118 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
will be exactly the same as when we consider the Earth disturbed by Venus. 
For the longitudes of perihelia and the longitude of the node will be the same : 
the sign of f will be different, but as the even powers only of this quantity enter 
into the expansion of R, and as its magnitude (without respect to its sign) is 
the same in both, that circumstance makes no difference. It is only necessary 
then to put rri instead of m in the multiplier of the term. 
68 . First, then, for the inequality in the epoch. Observing that in the ex- 
pression of (51) the multiplier m is included in P, p, Q, and q, it will be seen 
24 72 ^ CL Til! 
that for the perturbation of Venus we must use the multiplier — — in- 
. „ 39 ri 2 a' m 
stead of - — 
That is, the argument of the perturbation of Venus is the 
same as that of the Earth ; and its coefficient is found by multiplying the co- 
efficient for the Earth by — 
8 n 2 a m! 
13 n'~ a in' 
As 8 n — 1 3 rc' nearly, this fraction 
a m 
a' ’ m 
13 a 
m 
m 
. — nearly. Assuming = j( ^ , and the other 
13 401211 
quantities as before, this fraction is — -g- X 0,72333 X 30 ^ 30 : whence the long 
inequality in the epoch of Venus = 
{— 2", 946 + Y X 0",00029/0} X sin {8 l - 13 Z' +40° 44' 34" + Y X 239",7} 
= {2", 946 — Y X 0 ", 0002970} X sin {8 l - 13 /' + 220 ° 44' 34" + Y X 239", 7} 
The corresponding inequality in the axis major, like that for the Earth, is in- 
sensible. 
69. For the long inequality in the longitude of perihelion. This cannot be 
deduced from that of the Earth: but, calculating it independently in the same 
manner, it is found that 
•a = n - 0",008 sin (8 / — 13/') — 5",704 . cos (8 l — 13 V) 
70 . For the long inequality in the excentricity. This may be derived from 
that in the longitude of perihelion in the same manner in which it was done 
for the Earth : thus it appears that 
e = E - 0,0000001904 . sin (8 / - 13 l') + 0,0000000003 . cos ( 8 / — 13 t) 
71. For the inequality in latitude. The orbit of Venus must now be sup- 
