C(\ 



746 TII POPULAR SCIENCE MONTHLY. 



mountain which diverts the lead is found by a calculation of its form, 

 magnitude, and density, and the mean density of the earth is after- 

 ward 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 moun- 

 tain, 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, 



-^ : : : A B : A C, or since AC = BG, - : ::AB:BG. From 

 R, r R r" 



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. 



^ 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 Sey- 

 mour, after corrected calculations of the density 

 of Shehallien, obtained a mean density of 4*71 13. 

 Although no theoretical objections can be 

 offered to the manner in which these observa- 

 tions 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. 



Determinatiox by Means of the Pendu- 

 lum. A pendulum which is forced out of the 

 vertical direction tends to resvmie it as soon as 

 the deflectingr 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 os- 

 cillations 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 



B 



