IN THE MOTIONS OF THE EARTH AND VENUS. 
113 
+ 1", 969/ . cos {8 (n t + s) - 13 (ri * -f s') } 
= II' + 2",2683 . sin {8 (n t + s) - 13 (ri t + s') + 60° 16'} 
Section 1 /. 
Numerical calculation of the long inequality in the excentricity . 
« d c ii! cj} d R» 
60. On forming the expression for -jj , or + ^ it is immediately seen 
that the coefficients of cos {13 (ri t -f- s') — 8 (nt + s)} and sin {13 (ri t + s') 
— 8 (n t + s)} are related to those above, and that 
= + eV X (92,60190) . cos {13 (ri t + s') — 8 (nt + e)} 
— erix (92,35866) . sin { 13 (ri t + s') — 8 (n t + e) } 
Integrating, 
e — E' — e X (94,97997) . sin { 13 (ri t + 0 — 8 (n t + e) } 
— ex (94,73673) . cos { 13 (ri t + z) — 8 (n t + s) } 
= E' - (92,96240) cos {8(w/ + s)~ 13 (ri * + s')} 
+ (93,20564) . sin {8 (n £ + s) — 13 (n'f + s')} 
= E' — 0,0000001849 . cos {8 (n t + s) — 13 (w * + 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 
