Coming back 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, rejoining the 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, at page 99, that when the nebula was condensed from 403,000,000 to 274 times less dense than air, only one degree was 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 measurable radiation 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, at page 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 two would 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 to say 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 must at least equal 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 required would 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 against molecules of 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 the square of 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 the square of 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 gaseous vacua is 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 gaseous bodies, 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 had just 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 breadth of 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 sun or 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 at page 127 that 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.