54 OUTLINES OF NATURAL PHILOSOPHY. 



The circumference of the Equator is 24-896. 16 miles, 

 a little more than 40 miles greater than the prece- 

 ding. 



The circumference of the Meridian may be found 

 more accurately by the theorem for the rectifica- 

 tion of the ellipsis. See LA CAILLE, Lemons Ele- 

 mentaires de Math. 954-. Also Base Metrique, 

 torn. ii. p. 676. 



The French, from their late measurement, compared 

 with that in Peru, make the compression .00324, 

 and the quadrant of the meridian 5131111 toises ; 

 which gives for theentirecircumference5468481.54 

 fathoms, or 24856.72 miles ; about 1 mile great- 

 er than the result obtained above. 



e. The Geographical Mile, or that of which there are 

 60 in the length of the mean degree, is 1012.6 fa- 

 thoms, = 6075.6 feet. 



61. The semidiameter of the earth belonging 



x 



to any latitude \, is nearly equal to a (1 



sin* ^. 



a. This formula is found, by expressing the serai- 

 diameter of the elliptic meridian, in terms of the 

 latitude, in a manner similar to that employed 



$57, 



