IN THE MOTIONS OF THE EARTH AND VENUS. 
113 
+ l",9697 . cos {8 (n t + e) - 13 (n t + s')} 
= IT + 2" 2683 . sin [8 (n t + s) - 13 (n t + s') -f- 60° 16'} 
Section 17- 
Numerical calculation of the long inequality in the excentricity. 
de' 
60. On forming the expression for -g--, or + it is immediately seen 
that the coefficients of cos {13 (n t -f- s') — 8 (n t + s)} and sin {13 (n t + 0 
— 8 (n t + 0 } are related to those above, and that 
+eV X (92,60190) .cos {13 (ri t + 0 — 8 (nt + e)} 
— e rl X (92,35866) . sin {13 (n t + s') — 8 in t + s)} 
Integrating, 
e = E' - e X (94,97997) . sin {13 (n t + s') — 8 (n t + g)} 
— ex (94,73673) . cos {13 (n t + z) — 8 {n t + g)} 
= E' - (92,96240) cos {8 (n t + s) — 13 (n't + z)} 
+ (93,20564) . sin {8 (w ^ + s) — 13 (n't + e)} 
= E' — 0,0000001849 . cos {8 {n t + s) — 13 (n't + s') + 60° 16'} 
The principal inequality in the radius vector is that produced by the last 
term: it is however too small to be sensible. 
PART II. 
PERTURBATION OF THE EARTH IN LATITUDE, 
Section 18. 
Explanation of the method used here. 
61. If f be the inclination of the earth’s orbit to the plane of xy, and (f the 
longitude of the node, then 
MDCCCXXXII. 
Q 
