On the Figure of the Earth. 109 



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 43 ten-thousandths." 



This theorem is generally true, whatever may be the density 

 of the sea, and the manner in which it covers the earth. 



Experiments with the pendulum made in the two hemispheres, 

 agree in giving to the square of the sine of the latitude, a co- 

 efficient somewhat larger, and nearly equal to 54 ten-thousandths. 

 It is therefore well proved by these experiments that the earth is 

 not homogeneous in the interior, and that the density of the strata 

 increases from the circumference to the centre. 



But the earth, though heterogeneous in a mathematical sense, 

 may still be chemically homogeneous, if the increase of density of 

 its strata is caused only by the additional pressure they suffer 

 as they approach towards the centre. It is easy to conceive that 

 the immense weight of the superior strata may considerably 

 increase their density, though they may not be fluid ; for it is 

 known that solid bodies are compressed by their own weight. 

 The law of the densities which result from these compressions 

 being unknown, we cannot tell how far the density of the terres- 

 trial strata may be thus increased. The pressure and the heat 

 which we can produce are very small, compared to those which 

 exist at the surface, and in the interior of the sun and stars. It 

 is even impossible for us to have an idea of the effect of these 

 forces, united in those immense bodies. Every thing tends to 

 make Us believe that they have existed at one time in a high 

 degree on the earth, and that the phenomena which they have oc- 

 casioned, modified by their successive diminution, form the pre- 

 sent state of the surface of our globe ; a state which is nothing 

 more than the element of a curve, of which time is the abscissa, 

 and of which the ordinates will represent the changes that 

 this surface has suffered without ceasing. We are far from 

 knowing the nature of this curve, and we cannot therefore ascend 

 with certainty to the origin of what we observe on the earth ; 

 and if, to satisfy the imagination, always troubled by ignorance 

 of the cause of the phenomena which interest us, a few conjec- 

 tures are ventured, it is wise not to offer them except with ex- 

 treme caution 



