ELLIPSOID. 343 



If the ellipsoid is one of revolution about the minor axis c, we 

 have, if e is the eccentricity of the meridional ellipse, 



^^ i-* 2 ~| 

 --- , 



sin e e* J 



For an ellipsoid of revolution about the major axis, 



i->p s i+, -i 



= 47T -/. I 



e* \2e i-e 



Making * = in these formulas, we find again the results already 

 obtained for the sphere ; that is to say, 



M = N = - 



*J 



V 4 T 



F= -- TT!. 



For a very flat ellipsoid, in which the eccentricity e is near unity, 

 we have, at the limit, 



If the ellipsoid is very elongated, we have approximately 



M = N = 27T, 



and the coefficient L tends towards zero, when the eccentricity 

 tends towards unity. 



