SECT. VI. FIGURE OF EARTH FROM PENDULUM. 49 



torial circumference of the globe, is 24,899 English miles. 

 Eratosthenes, who died 194 years before the Christian era, was 

 the first to give an approximate value of the earth's circum- 

 ference, by the measurement of an arc between Alexandria and 

 Syene. 



There is another method of finding the figure of the earth, 

 totally different from the preceding, solely depending upon the 

 increase of gravitation from the equator to the poles. The force 

 of gravitation at any place is measured by the descent of a heavy 

 body during the first second of its fall. And the intensity of the 

 centrifugal force is measured by the deflection of any point from 

 the tangent in a second. For, since the centrifugal force balances 

 the attraction of the earth, it is an exact measure of the gravi- 

 tating force. Were the attraction to cease, a body on the surface 

 of the earth would fly off in the tangent by the centrifugal force, 

 instead of bending round in the circle of rotation. Therefore, 

 the deflection of the circle from the tangent in a second measures 

 the intensity of the earth's attraction, and is equal to the versed 

 sine of the arc described during that time, a quantity easily 

 determined from the known velocity of the earth's rotation. 

 Whence it has been found that at the equator the centrifugal 

 force is equal to the 289th part of gravity. Now, it is proved 

 by analysis that, whatever the constitution of the earth and 

 planets may be, if the intensity of gravitation at the equator be 

 taken equal to unity, the sum of the compression of the ellipsoid, 

 and the whole increase of gravitation from the equator to the 

 pole, is equal to five halves of the ratio of the centrifugal force to 

 gravitation at the equator. This quantity with regard to the 

 earth is | of 5 ^ or x^. Consequently, the compression of the 

 earth is equal to ^ diminished by the whole increase of gravi- 

 tation. So that itslform will be known, if the whole increase of 

 gravitation from the equator to the pole can be determined by 

 experiment. This has been accomplished by a method founded 

 upon the following considerations : If the earth were a homoge- 

 neous sphere without rotation, its attraction on bodies at its surface 

 would be everywhere the same. If it be elliptical and of variable 

 density, the force of gravity, theoretically, ought to increase 

 from the equator to the pole, as unity plus a constant quantity 

 multiplied into the square of the sine of the latitude (N. 127). 

 But for a spheroid in rotation the centrifugal force varies, by the 

 laws of mechanics, as the square of the sine of the latitude, from 



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