On the Early Babylonian Eclipse of the Sun. 251 
an approximate calculation showed that the only eclipses which could 
possibly correspond to the record are the following : — 
1235 
1217 
1163 
1135 
1123 
1116 
1069 
1062 
1014 
956 
947 
May 26th 
June 5th 
July 8th 
June 28th 
May 18th 
June 28th 
June 20th 
July 30th 
July 11th 
May 31st 
May 22nd 
These selected eclipses were then carefully computed according to 
Hansen's method as employed by Oppolzer, making use of the tabulated 
data given in the " Syzygien Tafelu," after removing the empirical correc- 
tions applied by Oppolzer. 
Taken unchanged, this would yield results corresponding to Hansen's 
final data as given in the Darlegung," after adding eleven seconds to the 
secular motion of the node. But as it was deemed best to make the 
fundamental calculation of the eclipses on the basis of pure theory, there 
were applied the requisite corrections to the secular acceleration of the 
mean longitude and to the secular motion and secular accelerations of the 
longitude of the lunar perigee and node to reduce them from the values 
derived from observation to the values derived from pure theory. These 
purely theoretical values, assuming the epoch of T to be 1800, were 
taken as — 
Mean longitude =Z = +17325593-796"T + 6-180"T^ +0-0062T3 
Longitude of Perigee =A = + 146435-473 -38-900 -0-0389 
Longitude of Node... =B=- 69679-281 + 6-560 +0-0066 
Values agreeing fairly well with those derived by theory by Professor 
Brown, except in the case of the secular motion of the mean longitude, 
which has to be deduced from observation, and for which Professor 
Brown's value seems to be too large. 
These correspond to — 
Z = Hansen's Darlegung Values... -30-00"T -6-377"T^ -0-006349"T3 
A= ,, ... +12-88 -0-322 -0-000322 
B= ,, ,, ... +33-83 -0-064 -0-000064 
and form similar corrections to the values adopted as the basis of 
Oppolzer's " Syzygien Tafeln " before the application of his empirical 
terms, except that in the case of the coefficient of T in the value of B, 
17 
