Page:Popular Science Monthly Volume 16.djvu/100

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adopt, we are equally driven to the conception of the existence of some form of matter in the celestial spaces. The fact that light and heat are propagated from one part of space to another in time demands that the medium of communication should possess inertia—an essential property of matter. According to the wave theory, the celestial bodies move in an attenuated and subtile ethereal medium; according to the corpuscular theory, they move in a perpetual shower of corpuscles emitted by the sun and stars. In both cases matter exists—inertia exists—therefore resistance must be encountered. The smallness of the resistance, however small we choose to suppose it, does not allow us to escape this certainty. There is resistance, and therefore the movements of satellites cannot escape its influence. Nevertheless, such attenuated and bulky masses as comets are best adapted to test the existence of a resisting medium.

3. In the last place, it is possible that Mars may have originally rotated on his axis in five or six hours, but that the tidal rotation-retardation produced by the action of his moons might have brought about its present rotation-period. It is evident that the solar tides, on a planet so small and so remote from the sun, must be inappreciable; and, at first sight, the lunar tides produced by such small masses might be supposed to be equally insignificant. But it must be recollected that the tide-generating power of a moon is (other things being equal) inversely proportional to the cube of its distance; so that nearness might more than compensate for smallness of mass. To be more specific: In the mathematical language, the tide-generating power is in proportion to the

Diameter of Primary X Mass of Satellite
(Distance of Satellite)3

Thus, for example, let us suppose the diameter of our moon to be twenty times the diameter of the inner satellite of Mars, and both moons to be equally dense; then the mass of our moon would be 8,000 times that of the Martial satellite. Taking the diameter of the earth as equal to twice the diameter of Mars (and it is not so great), and the distance of our moon from the center of the earth to be forty-one and a half times the distance of the inner satellite from the center of Mars, we then have the tide-generating power of our moon acting on the earth, will be to that of the inner satellite acting on Mars as

2 X 8000 to 1, or as 16000 to 1, or as 1 to 1, or as 1 to 4½.
(41½)3 71743

Hence, the tide-generating power of this small satellite would, in consequence of its nearness to Mars, be about four and a half times as great as the tide-generating power of our moon on the earth.

This view, however, is not free from the most serious physical difficulties. For it is evident that the tidal rotation-retardation produced by the moons would be limited by the final condition, that the