46 ARCS OF THE MERIDIAN. SECT. VI. 



poraneously. Were the lengths and curvatures of dif- 

 ferent meridians known, the figure of the earth might 

 be determined. But the length of one degree is suffi- 

 cient to give the figure of the earth, if it be measured 

 on different meridians, and in a variety of latitudes. 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 dif- 

 ferent parts of the earth's surface, will therefore deter- 

 mine its size and form. 



An arc of the meridian may be measured by observ- 

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

 measuring the distance between them in feet or fath- 

 oms. 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 lati- 

 tudes being the angle contained between the verticals 

 at the extremities of the arc. This would be easily ac- 

 complished were the distance unobstructed, and on a 

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

 obstacles on the surface of the earth, it is necessary to 

 connect the extreme points of the arc by a series of tri- 

 angles (N. 125), the sides and angles of which are either 

 measured or computed, so that the length of the arc is 

 ascertained with much laborious calculation. In conse- 

 quence of the irregularities of the surface, each triangle 

 is in a different plane. They must therefore be reduced 

 by computation to what they would have been had they 

 been measured on the surface of the sea. And as the 

 earth may in this case be esteemed spherical, they re- 

 quire a correction to reduce them to spherical triangles. 

 The gentlemen who conducted the trigonometrical sur- 

 vey, in measuring 500 feet of a base in Ireland twice 

 over, found that the difference in the two measurements 

 did not amount to the 800th part of an inch. Such is 

 the accuracy with which these operations are conduct- 

 ed, and which they require. 



Arcs of the meridian have been measured in a variety 

 of latitudes north and south, as well as arcs perpendicu- 

 lar to the meridian. From these measurements it ap- 



