SECT, vi.] FORM OF THE EARTH. 53 



The courses of the great rivers, which are in general navi- 

 gable to aconsiderable*extent, prove that the curvature of the 

 land differs but little from that of the ocean ; and, as the 

 heights of the mountains and continents are inconsiderable 

 when compared with the magnitude of the earth, its figure is 

 understood to be determined by a surface at every point per- 

 pendicular to the direction of gravitation, or of the plumb- 

 line, and is the same which the sea would have, if it 

 were continued all round the earth beneath the continents. 

 Such is the figure that has been measured in the following 

 manner: 



A terrestrial meridian is a line passing through both poles, 

 all the points of which have their noon contemporaneously. 

 Were the lengths and curvatures of different meridians known, 

 the figure of the earth might be determined. But the length 

 of one degree is sufficient to give the figure of the earth, if 

 it be measured on different meridians, and in a variety of lati- 

 tudes. For, if the earth were a sphere, all degrees would be 

 of the same length ; but, if not, the lengths of the degrees 

 would be greater, exactly in proportion as the curvature is 

 less. A comparison of the length of a degree in different 

 parts of the earth's surface will therefore determine its size 

 and form. 



An arc of the meridian may be measured, by observing the 

 latitude of its extreme points (N. 124), and then measuring 

 the distance between them in feet or fathoms. The distance 

 thus determined on the surface of the earth, divided by the 

 degrees and parts of a degree contained in the difference of 

 the latitudes, will give the exact length of one degree, the 

 difference of the latitudes being the angle contained between 

 the verticals at the extremities of the arc. This would be 

 easily accomplished were the distance unobstructed, and on a 

 level with the sea. But, on account of the innumerable ob- 

 stacles on the surface of the earth, it is necessary to connect 

 the extreme points of the arc by a series of triangles (N. 125), 

 the sides and angles of which are either measured or com- 



