IN THE MOTIONS OF THE EARTH AND VENUS. 
121 
The terms affecting the latitude may be at once neglected. The inequali- 
ties in longitude produced by the change of mean anomaly and excentricity, 
(n t + $ — ts and e ), and which are 
for the Earth 
— 0",0470X sin {8/- 12/'- 15° 34'} - 0",0346 . sin{ 14/'- 8 l- 139° 22'} 
for Venus 
+ 0",0671 . sin{9 l— 13/'— 24° 40'} + 0",0203 . sin {13 l' - 7 /— 168° 40'} 
can scarcely be detected from observation. The inequalities in the radii vec- 
tores are not sensible. 
The long inequalities in the epoch of longitude are however by no means 
to be neglected. To point out a single instance in which their importance will 
be sensible, I will estimate roughly their effect on the places of the Earth and 
Venus at the next transit of Venus over the Sun’s disk (in 18/4). The value 
of these inequalities at the time of .Bradley’s observations was small ; and they 
were at their maximum at the beginning of this century. If, then, the mean 
motions of the Earth and Venus were determined by comparing the observa- 
tions about Bradley’s time with the observations a few years ago ; the Earth’s 
longitude in 1874, when the inequalities are nearly vanishing, would be too 
small by nearly 4" ; that of Venus would be too great by 6" : their difference 
of longitude would therefore be nearly 10" in error ; and this would produce 
on the geocentric* longitude of Venus an effect of between 20" and 30". As 
another instance, I may mention that the secular motions of the Earth, deter- 
mined from observations of two consecutive centuries, would differ nearly 8", 
and those of Venus nearly 12". 
These inequalities vanish in the years 1622, 1742, and 1861 ; and have their 
greatest values, positive for the Earth and negative for Venus, in 1682 ; and 
negative for the Earth and positive for Venus, in 1802. At the principal 
transits of Venus their values are as follows : 
* In the Memoirs of the Astronomical Society I have pointed out the utility of observations of 
Venus near inferior conjunction for determining the coefficient of the inequality in the Earth’s motion, 
produced by the Moon. I take this opportunity of repeating my conviction, that observations of Venus 
near inferior conjunction are adapted better than any others to the detection and measurement of 
minute inequalities in the Earth’s motion. 
MDCCCXXXII. 
R 
