SECT, vi.] COMPRESSION OF THE EARTH. 57 



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 -^.3, shows that the compression of 

 the terrestrial spheroid is about 2S.I-3B- This value has been 

 deduced by the late Mr. Baily, 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 ex- 

 periments give the same result, probably from local attractions. 

 Therefore, the question cannot be considered as definitively 

 settled, though the differences are very small. The com- 

 pression 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. 143) 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 ^ and 3^3. 



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 allowance has been made for every cause of error, 

 such discrepancies are found, both in the degrees of the 

 meridian and in the length of the pendulum, as show that 

 the figure of the earth is very complicated. But they are so 

 small, when compared with the general results, that they 

 may be disregarded. The compression deduced from the 



