152 
SECOND REPORT - 1832 . 
was introduced* the coefficient of which was entirely empirical. 
In 1809, Zach put them in a portable form. In 1812, Burck- 
hardt’s Tables appeared, differing a little in the numbers, and a 
little in arrangement, from Burg’s, and containing also a greater 
number of equations ; still the coefficients were obtained from 
observation. It was felt that the lunar theory was imperfect 
so long as appeal to observation for more than the six funda¬ 
mental elements was necessary, and the Institute offered a prize 
for the lunar theories and Tables which should borrow nothing 
more. Two able theories were produced, and on one of these 
Damoiseau’s Tables (published 1824,) are founded. They in¬ 
clude a greater number of equations than the former, and are 
simpler in arrangement. In the Conn, cles Temps 1828, they 
are compared with observations. Laplace’s long equation is 
here entirely rejected. In fact, Burckhardt [Conn, des Temps 
1824,) shows that other equations will do as well; Carlini [Effe- 
meridi di Milano 1825,) on trying four equations depending on 
different arguments, shows that some are preferable to Laplace’s, 
but that the best of all is a term depending on the square of 
the time. The theory of the Moon therefore appears still de¬ 
fective. In the Milan Ephemeris 1827, is a most valuable paper 
by Carlini on the Moon’s variation ; in which, after comparing 
theory with his own observations, he arrives at the conclu¬ 
sion that they are not perfectly reconcileable. Among the 
materials that have been produced for correcting the lunar 
Tables I may mention 215 occultations calculated by Tries- 
necker ( Gottingen Transactions 1800) ; 100 by Carlini, and 
some by Oriani [Milan Ephemeris 1812 and 1814) ; several for 
the Moon’s diameter, by Wisniewski [Petersburgh Transactions 
tom. 8) ; the comparisons by the French Board [Conn, des 
Temps , and Introduction to the French Tables) ; comparison of 
Greenwich observations, by order of the English Board of 
Longitude; a few by Mr. Henderson [Ast. Nadir. No. 176) ; 
some by Carlini [Milan Ephemeris 1830) ; and nearly 200 right 
ascensions, and several occultations compared by me [Cam¬ 
bridge Observations). Of unreduced observations, none can 
be compared with the uninterrupted series made at Greenwich. 
For distant times, Mr. Baily, on the eclipses of Thales and Aga- 
thocles [Phil. Trans. 1811), and Oltmanns [Berliner Jahrbuch 
1823 and 1824), and Wurm on 20 ancient eclipses [Zeitsehrift 
vol. 3,) are worth consulting. In No. 102 of the Ast. Nadir. 
are observations of declination at Paramatta, for the Moon’s 
parallax. 
In the Conn, des Temps 1822, is a discussion by Nicollet of 
124 observations of one of the lunar spots, for the phenomena 
of libration. On comparison with theory he is led to the re- 
