OF AGATHOCLES, THALES, AND XERXES. 
Burg’s and Burckhardt’s Tables. 
185 
Coefficient for mean longitude _|_10-00 
Coefficient for longitude of perigee 29*98 
Coefficient for suppl. longitude of node — 7-35 
Damoiseau, Mern, Savans Etrangers, Third Series, tome i. p. 544, and Tables. 
Coefficient for mean longitude +10-72 
Coefficient for longitude of perigee —39-70 
Coefficient for suppl. longitude of node * . — 6*56 
Plana, Theorie de la Lune, vol. i. p. 724. 
Coefficient for mean longitude + 10-58 
Coefficient for longitude of perigee —40 23 
Coefficient for suppl. longitude of node — 6*79 
Hansen, Astronomische Nachrichten, No. 443. 
Coefficient for mean longitude +11-93 
Coefficient for longitude of perigee — 39-18 
Coefficient for suppl. longitude of node — 6*49 
Hansen, Astronomische Nachrichten, No. 597 . 
Coefficient for mean longitude +11-47 
Coefficient for longitude of perigee — 36-31 
(The coefficient for suppl. longitude of node is not computed). 
17-1 believe that I have now stated, without important omission, the progress of 
Lunar Theory, as bearing on distant eclipses, to the present time ; and I shall now 
proeeed with the special calculations of this paper. 
Section II. Methods of Computation adopted in this Paper. 
18 . The tables used in these computations, for the sun’s longitude and the obli- 
quity of the ecliptic, are Carlini’s tables attached to the Effemeridi di Milano, 1833 . 
The precepts of the tables have been strictly followed, with these exceptions ; that 
from Table V. the number has been taken which corresponds to lunar syzygies, and 
the mean values of Table VI. and Table XIII. have been taken, and the sum of these 
numbers or 7^'5 has been used as a constant. The sun’s semidiameter has been 
slightly altered for the change of excentricity of the earth’s orbit. The sun’s longi- 
tude is found for two adjacent hours, and is then changed into right ascension and 
north polar distance. The following error has been remarked in the printed tables: 
Table XXX., /or 16 ' 44"-10 read 16 ' 34"-10. 
19 . The lunar tables employed here are the same (except in the epochs) as those 
used in the Reduction of the Greenwich Lunar Observations. With the exception 
