68 PHILOSOPHICAL TRANSACTIONS. [AN^fO 1725. 



gravity on bodies is reciprocally as their distance from the earth's centre : that 

 though at a considerable distance we consider the earth, or any planet, or even 

 the sun, as a point endued with an absolute force, proportional to its quantity 

 of matter ; yet when we come so near the body as to consider the space it takes 

 up, we are to take notice, that the whole gravity of the body is made up of 

 the sum of the attractions of all its parts properly combined ; and therefore, 

 that when a corpuscle, or body attracted, comes to be within the planet, or 

 body attracting, the matter above it draws it back in such a manner, that it 

 leaves it only a force to go on towards the centre, which is directly as the 

 distance, as before said ; just as if a body concentric to the planet had its sur- 

 face just where the corpuscle is, and all the exterior crust or shell was an- 

 nihilated. 



Further, Mons. Mairan demonstrates, that in an oblong spheroid, the 

 diminution of gravity, by the centrifugal force, increases faster in going from 

 the poles to the equator, than it would do in a sphere, and faster in a sphere 

 than it would do in a broad spheroid; and therefore would show, "That 

 though the surface of the earth is nearer to the centre in M. Cassini's figure 

 than in Sir Isaac Newton's, yet the centrifugal force will diminish the gravity so 

 fast in going from Paris to the equator, that the shortening of pendulums, to 

 make them swing seconds at the equator, may very well be accounted for that 

 way." 



Now let us examine into this matter, to see whether the cause is adequate to 

 the effect. 



If the distance from the surface of the earth at the pole to the centre be 96, 

 and the distance of the surface at the equator be 95, the distance of the surface 

 at Paris, in the latitude of 48° 50', will be 95.562, by the property of the 

 ellipse. Now since the force of gravity, in different places on the earth's sur- 

 face, is reciprocally as the distance from the centre, and the lengths of pendu- 

 lums, that perform their vibrations in tlie same time, are directly as the force of 

 gravity ; therefore the length of penduhuns at Paris, will be to their length at 

 the equator, at 95 to 95.562, that is, as 440.555 to 443.165, and consequently 

 they must be lengthened '2.6 1 lines. But as, from M. Mairan's principles, the 

 diminution of gravity by the centrifugal force is greater at the equator than at 

 Paris, hardly -^^-j^^ part of the whole gravity at the equator, the pendulums must 

 be. shortened in that proportion ; so that then the length of a seconds pendu- 

 lum will be 440.555 -|- 2.6l — 1 lines. But as that quantity is greater than 

 440.555, therefore the pendulums on the whole must be lengthened : nay, 

 though we should allow a shortening of two lines; since by observation pendu- 

 lums are found to be about 2 lines shorter at the equator, the oblong sphe- 



