54 ARCS OP THE MERIDIAN. [SECT- vi. 



puted, so that the length of the arc is ascertained with much 

 laborious calculation. In consequence 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 

 require a correction to reduce them to spherical triangles. 

 The gentlemen who conduct the trigonometrical survey, 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 conducted, and which they require. 



Arcs of the meridian have been measured in a variety of 

 latitudes north and south, as well as arcs perpendicular to the 

 meridian. From these measurements it appears 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 

 (K 126). Consequently, the convexity of the earth dimi- 

 nishes from the equator to the poles. 



Were the earth an ellipsoid of revolution, the meridians 

 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, however, 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 vici- 

 nity of mountains has that effect. But one of the most re- 

 markable, though not unprecedented, anomalies takes place 

 in the plains of the north of Italy, where the action of some 

 dense subterraneous 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 towards the equator through a small 



