110 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
(n) 
^ — . cos (*• + 4 0) = + (1,3847917) + (97,49139) . n' t 
m ' 
(ll) 
°^ r - .sin(sr + 4 6) = + (1,7294138) - (97,14677) -n't 
55. Substituting these in the expressions of (50), we find 
P = - X (94,1302623) p = + y X (89,08397) . ri 
Q = - ^ X (94,0722348) q = + X (89,47976) . ra' 
1 . , 1674883 , . . 
and making y = 4010 T+ anc * ^ 71 ~ ® n — ~ 399993090 X w, m the expression 
of (51), we find for the long inequality 
{ _ (94,8787039) +ritX (89,82780) } . sin { 1 3 (n’t + s') — 8 (n t + e) } 
+ { + (94,8139258) — n! t X (90,22359)} . cos {13 (n’t + s') — 8 (n* + s)} 
which may be put in the form 
{+(94,9992364) — ritx (90,20461)} . sin {8 [n t + s) — 13 (n't + s') 
+ 40° 44' 34" — n’t X (94,91918)} 
where the degrees, &c. in the argument are sexagesimal. The coefficient is ex- 
pressed by a multiple of the radius : to express the principal term in sexage- 
simal seconds, it must be divided by sin 1". And if Y be the number of years 
after 1750, since n t = mean motion of the earth in Y years = 2r.Y-6. 60 3 . Y 
in seconds, the coefficients of n t must be multiplied by 6 . 60 3 . Y, and their 
values will then be exhibited in sexagesimal seconds. Thus we find at length 
for the inequality 
{2", 059 — Y X 0", 0002076} X sin {8 (n t + s) — 13 (n Z+s') 
+ 40° 44' 34" - Y X 10",76}. 
56. The mean longitudes n t + s, n t + s', are measured from the equinox of 
1750. But if Z, are the mean longitudes of Venus and the Earth measured 
from the place of the equinox Y years after 1750, then (in consequence of pre- 
cession) 
