REPORT ON ASTRONOMY. 
175 
Mec. Cel. ; the rule for retaining terms being directed prin¬ 
cipally by the magnitude of their numerical values, and not by 
the order of small quantities. The immense calculations of 
this theory are given with great clearness and attention to 
order. In the Conn, des Temps 1823, Laplace gave some 
remarks on the two memoirs, giving generally the preference to 
Damoiseau’s, partly because he had followed Laplace’s method. 
Carlini and Plana replied in an elaborate paper in Zach’s Cor- 
respondance , vol. 4. Without attempting to analyse it, I shall 
only remark that I think no one can have an idea of the deli¬ 
cacies and difficulties in a theory of the Moon in the present 
day, without examining this reply. In another paper in the 
same volume, they considered one of the most troublesome 
equations, depending on twice the distance of the perigee from 
the node. Damoiseau, as well as Carlini and Plana, found that 
the equation, depending on the difference on the hemispheres, 
would probably be insensible : and Laplace {Conn, des Temps 
1828,) assented to this. In the Conn, des Temps 1824, La¬ 
place has given the investigations of several lunar inequalities 
of long period. In the same volume, Burckhardt, after discuss¬ 
ing several occultations, maintains the necessity of some equa¬ 
tion not yet given by theory. In the Milan Ephemeris 1825, 
Carlini suggests an equation depending on six times the di¬ 
stance of the perigee from the node diminished by the Sun’s 
mean anomaly : the period of this would be 1760 years. In Mr. 
Lubbock’s papers, before alluded to, the lunar theory is con¬ 
sidered. The author has commenced the investigation in a 
manner different from that of Laplace, Damoiseau, Carlini, and 
Plana, by making the time the independent variable in the 
equations ; and has given Tables for facilitating the research of 
the terms arising from the combination of other terms. He 
has also given developments of the perturbing function adapted 
to this case. 
In the theory of Mercury, a discussion of an insignificant 
numerical quantity has taken place between Laplace and Plana, 
Mem. Ast. Soc. vol. 2, and Conn, des Temps 1829. In the 
theory of Venus, I believe, the only addition is the term inves¬ 
tigated by the writer of this paper, (before alluded to,) and de¬ 
pending on the difference between eight times the mean longi¬ 
tude of Venus, and thirteen times the mean longitude of the 
Earth. This inequality is small; but as the corresponding 
inequality of the Earth has the opposite sign, and as Venus at 
inferior conjunctions is very near the earth, the effect of the 
inequality at those times will be very sensible. In the Conn, 
des Temps 1820, Burckhardt gave the equations for the prin- 
