.. 1 2 3 4 5 6 7 8 9 10 11 12 13 May. 31. 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 .. .. .. .. .. .. .. 1 2 3 4 5 6 7 8 9 10 June 30. 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 .. Weight of the Earth and Precession. 85. _The Weight of the Earth._--There are several methods of ascertaining the weight and mass of the earth. The simplest, and perhaps the most trustworthy method is to compare the pull of the earth upon a ball of lead with that of a known mass of lead upon it. The pull of a known mass of lead upon the ball may be measured by means of a torsion balance. One form of the balance employed for this purpose is shown in Figs. 98 and 99. Two small balls of lead, _b_ and _b_, are fastened to the ends of a light rod _e_, which is suspended from the point _F_ by means of the thread _FE_. Two large balls of lead, _W_ and _W_, are placed on a turn-table, so that one of them shall be just in front of one of the small balls, and the other just behind the other small ball. The pull of the large balls turns the rod around a little so as to bring the small balls nearer the large ones. The small balls move towards the large ones till they are stopped by the torsion of the thread, which is then equal to the pull of the large balls. The deflection of the rod is carefully measured. The table is then turned into the position indicated by the dotted lines in Fig. 99, so as to reverse the position of the large balls with reference to the small ones. The rod is now deflected in the opposite direction, and the amount of deflection is again carefully measured. The second measurement is made as a check upon the accuracy of the first. The force required to twist the thread as much as it was twisted by the deflection of the rod is ascertained by measurement. This gives the pull of the two large balls upon the two small ones. We next calculate what this pull would be were the balls as far apart as the small balls are from the centre of the earth. We can then form the following proportion: the pull of the large balls upon the small ones is to the pull of the earth upon the small ones as the mass of the large balls is to the mass of the earth, or as the weight of the large balls is to the weight of the earth. Of course, the pull of the earth upon the small balls is the weight of the small balls. In this way it has been ascertained that the mass of the earth is about 5.6 times that of a globe of water of the same size. In other words, the _mean density_ of the earth is about 5.6. [Illustration: Fig. 98.] [Illustration: Fig. 99.]