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.”