ON THE TRUE POTENTIAL OF THE FORCE OF 



GRAVITY.* 



Alexander S. Chessin. 



1. Assuming that the form of the earth is that of a solid 

 spheroid covered by an ellipsoidal liquid mass of uniform 

 density, that the density of the spheroid varies from center 

 to surface but is constant in each one of the concentric layers, 

 and that the liquid mass is in a state of equilibrium, Laplace 

 arrives at the following expression for the potential of the 

 force of attraction exjercised by the earth on an external par- 

 ticle of unit mass : t 



E^ (^-3; 



M 

 R 



where M denotes the total mass of the earth, R the distance 

 of the particle from the center of the earth, a</> the ratio of 

 the centrifugal force to the force of attraction on the equator, 

 ah the oblateness of the earth, a the mean value of its ra- 

 dius, and, finally, /x = cos d, being the angle of the radius 

 vector of the particle with the axis of rotation of the earth. 

 ** According to the most probable hypotheses," says La- 



5 

 place,t *' the oblateness of the spheroid is less than j «</>,. . . , 



These assumptions are the more probable because they be- 

 come necessary in the case when the spheroid had originally 



• Presented, and read by title, before The Academy of Science of St. 

 Louis, December 2, 1901. 



t Laplace, Oeuvres completes, t. II. Livre III. p. 108. * ~ '; 



X Ibid. p. 101. (1) 



