Methods of Finding Cardinal Points
CONTENTS
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Finding Cardinal Points - Introduction
The meridian* of a place (and the True North) can be located with high degree
of accuracy with
the use of few fairly simple methods (possibly available to ancient builders):
Note: Using Polaris (Northern Star) or magnetic compass
would be much less reliable at the time ancient monuments were built.
* The line on the surface of the earth through the place and both
poles is called the meridian of the place: it is a half-circle since the
earth is spherical.
- - -
Pyramids, and many other types of religious structures, required strict
orientation to the cardinal points. The ancient builders oriented their
monuments using either the sun or the stars.
The Ancient Egyptians managed to line up the sides of their
pyramids to the points of the compass, with extraordinary accuracy.
The most accurate is the Pyramid of Khufu, also called the Great
Pyramid. The east and west sides miss true north by less than three
minutes of arc (roughly one tenth the diameter of the full moon).
With this kind of accuracy, it's no wonder they were one of the
Seven Wonders of the World. It took over 4,000 years before the
astronomer, Tycho Brahe, was able to take astronomical measurements
to a greater accuracy.
And this led to a problem that has bothered Egyptologists for a
long time - how did they manage to line up the east and west sides
of the Great Pyramid so accurately with the North Pole?
Now we're not talking about Magnetic North. We're talking about
Geographic North which is the pole about which the Earth seems to
spin. The Magnetic North Pole is currently wandering at a few
kilometres per year through the far north of Canada, while the
Geographic North Pole is in the Arctic.
One way to find Geographic North would be by looking at the Sun.
You'd note the rising position of the Sun in East,
and the setting position of the Sun in the West, and halve the angle
between them. This would give the direction of the True North.
The other way to find Geographic North involves the stars at
night.
The Celestial North Pole is a point in the sky about which
the stars appear to rotate. If you took a time lapse photograph over
a full night, you would see that all of the visible stars would
appear to move in circles (some big and some small).
The star
Polaris would make an incredibly small circle because it's right
next to the Celestial North Pole. So it's called the Pole Star.
But there's a slight problem with this method. The
North-South spin axis of the Earth is not fixed, but rotates slowly
like a giant top. Imagine you have a big basketball and it's
spinning. Now the spin axis is not straight up-and-down, but tilted
by 23 degrees from the vertical. This how the Earth is currently
spinning. Now start off with the North Pole of your spinning
basketball slightly to the right. Gradually, the North Pole sweeps
out a circle, so that it's next facing away from you, and then over
to your left, and then coming around to face you, and then finally
back over to the right again. The spin axis of the Earth sweeps
through one complete rotation in 26,000 years.
The most likely way to find Geographic North would be by
bisecting the angle formed by the two extreme positions of a
circumpolar star. The best candidate
for such a star would be Vega.
Using Magnetic Compass to locate local meridian
Considering that ancient civilizations most likely were lacking magnetic
compasses, this is the least likely explanation how precise alignments of
ancient structures had been accomplished. In fact, the magnetic compass would
provide lesser than observed precision due to errors inherent in this method.
 |
A floating fish-shaped iron leaf, mentioned in the Wu
Ching Tsung Yao which was written around 1040. The book describes how iron
can be heated and quenched to produce thermoremanent magnetisation. The
first clear account of suspended magnetic compasses in any language was
written by Shen Kua in 1088] |
| Modern Compass
|
 |
The magnetic poles are not situated in the same place as the true
geographic poles (defined by the northern end of the earth's axis of
rotation) and
thus an error (variation) occurs in the true reading of the compass (which
varies in time and from place to place across the world).
Another magnetic
compass errors, deviation, is caused by the magnetic influence of anything that
can distort local magnetic field located near the compass needle. Therefore,
compass readings must be corrected for such errors. Also, the magnetic compass
needle reading can be distorted by disturbances on the sun, and magnetic
influence of anything near the compass needle.
- - -
Magnetic Variations - Finding True North
Magnetic variations had first been noticed in the Age of Discovery. Until
then, compass bearings and charts based upon them referred to magnetic north
rather than true north as measured by the position of the Pole Star. This
distinction only became vital when sailors began using latitude as the way to
determine their course. As they were sailing along a latitude they noted that
the compass needle varied unexpectedly. It 'northeasted' or ‘northwested' that
is, the position of magnetic north shifted with the position of the ship (Berthon
and Robinson, 1991:118).
This discovery initially greatly dismayed the Portuguese pilots who first
discovered it. Having no idea of the real reason - alterations in the magnetic
field of the earth which varies greatly in direction from both decade to decade
and place to place - they wrongly attributed the moves to badly hung compass
needles, inferior lode stones or the leeway caused by ocean currents. Compass
makers began to make their own 'allowances' for the variations by off-setting
north on the compass and off-setting different points on the journey. Hence it
was that Columbus found that his Flemish and Italian compasses provided
different readings (Berthon and Robinson, 1991:119).
Soon the idea developed that one "true" meridian may exist along which the
magnetic variation from true north was zero. On either side of this meridian, it
was believed, the variation would increase uniformly in opposite directions,
thus creating the effect of northeasting and northwesting. If this was reality
it meant that the direction of magnetic north relative to true north could be
predicted at any point around the earth's circumference and this could then be
used by a ship to calculate longitude by comparison with its measured north.
Unfortunately this was not actually the case as first established by a Chief
Pilot of the Portuguese Indian Fleet, John de Castro. He was the first to show
that the variation did not follow any pre-determined pattern and certainly not
that of a true meridian. In 1638, more than a century later Henry Gellibrand, a
professor of mathematics confirmed that the variation altered over time as well
as place. It was in fact even more unpredictable than sailors had feared (Berthon
and Robinson, 1991:120).
Despite this finding, in 1698 Edmund Halley arranged to be commissioned
captain of a ship, the Paramour. Sailing through the Atlantic he measured the
magnetic variation from true north and then used these data to plot lines of
equal variation for the year 1700. However the map caused much scepticism
amongst sailors when Halley drew 'north' lying east-west at the coast of the now
United States and a 'true' meridian "that looked more like a parabola than a
straight line." (Berthon and Robinson, 1991:120). Halley’s research excluded
magnetic variation as a practical solution for the calculation of longitude,
although it remained theoretically possible if a great enough spread of
reference values, such as those plotted by Halley, were monitored year by year.
This was not a condition that was to be fulfilled until the twentieth century
with the advent of satellite (Berthon and Robinson, 1991:120 and Taylor,
1956:240).
Sailors were not able to rely on magnetic variation to determine longitude.
Another solution was required.
Related Links:
Using Polaris to find True North
Using Polaris to find True North would lead to errors due to
precession
(in fact, few thousand years ago Polaris was much further from the
North than it is today).
Polaris's location less than 1° from the pole (1992 position R.A. 2h23.3m,
Dec. +89°14′) makes it a very important navigational star even though it is only
of second magnitude; it marks due north from an observer.
The northern
Precession
Circle;
the circular path of the Northern Celestial Pole
around the
Northern Ecliptic Pole, a journey that takes
nearly 26,000 years.
Because of the precession of the equinoxes, Polaris will not remain
the polestar indefinitely; in 2300 B.C. the polestar was in the
constellation Draco, and by A.D. 12,000 the star Vega in the constellation Lyra
will be the polestar.
Polaris hasn't always been the Pole Star. In fact, it has only been close to
the Pole for the last thousand years or so, and over the next millennium it will
gradually move further away. This is because the Earth's motion is constantly
affected by the pull of other bodies in the Solar System, especially the Moon
and the Sun, which causes a 'wobble' in its orbit. This, in turn, causes the
Pole to move relative to the stars.
The effect of this wobble (properly called precession) is that
both Celestial Poles follow a broad circle through the sky. For most
of the time, there is no Pole Star at all, but occasionally the Pole
will pass near a conspicuous star - we are lucky to live in a time
when Polaris fulfils this role. For the ancient Egyptians, the Pole
Star was not Polaris, but Thuban in Draco, while observers in the
far future will see yet other stars at the Northern Celestial Pole.
More about
Precession>>
Related Links:
The primary theory of how the ancient Egyptians oriented most any building
that had to conform to true primary coordinates has been by stellar
measurements.
At the time of pyramid building, Polaris (our current Northern Star) was too
far from the North Celestial Pole to mark the true North so the most likely
method would be based on bisection of the angle created by lines pointing to a
star-rise and star-set.)
The circumpolar stars viewed from a northern hemisphere
trace circles around
the Celestial North Pole -- a point in the sky
about which the stars appear to rotate.
A time lapse
photo over a full night, shows that all of the visible stars appear to move in
circles (some big and some small). The star Polaris makes today an incredibly
small circle because it's right next to the Celestial North Pole.
An example how Vega could be used to find true North 2,250 B.C.
The pyramids were oriented to the North likely by the observation of stars.
The position of the meridian could have been obtained by bisecting the angle
formed by the two extreme positions of a circumpolar star. The best candidate
for such a star would be Vega.
Bisecting the angle between the set and rise of Vega would reveal the exact
location of the meridian (the true North).
Setting Vega viewed from the location of the Great Pyramid
on December 21, 2550 BC at 7:28 pm
Rising Vega viewed from the location of the Great Pyramid
on December 22, 2550 BC at 5:25 am
The measurements would involve using perfectly leveled string or
circular wall.
A man would stand
in a designated spot and through a straight pole with a forked top called a bay, sight a circumpolar
star as it rises. A second man at certain distance from the first would
then mark the "spot" where the star rose using a type of plumb line, or
merkhet. When the star set, the
process would be repeated. Measuring between the two spots would then provide
true north from the center sighting pole.
Bisection the angle created by lines pointing to a
star-rise and star-set.
Egyptian Merkhet
Using Merkhet
Crocodile god Sobek using Merkhet
Relief from the temple Kom Ombo.
Ancient "sighting" tools?
Circumpolar Stars Correlation - two stars in simultaneous transit
Back in 2467 BC, it would be quite easy to find True North. All you'd have to do
would be to build some scaffolding, and hang a string with a heavy weight. This
would hang perfectly vertically, pointing to the centre of the Earth. You'd then
wait until two stars, Mizar and Kochab, were vertically aligned exactly
with your hanging string. Then a line from you, to the hanging string, would
point due north to the horizon.
In the
year 2467 BC (when building pyramids was all the rage), two stars
appeared to rotate around the Celestial North Pole. These stars were Mizar (Eta-Ursae Majoris) in the Big Dipper and Kochab (Beta-Ursae
Minoris) in the Little Dipper.
A British scholar named K. Spence believes that the Egyptians used these two
stars to determine the position of True North.
Spence identifies that method as the observation of two stars in
simultaneous transit — that is, two stars on exact opposite sides of
true north which appear to rotate around it. When they are in
vertical alignment, as judged by a plumb line, their direction can
be taken to be true north with a high accuracy. By running computer
simulations of the night sky back to the time of the Egyptian
kingdoms, she has identified the stars that were most probably used
— Mizar and Kochab — one each from the
constellations of The Great and The Little Bear, which had
simultaneous transits in 2467 BC.
Because of the precession of the Earth’s axis, these two stars
would have simultaneous transits only for a year or so. One would
therefore expect errors in alignments to increase with time away
from 2467 BC. This is exactly what is seen — plotting the estimated
construction date of the pyramids against their error in orientation
produces a remarkably straight line, with those built before 2467 BC
pointing slightly east and those built afterwards pointing slightly
west. Two pyramids, Khafre and Ashure, do not fall near the straight
line, but even this can be explained by assuming that the
measurement was made when the two key stars were the other way up in
the sky, reversing the deviation.
Obtaining such a strong correlation confirms Spence’s theory, and
the plot can also be used in reverse, as a tool to refine the
estimates of construction dates. Thus, Spence calculates that the
Great Pyramid (Khufu) was set out in 2478 BC ± 5 years. Historians
currently place the beginning of King Khufu’s reign at 2554 BC at
the latest, so the result may trigger a rethink of the chronology of
the ancient Egyptian kings.
K. Spence believes that in order
to find True North
the Egyptians used two circumpolar stars:
Mizar (Eta-Ursae Majoris) in the Big Dipper and
Kochab (Beta-Ursae
Minoris) in the Little Dipper.
The position of the Celestial North Pole changes with time, and
this is what Kate Spence tried to use, to work out when the pyramids
were built. She took an existing proposal that a vertical alignment between two
stars was used to identify North, and attempted to correlate the slow drift of
this particular pair of stars with the slight clockwise variation in alignments
found on pyramids of sequential construction dates. In many respects this
correlation proved to be very good, although there is a minority of cases that
do not fit into this sequence.
It could be that this is just a coincidence - after all, she was
looking at only half a dozen pyramids. That's a very small sample
size. But if her method is correct, it means that we can calculate
the dates when the pyramids were built to within five years or so -
which is much better than the currently accepted hundred-year error.
Perhaps the only real error the Egyptian pyramid builders made
was forgetting to install some doors.
Related Links and References:
Solar Compass
method
of finding Cardinal Points
A line corresponding with the true meridian of the place may be made by
the solar method.
It turns out that highly precise alignment can be easily achieved with
very simple methods. With help of the Sun, few sticks and two ropes of equal
length would be all that was needed to find the cardinal points with high degree
of accuracy.
It is very likely that the ancient builders oriented
their monuments using the sun,
by means of wooden stakes and ropes. There are in
fact references in ancient texts referring to "the shadow", the
"stride of Ra" and "stretching the cord ceremony".
Direct Sighting method
The local meridian can be located by observing the shortest shadow of a
vertical obelisk. However much more accurate result can be obtained by
bisection the angle created by lines pointing to the sunrise and sunset.
With help of the Sun, few sighting poles and two ropes of equal length
would be all that was needed to orient a pyramid with high degree
of accuracy (and mark its corners). The Equinox sunset would mark True
West-East direction. Click on the image to
view more detailed
geometry behind this method.
In
Teotihuacán, Mexico the sun sets directly opposite the "Pyramid of the Sun"
(the azimuth of the sunset is 285º.5) on August 13. The above method would be
ideal for orienting the pyramid to the sunset on that day.
Using Shadow of an Obelisk
Another variation of this method (of finding the true meridian) would be based
on using the shadow of an obelisk (instead of direct sighting of the rising and
setting sun).
The sun rises and sets in equal but opposite angles to true north.
Using a plumb line, a pole would have been set as vertically as possible. Then,
few hours before noon, its shadow would be measured. This length then
becomes the radius of a circle. As the sun rises higher, the shadow shrinks back
from the line and then becomes longer in the afternoon. When it reaches the
circle again it forms an angle with the morning's line. The bisection of the
angle is true north.
Finding the true meridian using the path of an obelisk's shadow.
Click on the image to enlarge.
Learn more about
obelisks>>
A sacred ritual ceremony to find the cardinal directions
A sacred ritual ceremony to find the cardinal direction
indicated in ancient manuscripts. Among those ancient manuscripts the
Vishvakarmiam and Maymata are the oldest manuscript. Vishvakarma (Vishvakarmiam)
said to the chief architect for Gods and Mayan (Maymata) said to be the
architect for human beings
The ancient geometry may be originated and developed for finding the cardinal
points with reference with sun. In the beginning our ancestors would have been
initially intend to know sun's path to know the direction East and West. Later
they found four directions East, South, West and North, then other sub
directions Southeast, Southwest, Northwest and Northeast. In ancient time our
ancestors considered this as a most sacred practice and strictly followed as
ritual ceremony. Also a selected person called Sthapati (Architect) will perform
this ancient practice. It appears the ancient geometry would have developed from
this prime ritual practice. This ritual practice narrated in details in various
ancient texts. Even though I am not intended to go in depth; the following few
information is essential to understand the ancient geometry of finding the
cardinal points.
Ancient manuscript, Maya Mata, describes the geometrical
method of finding out the cardinal directions:
Chapter 6 - Orientation
6.1-2a: Now I give the method of determining the cardinal points with the
help of gnomon. (One should proceed) at sunrise during a month when the solar
path is towards the north during a bright fortnight when sunrise is beautiful,
when there are no spots in the solar disc and when the sun is in the asterism of
the appropriate fortnight.
6.2b- 3a: First of all a piece of ground in the middle of the chosen site
should be leveled by the water method; this must be square one square pole in
the center in the center of which the gnomon should be set.
6.3b- 5: Herewith the dimensions of the gnomon (Sanku): the largest kind
is one cubit long, its diameter at is one digit at the top and five at the
bottom, it is perfectly circular and without irregularities; one of medium size
(has a length of) eighteen digits and a small one a length of twelve or nine
digits, their diameter at the top and bottom being (in all case) proportionate
to their length.
6.6- 7a: The materials prescribed for the making the gnomon are as
follows: Ivory, sandalwood, wood of khadira, kadara, sami, saka or tinduka or
other hard wood; its tip should be perfectly circular.
6.7b- 8a: When the gnomon has been made it is set up in the chosen place
at sunrise, then a circle is drawn of which the gnomon is the center and which
the diameter is double the length of the gnomon.
6.8b-11a: The line which join the two points where the shadow (of gnomon)
has touched the circle in morning (A) and in the evening (B), gives the east -
west direction. The line which passes through the space between these two points
and (which is like that which) connects the head and tail of a carp, is the
north - south axis; the sage should draw these two lines, Then the circles which
have their centers at the east and west points should be drawn.
6.11b- 13: (When the sun) is in Taurus or Virgo there is apaccya; when it
is in Aries, Gemini, Leo or Libra the (east-west axis) must be put back two
digits; when it is in Cancer, Scorpio or Pisces it must be adjusted by four
digits, when it is in Sagittarius or Aquarius (it must be adjusted) by six
digits and when it is in Capricorn by eight digits. The east-west line is to be
fixed after it has been moved to the right or to left of the shadow.
6.27: (The east=west line) should be established with adjustments of the
following numbers of digits for each ten day period of each month: (Aries) two,
one, zero, (Taurus) zero, one, two, (Gemini) two, three, four, (Cancer) four,
three, two, (Leo) two, one, zero, (Virgo) zero, one, two, (Libra) two, three,
four, (Scorpio) four, five, six, (Sagittarius) six, seven, eight, (Capricorn)
eight, seven, six, (Aquarius) six, five, four, (Pisces) four, three, two.
6.28: When the course of the sun has been taken into
consideration in relation to the constellations, the indicated adjustment should
be made, when necessary; the correction once made, the line is drawn from the
stake and the ground can be prepared.
Related Links:
Nazca Lines - GGF
(Geometrical Nazca Marking)
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