SKCT. vi.] FORM OF THE EARTH FROM PENDULUM. 55 



space, instead of decreasing, as if the earth was drawn out at 

 the poles, instead of being flattened. 



Many other discrepancies occur, but from the mean of the 

 five principal measurements of arcs in Peru, India, France, 

 England, and Lapland, Mr. Ivory has deduced that the figure 

 which most nearly follows this law is an ellipsoid of revolution 

 whose equatorial radius is 3962*824 miles, and the polar 

 radius 3949'585 miles. The difference, or 13'239 miles, 

 divided by the equatorial radius, is 559 nearly. This fraction 

 is called the compression of the earth, and does not differ 

 much from that given by the lunar inequalities. If we assume 

 the earth to be a sphere, the length of a degree of the meridian 

 is 69r 2 ' 2 British miles. Therefore 360 degrees, or the whole 

 circumference of the globe, is 24,856 miles, and the diameter, 

 which is something less than a third of the circumference, is 

 about 7916, or 8000 miles nearly. Eratosthenes, who died 

 194 years before the Christian era, was the first to give an 

 approximate value of the earth's circumference, by the mea- 

 surement 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 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 de- 

 flection of th*e 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 



