falling on one of these curve lines would mark a division of
time for that day, and thus we should have a sun-dial which would divide
each period of daylight into twelve equal parts. These equal parts were
called _temporary hours_; and, since the duration of daylight varies
from day to day, the temporary hours of one day would differ from those
of another; but this inequality would probably be disregarded at that
time, and especially in countries where the variation between the
longest summer day and the shortest winter day is much less than in our
climates.

The dial of Berossus remained in use for centuries. The Arabians, as
appears from the work of Albategnius, still followed the same
construction about the year A.D. 900. Four of these dials have in modern
times been found in Italy. One, discovered at Tivoli in 1746, is
supposed to have belonged to Cicero, who, in one of his letters, says
that he had sent a dial of this kind to his villa near Tusculum. The
second and third were found in 1751--one at Castel-Nuovo and the other
at Rignano; and a fourth was found in 1762 at Pompeii. G. H. Martini in
his _Abhandlungen von den Sonnenuhren der Alten_ (Leipzig, 1777), says
that this dial was made for the latitude of Memphis; it may therefore
be the work of Egyptians, perhaps constructed in the school of
Alexandria.

Herodotus recorded that the Greeks derived from the Babylonians the use
of the gnomon, but the great progress made by the Greeks in geometry
enabled them in later times to construct dials of great complexity, some
of which remain to us, and are proof not only of extensive knowledge but
also of great ingenuity.

Ptolemy's _Almagest_ treats of the construction of dials by means of his
_analemma_, an instrument which solved a variety of astronomical
problems. The constructions given by him were sufficient for regular
dials, that is, horizontal dials, or vertical dials facing east, west,
north or south, and these are the only ones he treats of. It is certain,
however, that the ancients were able to construct declining dials, as is
shown by that most interesting monument of ancient gnomics--the Tower of
the Winds at Athens. This is a regular octagon, on the faces of which
the eight principal winds are represented, and over them eight different
dials--four facing the cardinal points and the other four facing the
intermediate directions. The date of the dials is long subsequent to
that of the tower; for Vitruvius, w