On the Figure of the Earth. 3/3 



density of the strata of the terrestrial spheroid. I have supposed 

 that some interest may be excited by the following analysis, from 

 which it appears that it is possible to explain all the known phee- 

 nomena depending on the law of the density of these strata. 

 These phsenomena are the variation of the degrees of the meri- 

 dian, and of gravity, the precession of the equinoxes, the nuta- 

 tion of the terrestrial axis, the inequalities which the flattening 

 of the earth produces in the motion of the moon, and lastly, the 

 ratio of the mean density of the earth to .that of water, which 

 Cavendish has fixed by an admirable experiment at five and a 

 half. In proceeding from the law already announced of the com- 

 pression of liquids and solids, I find that, if the earth be sup- 

 posed to be formed of a substance chemically homogeneous, of 

 which the density is 2| that of common water, and which com- 

 pressed by a vertical column of its own substance, equal to the 

 millionth part of half the polar axis, will augment in density 

 5.5345 millionths of its first density, it will account for all the 

 phaenomena. The existence of such a body may be easily ad- 

 mitted, and is apparent from the surface of the earth. 



If our globe were entirely formed of water ; and if, in confor- 

 mity with Canton's experiments, it be supposed that the density 

 of water at 10' (50° Fahr.) and compressed by a column of wa- 

 ter 10 metres (32.81925 ft.) in height increases by 44 millionths, 

 the flattening of the earth would be rhr') ^''^ coefficient of the 

 square of the sine of the latitude in the expression of the length 

 of the seconds pendulum vvould be 59 ten-thousandths, and the 

 mean density of the, earth would be nine times that of water. 

 These results diflfer from observations by more than the errors to 

 which they are liable. 



I have been supposing the temperature uniform throughout 

 the whole extent of the terrestrial spheroid ; but it is very possi- 

 ble that the heat is greater towards the centre, and that would 

 be the case if the earth, originally highly heated, were continu- 

 ally cooling. The ignorance in which we are with respect to the 

 internal constitution of this planet, prevents us from calculating 

 the law by which the heat decreases, and the resulting diminu- 

 tion in the mean temperature of climates ; but we can prove 

 this diminution to have been insensible for these 2,000 years. 



Let us suppose a space of a constant temperature, containing 

 a sphere possessing a rotary motion ; and that, after a long time 

 the temperature of the space diminishes one degree ; the sphere 

 will finally take this new temperature; its mass will not be at all 

 altered, but its dimensions will diminish by a quantity which I 

 will suppose to be a hundred thousandth, a diminution which is 

 nearly that of glass. In consecjuence of the principle of areas, 

 the sum of the areas which each molecule of the sphere will de- 

 A a 3 scribe 



