402 M. Laplace on the Figure of the Earth. [Dec. 



This theorem is generally true, whatever be the density of the 

 sea and the manner in which it covers a part of the earth. 



The experiments with the pendulum made in the two hemi- 

 spheres agree in giving to the square of the sine of the latitude 

 a greater coefficient, very nearly equal to 54 ten millionths. It 

 is then proved by these experiments that the earth is not homo- 

 geneous in its interior, and that the density of its strata increases 

 from the surface to the centre. 



But the earth, though heterogeneous in a mathematical sense, 

 would be homogeneous in a chemical sense, if the increase of 

 the density of these beds were owing merely to the increase of 

 pressure which they experience in proportion as they approach 

 the centre. We may conceive in fact that the immense weight 

 of the superior beds may increase their density considerably, 

 even supposing them not to be fluid ; for we know that solid 

 bodies are compressed by their own weight. The law of the 

 densities resulting from this compression being unknown, we 

 cannot determine how much the density of the strata of the 

 earth may be thus increased. The pressure and the heat which 

 we can produce are always very small when compared with 

 those which exist at the surface and in the interior of the sun 

 and stars. It is even impossible for us to have an approximate 

 idea of the effects of these forces united in these great bodies. 

 Every thing leads to the notion that they existed at first in a 

 great degree in the earth, and that the phenomena which they 

 have produced, modified by their successive diminution, form 

 the actual state of the surface of our globe — a state which is 

 only an element of the curve, of which time will constitute the 

 abscissa, and whose ordinates will represent the changes which 

 that surface undergoes without ceasing. We are far from know- 

 ing the nature of this curve. We cannot, therefore, deduce with 

 certainty the origin of what we see on the earth ; and if, to 

 satisfy the imagination, always uneasy at its ignorance of the 

 cause of the phenomena which interests us, we hazard some 

 conjectures ; it is the part of a wise man to state them with the 

 greatest caution. 



The density of any gas is proportional to its compression, 

 when the temperature remains the same. This law found accu- 

 rate within the limits of the density of gases which we are able 

 to examine, cannot, as is obvious, apply to liquids and solids, 

 whose density is very great when compared with that of gases, 

 when the pressure is small or nil. It is natural to think that 

 these bodies make the greater resistance to compression the 

 more they are compressed ; so that the ratio of the differential 

 of the pressure to that of the density, instead of being constant 

 as in the gases, increases with the density. The most simple 

 function which can represent this ratio is the first power of the 

 density multiplied by a constant quantity. 1 have adopted it 

 because it has the advantage of representing in the simplest 





