what goes up coming down again. But even the Earth is not omnipotent. As the velocity with which the body is projected increases, longer and longer time is needed for the Earth to overcome it and compel the body's return. Finally there would be reached a speed which the Earth would just be able to overcome if she took an infinite time about it. In that case the body would continue to travel away from her, at a constantly diminishing rate, but still at some rate, on and on into the depths of space, if there were no other bodies in the universe but the Earth and the molecule, till it attained infinity, at which point the truant would stop, and then reluctantly return. This velocity we may call the critical velocity. It is also known as the parabolic velocity, because it is at any point the velocity of a body moving in a parabola about the Earth, under the Earth's attraction; the parabola being the curve of a fall from infinity. The critical velocity is the parabolic velocity, inasmuch as gravity is able to destroy on the way up just the speed it is able to impart on the way down. But, now, if the body's departure were even hastier than this, the Earth would never be able wholly to annihilate its speed, and the body would travel out and out forever. If its speed at starting were less than twenty-seven miles a second, it would become thenceforth a satellite of the Sun; if its speed were yet greater, it would become an independent rover through space, paying brief visits only to star after star. In any case the Earth would know the vagabond no more.

As gravity depends upon mass, the larger the attracting planet the greater is its critical velocity, the velocity it can just control; and, reversely, the smaller the planet the less its restraining power. With the Earth the critical velocity is six and nine tenths miles a second. If any of us, therefore, could manage to acquire a speed greater than this, socially or otherwise, we could bid defiance to the whole Earth, and begin to voyage on our own account through space. [See Appendix]

This speed is actually attained, as we have seen, by the molecules of hydrogen. If, therefore, a molecule of free hydrogen were present at the surface of the Earth, and met with no other gas attractive enough to tie it down by uniting with it, the rover would, in course of time, attain a speed sufficient to allow it to bid good-by to Earth, and start on interspacial travels of its own. That it should reach its maximum speed is all that is essential to liberty, the direction of its motion being immaterial. To molecule after molecule would come this happy dispatch, till the Earth stood deprived of every atom of free hydrogen.

Now, it is a highly significant fact that there is no free hydrogen found in the Earth's atmosphere. There is plenty of it in the captivity of chemical combination, but none in the free state. This coincidence of lack of hydrogen with lack of liberty takes on yet more significance from the further fact that the same is not true of oxygen, water vapor, or indeed of any of the other gases we know. With them, freedom is not synonymous with absence. The Earth's atmosphere contains plenty of free oxygen, nitrogen, and the like. But, as we have just seen, [See Appendix] the maximum speed of all these gases falls short of the possibility of escape. This accounts for their presence. They have stayed with us solely because they must.

The appearance of the other heavenly bodies seems to confirm this conclusion. The Moon, for example, possesses no atmosphere, and calculation shows that the velocity it can control falls short of the maximum of any of our atmospheric gases, that velocity being but one and one half miles a second. All were, therefore, at liberty to leave it, and all have promptly done so. On the other hand, the giant planets give evidence of very dense atmospheres. They have kept all they ever had.

But the most striking confirmation of the theory comes from the cusps of Venus and Mercury; for an atmosphere would prolong, by its refraction, the cusps of a crescent beyond their true limits. Length of cusp becomes, consequently, a criterion of the presence of an atmosphere. Now, in the appearance of their cusps there is a notable difference between Venus and Mercury. The cusps of Venus extend beyond the semi-circle; Mercury's do not. We see, therefore, that Mercury has apparently little or no atmospheric envelope, and we find that his critical velocity is only 2.2 miles per second,--below that of water vapor, and perilously near that of nitrogen and oxygen.

Turning to the case of Mars, we find with him the critical velocity to be three and one tenths miles a second. Now, curiously enough, this is, like the Earth's, below the maximum for the molecules of hydrogen,