On the Mean Density of the Earth. .'323 



Thus, the super-stratum of the earth being about twice as dense 

 as the water, and the sub-strata becoming, in proportion to their 

 depth, three, four, and even five times more dense, it is probalile 

 that the whole mass of the earth is five or six times mure dense 

 than if it were formed of water." 



The theories of the figure of the planets, and of the oscilla- 

 tions of the fluids that cover them, which have been considerably 

 improved since the time of Newton, have confirmed the suppo- 

 sition. By this theory it appears that, for the stability of the 

 equilibrium of tlie sea, its density must be less than the mean 

 density of the earth, as I have shown in the fourth book of the 

 Mecanique Celeste. Notwithstanding the irregularities of mea- 

 sured degrees of meridians, they indicate a less flattening at the 

 poles, than that which agrees with the homogeneity of the earth ; 

 and the theory proves that this flattening requires, in the ter- 

 restrial strata, a density that increases from the surface to the 

 centre. In like manner, the experiments of the pendulum, more 

 exact and which agree better than the measurement of degrees, 

 indicate an increase of gravity, from the equator to the poles, 

 greater than in the case of its being homogeneous. A remark- 

 able theorem at which 1 have arrived (tome ii. des Nouveuvx 

 Alemoires de I' AcadSmie des Sciences) renders this rcoult, inde- 

 pendently of the continuous or discontinous figuie of the ter- 

 restrial spheroid, of the irregularities of its surface, of the man- 

 ner in which a great portion of it is covered by the sea, and of 

 the density of this fluid. 



If we imagine a very rare fluid to rise to a moderate height, 

 and envelope the whole earth and its mountains, this fluid will 

 assume a state of e(|uilibrium ; and I iiave shown in the volume 

 above cpioted, that the points of its exterior surface will lie all 

 equally raised above the sea. The interior points of the conti- 

 nents, lowered as much as those of the surface of the sea below 

 the upper surfaces of the supposed fluid, form, l)y their con- 

 tinuity, what I call the prolonged or extended level of the sea. 

 The height of a point of the continents, above this level, will be 

 determined by the difference of the pressure of this fluid, at this 

 point and at the level of the sea, — a difference that will be ap- 

 parent by observations on the barometer ; — for our atmosphere, 

 if supposed to be reduced every where to its mean density, be- 

 comes the fluid we have just imagined. 



This being admitted, let us conceive the earth to be some kiiwl 

 of an homogeneous spheroid, partly covered by the sea ; and 

 taking for unity, the length of the seconds pendulum, at the 

 equator and at the level of the sea. If to the length of this pen- 

 dulimi, observed on any point of the surface of the spheroid, be 

 added one-half of the height of this point above the Icvtl of the 

 S s 2 ocean, 



