ASTRONOMY. 43 



simplicity to the circle, viz. the Ellipsis, and also 

 to suppose the superficies of the earth to be that 

 of a spheroid generated by the revolution of this 

 ellipsis, about its shorter axis. 



In many complex cases, this mode of approximating 

 to the truth, by probable assumptions, is the sim- 

 plest that can be pursued. The hypothesis thus 

 assumed, must be rigorously submitted to the test 

 of experience. 



56. The solid contained by the radius of cur- 

 vature, at any point in an ellipsis, and the 

 square of the semiparameter of the greater axis, 

 is equal to the cube of the normal at the same 

 point. 



That is, if a and b are the semiaxes, r the radius of 

 curvature, n the normal at any point, ri* = x r. 



See FBISIUS de Anatysi Sect. Con. Opera, torn. i. 

 p. 96. prob. 32. NEWTON'S Conic Sections, prop. 

 78. cor. 2. 



57. Hence the radius of curvature, at any 

 point of the meridian, and consequently the 

 length of a degree at that point, may be express- 

 ed in terms of the latitude : if r be the radius of 

 curvature at a point, of which the latitude is A, 

 a and b denoting as before, 



a* I* 





( a* cos A* + b* sin A*)^ 



Let 



