ho describes the tower in the sixth
chapter of his first book, says nothing about the dials, and as he has
described all the dials known in his time, we must believe that the
dials of the tower did not then exist. The hours are still the temporary
hours or, as the Greeks called them, _hectemoria_.

The first sun-dial erected at Rome was in the year 290 B.C., and this
Papirius Cursor had taken from the Samnites. A dial which Valerius
Messalla had brought from Catania, the latitude of which is five degrees
less than that of Rome, was placed in the forum in the year 261 B.C. The
first dial actually constructed at Rome was in the year 164 B.C., by
order of Q. Marcius Philippus, but as no other Roman has written on
gnomonics, this was perhaps the work of a foreign artist. If, too, we
remember that the dial found at Pompeii was made for the latitude of
Memphis, and consequently less adapted to its position than that of
Catania to Rome, we may infer that mathematical knowledge was not
cultivated in Italy.

The Arabians were much more successful. They attached great importance
to gnomonics, the principles of which they had learned from the Greeks,
but they greatly simplified and diversified the Greek constructions. One
of their writers, Abu'l Hassan, who lived about the beginning of the
13th century, taught them how to trace dials on cylindrical, conical and
other surfaces. He even introduced _equal_ or _equinoctial hours_, but
the idea was not supported, and the temporary hours alone continued in
use.

Where or when the great and important step already conceived by Abu'l
Hassan, and perhaps by others, of reckoning by _equal_ hours was
generally adopted cannot now be determined. The history of gnomonics
from the 13th to the beginning of the 16th century is almost a blank,
and during that time the change took place. We can see, however, that
the change would necessarily follow the introduction of clocks and other
mechanical methods of measuring time; for, however imperfect these were,
the hours they marked would be of the same length in summer and in
winter, and the discrepancy between these equal hours and the temporary
hours of the sun-dial would soon be too important to be overlooked. Now,
we know that a balance clock was put up in the palace of Charles V. of
France about the year 1370, and we may reasonably suppose that the new
sun-dials came into general use during the 14th and 15th centuries.

Among the earliest of the