compound body after the collision. Thus we see that the dry probability of collision between two 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. In this connection it is most interesting to know from stellar astronomy, aided so splendidly as it has recently been by the spectroscope, that the relative motions of the visiblestars and our sun are generally very small in comparison with the velocity (612 kilometres per second) a body would acquire in falling into the sun, and are comparable with the moderate little velocity (29⋅5 kilometres per second) of the earth in her orbit round the sun.
To fix the ideas, 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 half a year. The collision will last for a few hours, in the course of which they will be transformed into a violently agitated incandescent fluid mass, with about eighteen million (according to the Pouillet-Helmholtz reckoning, of twenty million) years' heat ready made in it, and swelled out by this heat to possibly one and a half time, or two, or three, or four times, the sun's present diameter. If instead of being at rest initially they had had a transverse relative velocity of 1⋅42 kilometres per second, they would just escape collision, and would revolve in equal ellipses in a period of one year round the center of inertia, just grazing one another's surfaces every time they come round to the nearest points of their orbits.
If the initial transverse component of relative velocity be less than, but not much less than, 1⋅42 kilometre per second, there will be a violent grazing collision, and two bright suns, solid globes bathed in flaming fluid, will come into existence in the course of a few hours, and will commence revolving round their common center of inertia in long elliptic orbits in a period of a little less than a year. The quasi-tidal interaction will diminish the eccentricities of their orbits; and if continued long enough will cause the two to revolve in circular orbits round their center of inertia with a distance between their surfaces equal to ⋅644 of the diameter of each.
If the initial transverse component relative velocity of the two bodies were just sixty-eight metres per second, the moment of momentum, the same before and after collision, would be just equal to that of the solar system, of which seventeen eighteenths is Jupiter's and one eighteenth the sun's; the other bodies of the system being not worth considering in the account. Fragments of superficially melted solid, or splashes of fluid, sent flying away from the main compound mass could not possibly by tidal action or other resistance get into the actual
