year or a decade, and even if changes are seen they may be apparent rather than real. Fig. 64 contains two views of the crater Archimedes, taken under a morning and an afternoon sun respectively, and shows a very p.r.o.nounced difference between the two which proceeds solely from a difference of illumination.

In the presence of such large fict.i.tious changes astronomers are slow to accept smaller ones as real.

[Ill.u.s.tration: FIG. 64.--Archimedes in the lunar morning and afternoon.--WEINEK.]

It is this absence of change that is responsible for the rugged and sharp-cut features of the moon which continue substantially as they were made, while upon the earth rain and frost are continually wearing down the mountains and spreading their substance upon the lowland in an unending process of smoothing off the roughnesses of its surface. Upon the moon this process is almost if not wholly wanting, and the moon abides to-day much more like its primitive condition than is the earth.

109. THE MOON'S INFLUENCE UPON THE EARTH.--There is a widespread popular belief that in many ways the moon exercises a considerable influence upon terrestrial affairs: that it affects the weather for good or ill, that crops must be planted and harvested, pigs must be killed, and timber cut at the right time of the moon, etc. Our common word lunatic means moonstruck--i. e., one upon whom the moon has shone while sleeping. There is not the slightest scientific basis for any of these beliefs, and astronomers everywhere cla.s.s them with tales of witchcraft, magic, and popular delusion. For the most part the moon's influence upon the earth is limited to the light which it sends and the effect of its gravitation, chiefly exhibited in the ocean tides. We receive from the moon a very small amount of second-hand solar heat and there is also a trifling magnetic influence, but neither of these last effects comes within the range of ordinary observation, and we shall not go far wrong in saying that, save the moonlight and the tides, every supposed lunar influence upon the earth is either fict.i.tious or too small to be readily detected.

CHAPTER X

THE SUN

110. DEPENDENCE OF THE EARTH UPON THE SUN.--There is no better introduction to the study of the sun than Byron's Ode to Darkness, beginning with the lines--

"I dreamed a dream That was not all a dream.

The bright sun was extinguished,"

and proceeding to depict in vivid words the consequences of this extinction. The most matter-of-fact language of science agrees with the words of the poet in declaring the earth's dependence upon the sun for all those varied forms of energy which make it a fit abode for living beings. The winds blow and the rivers run; the crops grow, are gathered and consumed, by virtue of the solar energy. Factory, locomotive, beast, bird, and the human body furnish types of machines run by energy derived from the sun; and the student will find it an instructive exercise to search for kinds of terrestrial energy which are not derived either directly or indirectly from the sun. There are a few such, but they are neither numerous nor important.

111. THE SUN'S DISTANCE FROM THE EARTH.--To the astronomer the sun presents problems of the highest consequence and apparently of very diverse character, but all tending toward the same goal: the framing of a mechanical explanation of the sun considered as a machine; what it is, and how it does its work. In the forefront of these problems stand those numerical determinations of distance, size, ma.s.s, density, etc., which we have already encountered in connection with the moon, but which must here be dealt with in a different manner, because the immensely greater distance of the sun makes impossible the resort to any such simple method as the triangle used for determining the moon's distance. It would be like determining the distance of a steeple a mile away by observing its direction first from one eye, then from the other; too short a base for the triangle. In one respect, however, we stand upon a better footing than in the case of the moon, for the ma.s.s of the earth has already been found (Chapter IV) as a fractional part of the sun's ma.s.s, and we have only to invert the fraction in order to find that the sun's ma.s.s is 329,000 times that of the earth and moon combined, or 333,000 times that of the earth alone.

If we could rely implicitly upon this number we might make it determine for us the distance of the sun through the law of gravitation as follows: It was suggested in -- 38 that Newton proved Kepler's three laws to be imperfect corollaries from the law of gravitation, requiring a little amendment to make them strictly correct, and below we give in the form of an equation Kepler's statement of the Third Law together with Newton's amendment of it. In these equations--

_T_ = Periodic time of any planet;

_a_ = One half the major axis of its...o...b..t;

_m_ = Its ma.s.s;

_M_ = The ma.s.s of the sun;

_k_ = The gravitation constant corresponding to the particular set of units in which _T_, _a_, _m_, and _M_ are expressed.

(Kepler) a^{3}/T^{2} = h; (Newton) a^{3}/T^{2} = k (M + m).

Kepler's idea was: For every planet which moves around the sun, _a^{3}_ divided by _T^{2}_ always gives the same quotient, _h_; and he did not concern himself with the significance of this quotient further than to note that if the particular _a_ and _T_ which belong to any planet--e. g., the earth--be taken as the units of length and time, then the quotient will be 1. Newton, on the other hand, attached a meaning to the quotient, and showed that it is equal to the product obtained by multiplying the sum of the two ma.s.ses, planet and sun, by a number which is always the same when we are dealing with the action of gravitation, whether it be between the sun and planet, or between moon and earth, or between the earth and a roast of beef in the butcher's scales, provided only that we use always the same units with which to measure times, distances, and ma.s.ses.

Numerically, Newton's correction to Kepler's Third Law does not amount to much in the motion of the planets. Jupiter, which shows the greatest effect, makes the circuit of his...o...b..t in 4,333 days instead of 4,335, which it would require if Kepler's law were strictly true. But in another respect the change is of the utmost importance, since it enables us to extend Kepler's law, which relates solely to the sun and its planets, to other attracting bodies, such as the earth, moon, and stars.

Thus for the moon's motion around the earth we write--

(240,000^{3})/(27.32^{2}) = k (1 + 1/81),

from which we may find that, with the units here employed, the earth's ma.s.s as the unit of ma.s.s, the mean solar day as the unit of time, and the mile as the unit of distance--

k = 1830 10^{10}.

If we introduce this value of _k_ into the corresponding equation, which represents the motion of the earth around the sun, we shall have--

a^{3}/(365.25)^{2} = 1830 10^{10} (333,000 + 1),

where the large number in the parenthesis represents the number of times the ma.s.s of the sun is greater than the ma.s.s of the earth. We shall find by solving this equation that _a_, the mean distance of the sun from the earth, is very approximately 93,000,000 miles.

113. ANOTHER METHOD OF DETERMINING THE SUN'S DISTANCE.--This will be best appreciated by a reference to Fig. 17. It appears here that the earth makes its nearest approach to the orbit of Mars in the month of August, and if in any August Mars happens to be in opposition, its distance from the earth will be very much less than the distance of the sun from the earth, and may be measured by methods not unlike those which served for the moon. If now the orbits of Mars and the earth were circles having their centers at the sun this distance between them, which we may represent by _D_, would be the difference of the radii of these orbits--

D = a'' - a',

where the accents '', ' represent Mars and the earth respectively.

Kepler's Third Law furnishes the relation--

(a'')^{3}/(T'')^{2} = (a')^{3}/(T')^{2};

and since the periodic times of the earth and Mars, _T'_, _T''_, are known to a high degree of accuracy, these two equations are sufficient to determine the two unknown quant.i.ties, _a'_, _a''_--i. e., the distance of the sun from Mars as well as from the earth. The first of these equations is, of course, not strictly true, on account of the elliptical shape of the orbits, but this can be allowed for easily enough.

In practice it is found better to apply this method of determining the sun's distance through observations of an asteroid rather than observations of Mars, and great interest has been aroused among astronomers by the discovery, in 1898, of an asteroid, or planet, Eros, which at times comes much closer to the earth than does Mars or any other heavenly body except the moon, and which will at future oppositions furnish a more accurate determination of the sun's distance than any hitherto available. Observations for this purpose are being made at the present time (October, 1900).

Many other methods of measuring the sun's distance have been devised by astronomers, some of them extremely ingenious and interesting, but every one of them has its weak point--e. g., the determination of the ma.s.s of the earth in the first method given above and the measurement of _D_ in the second method, so that even the best results at present are uncertain to the extent of 200,000 miles or more, and astronomers, instead of relying upon any one method, must use all of them, and take an average of their results. According to Professor Harkness, this average value is 92,796,950 miles, and it seems certain that a line of this length drawn from the earth toward the sun would end somewhere within the body of the sun, but whether on the nearer or the farther side of the center, or exactly at it, no man knows.

114. PARALLAX AND DISTANCE.--It is quite customary among astronomers to speak of the sun's parallax, instead of its distance from the earth, meaning by parallax its difference of direction as seen from the center and surface of the earth--i. e., the angle subtended at the sun by a radius of the earth placed at right angles to the line of sight. The greater the sun's distance the smaller will this angle be, and it therefore makes a subst.i.tute for the distance which has the advantage of being represented by a small number, 8".8, instead of a large one.

The books abound with ill.u.s.trations intended to help the reader comprehend how great is a distance of 93,000,000 miles, but a single one of these must suffice here. To ride 100 miles a day 365 days in the year would be counted a good bicycling record, but the rider who started at the beginning of the Christian era and rode at that rate toward the sun from the year 1 A. D. down to the present moment would not yet have reached his destination, although his journey would be about three quarters done. He would have crossed the orbit of Venus about the time of Charlemagne, and that of Mercury soon after the discovery of America.

115. SIZE AND DENSITY OF THE SUN.--Knowing the distance of the sun, it is easy to find from the angle subtended by its diameter (32 minutes of arc) that the length of that diameter is 865,000 miles. We recall in this connection that the diameter of the moon's _orbit_ is only 480,000 miles, but little more than half the diameter of the sun, thus affording abundant room inside the sun, and to spare, for the moon to perform the monthly revolution about its...o...b..t, as shown in Fig. 65.

[Ill.u.s.tration: FIG. 65.--The sun's size.--YOUNG.]

In the same manner in which the density of the moon was found from its ma.s.s and diameter, the student may find from the ma.s.s and diameter of the sun given above that its mean density is 1.4 times that of water.

This is about the same as the density of gravel or soft coal, and is just about one quarter of the average density of the earth.

We recall that the small density of the moon was accounted for by the diminished weight of objects upon it, but this explanation can not hold in the case of the sun, for not only is the density less but the force of gravity (weight) is there 28 times as great as upon the earth. The athlete who here weighs 175 pounds, if transported to the surface of the sun would weigh more than an elephant does here, and would find his bones break under his own weight if his muscles were strong enough to hold him upright. The tremendous pressure exerted by gravity at the surface of the sun must be surpa.s.sed below the surface, and as it does not pack the material together and make it dense, we are driven to one of two conclusions: Either the stuff of which the sun is made is altogether unlike that of the earth, not so readily compressed by pressure, or there is some opposing influence at work which more than balances the effect of gravity and makes the solar stuff much lighter than the terrestrial.

116. MATERIAL OF WHICH THE SUN IS MADE.--As to the first of these alternatives, the spectroscope comes to our aid and shows in the sun's spectrum (Fig. 50) the characteristic line marked _D_, which we know always indicates the presence of sodium and identifies at least one terrestrial substance as present in the sun in considerable quant.i.ty.

The lines marked _C_ and _F_ are produced by hydrogen, which is one of the const.i.tuents of water, _E_ shows calcium to be present in the sun, _b_ magnesium, etc. In this way it has been shown that about one half of our terrestrial elements, mainly the metallic ones, are present as gases on or near the sun's surface, but it must not be inferred that elements not found in this way are absent from the sun. They may be there, probably are there, but the spectroscopic proof of their presence is more difficult to obtain. Professor Rowland, who has been prominent in the study of the solar spectrum, says: "Were the whole earth heated to the temperature of the sun, its spectrum would probably resemble that of the sun very closely."