By methods involving these principles, but applied in a manner more complicated as well as more precise, the mass of the earth is found to be, in tons, 6,642 × 10^{18}--i. e., 6,642 followed by 18 ciphers, or in kilogrammes 60,258 × 10^{20}. The earth's atmosphere makes up about a millionth part of this mass. If the length of the plumb line were 100 feet, the weight of the ball a ton, and the distance between the two positions of the ball, _1_ and _2_, six feet, how many inches, _d_, would the plumb bob be pulled out of place? Find from the mass of the earth and the data of § 40 the mass of the sun in tons. Find also the mass of Mars. The computation can be very greatly abridged by the use of logarithms. 46. PRECESSION.--That the earth is isolated in space and has no support upon which to rest, is sufficiently shown by the fact that the stars are visible upon every side of it, and no support can be seen stretching out toward them. We must then consider the earth to be a globe traveling freely about the sun in a circuit which it completes once every year, and rotating once in every twenty-four hours about an axis which remains at all seasons directed very nearly toward the star Polaris. The student should be able to show from his own observations of the sun that, with reference to the stars, the direction of the sun from the earth changes about a degree a day. Does this prove that the earth revolves about the sun? But it is only in appearance that the pole maintains its fixed position among the stars. If photographs are taken year after year, after the manner of Exercise 7, it will be found that slowly the pole is moving (nearly) toward Polaris, and making this star describe a smaller and smaller circle in its diurnal path, while stars on the other side of the pole (in right ascension 12h.) become more distant from it and describe larger circles in their diurnal motion; but the process takes place so slowly that the space of a lifetime is required for the motion of the pole to equal the angular diameter of the full moon.