110 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
— — . cos 0a + 4 6) — + (1,3847917) + (97,49139) . n t 
m 
(n) 
. sin (ta- + 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) . w' 
Q = - X (94,0722348) q = + ^ X (89,47976) . n' 
i i • m 1 . , 1674883 , . , 
and making = 4Q12I t , and 13n — 8 n= — 399 9 9 30 90 X »,m the expression 
of (51), we find for the long inequality 
{ - (94,8787039) +»'(X (89,82780) } . sin {13 (n't + s') — 8 (n t + g)} 
+ {+ (94,8139258) - n't X (90,22359)} . cos {13 (n't + i) — 8 (»./ + *)} 
which may be put in the form 
{ + (94,9992364) - n't X (90,20461)} . sin {8 (n t + s) — 13 (n! t + e') 
+ 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 1 750, 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 t+e) 
+ 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 1730, then (in consequence of pre¬ 
cession) 
