Fig. 2.
Fig. 2.
The accompanying rough sketch (Fig. 2), drawn to a scale of one-quarter inch to 1,000,000,000 miles shows that, supposing the Saturnian nebula to have been a perfect sphere, and to have abandoned matter till the velocity of rotation came to be equal in a region corresponding to the tropical region of the earth, the cylindrical part of it would present a straight side of more than 1,000,000,000 miles in length; providedalways that the general diameter of the nebula did not decrease through condensation and contraction during the operation; but as this could not be the case the length of the cylindrical part would be considerably less than that. How much less we have no means of calculating. On the other hand we have seen, when discussing, in the case of Jupiter, how matter must have been abandoned by any nebula, that from the time the original nebula began to abandon matter through centrifugal force, it must have gone on acquiring a constantly increasing length of straight side as it contracted. Thus the Saturnian nebula would begin work with the accumulated cylindrical length it had inherited from Neptune and Uranus, so that the straight side may have been very much longer than that shown by the sketch; a simple look at it is enough to make one believe that this would be the case. But this idea naturally leads us to another digression.
Looking again atFig. 2, we see that acceleration of rotation in the nebula would originate where condensation was greatest, that is at the region of greatest density, and have to be propagated from there to its periphery so that it would reach the middle of the cylindrical part sooner than the ends; and as the nebulous matter at the ends of the cylindrical part could not be abandoned until it had acquired the centrifugal force necessary to overcome gravitation, it would lag behind and overhang, as it were, the middle of the cylindrical part; which means that instead of continuing to be straight, the line of separation between the nebula and the abandoned matter would come to be concave; and in this manner the nebula would soon assume the form of a dumb-bell, gradually becoming more and more pronounced as condensation proceeded. One can hardly help concluding that this must have been the way in which the dumb-bell nebula near star 14 Vulpeculæ was formed. The representations of it given by Chambers, Vol. III., page 92, Figs. 76 and 77, as seen by Smyth and Sir John Herschel are most confirming of this idea; notwithstanding the changes of appearance shown by Lord Rosse's reflectors of 3 feet and 6 feet diameter, Figs. 78 and 79, which are not difficult to account for. It is easy to imaginehow Fig. 78 could be converted into Fig. 79 when observed with a much more powerful telescope. We can conceive the roundest end of it being reduced into the sort of compact segmental form on the left hand side of the figure, and the spread-out part of it into the more diffused segment on the other side; but the form of the whole figure forces us into another conception. Mr. Chambers says the general outline resembles a chemical retort, but to our eyes it is infinitely more like one half of a dumb-bell broken off from the other. So like it that we feel inclined to ask what has become of the other half. This again makes us think of an enormous dumb-bell nebula dividing itself into two parts, one of which has disappeared or broken up in some manner without leaving any distinguishable traces of its existence, and the other, either forming itself into a double star, assuming in the process the form of a dumb-bell, or actually of one rotating in a direction almost at right angles to that of the original one; more probably the former of the two. Perhaps we have allowed our ideas, or fancy, to run on too far; nevertheless, looking over the forms of nebulæ represented in Chambers's classical work, and duly considering how inconceivably strange some of them are, there is nothing impossible in all we have said.
Returning to the repeated changes of density in the solar planets, we know that the matter first abandoned by the original nebula, through centrifugal force, would be at the lowest stage of density, and that what followed would go on gradually increasing in density as it contracted to the Saturnian nebula. But, as we have shown that immense quantities of matter belonging, so to speak, to the sun, though actually separated from the original nebula, must have fallen in upon the sheet after being abandoned, it is not difficult to see that the part of the sheet out of which Neptune and Uranus were made, might be more dense than the Saturnian nebula, on account of this matter being added to it; and that, as the greater portion of it must, at the more advanced stage of the process of condensation, have fallen upon the Uranian part of the ring, because the space from which it fell would be higher, the density of that would be greater than the Neptunian partof the sheet; both of them exceeding the density of the Saturnian nebula. Again, we have supposed, very naturally we think, that all extraneous matter coming in from the equatorial direction would be intercepted by the rings destined for Neptune and Uranus, so that the density of the ring for Saturn would be only what had been acquired through condensation, and the planet formed out of it would be less dense than those made out of matter accumulated in a different way. It may be argued against this deduction, that density would depend on the degree of contraction, but it is natural to think that lighter would take longer time than heavier matter to condense to the same degree; besides Saturn is of necessity the youngest of the three planets, and may in due time come to be as dense as either of the other two, but his diameter will decrease proportionately.
Coming now to the Jovian nebula, whose diameter we have made to be 1,370,000,000 miles, we have seen, atpage 115, that—had it been a perfect sphere—by the time it had contracted one thousand miles in diameter, it must have had a flat side of more than 1,400,000 miles in length? then if we add to that length all that the nebula had inherited from Neptune, Uranus, and Saturn, the cylindrical part of it must have been many millions of miles in length, and the polar very much greater than the equatorial diameter of the nebula. In other words we have to deal with a body having the form of a very long cylinder terminating in spherical caps. To this we have to add that the density of the Jovian was more than 111 times greater than that of the original nebula. Still farther we have to take into account that the whole of the matter abandoned by that nebula must have been thrown off in less than one-half of the space in which the ring for even Saturn had been abandoned, the breadth of the two rings, as shown by us, seeTable III., having been 650,600,000, and 313,400,000 miles respectively. All these things considered, it is clear that the thickness of the ring for Jupiter's system must have been very much greater than what we have given it in the table; which, coupled with its matter being over six times more dense than that of the preceding ring, is sufficientto account for the rise in density, the immense size, and mass of Jupiter.
Next, we have the means of accounting for the fact that, the space occupied by the Asteroids is, and has always been, the least dense of any portion of space occupied by the solar system. It is easy to understand that the enormous mass of matter abandoned by the nebula for the formation of the Jovian ring—more especially towards the end of the process—would have a very appreciable effect, by its attractive power, in helping centrifugal force in freeing matter from the power of gravitation; the consequence of which would be, that the matter thrown off for the formation of the Asteroidal ring would be considerably less dense than it would otherwise have been. In this way, then, we have the decrease of density, as well as the quantity of matter, in that space very plausibly accounted for.
Then, as the nebula continued to contract, the attractive power of Jupiter's ring would decrease proportionally to the square of the distance of the receding mass, ceasing in doing so to lend so great assistance to centrifugal force in the nebula, and so letting it subside into its normal state; so that the matter abandoned would increase in density in comparison to the space over which it was distributed, thus accounting for the rise in density towards Mars and the Earth.
With regard to the fall towards Venus and final rise towards Mercury, we have to take into consideration the anomalies—already taken notice of—in the dimensions, densities, etc. etc., of the two planets Earth and Venus; it being, we may confidently say, certain that the whole of them have arisen from the same causes. Following up the idea of a dumb-bell nebula—as we might have done in the case of Jupiter also—as the breadth of space for receiving matter abandoned by the nebula went on rapidly decreasing, the thickness of the ring left behind would go on increasing, and the overhanging matter of the dumb-bell would be deposited always in greater quantity on the outer than the inner part of the ring as it broadened; we can conceive that the whole extent of the sheet of matter allotted to the Earth and Venuswould be thicker at the outer than the inner part. Hence, when this part of the sheet came to be divided into two parts for the formation of two planets, the outer would naturally be the greater and denser of the two, and thus occasion the rise in density from Mars to the Earth, and the fall to Venus. Finally the rise in density to Mercury would be only the beginning of the gradual, and final, rise to the sun as it is at present.
If the idea of a nebula in the form of a cylinder with hemispherical ends is admitted as possible, or somewhat like a dumb-bell, the extreme diameters of the 9 successive nebulæ we have dealt with would be considerably different in their equatorial directions to what we have given them, although their polar diameters might continue to be not far from the same; but that would have very little effect on the operations we have gone through, seeing we have shown that there could be no actual divisions between them such as we have adopted; and that the division of the sheet of matter abandoned into separate rings must have been brought about by some means which we cannot explain; a process, nevertheless, which has been subject to some law, or laws, operating evidently in a regular and steady manner throughout the whole time, during which the matter was being abandoned, as is proved by the general uniformity, or harmony, in the distances of the planets from the sun. Should anyone come to be able to account for the division of this sheet of matter into distinct and separate rings, he will also be able to account for the acceleration of rate of revolution from one planet to another, and for the anomalous rates in the cases of the Earth and Venus.
In a former part of our work we have followed up, at different stages, the condensation of the original nebula until it attained the dimensions, appearance, and some of the features of the sun as it is, but we have still something to add as to how the condensation could produce a body so strictly spherical as the sun is represented to be. All the other bodies of the solar system, as far as astronomers have been able to measure them, are spheroids more or less oblate, and it seems strange that the principal should be the only onethat does not conform to the general figure. It is rather hard on the notion that the original nebula gradually assumed the form of a lens, for it would require a special mode of manipulation of a very mechanical kind, rather than the steady, imperceptible self-action of the law of attraction, to transform a lens into even an oblate spheroid; to transform it into a perfect sphere would be absolutely impossible. For, if at the end of the process it was found that there was too much material to form a sphere, it would be hard to get rid of the superabundance, unless it was converted into meteorites—evidently another hand process. On the other hand, should a hole remain to be filled up, the material would have to be lugged in somehow from some of the errant masses, or lambeaux, which impact-theorists find it so easy to have at hand when required. Let us then think of why and how it came to pass that the sun is an almost perfect sphere.
If we suppose that, when cosmic matter ceased to be thrown off by it, the form of the nebula was that of a cylinder terminating in semi-spherical caps at the ends, it requires no great stretch of imagination to conceive that, between attraction and centrifugal force, the whole mass should be converted through time, first into a prolate spheroid, and then into a perfect sphere. And very possibly time only is required for the sun to become an oblate spheroid, the same as his dependent planets.
Should this form of nebula not be admissible—and we can see no mechanical reason why it should not—and we are thrown back on a lens-shaped nebula, the only resource left us is to suppose that through continued action of attraction, and of centrifugal force, or rather revolution constantly increasing, the latter gaining the victory over attraction, finally converted the lens into an actual ring, something of the nature of the ring in Lyra; and that that ring, no longer increasing in revolution, would have to yield to the law of attraction, and would condense and contract and close up into an oblate spheroid, and then into a sphere. It is a roundabout, rather fanciful, process, but any other way of converting a lens-shaped nebula into a sphere, under the law of attraction, is absolutely impossible.
Atthe end ofChapter VII., when making some remarks on the heat of the sun produced by gravitation, we said that according to the areolar law the condensation produced thereby would originate difference of rates of rotation in the nebula—provided it did rotate as Laplace assumed—depending on its degree of contraction and consequent density increasing as the centre was approached; and that these differences of velocity of rotation would give rise to achurning action in its interior which, owing to the friction caused thereby amongst the particles of its matter, would produce heat over and above what was produced by gravitation alone. Again, at the end ofChapter XII., we said it would not be difficult to show what tremendous commotions throughout the whole nebula would be produced by these differences of rotation; but that this could not be properly done until we had reconstructed the original nebula, and had shown how from it the solar system might be constructed. Now, therefore, that we have set forth, as fully as we can, our ideas of the formation of a hollow nebula and the construction from it of the solar system, we shall proceed to show how heat was, and must still be, produced by the churning action, over and above the definite quantity that could possibly be produced by simple gravitation. And also to show how our notions of the interior of the nebula first, and afterwards of the sun, are simplified and made more natural by looking upon it as a hollow sphere.
We will begin by considering, first, what would take place during the contraction and condensation of a rotating nebula solid to the centre—i.e. filled with cosmic matter to the centre—as that is the condition under which such a body has been studied hitherto—as far as we know at least....
Not to weary humanity—our own included—by repeating, what almost every one knows, who the parties were and how they came to the conclusion, that by far the greatest part—almost the whole—of the heat expended by the sun, ever since it had any to expend, has been produced by condensation caused by gravitation; we shall for the time being accept this as the general, almost universal, opinion at the present day. If any proof of this being the case is considered necessary, we have only to appeal to Sir William Thomson's lecture, delivered at the Royal Institution on January 21, 1877, in which he showed how a cone of matter, similar to that of which the sun is made, with base at the surface and apex near the centre, falling into a similar hollow cone excavated in his body, would, in descending a certain distance, generate as much heat as would maintain a proportional part of hisexpenditure for a year; and in which, beyond stating that a very small part might be produced by the fall of meteoric matter on his surface, he makes no mention whatever of any heat-producing power except gravitation pure and simple. The weight of the cone falling into the conical pit alone, produced almost the whole of the desired supply. That this manner of calculation is one of those modes which, as we have said from the very beginning of our work, could never have been adopted had a little more thought been expended on them, can be easily demonstrated even in the case we are now considering. This we say with all due deference to so great an authority; more especially as we know how difficult it is, how seeming unnecessarily laborious, to examine everything to the very bottom; and how pleasant and satisfying it is to feel contented, when we have obtained what suits our purpose.
When we began to consider, inChapter XV., what would be the interior construction of the nebula, we supposed, atpage 269, that it had assumed a somewhat globular form when its diameter came to be three times that of the orbit of Neptune, which would be 16,764,000,000 miles; and we will return to that supposition to set forth our conception of how heat would be produced in a nebula of that diameter solid to the centre—that is full to the centre of cosmic matter. In that case a particle of matter starting from the surface, under the power of gravitation, would have to travel 8,382,000,000 miles before it reached the centre, and would carry with it a constantly increasing power of producing heat, derived solely from the action of gravitation. Next, we have to consider what would stop it when it reached the centre and enable it to give out its heat—for until it was stopped it could give out no heat at all—and the most easily conceived means of stoppage would be to suppose that an equal and similar particle coming in from exactly the opposite side of the nebula met it there. If it was not that it would be something equivalent and much more difficult to describe, while the result would be the same. The result would be that, as each particle came in with equal power of producing heat, thethe amount produced when the two met and stopped each other would be just double what each of them brought with it; that is our way of looking at it at least, considering that the velocity with which they met would be just double what each brought with it, and the force of the shock would be double what it would have been had only one of them been stopped in some other way; that other way would have had to give or furnish its half of the shock, and would therefore be able to give out as much heat as the stopped particle. Whether two of Sir William Thomson's cones meeting at the bottom of his pit, from exactly opposite sides of the sun, would have the same effect as we have found for the two particles, may perhaps give rise to the discussion; but we do not see why the result should be in any way different. When a stone falls from a height upon the earth it gives out, in the form of heat, all the heat-producing power it had accumulated in its fall, but we are apt to forget, perhaps have never thought at all of, the why and the how it gives it out, especially of the latter. The why is because it is stopped, and the how is by the earth coming to meet it, and these two ways have an inseparable relation to each other. And if the earth comes to meet it, which it most undoubtedly does, though we cannot measure how far it travels, it must bring along with it an amount of heat-producing power equal to that possessed by the stone, when it in its turn is stopped by the stone; thus the amount of heat arising from the fall of a stone to the earth is, apparently, just double what it is usually estimated to be. This fact comes under the category of splitting hairs or, more truly speaking, of negligible quantities; but the whole mass of the sun falling to the centre cannot enter into that category, and whether we will or no we have to take it all into account.
We have conducted two particles of matter from exactly opposite points of the surface of the nebula to its centre, and shown that by simple gravitation a certain amount of heat would be produced by them when they met there and stopped each other; now, we propose to conduct two particles, not far from each other, from one side only of the nebula to the centre, and point out what would happen to them on theirvoyage thither. The road is long, as we have seen, and during their voyage there would be time enough for a good many things to happen, but we shall only take notice of two for the present, namely, gravitation—of which we have already almost disposed—and attraction; for as far as their journey is concerned there is a very marked difference in the meaning of the two words. Gravitation—that is, the action of a ponderable body falling—acts only in a straight line from any point to a centre of attraction, while attraction acts in every possible or imaginable direction. We have already seen what happened to the first particle despatched to the centre under the power of gravitation alone, and have only to say, that the same would happen, under that power, to the two we have now in hand; but attraction—actually the father or mother of gravitation—would have a good deal to do with their journey. From the moment they started—very likely they were practising before they left—they would rush at and continue to bombard each other during the whole voyage. At each encounter or collision, however caused, a certain amount of heat would be produced in each of them which they would carry along with them, and would augment the gravitational quantity they would have to give out when stopped in their fall, in the way we have pointed out would be the only one that could bring them to rest. It may be said that that heat would be left behind in space on the way but space cannot absorb heat unless it contains something to hold it in, and that something could only be similar particles of matter on the same voyage, also creating heat and having as much to dispose of, no doubt, as the two we are conducting. This lateral attraction, so to speak, is really what instituted rotary motion in the nebula, and produced the differences of rotation and the churning action in it with which we shall have to deal presently.
Having passed under examination the quantity of heat produced by the contraction and condensation of the solar nebula into a globe solid to the centre, we have now to do the same for the case of its being a hollow sphere, and we may say that our work has already almost come to an end; for wehave only to vary to a small extent what we have just set forth. Beginning then as before, with one particle of matter falling, or rather being attracted, from the surface of a hollow-sphere nebula, we find that it would not reach the centre at all, but would be stopped by another drawn out from the centre by its own attraction, which would meet it—say for brevity—half-way between the starting points of the two, each bringing along with it its own heat-producing power and giving it out to its opponent, there being nothing else to give it to; so that if each brought with itxheat-power they would have 2xheat-power between them, just as we have said would happen in the first case, and the heat of each one of them would consequently be doubled. In this case we have to observe, though it is really unnecessary, that as yet we have spoken of attraction as acting in one direction only, that is, in doing only the work of gravitation; so we have still to consider the voyage of two particles of matter proceeding from the surface and meeting two coming from the centre, and have only to say that their mutual collisions caused by lateral attraction on the way, would enable them to bring along with them certain quantities of heat produced by these collisions, which would be over and above what they acquired in their straight-line imaginary voyage.
If any one doubts that additional heat would be produced by this lateral attraction and bombarding, let him take two hammers and strike the one against the other as rapidly as he can for some time, and he will be able, by touch, to convince himself that heat can be produced by this lateral attraction as well as by theattraction of gravitation; and, if he could measure it afterwards, he would find that if he dropped the hammers on the ground, they would not give out any of that heat but only what they had derived from gravitation in falling from his hands to the ground, unless the ground was colder than they, and if the ground was not colder, the heat it had would be augmented from this source also.
If the heat produced in both of the cases we have been examining caused differences of rotation in the nebula—as we have said on a former occasion—increasing in velocity as theregion was approached where the stopping process came into action, it is clear that these differences would be greater near that region in a hollow-sphere nebula than near the centre of a solid sphere; for the reason that the particles of matter would there have more freedom, that is, more room to act in. We have shown that in the solid sphere the particles would come to be more or less inert, in proportion as they approached the centre; and also that in a hollow-sphere nebula no particle could ever come to be near to a state of rest, but that each could be freely driven by the collisions produced by lateral, angular, universal attraction over every part of the hollow shell—an effect that could by no means be produced in a nebula solid to the centre. We, therefore, think that there would be more life-power in a hollow-sphere sun than in the kind of sun from which all calculations of length of life have hitherto been made—at least, as far as we know.
It will be understood that we have spoken of particles of matter being stopped, or stopping each other, before they could give out their heat, only for facility of explanation; for no particle of matter can ever be brought to absolute rest, until all its heat and heat-producing power,i.e.motion, could be taken out of it, and that can only be when it is reduced to absolute zero of temperature. Cosmic matter could be reduced to the state of rock or steel, but its particles would not be at rest then, or else our ideas of the nature and construction of rock and steel are very erroneous; but it must be acknowledged that it would be much more easily reduced to the state of rock in a body solid to the centre than in the shell of a hollow sphere. In fact it is difficult to conceive how matter could exist at the centre of the sun at the present day without being as solid as rock, considering the enormous pressure it must be subjected to there, if its whole mass is condensing to the centre. But although the particles of the nebula could not be absolutely stopped, they might be so far retarded in their velocities derived from attraction that they would give out heat to each other, and wherever a collision took place there heat would be made evident, and condensation might take place. Particlesof matter would not have to fall to a centre, but only to a a meeting place, in order to condense and create heat, and might form layers of condensation anywhere between the centre and the surface, either in a solid or hollow sphere, which would ultimately, even in the former case, form a hollow shell, as we have supposed, atpage 274, might be the case. For even a small sphere formed around the centre in that way would be hollow, and would be undone when the different concentric layers approached each other, under proportionate forces of attraction, and formed into one hollow sphere. Thus we again come to the conclusion that the formation out of cosmic matter acted upon by the law of attraction, of a sphere full of that matter to the centre would be a mechanical impossibility. In either case the total quantity of heat produced by the contraction and condensation of the nebula would include, not only what has hitherto been looked upon as belonging to gravitation alone, but that other part derived from attraction in all other directions. So the age and duration of the sun still remain to be estimated.
We have not said, but we have not forgotten that it may be said that, if in Lord Kelvin's estimate of the sun's heat, a cone of matter falling in from one side of it was stopped by a similar cone falling in from the exactly opposite side, one half of the sun's mass stopping the other could only produce the amount of heat calculated by him. Neither do we deny that the same may be said of the two half-volumes of the sun meeting at the region of greatest density in a hollow sphere, and that the amount of heat produced by gravitation alone would be the same in both cases. All that we have wanted to show is that, in addition to the quantity so produced, the quantity produced by lateral attraction, so to speak, has to be taken into account, in order to estimate the total quantity ever possessed by the sun.
Referring now to what we have said towards the end ofChapter XV., of rotary motion being instituted at the region of greatest density of the nebula, and being propagated from there to all parts both outwards and inwards, we can at once account for the different periods of rotation observed ondifferent parts of the surface of the sun; and not only that, we can assert that these differences of rotation must exist throughout the whole volume and mass of its body up to the present day. We have no need to appeal for producing them to showers of meteors falling on its equatorial regions; neither do we pretend to say that such showers have no part in producing them; but we do say that the part they play in the affair, and the depth to which they can penetrate into the sun's body, must be altogether insignificant compared to what we have pointed out as the true and indisputable cause.
We may now proceed to consider what would result from the commotions produced by these differences of rotation in the interior of the sun, and we shall begin by observing that an enormous amount of heat would be produced thereby. The churning action, as we have called it, must be of a very formidable character, for, supposing the whole of the interior to be in a gaseous or gasiform state, it must be effected under a pressure of not less than 28 atmospheres at the surface, and at what pressures as the centre is approached no one can tell; and if the matter in the interior is in a viscous condition, the friction caused by the churning will only be the greater. But let us try to form an idea of what the force, or rather violence, of that churning action must be in the sun if constructed in the manner we are advocating; for which purpose we have to form some definite notion of what is the difference of velocity of rotation at different parts of its circumference, which can hardly be better shown than byTable X., in as far as these rotations have been approximately measured.
The first thing to be observed in the table is that the rate of rotation at the equator is 75·10 miles per minute, and that at Lat. 45° it is only 48·23 miles, giving a difference of 26·87 miles per minute in one-fourth part of the sun's circumference, which is a velocity 27 times greater than our fastest express trains. And the next is to note, in the last column, how these 26·87 miles of difference, when divided over spaces of 5° each, show decreases in velocity of from 0·39 at Lat. 5° to 5·06 miles between degrees 40 and 45.
A little thought bestowed on these two points will show what commotions must be produced at the surface by this enormous variation of rotation and make us speculate on how much greater it must be near the poles than at the half distance from the equator. Then, if we look upon the sun as a hollow sphere we have to consider that, according to the theory that the condensation of a nebula increases its rotation in proportion to its approach to the region of greatest density, of the velocities of all the rotations expressed in the table, the greatest must be at that region, the others diminishing from there outwards to those of the surface, and inwards to almost nothing at the centre; for we have seen that there must be gases enclosed in the hollow, and that motion must be communicated to them, through friction, down to the very centre. Taking all these things into consideration, it is certain that the churning must be very much greater than anything we have thought of up to the present moment, the commotions created more tumultuous, and the heat produced by friction incalculable.
TABLE X.—Showing the Differences in Velocity of Rotation of the Surface of the Sun, at Distances of 5° from each other, from the Equator to 45° of Latitude.
Note.—The times of rotation are taken from Messrs. Newcomb and Holden's "Astronomy," p. 290.
Lest we should have been misunderstood in what we have said a few pages back, and it be thought we consider that all the heat produced by this churning action ought to be added to that produced by gravitation alone, when attempts have been made to compute the total quantity ever possibly possessed by the sun, we have to insist that the idea of gravitation in itself—that is, of matter falling to a centre—is altogether erroneous in connection with the construction of the sun from a nebula, and that it is in truth utterly misleading. We know perfectly well that in the construction of the sun, heat could only be produced, in the main, by bodies colliding with, or rubbing against, each other, and that a large part of that produced by universal attraction must have been expended in producing rotary motion; but we also know that in its construction no particle of matter can ever, as yet, have been brought to the state of rest of solid matter even, that it has still the power of colliding with its neighbours and of producing heat, and that it will continue to preserve that power until it is bound up into a solid state along with its neighbours. Even then it will not be absolutely at rest, but will have lost its heat-producing power, and will begin to lose the quantity it then possesses when it gets permission from its neighbours. It is a fallacy, therefore, to suppose that the matter of which the sun is composed has no other heat-producing power than what is derived from its fall, through gravitation alone, from the potential position it held to the centre of the incipient nebula. The only end to heat-producing power is fixed position.
If science chooses to fix that position at the centre of the sun, or as near to it as successive particles can reach, there must be any quantity of it in a solid state even now in that neighbourhood, if due consideration is given to the pressure it must be subjected to there. If it chooses to entertain the idea of the sun's being a hollow sphere, somewhat in the form we have described, there can be nothing in its whole body so dense as even water up to the present time. In the first case it has to remember what we have done our best to prove: Thatgravitationceases to act when a body falls to a fixedcentre or position and can fall no farther. From there it cannot rise except through upper or exterior attraction, and in that case it would leave a hollow space in the place it had occupied. It is altogether illusory to dream of convection currents where no means or force of any other kind than attraction could give rise to them, in which case we should have attraction and gravitation working against each other, two things that have been confounded into one turning out to be antagonistic, as no doubt they sometimes actually are—as we have shown when treating of the discovery of Neptune—but when they are so, they never can produce convection currents. In the second case in which, as we have seen, there can be no matter at all near to the solid state or fixed position up to the present day, we can conclude that the life of the sun, measured by heat-producing power, must be very much longer than in the first case, in which a very large part of the matter of which it is composed must have lost that power ages ago.
We have still to bring to mind what we have said inChapter XV. of the region of greatest density of the nebula being the region of greatest activity and greatest heat; and to add now, that the whole space between that region and the centre must have been acting as a reservoir—partly material, partly gasiform—of heat, ever since the nebula began to contract and condense, quite independently of its carrying before it the minus or plus sign. From that time that region would be the regulator of the radiation of heat into space, or to wherever it was radiated; because no heat produced on the inner side could escape into space without passing through and acquiring the temperature of that region, or first giving out to the outer side any greater heat that it might have produced and accumulated; facts which involve the necessity of the whole of the interior space, or volume being heated up or lowered down to the same degree before any of it could be transmitted outwards. Thus, in addition to all we have said of the means of lengthening the sun's life, we have to take into consideration that all heat radiated from the surface must be conducted, or carried somehow, through a distance somewhere between about 2,000,000 and 90,000 miles, before itcould escape into space or elsewhere, according to when it began to be radiated at all. And we have also to take into consideration the probability that the heat produced and accumulated in the inner half of the volume would, by its repulsive force, retard the condensation of the nebula, and thus prolong its heat-giving life.
Looking back on our description of the construction of the sun, how rotary motion was established in it, and how that motion has produced the different velocities of rotation, not only on the surface where they have been observed and measured, but which must penetrate to the very centre; we may now proceed at the expense of some repetition—in which we have already somewhat indulged—to show how our mode of construction and development enables us to understand a great many things that have been observed in it, much better than we have been able to do from any explanations that have hitherto been available. It gives the most satisfactory reason possible for the sun-spots occupying principally two zones at marked distances from the equator. There is one belt round the equator of 16° to 20° wide on which we know, fromTable X., that the differences of velocity of its edges and of those of the contiguous zones, one on either side, hardly exceed 1 mile per minute. Towards the poles there are two segments measuring from 80° to 90° broad, at the borders of which the rotary velocity is slower by 26·37 miles per minute than it is at the equator, and 5·06 miles per minute slower than at 5° less latitude, as also shown by the table. And between the central belt and these segments there are two belts or zones, each 30° to 35° wide, in which sun-spots are almost only to be found. In these two zones the churning of the interior would be in all its vigour, most probably more active at their centres than where they meet the central belt and the polar segments; where our knowledge of the diminished velocity ceases, but where we have no reason to suppose that it actually stops.
Were the period of rotation the same throughout the whole body of the sun—with the exception of what has hitherto been considered to be a mere surface differenceproduced by external causes—we could conceive that the heat produced solely by condensation would find its way to the surface equally in all directions, even bubble up all round like steam rising from the surface of the water in a boiler, in this way forming what is called the sierra; and that there would be neither sun-spots nor eruptive prominences, hardly any of the violent movements recorded in works on astronomy. But the churning action we have been exhibiting, extending to the deepest recesses of the sun, must produce commotions quite adequate to give birth to the most violent phenomena that have been recorded. Viscous gases and vapours, gasiform vapours, ground against each other at depths of hundreds of thousands of miles, under pressures of hundreds, much more likely of many thousands, of atmospheres, and confined by superincumbent strata, so to speak, would acquire a dynamitical explosive force that could be conceived to be powerful enough to rend the sun into fragments, were it composed of anything comparable to solid matter. On the other hand, the friction of the solar matter operated under the pressure of 28 atmospheres at the surface, and up to the unknowable number at the greatest depth, converted into heat, would have explosive energy enough to give rise to all the phenomena that have been observed; from the veiled spot to Professor Young's prominence, which was thrown up to the height of 350,000 miles above the photosphere.
A veiled spot seems to be one that has broken through the photosphere, perhaps not even entirely, but not through the light or white clouds which float immediately over it; which, in consequence, goes a long way to prove that sun-spots have their origin in up-rushes of heated vapours from beneath; for a downfall of cooled metallic or other vapours would break through the light clouds first of all; and which is confirmed, as far as anything in solar physics can be confirmed, by what we are exposing. That there is a down-rush also, goes without saying, because there is no other way of giving account of what becomes of the vapours of metals and other elementary substances brought up by the outpours of heat, after they are cooled in the solar atmosphere. Thatthey should fall down into the same opening they had made in rising up, is the most natural supposition that can be made; for, otherwise, they would have to be carried beyond, or outside of, the spot before falling. Moreover, a sun-spot is said to be generally surrounded by prominences which bring up vapours of elementary substances, that we must believe to be much heavier than those from eruptions of sun-spots, because they issue much more violently, showing that they must have been expelled by much greater force, which must form a sort of wall all round the spot through which the matter, thrown out by it, would have to be carried before it could be deposited; and outside these walls there are no visible signs of where it falls, so that we are forced to believe that all the substances, those from prominences as well as those from sun-spots, fall into the same general receptacle. Surely it could not be argued that there can be no eruptions from a sun-spot, seeing that the force required to drive matter through it must be less than when it is expelled from depths very much greater than the depths of the spots. Thus we have both up-rush and down-rush in sun-spots accounted for very plainly; and they are always large enough for both operations being carried on at the same time. Besides, they have been credited by eminent astronomers with the faculty of sucking in the cooled vapours from the surrounding prominences into the common pit.
In some sun-spots, said to be about 3 per cent. of those observed, cyclonic motions have been observed in the umbræ and penumbræ, which under the churning process might be expected to be universal in all of them, but it is not necessarily so; even leaving out the consideration of the difficulty of detecting them. We see in a deep smooth-flowing river eddies revolving in all directions, caused by currents of different velocities approaching each other, quite independent of the form of the banks of the river or obstructions in the places where we see them, but without doubt derived from sources of that kind higher up in the river; and so it may be with cyclonic motions in the sun-spots. The velocity and direction might be given to the vaporous matter by thechurning action before issuing into the spot, which would cause eddies in it in all directions, the same as those in the water of the river. It would be absurd to think that in a space so immense as the bottom of a sun-spot, there should be only one orifice of emission of vaporous matter: there might be any number; consequently, there may be times when the out-flowing currents annul each other and none at all are seen, or when there are partial currents in any direction; others when they may be all so uniform as to produce a cyclonic motion all round a spot, or nearly all round it, or two or more in opposite directions, all as has been recorded on more than one occasion. Neither could it be supposed that any cyclonic motion, caused by the churning, could depend on which side of the equator the spot was formed in. There must be little churning going on under the surface at the equatorial belt, hence the paucity of spots there; but between the surface and the centre there must be some point of meeting of the motions that are produced on each side of the equator which, even were there no special reason for it, would destroy all chance of uniformity, or distinctive direction, in the upheaved matter when it arrived at the surface, let it reach that place on whichever side of the equator it might. The original salient motion at the bottom of a sun-spot might be to right or left, or according as the material from which it proceeded had been tumbled about, and the issuing motion might also be controlled greatly by the form and position of the orifice, or rather tunnel, through which it escaped. Common churning, we know, could not drive all the milk in one direction, even were the paddles of the churn solid; and in our case, the paddles have to be looked upon as even more divided, magnitude for magnitude, than they are in an ordinary churn, for the matter itself forms the paddles.
The cyclonic motions observed in prominences must come from the same causes, and ought to be more general in them, seeing that they must proceed from apertures much fewer in number than in the sun-spots, and very probably from one orifice in the case of jet prominences. One would expect also that these cyclonic motions would be more regular in theprominences, from being generated deeper down in the interior than those of the sun-spots, and less affected by the motions they encountered on their way out, owing to the great original energy required to force them through the superincumbent mass of matter, and might even have—in jet prominences especially—the motion to be expected according to the hemisphere from which they proceeded. But we have already said that, deep in the interior, the churning motion may be in any direction whatever. It is natural to suppose that the highest prominences are ejected from the greatest depths, because they require the greatest ejective force to throw them to such immense heights, and because the greatest ejective force must be where the heat and pressure are greatest, that is, at the densest and most active depths. And probably the reason why prominences generally surround sun-spots is that they have had their exits facilitated by the relief from pressure, brought about by the discharge of churned matter into them (the sun-spots), and thus, as it were, attracting the eruptions of the prominences towards them.
We had almost omitted to say that the churning theory would very well account for almost every sun-spot having more or less proper motion of its own independent of all others, and for all of them drifting towards the central belt, or towards the polar segments when they begin to dissolve and disappear.
There are many other things in connection with the sun that could be explained through our mode of construction, some of which are so evident that they will occur to anyone, and others that lead into depths too profound for us to enter.
To conclude. The construction of the sun we have set forth would be of great service towards the completion of either of what Professor A. C. Young calls the competing theories of M. Faye and Fr. Secchi, in which the former would find the origin of the solar storms, to which he appeals for producing sun-spots in particular zones, and a better way of accounting for the differences in velocity of rotation between the equator and the poles than in the depths of the strata between these regions; and the latter the means of forming the dense cloudsof eruption which he assumes to form sun-spots by settling down into the photosphere. But theorists seem to be partially right by a divination, and to have only failed through their not having found out the sources of the powers they called into existence, in order to have some foundation to build their theories upon.
Whenwe were attempting to describe in some measure the region of space from which the sun obtained the nebulous matter out of which it was formed, we found that it would produce a nebula somewhat resembling a most gigantic starfish, with arms or legs stretching out from it in every direction, which might be likened to mountain-peaks rising from a tableland or range of mountains; and when we began to condense the nebula we concluded that these peaks would very soon, comparatively, be left behind the main condensation, owing to their being more under the influence of the attraction of surrounding suns. And we might then have added less under the attraction of the main body, on accountof its gradually increasing distance arising from its greater rapidity of contraction. Now, we propose to return to these portions of the sun's property so long left out in the cold, to think of what in all probability became of them, seeing that they must all have had somehow a part of some kind to take in the formation of the solar system.
First of all, we have to form some idea, however vague, of their number, which may be divined to a very limited extent from the following considerations: We see, fromTable VIII., that the sun's sphere of attraction extends to more than 4000 Neptune distances in the direction of α Centauri, the star nearest to the earth, which corresponds to 11 billions of miles. Then, although we have said, inChapter XV., that instead of there being a peak on the nebula in that direction there would be a deep hollow in it, we shall proceed to find out what might be the diameter of the base of a peak at that distance supposing it to be somewhat in the form of a cone. We know that the moon does more than eclipse the sun, which is 867,000 miles in diameter; so, for facility of calculation, we may suppose that it eclipses a portion of space at its distance of 1,000,000 miles in diameter. Consequently, the base of a peak such as we are measuring would be eclipsed were it 129,000 millions of miles in diameter, and then only. Moreover, we have deduced the diameter of the base of such a peak fromonediameter of the moon; so that wherever we see two stars only one breadth of the moon from each other, there we have room for at least one peak with a base of the above diameter. Last of all, when we come to think that there are as many as six to seven thousand stars visible to the naked eye, and of the intervening spaces between them, we have to conclude that the number of peaks surrounding the original nebula before they began to be left behind, or cut off, must have been almost beyond our conception; more especially if we look atTable VII., where we see that the star Canopus is 25 times farther from the sun than α Centauri. We are accustomed to look with wonder on the volcanic peaks of the moon, but they can do nothing more than give us an exceedingly faint representation of the original nebula seen from an appropriatedistance outside, when it had begun to contract more rapidly than the peaks could follow it; seeing that we are comparing a diameter of 2,160 miles with one really almost infinitely greater.
Finding ourselves, then, with an innumerable host of peaks, or cones, of cosmic matter on our hands, we have to think of what can be done with them, and we begin by saying that the use to be made of them was suggested to us when we discovered the jagged nature of the domains of the sun. Some of them have been most probably swallowed up in the formation of the sun, and could we believe in the plenum of meteorites in all space, that has been fancied to exist by some physicists, we might derive its origin from a part of these peaks; but if there can be such a plenum in space, its origin might be much more naturally derived from a suggestion made in a former chapter, atpage 258, to which we shall refer presently. In the meantime, looking upon the multitude of comets, meteor-swarms, etc., which revolve around the sun, or are supposed to exist somehow in its neighbourhood, it is very natural to entertain the belief that they have been made out of some of the most important peaks—or the refuse from them—that must have formed part of the original nebula. To deal with all of them when we cannot number them, or even with the six ofTable VIII., about which we actually know something, is out of the question, so we shall only try to show what could be made out of one of them.
Confining ourselves, then, to the peak of α Geminorum, whose collecting ground had originally reached to 24,000 Neptune distances, or 67 billions of miles—this being the point of space where the attractions of the sun and that star balance each other—if we suppose it to have been contracted till its base was of the same diameter, and its distance the same from the sun, as that of the base of the peak we measured not many minutes ago, 129,000 million miles, and 11 billions of miles, respectively, we can easily conceive that its height may have been 10 times as great as the diameter of the base, or more than 1¼ billions of miles. Herethen we have in the direction of only one star a mass of cosmic matter out of which something more than a comet, even of the grandest known to modern astronomy, could be made. Of its tenuity, all that we have any necessity to think is, that it would be much less—i.e. more dense—than that of the original nebula.
Beginning then with the dimensions we have just stated, we know that the attraction of the nebula would draw the matter of the base-end of the peak more rapidly towards itself than that of the apex-end; we know also that there would be different rates of contraction going on in different parts of the length of the peak—for the same reason we have given for the peaks being cut off from the nebula; so that the condensation throughout its whole height, or length, would be proceeding at different rates at different places, which would certainly divide the peak into several parts, perhaps into many. If now we suppose that the leading part of it—the one nearest to the nebula or sun—or even the whole of it, formed itself into a comet, it is not difficult to see that it might have a tail infinitely longer than any comet the length of whose tail has been measured.
There can be no doubt that in the whole length of the peak the action of attraction would be exactly the same as we have found it to be in the nebula itself; that is to say there is no reason why it should not come to be a hollow cone—comets are reported to be hollow in most cases—condensed into layers, and to revolve on their axes throughout a great part at least of where their diameters are greatest. This mode of formation seems to throw light on some of the phenomena that have been observed in comets. We have just said that our peak would be divided into several parts, so if we suppose the leading part of it to have been made into a comet, we can see why its tail should have the appearance of a hollow cylinder; and there might be no reason why the second division, or even the third, should not become a comet also. Then for further divisions, where the diameter came to be too small to make a comet, its matter mighthave formed itself into a meteor-swarm, and account for the fact of some comets and meteor-swarms revolving round the sun in the same orbits; perhaps even for some of the observed meteor-swarms being denser at one part than another, owing to two or more of the sections of the peak following each other at some distance. We have to notice, after what we have just said, that it is quite possible that if the different sections of our peak did come to revolve round the sun, their perihelion distances might be so different that it would be impossible to trace any connection between them and the peak from which they were derived. But if we were to attempt to set forth all the explanations of the phenomena of comets and meteor-swarms that have occurred to us, there would be no end to our labour.
Passing now from one to the whole host of peaks, we have seen that at one time they projected from all sides of the nebula; it is clear, therefore, that the bodies formed from them must have fallen in towards the sun from all directions, which is exactly what they have been found to do. Then, if we think of the multitude of them there would be, we have also to think that there would most certainly be collisions among them, which would smash them to atoms, and thus help to make the plenum, or host of independent meteorites that are supposed to exist, or would be swallowed up by the sun in mouthfuls. Others might coalesce, which they could only do through coming in from slightly different directions and with nearly similar velocities; and they would thus account to us for comets with a plurality of tails. Again, looking back to what we have just said of the form that might be assumed by the leading end of the peak α Geminorum, which was suggested by Donati's comet, we could imagine another, the same in almost all respects, coalescing with it, and between the two showing us how Coggia's comet was formed. Furthermore, with respect to one of the gigantic comets with endless tails: If we suppose it to rotate on its axis, and to be not so smooth on its outside as a cone formed in a turning lathe, we could account for the light from thesun reflected from it having an appearance of flickering; and, were the outside very rough, for the reflected light flashing from millions of miles of its length in a few seconds.
All this about nebular peaks, comets, etc. formed from them, will, far more than likely, be looked upon as imagination or speculation run mad; but if it is looked into properly, it will be found that no part of it is based on assumption; farther than that, the universe has been formed out of cosmic matter of some kind. There is no step in the whole process, from cosmic matter to the sun—even myriads of suns—that does not conform to what are generally called the laws of nature; whereas it is not difficult to show that some other speculations on the same subject have never been carried beyond the stage of conception.
When thinking of how comets might be formed, we could not help thinking of their orbits and periods of revolution. It was easy to see that their orbits depended on where, and how far, they came from; that the where might be from any and every direction, and that the how far would be the principal element in their greater or lesser ellipticity, which could only be determined by measurement; but their periods of revolution, as far as we can see, could only be determined by observation, which would involve the study of several revolutions. On these points the data we have been able to collect are not very satisfying, neither are they given to us as very reliable, except as to those whose orbits have been often observed and measured; and even among these the orbits are said to vary, and some of the comets to disappear altogether. Again, some of them are said to have a disposition to become associated with particular planets; and yet again, some people have gone the length of supposing that they have been ejected from some of the planets. To us it seems much more rational to suppose that the known periodical comets have been made out of part of the multitude of peaks which must have surrounded the nebula at one time, if the sun was formed out of nebulous matter, subject to the attraction of similar matter surrounding it on all sides. It seems to be only a wayof getting out of a difficulty to suppose that matter ejected from, say the earth, with a velocity of 7 miles per second would be freed from its attraction, that it would be involved somehow in the sun's attraction, and that it would revolve thenceforth round the sun like any other wanderer; because we cannot see what would stop its progress upwards, so to speak, from the earth after getting beyond its control, or communicate to it at the right height and time, the exact velocity required to make it revolve for ever afterwards round the sun; nor, supposing the sun would have nothing to do with it, where it would go. When it left the earth, it might have a direct motion of near one-third of a mile per second derived from its rotation, and also one of 18 miles per second due to the revolution of the earth round the sun. It might also be ejected in a direction exactly away from, or directly towards the sun; so we should have two very different cases to reconcile in order to set up the theory of ejection of comets from planets, and of their being involved somehow in the sun's attraction. It presents us with a very strong case for calling for either the immediate intervention of some power other than what we conceive attraction to be, and of which we know nothing physically, or we have to trust inmanipulation of which we have no very exalted idea. We prefer to look upon the formation of all comets as derived from the peaks we have been treating of, or, if that is inadmissible, from shreds and patches of the original nebula; where no immediate intervention, or instant application, of supernatural power is required, but only the even and tranquil operation of original design.