&c. &c.

These determine the sides AB, AC, &c., that is, the angles AEB, AEC,
&c., required.

The I o'clock hour-line EB must make an angle with the meridian EA of
11 deg. 51' on a London dial, of 12 deg. 31' at Edinburgh, of 11 deg. 23'
at Paris, 12 deg. 0' at Berlin, 9 deg. 55' at New York and 9 deg. 19' at
San Francisco. In the same way may be found the angles made by the other
hour-lines.

The calculations of these angles must extend throughout one quadrant
from noon to VI o'clock, but need not be carried further, because all
the other hour-lines can at once be deduced from these. In the first
place the dial is symmetrically divided by the meridian, and therefore
two times equidistant from noon will have their hour-lines equidistant
from the meridian; thus the XI o'clock line and the I o'clock line
must make the same angles with it, the X o'clock the same as the II
o'clock, and so on. And next, the 24 great circles, which were drawn
to determine these lines, are in reality only 12; for clearly the
great circle which gives I o'clock after midnight, and that which
gives I o'clock after noon, are one and the same, and so also for the
other hours. Therefore the hour-lines between VI in the evening and VI
the next morning are the prolongations of the remaining twelve.

Let us now remove the imaginary sphere with all its circles, and
retain only the style EP and the plane HMA with the lines traced on
it, and we shall have the horizontal dial.

On the longest day in London the sun rises a little before 4 o'clock,
and sets a little after 8 o'clock; there is therefore no necessity for
extending a London dial beyond those hours. At Edinburgh the limits
will be a little longer, while at Hammerfest, which is within the
Arctic circle, the whole circuit will be required.

Instead of a wire style it is often more convenient to use a metal
plate from one quarter to half an inch in thickness. This plate, which
is sometimes in the form of a right-angled triangle, must have an
acute angle equal to the latitude of the place, and, when properly
fixed in a vertical position on the dial, its two faces must coincide
with the meridian plane, and the sloping edges formed by the thickness
of the plate must point to the pole and form two parallel styles.
Since there are two styles, there must be two dials, or rather two
half dials, because