THE IMPACT THEORY OF STELLAR EVOLUTION.

Upwards of twenty years ago^[1] the theory—or, I should rather say, the hypothesis—was advanced^[2] that our sun was formed from a hot gaseous nebula produced by the colliding of two dark stellar masses; and that, as the stars are suns like our own, they in all likelihood had a similar origin. The probability of this theory has been very much strengthened by the facts, both astronomical and physical, which have accumulated since the theory was enunciated. Before proceeding to the consideration of these facts, and the conclusions to which they lead, it will be necessary to give a statement of the fundamental principles of the theory.

In the theory here discussed the truth of the nebular hypothesis, which begins by assuming the existence of a solar nebulous mass, is taken for granted. The present theory deals not so much with the nebulous mass itself as with the formation of the nebula, and with those causes which led to its formation. For convenience of reference, and to prevent confusion, I have called it the “Impact Theory,” by which name it may be distinguished, on the one hand, from the nebular theory, and, on the other hand, from the meteoric theory, and all other theories which regard gravitation as the primary source of the solar energy.

The theory starts with the assumption that the greater part of the energy possessed by the universe exists or is stored up in the form of the motion of stellar masses. The amount of energy which may thus be stored up is startling to contemplate. Thus a mass equal to that of the sun, moving with a velocity of 476 miles per second, would possess, in virtue of that motion, energy sufficient, if converted into heat, to maintain the present rate of the sun’s radiation for 50,000,000 years.^[3] There is nothing extravagant in the assumption of such a velocity. A comet, for example, having an orbit extending to the path of the planet Neptune, approaching so near the sun as to almost graze his surface in passing, would have a velocity within 86 miles of what we have assumed. Twice this assumed velocity would give 200,000,000 years’ heat; four times the velocity would give 800,000,000 years’ heat; and so on.

We are at perfect liberty to begin by assuming the existence of stellar masses in motion; for we are not called upon to explain how the masses obtained their motion, any more than we have to explain how they came to have their existence. If the masses were created, they may as likely have been created in motion as at rest; and if they were eternal, they may as likely have been eternally in motion as eternally at rest.

Eternal motion is just as warrantable an assumption as eternal matter. When we reflect that space is infinite—at least in thought—and that, for aught we know to the contrary, bodies may be found moving throughout its every region, we see that the amount of energy may be perfectly illimitable.

But, illimitable as the amount of the energy may be, it could be of no direct service while it existed simply as the motion of stellar masses. The motion, to be available, must be transformed into heat: the motion of translation into molecular, or some other form of motion. This can be done in no other way than by arresting the motion of the masses. But how is such motion to be arrested? How are bodies as large as our earth, moving at the rate of hundreds of miles per second, to have their motion stopped? According to the theory this is effected by collision: by employing the motion of the one body to arrest that of the other.

Take the case of the formation of our sun according to the theory. Suppose two bodies, each one-half of the mass of the sun, moving directly towards each other with a velocity of 476 miles per second. These bodies would, in virtue of that velocity, possess 4149 × 10³⁸ foot-pounds of energy, which is equal to 100,000,000,000 foot-pounds per pound of the mass; and this, converted into heat by the stoppage of their motions, would suffice to maintain, as was previously stated, the present rate of the sun’s radiation for a period of 50,000,000 years. It must be borne in mind that, while 476 miles per second is the velocity at the moment of collision, more than one-half of this would be derived from the mutual attraction of the two bodies in their approach to each other.

Coming in collision with such a velocity, the result would inevitably be that the two bodies would shatter each other to pieces. But, although their onward motions would thus be stopped, it is absolutely impossible that the whole of the energy of their motions could be at once converted into heat; and it is equally impossible that it could be annihilated. Physical considerations enable us to trace, though in a rough and general way, the results which would necessarily follow. The broken fragments, now forming one confused mass, would rebound against one another, breaking up into smaller fragments, and flying off in all directions. As these fragments receded from the centre of dispersion they would strike against each other, and, by their mutual impact, become shivered into still smaller fragments, which would in turn be broken up into fragments yet smaller, and so on as they proceeded outwards. This is, however, only one part of the process, and a part which would certainly take place, though no heat were generated by the collisions.

A far more effective means of dispersing the fragments and shattering them to pieces would be the expansive force of the enormous amount of incandescent gas almost instantaneously generated by the heat of collision. The general breaking up of the two masses and the stoppage of their motions would be the work of only a few minutes, or a few hours at most. The heat evolved by the arrested motion would, in the first instance, be mainly concentrated on the surface layers of the broken blocks. The layers would be at once transformed into the gaseous condition, thus enveloping the blocks and filling the interspaces. It is difficult to determine what the temperature and expansive force of this gas would at the moment be, but evidently it would be excessive; for, were the whole of the heat of the arrested motion distributed over the mass, it would, as has been stated, amount to 100,000,000,000 foot-pounds per pound of the mass—an amount sufficient to raise 264,000 tons of iron 1° C. Thus, if we assume the specific heat of the gas to be equal to that of air (viz. ·2374), it would have a temperature of about 300,000,000° C. or more than 140,000 times that of the voltaic arc.

I hardly think it will be deemed extravagant to assume that at the moment after impact the temperature of the evolved gas would be at least as great as here stated. If we assume it to be so, it is obvious that the broken mass would, by the expansive force of the generated gas, be dispersed in all directions, breaking up into fragments smaller and smaller as they knocked against one another in their progress outwards from the centre of dispersion; and these fragments would, at the same time, become gradually converted into the gaseous state, and gradually come to occupy a space as large as that embraced in our solar system. In the course of time the whole would assume the gaseous condition, and we should then have a perfect nebula—intensely hot, but not very luminous. As its temperature diminished, the nebulous mass would begin to condense, and ultimately, according to the well-known nebular hypothesis, pass through all the different phases of rings, planets, and satellites into our solar system as it now exists.

I am glad to find that the theory, in one of its main features, has been adopted by Sir William Thomson,^[4] the highest authority we have on all points relating to the source of the sun’s heat.

“We cannot,” says Sir William, “help asking the question, What was the condition of the sun’s matter before it came together and became hot? (1) It may have been two cool, solid masses, which collided with the velocity due to their mutual gravitation; or (2), but with enormously less of probability, it may have been two masses colliding with velocities considerably greater than the velocities due to their mutual gravitation.”

He adopts the first of these suppositions. “To fix the idea,” he continues, “think of two cool, solid globes, each of the same mean density as the earth, and of half the sun’s diameter, given at rest, or nearly at rest, at a distance asunder equal to twice the earth’s distance from the sun. They will fall together and collide in exactly half a year. The collision will last for about half an hour, in the course of which they will be transformed into a violently agitated incandescent fluid mass flying outward from the line of the motion before the collision, and swelling to a bulk several times greater than the sum of the original bulks of the two globes. How far the fluid mass will fly out all around from the line of collision it is impossible to say. The motion is too complicated to be fully investigated by any known mathematical method; but with sufficient patience a mathematician might be able to calculate it with some fair approximation to the truth. The distance reached by the extreme circular fringe of the fluid mass would probably be much less than the distance fallen by each globe before the collision, because the translational motion of the molecules constituting the heat into which the whole energy of the original fall of the globes becomes transformed in the first collision is probably about three-fifths of the whole amount of that energy. The time of flying out would probably be less than half a year, when the fluid mass must begin to fall in again towards the axis. In something less than a year after the first collision the fluid will again be in a state of maximum crowding round the centre, and this time probably even more violently agitated than it was immediately after the first collision; and it will again fly outward, but this time axially towards the places whence the two globes fell. It will again fall inwards, and after a rapidly subsiding series of quicker and quicker oscillations it will subside, probably in the course of two or three years, into a globular star of about the same dimensions, heat, and brightness, as our present sun, but differing from him in this, that it will have no rotation.”^[5]

This is precisely what I have been contending for during the past twenty years, with the simple exception that I assume, according to his second supposition, that the “two masses collided with velocities considerably greater than the velocities due to mutual gravitation.” Sir William admits, of course, my supposition to be quite a possible one, but rejects it on the supposed ground of its improbability. His reasons for this, stated in his own words, are as follows:

“This last supposition implies that, calling the two bodies A and B for brevity, the motion of the centre of inertia of B relatively to A must, when the distance between them was great, have been directed with great exactness to pass through the centre of inertia of A; such great exactness that the rotational momentum or moment of momentum after collision was no more than to let the sun have his present slow rotation when shrunk to his present dimensions. This exceedingly exact aiming of the one body at the other, so to speak, is, on the dry theory of probability, exceedingly improbable. On the other hand, there is certainty that the two bodies A and B at rest in space if left to themselves, undisturbed by other bodies and only influenced by their mutual gravitation, shall collide with direct impact, and therefore with no motion of their centre of inertia, and no rotational momentum of the compound body after the collision. Thus we see that the dry probability of collision between two neighbours of a vast number of mutually attracting bodies widely scattered through space is much greater if the bodies be all given at rest than if they be given moving in any random directions and with any velocities considerable in comparison with the velocities which they would acquire in falling from rest into collision.”

Sir William here argues that the second supposition is far less probable than the first, because, according to it, the motion of the one body relatively to the other must, in order to strike, be directed with great exactness. The result, in such a case, is that collision will rarely occur; whereas, according to the first supposition, the two bodies starting from a state of rest will, by their mutual gravitation, inevitably collide. According to the second hypothesis they will generally miss; according to the first they will always collide.

I have been led to a conclusion directly opposed to Sir William’s. The fact, that, according to the second supposition, collisions can but rarely occur is one reason, amongst others, why I think that supposition to be true; and the fact that, according to the first supposition, collisions must frequently occur is also one reason, amongst others, why I think it very improbable that it can represent the true condition of things.

It by no means adds anything to the probability of the first supposition to assert that, according to it, such collisions will occur readily and frequently. On the contrary, it would show that the supposition was the less likely to be true. If the collisions were insufficient in character, the fewer of them that occurred, the better; for the result of such collisions would simply be a waste of the potential energies of the universe. We should in this case have an innumerable host of imperfect suns without planets, or with at most only one or two, and these at no great distance from the luminary. There would thus be evolved a universe without any grand planetary systems. There is still another objection to the supposition. The same gravitating force which makes the dark bodies liable to come into collision with each other must, of course, make them equally liable to come into collision with the luminous bodies, and with our sun amongst the rest. Our sun would, accordingly, be at the mercy of any of those masses which might happen to come within the reach of its attractive influence. It would pull the mass towards it, and a collision would be inevitable, unless it so happened that a transverse motion of the sun itself might enable it to escape destruction. Even in such a case it could not by any means manage to get rid of the entangling mass.

All this risk, in so far as gravitation is concerned, would have been completely averted if an original projected velocity of some thirty or forty miles per second had been conferred on the dark mass; for, in this case, the attractive force of the sun would fail to arrest its motion, and the mass would pass onward through space, never to return. This simple conception of an original motion removes entirely those objections which, we have seen, besets the supposition we have been considering. With such a motion, not only would the risk to our solar system be removed, but the collisions between the dark bodies themselves would be a matter of rare occurrence; and hence the energy of the universe would be conserved. And when a collision did happen it would be on a grand scale, and the result would be not an imperfect sun without planets, but an incandescent nebula, out of which, by condensation, a complete solar system would be evolved. In fact, within the whole range of cosmical physics, I know of nothing more impressive in its sublime simplicity than this plan, by which the stability and perfection of the universe is thus secured. How vast the ends—how simple the means!

Recent researches establish beyond doubt that stars, nebulÆ, comets and meteorites, do not differ much from our earth in their chemical constitution. Meteorites, it is true, differ in their physical characteristics from ordinary rock such as is found on the earth’s surface. But it is possible, if not probable, that the earth’s interior mass “may,” as Sir Henry Roscoe remarks, “partake of the physical nature of these metallic meteorites, and that if we could obtain a portion of matter from a great depth below the earth’s surface we should find it exactly corresponding in structure as well as in chemical composition with a metallic meteorite, and the existence of such interior masses of metallic iron may go far to explain the well-known magnetic condition of our planet.”^[6] I think there can be little doubt that, were our earth broken up into small fragments, and these scattered into space, it would probably be impossible to distinguish them from ordinary meteorites. The two would be so like in character that one can hardly resist the conviction that meteorites are but the fragments of sidereal masses which have been shattered by collision. That meteorites are broken fragments is the opinion expressed by Sir William Thomson, who says “that he cannot but agree with the common opinion which regards meteorites as fragments broken from larger masses, and that we cannot be satisfied without trying to imagine what were the antecedents of those masses.” The theory we have been considering appears to afford an explanation of their antecedents. According to it, they are broken fragments of two dark stellar masses which were shattered to pieces by collision. After what has been stated concerning the production of the gaseous nebulÆ out of which our solar system was formed, it must be regarded as highly improbable, if not impossible, that the whole of the fragments projected outwards with such velocity should be converted into the gaseous condition. Multitudes of the smaller fragments, especially those towards the outer circumference of the nebulous mass, meeting with little or no obstruction to their onward progress, would pass outwards into space with a velocity which would carry them beyond the risk of falling back into the nebula. They would then continue their progress in their separated forms as meteorites. If this be their origin, then meteorites are the offspring of sidereal masses, and not their parents, as Mr. Lockyer concludes.

These meteorites must be of vast antiquity, for if they are fragments of the dark bodies then they must be not only older than our solar system, but older than the nebula from which that system was formed. Some of them, however, may have come from other systems. They are fragments which may yet cast some light on the history of the dark bodies.

Comets, bodies which in many points seem allied to meteorites, probably have, as we shall shortly see, a similar origin.

It will be only when the two bodies, coming from contrary directions, collide with equal momentum that the entire motion will be stopped. But in the case of stellar masses moving, as it were, at random in every direction this is a condition which will but rarely occur. Accordingly, in most cases the resulting stars will have more or less motion. In short, the stars should, according to the theory, be moving in all directions and with all varieties of velocity. Further, it follows that these motions ought to be in perfectly straight lines, and not in definite orbits of any kind. So far as observation has yet determined, all these conditions seem to be fulfilled. Sometimes it will happen that the two bodies will strike each other obliquely. In this case the resulting star, both as to the direction and velocity of its motion, will, to a large extent, be the resultant of the two concurrent forces.

According to the theory the absolute motion of the stars is due, not to the influence of gravity, but to motions which originally belonged to the two component masses out of which the star arose; motion regarding the origin of which science can no more inform us than it can regarding the origin of the masses themselves. There is strong presumptive evidence that the motion of the stars is due to this cause. We know that there are stars which have a far greater velocity than can result from gravitation, such, for example, as the star 1830 Groombridge, which has a velocity of 200 miles per second. Suppose, with Professor Newcomb, that the number of stars belonging to the universe amounts to 100,000,000, and that these have, on the average, five times the mass of the sun, and are spread out in a layer across which light requires 30,000 years to pass. Then computation shows that, unless the attractive power of the whole were sixty-four times greater than it really is, it could not have conferred on Groombridge the motion which it possesses, or arrest it in its onward course.^[7] We are therefore forced, as Professor Newcomb remarks, to one of two alternatives, viz.: “Either the bodies which compose our universe are vastly more massive and numerous than telescopic examination seems to indicate, or 1830 Groombridge is a runaway star, flying on a boundless course through infinite space, with such momentum that the attraction of all the bodies of the universe can never stop it.”

As regards the theory we are discussing, it is the same which alternative is taken, for both are equally favourable. If the former, then, according to the theory that stellar heat had its origin in collision, it is presumptive evidence that space is occupied by dark bodies far more numerous and massive than the luminous ones which the telescope reveals. If the latter, viz. that the star has a velocity which never could have been produced by attraction, “then,” as says Professor Newcomb, “it must have been flying forward through space from the beginning, and, having come from an infinite distance, must now be passing through our system for the first and only time.” The probability is, however, that the star derived its motion from the source from which it derived its light and heat; namely, from the collision of the two masses out of which it arose. If the star is ever to be arrested in its onward course, it must be by collision; but such an event would be its final end.

There are other stars, such as 61 Cygni, e Indi, Lalande 21258, Lalande 21185, CassiopeiÆ, and Arcturus, possessed of motions which could not have been derived from gravity. And there are probably many more of which, owing to their enormous distances, the proper motions have not been detected. a Centauri, the nearest star in the heavens, by less than one-half, is distant twenty-one millions of millions of miles; and there are, doubtless, many visible stars a thousand times more remote. A star at this distance, though moving transversely to the observer at the enormous rate of 100 miles per second, would take upwards of thirty years to change its position so much as one second, and consequently 1,800 years to change its position one minute. In fact, we should have to watch the star for a generation or two before we could be certain whether it was moving or not.

Great difficulty has been experienced in accounting for the origin of comets upon the nebular hypothesis. They approach the sun from all directions, and their motions, in relation to the planets, are as often retrograde as direct. Not only are their orbits excessively elliptical, but they are also inclined to the ecliptic at all angles from 0° to 90°. It is evidently impossible to account satisfactorily for the origin of comets if we assume them all to have been evolved out of the solar nebula, although this has been attempted by M. Faye and others. Comets are evidently, as Laplace and Professor A. Winchell both conclude, strangers to our system, and have come from distant regions of space. If they belonged to the solar system they could not, says Professor Winchell, have parabolic and hyperbolic paths. “Only a small portion of the comets,” he remarks, “are known to move in elliptic orbits.”^[8] This assumption that they are foreigners will account for all the peculiarities of their motions; but how are we to account for their coming into our system? How did they manage to leave that system in which they had their origin? If a comet have come from one of the fixed stars trillions of miles distant, the motion by which it traversed the intervenient space could not, possibly, have been derived from gravity. We are therefore obliged to assume that the motion was a projected motion. Comets, in all probability, have the same origin as meteorites. The materials composing them, like those of the meteorites, were probably projected from nebulÆ by the expulsive force of the heat of concussion which produced the nebulÆ. Some of them, especially those with elliptic orbits, may have possibly been projected from the solar nebula.

It is a curious circumstance that the theory here advanced seems to afford a rational explanation of almost every peculiarity of nebulÆ, as I have, on former occasions, endeavoured, at some length, to prove.^[9]

1. Origin of nebulÆ.—We have already seen that the theory affords a rational account of the origin of nebulÆ.

2. How nebulÆ occupy so much space.—It accounts for the enormous space occupied by nebulÆ. It may be objected that, enormous as would be the original temperature of the solar system produced by the primeval collision, it would nevertheless be insufficient to expand the mass, against gravity, to such an extent that it would occupy the entire space included within the orbit of Neptune. But it will be perceived, from what has already been stated regarding the dispersion of the materials before they had sufficient time to assume the gaseous condition, that this dispersion was the main cause of the gaseous nebula coming to occupy so much space. And, to go farther back, it was the suddenness and almost instantaneity with which the mass would receive the entire store of energy, before it had time to assume even the molten, not to say the gaseous, condition, which led to tremendous explosions, followed by a wide dispersion of materials.

3. Why nebulÆ are of such varied shapes.—Although the dispersion of the materials would be in all directions, it would, according to the law of probability, very rarely take place uniformly in every direction. There would generally be a greater amount of dispersion in some directions than in others, and the materials would thus be carried along various lines and to diverse distances; and, although gravity would tend to bring the widely scattered materials ultimately together into one or more spherical masses, yet, owing to the exceedingly rarified condition of the gaseous mass, the nebulÆ would change form but slowly.

4. Broken fragments in a gaseous mass of an excessively high temperature the first stage of a nebula.—From what has already been shown, it will be seen that after the colliding of the two dark bodies the first condition of the resulting nebula would be an enormous space occupied by broken fragments of all sizes dashing against each other with tremendous velocities, like the molecules in a perfect gas. All the interspaces between those fragments would be entirely filled with a gaseous mass, which, at its earliest stages at least, as in the case of the solar nebula, would have a temperature probably more than one hundred thousand times that of the voltaic arc. Whether such a mass would be visible is a point which can hardly be determined, as we can have no experience on earth of a gas at such a temperature.

That there are some of the nebulÆ which appear to consist of solid matter interspersed in a gaseous mass is shown by the researches of Mr. Lockyer^[10] and others. In fact, the theory is held by Professor Tait^[11] that nebulÆ consist of clouds of stones—or meteor-swarms, as Mr. Lockyer would term them—in an atmosphere of hydrogen, each stone of which, moving about and coming into collision with some other, is thereby generating heat which renders the circumambient gas incandescent. In reference to this theory of Professor Tait, Mr. Lockyer says that the phenomena of the spectroscope can be quite well explained “on the assumption of a cloud of stones, providing always that you could at the same time show reasonable cause why these clouds of stones were ‘banging about’ in an atmosphere of hydrogen.”^[12] The theory, however, does not appear to afford any rational explanation of this banging about of the stones to and fro in all directions; for, according to it, the only force available is gravitation, and this can produce merely a motion of the materials towards the centre of the mass. Under these conditions very little impinging of the stones against each other would take place. But, according to the theory here adopted, we have an agency incalculably more effective than gravity, one which accounts not merely for the impact of the stones, but for their very existence as such, inasmuch as it explains both what they are and whence they came.

Mr. Lockyer has recently fully adopted Professor Tait’s suggestion as to the nature and origin of nebulÆ, and has endeavoured to give it further development. He considers the nebulÆ to be composed of sparse meteorites, the collisions of which give the nebulÆ their temperature and luminosity. He divides the nebulÆ into three groups, “according as the formative action seems working towards a centre; round a centre in a plane, or nearly so; or in one direction only.” As a result we have globular, spheroidal, and cometic nebulÆ.

Globular nebulÆ he accounts for in the following manner. “If we,” he says, “for the sake of the greatest simplicity consider a swarm of meteorites at rest, and then assume that others from without approach it from all directions, their previous paths being deflected, the question arises whether there will not be at some distance from the centre of the swarm a region in which collisions will be most valid. If we can answer this question in the affirmative, it will follow that some of the meteorites arrested here will begin to move in almost circular orbits round the common centre of gravity.

“The major axes of these orbits may be assumed to be not very diverse, and we may further assume that, to begin with, one set will preponderate over the rest. Their elliptic paths may throw the periastron passage to a considerable distance from the common centre of gravity; and if we assume that the meteorites with this common mean distance are moving in all planes, and that some are direct and some retrograde, there will be a shell in which more collisions will take place than elsewhere. Now, this collision surface will be practically the only thing visible, and will present to us the exact and hitherto unexplained appearance of a planetary nebula—a body of the same intensity of luminosity at its edge and centre—thus putting on an almost phosphorescent appearance.

“If the collision region has any great thickness, the centre should appear dimmer than the portion nearer the edge.

“Such a collision surface, as I use the term, is presented to us during a meteoric display by the upper part of our atmosphere.”^[13]

Spheroidal nebulÆ, he considers, are produced by the rotation of what was at first a globular rotating swarm of meteorites.

Cometic nebulÆ are explained, he considers, “on the supposition that we have either a very condensed swarm moving at a very high velocity through a sheet of meteorites at rest, or the swarm at rest surrounded by a sheet, all moving in the same direction.”

In an able and interesting work, which seems almost utterly unknown in England,^[14] Professor Winchell has advanced views similar to those of Tait and Lockyer regarding the nature and origin of nebulÆ. But he, in addition, discusses the further question of the origin of those swarms. I shall have occasion to refer to Professor Winchell’s views more fully when we come to the consideration of the pre-nebular condition of the universe.

Amongst the first to advance the meteoric hypothesis of the origin and formation of the solar system was probably the late Mr. Richard A. Proctor. This was done in his work, “Other Worlds than Ours,” published in 1870. “Under the continual rain of meteoric matter,” he says, “it may be said that the earth, sun, and planets are growing. Now, the idea obviously suggests itself that the whole growth of the solar system, from its primal condition to its present state, may have been due to processes resembling those which we now see taking place within its bounds.” He further adds: “It seems to me that not only has this general view of the mode in which our system has reached its present state a greater support from what is now actually going on than the nebular hypothesis of Laplace, but that it serves to account in a far more satisfactory manner for the principal peculiarities of the solar system. I might, indeed, go farther, and say that where those peculiarities seem to oppose themselves to Laplace’s theory they give support to those I have put forward.”^[15] He then goes on to show the points wherein his theory seems to him to offer a better explanation of those peculiarities than that of Laplace.

5. The gaseous condition the second stage of a nebula.—The second stage obviously follows as a necessary consequence from the first; for the fragments, in the case under consideration, possess energy in the form of motion, which, with the heat of their circumambient vapour, is more than sufficient not only to convert the fragments into the gaseous state, but to produce complete dissociation of the chemical elements. The complete transformation of the first stage into the second must, therefore, be simply a matter of time.

According to the laws of probability it may, however, sometimes happen that the two original dark bodies will not collide with force sufficient to confer on the broken fragments the energy required to convert them all into the gaseous condition. The result in this case would, no doubt, be that the untransformed fragments, drawn together by their mutual attractions, would collide and form an imperfect star or sun, without a planet. Such a star might continue luminous for a few thousands or perhaps a few millions of years, as the case might be, when it would begin to fade, and finally disappear. We have here an imperfect nebula, resulting in an imperfect star. In short, we should have in those stellar masses, on a grand scale, what we witness every day around us in organic nature, viz. imperfect formations. Such occasional imperfections give variety and add perfection to the whole. How dreary and monotonous would nature be, were every blade of grass, every plant, every animal, and every face we met formed after the most perfect model!

6. The gaseous condition essential to the nebular hypothesis.—It is found that the density of the interior planets of our solar system compared with that of the more remote is about as five to one. The obvious conclusion is that there is a preponderance of the metallic elements in the interior planets and of metalloids in the exterior. It thus becomes evident, as Mr. Lockyer has so clearly shown,^[16] that when our solar system existed in a nebulous condition the metallic or denser elements would occupy the interior portion of the nebula and the metalloids the exterior. Taking a section of this nebula from its centre to its circumference, the elements would in the main be found arranged according to their densities: the densest at the centre, and the least dense at the circumference. If we compare the planets with their satellites, we find the same law holding true. The satellites of Jupiter, for example, have a density of about only one-fifth of that of the planet, or about one twenty-fifth of that of our earth, showing that when the planet was rotating as a nebulous mass the more dense elements were in the central parts and the less dense at the outer rim, where the satellites were being formed. Again, if we take the case of our globe, we find, as Mr. Lockyer remarks, the same distribution of materials, proving that when the earth was in the nebulous state the metallic elements chiefly occupied the central regions, and the metalloids those outer parts which now constitute the earth’s crust.

All these facts show that the sifting and sorting of the chemical elements according to their densities must have taken place when our solar system was in the condition of a nebula. But, further, it seems impossible that this could have taken place had the materials composing the nebula been in the solid form, even supposing that they had taken the form of clouds of stones.

It is equally impossible that the nebula could have been in the fluid or liquid state during this process. This is obvious, for the nebula must then have occupied, at least, the entire space within the orbit of the most remote planet. But our solar system in the liquid condition could not occupy one-millionth part of that space. It is therefore evident that the nebula must have been in the state of a gas, and a gas of extreme tenuity.

7. The mass must have possessed an excessive temperature.—There is ample evidence, Mr. Lockyer thinks, to show that the temperature of the solar nebula was as great as that of the sun at the present time. But I think it is extremely probable that, in some of its stages, the nebula had a very much higher temperature than that now possessed by the sun. There must, during the sifting period, have been complete chemical dissociation, so as to keep the metals and the metalloids uncombined, and thus allow the elements to arrange themselves according to their densities. The nebula hypothesis, remarks Mr. Lockyer, “is almost worthless unless we assume very high temperatures, because, unless you have heat enough to get perfect dissociation, you will not have that sorting out which always seems to follow the same law.”

8. Gravitation could, under no possible condition, have generated the amount of heat required by the nebular hypothesis.—The nebular hypothesis does not profess to account for the origin of nebulÆ. It starts with matter existing in space in the nebulous condition, and explains how, by condensation, suns, planets &c. are formed out of it. In fact, it begins at the middle of a process: it begins with this fine, attenuated material in the process of being drawn together and condensed under the influence of attraction, and professes to explain how, as the process goes on, a solar system necessarily results. To simplify our inquiry we shall confine our attention to the solar nebula, and consider in the first place how far condensation may be regarded as a sufficient source of heat.

A. Condensation.—The heat which our nebula could have derived from condensation up to the time that Neptune was detached from the mass, no matter how far the outer circumference of the mass may have originally extended beyond the orbit of that planet, could not have amounted to over 1/7,000,000 of a thermal unit (772 foot-pounds) for each cubic foot. It is perfectly obvious that this amount could not have produced the dissociation required; and without the required dissociation Neptune could never have been formed. Further, it is physically impossible that the materials of which our solar system are composed could have existed in the gaseous state in a cool condition prior to condensation. Unless possessed of great heat, even hydrogen could not exist in stellar space in the gaseous form; and far less could carbon, iron, platinum, &c. Before Neptune could have been formed the whole of the materials of the system must have possessed heat, not only sufficient to reduce them to the gaseous state, but sufficient to produce complete dissociation. But by no conceivable means could gravitation have conferred this amount of heat by the time that the mass had condensed to just within the limits of the orbit of Neptune.

B. Solid globes colliding under the influence of gravity alone.—As we have already seen, the view has been adopted by Sir W. Thomson that the solar nebula may have resulted from the colliding of cold, solid globes with the velocity due to their mutual gravitation alone. He states his views as follows:

“Suppose, now, that 29,000,000 cold, solid globes, each of about the same mass as the moon, and amounting in all to a total mass equal to the sun’s, are scattered as uniformly as possible on a spherical surface of radius equal to one hundred times the radius of the earth’s orbit, and that they are left absolutely at rest in that position. They will all commence falling towards the centre of the sphere, and will meet there in 250 years, and every one of the 29,000,000 globes will then, in the course of half an hour, be melted, and raised to a temperature of a few hundred thousand or a million degrees Centigrade. The fluid mass thus formed will, by this prodigious heat, be exploded outwards in vapour or gas all round. Its boundary will reach to a distance considerably less than one hundred times the radius of the earth’s orbit on first flying out to its extreme limit. A diminishing series of out-and-in oscillations will follow, and the incandescent globe, thus contracting and expanding alternately, in the course, it may be, of 300 or 400 years, will settle to a radius of forty times the radius of the earth’s orbit.”^[17]

The reason which he assigns for the incandescent globe settling down at a radius forty times that of the earth’s orbit is as follows: “The radius of a steady globular gaseous nebula of any homogeneous gas is 40 per cent. of the radius of the spherical surface from which its ingredients must fall to their actual positions in the nebula to have the same kinetic energy as the nebula has.”

If the solar nebula thus produced would be swelled out into a spherical incandescent mass with a radius 40 times the radius of the earth’s orbit, simply because the globes fell from a distance of 100 times the radius of that orbit, then for a similar reason the mass would have a radius of 400 times that of the earth’s orbit had the globes fallen from a distance of 1,000 times the radius, and 400,000 times if the globes had fallen from a distance of 1,000,000 times the radius, and two-fifths of any conceivable distance from which they may have fallen.

Supposing all this to be physically possible, which it undoubtedly is not, still the heat generated would not be sufficient; for, whatever the radius of the nebula might be, its entire energy, both kinetic and potential, is simply what is obtained from gravitation, and this, as we have seen, is insufficient.

9. Condensation the third and last condition of a nebula.—According to the gravitation theory, condensation is the first stage of a nebula as well as the last; for, according to it, gravity is the force which both collects together the scattered materials and gives them their heat.^[18] Before condensation begins there can, according to the gravitation theory, be no such thing as a nebula properly so called. The materials exist, of course, but they do not exist in the form of a nebula. According to the impact theory which I here advocate, condensation cannot begin till after the nebula has begun to lose the heat with which it was originally endowed.

10. How nebulÆ emit such feeble light.—The light of nebulÆ is mainly derived from glowing hydrogen and nitrogen in a condition of extreme gaseous tenuity; and it is well known that these gases are exceedingly bad radiators. The oxyhydrogen flame, although its temperature is surpassed only by that of the voltaic arc, gives a light so feeble as to be scarcely visible in daylight. The small luminosity of nebulÆ is, however, mainly due to a different cause. The enormous space occupied by those bodies is not so much due to the heat which they possess as to the fact that their materials were dispersed into space before they had time to pass into the gaseous condition; so that, by the time that this latter state was assumed, the space occupied was far greater than was demanded either by the temperature or by the amount of heat which they originally received. If we adopt the nebular hypothesis of the origin of our solar system, we must assume that our sun’s mass, when in the condition of a nebula, extended beyond the orbit of the planet Neptune, and consequently filled the entire space included within that orbit. Even supposing Neptune’s orbit to have been its outer limit, which, obviously, was not the case, it would nevertheless have occupied 274,000,000,000 times the space it does at present. We shall assume, as before, that 50,000,000 years’ heat was generated by the concussion. Of course, there might have been twice or even ten times that quantity; but it is of no importance what amount is in the meantime adopted. Enormous as 50,000,000 years’ heat is, it yet gives, as we shall presently see, only 32 foot-pounds of energy for each cubic foot. The amount of heat due to concussion being equal, as before stated, to 100,000,000,000 foot-pounds for each pound of the mass, and a cubic foot of the sun at his present density of 1·43 weighing 89 pounds, each cubic foot must have possessed 8,900,000,000,000 foot-pounds. But when the mass was expanded sufficiently to occupy 274,000,000,000 times its original space (which it would do when it extended to the orbit of Neptune), the heat possessed by each cubic foot would then amount to only 32 foot-pounds.

In point of fact it would not even amount to so much, for a quantity equal to upwards of 20,000,000 years’ heat would necessarily be consumed in work against gravity in the expansion of the mass, all of which would, of course, be given back in the form of heat as the mass contracted. During the nebulous condition, however, this quantity would exist in an entirely different form, so that only 19 out of the 32 foot-pounds per cubic foot generated by concussion would then exist as heat. The density of the nebula would be only 1/16,248,160 that of hydrogen at ordinary temperature and pressure. The 19 foot-pounds of heat in each cubic foot would thus be sufficient to maintain an excessive temperature; for there would be in each cubic foot only 1/440,000 of a grain of matter. But, although the temperature would be excessive, the quantity both of light and heat in each cubic foot would of necessity be small. The heat being only 1/71 of a thermal unit, the light emitted would certainly be exceedingly feeble, resembling very much the electric light in a vacuum-tube.

The theory affords a rational explanation of the origin of binary stars. Binary stars, in so far as regards their motion, follow also, of course, as a consequence, from the gravitation theory. If two bodies come into grazing collision, “they will,” says Sir William Thomson, “commence revolving round their common centre of inertia in long elliptic orbits. Tidal interaction between them will diminish the eccentricities of their orbits, and, if continued long enough, will cause them to revolve in circular orbits round their centre of inertia.”^[19] This conclusion was pointed out many years ago by Dr. Johnstone Stoney.

The case of a star suddenly blazing forth and then fading away, such as that observed by Tycho Brahe in 1572, may be accounted for by supposing that the star had been struck by one of the dark bodies—an event not at all impossible, or even improbable. In some cases of sudden outbursts, such as that of Nova Cygni, for example, the phenomenon may result from the star encountering a swarm of meteorites. The difficulty in the case of Nova Cygni is to account for the very sudden decline of its brilliancy. This might, however, be explained by supposing that the outburst of luminosity was due to the destruction of the meteorites, and not to any great increase of heat produced in the star itself. A swarm of meteorites converted into incandescent vapour would not be long in losing its brilliancy.

Mr. Lockyer thinks that the outburst was produced by the collision of two swarms of meteorites, and not by the collision of the meteorites with a previously existing star.^[20]

Amongst the millions of stars occupying stellar space catastrophes of this sort may, according to the theory, be expected sometimes to happen, although, like the collisions which originate stars themselves, they must, doubtless, be events of but rare occurrence.

A star cluster will result from an immensely widespread nebula breaking up into a host of separate nuclei, each of which becomes a star. The irregular manner in which the materials would, in many cases, be widely distributed through space after collision would prevent a nebula from condensing into a single mass. Subordinate centres of attraction would be established, as was long ago shown by Sir William Herschel in his famous memoir on the formation of stars;^[21] and around these the gaseous particles would arrange themselves and gradually condense into separate stars, which would finally assume the condition of a cluster.

When we come to the question of the age of the sun’s heat, and the length of time during which that orb has illuminated our globe, it becomes a matter of the utmost importance which of the two theories is to be adopted. On the age of the sun’s heat rests the whole question of geological time. A mistake here is fundamental. If gravitation be the only source from which the sun derived its heat, then life on the globe cannot possibly date farther back than 20,000,000 years; for under no possible form could gravitation have afforded, at the present rate of radiation, sufficient heat for a longer period. It will not do to state in a loose and general way, as has been frequently done, that the sun may have been supplying our globe with heat at its present rate for 20,000,000 or 100,000,000 years, for gravitation could have done no such thing; a period of 20,000,000, not 100,000,000, years is the lowest which is admissible on that theory. Not even that length of time would be actually available; for this period is founded on Pouillet’s estimate of the rate of solar radiation, which has been proved by Langley to be too small, the correct rate being 1·7 times greater. “Thus,” as says Sir W. Thomson, “instead of Helmholtz’s 20,000,000 years, we have only 12,000,000.” But the 12,000,000 years would not in reality be available for plant and animal life; for undoubtedly millions of years would elapse before our globe could become adapted for either flora or fauna. If there is no other source of heat for our system than gravitation, it is doubtful if we can calculate on much more than half that period for the age of life on the earth. Professor Tait probably over-estimates the time when he affirms “that 10,000,000 years is about the utmost that can be allowed, from the physical point of view, for all the changes that have taken place on the earth’s surface since vegetable life of the lowest known form was capable of existing there.”^[22] And this is certainly about all that can ever be expected from gravitation; mathematical computation has demonstrated that it can give no more. The other theory, founded on motion in space—a cause as real as gravitation—labours under no such limitation. According to it, so far at least as regards the store of energy which may have been possessed by the sun, plant and animal life may date back, not to 10,000,000 years, but to a period indefinitely more remote. In fact, there is as yet no known limit to the amount of heat which this cause may have produced; for this depended upon the velocities of the two bodies at the moment prior to collision, and what these velocities were we have no means of knowing. They might have been 500 miles a second, or 5,000 miles a second, for anything which can be shown to the contrary. Of course I by no means affirm that it is as much as 100,000,000 years since life began on our earth; but I certainly do affirm that, in so far as a possible source of the sun’s energy is concerned, life may have begun at a period as remote.