228 
Mr. Baily on the Solar Eclipse 
such eclipse could not be total any where near the place where 
the battle was probably fought. 
But none of these calculations can have much weight at the 
present day, since they must have been formed from tables 
which the subsequent improvements in astronomy have shown 
to be exceedingly defective and incorrect. Even the mean 
motions of the sun and moon are not given with a sufficient 
degree of accuracy, either in the Rudolphine or Halleian 
tables, to enable us to determine, with any tolerable correct- 
ness, their true mean place of conjunction at so remote a pe- 
riod : neither can the lunar equations, there given, be safely 
depended upon. The secular variations also are wholly omitted: 
and these must have an important effect in all inquiries of this 
kind, since they increase in proportion to the period of time 
elapsed. 
Under these circumstances, and in order to set this question 
at rest, as far as it can now be done by the aid of astronomi- 
cal science, I have been induced to re-calculate the elements 
of the several eclipses, above alluded to, from the new Tables 
Astronomiques , lately published by the Bureau des Longitudes 
in France. In these tables, the mean motions of the sun and 
moon are given with the greatest exactness for the most dis- 
tant periods : and, by the successive labours of Mayer, Mason, 
and Burg, the lunar equations are carried to an astonishing 
correctness ; which, together with the secular variations de- 
duced from the formulae of M. Laplace, enable us to deter- 
mine the true place of the sun and moon with considerable 
accuracy for many centuries prior to the Christian era. These 
calculations, at full length, together with a map containing 
the paths of the moon’s shadow in the several eclipses there 
