PHILOSOPHICAL TRANSACTIONS. 
Vn. On the Eclipses q/* Agathocles, Thales, and Xerxes. 
By G. B. Airy, Esq., Astronomer Royal. 
Received December 15, 1852, — Read February 3, 1853. 
Section I. Preliminary . — On the Elements of the Lunar Tables. 
1. Till the beginning of the present century, neither the mechanical theory of the 
moon’s motion, nor the numerical determination of her principal elements, nor the 
lunar tables founded on these, were sufficiently accurate for the computation of a 
distant eclipse. And (perhaps in consequence of the evident imperfection of these 
essential grounds of calculation) the mode of treating chronological eclipses was, in 
most instances, extremely lax. The general result of these deficiencies is, that in 
any point of the slightest delicacy, the calculations made before 1810 are absolutely 
worthless. 
2. The extension and general improvement of the lunar theory by Laplace, and 
in particular the determination of the secular equations depending on the square of 
the time, very greatly altered the state of lunar and chronological science. Partly 
by the stimulation of foreign academies, partly by individual enterprise, lunar tables 
were soon produced which embodied the principal results of the new theory, and 
which were founded on more numerous and more carefully reduced observations 
than had been used before. The extensive tables by Burg, printed by the Bureau des 
Longitudes in 1806, and the smaller tables by Oltmanns from the same elements, 
printed in the fourth supplementary volume of the Berliner Jahrbuch in 1808, will 
long be remarked as important steps in lunar calculation. 
3. The first valuable deduction which was drawn from these, in reference to chro- 
nological computation, was the series of calculations in the paper by our late Fellow, 
Mr. Francis Baily, “On the Solar Eclipse which is said to have been predicted by 
Thales,” communicated to the Royal Society on 1811, March 14, and printed in the 
Philosophical Transactions for 1811. Although there can now be no doubt that the 
eclipse on which Mr. Baily fixed was a wrong one, yet this paper (the first, I believe, 
MDCCCLIII. 2 B 
