110 On the Figure of the Earth. 



The density of a gas is proportional to its compression, when 

 the temperature remains the same. This law which is found 

 true within those limits of density, where we have been able to 

 prove it, evidently cannot apply to liquids and solids, of which 

 the density is very great, compared to that of gas, when the 

 pressure is very small, or even nothing. It is natural to sup- 

 pose that these bodies resist 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 with gases, 

 increases with the density. The most simple function which 

 can represent the ratio, is the first power of the density, multi- 

 plied by a constant quantity. It is this which I have adopted, 

 because it unites to the advantage of representing in the simplest 

 manner what we know of the compression of liquids and solids, 

 a facility of calculation in researches on the figure of the earth. 

 Until now, mathematicians have not included in this research the 

 effect resulting from the compression of the strata. Dr. Young 

 has called their attention to this object, by the ingenious remark, 

 which may be thus stated, the increase of 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 phenomena depending on 

 the law of the density of these strata. These phenomena are the 

 variation of the degrees of the meridian, and of gravity, the 

 precession of the equinoxes, the nutation 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 ad- 

 mirable experiment at five and a half. In proceeding from the 

 law already announced of the compression of liquids and solids, 

 I find that, if the earth be supposed to be formed of a substance 

 chemically homogeneous, of which the density is 2^ that of 

 common water, and which compressed 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 phenomena. The existence of such a 

 body is very admissible, and there are apparently such on the 

 surface of the earth. 



