Page:In the high heavens.djvu/326

 by mathematical principles, on which it is not necessary now to enter, that the critical velocity for each globe will be directly proportional to the square root of its mass, and inversely proportional to the square root of its radius. It can hence be easily shown that, supposing a number of globes are all made from the same materials, but are of different sizes, the critical velocity with which a body will have to be projected upwards varies simply as the radius of the globe. Of course, the condition supposed does not apply exactly to the various heavenly bodies, and, consequently, it would not be correct to assume that the law is quite so simple as that here stated. But for the purpose of our illustration we may so regard it, and this being so, let us consider a globe which has a diameter of 650 miles.

Such a body would be large enough for one of the greater of the minor planets, as large, perhaps, as the planet Ceres. As this is about one-twelfth part of the diameter of the earth it will follow, from the principle we have already laid down, that the speed with which a missile would have to be projected from Ceres, in order to carry it away from that globe altogether, would have to be one-twelfth of that which would be necessary to carry it away from the earth. As already stated, this is a speed quite comparable with that attained by our modern artillery; it therefore follows that if Ceres were 650 miles in diameter, and it must be of dimensions not very greatly differing from this amount, one of our great cannons, pointed vertically on this particular globe, would discharge its missile so that it would not return. It might therefore seem that by locating the volcano on one of the minor planets, a way is offered of getting out of the great difficulty, with regard