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Page:Popular Science Monthly Volume 19.djvu/766

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mountain which diverts the lead is found by a calculation of its form, magnitude, and density, and the mean density of the earth is afterward obtained by a calculation based upon the following data: Let A C (Fig. 2) represent the amount and direction of the attraction which the mountain exercises on the plummet, A B that of the earth upon the same; then A G represents the resultant attraction to which the lead is subjected. If, further, we make R represent the distance of the earth's center, and r that of the center of gravity of the mountain, from the lead, and M and m respectively, the masses of the earth and of the mountain, then we have, according to the law of attraction, , or since From this proportion the mass and density of the earth are deduced by a series of mathematical formulas which it is not necessary to give in detail here. PSM V19 D766 Calculating earth mass by triangulation.jpgFig. 2. Proceeding by this method, Maskelyne and Hutton undertook, between 1774 and 1776, the first efforts to estimate the specific gravity of the earth. They conducted their experiments near Mount Shehallien in Perthshire, Scotland, and found that the lead was deflected by the mountain to the amount of fifty-three seconds, whence they calculated the mean density of the earth to be 4·7. Making use of the observations of these two philosophers, Playfair and Seymour, after corrected calculations of the density of Shehallien, obtained a mean density of 4·7113. Although no theoretical objections can be offered to the manner in which these observations were applied, great exactness can not be claimed for the results, because the calculations of the mass of the mountain, of its mean density, and of the distance of its center of gravity from the lead, were based on estimates, and liable to errors.

Determination by Means of the Pendulum.—A pendulum which is forced out of the vertical direction tends to resume it as soon as the deflecting force is removed. Its momentum carries it beyond the vertical position, and it therefore swings back and forth in times proportionate to its length. The durations of single oscillations of the same pendulum may be considered to be equal to each other if the departure from the vertical does not exceed five degrees. The cause of the oscillations is gravity, or the attractive power of the earth. Since this force diminishes as the square of the distance from the earth's center increases, its amount at different elevations above