be in round numbers 6,000,000,000,000,000,000,000 tons, or, as it is more conveniently written, 6 1021, where the 21, of course, denotes the number of ciphers after the 6. The moon's mass is nearly one eightieth (181) as great, or, in other words, if it lay upon the surface of the earth, it would weigh 75,000,000,000,000,000,000 tons (75 1018). This, however, must be diminished because the moon is, in fact, sixty times farther off, measuring in both cases from the center of the earth. Dividing, then, the moon's weight by the square of 60, or 3,600, we have for the weight at its actual distance something more than 21 1015 (21,000,000,000,000,000) tons after adding one eightieth for the attractive power of the moon itself, for there is a mutual attraction.
To get, then, the number of unit-bars necessary to equal this effect, we have only to divide the weight of the latter by the amount which one of these bars will sustain. That is, we divide 21 1015, by 24 1010, and find the quotient to be 87,500, which agrees with our statement.
It will be interesting to stop here, and endeavor to get some faint idea of what these enormous numbers mean. A bar of steel whose section is 87,500 square miles would include within its four sides a territory as large as that of New York State, and still leave enough to cover the State of Ohio, with a surplus of 536 square miles for good measure. We read in a certain book of a traveler who, coming into Lilliput, was held immovable by thousands of tiny threads. If a web of steel were stretched from the earth to the moon to hold our satellite from flying off into space, each tiny thread being represented by a bar of steel one fourth of an inch square no trifle, for each could hold 7,500 pounds—they would cover our globe on the side toward the moon with a network whose threads would be only six inches apart, and through which none but the smallest animals could pass.
It may aid us, while seeking to grasp such a force, if we reflect that the very small difference between the moon's pull upon the ocean and that upon the earth's center suffices to lift the tides; how vast, then, must be the whole pull upon the earth!
All this inconceivably great force is needed to bend our satellite's course from the straight line in which it would move if left to itself. This force is exerted, not once for all, as in case of the original impulse that sent the moon forward in its path, but afresh every second; for otherwise, after such an indrawing, it would move thenceforth in a straight line. To give a circular orbit, the direction of the moon needs to be changed every moment, and this requires a series of impulses.
Thus much for our earth's satellite. We may extend our reasoning to more distant bodies. The earth is 81 times the mass of the moon; the sun is 315,000 times the mass of the earth, and something more than 381 times as far from it as we are from the moon. Combining these in an easy calculation, we find that the sun puts forth upon our earth a coercive force to bend its path into an ellipse, a force
