They circle about each other as long as these forces endure; for the first world does not stand still and the second do all the going; both revolve around the centre of gravity common to both. In case the worlds are equal in mass, they will both take the same orbit around a central stationary point, midway between the two. In case their mass be as one to eighty-one, as in the case of the earth and the moon, the centre of gravity around which both turn will be 1/81 of the distance from the earth's centre to the moon's centre. This brings the central point around which both worlds swing just inside the surface of the earth. It is like an apple attached by a string, and swung around the hand; the hand moves a little, the apple very much. Thus the problem of two revolving bodies is readily comprehended. The two bodies lie in easy beds, and swing obedient to constant forces. When another body, however, is introduced, with its varying attraction, first on one and then on the other, complications are introduced that only the most masterly minds can follow. Introduce a dozen or a million bodies, and complications arise that only Omniscience can unravel. [Page 10] [Illustration: Fig. 2.] Let the hand swing an apple by an elastic cord. When the apple falls toward the earth it feels another force besides that derived from the hand, which greatly lengthens the elastic cord. To tear it away from the earth's attraction, and make it rise, requires additional force, and hence the string is lengthened; but when it passes over the hand the earth attracts it downward, and the string is very much shortened: so the moon, held by an elastic cord, swings around the earth. From its extreme distance from the earth, at A, Fig. 2, it rushes with increasing speed nearly a quarter of a million of miles toward the sun, feeling its attraction increase with every mile until it reaches B; then it is retarded in its speed, by the same attraction, as it climbs back its quarter of a million of miles away from the sun, in defiance of its power, to C. All the while the invisible elastic force of the earth is unweariedly maintained; and though the moon's distances vary over a range of 31,355 miles, the moon is always in a determinable place. A simple revolution of one world about another in a circular orbit would be a problem of easy solution. It would always be at the same distance from its centre, and going with the same velocity. But there are over sixty causes that interfere with such a simple orbit in the case of the moon, all of which causes and their disturbances must be considered in calculating such a simple matter as an eclipse, or predicting the moon's place as the sailors guide. One of the most puzzling of the irregularities [Page 11] of our night-wandering orb has just been explained by Professor Hansen, of Gotha, as a curious result of the attraction of Venus. [Illustration: Fig. 3.--Changes of orbit by mutual attraction.]