120 PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
— 0", 0123 . sin {9 (n t + g) — 13 [n r t + e) — 6} — 0",0086 . cos {9 (n t + s) 
- 13 (ii t -f e) - 6) 
or 
+ 0",0151 X sin {9 (wi + g)— 13 (nt + 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 /' 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 /- 13 /' + 40° 44' 34" + Y X 239",7} 
To the epoch of longitude of perihelion 
-f2",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 {8/- 13/'} 
To the excentricity 
- 0,000000190 . sin {8 /- 13 /'} 
To the latitude 
+ 0",0 151 . sin {9/- 13/'+ 140° 31'} 
