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IV. On an inequality of long period in the motions of the Earth and Venus. 
By George Biddell Airy, A.M ., F.R. Ast. Soc ., F.G.S., late Fellow of 
Trinity College, Cambridge, and Plumian Professor of Astronomy and Ex¬ 
perimental Philosophy in the University of Cambridge. Communicated by 
Sir J. F. W. Herschel, F.R.S. fyc. 8$c. fyc. 
Read November 24, 1831- 
In a paper “ On the corrections of the elements of Delambre’s Solar Tables,” 
published in the Philosophical Transactions for 1828, I stated that the compa¬ 
rison of the corrections in the epochs of the sun and the sun’s perigee given by 
late observations, with the corrections given by the observations of the last 
century, appeared to indicate the existence of some inequality not included in 
the arguments of those Tables. As soon as I had convinced myself of the ne¬ 
cessity of seeking for some inequality of long period, I commenced an exami¬ 
nation of the mean motions of the planets, with the view of finding one whose 
ratio to the mean motion of the earth could be expressed very nearly by a pro¬ 
portion whose terms were small: and I did not long seek in vain. 
It is well known that the appearances of Venus recur in very nearly the same 
order every eight years : and therefore some multiple of the periodic time of 
Venus is nearly equal to eight years. It is easily seen that this multiple is 
thirteen: and consequently eight times the mean motion of Venus is nearly 
equal to thirteen times the mean motion of the Earth. According to Laplace, 
(Mec. Cel. liv. vi. chap. 6.) the mean annual motion of Venus is 650^198; 
that of the Earth 399&-993. Hence 
8 X mean annual motion of Venus . . . . = 5201S-584 
13 X mean annual motion of the Earth . . =5199 ’909 
Difference.= 1 ‘675 
The difference is about ^ of the mean annual motion of the Earth ; and it 
k 2 
