priestly legends with a sacred
character. They were said to have been instituted by the Idaean
Heracles, to commemorate his victory over his four brothers in a
foot-race. According to a tradition, possibly more authentic, they were
re-established by Iphitus, king of Elis, in concert with the Spartan
Lycurgus and Cleosthenes of Pisa. The practice was long afterwards
adopted of designating the Olympiad, or period of four years, by the
name of the victor in the contests of the stadium, and of inscribing his
name in the gymnasium of Olympia. The first who received this honour was
Coroebus. The games in which Coroebus was victor, and which form the
principal epoch of Greek history, were celebrated about the time of the
summer solstice 776 years before the common era of the Incarnation, in
the 3938th year of the Julian period, and twenty-three years, according
to the account of Varro, before the foundation of Rome.

Before the introduction of the Metonic cycle, the Olympic year began
sometimes with the full moon which followed, at other times with that
which preceded the summer solstice, because the year sometimes contained
384 days instead of 354. But subsequently to its adoption, the year
always commenced with the eleventh day of the moon which followed the
solstice. In order to avoid troublesome computations, which it would be
necessary to recommence for every year, and of which the results differ
only by a few days, chronologers generally regard the 1st of July as the
commencement of the Olympic year. Some authors, however, among whom are
Eusebius, Jerome and the historian Socrates, place its commencement at
the 1st of September; these, however, appear to have confounded the
Olympic year with the civil year of the Greeks, or the era of the
Seleucidae.

It is material to observe, that as the Olympic years and periods begin
with the 1st of July, the first six months of a year of our era
correspond to one Olympic year, and the last six months to another.
Thus, when it is said that the first year of the Incarnation
corresponds to the first of the 195th Olympiad, we are to understand
that it is only with respect to the last six months of that year that
the correspondence takes place. The first six months belonged to the
fourth year of the 194th Olympiad. In referring dates expressed by
Olympiads to our era, or the contrary, we must therefore distinguish
two cases.

_1st._ When the event in question hap