Radiocarbon Dating: Its Limitations and Usefulness +quot;Combining the effects of these tw
Radiocarbon Dating:
Its Limitations and Usefulness
"Combining the effects of these two trees, we see a site that
was actually occupied for 245 years (from 2095 to 1850 BCE)
appearing - using conventional radiocarbon dating - to have
been occupied for 30,600 years (from 40,000 to 9,400 BCE)."
- See Page 12
Table of Contents
How Accurate is Radiocarbon Dating? . . . . . . . . . . . . . 2
Basis of Radiocarbon Dating . . . . . . . . . . . . . . . . . 2
Problems with Radiocarbon Dating . . . . . . . . . . . . . . 3
The Earth's Magnetic Field . . . . . . . . . . . . . . . . 4
Table 1 - Effect of Increasing Earth's Magnetic Field . 6
Removal of Carbon From the Biosphere . . . . . . . . . . . 6
Water Vapour Canopy . . . . . . . . . . . . . . . . . . . . 7
Effect on Radiocarbon Dating . . . . . . . . . . . . . . . . 8
Heartwood and Frozen Time . . . . . . . . . . . . . . . . . 10
Early Post-Flood Trees . . . . . . . . . . . . . . . . . 11
Appendix
Radiocarbon Date Table . . . . . . . . . . . . . . . . . 12
Copyright 1994
Central Highlands Church of God
Stag Road, Kingston, Vic
Australia, 3364
Ph 053-457-367 or 053-453-109
Internet: s920331@fs2.ballarat.edu.au (Bruce Armstrong)
This article may be copied freely provided it is copied in
full and distributed without charge.
2 Radiocarbon Dating
HOW ACCURATE IS RADIOCARBON DATING?
Radiocarbon dating is frequently used to date ancient human
settlements or tools. These dates are often claimed to be very
precise. But how accurate is radiocarbon dating?
How does radioactive carbon dating work? What are its
limitations? What effect would the declining strength of the
earth's magnetic field and a catastrophic worldwide flood have
on radiocarbon dates?
BASIS OF RADIOCARBON DATING
Radiocarbon dating compares the amount of normal carbon with
the amount of radioactive carbon in a sample. The normal
carbon atom has six protons and six neutrons in its nucleus,
giving a total atomic mass of 12. It is a stable atom that
will not change its atomic mass under normal circumstances.
The radioactive carbon has six protons and eight neutrons in
its nucleus, giving it a total atomic mass of 14. This atom
is not stable, and will break down, releasing nuclear energy
in the process.
Radioactive carbon (Carbon 14) is formed in the upper
atmosphere as a byproduct of cosmic radiation. Cosmic rays are
positively charged atoms moving at enormous speeds. When they
strike ordinary atoms in the upper atmosphere, the cosmic rays
smash them apart. Some fragments produced in this way are
neutrons. Some of these neutrons then collide with nitrogen
atoms. This collision is less destructive than the initial
collision that produced them. Usually a proton is knocked out
of the nitrogen atom's nucleus and is replaced with the
neutron. The proton takes an electron with it and becomes an
atom of hydrogen. The nitrogen atom, which began with seven
protons and seven neutrons, is left with only six protons and
eight neutrons. As the number of protons decides the chemical
nature of an atom, the atom now behaves like a carbon atom.
However, because it has too many neutrons for the number of
protons it contains, it is not a stable atom. Every 5,700
years, approximately half of this radioactive carbon
spontaneously converts itself back into nitrogen by emitting
an electron from a neutron.
As you might guess, radioactive carbon (C_14) is quite rare.
Only one out of every trillion carbon atoms is C14. However,
it is present in all living organisms. The C14 created in the
upper atmosphere reacts with oxygen to become carbon dioxide.
The carbon dioxide is absorbed by plants, and the plants are
eaten by animals, thus contaminating every living thing on
earth with radioactive carbon.
Once an organism dies, it stops absorbing C14. As time
passes, the C14 in its tissues is converted back into
nitrogen. If we know what the original ratios of C14 to C12
were in the organism when it died, and if we know that the
sample has not been contaminated by contact with other carbon
since its death, we should be able to calculate when it died
by its C14 to C12 ratio. But in actual practice, we know
neither the original ratios nor if the specimen has been
RADIOCARBON DATING 3
contaminated and are forced to make what we hope are
reasonable assumptions.
The tiny initial amount of C14, the relatively rapid rate of
decay (the half-life of C14 is currently about 5700 years) and
the ease with which samples can become contaminated make
radiocarbon dating results for samples "older" than about
50,000 years effectively meaningless. This limit is currently
accepted by nearly all radiocarbon dating practitioners. It
follows that the older a date is, even within this 'limit',
the greater are the doubts about the date's accuracy.
PROBLEMS WITH RADIOCARBON DATING
During the last 30 years, a new method of determining C14/C12
ratios has been developed. It uses accelerator mass
spectrometry to determine the amounts of C14 and C12 in a
small sample which is vaporised in the test. The ions produced
are forced into a magnetic field where the different mass of
the carbon isotopes causes a different deflection, allowing
the quantity of each isotope to be measured. This method is
claimed to be more accurate than the older and slower method
of counting the number of radioactive decay emissions from a
quite large sample. It is the supposed accuracy of the new
method that allows measurements sensitive enough to date
objects claimed to be more than twenty or thirty thousand
years old.
A recent test by the British Science and Engineering Research
Council has shown that the accuracy of the new technique is
greatly overrated. They found large variations in the
radiocarbon 'dates' of objects of known age sent to 38
radiocarbon 'dating' laboratories around the world. Thirty-one
of the labs gave results that the British group called
unsatisfactory. Their results were 'two to three times less
accurate than implied by the range of error they stated.' They
thought the variations might have been caused by poor
laboratory standards allowing contamination of the samples.
Some scientists believe the problem runs far deeper than
this, as the following quote shows:
In the light of what is known about the
radiocarbon method and the way it is used, it is
truly astonishing that many authors will cite
agreeable determinations as "proof" for their
beliefs...
Radiocarbon dating has somehow avoided collapse
onto its own battered foundation, and now lurches
onward with feigned consistency. The implications
of pervasive contamination and ancient variations
in carbon-14 levels are steadfastly ignored by
those who base their argument upon the dates.
...[Some authors have said] they were "not aware of
a single significant disagreement" on any sample
that had been dated at different labs. Such en-
thusiasts continue to claim, incredible though it
4 Radiocarbon Dating
may seem, that "no gross discrepancies are
apparent". Surely 15,000 years of difference on a
single block of soil is indeed a gross discrepancy!
And how could the excessive disagreement between
the labs be called insignificant, when it has been
the basis for the reappraisal of the standard error
associated with each and every date in existence?
Why do geologists and archaeologists still spend
their scarce money on costly radiocarbon
determinations? They do so because occasional dates
appear to be useful. While the method cannot be
counted on to give good, unequivocal results, the
numbers do impress people, and save them the
trouble of thinking excessively. Expressed in what
look like precise calendar years, figures seem
somehow better--both to the layman and professional
not versed in statistics--than complex strati-
graphic or cultural correlations, and are more
easily retained in one's memory. "Absolute" dates
determined by a laboratory carry a lot of weight,
and are extremely useful in bolstering weak
arguments...
No matter how "useful" it is though, the
radiocarbon method is still not capable of yielding
accurate and reliable results. There are gross
discrepancies, the chronology is uneven and
relative, and the accepted dates are actually
selected dates. This whole blessed thing is nothing
but 13th century alchemy, and it all depends upon
which funny paper you read.
Robert E. Lee, Radiocarbon: Ages in Error.
Anthropological Journal of Canada, vol. 19 (3),
1981, pp. 9-29
Though there is a general trend towards older objects having
less C14 in them than younger objects, clearly there are
serious problems in converting the C14/C12 ratios into precise
dates.
However, there are other sources of error which make the
dating problems even worse. I believe that the C14/C12 ratios
in the past were drastically altered by three powerful
factors. These factors are changes in the strength of the
Earth's magnetic field; changes in the total amount of normal
carbon available to organisms and changes in the structure of
the atmosphere. Changes which cause lower initial quantities
of C14 and higher levels of C12 mean that radiocarbon date
calculations which assume constant conditions in the past give
falsely "old" dates.
THE EARTH'S MAGNETIC FIELD
A major force altering the formation rate of C14 is the
earth's magnetic field.
This field has a dramatic effect on cosmic radiation heading
towards the earth. The magnetic field works like a huge
RADIOCARBON DATING 5
bumper-bar. When the radiation strikes the field, it is bent
towards the earth's polar regions. Some radiation is deflected
so much that it totally misses the earth. Much of the
remaining radiation is channelled into the relatively
unoccupied polar regions. As the magnetic field extends far
beyond the earth's atmosphere, some cosmic radiation never
gets a chance to produce C14. Increasing the strength of the
magnetic field will increase the shielding effect, reducing
the amount of C14 produced.
It is an accepted fact that the measurements of the Earth's
magnetic field strength show that the field is rapidly growing
weaker. Professor Thomas G. Barnes, who has studied the
earth's magnetic field, says that the magnetic field is
declining in strength exponentially. Prof. Barnes, who has
developed the earlier work of Horace Lamb, demonstrates
mathematically that the observed exponential decline in the
strength of the earth's magnetic field is exactly what one
would expect if the earth's magnetic field is generated by an
enormous electric current flowing in the earth's iron core.
The decline is due to a continuous loss of electrical energy
caused by electrical resistance in the core.
If this type of decline has been occurring in the past, the
field loses half of its strength every 1400 years. Scientific
research suggests that an increase in the earth's magnetic
field to 100 times its present strength would result in
complete shielding from cosmic radiation. As a crude
approximation, I have accordingly allowed a 1% decrease in C14
formation for each doubling of the current field strength in
the calculations of radiocarbon dates. As Table 1 shows, the
effect of the magnetic field increase does not become large
until times earlier than Noah's Flood.
However, as we go even further back in time, the effect of
the magnetic field becomes staggering. The field strengths for
dates as recent as 20,000 BCE are so intense that the electric
current required to produce such a field would destroy the
earth's core. Barnes estimates that the heating effect of the
current required would be about 250 million times what it is
today. Unless one is prepared to believe that the magnetic
field in the past was stable - an idea that conflicts with all
the direct observational evidence - one must accept that the
earth is young, very young. The rapid decline of the earth's
magnetic field makes a recent beginning point for the field
(and thus the earth) a necessity.
The increased magnetic shielding of the earth's surface would
also make life easier than it is today. This would result from
the reduction in incoming radiation, which would make
radiation-induced cancers and mutations rarer than they are
today.
6 Radiocarbon Dating
TABLE 1 Effect of increasing Earth's magnetic field on
Carbon 14 production in the upper atmosphere. Using current
rates of change for the Earth's Magnetic Field, less than
10,000 years ago the field would have been strong enough to
have totally stopped the formation of radioactive carbon.
DATE MAGNETIC FIELD EFFECT ON C14
STRENGTH PRODUCTION
(Current Field = 1) (Reduction in %)
1990 CE 1 1
590 CE 2 2
809 BCE 4 4
2209 BCE 8 8
3609 BCE 16 16
5009 BCE 32 32
6409 BCE 64 64
7809 BCE 128 100
9209 BCE 256 100
10609 BCE 512 100
12009 BCE 1,024 100
13409 BCE 2,048 100
14809 BCE 4,096 100
16209 BCE 8,192 100
17609 BCE 16,384 100
19009 BCE 32,768 100
20409 BCE 65,536 100
21809 BCE 131,072 100
23209 BCE 262,144 100
24609 BCE 524,288 100
26009 BCE 1,048,576 100
27409 BCE 2,097,152 100
28809 BCE 4,194,304 100
30209 BCE 8,388,608 100
31609 BCE 16,777,216 100
REMOVAL OF CARBON FROM THE BIOSPHERE
The Flood not only altered the structure of the atmosphere,
it also buried nearly all of the organisms which had lived on
the earth before the Flood. The burial of these organisms also
meant the burial of the normal carbon that they contained. As
the rate of C14 formation is independent from the levels of
normal carbon, the drop in available C12 would not have
reduced the rate of C14 production. Even if the rate of C14
formation had not increased after the Flood, there would have
been a fundamental shift in the ratio towards a relatively
higher radiocarbon content.
The last 150 years have seen this effect occur in reverse.
RADIOCARBON DATING 7
Our massive consumption of fossil fuels is releasing the
carbon which has been locked up in the Earth's crust for the
last four or five millennia. This carbon is virtually pure C12
and has been decreasing the C14/C12 ratio. The effect has been
complicated by the addition of manmade radioactive carbon to
the biosphere because of nuclear explosions and
experimentation.
WATER VAPOUR CANOPY
When God created the earth, He made a special water vapour
layer that He placed above our normal atmosphere. Genesis 1:6
to 1:8 tells us of this event:
And God said, Let there be a space in the midst
of the waters, and let it divide the waters from
the waters.
And God made the space, and divided the waters
which [were] under the space from the waters which
[were] above the space: and it was so.
And God called the space Heaven. And there was
evening and there was morning - Day Two.
The water vapour layer had many significant effects. It
increased atmospheric pressure, making absorption of oxygen by
living creatures a much easier process than it is today. The
increased pressure and the presence of a huge quantity of
atmospheric water vapour kept the humidity high, thus
encouraging lush plant growth.(1) The water vapour layer also
had a greenhouse effect on the climate, both trapping and
distributing the warmth more uniformly than it is today. Warm,
moist conditions allowed the growth of "tropical" species in
areas that are temperate today and the growth of "temperate"
species in polar regions. The water vapour layer was
responsible for the fossilised forests found in Antarctica
today.
The surface of the earth was also shielded from the effects
of ultraviolet radiation by the water vapour layer, another
factor making life easier in the past. All of these effects
reduced environmental stress on living creatures, thus
allowing larger species to flourish. The water vapour canopy
and the strengthened magnetic field would also have reduced
the number of damaging mutations to a rarity. These effects
would have contributed significantly to the long life spans
the Bible gives the Pre-Flood humans.
----------------
1 Another possibility is that the water layer was totally
separate from our normal atmosphere and suspended in a
similiar manner to orbiting satilites. In this case, it would
have still shielded the earth from UV radiation and moderated
the climate, but would have had little effect on atmospheric
pressure and humidity.
8 Radiocarbon Dating
Significantly, the water vapour layer also had an effect on
the formation of C14. As Carbon 14 is formed by neutrons
produced from cosmic radiation striking nitrogen atoms in the
upper atmosphere, the thick layer of almost pure water
molecules above our 'normal' upper atmosphere absorbed many
neutrons before they could reach the atmospheric nitrogen.
This greatly decreased the amount of C14 being produced.
The water vapour canopy was one source of the rain during the
Great Flood. The event that triggered the massive geothermal
upheaval during Noah's life also made the water vapour canopy
unstable.(2) (See Genesis chapters 6 to 8 for the reason for
the Flood and details of this event that reshaped the earth's
crust.) Over a period of forty days the water vapour layer was
totally destroyed. This would have allowed production of C14
to immediately increase enormously.
EFFECT ON RADIOCARBON DATING
The total effect that the water vapour canopy, magnetic field
and the changes in the available mass of C12 might have on the
C14/C12 ratios and thus on radiocarbon dating are shown in the
Radioactive Carbon Dating Table and the Radiocarbon Date
Graph.
The values have been calculated using a computerised
simulation that assumes the ratio of Carbon 14 to Carbon 12 at
the time of the Flood was one-thousandth of what it is today.
It also assumes that the C14/C12 ratio slowly came to its
current ratio over a period of two thousand years, using a
sine curve to model the total amount of C14, which would
initially increase rapidly. This rate would slow over time as
greater amounts of C14 present would lead to greater amounts
of C14 decaying, eventually balancing the amount produced. The
Magnetic Field effects have been superimposed on these values
as stated above.(3)
The graph plots the true date against the radiocarbon 'date'.
As we go farther back in time, the difference between the two
dating systems becomes greater. The graph shows a relatively
smooth variation before 2348 BCE, the year of the Great Flood.
After the Flood, there is a sharp increase in the production
--------------------
2 The geothermal activity was probably the main source of
the rain. During the Flood the earth's surface was basically
levelled. (Note that if the world was level today, there is
enough water to cover all the land to a depth of three
thousand meters.) Then new mountain ranges and ocean troughs
were formed. This unparalleled activity released massive
amounts of superheated groundwater and the associated
volcanism produced massive amounts of water vapour. This
initially condensed to form the rain. As the atmosphere
cooled after the water vapour layer collapsed, most of this
moisture was carried to the mountain ranges and polar regions
where it fell as snow and formed the massive glaciers of the
Ice Ages.
3 The MS-DOS computer program used is called RADCARBN.EXE
and is available (free) upon request.
RADIOCARBON DATING 9
rate of carbon 14. This, coupled to the removal of most of the
Carbon 12, results in a sharp decrease in the difference
between the actual dates and the radiocarbon dates. In the
hundred-year period from 2350 BCE to 2250 BCE, the difference
between the two dates shrinks from 61,600 years to 17,900
years. The Radiocarbon Date Table (Appendix) shows the
effect more clearly.
Though the atmospheric changes are quite dramatic, these
changes were only slowly incorporated into the massive amount
of almost pure common carbon found in the Biosphere.(4) Thus
there would be a fairly long delay in reaching the point where
the C14/C12 ratios in the organisms would exactly match the
atmospheric ratios.
Figure 1 Apparent Radiocarbon Dates After the Flood
Another factor which may be involved in all these events has
----------------------
4 The biosphere is all the plants and animals living on
earth plus the soil, water and air that they occupy.
10 Radiocarbon Dating
been proposed by physicist Dr Russell Humphreys. He has
suggested that the main driving force behind many of the Flood
processes may have been a temporary relaxation of the nuclear
binding forces.(5) Such a 'relaxation' would allow an enormous
increase in radioactive decay rates of all unstable atoms.
This acceleration of radioactivity would result in bulk
heating of all rocks containing moderate to high levels of
radioactive material. This heat could vaporise massive amounts
of water, some of which would condense as snow and form
gigantic glaciers. The heat would also liquefy nearly molten
rocks, causing vast volcanic eruptions and assist the sliding
of tectonic plates during and after the Flood. The rapid
accumulation of radioactive decay end products would give the
rocks an appearance of enormous age.(6)
This scenario would also explain the age gradient seen in
sedimentary rock strata. If the accelerated decay rate lasted
the entire 150 days that the Ark was afloat (when the water
would provide effective shielding for its occupants), it
would cover the most active phase of sedimentation during the
Flood.
If such accelerated decay actually occurred, it is probable
that whatever C14 had existed before that time would have been
converted back into nitrogen.
Heartwood and Frozen Time
The way that trees form heartwood as they grow allows them to
preserve a biological record of the C14/C12 ratios. Sapwood
layers (the living xylem and phloem) are the tree's
transportation system. Xylem carries the supply of water and
minerals that the roots extract from the soil up to the
leaves. Leaves absorb carbon dioxide and oxygen from the air
and combine them with the minerals and water from the roots.
With the added input of energy from the sun, the leaves create
a variety of sugars and other organic compounds that the tree
requires. The phloem layer, just inside the bark, carries this
food to the rest of the tree. As the tree grows, the inner
layers of xylem are sealed up and die, forming heartwood. New
sapwood layers form each year to replace the 'lost' sapwood.
When the xylem turns into heartwood, it stops gathering
radiocarbon. Its radiocarbon content then begins to decrease.
In a stable situation where the atmospheric C14/C12 ratios
remain unchanged during the life of the tree, these
differences make only a slight change in the radiocarbon
"dates" of different parts of the tree. However, after the
Flood, the ratios were not stable. A look at the different
dates that would be given by samples taken from various layers
of trees tells the story:
--------------------
5 Russell Humphreys, Radiocarbon, Creation and the Flood,
Lecture Tape, Creation Science Foundation
6 In long-term dating, isotopes of heavy metals such as
Uranium are usually involved, with decay half lives normally
being in the millions of years.
RADIOCARBON DATING 11
Early Post-Flood Trees
We will look at the radiocarbon 'dates' that would result
from samples taken from different parts of a tree that began
growing in 2345 BCE (BC), possibly three years after the
Flood. Let's assume that the tree grew for 250 years, when it
blew down and the tree was used by people for firewood and
building materials.
A beam split from heartwood formed in 2105 BCE (near the
outside of the tree) would have a radiocarbon date of 14,950
BCE. Another beam cut from heartwood formed in 2220 BCE
(halfway to the centre of the trunk) would have a radiocarbon
date of 20,190 BCE. A final beam split out of the centre of
the tree, made of heartwood that had formed in 2335 BCE, would
give a radiocarbon date of 39,610 BCE.
The beams made from this one tree would give a range of
radiocarbon 'dates' from 14,950 to 39,610 BCE. If pieces of
these three beams were later found by archeologists, they
could claim that the site had been occupied for 25,000 years,
from about 15,000 to 40,000 BCE. The reality might be that the
site was occupied for thirty years from 2095 to 2065 BCE.
Assuming that the site was genuinely occupied for several
hundred years, we can look at the effects that another tree
which started growing in 2100 BCE would have on radiocarbon
dates. We will assume that this tree also lived for 250 years
before it was cut down.
This time, a beam split from heartwood near the outside of
the tree, formed in 1860 BCE would have a radiocarbon date of
9,400 BCE. Another beam cut from heartwood formed in 1975 BCE
(halfway to the centre of the trunk) would have a radiocarbon
date of 11,510 BCE. A final beam split out of the centre of
the tree, made of heartwood that had formed in 2090 BCE, would
give a radiocarbon date of 14,470 BCE.
The beams made from the second tree would give a range of
radiocarbon 'dates' from 14,470 to 9,400 BCE.
Combining the effects of these two trees, we see a site that
was actually occupied for 245 years (from 2095 to 1850 BCE)
appearing - using conventional radiocarbon dating - to have
been occupied for 30,600 years (from 40,000 to 9,400 BCE).
This shows the dramatic effect that changes in the C14/C12
ratio could have on radiocarbon dating results. It is
difficult, perhaps impossible, to prove that the C14/C12
ratios in the distant past have not undergone variations
similar to those proposed here. Logs that show an enormous
span of years from one point to another are simply dismissed
as contaminated samples.
We have demonstrated that there are definitely reasons to
12 Radiocarbon Dating
doubt the accuracy of the radiocarbon dates that are so widely
used to 'prove' the age of an artefact. The quotes given
above, from authorities working in the radiocarbon dating
field, show that even without invoking major changes in the
past there are good reasons to be very sceptical about
radiocarbon dates.
Radiocarbon Dating is useful to compare the relative ages of
equivalent samples where it is likely the samples have all
been exposed to similar environmental conditions. However, for
older samples, the data can only suggest that Sample A is
probably older than Sample B, etc. It is merely speculation when
the results are used to 'establish' an absolute date for old material.
Appendix
Radiocarbon Date Table
Actual Calculated Apparent
Date Carbon-14/Carb Radiocarbon
(BCE) on-12 Ratio Date
(BCE)
-2600.000 0.0009 -60476.265
-2550.000 0.0009 -60404.066
-2500.000 0.0009 -60332.472
-2450.000 0.0009 -60261.466
-2400.000 0.0009 -60191.030
-2350.000 0.0009 -60121.147
-2300.000 0.0428 -28350.035
-2250.000 0.0874 -22395.716
-2200.000 0.1311 -18996.372
-2150.000 0.1738 -16615.327
-2100.000 0.2155 -14786.660
-2050.000 0.2563 -13305.834
-2000.000 0.2960 -12064.668
-1950.000 0.3347 -10998.957
-1900.000 0.3723 -10067.467
-1850.000 0.4089 -9242.137
-1800.000 0.4445 -8503.013
-1750.000 0.4790 -7835.399
-1700.000 0.5124 -7228.165
-1650.000 0.5447 -6672.682
-1600.000 0.5759 -6162.128
-1550.000 0.6060 -5691.021
-1500.000 0.6349 -5254.893
-1450.000 0.6628 -4850.057
-1400.000 0.6895 -4473.439
-1350.000 0.7151 -4122.453
-1300.000 0.7395 -3794.905
-1250.000 0.7627 -3488.922
-1200.000 0.7848 -3202.896
-1150.000 0.8058 -2935.437
-1100.000 0.8255 -2685.344
-1050.000 0.8440 -2451.568
RADIOCARBON DATING 13
Radiocarbon Date Table - Part 2
Actual Calculated Apparent
Date Carbon-14/Carb Radiocarbon
(BCE) on-12 Ratio Date
(BCE)
-1000.000 0.8614 -2233.199
-950.000 0.8776 -2029.440
-900.000 0.8926 -1839.598
-850.000 0.9063 -1663.066
-800.000 0.9189 -1499.316
-750.000 0.9302 -1347.893
-700.000 0.9404 -1208.400
-650.000 0.9493 -1080.501
-600.000 0.9569 -963.912
-550.000 0.9634 -858.397
-500.000 0.9686 -763.766
-450.000 0.9726 -679.871
-400.000 0.9753 -606.608
-350.000 0.9768 -543.909
-300.000 0.9786 -478.900
-250.000 0.9794 -422.352
-200.000 0.9801 -365.970
-150.000 0.9809 -309.751
-100.000 0.9816 -253.690
-50.000 0.9823 -197.782
1.000 0.9830 -140.911
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