SECT. VI. FORM OF EARTH FROM PENDULUM. 47 



pears that the length of the degrees increases from the 

 equator to the poles, nearly in proportion to the square 

 of the sine of the latitude (N. 126). Consequently, the 

 convexity of the earth diminishes from the equator to 

 the poles. 



Were the earth an ellipsoid of revolution, the merid- 

 ians would be ellipses whose lesser axes would coincide 

 with the axis of rotation, and all the degrees measured 

 between the pole and the equator would give the same 

 compression when combined two and two. That, how- 

 ever, is far from being the case. Scarcely any of the 

 measurements give exactly the same results, chiefly on 

 account of local attractions, which cause the plumb line 

 to deviate from the vertical. The vicinity of mountains 

 has that effect. But one of the most remarkable, though 

 not unprecedented, anomalies takes place in the plains of 

 the north of Italy, where the action of some dense sub- 

 terraneous matter causes the plumb-line to deviate seven 

 or eight times more than it did from the attraction of 

 Chimborazo, in the experiments of Bouguer, while 

 measuring a degree of the meridian at the equator. In 

 consequence of this local attraction, the degrees of the 

 meridian in that part of Italy seem to increase toward 

 the equator through a small 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 differ- 

 ence, or 13-239 miles, divided by the equatorial radius, 

 is -i-g. 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 

 69J^ 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 



