324 On the Mean Density of the Earth. 



ocean, divided by the semi-axis of the earth, the increase of this 

 length thus corrected, from the equator to the poles, will b& 

 equal to the product of the square of the sine of the latitude by 

 five-fourths of the ratio of the centrifugal force, to the gravity at 

 the equator, or by forty-three ten-thousandths. The multi- 

 plied experiments of the pendulum, made in both hemispheres, 

 and reduced to the level of the sea, agree in giving to the squa»e 

 of the sine of the latitude, a coefficient of more tlian forty-three 

 ten-thousandths, and very nearly equal to fifty-four ten-thou- 

 sandths. It is therefore fully proved by these experiments, that 

 the earth is not homogeneous, and that the densities of its strata 

 intrease from the surface to the centre. 



1 have shown in the volume before quoted, that the lunar in- 

 equalities, owing to the flattening of the earth, and the phaeno- 

 mena of precession and nutation, lead to the same result, which 

 can therefore admit of no doubt. 



But all these phaenome.oa, indicating a mean densitv of the 

 earth, greater than that of water, yet they do not give the pro- 

 portion of their densities; experiments on the attraction of bodies 

 on the surface of the earth, can alone determine this proportion. 

 In order to ascertain it, it was first attempted to measure the 

 attraction of high mountains. This object particularly excited 

 the attention of the French academicians who were sent to Peru 

 to measure a degree of the meridian. This attraction may be 

 observed either by the pendulum, the rate of which it increases, 

 or by the deviation that it occasions in the direction of the 

 plumb-line of astronomical instruments. Both these methods 

 were employed at Peru. The result of the comparisons of the 

 experiments made on the pendulum at Quito, and on the sea- 

 shore, is that, by the action of the Cordilleras, the gravity at 

 Quito is greater than it would be if only the elevation of Quito 

 were considered; and this indicates a density in these mountains 

 nearly equal to one-fifth of the mean density cf the earth. 

 The deviations of the plumb-line have given a result that differs 

 a little. But our ignorance of the interior constitution of these 

 mountains, the certainty that they are volcanic, joined to the un- 

 certainty of the observations, do not admit of a positive decision 

 on the true specific density of the earth. A mountain was 

 therefore to be sought, of considerable size, and well known as 

 to its interior consMtution. Schihallien in Scotland seemed to 

 unite these advantages. Dr. Maskeiyne observed the deviation 

 of the plumb-line by an astronomical instrument, on two oppo- 

 site sides of the mountain, and found tlieir sum equal to 1 \"6. 

 But it was then necessary to ascertain the sum of the attractions 

 of all the parts of the mountain, on the plumb-line, which re- 

 duired a delicate, long and troublesome calculation, and the 



iuvpntioi^ 



