SKCT. VI. OSCILLATIONS OF PENDULUM. . 49 



spheroid in rotation, the centrifugal force varies, by the 

 i\vs of mechanics, as the square of the sine of the lati- 

 tude, from the equator, where it is greatest, to the pole, 

 where it vanishes. And as it tends to make bodies fly 

 off the surface, it diminishes the force of gravity by a 

 small quantity. Hence, by gravitation, which is the dif- 

 ference of these two forces, the fall of bodies ought to 

 be accelerated from the equator to the poles proportion- 

 ably to the square of the sine of the latitude ; and the 

 weight of the same body ought to increase in that ratio. 

 This is directly proved by the oscillations of the pendu- 

 lum (N. 127), which, in fact, is a falling body; for if the 

 faH of bodies be accelerated, the oscillations will be more 

 rapid : in order, therefore, that they may always be per- 

 formed in the same time, the length of the pendulum 

 must be altered. By numerous and careful experi- 

 ments, it is proved that a pendulum which oscillates 

 86,400 times in a mean day at the equator, will do the 

 same at every point of the earth's surface, if its length 

 be increased progressively to the pole, as the square of 

 the sine of the latitude. 



From the mean of these it appears that the whole 

 decrease of gravitation from the poles to the equator is 

 0-005.1449, which, subtracted from -j-f^.o' shows that 

 the compression of the terrestrial spheroid is about 

 _|^ _ 7 . This value has been deduced by the late Mr. 

 Bally, president of the Astronomical Society, who has 

 devoted much attention to this subject ; at the same 

 time, it may be observed that no two sets of pendulum 

 experiments give the same result, probably from local 

 attractions. Therefore, the question cannot be con- 

 sidered as definitively settled, though the differences 

 are very small. The compression obtained by this 

 method does not differ much from that given by the 

 lunar inequalities, nor from the arcs in the direction of 

 the meridian, and those perpendicular to it. The near 

 coincidence of these three values, deduced by methods 

 so entirely independent of each other, shows that the 

 mutual tendencies of the centers of the celestial bodies 

 to one another and the attraction of the earth for bodies 

 at its surface result from the reciprocal attraction of all 

 their particles. Another proof may be added. The 

 4 K 



