1819.] Royal Academy of Sciences. 219 



a degree for Jupiter, and to four-fifths of a degree for Saturn, 

 and affects the whole system through the action of these two 

 large masses. Fortunately the coefficients of the inequalities 

 produced by this cause in the elements of the planetary motions 

 are insensible ; they only amount to about one centesimal second 

 for Mars and Uranus ; to six-tenths of a second for the earth ; 

 and to one centesimal second for the moon. A more sensible 

 effect is produced upon the satellites of Jupiter. In this case 

 the coefficients are, in centesimal seconds, 1" for the first satel- 

 lite, 12-8" for the second, 18-8" for the third/and 44-3" for the 

 fourth. Still more fortunately the motion of these satellites is so 

 rapid, that as these four coefficients are, like the former ones, 

 fractions of a degree, and not of time, it may therefore be said 

 that these inequalities are lost in the uncertainties of observa- 

 tions. They do not alter in the least the remarkable ratio which 

 exists in the motions of the first three satellites. 



The third memoir is entitled, " On the Law of Gravity, sup- 

 posing the terrestrial Spheroid was homogeneous, and of the 

 same Density as the Sea." 



Upon the hypothesis of the homogeneousness of the terrestrial 

 spheroid, analysis reduces the gravity on the surface of the sea 

 to a very simple expression, and one that offers a remarkable 

 result ; namely, that if the sea was of the same density as the 

 spheroid, the force of gravity on its surface would be indepen- 

 dent of the figure. Taking any point situated either on the 

 surface of the sea, or on a continent, or an island, the force of 

 gravity would be equal to a constant quantity, plus the product 

 of the square of the sine of the latitude by five-fourths of the ratio 

 between the centrifugal force and the gravity at the equator, 

 minus the product of the gravity at the equator by half the 

 height of the given point above the level of the sea, a height 

 which might be determined by the barometer ; the mean radius 

 of the earth is here to be taken as unity. 



As this law does not agree with the experiments on pendu- 

 lums made in both hemispheres, the hypothesis of the homoge- 

 neousness of the earth is, therefore, shown by these experiments 

 to be false : at the same time they prove, 



1. That the density of the strata of the terrestrial spheroid 

 increases from the surface to the centre. 



2. That these strata are disposed very nearly in a regular 

 manner round the centre of gravity of the earth. 



3. That the surface of this spheroid, covered in part by the 

 wa, has a figure slightly differing from that which, if it were 

 fluid, it would assume by virtue of the law of equilibrium. 



4. That the depth of the sea is but a small fraction of the 

 difference between the two axes of the earth. 



5. That the inequalities on the surface of the earth, and the 

 causes which occasion them, have very little depth. 



(>. That the whole earth was originally fluid. 



