To understand how one determines the
timescale of a horizontal sundial one starts with
the equatorial sundial. It consists of a disc and
of an axis, which is normal to the plane of the
disc (figure 8). The axis is parallel to Earth’s axis
so that the disc is parallel to the equatorial plane
of the Earth, as well as to the tangential plane at
the poles. It follows from this that the equatorial
sundial is a simplified form of a globe which
simulates Earth’s orientation and has an extended
axis.
The shadow of the axis on the disc is parallel
to the shadow which a vertical column on Earth’s
pole would throw on the tangential surface around
the pole. Both shadows have constant length
during the day and rotate uniformly. This is
because: (1) the Earth rotates uniformly, and
(2) the angle between Earth’s axis and Sun’s rays is
approximately constant during a day. During one
hour the shadow of the axes rotates by an angle of
15◦. This is why the hour lines on an equatorial
sundial are spaced at 15◦ intervals. The noon line
connects the disc centre and its bottom, 6 am is on
the western edge, and 6 pm on the eastern edge.
Angles are measured from the noon line towards
the east and towards the west.