Does the Foot Fit Britannia?
"At
Stonehenge, there are 365,000 feet per meridian degree"

2009.01.27
 A recent email exchange led to reconsidering the English foot as a
geodetic construct. Long ago when dividing circumference by days per
orbit I noted the result was nearly 100,000 yards. I'm told this has
shown up in books, except as equator divided by days per year. I posted
this in online discussion long ago, without much detail. I comment
further now because I've been told confusion on this "coincidence" is
in print.
First, if a metric is
geodetic, it will be related to land, not to sea level on the equator.
Sea level is not a valid archaeological benchmark for the size of the
earth due to sea level changes. Anyway, the size of the earth is just
expressed, not determined at sea on the equator. A geodetic metric
should reflect the arc meridian, the latitude, or the method used to
determine the size of the earth. If the English foot fits the earth, it
should fit the earth where the unit presumedly arose, on land in
Britannia in the fog of long ago when sea level was different.
Second, if a metric is
related to circumference, it should be subdivided by an orbit number,
not based on the year. The year is not equal to orbital circumference,
it is shorter than solar orbit. A culture ignorant of this difference,
the effect of axial precession, is less likely to utilize accurate
geodetic metrics.
So, calculating, at
Avebury's latitude, a meridian degree measures 365,015 feet, not
365,256 as would be expected for days per solar orbit (1.0 : 1.00066).
At Avebury, the degree of local meridian measure in feet presents,
instead of days per orbit or year, a lunar constant number, 0.036501
rotations per lunar orbit. This Avebury meridian degree number string,
365,014.7 is quite precise in relation to the rotation : lunar orbit
ratio; as determined centered on Avebury it is off by only 4.1 feet per
degree. This represents earth's circumference to within 1500 feet
accuracy IF the foot is supposed to represent this fundamental
astronomical constant at Avebury. At Stanton Drew, Britannia's second
largest stone circle, accuracy is within 90 feet of circumference, or
three inches per degree.
Avebury, the largest stone
circle and henge. Latitude = 360/7.
Google Earth Placemarks: neolithic_calc.kmz  avebury_lunar.kmz
In 365 lunar orbits there are 10,000 rotations
and in 366 lunar orbits there are 10,000 days.

Distracted by lunar
constants and given the astronomical import of 0.036501, of course I
diverged. Avebury, while an important latitude at oneseventh of
circumference, is not Britannia. Where to check next, Stonehenge or
Thornborough, the Stonehenge of the North? Geodetic radius is a local
variable; radius of curvature of the ellipsoid varies with latitude,
being the longest at the pole and shortest at the equator. Thornborough
is closer to the mean latitude of the island, and the radius is longer.
So, archaeogeodesy.xls
calculations set up, simply changing the site to Thornborough South
provided 365,186.3 feet. Almost, and an interesting number, maybe even
clever, but not days per orbit.
The latitude in ancient
Britannia where days per orbit matches feet per degree is 70 km north
of Long Meg stone circle. Ring of Brodgar, another of the largest stone
circles along with the inner Avebury stone circles and Long Meg—is too
far north, but the mean latitude of Brodgar and Avebury provides
365,242.1 feet (1.0 : 1.0000011). IF the foot represents an
astrogeodetic metric, this mean value string for the astronomical
constant days per year represents earth's circumference to within 150
feet of accuracy.
I conclude for Britannia
that feet per mean meridian degree/1,000 equals near days per orbit or
year. A fair and accurate statement would be, "Britannia's mean
geodetic radius inscribes a circle about 365.25 times 360,000 feet in
circumference." So, the foot fits that test, albeit mean latitude for
Britannia is a fuzzy determination.
Avebury henge and the five
greatest stone circles of Britannia suggest the English foot, IF a
geodetic metric, may precisely express astronomical constants.
Nonetheless, these are not "intentionality" tests! A phrase is trying
to turn from reflection on the calculations and results. "If the foot
fits wear it." No. "For the foot to fit, where it." No. Okay, now I've
got it, "How precisely the foot fits where matters."
To put a fitting final
punctuation to this point, let's not forget Stonehenge. At Stonehenge,
there are 365,000 feet per meridian degree. "Does the foot fit
Stonehenge?" seems to also be a fitting question. Addressing that
question will be continued in discussions below, as this semester
progresses. This story is just beginning to be told.
ArchaeoBlog  2009.01.27
An archaeology web log by James
Q. Jacobs

The 1893 Office of Weights and Measures fixed the U.
S. yard:meter ratio at 3600:3937,
a fit slightly in error. The 1959 national standards of
Englishspeaking nations equates
the yard and the meter at: one yard equals 0.9144 m, one foot equals
0.3048 m.
"In 1824 by
Act of Parliament the length of the Bird rule became the official
length of the English foot (304.79974 mm). Since the English foot is no
longer used as an instrument for scientific research, the custom
prevailed very early in the United States and later in England
according to the rules adopted by of the Board of Trade, in 1895 to
calculate the English foot as a fraction of the Paris meter, making it
304.8 mm."
"Girolamo
Cardano in 1553 A.D. suggested that all measures of length and weight
should be based on a mensura perpetua embodied in a
geographical distance."
A History
of Measures by Livio C. Stecchini.

Back to
the ArchaeoBlog
2009.01.30
 My next question is taking form, "Stonehenge's geodetic radius, to
the top of the Sarsen Circle, inscribes a circle [365 * 360,000] feet
in circumference, plus or minus how many inches?" In
other words, "What is the precise geodetic radius length at Stonehenge,
monument elevation included?" For the Stonehenge latitude, the archaeogedesy.xls output of
111,251.68 m per merdian degree is based on the form of the geoid.
Taking elevation into account will alter the simulation of measure. If
the question begs an immediate answer, enjoy the puzzle. I'm enjoying
new features in the application designed for new questions.
2009.02.01
 Earlier, for this semester, I offered these questions: "Are we as
'wise' as humans were in prehistory?" and "If not, how would we know?"
Consider how the foot fits Britannia at Stonehenge, precisely
subdividing one meridian degree by 365,000—like a glass slipper on the
Cinderella of monuments (elevation unaccounted for!). Yet those who try
to fit the foot to astronomy and the equator both accepted an
incorrect, close fit as good enough AND failed to notice the latitude
of Britannia matches their inferred hypothesis of equatorial
circumference divided by days per year producing the foot. This begs
the question of wisdom today.
"Did the builders of
Stonehenge think they should meter their foot based on the equatorial
circumference?" is the question the claim poses. Posing the question
makes me ponder, "Were the builders of Stonehenge wiser than
pseudoscience writers?" Are we wise enough to understand what the
builders of Stonehenge knew or did not know? Were they wise about
astronomy and geodesy, or would they have to ask, "What is geodetic?"
Let's examine the evidence and the reasoning, and the methods. So also,
let's consider in parallel who is the wiser?
First, the foot has a very
short history, with the recent standard originating in England based on
an older, now lost standard rule. Standards of measure as old as
Stonehenge are inferred elsewhere, so the deep antiquity question
cannot be ruled out based on lack of evidence about the foot's origins.
Absence of evidence is NOT evidence. Plus, the words rule and ruler
have their multiple meanings since antiquity for a reason; standards of
measure are as old as law giving.
Second, "Close is good
enough" is NOT an acceptable methodology for astronomy, metrology or
geodesy. Any hypothesis that begins with an expectation that inaccuracy
is the best we can expect of an ancient culture is unacceptable. We
humans are capable of extremely fine measure and surveying. We are also
capable of accurate astronomy. Humans are capable of science, and have
been for longer than the time depths under discussion. Fact check: the
foot does not fit the hypothesis at the equator. Approximation is all
there is at the equator, at least until the ocean rises further. Plus,
sea level was lower in the past.
Third, Why don't the
pseudoscientists think through the process of determining equatorial
circumference? It's quite obvious noone would measure the sea along the
equator, right? In fact, if you do not already know the earth is an
oblate ellipsoid, measuring a meridian centered on the equator produces
a false answer because the longitude and latitude angular units are not
equal in length. Measuring the earth requires using the cosmos to
determine two geodetic angles, then comparing the angles with their
measured spatial relationship. This is most easily accomplished on a
merdain arc, between two points forming a northsouth line. The
ellipsoidal shape of the earth becomes apparent AFTER comparing
measures of meridians at distinct latitudes. Only after measures with
high accuracy at several latitudes are compared can the figure of an
equatorial circumference be deduced.
"The most logical way in which the foot came to be
defined is via the Equator
for there are 360,000 feet within a DAY (one 365.242th part of the
equator in longitude)
upon the equator of the Earth."
Landscape
Alignments at Significant Latitudes by R. Heath

Eliminating "close is good
enough" methods does not eliminate all short sightedness. If
pseudoscience writers knew what geodetic means, obviously consideraton
of where the earth was measured would have mattered, and the obvious
historiography of geographic discovery would not have been overlooked.
Obviously also, proving the pseudoscientist ignorant does not prove
the Stonehenge builder was equally ignorant. Cultural evolution is not
a gradual climb with ever more erect posture and refined science. "Who
is the wiser?" is neither a question of chronology, mean intelligence,
nor technological wizardry, neither now nor then.
2009.02.10
 So, who is in the dark? Precession, the slow backward spin of the
rotation axis' inclination defines the error in the quote above. Heath
writes "a DAY" is one 365.242th part of the equator in longitude, when
there are actually 365.252 days in solar orbit. The year is confused
with orbit and only orbit corresponds to one circumference. Herein lies
a cultural astronomy intelligence divide, the truefalse,
heliocentricgeocentric divide. Knowing the yearorbit difference
removes a stumbling block to navigation and longitude determination,
and to doing accurate astronomy easily. Knowledge of the motion of
precession defines this difference in cultural astronomies. Just one
wobble backwards during 26,000 years of only the inclination of earth's
rotational reference frame in fixed, heliocentric space makes all the
difference.
If I were Howard Carson, the
Motel of the Mysteries fictional archaeologist who
was never too busy to entertain his helpers (Macauley 1979:31), and
writing in 4,022 (this would be in Carson's later years, of course,
after abandonng his "delicate" excavation kit, digging much deeper, and
finding the older glyphs) the story in Carson's tome Deep
Archaeology would go like this:
"On one side
of the cultural divide were the Day People. They counted the days and
the year and divided circumference by days per year, and they slept at
night. The Night People worked in the dark, not blinded by the day and
the Bright One. They used many Bright Stars to measure lunar motions
and eclipses, the hours of the night, and the times of starry dark or
moonlight. These two cultures counted using different numbers, 365 vs.
0.03650.
"Today we
know that when the stars rotate once the earth has rotated once, an equality of one to one, unlike
the year and the orbit. We know when the moon has passed the
same star in longitude, one lunar orbit completes. Lunar orbit and
rotation are fundamental motions referenced to fixed celestial space,
hence doing nocturnal astronomy is accurate. This is why the Night
People had accurate astronomy.
"On the two
continents, only the Day People were blinded by
the belief that the Bright One was going around them.
Nonetheless, those who wish to ascribe names like 'Side Real People'
and 'Synodical Mythological Tradition' overstate the limited awareness
of humans in such a remote time. All they really accomplished was the
counting required to tally the tithe every twelve moons."

So, working in the dark is
a great thing for astronomers, because you equate to the sidereal half
of cosmic reference. People can be good civil calendar keepers
and—blinded by culture and historical traditions—in the dark about
taking astronomical and geodetic measure. Working in the dark is not a
great thing for archaeologists. Part of the wisdom divide can be blamed
on traditions and beliefs. However, culture is no excuse for not
thinking. Thinking about astronomy requires counting, and counting
reveals ratios. The proper combination of counting, observation, and
logic reveals precession with precision.
Asking "Am I wiser than the
Greeks over 2,400 years ago?" consider the following story, handed down
in part by Diodorus. Meton revealed to the public in Athens the
nineteenyear circuit of a Great Year.
History remembers the astronomer by naming the Metonic eclipse cycle
after him. Today, archaeoastronomers and historians of science consider
the Metonic cycle to be noteworthy as a short eclipse cycle with the
eclipses on the same day of the calendar year 19 years later. Meton
instituted a '19yeareclipse' period calendar in Athens on the summer
solstice of 432 B.C. While formatting Epoch
v2009, I noticed the Metonic lunar orbit and lunar synodic ratio is
more accurate than the Saros eclipse ratio. I asked, "Were ancient
astronomers aware of this?" History affords some answers, in
combination with the counting.
The Metonic Cycle


Period, Days

Multiple

Degrees

Days

Rotations

Lunar Nodal

27.21222

255 n

6839.256

6939.116

6958.114

Tropical Year

365.24219

19 y

6839.735

6939.602

6958.601

Lunar Synodic

29.53059

235 m

6839.82

6939.688

6958.688

Lunar Orbit

27.32166

254 l

6839.833

6939.702

6958.702

Solar Orbit

365.25636

19 o

6840.0

6939.871

6958.871

"the god
visits the island every nineteen years, the period in which the return
of the stars to the same place in the heavens is accomplished."
Diodorus Siculus
"the Greeks
[who] use the nineteenyear cycle ... are not cheated of the truth."
Diodorus Siculus
76 *
365.25636 days per orbit = 27759.48 days
76 * 365.24248 days per
year = 27758.43 days
Callippus
began his cycle June 28, 330 B.C., as the beginning
of the lunar cycles nearly coincided with the
moment of solstice.

Geminus reports Callippus corrected the
19year cycle, deducting one day every four Metonic periods, or 76
years comprising 940 months. Apparently, Callippus knew of the one day
difference between days per 76 orbits and days per 76 years, after four
Metonic cycles. The yearorbit difference infers Callippus knew
precession. Callipus observed the sequence of the Metonic cycle numbers
above against sidereal space. Observing the second Metonic eclipse
occur, in the context of keeping a lunar and solar count, one observes
the same specific sequence of the events in the table above:

the 19
years complete

the
235th moon is eclipsed

the
254th lunar orbit completes

the 19
orbits complete

Given the logic of geometry, you cannot
have the 19th synodic node precess (precede) the 19th circumference
orbit. The 19th node IS the 19th solar orbit, equaling 254.0062 lunar
orbits
and 235.0062 lunar synodic. Precessions are revealed because 19 years
is shorter
than 19 orbits. First, 19 years is of shorter duration, precessing
the Metonic eclipse point. Second, the eclipse of the 235th lunar
synodic occurs
just before 254 lunar orbits. Only when 19 solar orbits complete are
there 19 more
lunar orbits than moons.
Comparison with the following
formulations and counts illustrates why the sequence above solves a
cosmic conundrum. This formulation reveals the precession wheels in the
clockworks, wheels turning backwards and contradicting geocentrism.
Eclipses allow observing what fraction over 235th lunar synodic periods
occurs at 254 lunar orbits. When 254 orbits occur, there are 18.99954
fewer moons, hence only 18.99954 solar orbits have completed at 254
lunar orbits (254 / 18.99954 = 13.36875). From a tally of rotations,
the value of rotations per orbit also computes (6958.70/18.99954 =
366.25624).
y = x orbits  1
solar
orbit = 13.36875 lunar orbits
solar orbit = 12.36875 lunar synodic
solar
orbit = 366.25636 rotations
solar orbit = 365.25636 days

There is more supportive historical
data, but with the counts, the sequence, and the "fit" of the numbers
with theory this much should be obvious; the Ancients knew precession,
the yearorbit difference.
2009.02.11
 The Metonic cycle history and Metonic eclipse clock methods
reinterpret what ancient astronomers knew or did not know. You can
watch and calibrate precession with the naked eye in just one Metonic
eclipse cycle. A tiny sliver of circumference (19/25,770th of
precession at today's rate) is very easy to measure when multiplied by
the 350,000 lunar orbits per precession cycle. With this understanding,
we can reinterpret the historical data in a new light. The longer the
ruler, the better the accuracy. Likewise with counting, the longer the
count the greater the accuracy of the ratios. Simple logic prevails;
anyone who counts and thinks can see precession, and this ability has
always been right before our naked eyes.
Importantly to archaeology,
a simple nakedeye method for demonstrating precession, of readily
quantifying all astronomical variables, and of finding longitude alters
the prehistoric context. Archaeology is all about context and
chronology. New data and new information can force the scientist to
return to the very beginning of the puzzle, to ask of necessity anew
the same questions, knowing the answers will now all be different.
Fundamental knowledge didn't
just shift gears, there are new gears in the works and that changes
everything, just like precession. Considerable ancient records of
historical astronomy can now also be reexamined in light of a new
context, accurate ancient knowledge of astronomy. When I ask anew "Does
the Foot Fit Britannia?" or "Are we wiser?" how does the change in the
context impact your thinking?
Long ago, when I studied the
arc distances of the Mayan pyramids, an error kept recurring in a
statistical accuracy routine. I recorded the incongruity with
hypothetical as the proportion of hypothetical equaling one, the ratio
of the actual result to the expected whole. That equalized all line
lenghts to reveal proportionality error in the hypothetical framework.
My reasoning was if the Ancients are 'off the mark' in their
fundamental astronomy, the impact would be "to proportion." I did
notice a recurring proportion error, and the error was quickly
recognized—the inverse of precession. Then I discovered the Ancient's
arcs were correct, and the recurring error was in my analytical
modules. The hypothetical lengths did not fit because I had made the
mistake my culture taught me to make, I had divided circumference by
days per year. In this context the Maya taught me they knew precession,
and taught me who was wiser. So, I had to go back to the start and ask
every question over again, and every answer was proportionally
different, of course.
To bring my metaphors full
circle, I was working in the dark while the Ancients were doing
accurate astronomy in the dark. Their monuments still show us their
light, an understandable codex of accurate astronomy in new context.
Thanks to the noble efforts of our Ancestors, I feel I am a bit wiser.
I leave this thread having added new context for two question, now well
asked I hope, "Are we as 'wise' as humans were in prehistory?" and "If
not, how would we know?" While "Does the Foot Fit Britannia?" remains a
'fitting' question, hopefully you now find yourself in the dark with
much bigger questions.
The Longitude Act of 1714
"The Act
promised a reward of £20,000 for the discoverer of a method of
finding longitude that was accurate to 1/2 degree of a great circle,
i.e., to 30 nautical miles; lower rewards of £15,000 and
£10,000 were to be granted for an accuracy of 2/3 and 1 degree,
respectively. The method had to be practicable and useful, both aspects
to be demonstrated on a voyage to the WestIndies and back."
"... in 1675
the Royal Observatory was founded in Greenwich with the explicit object
of improving astronomy for the sake of navigation and in particular
longitude finding ..." The Quest for Lunar Theory

Alexis
Claude Clairaut
In 1741 (Alexis Claude) Clairaut accompanied Maupertius on a scientific
expedition to Lapland in the Artic circle to collect data to be used in
measuring the length of a meridian degree on the earth’s surface. A
similar expedition led by Charles Marie de la Condamine measured the
equatorial curvature in the Andes. The purpose of the expedition was to
determine the shape of the earth by measuring its curvature at the
places where it differed most – the equator and the poles ... Clairaut
produced his classic work Théorie de la figure de la Terre (Theory
and Shape of the Earth 1743) ... Clairaut reported that as Newton
had predicted, the Earth has a larger diameter through the equator than
through the poles, a shape known to geometers as an oblate spheroid. In
1749, using Newton’s laws, Clairaut showed that the north pole of the
Earth precesses (change in direction of the earth’s axis) with a period
of 25,800 years. Alexis Claude Clairaut

