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.
VI. Binary Systems.