New Theories in Astronomy

by William Stirling

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 their voyage 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 we have 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 it x heat-power they would have 2x heat-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 the attraction 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 the region 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. Particles of 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, at [page 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 of [Chapter 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 on different 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 by [Table 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.