IN THE MOTIONS OF THE EARTH AND VENUS. 
Ill 
n t + s = l — Y X 50",1 
n't + s'= V- Y X 50", 1 
Consequently 8 (n t + s) — 13 (ri t + s') = 8 l — 13 V -f" Y X 250", 5. 
Substituting this, the expression for the inequality is 
{2",059 — Y X 0",00020/6} X sin {8 l — 13 V + 40° 44' 34" + Y X 239", 7} 
57- I have compared the calculations of the principal part of this inequality 
with the calculations made in 1827- Two errors were discovered in the former 
calculations, one of which was important. I am quite confident that there is 
no sensible error in the results now presented. The terms depending on Y 
were not calculated on the former occasion : but the calculations now made 
have been carefully revised. 
Section 15. 
Numerical calculation of the long inequality in the length of the axis major. 
58. This being very small, we shall omit the variable terms. Thus we have 
~dt— + — -1 — P. sin {13 (n't + s') — 8 (n t + t)} 
26 v! a n 
Q . cos { 13 (n 1 1 + s') — 8 (n t -f- e) } 
whence 
a ' = A '~ 1 3u' n -S~n ‘ cos {13 (rit + e') -8 (nt + e)} 
26 v! a' 
13w' — 8 n 
Q a! 
sin { 13 (n 1 1 -f g') — 8 (n t + 2 ) } 
= A 1 -a! . (92,31993) . cos { 13 (n't + s') — 8 (n t + g)} 
- a' . (92,26190) sin { 13 (n' t + s') - 8 (n t + e) } 
= A'-a'x 0,000000027756 X cos {8 (n t + g) — 13 (n' t + s') + 41° 1 1'} 
The magnitude of the coefficient is barely ^th of Laplace’s minimum, and 
this inequality may therefore be neglected. 
