OUTLINES OF NATURAL PHILOSOPHY. 



Let ADB be one half of the meridian, A and B 

 points in the Equator, C the centre of the earth, 

 D the Pole, EA a perpendicular to the meridian 

 at E, a point of which the latitude is A = EGA, H 

 the centre of curvature* F a perpendicular on the 

 axis ; then EG is the normal, or n, GF the sub- 

 normal = 5 ; let CF = x, and FE = y ; then 



b z 

 if (a* x 31 }. But, by the property of the 



subtangents of the ellipsis, x = ^ s ; also 



s = n cos A, and y = n sin A ; therefore, by substi- 

 tution, 



n* (b* sin A* + a* cos A*) = b* 9 



and n = ^ 



(a* cos ** + b z sin A z ) 4 



Now, by 56. r == --; n 3 - 9 therefore, 



If D be the length of a degree in lat. A, and m r= 

 57.2957795, the number of degrees in an arc 

 equal to the radius, then r = m D, 



and D = 



m (a* cos A* + 



58. In 



