A Text-Book of Astronomy Part 23

The Milky Way is not so simple in its structure as might at first be thought, but a clear and moonless night is required to bring out its details. The nature of these details, the structure of the galaxy, its shape and extent, the arrangement of its parts, and their relation to stars and nebulae in general, have been subjects of much speculation by astronomers and others who have sought to trace out in this way what is called the _construction of the heavens_.

220. DISTRIBUTION OF THE STARS.--How far out into s.p.a.ce do the stars extend? Are they limited or infinite in number? Do they form a system of mutually related parts, or are they bunched promiscuously, each for itself, without reference to the others? Here is what has been well called "the most important problem of stellar astronomy, the acquisition of well-founded ideas about the distribution of the stars." While many of the ideas upon this subject which have been advanced by eminent astronomers and which are still current in the books are certainly wrong, and few of their speculations along this line are demonstrably true, the theme itself is of such grandeur and permanent interest as to demand at least a brief consideration. But before proceeding to its speculative side we need to collect facts upon which to build, and these, however inadequate, are in the main simple and not far to seek.

Parallaxes, proper motions, motions in the line of sight, while pertinent to the problem of stellar distribution, are of small avail, since they are far too scanty in number and relate only to limited cla.s.ses of stars, usually the very bright ones or those nearest to the sun. Almost the sole available data are contained in the brightness of the stars and the way in which they seem scattered in the sky. The most casual survey of the heavens is enough to show that the stars are not evenly sprinkled upon it. The lucid stars are abundant in some regions, few in others, and the laborious star gauges, actual counting of the stars in sample regions of the sky, which have been made by the Herschels, Celoria, and others, suffice to show that this lack of uniformity in distribution is even more markedly true of the telescopic stars.

The rate of increase in the number of stars from one magnitude to the next, as shown in -- 187, is proof of another kind of irregularity in their distribution. It is not difficult to show, mathematically, that if in distant regions of s.p.a.ce the stars were on the average as numerous and as bright as they are in the regions nearer to the sun, then the stars of any particular magnitude ought to be four times as numerous as those of the next brighter magnitude--e. g., four times as many sixth-magnitude stars as there are fifth-magnitude ones. But, as we have already seen in -- 187, by actual count there are only three times as many, and from the discrepancy between these numbers, an actual threefold increase instead of a fourfold one, we must conclude that on the whole the stars near the sun are either bigger or brighter or more numerous than in the remoter depths of s.p.a.ce.

221. THE STELLAR SYSTEM.--But the arrangement of the stars is not altogether lawless and chaotic; there are traces of order and system, and among these the Milky Way is the dominant feature. Telescope and photographic plate alike show that it is made up of stars which, although quite irregularly scattered along its course, are on the average some twenty times as numerous in the galaxy as at its poles, and which thin out as we recede from it on either side, at first rapidly and then more slowly. This tendency to cl.u.s.ter along the Milky Way is much more p.r.o.nounced among the very faint telescopic stars than among the brighter ones, for the lucid stars and the telescopic ones down to the tenth or eleventh magnitude, while very plainly showing the cl.u.s.tering tendency, are not more than three times as numerous in the galaxy as in the constellations most remote from it. It is remarkable as showing the condensation of the brightest stars that one half of all the stars in the sky which are brighter than the second magnitude are included within a belt extending 12 on either side of the center line of the galaxy.

In addition to this general condensation of stars toward the Milky Way, there are peculiarities in the distribution of certain cla.s.ses of stars which are worth attention. Planetary nebulae and new stars are seldom, if ever, found far from the Milky Way, and stars with bright lines in their spectra especially affect this region of the sky. Stars with spectra of the first type--Sirian stars--are much more strongly condensed toward the Milky Way than are stars of the solar type, and in consequence of this the Milky Way is peculiarly rich in light of short wave lengths.

Resolvable star cl.u.s.ters are so much more numerous in the galaxy than elsewhere, that its course across the sky would be plainly indicated by their grouping upon a map showing nothing but cl.u.s.ters of this kind.

On the other hand, nebulae as a cla.s.s show a distinct aversion for the galaxy, and are found most abundantly in those parts of the sky farthest from it, much as if they represented raw material which was lacking along the Milky Way, because already worked up to make the stars which are there so numerous.

222. RELATION OF THE SUN TO THE MILKY WAY.--The fact that the galaxy is a _great circle_ of the sky, but only of moderate width, shows that it is a widely extended and comparatively thin stratum of stars within which the solar system lies, a member of the galactic system, and probably not very far from its center. This position, however, is not to be looked upon as a permanent one, since the sun's motion, which lies nearly in the plane of the Milky Way, is ceaselessly altering its relation to the center of that system, and may ultimately carry us outside its limits.

The Milky Way itself is commonly thought to be a ring, or series of rings, like the coils of the great spiral nebula in Andromeda, and separated from us by a s.p.a.ce far greater than the thickness of the ring itself. Note in Figs. 149 and 150 how the background is made up of bright and dark parts curiously interlaced, and presenting much the appearance of a thin sheet of cloud through which we look to barren s.p.a.ce beyond. While, mathematically, this appearance can not be considered as proof that the galaxy is in fact a distant ring, rather than a sheet of starry matter stretching continuously from the nearer stellar neighbors of the sun into the remotest depths of s.p.a.ce, nevertheless, most students of the question hold it to be such a ring of stars, which are relatively close together while its center is comparatively vacant, although even here are some hundreds of thousands of stars which on the whole have a tendency to cl.u.s.ter near its plane and to crowd together a little more densely than elsewhere in the region where the sun is placed.

223. DIMENSIONS OF THE GALAXY.--The dimensions of this stellar system are wholly unknown, but there can be no doubt that it extends farther in the plane of the Milky Way than at right angles to that plane, for stars of the fifteenth and sixteenth magnitudes are common in the galaxy, and testify by their feeble light to their great distance from the earth, while near the poles of the Milky Way there seem to be few stars fainter than the twelfth magnitude. Herschel, with his telescope of 18 inches aperture, could count in the Milky Way more than a dozen times as many stars per square degree as could Celoria with a telescope of 4 inches aperture; but around the poles of the galaxy the two telescopes showed practically the same number of stars, indicating that here even the smaller telescope reached to the limits of the stellar system. Very recently, indeed, the telescope with which Fig. 140 was photographed seems to have reached the farthest limit of the Milky Way, for on a photographic plate of one of its richest regions Roberts finds it completely resolved into stars which stand out upon a black background with no trace of nebulous light between them.

224. BEYOND THE MILKY WAY.--Each additional step into the depths of s.p.a.ce brings us into a region of which less is known, and what lies beyond the Milky Way is largely a matter of conjecture. We shrink from thinking it an infinite void, endless emptiness, and our intellectual sympathies go out to Lambert's speculation of a universe filled with stellar systems, of which ours, bounded by the galaxy, is only one.

There is, indeed, little direct evidence that other such systems exist, but the Andromeda nebula is not altogether unlike a galaxy with a central cloud of stars, and in the southern hemisphere, invisible in our lat.i.tudes, are two remarkable stellar bodies like the Milky Way in appearance, but cut off from all apparent connection with it, much as we might expect to find independent stellar systems, if such there be.

These two bodies are known as the Magellanic clouds, and individually bear the names of Major and Minor Nubecula. According to Sir John Herschel, "the Nubecula Major, like the Minor, consists partly of large tracts and ill-defined patches of irresolvable nebula, and of nebulosity in every stage of resolution up to perfectly resolved stars like the Milky Way, as also of regular and irregular nebulae ... of globular cl.u.s.ters in every stage of resolvability, and of cl.u.s.tering groups sufficiently insulated and condensed to come under the designation of cl.u.s.ters of stars." Its outlines are vague and somewhat uncertain, but surely include an area of more than 40 square degrees--i. e., as much as the bowl of the Big Dipper--and within this area Herschel counted several hundred nebulae and cl.u.s.ters "which far exceeds anything that is to be met with in any other region of the heavens." Although its excessive complexity of detail baffled Herschel's attempts at artistic delineation, it has yielded to the modern photographic processes, which show the Nubecula Major to be an enormous spiral nebula made up of subordinate stars, nebulae, and cl.u.s.ters, as is the Milky Way.

Compared with the Andromeda nebula, its greater angular extent suggests a smaller distance, although for the present all efforts at determining the parallax of either seem hopeless. But the spiral form which is common to both suggests that the Milky Way itself may be a gigantic spiral nebula near whose center lies the sun, a humble member of a great cl.u.s.ter of stars which is roughly globular in shape, but flattened at the poles of the galaxy and completely encircled by its coils. However plausible such a view may appear, it is for the present, at least, pure hypothesis, although vigorously advocated by Easton, who bases his argument upon the appearance of the galaxy itself.

225. ABSORPTION OF STARLIGHT.--We have had abundant occasion to learn that at least within the confines of the solar system meteoric matter, cosmic dust, is profusely scattered, and it appears not improbable that the same is true, although in smaller degree, in even the remoter parts of s.p.a.ce. In this case the light which comes from the farther stars over a path requiring many centuries to travel, must be in some measure absorbed and enfeebled by the obstacles which it encounters on the way.

Unless celestial s.p.a.ce is transparent to an improbable degree the remoter stars do not show their true brightness; there is a certain limit beyond which no star is able to send its light, and beyond which the universe must be to us a blank. A lighthouse throws into the fog its beams only to have them extinguished before a single mile is pa.s.sed, and though the celestial lights s.h.i.+ne farther, a limit to their reach is none the less certain if meteoric dust exists outside the solar system.

If there is such an absorption of light in s.p.a.ce, as seems plausible, the universe may well be limitless and the number of stellar systems infinite, although the most attenuated of dust clouds suffices to conceal from us and to shut off from our investigation all save a minor fraction of it and them.

CHAPTER XV

GROWTH AND DECAY

226. NATURE OF THE PROBLEM.--To use a common figure of speech, the universe is alive. We have found it filled with an activity that manifests itself not only in the motions of the heavenly bodies along their orbits, but which extends to their minutest parts, the molecules and atoms, whose vibrations furnish the radiant energy given off by sun and stars. Some of these activities, such as the motions of the heavenly bodies in their orbits, seem fitted to be of endless duration; while others, like the radiation of light and heat, are surely temporary, and sooner or later must come to an end and be replaced by something different. The study of things as they are thus leads inevitably to questions of what has been and what is to be. A sound science should furnish some account of the universe of yesterday and to-morrow as well as of to-day, and we need not shrink from such questions, although answers to them must be vague and in great measure speculative.

The historian of America finds little difficulty with events of the nineteenth century or even the eighteenth, but the sources of information about America in the fifteenth century are much less definite; the tenth century presents almost a blank, and the history of American mankind in the first century of the Christian era is wholly unknown. So, as we attempt to look into the past or the future of the heavens, we must expect to find the mists of obscurity grow denser with remoter periods until even the vaguest outlines of its development are lost, and we are compelled to say, beyond this lies the unknown. Our account of growth and decay in the universe, therefore, can not aspire to cover the whole duration of things, but must be limited in its scope to certain chapters whose epochs lie near to the time in which we live, and even for these we need to bear constantly in mind the logical bases of such an inquiry and the limitations which they impose upon us.

227. LOGICAL BASES AND LIMITATIONS.--The first of these bases is: An adequate knowledge of the present universe. Our only hope of reading the past and future lies in an understanding of the present; not necessarily a complete knowledge of it, but one which is sound so far as it goes.

Our position is like that of a detective who is called upon to unravel a mystery or crime, and who must commence with the traces that have been left behind in its commission. The foot print, the blood stain, the broken gla.s.s must be examined and compared, and fas.h.i.+oned into a theory of how they came to be; and as a wrong understanding of these elements is sure to vitiate the theories based upon them, so a false science of the universe as it now is, will surely give a false account of what it has been; while a correct but incomplete knowledge of the present does not wholly bar an understanding of the past, but only puts us in the position of the detective who correctly understands what he sees but fails to take note of other facts which might greatly aid him.

The second basis of our inquiry is: The a.s.sumed permanence of natural laws. The law of gravitation certainly held true a century ago as well as a year ago, and for aught we know to the contrary it may have been a law of the universe for untold millions of years; but that it has prevailed for so long a time is a pure a.s.sumption, although a necessary one for our purpose. So with those other laws of mathematics and mechanics and physics and chemistry to which we must appeal; if there was ever a time or place in which they did not hold true, that time and place lie beyond the scope of our inquiry, and are in the domain inaccessible to scientific research. It is for this reason that science knows nothing and can know nothing of a creation or an end of the universe, but considers only its orderly development within limited periods of time. What kind of a past universe would, under the operation of known laws, develop into the present one, is the question with which we have to deal, and of it we may say with Helmholtz: "From the standpoint of science this is no idle speculation but an inquiry concerning the limitations of its methods and the scope of its known laws."

To ferret out the processes by which the heavenly bodies have been brought to their present condition we seek first of all for lines of development now in progress which tend to change the existing order of things into something different, and, having found these, to trace their effects into both past and future. Any force, however small, or any process, however slow, may produce great results if it works always and ceaselessly in the same direction, and it is in these processes, whose trend is never reversed, that we find a partial clew to both past and future.

228. THE SUN'S DEVELOPMENT.--The first of these to claim our attention is the shrinking of the sun's diameter which, as we have seen in Chapter X, is the means by which the solar output of radiant energy is maintained from year to year. Its amount, only a few feet per annum, is far too small to be measured with any telescope; but it is c.u.mulative, working century after century in the same direction, and, given time enough, it will produce in the future, and must have produced in the past, enormous transformations in the sun's bulk and equally significant changes in its physical condition.

Thus, as we attempt to trace the sun's history into the past, the farther back we go the greater shall we expect to find its diameter and the greater the s.p.a.ce (volume) through which its molecules are spread.

By reason of this expansion its density must have been less then than now, and by going far enough back we may even reach a time at which the density was comparable with what we find in the nebulae of to-day. If our ideas of the sun's present mechanism are sound, then, as a necessary consequence of these, its past career must have been a process of condensation in which its component particles were year by year packed closer together by their own attraction for each other. As we have seen in -- 126, this condensation necessarily developed heat, a part of which was radiated away as fast as produced, while the remainder was stored up, and served to raise the temperature of the sun to what we find it now. At the present time this temperature is a chief obstacle to further shrinkage, and so powerfully opposes the gravitative forces as to maintain nearly an equilibrium with them, thus causing a very slow rate of further condensation. But it is not probable that this was always so.

In the early stages of the sun's history, when the temperature was low, contraction of its bulk must have been more rapid, and attempts have been made by the mathematicians to measure its rate of progress and to determine how long a time has been consumed in the development of the present sun from a primitive nebulous condition in which it filled a s.p.a.ce of greater diameter than Neptune's...o...b..t. Of course, numerical precision is not to be expected in results of this kind, but, from a consideration of the greatest amount of heat that could be furnished by the shrinkage of a ma.s.s equal to that of the sun, it seems that the period of this development is to be measured in tens of millions or possibly hundreds of millions of years, but almost certainly does not reach a thousand millions.

229. THE SUN'S FUTURE.--The future duration of the sun as a source of radiant energy is surely to be measured in far smaller numbers than these. Its career as a dispenser of light and heat is much more than half spent, for the shrinkage results in an ever-increasing density, which makes its gaseous substance approximate more and more toward the behavior of a liquid or solid, and we recall that these forms of matter can not by any further condensation restore the heat whose loss through radiation caused them to contract. They may continue to shrink, but their temperature must fall, and when the sun's substance becomes too dense to obey the laws of gaseous matter its surface must cool rapidly as a consequence of the radiation into surrounding s.p.a.ce, and must congeal into a crust which, although at first incandescent, will speedily become dark and opaque, cutting off the light of the central portions, save as it may be rent from time to time by volcanic outbursts of the still incandescent ma.s.s beneath. But such outbursts can be of short duration only, and its final condition must be that of a dark body, like the earth or moon, no longer available as a source of radiant energy. Even before the formation of a solid crust it is quite possible that the output of light and heat may be seriously diminished by the formation of dense vapors completely enshrouding it, as is now the case with Jupiter and Saturn. It is believed that these planets were formerly incandescent, and at the present time are in a state of development through which the earth has pa.s.sed and toward which the sun is moving.

According to Newcomb, the future during which the sun can continue to furnish light and heat at its present rate is not likely to exceed 10,000,000 years.

This idea of the sun as a developing body whose present state is only temporary, furnishes a clew to some of the vexing problems of solar physics. Thus the sun-spot period, the distribution of the spots in lat.i.tude, and the peculiar law of rotation of the sun in different lat.i.tudes, may be, and very probably are, results not of anything now operating beneath its photosphere, but of something which happened to it in the remote past--e. g., an unsymmetrical shrinkage or possibly a collision with some other body. At sea the waves continue to toss long after the storm which produced them has disappeared, and, according to the mathematical researches of Wilsing, a profound agitation of the sun's ma.s.s might well require tens of thousands, or even hundreds of thousands of years to subside, and during this time its effects would be visible, like the waves, as phenomena for which the actual condition of things furnishes no apparent cause.

230. THE NEBULAR HYPOTHESIS.--The theory of the sun's progressive contraction as a necessary result of its radiation of energy is comparatively modern, but more than a century ago philosophic students of Nature had been led in quite a different way to the belief that in the earlier stages of its career the sun must have been an enormously extended body whose outer portions reached even beyond the orbit of the remotest planet. Laplace, whose speculations upon this subject have had a dominant influence during the nineteenth century, has left, in a popular treatise upon astronomy, an admirable statement of the phenomena of planetary motion, which suggest and lead up to the nebular theory of the sun's development, and in presenting this theory we shall follow substantially his line of thought, but with some freedom of translation and many omissions.

He says: "To trace out the primitive source of the planetary movements, we have the following five phenomena: (1) These movements all take place in the same direction and nearly in the same plane. (2) The movements of the satellites are in the same direction as those of the planets. (3) The rotations of the planets and the sun are in the same direction as the orbital motions and nearly in the same plane. (4) Planets and satellites alike have nearly circular orbits. (5) The orbits of comets are wholly unlike these by reason of their great eccentricities and inclinations to the ecliptic." That these coincidences should be purely the result of chance seemed to Laplace incredible, and, seeking a cause for them, he continues: "Whatever its nature may be, since it has produced or controlled the motions of the planets, it must have reached out to all these bodies, and, in view of the prodigious distances which separate them, the cause can have been nothing else than a fluid of great extent which must have enveloped the sun like an atmosphere. A consideration of the planetary motions leads us to think that ... the sun's atmosphere formerly extended far beyond the orbits of all the planets and has shrunk by degrees to its present dimensions." This is not very different from the idea developed in -- 228 from a consideration of the sun's radiant energy; but in Laplace's day the possibility of generating the sun's heat by contraction of its bulk was unknown, and he was compelled to a.s.sume a very high temperature for the primitive nebulous sun, while we now know that this is unnecessary. Whether the primitive nebula was hot or cold the shrinkage would take place in much the same way, and would finally result in a star or sun of very high temperature, but its development would be slower if it were hot in the beginning than if it were cold.

But again Laplace: "How did the sun's atmosphere determine the rotations and revolutions of planets and satellites? If these bodies had been deeply immersed in this atmosphere its resistance to their motion would have made them fall into the sun, and we may therefore conjecture that the planets were formed, one by one, at the outer limits of the solar atmosphere by the condensation of zones of vapor which were cast off in the plane of the sun's equator." Here he proceeds to show by an appeal to dynamical principles that something of this kind must happen, and that the matter sloughed off by the nebula in the form of a ring, perhaps comparable to the rings of Saturn or the asteroid zone, would ultimately condense into a planet, which in its turn might shrink and cast off rings to produce satellites.

[Ill.u.s.tration: PIERRE SIMON LAPLACE (1749-1827).]

Planets and satellites would then all have similar motions, as noted at the beginning of this section, since in every case this motion is an inheritance from a common source, the rotation of the primitive nebula about its own axis. "All the bodies which circle around a planet having been thus formed from rings which its atmosphere successively abandoned as rotation became more and more rapid, this rotation should take place in less time than is required for the orbital revolution of any of the bodies which have been cast off, and this holds true for the sun as compared with the planets."

231. OBJECTIONS TO THE NEBULAR HYPOTHESIS.--In Laplace's time this slower rate of motion was also supposed to hold true for Saturn's rings as compared with the rotation of Saturn itself, but, as we have seen in Chapter XI, this ring is made up of a great number of independent particles which move at different rates of speed, and comparing, through Kepler's Third Law, the motion of the inner edge of the ring with the known periodic time of the satellites, we may find that these particles must rotate about Saturn more rapidly than the planet turns upon its axis. Similarly the inner satellite of Mars completes its revolution in about one third of a Martian day, and we find in cases like this grounds for objection to the nebular theory. Compare also Laplace's argument with the peculiar rotations of Ura.n.u.s, Neptune, and their satellites (Chapter XI). Do these fortify or weaken his case?

Despite these objections and others equally serious that have been raised, the nebular theory agrees with the facts of Nature at so many points that astronomers upon the whole are strongly inclined to accept its major outlines as being at least an approximation to the course of development actually followed by the solar system; but at some points--e. g., the formation of planets and satellites through the casting off of nebulous rings--the objections are so many and strong as to call for revision and possibly serious modification of the theory.

One proposed modification, much discussed in recent years, consists in subst.i.tuting for the primitive _gaseous_ nebula imagined by Laplace, a very diffuse cloud of meteoric matter which in the course of its development would become transformed into the gaseous state by rising temperature. From this point of view much of the meteoric dust still scattered throughout the solar system may be only the fragments left over in fas.h.i.+oning the sun and planets. Chamberlin and Moulton, who have recently given much attention to this subject, in dissenting from some of Laplace's views, consider that the primitive nebulous condition must have been one in which the matter of the system was "so brought together as to give low ma.s.s, high momentum, and irregular distribution to the outer part, and high ma.s.s, low momentum, and sphericity to the central part," and they suggest a possible oblique collision of a small nebula with the outer parts of a large one.

232. BODE'S LAW.--We should not leave the theory of Laplace without noting the light it casts upon one point otherwise obscure--the meaning of Bode's law (-- 134). This law, stated in mathematical form, makes a geometrical series, and similar geometrical series apply to the distances of the satellites of Jupiter and Saturn from these planets.

Now, Roche has shown by the application of physical laws to the shrinkage of a gaseous body that its radius at any time may be expressed by means of a certain mathematical formula very similar to Bode's law, save that it involves the amount of time that has elapsed since the beginning of the shrinking process. By comparing this formula with the one corresponding to Bode's law he reaches the conclusion that the peculiar s.p.a.cing of the planets expressed by that law means that they were formed at successive _equal_ intervals of time--i. e., that Mars is as much older than the earth as the earth is older than Venus, etc. The failure of Bode's law in the case of Neptune would then imply that the interval of time between the formation of Neptune and Ura.n.u.s was shorter than that which has prevailed for the other planets. But too much stress should not be placed upon this conclusion. So long as the manner in which the planets came into being continues an open question, conclusions about their time of birth must remain of doubtful validity.

233. TIDAL FRICTION BETWEEN EARTH AND MOON.--An important addition to theories of development within the solar system has been worked out by Prof. G. H. Darwin, who, starting with certain very simple a.s.sumptions as to the present condition of things in earth and moon, derives from these, by a strict process of mathematical reasoning, far-reaching conclusions of great interest and importance. The key to these conclusions lies in recognition of the fact that through the influence of the tides (-- 42) there is now in progress and has been in progress for a very long time, a gradual transfer of motion (moment of momentum) from the earth to the moon. The earth's motion of rotation is being slowly destroyed by the friction of the tides, as the motion of a bicycle is destroyed by the friction of a brake, and, in consequence of this slowing down, the moon is pushed farther and farther away from the earth, so that it now moves in a larger orbit than it had some millions of years ago.

Fig. 24 has been used to ill.u.s.trate the action of the moon in raising tides upon the earth, but in accordance with the third law of motion (-- 36) this action must be accompanied by an equal and contrary reaction whose nature may readily be seen from the same figure. The moon moves about its...o...b..t from west to east and the earth rotates about its axis in the same direction, as shown by the curved arrow in the figure. The tidal wave, _I_, therefore points a little _in advance_ of the moon's position in its...o...b..t and by its attraction must tend to pull the moon ahead in its...o...b..tal motion a little faster than it would move if the whole substance of the earth were placed inside the sphere represented by the broken circle in the figure. It is true that the tidal wave at _I''_ pulls back and tends to neutralize the effect of the wave at _I_, but on the whole the tidal wave nearer the moon has the stronger influence, and the moon on the whole moves a very little faster, and by virtue of this added impetus draws continually a little farther away from the earth than it would if there were no tides.

234. CONSEQUENCES OF TIDAL FRICTION UPON THE EARTH.--This process of moving the moon away from the earth is a c.u.mulative one, going on century after century, and with reference to it the moon's...o...b..t must be described not as a circle or ellipse, or any other curve which returns into itself, but as a spiral, like the balance spring of a watch, each of whose coils is a little larger than the preceding one, although this excess is, to be sure, very small, because the tides themselves are small and the tidal influence feeble when compared with the whole attraction of the earth for the moon. But, given time enough, even this small force may accomplish great results, and something like 100,000,000 years of past opportunity would have sufficed for the tidal forces to move the moon from close proximity with the earth out to its present position.

For millions of years to come, if moon and earth endure so long, the distance between them must go on increasing, although at an ever slower rate, since the farther away the moon goes the smaller will be the tides and the slower the working out of their results. On the other hand, when the moon was nearer the earth than now, tidal influences must have been greater and their effects more rapidly produced than at the present time, particularly if, as seems probable, at some past epoch the earth was hot and plastic like Jupiter and Saturn. Then, instead of tides in the water of the sea, such as we now have, the whole substance of the earth would respond to the moon's attraction in _bodily tides_ of semi-fluid matter not only higher, but with greater internal friction of their molecules one upon another, and correspondingly greater effect in checking the earth's rotation.

But, whether the tide be a bodily one or confined to the waters of the sea, so long as the moon causes it to flow there will be a certain amount of friction which will affect the earth much as a brake affects a revolving wheel, slowing down its motion, and producing thus a longer day as well as a longer month on account of the moon's increased distance. Slowing down the earth's rotation is the direct action of the moon upon the earth. Pus.h.i.+ng the moon away is the form in which the earth's equal and contrary reaction manifests itself.

235. CONSEQUENCES OF TIDAL FRICTION UPON THE MOON.--When the moon was plastic the earth must have raised in it a bodily tide manifold greater than the lunar tides upon the earth, and, as we have seen in Chapter IX, this tide has long since worn out the greater part of the moon's rotation and brought our satellite to the condition in which it presents always the same face toward the earth.

These two processes, slowing down the rotation and pus.h.i.+ng away the disturbing body, are inseparable--one requires the other; and it is worth noting in this connection that when for any reason the tide ceases to flow, and the tidal wave takes up a permanent position, as it has in the moon (-- 99), its work is ended, for when there is no motion of the wave there can be no friction to further reduce the rate of rotation of the one body, and no reaction to that friction to push away the other.

But this permanent and stationary tidal wave in the moon, or elsewhere, means that the satellite presents always the same face toward its planet, moving once about its...o...b..t in the time required for one revolution upon its axis, and the tide raised by the moon upon the earth tends to produce here the result long since achieved in our satellite, to make our day and month of equal length, and to make the earth turn always the same side toward the moon. But the moon's tidal force is small compared with that of the earth, and has a vastly greater momentum to overcome, so that its work upon the earth is not yet complete.

According to Thomson and Tait, the moon must be pushed off another hundred thousand miles, and the day lengthened out by tidal influence to seven of our present weeks before the day and the lunar month are made of equal length, and the moon thereby permanently hidden from one hemisphere of the earth.

236. THE EARTH-MOON SYSTEM.--Retracing into the past the course of development of the earth and moon, it is possible to reach back by means of the mathematical theory of tidal friction to a time at which these bodies were much nearer to each other than now, but it has not been found possible to trace out the mode of their separation from one body into two, as is supposed in the nebular theory. In the earliest part of their history accessible to mathematical a.n.a.lysis they are distinct bodies at some considerable distance from each other, with the earth rotating about an axis more nearly perpendicular to the moon's...o...b..t and to the ecliptic than is now the case. Starting from such a condition, the lunar tides, according to Darwin, have been instrumental in tipping the earth's rotation axis into its present oblique position, and in determining the eccentricity of the moon's...o...b..t and its position with respect to the ecliptic as well as the present length of day and month.

337. TIDAL FRICTION UPON THE PLANETS.--The satellites of the outer planets are equally subject to influences of this kind, and there appears to be independent evidence that some of them, at least, turn always the same face toward their respective planets, indicating that the work of tidal friction has here been accomplished. We saw in Chapter XI that it is at present an open question whether the inner planets, Venus and Mercury, do not always turn the same face toward the sun, their day and year being of equal length. In addition to the direct observational evidence upon this point, Schiaparelli has sought to show by an appeal to tidal theory that such is probably the case, at least for Mercury, since the tidal forces which tend to bring about this result in that planet are about as great as the forces which have certainly produced it in the case of the moon and Saturn's satellite, j.a.petus. The same line of reasoning would show that every satellite in the solar system, save possibly the newly discovered ninth satellite of Saturn, must, as a consequence of tidal friction, turn always the same face toward its planet.