IN our first two chapters we saw what sign-posts in the sky there are pointing to the course evolution of a solar system probably follows, and secondly, what evidence there is that our system took this road. We now come to a question not so easy to precise,—the actual details of the journey. It is always difficult to descend from a glittering panoramic survey to particular path-finding. The obstacles loom so much larger on a near approach. Most men shy at decisions and shun self-committal to any positive course, but when it comes to constructing a cosmogony, few at all qualified hesitate to frame one if the old does not suit. The safety in so doing lies in the fact that nothing in particular happens if it refuses to work. Its absurdity is promptly shown up, it is true, by some one else. For there is almost as good a trade in exposing cosmogonies as in constructing them. But no special opprobrium attaches to failure, because everybody has failed, from Laplace down, or up, as you are pleased to consider it. Besides it is really not so easy to do, Attacking the subject in this judicial spirit, the reader can hardly expect me to satisfy him with a cosmogony entirely home-made, but at best to pursue a happy middle course between creator and critic, advocating only such portions as happen to be my own, while sternly exposing the mistakes of others. In undertaking the hazardous climb toward the origin of things two qualities are necessary in the explorer: a quick eye for possibilities and a steady head in testing them. Without the discernment to perceive relations no ascent to first principles is possible; and without the support of quantitative criterion, one is in danger of becoming giddy from one’s own imagination. Congruities must first hint at a path; physical laws then determine its feasibility. An eye for congruities is the first essential. For congruity alone accuses an underlying law. It is the analogic that with logic leads to great generalizations. Certain concords of the sort in the motions of This basic fact we may consider certain. But from it we would fain go on to find out how it evolved. To do so the same process must be followed. Considering, then, our solar system from this point of view, one cannot but be struck by some further congruities it presents. These are not quite those that inspired Laplace, because of discoveries since, and demand in consequence a theory different from his. The out about constructing a theory is that fresh facts will come along and knock for admission after the door is shut. They prove irreconcilables because they were not consulted in advance. The consequence is that since Laplace’s time new relations have come to From the relations which advance has left unchanged we pass to those phenomena which seemed to present congruities in Laplace’s day, but which have since proved void owing to subsequent detection of exceptions. Time prevents my making the catalogue complete, but the reader shall be shown enough to satisfy him of the problem’s complexity and to whet his desire for further research—on the part, preferably, of others. Chart showing increasing tilts of the major planets. First comes, then, the rotations of the planets upon their axes, which Laplace supposed to be all in the same direction, counter to the hands of a clock; for the heavens mark time oppositely from us. All those within and including Saturn, the only ones he knew, turn, indeed, in the same sense that they travel round the Sun. But Uranus departs from that direction by a right angle, wallowing rather than spinning in his Another congruity supposed to exist a century ago was the exemplary agreement of all the satellites to follow in their planetary circuits the pattern set them by their primaries round the Sun. But as man has penetrated farther into space and photographic plates have come to be employed, satellites have been revealed which depart from this orderly arrangement. This is the case with the ninth, the outermost, satellite of Saturn and with the eighth, the outermost, of Jupiter. But, as before, the breaking down of one congruity seems but the establishing of another. It appears that only the most distant satellites are permitted such unconformity of demeanor. For departure from the supposed orthodoxy occurs in both instances where the distance is most, and does not occur in the case of all the other satellites found since Laplace’s day, eleven in number, nearer their planets. A third congruity formerly believed in has suffered a like fate; to wit, that satellites always moved in or near the equatorial plane of their primary. All those first discovered did; the four large ones of Jupiter, the main ones of Saturn, and probably those of Uranus and Neptune. Even the satellites of Mars conformed. Iapetus alone seemed to make exception, and that by a glossable amount. But this orderliness, too, has been disposed of, only, like the others, to experience a resurrection in a different form. On examining more precisely the inclinations of these orbits some years ago, an interesting relation between them and the distances of the satellites from their primaries forced itself on my notice. The tilt A diagram will make this clear. The kernel of it dates from the lectures then delivered before the Massachusetts Institute of Technology in 1901. The interesting thing now about it is that the congruity there pointed out has been conformed to by every satellite discovered since,—the sixth, seventh, and eighth of Jupiter and the ninth and tenth of Saturn. It is evident that we already know enough of the geniture of our system to prophesy something about it and have the prophecy come true. Closely connected with the previous relation is a fourth concordance clearly of mechanical origin, the relation of the orbital eccentricities of the satellites to their distances from their respective planets. The satellites pursue more and more eccentric orbits according as they stand removed from planetary proximity. A fifth congruity is no less striking. All the satellites of all the planets that we can observe well enough to judge of turn the same face always to their lords. That the Moon does so to the Earth is a fact of everyday knowledge, and the telescope hints that the same respectful regard is paid by Jupiter’s and Saturn’s retinues to them. What is still more remarkable, Mercury and Venus turn out to observe the like Last is a remarkable congruity which study disclosed to me likewise some years ago, and which has received corroboration in discoveries since. This congruity is the peculiar arrangement of the masses in the solar system. Consider first the way in which the several planets, as respects size, stand ordered in distance from the sun. Nearest to him is Mercury, the smallest of all the principal ones. Venus and the Earth follow, each larger than the last; then comes Mars, of distinctly less bulk, and so to the asteroids, of almost none. After this the mass rises again to its maximum in Jupiter, and then subsequently falls through Saturn to Uranus and Neptune. Here we mark a more or less regular gradation between mass and position, a curve in which there are two ups and downs, the outer swell being much the larger, though the inner, too, is sufficiently pronounced. Now turn to Saturn and his family, which is the most numerous of the secondary systems and that having the greatest span. Under Saturn’s wing, as it were, is the ring, itself a congeries of tiny satellites. Then comes Mimas, the smallest of the principal ones; then Enceladus, a Masses of planets and satellites. Striking as such analogous ordering is, it is not all. For, scanning the Jovian system, we find the main curve here again; Ganymede, the Jupiter or Titan of the system, standing in the same medial position as they. Lastly, taking up Uranus and his family of satellites, the same order is observable there. Titania, the largest, is posted in the centre. Thus the order in which the little and the big are placed with One point to be particularly noticed in these latter-day congruities is that they are not simply general concords like the older ones—the fact that the planets move in one plane or in the same sense in that plane—but detailed placings, ordered according to the distances of the planets from the Sun or of the satellites from the planets. They are thus not simply of the combinative but of the permutative order of probabilities, a much higher one; in other words, the chance that they can be due to chance is multiplicately small. Thus just as these analogies are by so much more remarkable, so are they by so much more cogent. They tell us not only of an evolution, but they speak of the very manner of its work. They do not simply generalize, they specify the mode of action. The difficulty is to understand their language. It is a case of celestial hieroglyphics to which we lack the key. In attempting now to discover how all this came about we notice first that the system could not have originated in the beautifully simple way suggested by Laplace, because of several impossibilities in the path. If rings were shed, as he supposed, from a symmetric contracting mass, they should have resulted in something even more symmetric than we observe to-day. In the next place they could not, it would appear, even if formed, have collected into planets. Nor could there have been an original “fire-mist” with which as a stock in trade Laplace thriftily endowed his nebula to start with—the necessity for which has been likened to our supposed descent from monkeys; but which in truth is as misty a conception of the facts in the one case as it is a monkeying with them in the other. Darwin’s theory distinctly avers that we were not descended from monkeys; and Laplace’s fire-mist under modern examination evaporates away. It is an interesting outcome of modern analysis that the very fact which suggested the annular genesis of planets to Laplace, the rings of Saturn, should now probably be deemed a striking instance of the reverse. Far from its being an exemplar in the heavens of the pristine state of the solar system, we may now see in it a shining pattern of how the devolution of bodies comes about. For instead of typifying an unfortunate set of particles which untoward circumstance has prevented No, the planets probably were otherwise generated and may have looked in their earlier stages as the knots in the spiral nebulÆ do to-day. But this does not mean that we can detail the process [see NOTE 5]. Taking now the congruities for guide, we proceed to see what they affirm or negative. Laplace, when he ventured on his exposition of the system of the world, did so “with the mistrust which everything which is not the direct outcome of observation or calculation must inspire.” To all who know how even figures can lie this caution will seem well timed. The best we can do to keep our heads steady is to lay firm hold Now this generalization finds immediate use in explaining certain features of the solar system. In looking over the congruities it will be seen that deviation from the principal plane of the system or departure from a circular orbit is always associated with smallness in size. The insignificant bodies are the erratic ones. Now it has been shown mathematically in several different ways that when small particles collect into a larger mass, the collisions tend to make the resultant orbit of the combination both more circular and more conformant to the general plane than its constituents. But we may see this more forthrightly by means of the general principle enunciated above. For in fact both results are direct outcomes of the conservation of moment of momentum. Given a certain moment of momentum for the Given a certain moment of momentum, then the energy is least when the bodies all move in one plane and all travel in circles in that plane. As energy is constantly being dissipated while any alteration among the bodies is going on, to coplanarity and circularity of path all the The next principle is of a different character. Half a century ago celestial mechanics dealt with bodies chiefly as points. The Earth was treated as a weighted point, and so was the Sun. This was possible because a sphere acts upon outside bodies as if all its mass were collected at its centre, and the Sun and many of the planets are practically spheres. But when it came to nicer questions of their present behavior and especially of their past career, it grew necessary to take their shape into account in their mutual effects. One of the results was the discovery of the great rÔle played in evolution by tidal action. Inasmuch as the planets are not perfectly rigid bodies, each is subject to tidal deformation by the other, the outside being pulled more than the centre on one side and less on the other. Bodily tides are thus raised in it analogous to the surface tides we see in the ocean, only vastly greater, and these in turn act as a brake on its rotation. Now the retrograde motions occurring in the outermost parts of all the systems, principal and subsidiary, only and always there: the Let us see how tidal action would work. Tidal force would raise bulges, and these, not being carried round with the planet’s rotation except to a certain distance, due to viscosity, must necessarily act as brakes upon the planet’s spin. In consequence of the friction they would thus exert, energy of motion must be lost. So long, then, as tidal forces can come into play, the energy of the system is capable of decrease. According to the last principle we considered, the system cannot be in stable equilibrium until this superfluous energy is lost or until tidal To see this more clearly, take the case of a retrograde spin of a planet as compared with a direct one. The energy of the planet’s spin is the same in both cases, because energy depends on the square of a quantity; to wit, that of the velocity, and is therefore independent of sign. Not so the moment of momentum. For this depends on the first power of the speed, and if positive in the one case, must be negative in the other. The moment of momentum of the whole system, then, is less in the former case, since the moment of momentum of the retrograde rotation must be subtracted from, that of the direct rotation be added to, that of the rest of the system. For a given initial moment of momentum with which the system was endowed at the start, there is, then, superfluous energy in the first state which can be got rid of through reduction to the second. Nature, according to her principles of least exertion, avails herself of the chance of dispensing with it, and a direct rotation results. Sir Robert Ball first suggested this argument. Tidal action accomplishes the end. In checking up a body rotating contrary to the general consensus of spin, its first effect is to start to turn the axis over. For the body is in dynamical unstable equilibrium with regard to the rest of the system. The righting would Related to the initial retrograde rotations of the planets, and in a sense survivals from an earlier state of things, are two of the latest discoveries of motions in the solar system, the retrograde orbital movements of the ninth satellite of Saturn and the eighth of Jupiter. Considered so anomalous as scarcely at first to be believed, it has been stated that they directly contradict the theory of Laplace. This is true; in the same sense and no more in which they directly contradict the contradictor, one of the latest theories. For neither theory has anything to explain them as the result of law. That they cannot be the sport of indifferent chance seems evidenced by their occupying similar external positions in their respective systems. As the product of a law we must regard them, and to find that law we now turn. Suppose the planet originally to have been rotating backward, or in the direction of the hands of a clock. At this time the satellite, After the axial spins have been made over to the same sense, the second consequence of tidal action in the case of two bodies revolving about their common centre of gravity is to slow down both spins until first the smaller and then the larger turn the same face to each other and remain thus constant ever after. Now such is precisely the pass to which we observe the satellites of the planets have come. All that we can be sure of now turn the same face always to their primary. The Moon was the first to betray her attitude, because the one we can best note. On scrutiny, however, Jupiter’s satellites, so far as we can make out, do the like; and Saturn’s, too. And a very proper attitude it is, this regard paid to compelling attraction. Thus one of the congruities we noticed stands accounted for. The satellites could hardly have been at first so observant; time has brought about this unfailing recognition of their lords. Of the peculiar massing of the bodies in the family of the Sun, and the still stranger copying of it in their own domestic circles, little can as yet be said in interpretation. That the planetary families and their ancestral group should agree is not the least strange part of the So much for the details we may deduce of the method of our birth. We perceive unmistakably that our solar system grew to be what it is, and that it developed by agglomeration of its previously shattered fragments into the planets we behold to-day, but exactly how the process progressed we are as yet unable to precise. We are, however, as what I have mentioned and tabled show, every day accumulating data which will enable an eventual determination probably to be reached. From the fact of agglomeration, the essence of the affair, we turn to the traces it has left upon its several offspring. Just as the continued existence to-day of meteorites in statu quo informs us of a previous body from which our nebula sprang; so a physical characteristic of our own earth at the present time shows it to have evolved from that nebula—even though we cannot make out all the steps. Of its having done so, we are far more sure than of how it did. That primitive man perceived that somewhere below him was a fiery region which was not an agreeable abode, is plain from his consigning to such Tophet those whose religious tenets did not square with his own. It was not till man began to bore into the Earth for metallic or potable purposes that he brought to light the generic fact that it was everywhere hotter as one went down. And this not only in a very regular, but in a most speedy, manner. The temperature increased in a really surprising way 1° F. for every sixty-five feet of descent. As the rise continued unabated to the limit of his borings, becoming very unpleasant at its end, it was clear that at a depth of thirty-five miles even so refractory a substance as platinum must melt, and practically all the Earth except a thin crust be molten or even gaseous. Now heat, like money, is easy to dissipate but hard to acquire, as primitive man was the first to realize. It does not come without cause. Being a mode of motion, other motion must have preceded it from which it sprang. So much the doctrine of the conservation of energy teaches us, a doctrine considered now to have been the great scientific heirloom of the nineteenth century to the twentieth, yet which in its The only conceivable motion for thus heating the Earth as a whole was the falling together of its parts. The present heat of the Earth, then, accuses the concourse of particles in the past to its formation, or in other words proves that the Earth was evolved out of material originally more sparcely strewn. It does so not only in a generic but in a most particular manner, for the heat is distributed just where it would be by such a process. It is greater to-day within, increasingly, because when the globe began to cool, the surface necessarily cooled first and established a regular gradient of heat from core to cuticle. It is possible to test this qualitative inference quantitatively and see if the falling together of the meteorites was equal to the task. Knowing the mechanical equivalent of heat, what we do is to calculate the quantity of motion involved and then evaluate it in heat. As we are unaware of the exact law of density of the Earth, and are ignorant of how much was radiated away in the process, the problem is a little like estimating the fortune of a man when we do not know the stocks in which Nor is the Earth the only body in the system which thus argues itself evolved by the falling together of its present constituents. In the larger planets Jupiter and Saturn we seem to see the heat, far as we are away. For the cherry hue they disclose between their brighter belts proves to come from greater absorption there of the green and blue rays of the spectrum, indicating a greater depth of atmosphere traversed. Thus these parts lie at a lower level, and their ruddy hue is just what they should show were they still glowing with a dull red heat. Spectrogram of Jupiter, Moon Comparison. Lowell Observatory. V. M. Slipher. Curiously enough, heat both must have been and then must have been lost. Like the loss of fortune or of friends sometimes in the ennobling of character, it is through its passing away that its effects are realized. For in cooling down from a once heated condition, that train of events occurs which we most commonly particularize as evolution. So far in our survey the march of advance has been through masses of matter, a molar evolution; from this point on it passes into its minute constituents and becomes a molecular one. The one is the necessary prelude to the other. Up to this great turning-point in the history of each member of a solar system we have been busied with the acquisition of heat, though we may not have been aware of it the while. All the motions we have studied tended to that end. During these three |