Astronomers have learnt the lesson as far as it has gone, have noted and registered the state of affairs as it is at present, and their successors will no doubt do the same as changes succeed each other. The day may be inconceivably remote, but it will inevitably come for the rings to be changed into satellites, unless they are disposed of in some other way. It has been said that were the rings to break up, in consequence of their being in a state of unstable equilibrium, they would fall back upon the planet, but that would depend on circumstances. If the motion of their revolution were stopped altogether, they would certainly fall back upon the planet; but if it were not stopped then each molecule would retain its centrifugal force, and would revolve around the primary on its own account, just as, according to very general opinion, it does at present. We do not see why, or for what purpose, these rings could have been separated from Saturn merely to fall back upon him again. It would be rather a strange way of giving a lesson if it were stopped, by a cataclysm of some kind, just when the most interesting part of it was in a fair way of being exhibited. Such a proceeding would assuredly not suit the ideas of those who believe that the solar system has been self-formed by a simple process of evolution.
During the whole process of separation of rings from the original nebula, the nebulous matter would be abandoned in what we may call the form of thin hoop-shaped rings, so that the equatorial region of the nebula would be flat—as we have shown atp. 115—and when the nebula came to be so much reduced that it could abandon no more matter through centrifugal force, its form would be, in some measure, like that of a rotating cylinder terminating at each end in a cap in the form of a segment of a sphere. When explaining the formation of planetary rings, we have seen that in the Jovian nebula thelength of the flat part would have come very soon to be nearly 1,500,000 miles, and that it would increase rapidly. But, remembering that the flattening of the equatorial part must have begun on the original nebula, we see that the flat part must have increased vastly in length before it reached Jupiter, and that by the time the residuary, or solar, nebula was reached—which we made to be only a little over 63,000,000 miles in diameter—the cylindrical part of it would bear no small proportion to that diameter. Taking this form of the nebula into consideration, and also the fact that the separation of matter from it by centrifugal force could not always be absolutely equal all around it, the swaying in its rotary motion produced by the all but inevitable inequality of mass, at the two ends of the cylindrical part, and at the sides of the segmental caps, may have been the cause of the differences in the inclinations of the orbits of the planets to the ecliptic; and especially of why the difference came to be so much greater in the case of Mercury than in any of the others.
In connection with this very reasonable conclusion as to the form of the nebula almost from the beginning, we may add that, when it ceased to throw off rings, it would be very much in the same condition as Saturn is at the present day. Therefore we may conclude with very great safety, that the present form of Saturn is that of a cylinder with segments of spheres forming the ends; and in this manner can account for his square-shouldered appearance, which has puzzled more than one astronomer.
The idea has been very general that in condensing and contracting, the nebula would gradually come to assume the form of a lens of a very pronounced character, from the circumference of which the rings would be abandoned one after the other; but when thoroughly looked into, it is difficult to see how this could be the case. In a sphere of cosmic matter contracting equally all round towards the centre through the force of attraction, it is more natural to suppose that the separation of matter from its equator through centrifugal force, would have a tendency to diminish the equatorial more rapidly than the polar diameter, as we have been trying toshow above, more especially as the attraction of the matter in the rings as they were abandoned one after the other would, in a constantly increasing degree, assist the centrifugal force in facilitating the separation by drawing the matter outwards. Matter falling in from the polar regions would afterwards require to have its motion turned off at right angles before it could be sent off by centrifugal force to the equator, an operation which would be more easily effected in the equatorial regions, where the gravitating motion had only to be retarded; and as very unequal amounts of density could not be created in the interior parts of such a sphere by gravitation, so as to cause pressure outwards, it is difficult to show how the polar diameter could be more rapidly reduced than the equatorial diameter, which was being continually shorn of its length. It may be said that all that we have been writing in the last few pages is absurd, because we have been proceeding on the supposition that the condensation of the nebula was effected at or near its surface. Laplace procured this condition by piling up imponderable heat in his nebula, but he might have got it otherwise. Given a nebula such as the one we are dealing with of 6,600,000,000 miles in diameter, where would condensation be most active? Most undoubtedly where there was the greatest mass of matter. Compare, then, the mass of 1,000,000 miles in diameter at the surface with the mass of the same diameter at the centre, and we cannot hesitate for a moment in concluding that the most active condensation would not be very far from the surface. Not only so, but the same would continue to be the case, at least until the last ring was abandoned. Thus by working upon what may have appeared to be an absurd foundation, i.e. condensation at the surface due to the intense heat of the nebula, we have been able to acquire more correct ideas than we had before, of how the solar system was elaborated. But we shall have much more to say on the same subject hereafter.
There has been a great outcry raised about the rotation of the planets Neptune and Uranus being retrograde, as is correctly concluded to be the case from the revolution of their satellites being retrograde, but we do not see that there has been anygood reason for it. Laplace, no doubt, concluded, wrongly, that the motions of all the bodies of the solar system—as known to him—were direct, and therefore used that conclusion in showing that there were 4000 milliards against 1 in favour of his hypothesis being right; but at the same time it cannot be concluded that he thought that it would be destroyed by the motion of rotation of one or even several of the forty-three bodies turning out to be retrograde; because, when discussing the hypothesis of Buffon, he states, most distinctly, that it is not necessary that the rotation of a planet should be in the same sense as that of its revolution, and that the earth might revolve from east to west, and at the same time the absolute movement of each of its molecules might be directed from west to east. His words as cited by M. Faye in "L'Origine du Monde," at page 158, are:
"A la verité, le mouvement absolu des molécules d'une planète doit être alors dirigé dans le sens du mouvement de son centre de gravité, mais il ne s'ensuit point que le mouvement de rotation de la planète soit dirigé dans le même sens; ainsi la Terre pouvait tourner d'orient en occident, et cependant le mouvement absolu de chacune de ses molécules serait dirigé d'occident en orient, ce qui doit s'appliquer au mouvement de révolution des satellites, dont la direction, dans l'hypothèse dont il s'agit, n'est pas nécessairement la même que celle de la projection des planètes." He seems to say, "This would suit Buffon's hypothesis, but I do not require it for mine." Even were this not so, it would not be very difficult to account for the retrograde rotation of these two planets, but we are not yet prepared to show, in a convincing manner, how these motions were produced. We have to show first how the nebula itself was brought to the dimensions at which we took it up, and there is a great deal to be done before we can show that.
Should our belief in being able to explain how the retrograde rotations of Uranus and Neptune were brought about turn out to be unacceptable, we would not condemn the nebular hypothesis, because, as M. Faye himself says, if we add the asteroids to Laplace's 43 we should have somewhere about 500 bodies, all with direct motion, agreeing with thehypothesis, against 4 that do not, that is about 125 to 1 instead of 43 to 1, which was all Laplace could claim. Moreover, we have not been able to see that M. Faye's objections to it are well founded, rather the contrary; nor can we agree with him when he says that when one point in a hypothesis is found to be erroneous it ought to be abandoned altogether, and something better sought for. Is his something any better? All acquired knowledge has been built up from ideas collected from all sides, and from errors reformed. What would a grammarian say were we to return to him his grammar as useless, because we had found one exception to one of his rules against 125 cases in which we had found it to be right? Perhaps it would put him in mind of the name of a tree. And grammar is not the only case in which we say that the exception confirms the rule.
In taking the nebula to pieces, we have taken no notice of the satellites of Mars, not only because they are so small that they would have had no sensible effect on our calculations, but because we cannot conceive that they could have been abandoned by the planet, when in a nebulous state, in the same manner as the planetary rings are supposed to have been by the parent nebula; and we might simply refer to the dimensions, especially the thinness, we have found for the ring out of which Mercury was formed, for proof of our assertion; but for more satisfactory corroboration, we will go a little deeper into the affair. Let us take the diameters of Mars and of the orbits of his satellites, as they are stated in text-books of astronomy; that is 2957, 11,640 and 29,200 miles respectively, and suppose the diameters of what—in the method we have applied to the planets—we would call the Deimos and Phobos nebulæ to have been 40,000 and 20,420 miles also, respectively; then these two diameters would make the breadth of the ring for the formation of Deimos to have been 9790 miles. With these data, if we go through a series of calculations with respect to this outer satellite, in all respects similar to those we have made for each of the rings of the planets, we shall find that the ring for Deimos would have been only 5·64inchesthick, without taking into account itscondensation during the process of separation. This, of course, points out at once the impossibility of any such operation going on in Nature. We can imagine the possibility of a ring of even millions of miles broad, and of very great tenuity, holding together provided it be hundreds of thousands ofmilesthick, but to think of one 10,000 miles broad and less than 6inchesthick holding together is another affair altogether. With respect to Phobos, it is only necessary to say that he revolves round Mars in considerably less than one-third of the time that he ought to, and is therefore not a legitimate production of the nebular hypothesis any more than Deimos can be. Here, then, we have come upon two bodies, one of which has not been formed in the way, and the other has not the proper motion, prescribed in the hypothesis; but we do not think ourselves justified in declaring it to be worthy of condemnation on that account, seeing that we have found no other difficulty in working out the solar system from it.
Moreover, it is not impossible, nor do we think it at all improbable, that through the course of time astronomers may discover that Phobos is a captured asteroid—perhaps Deimos also—gradually working its way into final annexation. And who can tell how many of these erratic bodies Jupiter and Mars may have captured already? In the dark as it were, for they may have been too small to be noticed when they were being run in. Neither of these two worthies has ever been very much celebrated in song or history for respect for his neighbour's property. Jupiter is credited with sorting out the asteroids and arranging them in bands, and perhaps he has been human enough to exact a commission for his labour; and it might be more in his line, and certainly much more easy for Mars, to take forcible possession of as many of them as came within his reach.
Comingback to the period when we reduced the residuary nebula to the density of our atmosphere with temperature of 0°, or freezing water, we can with confidence affirm that none of the rings abandoned by it for the formation of planets, could have carried with them any contingent of heat to help them in their formation—any beyond the temperature of space—for even if they did it would very soon be reduced to that. Each one of them in condensing, breaking up, rejoiningthe broken fragments, converting itself into a minor nebula, and finally constituting itself as a planet, must have accumulated in the process its own heat requisite to convert it into a molten liquid globe—a stage of existence through which they are all, that is, the major planets, acknowledged to have passed, or have to pass. During that process its primitive annular form, and the multitude of fragments into which each one of them broke up, would present sufficient radiating surface, not only to dispose of all the heat it could have brought with it from the nebula, but a considerable part of the little it could create for itself while contracting and condensing. We may even go farther and assert that no one of them would have any necessity for being supplied with extraneous heat until it had, in a great measure, exhausted the stock it had produced for itself, or so far as to cool down from the molten liquid to the solid state, and to the stage when vegetable and animal life could exist upon its surface. We have no reason for supposing that an enormous supply of extraneous heat was crammed into each nebula, merely to be radiated into space before condensation could take place, and thus retard the execution of the work in hand. If there are astronomers or physicists who believe that the sun could not acquire by gravitation, all the heat he must have expended during geological time, they must look for it in some other source than that of useless and impossible cramming.
Hitherto we have said nothing of heat being radiated into space by the nebula during our operations, because there could be almost absolutely none to radiate from it at 0° of temperature. No doubt there is a large range between this and the absolute zero of temperature which is -274°; but we have seen, atpage 99, that when the nebula was condensed from 403,000,000 to 274 times less dense than air, onlyone degreewas added to its temperature—that is, it was raised from -274° to -273°—and that these -273° of absolute temperature were added to it in its condensation from being only 274 times less dense than air to atmospheric pressure, when its temperature became 0° of the ordinary Centigrade scale. Therefore the only period when there could be any measurableradiation of heat into space would be between the times when the diameter of the nebula was (see Table III.) between 58,000,000 miles and 9,000,000 miles. Even when the end of this period came, the temperature, after a contraction of 49,000,000 miles in diameter, would be only -1° raised to 0°—in other words -273° raised to 0°—and that would not furnish much positive heat—heat such as we are accustomed to deal with—to be radiated into space, whose temperature is without doubt somewhat warmer, so to speak, than -273°. And let us repeat, and fix it in our memory, that this -273° was equal to only 1° of positive heat.
If we now suppose the nebula to be condensed to one-tenth of its volume, with consequent density of 10 atmospheres, and corresponding diameter of about 4,150,000 miles, its temperature would be 2740° of the ordinary Centigrade scale—according to our mode of calculating hitherto—provided no heat had been radiated from it into space in the meantime. Of course this could not be the case, but we have no means of calculating what the amount of radiation would be, and it will not make much difference on our operations to take no notice of it. However, it is here necessary to take into consideration that 2740° would be the average temperature of the nebula; consequently, if condensation was most active where the greatest mass was, which certainly could not be at the centre or even near it, there also heat would be produced most rapidly, from whence it would spread towards the centre and surface. From the centre it would have no outlet, and would accumulate there as condensation advanced; whereas from the surface it would be radiated into space, and would tend to decrease in amount, so that we may conclude that the surface must have been considerably colder than the centre. If to this we add the fact that, in order to get to the surface, heat would have to be conducted, or conveyed by currents; over from one to two millions of miles, it becomes all the more certain that the central heat would be very much greater than that of the surface. How much less it would be at the surface we cannot pretend to calculate, but we may suppose it to have been from one-fifth to one-third of the average, or rather,somewhere between 370° and 1000°, which we have taken, atpage 110, to be the temperatures of red-heat and white-heat. And thus we come to find that the nebula, which was supposed to be endowed with excessive heat when it extended far beyond the orbit of Neptune, could not have radiated either heat or light into space to much purpose, until it had been condensed into not much more than 4,000,000 miles in diameter. This then we must acknowledge to be the earliest period at which the sun began to act as the life sustainer of his system; because, even were it to be found that there are other planets revolving within the orbit of Mercury, which we do not think very probable, we have seen that he could have no light or heat with sufficient vivifying power to radiate to them, till his diameter was reduced to not far from what we have shown above. Even then the sun would most likely be very much less brilliant than he is now, but the light may have been sufficient to promote vegetation on Mars—or the earth, if it was sufficiently cooled down from its molten state—and not much heat would be required by him, as there would probably be a remnant of his own interior heat, still sensible at the surface, sufficient for vegetation at least.
We have had occasion to refer several times to the temperature of space, and, though we cannot pretend to determine what it is, our operations enable us to show that it must be very much less than any estimate of it that has ever come under our notice. The nearest approach made to absolute zero by M. Olzewski, in his experiments on the liquefaction of gases, as reported in the "Scientific American" of June 2, 1887, was -225°, or so-called 49° of absolute temperature,[D]which would correspond to a density of 0·1788 of an atmosphere. This could not be the density of space, because it can be easily shown that our nebula, when at the same density, must have had a diameter of about 29,000,000 miles, and we must admit that were a globe of this diameter rotating in a medium of its own density, the friction between the twowould have been so great as to put a stop to the rotation before very long. We may even say that distinct rotation could never have been imparted to it. Following the same reasoning, we must acknowledge that the density of space must be much lower than that of our original nebula, if that could be, and therefore we can assert with confidence that the temperature of space must be far below -225°.
Here our operations put us in mind that we have said nothing yet about the ether, or what effect it might have on our nebula and the bodies formed out of it. We have not done so for the simple reason that, with one exception, it has never been taken into account in any scientific work that has come into our hands, except so far as its being called upon to perform the offices of a dog that has been taught to carry and fetch, and we have not known how to deal with it. But as we have come along, we have seen that it must have had something to do with the density, and consequent temperature, of all the bodies we have been dealing with, and that, if properly studied, it may enable us to account for some things that we have never seen, to our mind, properly explained. We know that it was devised, or conceived of—somewhere between thousands of years ago and the birth of modern astronomy—as a medium for carrying light, heat, and anything that was hard to move, through space, or to where it was wanted to be moved, by its vibrations or undulations, in the same way that sound is conveyed by wave motion, or vibration, through air, water, and a multitude of bodies; and we understand that some time during that long period it began to be looked upon as a material substance. We are told that it is supposed to pervade all bodies of all classes, but we think this idea must be taken in a limited sense, because, whether it is combined with electricity, as some suppose, or is only a carrier of electricity, a good conductor must have a larger supply of it than a bad one, and an absolute non-conductor, if there be such a substance, must contain none at all, always provided the ether is the conducting or carrying power. We are told also, that it is neither of the nature of a gas nor a liquid, but may be of the nature of a jelly, and of its nature we shall have more tosay hereafter. It was natural that it should be conceived to be a material substance, because if light and heat were to be carried from one place to another by wave motion, as sound is by water and air, then the medium for carrying it must be of the same nature as air and water—or any other carrier of sound—that is, it must be a material substance and, in consequence, possessed of some density or specific gravity. The only place where we have seen any density assigned to it has been, in a series of articles on the "Origin of Motion," published in "Engineering" of 1876, where it is estimated to be 1/5,264,800th[E]of the density of air. How this estimate was formed is explained in the number for December 1, 1876, page 461, from which we make the following very long quotation, because we look upon it as of great importance.
"Steel of the best quality in the form of fine wire has been known to bear a tensile strain represented by not less than 150 tons per square inch before breaking, and even this cannot be said to be the limit to the tensile strength of steel, since the tenacity increases as the diameter of the wire is reduced. Rejecting 'action at a distance,' therefore, these molecules of the wire must be controlled by some external agent, and therefore, the pressure of the external agent mustat leastequal the static value of the strain. The pressure of the ether therefore cannot be less than 150 tons per square inch. Now, since it is a known fact that the strain required to separate molecules in 'chemical union' would be very much greater than in a mere case of 'cohesion,' it follows that the ether pressure must be greater than the above figure. If we suppose the strain required to separate the molecules of oxygen and hydrogen combined in the state of water (one of the most powerful cases of chemical union) to be only three times greater than in the case of the molecules of steel, then this would give 450 tons per square inch as the effective ether pressure. It may be taken as certain that the strain requiredwould be greater than this, as it has not been found possible by any ordinary mechanical means to separate molecules in chemical union. However, as it is only our object to fix a limiting value for the ether pressure, or a value that is less than the actual fact, we will therefore take in round numbers 500 tons per square inch as the total ether pressure, having thus valid grounds for inferring that this estimate is within the facts as they actually exist. The existence of such a pressure as this might well be sufficient to strike one with astonishment and legitimately excite incredulity, if it were not kept in mind that this pressure is exercised againstmoleculesof matter, a perfect equilibrium of pressure existing, so that it may be deduced with certainty beforehand, that, however great this pressure might be, it could not make itself apparent to the senses. The air exercises a pressure of some tons on the human body without such pressure being detected, how much more cause, therefore, is there for the perfect concealment of the ether pressure, which is exercised against the molecules of matter themselves. This great pressure is the absolutely essential mechanical condition to enable the ether to control forcibly the molecules of matter in stable equilibrium, and to produce forcible molecular movements when the equilibrium of pressure is disturbed (as exemplified in the molecular movements of 'chemical action,' etc.).
"It is generally admitted that the ether must have a very low density, one reason being the almost imperceptible resistance opposed by it to the passage of cosmical bodies (the planets, etc.) at high speed through its substance. The pressure of an aëriform body constituted according to the theory of Joule and Clausius, being less as its density is less, it will therefore be necessary to show that the ether can exert so great a pressure as the above, consistent with a very low density. From the known principles belonging to gases, the pressure exerted by an aëriform medium is as thesquareof the velocity of its component particles, and as the density. We will, in the first place, consider what the density of the ether would be, if it only gave a pressure equal to that of the atmosphere (15 lb. per square inch). From the above principles,therefore, it follows that for the ether to give a pressure equal to that of the atmosphere, the ether density will require to be as much less than that of the atmosphere, as thesquareof the velocity of the other particles is greater than the square of the velocity of the air molecules. The velocity of the air molecules giving a measure of 15 lb. per square inch is known to amount to 1600 feet per second. Taking, therefore, the square of the velocity of the ether particles in feet per second, and the square of the velocity of the air molecules and dividing the one by the other, we have the number of times the ether density must be less than that of the atmosphere, in order for the ether to give a pressure of 15 lb. per square inch, or we have
(190,000 × 5280)2———————— = 393,120,000,000.1600
This result shows therefore that the density of ether, if it only gave a pressure equal to that of the atmosphere, would be upwards of 390,000,000,000 times less than the density of the atmosphere. This result expresses such an infinitesimal amount of almost vanishing quantity, that the ether density might be well much greater than this. We will now, therefore, consider what the ether density would be to give a pressure of 500 tons per square inch. Pressure and density being proportional to each other, it follows that for the ether to give a pressure of 500 tons per square inch, the ether density would require to be as much greater than the above value, as 500 tons is greater than 15 lb. Multiplying, therefore, the above value for the density by this ratio, we have
1 (500 × 2240) 1———————— × ———————— = ————————;393,120,000,000 15 5,264,800
or this shows that the density of the ether to give a pressure of 500 tons per square inch would be only 1/5,000,000th of the density of the atmosphere. This value representing a density less than that of the best gaseousvacuais therefore quite consistent with the known fact of the extremely low density of the ether. It follows, therefore, as a mathematical certainty dependent on the recognised principles belonging to gaseousbodies, that the ether could exert a pressure of not less than 500 tons per square inch consistent with such an extremely low density as to harmonize with observation."
If the ether is possessed of a density equal to that shown above, then the density of our original nebula must have been greater than what we have shown it to be. The density we found for it was 1/403,000,000th that of air, or 0·000000002481 of an atmosphere, and 1/5,264,800th is equal to 0·00000019 of an atmosphere; if then we add these two together we get 0·0000001925 of an atmosphere as the density of our nebula. This comes to be very slightly greater than the density of the ether, and shows that the estimate in the foregoing quotation is too high; unless it is asserted that the ether can exert no frictional action at all, which, we believe, no one has ever done; while the absolute temperature of the nebula at the new density would be 0·000053°, which would be a very small addition indeed to the 0·00000068°, we found for it at first. On the other hand, when the nebula was reduced to 29,000,000 miles in diameter the density of the ether would have increased its density from 0·1788, which we showed it then to have, only to 0·17880019 of an atmosphere, which would make no appreciable difference on its temperature, and would be so immensely greater than the 0·00000019 of an atmosphere of the ether that it could hardly be supposed to have any effect in retarding the rotation of so much heavier a body. And should it be found that the density of the ether is 1/4, 1/3, or 1/2 less, or even a great deal more, than that shown in the above quotation, it would only have proportionately less effect on our nebula, in every sense, than what we have just shown. We may, therefore, conclude that the introduction of the element ether has not vitiated our operations in any way up till now, and we shall leave it until we have acquired more knowledge of its nature and effects.
Although we have already condensed our nebula to somewhere about 4,000,000 miles in diameter, where we have shown it might begin to radiate light—radiation of heat may have begun when the diameter was ten times as great, or even before that—we propose to return to the period when it hadjust abandoned the ring for the formation of Mercury and was 63,232,000 miles in diameter, and became what we have called the Solar nebula; because there is a good deal to be learned from a careful study of our operations up to that period, and of what must have taken place during further condensation up till the final establishment of the sun such as it is at the present time.
When the planet Neptune was discovered, Bode's Law fell into disrepute for a time, because the new planet was found to be much nearer to the sun than, according to it, it should have been. All the other planets occupied the places assigned to them within 5 per cent. of the exact appointed distance from the sun, but Neptune turned out to be 22·54 per cent. out of his exact place, and hence the discredit thrown upon the law. It was hard treatment for a servant that had helped so unmistakably—as we know to have been the case—to the discovery of the first four asteroids, which has afterwards been followed by the discovery of a whole host of them, and that had been pressed into the service for the discovery of the very planet which was the cause of its discredit—but such is the world. However, first offences against the law are generally looked upon with merciful eyes, and the Series of Titius seems to have been so far received into favour again that, some astronomers are said to have been looking out for another planet farther off than Neptune, being convinced that there must be some reason why a law that has shown itself to be right in eight cases should be altogether wrong in the ninth. Here, we think that the most likely explanation that can be given is, that the ring out of which Neptune was formed divided itself, after breaking up, into two planets instead of one, and that this is the reason why, Bode's Law could not point out the true position of either of them. It is hard enough to believe that the ring out of which Uranus was made—which we have seen may have been 954,000,000 miles broad, and over 3,400,000,000 miles in extreme diameter—could have united its fragments, after breaking up, into one planet, and the difficulty of belief becomes greater the greater the diameter comes to be. We have, in our work, considered the breadthof Neptune's ring to have been 1,010,000,000 miles, but then we limited the diameter of the nebula to 6,600,000,000 miles—we had to draw the line somewhere—whereas it may have been a thousand million miles greater, which would very greatly increase the probability of two planets, perhaps even more, having been formed out of the ring. If it has been so, the law could not apply to the case. A new Act was required. Besides, it is not a law, never has been, but only a register of facts; and we know that truths are often discovered from similar registers. It registers, and at the same time shows, that there is a nearly fixed inter-relation, even proportion, in the distances of the planets from the centre of the sun as far out as Uranus; and were we to make a similar register, beginning at the (present) outside of the planetary system, and registering the number of revolutions, beginning with 1 for Neptune, rates of acceleration of revolution in number of days, and densities of the planets, we may draw from it some useful knowledge. But we shall first extend Bode's Law to embrace Neptune, and show the discrepancies between the actual positions of the planets and those pointed out by the law.
Here we see that, with the exception of the first step from Neptune to Uranus which is only 1·9577, we have an average gradation of acceleration of 2·5898 times, from one planet to another, from the outermost as far in as Mars; and that had Neptune had the period of revolution sought for by Leverrier in his discovery of that planet, viz. 217·387 years, or 79,399·602 days, the average rate of acceleration would have been 2·5896 times, from planet to planet, as far in as Mars. This, we think, is pretty strong evidence that one law of acceleration was in force from the beginning of the separation of rings from the nebula up to the time when the ring for Mars was separated—the departure from it in the case of Neptune, notwithstanding—and goes far to prove that part of the nebular hypothesis which implies that each of the planets is now revolving round the sun in the orbit, and with the velocity, belonging to the centre of gyration of the ring out of which it was formed. From Mars to Venus the law—the areolar law, of course—had changed to a variable decreasing law, as seen from the foregoing register, which then again changed into an increasing one, till at Mercury the rate of acceleration rose again to 2·5543 times from Venus, or very nearly the same rate of increase that existed from Uranus to Mars. The causes of these changes may or may not be able to be accounted for—we shall have to return to them hereafter, in the cases of Neptune, the earth and Venus—but there is one thing of some importance that is deducible from the register, which we shall endeavour to make clear.
Bode's Law Extended.
Our register as specified above will be the following:—
A good deal has been written about planets or other bodies existing between Mercury and the sun, especially about Vulcan whose existence seemed to be so certain, that his distance from the sun and period of revolution were calculated to be about 13,000,000 miles and 20 days respectively. Now, with what we have seen about the rate of acceleration of planets as their orbits approach the sun, we may endeavour to form some notion of where any within the orbit of Mercury may be found. If we take the same rate of acceleration we have found between Venus and Mercury—that is 2·5543, which may be looked upon as almost the general rate for all the planets—we find that there might be a planet revolving round the sun in 34·4436 days; but here we must stop, because, though we could make no objection to the existence of a planet with the period of revolution just shown, were we to take another equal step towards the centre of the nebula, the same acceleration of rotation would give us a planet, or ring for a planet, revolving round the sun in 13·4454 days; not much more than one-half the average of his rotation round his axis at the present day, which would knock on the head most completely the theory that each planet was detached from the nebula at the time that it was rotating with the velocity of the planet's orbit, or we should have to conclude that the nebula had passed, by a long way, its power to abandon matter through centrifugal force. No one could suppose that a ring for a planet could be formed within the body of the nebula and abandoned, or thrown out, afterwards, because centrifugal force could not throw out the ring and at the same time retain the surrounding matter.
Turning our thoughts now to the supposed planet Vulcan, which was calculated to revolve round the sun in about 20 days, we have either to conclude that it was formed in the body of the nebula and come to the same breakdown of the nebular hypothesis, or we have to acknowledge that the sun is now rotating much more slowly on its axis than the nebula did at the time the ring for Vulcan was abandoned.
If we now direct our attention to the densities of the several planets, we shall find some suggestive matter in their study. A general look shows us at once that there are four periods of rise and fall in their densities. There is one rise and fall (referring to our register) from Neptune to Uranus and on to Saturn; then another rise to Jupiter and fall to, we suppose, the asteroids, because we are told that the quantity of matter in the region where the asteroids travel is less than in any other zone of the solar system, and the general density must in consequence have been less there than anywhere else; still another rise from the Asteroids to the Earth, and fall to Venus; and then a final rise to Mercury accompanied, without doubt, by a fall after the planet was abandoned, because the centrifugal force of the rotating nebula must have been decreasing, at the least, preparatory to its ceasing to have the power to throw off more matter. The first rise and fall would seem to indicate that there had been a much closer mutual relation in the births of Neptune, Uranus and Saturn than is indicated in any way in the nebular hypothesis. We could imagine that at one time they formed one flat ring, which afterwards divided itself into three, following the same law as we see dividing the rings of Saturn at the present day. With respect to Jupiter, his enormous size is sufficient to entitle us to believe that his ring was separated from the nebula independently of any of the others, and to account for there having been the rise and fall in the density that we have noted between Saturn and the Asteroids. Then the rise and fall from Mars to Venus, or further on towards Mercury as it would be, may indicate one ring divided into three in the same manner as we have supposed for the three outer planets. And the final rise to Mercury and subsequent fall to the sunor to the solar nebula might be either due to one operation or to complication with other unknown bodies that may be travelling between Mercury and the sun.
In support of the foregoing ideas, we may also refer to our having said on a previous occasion, that the whole of the matter separated from the nebula in the form of thin hoop-shaped rings, would condense into one continuous sheet, perhaps even up to the time when centrifugal force could not throw off any more matter against the force of gravitation. In that case we can conceive that the radial attraction, outwards and inwards, of the particles of the matter forming the sheet would gradually establish lines of separation, dividing off the matter into distinctly separate rings, preparatory to their transformation into planets; but we cannot explain how these separate rings came to be more dense in one place than another. We must leave that for future discovery. Meanwhile the idea of one continuous sheet of matter extending from the sun out to Neptune, suggests the possibility of all the rings having been in existence as rings, more or less advanced in their evolution, at the same time; and if not so much as that, makes it more easy for us to see how the four inner planets, being made out of more condensed cosmic matter, and being of so much smaller volume, have arrived at a much more advanced stage of their being than the four outer ones. Going a little further, we can see how the cosmic matter of the rings condensing from both sides in the direction of their thickness, and falling in impeded, so to speak, the tendency to contract in length, or circularly, until they arrived at a certain stage of density, when they began to contract in their orbital direction, to break up into pieces, each one of which would form itself into a small, probably shapeless, nebula with a tendency to direct rotation, as explained and shown by M. Faye in "L'Origine du Monde," chapter xiii., page 267, entitled "Formation de l'Universe et du Monde Solaire"—an explanation which must have occurred to everyone who has taken the trouble to think seriously, of how nebulous spheres could be formed out of a flat nebulous ring endowed with a motion of revolution.
We have seen atpage 127that when the nebula was condensed to a little over 4,000,000 miles in diameter, its average temperature might have been 2740°, provided no heat had been radiated into space. In like manner, we can see that the sun being now condensed to 1·413 times the density of water, or 1093 times the density of air, in other words, that number of atmospheres, its present average temperature might be about 300,000°—as each atmosphere corresponds to 274°—provided no radiation of heat into space had been going on. But this way of estimating could not in any way apply to the nebula after it had ceased to throw off planetary matter; because from that time, or at all events from the time when it came to be of a density equal to one atmosphere and temperature of 0°, or freezing point of water, that would be accumulated within it, owing to the difficulty of carrying to the surface, to be radiated into space, what was produced by condensation in the interior, as we have shown before. Both heat and pressure would increase from the surface towards the centre, the former rising, in spite of surface radiation, to something far beyond what we have stated above that it might be, aided by the increase of pressure which near the centre must be enormously greater than the average of 1093 atmospheres, seeing that the pressure at the surface of the sun is estimated to be not far from 28 atmospheres. The first cause of the increase of pressure would be the condensation produced by gravitation, which according to the areolar law would increase the rotary velocity of the nebula in proportion as the centre was approached; and as this would begin long before it had given up abandoning rings, or rather from the very beginning of its rotation; from that time, there would be different rates of rotation at different distances between the surface and the centre, which would cause friction among the particles of its matter, in other words a churning of the matter shut up in the interior of the nebula, and thus produce heat over and above that produced by the condensation of gravitation alone. If two particles of matter would produce a given quantity of heat, in falling from the surface of the nebula to any point nearer to the centre, they would surely produce more if they were rubbed against each other by churning action during their fall.
Reflecting on what we have written up till now, we see that the analysis of the nebular hypothesis we have made, which at first may have appeared to be unnecessary or even useless, has shown us and made us think over many details, of which we had only a vague notion previously. It has shown us that without condensation at or near the surface of the nebula—which we have pointed out must have been caused by its greatest mass being near that region, and which Laplace procured by endowing it with excessive heat—the various members of the solar system could not have been evolved from it in terms of the hypothesis. From it we have been able to learn, by means of the register of the acceleration of revolution from one planet to another, when, and for what reason, the nebula ceased to be able to throw off any planet nearer to the sun than the supposed Vulcan, or almost even so near. Finally, and not to go into greater detail, it has so far given us some ideas, that we had not before, of the internal structure of the sun, and has made us believe that a great deal may be learnt by attempting to find out what that structure really is. For this purpose, it appears to us that a careful examination into, and study of, the interior of the earth might be a great help, and to this we shall appeal, as we cannot think of any other process by which our object can be attained. This, therefore, we shall endeavour to do in the following chapters.
Beforeattempting to inquire into the nature and structure of the interior of the earth, it will be convenient to specify the bases on which the inquiry is to be made, in other words, the data we have to proceed with; which data should be denuded of everything whatever having the semblance of a hypothesis or theory, and should consist of simple facts. Anything founded upon theory must come to an end should the theory be afterwards found to be erroneous, and all the labour would be lost.
What we really know of the earth in this way may be stated as follows:—
Of the exterior or surface we know that it is of a spherical form, surrounded by an atmosphere of probably 200 miles oreven more, in height, consisting of common air mixed with vapour of water in more or less degree; that, of its surface, nearly three-fourths are covered by water, and the remaining fourth consists of dry land, intersected in all directions by rivers; that on the dry land there are elevated tablelands and ranges of mountains from two to three miles high, with occasional ridges and peaks rising up to altitudes of from five to near six miles, and that in the part covered by water or sea, there are depressions or furrows with depths in them probably exceeding the heights of the highest mountains; that the sea does not remain constantly at the same level but rises and falls twice in every twenty-four hours, or thereby, in obedience to the attraction of the moon and sun, forming what are called tides; and that its polar regions are enveloped in dense masses of snow and ice, which the persevering energy of man has not been able to penetrate in centuries of continued and determined effort.
What we know of the interior of the earth is found in great measure from the exterior, that is, from the construction of the rocks as seen in deep ravines, in precipices, and on the sides of hills or mountains; and also from what we have been able to learn from the exploration of mines and from deep wells, the deepest of which have penetrated it very little beyond one mile in depth; all of which knowledge may be summarised as follows: That the substances which compose the earth are manifold and of manifold nature—or, more appropriately speaking, simply the elements of chemistry—varying in density, or specific gravity, from the same as that of water, or in some cases much less, to three or four times as much in some kinds of rock and earths (disintegrated rock), to more than twenty times in the heaviest metals; that from a depth great enough not to be affected by the changes of seasons, the heat of the earth increases in descending towards the centre, by one degree of Fahrenheit's thermometer for every fifty to sixty feet in depth—that is about thirty metres for each degree of the Centigrade scale—as far down as we have been able to penetrate; that at the greatest of these depths abundant supplies of water are found, which shows that itmust exist at much greater depths than any that have yet been reached; and that at unknown depths, as shown by the eruptions of volcanoes, there are masses of matter in a molten liquid state, or that, owing to their great heat, can be suddenly liquefied by diminution of pressure.
Over and above what has been stated, little can be learnt from geology, because the earth must have been formed and fashioned almost to its present condition before geology could begin to exist, and all its teachings are confined to a very few miles from its surface. Its first lesson could only begin when the earth was so far cooled down that a crust could be formed on its surface, and that crust could be deluged by copious falls of rain on it. Some help or guidance may be obtained however, from the ideas which astronomers and physicists have formed on its interior, and it may be useful to have the principal of these ideas specified, as they may help to strengthen arguments that may be advanced, or conclusions that may be drawn.
When it was discovered that the temperature of the earth increases, as we go downwards, at what may be considered a rapid rate, it was calculated that at a depth of from twenty-five to thirty miles, the heat would be great enough to melt any substances that have been found near the surface; and it was immediately concluded that from that depth to the centre the whole of the interior was a molten liquid mass, whose temperature far exceeded any heat that could be produced upon the surface. Even up to the present day, the belief in a liquid interior has not disappeared.
Many years afterwards, the supposed liquid state of the interior of the earth was taken advantage of, to frame a theory that earthquakes and eruptions of volcanoes are caused by the attraction of the moon on the liquid interior producing tides, in the same manner as it produces tides in the sea, which in their turn act upon the crust, cracking and rending it to produce the one, and forcing the liquid matter out through the rents, or up through the vents of volcanoes to produce the other, in some way that it is more easy to imagine than to explain mechanically. Also when the effect of the attraction ofthe moon on the liquid internal matter came to be duly considered, it was concluded that the crust, with only 25 to 30 miles in thickness, could not be rigid enough to resist the pressure brought upon it by the movements of the interior tides; and it began to be thought that, owing to the pressure of the superincumbent strata, the density of the matter at that depth might be so great that it would become solid at a much higher temperature than it does at the surface; and some physicists went the length of supposing that the earth has a solid crust and solid nucleus with liquid matter between them. On the other hand Sir William Thomson, Lord Kelvin, looking more as it would appear to the effects of the moon's attraction on the crust than on the liquid interior, concluded that the earth must be a solid globe, contracting through gravitation in the interior, and cooling at the surface, because a crust so thin as 25 to 30 miles, or even 100 miles, would be continually rent and broken up by the tidal action of the moon; but Professor Clerk Maxwell and others have thought that the elasticity of the crust would be great enough to admit of its accommodating itself to all the changes of form that would be caused by the action of those tides. Notwithstanding that they agree with Lord Kelvin in the main, in his objections to the existence of a liquid interior, many scientific men suppose that, through the effects of pressure, the liquid interior of the earth may have been changed into a viscous state, as it went on contracting through gravitation, which would, according to the degree of viscosity, either annul, or almost annul, the tidal action on it of the moon. To which it may be added that that action would not raise such high waves in even perfectly liquid molten matter as it would upon water; because it would be easier for the moon to lift a cubic mile of water three or four feet high, than to lift a cubic mile of melted rock or metal to the same height.
Other parties look upon the earth as mainly solid to the centre, but with large reservoirs of liquid matter in various parts of it near the surface, which furnish all the material for volcanic eruptions and are the causes of earthquakes. There are others also who, believing the earth to be altogether solid,consider that when any part of the intensely heated and dense interior is relieved suddenly from pressure, as, for example, by the convulsive action of an earthquake, it will immediately assume the liquid state and become material for volcanic eruptions; a theory which they consider to be substantiated by the fact of these two phenomena generally accompanying each other. And Mr. Mallet seems to have demonstrated that earthquake-shocks proceed from centres not far from the surface, which would seem to point out that if a liquid interior did exist at 25 to 30 miles from the surface, it could have no part in causing earthquakes. There are others still who consider earthquakes and volcanic eruptions to be caused by water penetrating deeply into the interior, but it is difficult to understand how water could penetrate into the interior to a greater depth than where it would be converted into steam, that is to a greater depth than from three to four miles.
Many other notions about the interior state and conditions of the earth have been formed, more or less entertainable, more or less fanciful, to provide liquid matter for volcanic eruptions. One of these, referred to in "Nature" of December 12, 1889, takes for granted "that granite has consolidated from a state of igneo-aqueous fusion, and that the liquid magma from which all granitic intrusions have proceeded contains water-substance," and proceeds, "It is, therefore, only a further step to assume that this water-substance is an essential constituent of the liquid substratum (assumed by the author), and to suppose that it has been there since the consolidation of the earth." This mixture of water, fire, and molten granite is one that does not agree with what we have been taught of the nature of any of the three components, and we cannot accept it. Why we refer to it more particularly than to the other ideas we have cited, is because it so far comprehends some of them, and that we shall have to return to it hereafter, when we think it will be seen that it has not been properly thought out.
Bearing in mind all these ideas we have cited, and working with the data we have considered as actual facts, we may now proceed with our inquiry.
The belief that the earth is a mass of matter increasing, whether liquid or solid, or part of both, in density from the surface to the centre is so general that we shall look at it in that light first, and endeavour to find out what must be its density at any place between its surface and its centre.
Astronomers and geologists concur in telling us that the mean density of the earth is very near to 5·66 times that of water: knowledge that has been acquired by measuring the attraction of high and precipitous mountains for plummets; by the attraction of masses of metals for each other, measured by the torsion balance; and by the acceleration or retardation of the vibrations of pendulums, as observed in the depths of mines and on the tops of mountains, compared with each other. They also tell us that the average density of the matter and rocks of which the crust is composed is about 2½ times that of water; and then, in a general way, that the average density of the crust, taking into consideration that so much of its surface is covered by the sea, is not much more than 1½ times that of water. This estimate is manifestly incorrect, for it implies that the whole of the crust of twenty-five to thirty miles is affected by the presence of water, when we know that the depth of the sea at any place does not exceed one-fourth of that thickness. Therefore, we shall endeavour to obtain some more accurate computation, as it is the only datum we have to go upon, and has a greater effect upon the result, and upon all things relating to the interior, than might at first sight be supposed.
We find in "Nature," of January 19, 1888, that Mr. John Murray has calculated that if the whole solid land of the earth were reduced to one level under the sea, its surface would be covered by an ocean with a uniform depth of about 2 miles. Here we have a very good beginning for our calculations.
Without taking into consideration the increase of density in water at 2 miles deep, at that depth we may suppose we have come to solid matter, the specific gravity of which could not be less than twice that of water, on account of the pressure of that depth of water upon it. If we now go down2½ miles further we shall have the solid matter subjected to a pressure proportioned to that depth; and if we take its weight per cubic foot at an average between granite (at 163 lb.) and earth (at 77 lb.), or 120 lb., the pressure at 2½ miles deep of solid matter alone will be about 700 tons per square foot, or just about the crushing strain of our strongest granites, and therefore, the density of the matter under it must be equal to that of granite, or 2·5 times that of water. We do not add the pressure of the water, at present, because that may be looked upon by some people as of the same nature as of the atmosphere upon a human body, which neither increases the pressure upon it nor adds to its weight; but we see that at that depth the solid matter must have a density equal to the average between water on its surface and 2·5—that of granite; and if we choose to take the average between 2 miles of water and 2½ miles of solid matter, we shall have 1·82 as the average density of the outer 4½ miles in thickness of the crust of the earth. For our purposes, however, and for obvious reasons, we shall consider the average density of the 2½ miles alone of solid matter to be 2·25 times that of water.
We shall now go down to 9 miles deep, because the diameter of 7918 miles we have adopted for the earth will there be reduced to 7900 miles, which will be convenient for our further operations. At that depth we shall have a superincumbent pressure at the very least as follows:—
or just about 4 times the crushing strain of our best granites. Then, as when crushing takes place compression begins, it will, we believe, be far below the mark to estimate the general specific gravity of the earth at 9 miles deep to be 3 times that of water.
We have now added the pressure of the 2 miles of water, because there could be no water at the depth of 9 miles; forthe critical temperature of water is known to be 412°, beyond which temperature water cannot be maintained in its liquid state by any amount of pressure, however great; and 9 miles would give 483° temperature at 1° for each 30 metres. At that depth there might be steam, although it is difficult to see how it could penetrate so far, because the only force to help it to penetrate would be gravitation, and that would have to act against the increasing repulsion of heat.
There is another circumstance to be considered which would tend to increase the density of the outer portion of the crust, if there be a crust, and if not, of the outer portion of the earth itself.
When the earth was in the molten liquid state, it is generally supposed to have been surrounded by vapours of a great proportion of the metals and of some of the metalloids, in addition to the vapour of water, air, and other gases, which floated above them higher up in the atmosphere. In that case when the crust began to be formed through cooling, these vapours would be precipitated on the surface and mixed with the half-liquid half-solid matter there, but the proportion of condensed vapours would be very small compared with what they fell upon, and the specific gravity of the mixture would not be great enough to cause it to sink much below the surface, because it would soon meet with matter as dense as itself; consequently we must consider that all these metals would remain near the surface—most likely much nearer to it than the 9 miles which we have as yet descended to—and whatever may have been the proportion of their density it ought to be added to the weights and pressures that have been taken into account above. We believe that it will be shown later on that this estimate of a density of three times that of water at 9 miles deep in the earth is very much lower than it should be; because, when the pressure upon the matter there came to be greater than its crushing strain, compression would go on more rapidly than shortly afterwards, and it might so be that with a strain of very much less than four times that of crushing, compression would be reduced to its utmost limit. But more of this hereafter.