EAR 



The following are the five arcs, which have been measured with th 

 greatest care : 



By combining these in pairs, and taking the mean, we get the follow- 

 ing results. 



a : b :: 312 : 311. 



D 69.044 .3299 X cos. 2 A in miles, 



or D = 60759.472 290.576 X cos. 2 A in fathoms, which ex- 

 presses the degrees of the meridian in any latitude. 



- = .0032 = 



1 



312.5 * 

 c 12.<580 miles. 

 a 3962.349 miles. 

 b 3949.669 miles. 



Hence circumference of elliptic meridian = 24855.84 miles ; do. of equa- 

 tor 24896.16 miles ; .'. difference 40 miles nearly. 



3. The figure of the earth may also be determined, by comparing a de- 

 gree of the meridian with the degree of a great circle perpendicular to 

 the meridian in the same latitude, by the following formulae. 



Let A be the degree of the curve perpendicular to the meridian, the 

 rest as before, then 



e = (A D) X V-. 

 2 * cos.* A 



and = 



A D 



i nearly. 



2 A cos. A 



4k To find the compression by means of a second's pendulum, consider- 

 ing the earth as a spheroid of equilibrium. 

 67 



