48 FORM OP THE EARTH. SECT. VI. 



era, was .the first to give an approximate value ->f the 

 earth's circumference, 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 depend- 

 ing 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 bal- 

 ances the attraction of the earth, it is an exact measure of 

 the gravitating 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 cir- 

 cle 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 rota- 

 tion. 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 consti- 

 tution 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 4 of -^ ? , or tiT-^- Consequently, the 

 compression of the earth is equal to y-fj.-o diminished by 

 the whole increase of gravitation. So that its form 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 homo- 

 geneous 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. 126). But for a 



