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These things used to be understood intuitively by everybody, and their rules and special terminology were a part of the intellectual baggage of all well-educated people. Midsummer's day was celebrated at the summer solstice on June 21. Christmas is close to the Winter solstice on December 22. The vernal and autumnal equinoxes mark the beginning of Spring and Fall when the sun moves into Cancer and Capricorn, respectively. It is instructive to learn how a sundial works and watch its shadow advance through the day and vary with the seasons. In this way we can come to a better understanding of these natural phenomena and relearn the meanings of those half-understood, half forgotten names like "gnomon", "ecliptic" and "zodiac."
Until the end of the 19th century, all time was local and related to the sun. Noon in Boston was not the same time as noon in New York. With the development of railroads and telegraphs widely spaced locations became linked to each other more closely in time and, there was a need to standardize time areas. In 1884 an international convention in Washington D.C. agreed on a worldwide system of time zones of 15° each. Local adjustments were allowed, as necessary, to keep political subdivisions in a single zone.
Dials
A sundial consists of the dial plate marked out with hour
lines, and a "gnomon", the raised projection that casts the
shadow. The inclined edge of the gnomon, called the "style",
produces the working edge of the shadow that is used to tell the
time. It is oriented parallel to the earth's axis, pointing
toward the point in the sky around which the (imaginary)
celestial sphere rotates once every 24 hours, which is very close
to the location of Polaris, the pole star visible at night.
There are many different types of sundials, including vertical
dials and tilted dials. Virtually anything casting a shadow can
be made into a sundial; the trick is to calculate the proper
placement of the time marks. The most straightforward type of
dial is the "polar" dial. It has marks placed at equal
intervals. Its disadvantage, however, is that it has to be
angled to face up toward the north pole. Vertical dials on public
buildings used to be widespread. Now, the type of dial seen most often
is the horizontal dial, generally used as a decorative element in gardens.
Sundials sold in garden shops will not generally tell accurate time, however,
except by coincidence.
| Vertical Declining Dial | Horizontal Dial |
|---|---|
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To be accurate, a sundial must be specially designed for the spot it is to be used in and must also be pointed in the right direction. The two dials pictured above were made for a specific location in Maine. Note that the times on the vertical dial are asymmetrical. This is necessary because the dial "declines" from true north by about 20°. The barn was built using a compass but at this point on the earth's surface, magnetic north is about 20° east of true north.
The angle made by the style with respect to the earth's surface -- or with the plate in the case of a horizontal dial -- must be equal to the local latitude, which will point it to the proper elevation. The time lines are also a function of local latitude; they must be arrayed around the center of the dial differently in different places. Finally, the dial must be oriented so that the gnomon lies on a true north-south axis to insure that it points to the north pole of the sky. When these alignments are all correct, the edge of the gnomon whose shadow marks out the time will be exactly parallel to the axis on which the sky's imaginary globe is turning. When the sun is at its zenith, the gnomon's shadow will fall on the line representing solar noon.
A garden sundial can be set to tell the right time if
it was correctly constructed for some point on the earth's
surface. Assuming that the hour lines were drawn correctly to
match the elevation of the gnomon at a given latitude the sundial
will be accurate if the whole thing, including the plate, is
tilted so it sits at the angle of the earth's surface at its
"home location" or in other words if the gnomon points to the
north celestial pole. If you are at latitude 42° at
washington and the gnomon makes an angle of 39° with the
plate, simply tip the plate by 3°.
Construction of a vertical declining dial
Vertical declining dials are those attached to walls that do not face directly north, south, east or west. Although this is not the most straightforward type of sundial, it is probably the best kind to construct oneself as a project, since it can be put on the side of a house, barn or garage and executed using easily available materials including wood, paint, and pre-made numbers for the dial itself and dowels, pipes, or rods to construct the gnomon-pointer. The following procedure shows how to lay out the angles for the gnomon and the hour lines on paper using a standard geometric methods (straightedge and compass). A protractor will also be necessary to establish the lines dependent on latitude. The drawing should be laid out on a large sheet of pa per and subsequently transferred to the wall. If you are actually going to do this, you will obviously want to send this page to your printer so you can refer to it.
Since you generally do not have the option of reorienting your garage to line up with the compass, it will probably be necessary for the dial to "decline" from the cardinal points. First, you have to ascertain which of the four categories (shown in figur
e 1) your building or wall falls into.
The first step is to find the substyle line, which is the line on the dial plate on which the gnomon is to be erected perpendicular to the dial plate -- or in this case, the wall. In a more typical dial, the gnomon would follow the 12-o'clock line, but w ith vertical decliners this is no longer the case. In all vertical dials the 12-o'clock line is vertical, but with declining dials the line on which the gnomon is placed (called the substyle) is twisted out of the vertical, lying to the right or east of the 12-o'clock vertical line and thus among the afternoon hour lines if the dial declines toward the west of south or to the left or west among the morning hour lines with the southeast decliners. (As with the example.) The angle between the vertical 12 -o'clock line and the substyle is called the substyle distance, or SD. To find this substyle graphically we proceed as follows using figure 2.
These lines are to be transferred from the worksheet to the dial plate or perhaps directly to the wall, remembering that the 12-o'clock line will be vertical. You will also need the substyle line to attach the gnomon perpendicular to the dial plate.
In principle, north can be located by using a magnetic compass and
making an appropriate the correction.
Magnetic north is substantially off from true north -- the exact
amount varies by location. But there are better ways.
Polaris, the north star, can be used, but this is
inconvenient -- you have to wait for a clear night -- and not
entirely accurate either. The most accurate way to find a true
north south orientation is by using the sun itself to find the
direction of a shadow cast by a vertical object when the sun is
at its zenith. This is easier than it sounds, and can be done by
measuring the length of the shadow cast by the upright before and after noon.
Set up a vertical pole (or a use a rope with a weight) to cast a shadow on
the ground. If you use a rope you will need to make the reference point
somewhere near the top cast a visible shadow -- like a stick knotted
into the rope) The base of the shadow will be the first point for
your south-north axis and the reference point or top of the pole will trace the second
point. At some time in the morning, mark the spot on the ground where the
reference point casts its shadow. Measure the length from the base to the end
of the shadow, and using a string of that length, trace out a semi-circle
on the ground with the base of the shadow as its center point. As the sun
rises higher in the sky, the shadow will first shorten as noon approaches, and
and then will lengthen. At some in the afternoon it will reach the semi-circle
you traced in the morning. Note the spot when it crosses the arc
the second time. The midway point between the morning and
afternoon points, will be directly north of the base point of vertical object.
Adjusting for clock time
The north "noon" line cast by the sun at its zenith will not correspond to noon clock time. Two adjustments are necessary. The first of these has to do with local placement within the time zone and is different for every longitude; the second is a function of the day of the year and can be found with an Analemma.
The second adjustment is more complex and is captured in
what is by tradition called "the equation of time." This results from
the fact that the apparent motion of the
sun across a spherical sky is a fiction; the earth actually
orbits around the sun in an elliptical path. Therefore
the sun's apparent motion across the sky is not uniform
throughout the year and can run almost 15 minutes fast or slow.
For practical purposes, however, it is important that the
hour-unit of time be kept constant and the days divided into 24
equal sized hours, regardless of the season. This means that for
clock time it is necessary to create a "mean sun" -- an imaginary
sun that moves across the sky at a constant rate. The
equation of time is is the sum of two curves, one caused by the
earth's eliptical orbit; the other caused by its inclination. The equation has long
ago been worked out with great precision and incorporated in tables.
If plotted against the days of the year, it looks like an irregular pattern with four peaks
and four troughs. It is commonly represented graphically on old globes and sundials by the
"Analemma," a figure-8 shaped device that shows the number of
minutes that must be added or subtracted from solar time at each
date in the year.
The Seasons
A line traced around the center of the celestial sphere
perpendicular to the pole it rotates around is called the
celestial equator. This line is not directly overhead, but is
tilted as a function of the observer's local latitude. In the
northern hemisphere it angles toward the south. In the
Washington DC area, it makes an angle with the horizon of 52
degrees. Through the course of a year, the sun migrates around
the celestial sphere. If it moved along the equator, there would
be no seasons. But because the earth's axis is tilted with
respect to its orbit around the sun, this requires another
imaginary line on the imaginary celestial sphere, known as the
ecliptic. On the longest day of the year (the summer solstice),
the ecliptic is 23.4° higher than the equator so that the
sun reaches 75.4° at high noon. At the winter solstice,
the year's shortest day, the sun only reaches 28.6° above
the horizon. At the vernal and autumnal equinoxes when days and
nights are equal, the sun's path along the ecliptic coincides
with the celestial equator and the sun reaches 52°
elevation above south at the latitude of Washington.
This is confusing and difficult to visualize. It may help to
bear in mind that the equator line is related to the sky's daily
rotation, while the sun moves on the ecliptic by only a short
distance every day. The sun therefore moves across the sky on a
path (almost) parallel each day to the equator, but displaced
from it by a distance that varies slowly throughout the year. In
this figure, which is meant to represent the sky, the sun is at
its high point, the summer solstice. It rotates in one day on
the axis of the pole, parallel to the celestial equator. It does
not rise in the east and set in the west, but cuts the horizon
quite far north side of an east-west line, The sun's motion
along the ecliptic takes a year to complete. When it has moved
to the opposite side as shown in the diagram, its path will be
very low and it will rise and set south of an east-west line
through the horizon.
The Tropics: Cancer and Capricorn
The word "tropic" has an older meaning from which the present
use is derived. What we call "the tropics" lies between two lines, the
tropics of Cancer and Capricorn that when drawn on the surface of
the earth represent the northernmost and southernmost points at which
the sun can be found overhead on the longest day. The words derive from
the lines drawn on a sundial (at any latitude) which represent the
longest (and shortest) days of the year.
The length of the shadow cast at a given time by a sundial's
gnomon -- or any other shadow-- is a function of the season. It
is longer in winter than in summer. The line that is traced out
on the ground by the tip of a shadow from dawn to dusk has a
different shape depending on the season and is called the "line
of declination". If, on the summer solstice you were to plot the
sun's shadow cast by the tip of the style (the nodus) on a
sundial at short intervals over a full day, the line traced out
crossing the hour lines would form a parabola. Similarly, the
line traced out by the shorter series of shadows on December 21
is also a parabola, but faces in the opposite direction. These
two lines were called "tropics" and on old dials are sometimes
labelled the tropics of Cancer and Capricorn. These names come
from the fact that they are traced out at the times of year when
the sun is in the respective constellation.
The Zodiac
During the day, the stars lying along the ecliptic cannot be seen, but they are nevertheless there. The constellations near the ecliptic have a special status. There are 12 of them, which collectively make up the zodiac, which aside from their use in the newspaper astrology column, represent traditional star patterns in the night sky and hold official sway over 15° of arc each. At the summer solstice the sun enters the constellation Cancer. When it sets in the evening of June 21 along with (then invisible) Cancer, the constellation on the opposite side of the zodiac, Capricorn, will be rising into view. At the winter solstice, the sun is in Capricorn. The shadow traced by the nodus is the tropic of Capricorn, and as Capricorn sets at dusk, Cancer will be rising in the night sky. On the two equinoxes, March 21 and September 21, the nodus traces out a straight line.