50 COMPRESSION OF THE EARTH. SECT. VI, 



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 difference 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 pendulum (N. 129), which, in 

 fact, is a falling body ; for, if the fall of bodies be accelerated, 

 the oscillations will be more rapid : in order, therefore, that they 

 may always be performed 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 7^.5, shows that the compression of the terres- 

 trial spheroid is about ^.^. This value has been deduced by 

 the late Mr. Baily, president of the Astronomical Society, who 

 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. 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 centres 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 nutation 

 of the earth's axis and the precession of the equinoxes (N. 146) are 

 occasioned by the action of the sun and moon on the protuberant 

 matter at the earth's equator. And, although these inequalities 

 do not give the absolute value of the terrestrial compression, they 

 show that the fraction expressing it is comprised between the 

 limits 5J 5 and ^. 



It might be expected that the same compression should result 

 from each, if the different methods of observation could be made 

 without error. This, however, is not the case ; for after allow- 



