Page:In the high heavens.djvu/335

 describe a little circle, about a second and a half in diameter. This is extremely small, it is about as large as a penny piece would look if placed three miles from the observer. The number of such circles, whose collective areas would be required to cover the sky, would be about 500,000,000,000. Now what would be the chance that a rifle bullet, supposing it could carry far enough, directed perfectly at random, would strike a bull's eye the size of a penny piece at a distance of three miles?

It is obvious that the solution to this is to be found in the following manner. Suppose a sphere to be constructed with a radius of three miles, and that the whole inside of this sphere be divided into a mosaic each with an area as large as a penny piece; then as each one of those pieces would be just as likely as any other to be struck by a bullet discharged absolutely at random, the improbability that any particular piece would be hit will be expressed by unity divided by their entire number. A volcano placed at the distance of Alpha Centauri, and discharging missiles quite at random, could only hit that ring which represents the earth's track in one shot out of every five hundred thousand millions. But even these figures do not express the improbability that a meteorite should arise in this manner. For if the missile happened to pass through the interior of the earth's orbit, it would not fall on the earth any more than if it had passed outside the orbit altogether. It is, as we have already explained, an indispensable condition that the body should pierce that particular zone eight thousand miles in width which marks the track of the earth in the ecliptic. As the area of this ring is not the five- thousandth part of the whole area of its orbit, it follows that to pierce the ring