ANNALS 



OF 



PHILOSOPHY. 



DECEMBER, 1819. 



Article I. 



On the Figure of the Earth* By M. de Laplace. (Read at the 

 Meeting of the Board of Longitude on May 26, 1819.) 



1 HE numerous experiments on the pendulum have shown that 

 the increase of gravitation follows a very regular law, and that it 

 is very nearly proportional to the square of the sine of the lati- 

 tude. This force being the result of the attractions of all the 

 particles of the earth, these observations compared with the 

 Iheory of the attractions of spheroids, furnish the only means 

 which we have to penetrate into the interior constitution of the 

 earth. It follows from them that this planet is formed of beds 

 whose density increases from the surface to the centre, and 

 which are disposed regularly round this point. I published at 

 the end of the Connaissance des Temps for 1821 the following 

 theory, which I have demonstrated in the second volume of the 

 New Memoirs of the Academy of Sciences. 



" If we take for unity the length of the seconds pendulum at 

 the equator, and if to the length of this pendulum observed at 

 any point of the surface of the terrestrial spheroid, we add half 

 the height of this point above the level of the ocean, divided by 

 the demiaxis of the pole— a height which the observation of the 

 barometer furnishes, the increase of this length thus corrected 

 will be, on the hypothesis of a constant density below a mode- 

 rate depth, equal to the product of the square of the sine of the 

 latitude by five-fourths of the ratio of the centrifugal force to 

 that of gravitation at the equator, or by 43 ten millionths." 



• Translated from the Aun. de Cbim. et de Pliys. xi. 31. 



Vol. XIV. N° VI. 2 C 



