Sundials: Their Theory and Construction
by Albert E. Waugh
Dover 0-486-22947-5
Original (1973) publication.
ISBN 0-486-22947-5
$8.95
Chap. 6 Vertical Direct South Dials
p. 52 - If the building is so oriented that its walls face exactly toward
the cardinal points of the compass (north, south, east, and west), dials
attached to its walls are called vertical direct dials -- vertical
because the dial plate lies in a vertical plane, and direct because it
faces directly toward one of the cardinal compass points.
The wall ... faces due south. A dial placed on this wall would be called a
vertical direct south dial. Note that vertical dials take their
names from the direction their wall faces, which is at right abgles
to the direction the wall runs.
... the hour lines on any vertical direct south dial are precisely the
same as those on a horizontal dial at the colatitude.
Footnote: The colatitude is the remainder obtained by subtracting the
latitude from 90d.
p. 53 - The numbering on a direct south vertical dial runs
counterclockwise around the dial face, as contrasted with the clockwise
sequence on a horizontal dial. On the vertical dial the dial center is at
the top, with the 12-o'clock hour line running down vertically to the
bottom, with the morning hours on the left and the afternoon hours on the
right. And the gnomon makes an angle with the dial face equal to the
colatitude rather than the latitude.
p. 55 - On every vertical direct south dial the 6-o'clock hour line is a
horizontal line at the top, and the 12-o'clock line is vertical. The Sun
can never shine on these dials earlier than 6 a.m. or later than 6 p.m.,
so we need not include any hour lines other than those .... As with
horizontal dials, if we use a gnomon of appreciable thickness our [dial]
must be cut in half along [the meridian, or 12-noon hour line] and the two
halves separated by the thickness of the gnomon. The gnomon must make an
angle with the dial plate equal to the colatitude .... The base of the
gnomon lies along [the 6A-6P] line ....
... it should be clear that the vertical direct south dial and the
horizontal dial are intimately related. The two are, in fact, sometimes
combined.
--
Chap. 10 - Vertical Declining Dials
p. 74 - Vertical declining dials are those which are attached to vertical
walls which do not directly face north, south, east, or west, but face
instead some intermediate compass point. ... Every declining wall falls
into one or another of four categories as shown in Figure 10.1:
N
^ P
| /
v /
S P/
p. 75
(a) Southwest decliners, like the wall at the lower left of the figure.
(b) Southeast decliners, on the wall at the lower right.
(c) Northwest decliners, on the wall at the upper left.
(d) Northeast decliners, on the wall at the upper right.
We name the declining wall from the direction we face if we stand with our
back to the wall looking straight ahead at right angles to the wall. The
amount of declination is measured by the angle between the meridian and a
line at right angles to the face of the wall, as shown ....
Before we can design a sundial to attach to ... a declining wall we must
know the latitude (as with other dials) and also the amount of the wall's
declination. ... The amount of the declination is usually expressed as an
angle accompanied by letters to show the direction the wall faces. ...
this wall declines S 24d E, which means that it faces somewhat toward the
south, but has been twisted around toward the east through an angle of
24d.
Graphical Method. [Directions for constructing a vertical declining
sundial for (symbol of Greek letter, phi) = 40d N lat and D is S 24d E.]
p. 78 - The Computational Method.
p. 81 - What Hour Lines to Include. No vertical dial can ever catch the
Sun's rays for more than 12 of the 24 hours in a day. A vertical direct
south dial shows the hours from 6 a.m. to 6 p.m., ....
... Again, we are limited to a 12-hour span. And how do we know which 12
hours? There are several complicated mathematical rules, but simplest of
all is the statement, "Include only those hour lines which lie below line
AB in Figure 10.5."
Figure 10.5 (p. 82)
(horizon)
A----C----B
|
| (vertical)
|
D
p. 87 - Measuring a Wall's Declination.
\
W \ (wall declines toward the southwest)
\
S
/
/ E (wall declines toward the southeast)
/
S
Perhaps the simplest way of measuring the angle of declination is to place
a horizontal table or shelf against the wall, hold up a plumb line just
when the Sun souths (see Chapter 2), and mark the position of the noon
shadow. Since at the moment of local apparent noon the Sun is due south,
the shadow of the plumb line will lie in ...
O
|
F\ |
\|
B
p. 88
... the meridian and if we mark its position on the horizontal table it
will give us line OB of Figure 10.9. If we draw line FB perpendicular to
the face of the wall, the declination can be measured from angle FBO. Let
us measure on the tabletop the distance FO and the distance FB and divide
the former by the latter [TAN declination of wall = FO/FB]. This will give
us the tangent of the wall's declination. ...
An Alternative Method of Finding a Wall's Declination. One need not wait
for the moment of local apparent noon to ascertain the declination of a
wall. If at any moment [we] can determine: (a) the direction of the Sun
from the wall, and (b) the direction of the Sun from the south point, [we]
can determine the orientation of the wall by comparing the two. [Lengthy
directions follow, 88-99.]
--
Chap. 11 - Direct Reclining or Inclining Dials pp. 100-105
--
Chap. 12 - Dials Which Both Decline and Recline pp. 106-107