272 POOR 



P 



^e: S^ =/ cos 57 + 



cos F. 

 2'Ar sin i/) 



3i'« sin 1/ 

 {^N : e) = — ^L sin i/> cos v. 



In these formulas, a, the semi-axis major is always taken as 

 positive and if', u, N, and F are auxiliary quantities in the 

 hyperbola, analogous to the quantities, f, //., M, and E, in the 

 ellipse, and are given by the equations, 



where / is the modulus of common logarithms. 

 The perturbation of N is given in the form 



where (-/-^V)^ is derived directly by mechanical quadrature from 

 the above formula, and 



(AX),,^.^//;^;,/.^, 



this being derived by double integration from the variation of u 

 as computed above. 



The integrated perturbations, as thus computed, are given in 

 the following table ; in which the changes in e\ v, and N are ex- 

 pressed in units of the sixth decimal place. • 



