IN THE MOTIONS OF THE EARTH AND VENUS. 
Ill 
nt + a = l— Y X 50",1 
n't + s'= V- Y X 50", 1 
Consequently 8 (n t + s) — 13 (n't + s') = 8 l — 13 V -j- 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 
ft n} Qf] qf /yj% 
= + —^ 7 — P . sin {13 (n'1 + s') — 8 (n t + s)} 
dt 
r 
26 n’ a!* 
Q . cos {13 (n 1 1 + s') — 8 (n t -}- s)} 
whence 
«' = A '~ vfu'-Vn • cos {13 (V t + 0 — 8 (« t + e)} 
Of] qil sil O ri! 
- 1 • YT • sin * 13 K' + 0-8 (nt + t)} 
= A' - a 1 . (92,31993) . cos {13 (n't + s') - 8 (nt + s)} 
- a' . (92,26190) sin { 13 (n't + s') - 8 (n t + s)} 
— A! -a! X 0,000000027756 X cos {8 (n t + s) - 13 (n' t + s') + 41° 11'} 
The magnitude of the coefficient is barely ^oth of Laplace’s minimum, and 
this inequality may therefore be neglected. 
