122 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
In 1639 
For the Earth. 
.... + 0",89 . 
For Venus. 
.... - 1",28 
1761 
. . . . — 0,98 . 
. ... + 1,41 
1769 
.... — 1 ,34 . 
. . . . + 1 ,91 
1874 
.... + 0,68 . 
. ... - 0,97 
1882 
. . . . + 1 ,07 . 
. . . . - 1 ,53 
I shall now show the coincidence of the theoretical results with the observa- 
tions that first suggested their necessity. 
From Burckhardt’s examination of Maskelyne’s observations (Connais- 
sance des Temps, 1816), and from my examination of Mr. Pond’s observations 
(Phil. Trans. 1828), it appeared that the mean longitudes of Belambre’s tables 
ought to be increased 
in 1783 by 0",25 
in 1801 by 0 ,08 
in 1821 by 2 ,05 
These observations are all reduced by the same catalogue. The differences of 
the corrections are not proportional to the intervals ; and this is the circum- 
stance that shows the existence of some periodical inequality. 
Now the values of the argument of the long inequality in the epoch are 
for 1783 ... . 240° 59' 
for 1801 . . . . 268 4 
for the middle of 1821 . . . . 298 46 
The sines of these angles are — 0,8745, — 0,9994, — 0,8766 ; and hence the 
values of the inequality were 
in 1783 . . . . — 1",80 
in 1801 . . . . -2,06 
in 1821 . . . . -1,81 
If these had been applied in the tables, the corrections given by the observa- 
tions above would have been 
in 1783 . . . . 2",05 
in 1801 . . . . 2,86 
in 1821 .... 3 ,86 
