This result was founded on the computations of his friend Mayer,
who, by the assistance of the best astronomical tables then in use,
found that neither the eclipse mentioned by Pliny, Scaligcr, Calvisius, Petavius, or Usher, could possibly be the eclipse alluded to
by Herodotus. Mayer calculated all the eclipses from 608 to 556 before Christ, and found that of May 603 to be that which best accorded in position and magnitude with that described by Herodotus.
In the Philosophical Transactions for the year 1753, Mr. Costard, by computations similar to those of Mayer, arrived at the same conclusion with respect to this eclipse; but nevertheless, by introducing an allowance for the moon's acceleration, which was not attended to by Mayer, he has assigned a path to the centre of the moon’s shadow, which Baily observes does not pass over any part of Asia Minor, and consequently is too much to the southward for the eclipse of Herodotus.
Since the improvements which have been made of late years in astronomy, have shown the tables employed by Mayer and by Costard to be extremely defective, even in respect to the mean motions of the sun and moon, as well as the lunar equations; and since the secular variations derived from the formula of M. Laplace were wholly unknown at the time when those tables were constructed, and must have an important efl'ect in determining the place of conjunction at so distant a period, the author has been induced to recalculate the elements of several of these eclipses, from the new Tables Astrono- miques, published a few years since by the Bureau des Longitudes in France. TheSe calculations, at full length, together with a map containing the paths of the moon’s shadow in these eclipses, accompany this paper, for the satisfaction of those who may be interested to enter more minutely into the subject.
The eclipses here calculated are, first, that of Pliny in May, 585 B. C.; next that of Calvisius, 607 B. 0., each of which, as well as that of Bayer, passed too much to the south for the eclipse mentioned by Herodotus; while that of Petavius, in July, 597, and that of Usher, September, 601 B. 0., passed much too far to the north to have been seen in Asia Minor. With respect to the eclipse of the year 626, suggested by Volney, it was not total, but only annular, and moreover was not visible but to countries far eastward of Asia Minor.
Mr. Baily’s inquiries have consequently taken a greater range than those of his predecessors. He has taken the pains to calculate all the solar eclipses from 650 before Christ to 580, and has found only one that was central and total in or near any part of the peninsula of Asia Minor.
This eclipse took place on the 30th of September, 610. The centre of the moon's shadow, in this instance, passed in the forenoon of that day, in a straight line, over the north-eastern part of Asia Minor, through Armenia into Persia, where the sun was centrally eclipsed on the meridian. The path of the moon’s shadow is estimated by the author to have passed over the very mouth of the river Halys,
