120 PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
— O'',0123 . sin {9 (n t + s) — 13 (n't + z) — 0} — 0",0086 . cos {9 (n t + «) 
— 13 (ii t -J- g) — $} 
or 
+ 0",0151 X sin {9 (nt-{-&)— 13(«7 + e') + 140° 31'} 
which, though larger than the Earth’s perturbation in latitude, is too small to 
be observable. 
Conclusion. 
It appears, then, that in calculating the Earth’s longitude (or 180° + Sun’s 
longitude), the following terms should be used in addition to those that have 
hitherto been applied ; (where / and V are the mean tropical longitudes of Venus 
and the Earth, and Y the number of years after 1750:) 
To the epoch of mean longitude 
+ {2",059 - Y X 0",0002076} X sin{8 1— 13 /' + 40° 44' 34" +Y X 239",7} 
To the epoch of longitude of perihelion 
+ 2",268X sin {8/-13/' + 60° 16'} 
To the excentricity 
- 0,0000001849 . cos { 8 / - 13 /'+ 60° 16'} 
and that, in calculating the Earth’s latitude (or the Sun’s latitude with sign 
changed), the following term should be used ; 
+ 0",0105 . sin (8 /— 12 /' - 39° 29'} 
Similarly, it appears that in calculating the place of Venus, the following terms 
should be applied: 
To the epoch of mean longitude 
+ {2",946— Y X 0",0002970} X sin {8/- 13/' + 220° 44' 34" +Y X 239",7} 
To the longitude of perihelion 
— 5",70 . cos {81- 13/'} 
To the excentricity 
- 0,000000190 . sin {8 l— 13 1} 
To the latitude 
+ 0",0151 .sin {9/- 13/'+ 140° 31'} 
