| Topic: |
Science > Physics |
| User: |
"Hannu Poropudas" |
| Date: |
30 Apr 2007 08:12:18 AM |
| Object: |
Using Coral as a Clock (Update 30.4.2007) |
My Updating Notes (30.4.2007):
I=2E The coefficient of the asymptotic straight line for the month
formula is
-7
about 3.53 * 10 from my calculations (1, Allen 1973) and the
little
uncertain period of oscillation about this line is roughly
4
429.4 * 10 centuries from (Pannella MacClintoc and Thompson 1968).
-7 4
P(T) =3D 29.53 - 3.53 * 10 * ( 1 - e*sin ( 2 P T / (429.4 * 10 )))*
T
P(T)=3D number of mean solar days per synodic month at a
certain
point T of time
0 <=3D e <=3D 1, (e =3D 1 in first approximation)
P =3D 3.14159 radians
(This month formula is not used because it is still under testings.
Existence of this oscillation is needed to be confirmed with more
complete
fossil data and with more accurate age determinations.)
(The coefficient is 2.60 * 10^(-7) from (Scrutton 1978) and 4.29 *
10^(-7)
from (Pannella MacClintoc and Thompson 1968) and 3.50 * 10^(-7) from
(Scrutton 1964, 1970, Kulp 1961).)
II.
(abstract updated.)
(In the text wrong word "speeds up" is corrected to "slows down".)
III. The depositional age of the Gunflint Formation is
1878.3 Ma +- 1.3 Ma (2) (The sample YPM-IP-28510 & YPM-IP-28511
is only complete test point of stromatolites.)
MAINLY PANNELLA'S STROMATOLITE DATA:
TABLE 9
MAINLY PANNELLA'S STROMATOLITE DATA:
4
1. =3D T / 10 (centuries)
2. =3D calculated value from the first time formula (days/year)
3. =3D calculated value from the second time formula (days/year)
7. =3D experimental value (Pannella 1972 a).
9. =3D the code of the fossil specimen
10. =3D Highest count=3D(days/month)?, (Pannella 1972 a and Pannella
1972 b).
11. =3D Mode=3D(days/(month/4))-(days/(month/2))-(days/month) ?,
(Pannella 1972 a and Pannella 1972 b ).
12. =3D Tidal cycles per year =3D (months/year) ?,
(Pannella 1972 a and Pannella 1972 b ).
U =3D Upper, M =3D Middle, L =3D Lower.
YPM-IP =3D The collection of Division of Invertebrate Paleontology,
Peabody Museum, Yale University
1. 2. 3. 7. 10. 11. 12. 9.
----------------------------------------------------------------------------
-1878 507.73 561.10 504-546 39 18-36 14 YPM-IP-28510
YPM-IP-28511
=20
----------------------------------------------------------------------------
----------------------------------------------------------------------------
-(2715- 571.69 762.65 41 10-20-40 UCLA-BUL-7
-2672) (=3D P.P.R.G.
253)
=20
----------------------------------------------------------------------------
Somewhat uncertain data about UCLA-Bul-7 (The sample
UCLA-Bul-7 is a incomplete test point. I recall that possible
"year" marks were not found by Pannella (Pannella 1972 a, b)):
A=2E Huntsman limestone stromatolites of MacGregor belong in the
Upper Bulawayan Greenstones (3)(if I can rely on J.F.Wilson, this
needs still to be confirmed):
"J.F.W.'s correlations across the greenstone belts also allow the
rationalization of the known occurrences of Rhodesian Archean
stromatolites which now number five (Fig.1).
All of these occur in the Upper Greenstones. ... Three occur in
limestones
above the tholeiitic pile; one at Belingwe, one south-east of
Redcliff ...
and one the Huntsmann limestone stromatolites of MacGregor, some
60 km north of Bulawayo."
B=2E Age of the Upper Bulawayan Greenstones (4) (this needs still to
be confirmed with more local age data):
"Timespan of deposition of Upper Bulawayan Greenstones is
2715 Ma +- 15 Ma (Iron Mask Formation, ZIM-74)- 2672 Ma +- 12 Ma
(Harare-Shamva greenstone sequence ,,Black Cat porphyry", ZIM-29)"
(The Stromatolite UCLA-Bul-7 (found by K.A. Kvenvolden from one
tailings
of pile of Huntsman Limestone Quarries) could be a little older than
this
age, because it could originate little below Upper Bulawayan
Greenstones in Huntsman Limestone Quarries (5)?)
C=2E About geology of the Bulawayan Supergroup is in the reference (6)
written by M.D. Prendergast.
References:
1=2E Poropudas Hannu, 1996.
Harrastelijan ajatuksia p=E4iv=E4n, kuukauden ja vuoden pituudesta
muinaisina aikoina.
Geologi, 4-5/1996, Pages 92-96.
2=2E Fralick Philip, Davis Don W., and Kissin Stephen A. 2002.
The age of the Gunflint Formation, Ontario, Canada:
single zircon U-Pb age determinations from reworked volcanic ash.
Can. J. Earth Sci. vol. 39: 1085-1091.
3=2E Wilson, J.F. et al, 1978.
Granite-greenstone terrain of the Rhodesian Archean craton.
Nature, vol. 271, 1978, 23-27.
4=2E Jelsma,H.A., Vinyu,M.L., Valbracht,P.J., Davies,G.R.,
Wijbrans,J.R., Verdurmen,E.A.T., 1996.
Constraints on Archean crustal evolution of the Zimbabwe craton:
a U-Pb zircon, Sm-Nd and Pb-Pb whole rock isotope study.
Contrib. Mineral Petrol. (1996) 124: 55-70.
5=2E Bond,G., Wilson,J.F. & Winall,N.J., 1973.
Age of the Huntsman Limestone (Bulawayan) Stromatolites.
Nature 244, 275-276. (the map of the Huntsman Limestone Quarries).
6=2E Prendergast,M.D., 2004.
The Bulawayan Supergroup: a late Archean passive margin-related
large igneous province in the Zimbabwe craton.
Journal of the Geological Society, London, Vol. 161,
2004, pp. 431-445. Printed in Great Britain.
Kiiminki 30.4.2007
Hannu K.J. Poropudas
Vesaisentie 9E,
90900 Kiiminki,
Finland.
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D
Author: Hannu K. J. Poropudas
Title: Using Coral as a Clock
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D
APPROXIMATE ANCIENT TIME FORMULA BASED ON FOSSIL DATA
Hannu K. J. Poropudas
Vesaisentie 9E,
90900 Kiiminki,
Finland
ABSTRACT
Time formula, also called fossil formula, gives an answer to the
question:
how many mean solar days are in a tropical year at a certain point in
time.
It is the simplest possible expression that has been worked out from
experimental fossil points (Eicher/Wells 1976, Pannella MacClintock
Thompson 1968 and Scrutton 1978).
The formula is intended for use mainly in the experimental fossil
point's
area, which goes back, at maximum, as far as the approximately 3.556
(+ 0.032)
=20
-
billion years old Warrawoona stromatolite fossils (The Cambridge
Encyclopaedia
of Earth Sciences 1982 diagram page 357, Schopf 1983).
At the present, the time formula have been tested over an interval
as far
back as about 2000 million years and consistency with the
experimental points
looks good (formula's safe area of use).
TIME FORMULA
The time formula is the following expression given over the widest
possible time area. The time area can be limited on the basis of
experimental measurement data, if the deviations of the measured
results
are, for example, greater than five to ten days.
2
M - A(T)* T - B(T)* T
N(T) =3D ---------------------
1 + C(T)* T
N(T) =3D Number of mean solar days in tropical year at the point T
T =3D time in uniform centuries
M =3D 365.2422
Here is taken into account lengthening of measured uniform mean
solar day as a first approximation (Allen 1973).
15 1 -8
1 + C* T =3D 1 + ----- * ----- * T =3D 1 + 1.7361 * 10 T
10000 86400
The uniform shortening formula of the tropical year (Allen 1973)
-6
365.24219878 - 6.16 * 10 T
has been corrected by one nonlinear term and also the coefficient of
the
linear term has been corrected. As a first approximation the
coefficients
A(T) and B(T) are also assumed to be constants.
If (N1, T1) and (N2, T2) are two fossil points and if C(T) is
assumed
constant value then the coefficients of the formula have the
following
values:
A =3D T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C*(N2T1-N1T2)/(T2-
T1)
B =3D (M-N2)/T2/(T2-T1) - (M-N1)/T1/(T2-T1) + C*(N1-N2)/(T2-T1)
The coefficients of the terms are achieved from two reliable fossil
points.
1. From coral fossil data approximately 400 million years ago. It has
been
estimated that there were little over 400 days in a year at that
time.
These fossil corals were ancient marine invertebrates that secreted
a microscopically thin layer of calsium carbonate each day; the
layers laid
down in summer were thicker than those laid down in winter.
Estimations are based on careful countings of calcium carbonate
layers in
fossil corals formed due to the changes of lightness of night and day
(The Cambridge Atlas of Astronomy 1985, Pages 55 and 54, Photograph:
J. C. Revy. The specimen is from the collection of the Brittish
National
Museum of the Natural History).
2. From fossil data approximately 180 million years ago, when there
were
approximately 381 days of that time in a year (Wells 1963).
-6 -13
A =3D 2.46 * 10 and B =3D 1.79 * 10 (in first time
formula).
If fossil points from (Eicher 1976) are used.
1. From fossil data approximately 190 million years ago, when there
were
approximately 382 days of that time in a year (Eicher/Wells 1976).
2. From fossil data approximately 395 million years ago, when there
was
approximately 401 days of that time in a year (Eicher/Wells 1976).
then
-6 -14
A =3D 2.28 * 10 and B =3D 4.74 * 10 (in second time
formula)
(see for basis growth increments in fossils: Rosenberg Runcorn 1975).
This seems to be a good form for the approximation even when C is
afterwards
set to depend on T. This new setting is possible because the formula
allows
quite wide range of variations of C's magnitude and it still gives a
good
fit to the fossil data.
A(T) =3D T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C(T)*(N2T1-N1T2)/
(T2-T1)
B(T) =3D (M-N2)/T2/(T2-T1) - (M-N1)/T1/(T2-T1) + C(T)*(N1-N2)/(T2-T1)
The best C(T) is achieved from Geologic Rock and Fossil Record
Data, if
the distance between Earth and Moon can be estimated at different
points
on the geologic time scale. Solar tides must also be accounted
because
these tides slows down Earth's rotation (see fossil data of past 500
million
years: Pannella MacClintock and Thompson 1968, and Scrutton 1978, Fig
8,
Page 185).
The coefficient of the asymptotic straight line for the month
formula is
-7
about 2.60 * 10 from (Scrutton 1978) and the little uncertain period
of
4
oscillation about this line is roughly 429.4 * 10 centuries from
(Pannella MacClintoc and Thompson 1968).
-7 4
P(T) =3D 29.53 - 2.60 * 10 * ( 1 - e*sin ( 2 P T / (429.4 * 10 )))*
T
P(T)=3D number of mean solar days per synodic month at a
certain
point T of time
0 <=3D e <=3D 1, (e =3D 1 in first approximation)
P =3D 3.14159 radians
(This month formula is not used because it is still under testings).
4
If dT =3D + 5 * 10 centuries and dN =3D + 0.5 mean solar days/tropical
year
- -
are the accuracy of determination of the absolute age of the fossil
samples,
and latter is roughly the accuracy of determination of the number of
days in
year from fossil samples, then calculations gives the same order
error
magnitudes as A and B themselves are, so at present accuracy the
coefficients
cannot be estimated very reliable.
The coral and bivalve fossil data suggests that the value of
derivative
of the time formula at the point T =3D 0 is (Schopf 1983):
-6
-(9.5 + 0.9) * 10 (coral data)
- -6
-(10.0 + 1.2) * 10 (bivalve data)
-
Further data (Schopf 1983):
(d W / dt) / (dW / dt) =3D 42 + 11 (coral data)
Earth Earth-Moon -
=3D 46 + 8 (bivalve data)
-
=3D 51 + 5 (modern astronomical data)
-
=3D 48 (present day value predicted by Kepler's third law and the
conservation of angular momentum)
TABLE OF CALCULATED VALUES COMPARED WITH THE FOSSIL DATA (FIRST TIME
FORMULA, WELL'S CORAL FOSSIL DATA)
The time formula give the following table with different values of
T:
TABLE 1
4
1. =3D T / 10 (centuries)
2. =3D calculated value from the first time formula (days/year)
3. =3D calculated value from the second time formula (days/year)
7. =3D experimental value (days/year), (Wells 1963). 8. =3D era (end
time).
1. 2. 3. 7. 8.
=20
------------------------------------------------------------------------
0 365.24 365.24 365.24 Cenozoic
=20
------------------------------------------------------------------------
- 65 370.95 370.89 371 Cretaceous
=20
------------------------------------------------------------------------
-135 377.07 377.07 377 Jurassic
=20
------------------------------------------------------------------------
-180 381.00 381.10 381 Triassic
=20
------------------------------------------------------------------------
-230 385.34 385.63 385 Permian
=20
------------------------------------------------------------------------
-280 389.67 390.22 390 Pennsylvanian
=20
------------------------------------------------------------------------
-310 392.26 393.01 393 Mississippian
=20
------------------------------------------------------------------------
-345 395.27 396.28 396 Devonian
=20
------------------------------------------------------------------------
<-405 400.42 401.96 >400
=20
------------------------------------------------------------------------
-405 400.42 401.96 402 Silurian
=20
------------------------------------------------------------------------
-425 402.14 403.88 Ordovician
=20
------------------------------------------------------------------------
-500 408.53 411.15 412 Cambrian
(the fossil can be older)
=20
------------------------------------------------------------------------
-600 416.99 421.08 424 Precambrian
(no fossil evidence)
=20
------------------------------------------------------------------------
-390- 399.14- 400.53->400 Devonian (The Cambridge Atlas of)
-400 400.00 401.48 Astronomy 1985, p.55 and p.54)
=20
------------------------------------------------------------------------
WELL'S CORAL FOSSIL SAMPLES:
TABLE 2
WELL'S CORAL FOSSIL SAMPLES (1. Wells 1963 and 2. Wells 1970):
Era 1. Sample 1. Data 1.
=20
-------------------------------------------------------------------------
Pensylvanian Caninia 385 day layers
=20
-------------------------------------------------------------------------
Pennsylvanian Lophophyllidium 390 day layers
=20
-------------------------------------------------------------------------
Middle-Devonian Heliophyllum halli usually about 400 day
layers,
(13 annual growth
increments) ranging between extremes
of 385
Eridophyllum archiaci and 410
Favosites
=20
-------------------------------------------------------------------------
Lower-Silurian Holophragma calceoloides
=20
-------------------------------------------------------------------------
Cambrian An estimation=3D 21-hr
Cambrian day
(Munk MacDonald 1960).
Era 2. Sample 2. Data 2.
=20
-------------------------------------------------------------------------
Mississippian Lithostrontion 398 day layers.
=20
-------------------------------------------------------------------------
Mississippian Lophophylldium 380 and 390 day layers.
=20
-------------------------------------------------------------------------
Middle-Devonian Heliophyllum halli average of 398 with a
range from
Eridophyllum archiaci 385 to 405.
(Fig. 3.)
Cylindrophyllum
Favosites
=20
-------------------------------------------------------------------------
Middle-Silurian Holophragma calceoloides.
(Fig. 1. and 2.)
=20
-------------------------------------------------------------------------
Middle Silurian Ketophyllum about 400 day layers.
=20
-------------------------------------------------------------------------
Upper Ordovician Streptelasma about 412 day layers.
=20
-------------------------------------------------------------------------
Cambrian Escherichia coli An estimation =3D 21-hr
Cambrian
day (Halberg Conner
1961).
TABLE OF CALCULATED VALUES COMPARED WITH THE FOSSIL DATA, (SECOND
TIME
FORMULA, WELL'S CORAL FOSSIL DATA)
The time formula the following table with different values of T:
TABLE 3
7. =3D experimental value (days/year), (Eicher/Wells 1976).
1. 2. 3. 7. 8.
=20
------------------------------------------------------------------------
0 365.24 365.24 365.24 Cenozoic
=20
------------------------------------------------------------------------
- 65 370.95 370.89 371 Cretaceous
=20
------------------------------------------------------------------------
-136 377.16 377.16 377 Jurassic
=20
------------------------------------------------------------------------
-190 381.87 382.00 382 Triassic
=20
------------------------------------------------------------------------
-225 384.91 385.18 385 Permian
=20
------------------------------------------------------------------------
-280 389.67 390.22 390 Pennsylvanian
=20
------------------------------------------------------------------------
-325 393.55 394.41 394 Mississippian
=20
------------------------------------------------------------------------
-345 395.27 396.28 396 Devonian
=20
------------------------------------------------------------------------
-395 399.57 401.00 401 Silurian
=20
------------------------------------------------------------------------
-435 402.99 404.84 405 Ordovician
=20
------------------------------------------------------------------------
-500 408.53 411.15 412 Cambrian
=20
------------------------------------------------------------------------
-570 414.46 418.07 421 Precambrian
=20
------------------------------------------------------------------------
Three coral species from Middle Devonian rocks of New York and
Ontario,
the numerous counts range between 385 and 410 and they accumulate
near the
median of 398.
AWRAMIK'S AND VANYO'S STROMATOLITE DATA FROM THE BITTER SPRINGS
FORMATION,
(Anabaria Juvensis), CALCULATED AND THE FOSSIL DATA COMPARED
(FIRST AND SECOND TIME FORMULA)
(Vanyo Awramik 1985, error limit of the age determination 50 million
years)
This research was supported in part by the NSF Grant EAR 83-03754
and is
contribution no. 145 of the Preston Cloud Research Laboratory.
All samples are in collections of the Preston Cloud Research
Laboratory.
TABLE 4
7. =3D experimental value (days/year), (Vanyo Awramik 1985).
1. 2. 3. 7.
=20
------------------------------------------------------------------------
-850 437.83 447.19 435 (best) or 454 or 409 or 485
=20
------------------------------------------------------------------------
This, approximately 850 million years old, stromatolite
investigated by Vanyo and Awramik had a wavy sinusoidal year growth
"wave length" of 87 mm in the best sample and the depth of a days
growth
was 0.2 mm. This gave about 435 days in year at that time. Extreme
values
were measured to be 409 and 485, and one measurement gave the value
454.
This wavy nature of the growth is due the point of view that the
growth has
been directed towards the Sun and the same direction is repeated
annually.
THE STROMATOLITE FROM THE AREA OF GREAT SLAVE LAKE (Hearne Formation)
GSM 77325
(Jones 1981 and Schopf 1983, age determination is too inaccurate)
The specimen is stored in the collection of Institute of Geological
Sciences.
TABLE 5
7. =3D experimental value, Highest count=3D(days/month) ?,(Jones
1981,
Schopf 1983).
8. =3D experimental value, Mode=3D(days/(month/2))-(days/month) ?,
(Jones 1981, Schopf 1983).
9. =3D experimental value, Tidal cycles per year=3D( months/year ) ?,
(Pannella 1972 b).
1. 2. 3. 7. 8. 9.
=20
------------------------------------------------------------------------
-1790- 510.60- 567.10-
-2170 536.42 629.58 13
=20
------------------------------------------------------------------------
Pannella has estimated (Pannella 1972 b) that there have been about
13
tidal cycles in a year at that time. He has always counted two groups
of
laminae of the stromatolite as a unit. The very clear accumulation in
the
magnesium spectrum of the stromatolite laminations at the number 25
remains
unclear.
GSM 77325 spectrum:
Mg: 21-25-(33-34)-44-51-(75-76).
? -------
Si: 5-8-10-17-21-25-(26-28)-(35-36)-(43-45)-54-73-100.
-------
Al: 5-19-21-25-27-29-(30-36)-41-50-53.
----------
Ca: 8-11-17-21-25-27-34-43-46-(50-51)-66-81-101-121.
--
( )=3D between.
BULAWAYAN STROMATOLITE BUL-6/BUL-7 OR UCLA-BUL-7 OR P.P.P.G 253
(Schopf 1983 , error limit 140 million years, age determination too
inaccurate, see pages 385-413)
The specimen code is P.P.R.G (Precambrian Paleobiology Research
Group)
number.
TABLE 6
4
1. =3D T / 10 (centuries),(Schopf 1983) .
7. =3D experimental value, Highest count=3D(days/month)?, (Pannella
1972 a).
8. =3D experimental value,
Mode=3D(days/(month/4))-(days/(month/2))-(days/month)?, (Pannella
1972 a).
9. =3D experimental value, Tidal cycles per year (months/year)?,
(important)
1. 2. 3. 7. 8. 9.
=20
------------------------------------------------------------------------
-2460- 556.33- 693.70- 41 10-20-40 ?
-2740 571.69 762.65
=20
------------------------------------------------------------------------
There are very clear growth layers and time marks in the
Bulawayan stromatolite ?
(Pannella 1972 a):
Mode =3D 10-20-40 and Highest Count =3D 41 .
The latter could mean 41 mean solar days in a synodic month at that
time
(from new Moon to new Moon).
The highest number in the stromatolite's mode could mean the same.
The mode's number 20 could be a sign of the high tide repeated twice
monthly. The mode's number 10 could mean that there has been two high
tides
and two low tides in synodic month at that time. If it has been so,
this
would mean that the solar tides had been larger at that time than
they are
at present. The age determination is too inaccurate in this case and
the
names of the samples are not all clear (Pannella 1972 a, BUL-6/BUL-7
or
UCLA-Bul-7 ).
WARRAWOONA STROMATOLITE, CALCULATED VALUES
The specimens are named in reference (Schopf 1983)
P.P.R.G 001-018,046,349,511-514,517,522,534-542
P.P.R.G =3D Precambrian Paleobiology Research Group.
(Schopf 1983 and error limit 32 million years, sample is partially
melted).
TABLE 7
7. =3D experimental value, Highest count =3D (days/month) ?.
8. =3D experimental value,
Mode=3D (days/(month/4))-(days/(month/2))-(days/month) ?.
9. =3D experimental value, Tidal cycles per year =3D (months/year) ?.
1. 2. 3. 7. 8. 9.
=20
------------------------------------------------------------------------
-3556 591.60 1009.77
=20
------------------------------------------------------------------------
TABLE OF THE FOSSIL DATA ABOUT SOLAR DAYS PER SYNODIC MONTH
(Pannella 1972 a, Pannella 1972 b, Pannella MacClintock Thompson
1968,
Scrutton 1978 and Berry Barker 1975 a, see also: Pannella 1976):
PANNELLA'S FOSSIL DATA
TABLE 8
7. =3D experimental value, interpreted as (days/month), (Pannella
1972 a
and Pannella MacClintock Thompson 1968).
8. =3D standard deviation in experimental value (days/month)
9. =3D the code of the fossil specimen
10. =3D Highest count=3D(days/month)?, (Pannella 1972 a and Pannella
1972 b).
11. =3D Mode=3D(days/(month/4))-(days/(month/2))-(days/month) ?,
(Pannella 1972 a and Pannella 1972 b ).
12. =3D Tidal cycles per year =3D (months/year) ?,
(Pannella 1972 a and Pannella 1972 b ).
U =3D Upper, M =3D Middle, L =3D Lower.
YPM-IP =3D The collection of Division of Invertebrate Paleontology,
Peabody Museum, Yale University
Approximate absolute ages are estimated from Kulp (Kulp 1961).
(*) =3D in reference (Pannella 1972 a) and absolute age
determination
method different than in reference (Pannella MacClintock Thompson
1968).
(**)=3D Pannella 1972 b.
(***)=3D The well preserved specimen from Belt Supergroup.
1. 2. 3. 7. 8. 9.
=20
----------------------------------------------------------------------------
0 365.24 365.24 29.1 1.22 YPM-IP-26310
29.6 1.35 26307
29.0 0.87 26305
29.3 1.04 26312
29.2 1.05 26309
29.1 0.90 26304
29.4 1.45 28493 (*)
=20
----------------------------------------------------------------------------
U- -10 366.12 366.11 29.7 1.05 YPM-IP-28494 (*)
29.4 0.97 26376 (*)
29.8 1.27 28495 (*)
=20
----------------------------------------------------------------------------
M- -17 366.74 366.71 29.4 1.08 28483 (*)
=20
----------------------------------------------------------------------------
-18 366.83 366.80 29.4 0.97 YPM-IP-26376
=20
----------------------------------------------------------------------------
L- -27 367.62 367.58 29.2 0.99 28482 (*)
=20
----------------------------------------------------------------------------
L- -35 368.32 368.27 29.6 0.97 26377 (*)
=20
----------------------------------------------------------------------------
-40 368.76 368.71 29.6 0.97 YPM-IP-26377
=20
----------------------------------------------------------------------------
M- -45 369.20 369.14 29.9 0.90 28496 (*)
=20
----------------------------------------------------------------------------
-46 369.29 369.23 30.0 0.88 YPM-IP-26380
=20
----------------------------------------------------------------------------
L- -50 369.64 369.58 29.4 1.03 28480 (*)
=20
----------------------------------------------------------------------------
L- -54 369.99 369.93 29.6 1.55 28485 (*)
=20
----------------------------------------------------------------------------
U- -58 370.34 370.27 30.0 0.88 26380 (*)
=20
----------------------------------------------------------------------------
U- -70 371.39 371.33 29.7 1.03 26322 (*)
=20
----------------------------------------------------------------------------
-72 371.57 371.50 29.7 1.03 YPM-IP-26322
29.9 1.16 26801
29.7 0.70 26802
30.2 1.03 26381
30.0 0.84 26382
=20
----------------------------------------------------------------------------
U- -70 371.39 371.33 29.8 1.69 28497 (*)
29.6 0.80 11655 (*)
=20
----------------------------------------------------------------------------
-205 383.17 383.36 29.8 1.24 YPM-IP-26803
29.8 1.15 26804
29.3 1.25 26805
=20
----------------------------------------------------------------------------
M- -220 384.47 384.72 30.0 1.32 26803 (*)
29.4 1.18 26804 (*)
29.4 1.16 26805 (*)
=20
----------------------------------------------------------------------------
-290 390.53 391.15 30.7 0.70 YPM-IP-26383
30.0 0.83 26378
29.9 0.52 26384
=20
----------------------------------------------------------------------------
-305 391.83 392.54 30.2 1.20 YPM-IP-26323
=20
----------------------------------------------------------------------------
L- -330 393.98 394.87 30.2 1.20 26323 (*)
=20
----------------------------------------------------------------------------
-340 394.84 395.81 30.3 1.30 YPM-IP-26806
30.5 1.28 26807
=20
----------------------------------------------------------------------------
M- -360 396.56 397.69 30.5 1.25 26808 (*)
30.2 1.56 28499 (*)
=20
----------------------------------------------------------------------------
-380 398.28 399.58 30.5 1.25 YPM-IP-26808
U- -420 401.71 403.40 29.8 1.40 28505 (*)
=20
----------------------------------------------------------------------------
L- -470 405.98 408.22 30.7 1.60 ? (*)
=20
----------------------------------------------------------------------------
-510 409.38 412.13 31.6 3.15 YPM-IP-13849
=20
----------------------------------------------------------------------------
MAINLY PANNELLA'S STROMATOLITE DATA:
TABLE 9
MAINLY PANNELLA'S STROMATOLITE DATA:
1. 2. 3. 10. 11. 12. 9.
=20
----------------------------------------------------------------------------
-510 409.38 412.13 33 16-31 YPM-IP-13849
=20
----------------------------------------------------------------------------
-510(**) 409.38 412.13 13 YPM-IP-13849
13 28473
=20
----------------------------------------------------------------------------
-950(***)446.02 458.19 31 16-31 YPM-IP-28459
=20
----------------------------------------------------------------------------
-900- 441.94- 452.65-
473.94 499.64
-1300(**) 13 YPM-IP-28459
13 28471/2
=20
----------------------------------------------------------------------------
-1750 507.73 561.10 39 18-36 YPM-IP-28510
28511
=20
----------------------------------------------------------------------------
-1800- 511.31- 568.62-
518.34 584.13
-1900(**) 13 YPM-IP-28465
YPM-IP-28513
38 ? (Biwabik, Mohr 1975)
=20
----------------------------------------------------------------------------
-1845- 514.50- 575.52-
548.81 667.16
-2370(**) 13 YPM-IP-28469
13 28468
? (Great Slave,GSM 77325,Jones,
1981)
=20
----------------------------------------------------------------------------
<-2500 556.33 693.70 YPM-IP-28467
(**)
=20
----------------------------------------------------------------------------
<-2800 571.69 762.65 41 10-20-40 BUL-6/BUL-7 ? or UCLA-
BUL-7
=20
----------------------------------------------------------------------------
Biwabik stromatolite's spectrum (Mohr 1975):
(12-13)-18-(24-26)-32-44-48 (Mohr's counting method) and
--
(12-13)-18-(24-26)-32-38-44 (Pannella's counting method), ( ) =3D
between.
-----
THE BIVALVE FOSSIL DATA OF BERRY AND BARKER:
TABLE 10
4
1. =3D T / 10 (centuries), (Kulp 1961, ( )=3DBerry Baker 1975 a, Fig 2,
p=2E 21)
7. =3D experimental value, interpreted as (days/month),(Berry Barker
1975 a)
9. =3D the name of the bivalve fossil specimen, era and formation.
1. 2. 3. 7. 9.
=20
----------------------------------------------------------------------------
0- 365.24- 365.24- PLEISTOCENE
-1 365.33 365.33 29.5 Chione californiensis (Sandstone near
Punta
Cholla, Sonora,
Mexico)
29.5 Chione succincta (Palos Verdes
Formation,
Newport Beach,
California)
29.6 Chione undatella (San Pedro
Sandstone, San
Pedro, California)
=20
----------------------------------------------------------------------------
-1- 365.33- 365.33- PLIOCENE
-13 366.39 366.36
(-10) 29.6 Chione cancellata (Caloosahatchee
Formation,
Southern Florida)
29.7 Codakia orbicularis (Caloosahatchee
Formation,
Southern Florida)
=20
----------------------------------------------------------------------------
-25- 367.44- 367.40- OLIGOCENE
-36 368.41 368.36
(-40) 29.6 Crassatella lincolnensis (Sacate-
Gaviota
Formation, Santa Inez,
California)
29.5 Macrocallista hornii (Sacate-Gaviota
Formation, Santa Inez,
California)
=20
----------------------------------------------------------------------------
-36- 368.41- 368.36- ECOCENE
-58 370.34 370.28
(-45) 29.7 Meretrix splendida (Lutetian, Morigny,
France)
=20
----------------------------------------------------------------------------
-58- 370.34- 370.28- PALEOCENE
-65 370.95 370.89
(-50) 29.7 Venerid (Venerid shell fragments in
thin
sections of Meganos
Sandstone, Byron
Quadrangle, California)
=20
----------------------------------------------------------------------------
-65- 370.95- 370.89- CRETACEOUS
-135 377.07 377.07
(-100) 29.7 Crassatella vadosus (Ripley Formation,
Coon
Creek, Tennessee)
29.6 Idonearca vulgaris (Ripley Formation,
Coon
Creek, Tennessee)
29.8 Glycymeris lacertosa (Ripley
Formation, Coon
Creek,
Tennessee)
29.8 Lucina subundata (Cody
Shale,Greybull,Wyoming)
=20
----------------------------------------------------------------------------
-135- 377.07- 377.07- JURASSIC
-180 381.00 381.10
(-160) 29.8 Lima gigantea (Leamington, England)
=20
----------------------------------------------------------------------------
-180- 381.00- 381.10 TRIASSIC
-230 385.34 385.63
(-220) 29.8 Septocardia sp. (Luning Formation,
Pilot
Mountains, Nevada)
=20
----------------------------------------------------------------------------
-280- 389.67- 390.22- CARBONIFEROUS
-345 395.27 396.28
(-310) 30.0 Astartella concentrica (Gramham
Formation,
Texas)
30.2 Myalina subquadrata (Wayland
Formation,
Brownwood, Texas)
30.2 Conocardium sp. (Carboniferous,
Belgium)
=20
----------------------------------------------------------------------------
-345- 395.27- 396.28- DEVONIAN
-405 400.42 401.96
(-350) 30.5 Conocardium sp. (Alpena Limestone,
Michigan)
=20
----------------------------------------------------------------------------
SCRUTTON'S MIDDLE DEVONIAN CORAL FOSSIL DATA:
TABLE 11
7. =3D experimental values and average, interpreted as (days/month),
(Scrutton 1964 and Scrutton 1970)
8. =3D experimental average, months/year
9. =3D the code of the fossil specimen and the era.
10. =3D Number of consecutive bands.
11. =3D Ridges per band 27 28 29 30 31 32 33 34 35
1. 2. 3. 7. 8. 9.
=20
----------------------------------------------------------------------------
-365- 397.00- 398.16- Middle
Devonian
-390 399.14 400.53
11.
10. 27 28 29 30 31 32 33 34 35
=20
----------------------------------------------------------------------------
5 1 2 1 1 30.4
4 1 1 1 1 31.5
3 1 1 1 31.0
----
30.9 12.91 BM
R44851
=20
----------------------------------------------------------------------------
13 1 2 3 1 4 2 30.85 12.93 OUM
DT2
=20
----------------------------------------------------------------------------
8 1 3 2 2 30.9
2 2 30.0
----
30.7 12.99 OUM
DT3
=20
----------------------------------------------------------------------------
16 1 1 8 4 2 30.7 12.99 OUM
DT4
=20
----------------------------------------------------------------------------
7 1 1 1 2 2 30.15
5 2 2 1 30.8
----
30.4 13.12 OUM
DT5
=20
----------------------------------------------------------------------------
7 4 1 2 30.7
5 2 1 2 31.0
2 1 1 31.0
----
30.8 12.95 OUM
DT6
=20
----------------------------------------------------------------------------
12 2 4 2 1 2 1 31.0 12.87 OUM
DT7
=20
----------------------------------------------------------------------------
7 1 1 4 1 30.6 13.04 OUM
DT8
=20
----------------------------------------------------------------------------
9 3 4 1 1 30.0 13.3 OUM
DZ32
=20
----------------------------------------------------------------------------
8 2 1 2 2 1 29.9 13.34 OUM
DZ33
=20
----------------------------------------------------------------------------
=20
Silurian
BM
R21668
=20
----------------------------------------------------------------------------
=20
Cretaceous
BM
R41812
=20
----------------------------------------------------------------------------
In the very well preserved specimen OUM DT2, the interval betveen
the top
edges of the two swells is 401 ridges (days/year). This unit
comprises
thirteen bands (months/year), each on average with 30.85 ridges
(days/month). Scrutton has achieved values for months/year by
dividing 399
(days/year) with corresponding value days/month. The interpretation
of
ridges is my own.
OUM =3D Oxford University Museum. BM =3D British Museum (Natural
History).
THE SEDIMENT SAMPLE OF WILLIAMS:
From the time about 650 million years ago Williams has investigated
sediment layers and acieved result that there has been about 13.1
synodic
months in tropical year at that time (error limit 0.5 days/month was
given,
the error limit from the age determination was not given but it is
probably
about 50 million years) (Williams 1989).
TABLE 12
7. =3D experimental value (months/year), (Williams 1989)
8. =3D error limit for 7. (months/year)
9. =3D experimental value (days/month), (Williams 1989)
10. =3D error limit for 9. (days/month)
11. =3D experimental value (days/year), (Williams 1989)
12. =3D error limit for 11. (days/year)
1. 2. 3. 7. 8. 9. 10. 11. 12.
=20
----------------------------------------------------------------------------
-650 421.20 426.15 13.1 0.5 30.5 1.5 400 20
=20
----------------------------------------------------------------------------
IMAGINED SITUATION OF THE AREAS EXTERNAL TO THE DEFINED AREA
-4.55 billion years < T < -4.5 billion years and
-4.5 billion years < T < -4.4 billion years and
-4.4 billion years < T < -3.8 billion years.
Earth was supposedly created approximately 4.55 billion years ago
as
condensating from carbonaceous chondrite meteorites (The Cambridge
Encyclopedia of Earth Sciences 1982). Before 4.55 billion years ago
the
"length of a day" may have been very large. The very large value of
the
denominator corresponds approximately to the non-rotating galactic
"dust
cloud". The "tropical year" could have had a value prior to the
denominator's large value, if the creation of the Sun had occured
before
Earth's creation. This would correspond to the rotation of the
galactic
"dust cloud" around the recently created Sun (compare for example:
Lada
and Shu 1990). Before the first area, the number of days in a year
would
have been nearly zero. On the first area, the denominator would have
decreased from the very large value to 5 - 7 of our present hours at
approximately 4.5 billion years ago. (Schopf 1983, Pages 260-263). On
the
second area the denominator would have decreased further to a minimum
at a
point 4.4 billion years ago, which is due to the formation of Earth's
iron
core (Wilhelms McCauley Trask 1987). This point of time is very
inaccurate,
because it is roughly located in the time period 4.5 to 4 billion
years ago
At that time, the length of a day on Earth would have been at least
four of
our present hours, due to the holding together of the globe. The
length of
a day may have been about 12 - 15 present hours approximately 4.0
billion
years ago according to the reference (Schopf 1983).
The probable compression or capture or fission of the Moon has also
apparently happened 4.55 - 4.4 billion years ago. The Moon's crust is
a
little thinner on the Moon's visible face than on the hidden face,
which
explains the relative rarity of volcanism on the latter. This
asymmetry in
the mass distribution (an excess of crust on the hidden face) can be
related to the synchronism of the rotation and revolution of our
satellite
(The Cambridge Atlas of Astronomy 1985, Pages 82-117).
The radius of the Moon towards the Earth is about four kilometers
greater
than it is in directions at right angles. This is in fact much
greater than
any tidal effect and the Moon's elongated shape must have been formed
when
Moon was younger and hotter, and the shape of the Moon has been
frozen when
it cooled and formed its extensive lithosphere. The effects of tides
in the
solid body of the Moon slowed down its rotation until it locked into
syncronism with its orbital motion. Today there is no net torque on
the
Moon but were it to spin up or spin down, the torque on its elongated
shape
would in each case act to return the rotation to synchronism; the
situation
is stable (The Cambridge Encyclopaedia of Astronomy 1977).
For a long time astronomers have noted that all the Moon's
topographical
features are statistically oriented in three dominant directions:
north-south, north-east-south-west and north-west-south-east. This
arrangement which has been called the 'lunar grid' is the reflection
of
former disclocations caused by the slowing down of the Moon's
rotation
under the effects of the tides.
The whole surface of the Moon is affected everywhere by faults and
stress-induced rilles, certifying to a tendency of the Moon's surface
to be
under stress at the very moment when the volcanism of the seas was in
full
development. These rilles are in the main directed radially or
tangentially
to the Imbrium basin (old crater), whose presence seems to have
'oriented'
the Moon's expansion. (The Cambridge Atlas of Astronomy 1985, Pages
82-117).
After 3.8 billion years, the coefficients of the time formula can
have
slight undulation in the places where the distance from the Earth to
the
Moon has a minimum or maximum, if there exists any minimums or
maximums in
Earth-Moon distance in ancient times.
CRITICAL EXAMINATION OF TIME FORMULA
There is some inaccuracy in the determination of the age of
fossils,
there values are typically in steps of 10 million years. In
determination of
the age of the oldest fossils the relative error can be large. Time
limits
of the geological time scale have changed from the geological time
scale
which Kulp drafted in 1961 (Kulp 1961) and many points are still
uncertain.
In the future the test points from the oldest fossils will
hopefully give
answer to the question: how the coefficient of T in the denominator
of the
time formula depends on T. Well preserved stromatolites whose ages
can be
determined accurately could have conclusive meaning in solving this
problem.
It is also possible that any sharp distinction between the numerator
and
the denominator of the time formulae cannot be made. Ages of the
fossil
specimens should be determined at least to an accuracy of 10 million
years
and experimental fossil points should be more complete in order to
make more
accurate month formula for approximating of the C(T). The poor
accuracy of
the age determination of the well preserved Bulawayan stromatolite as
well
as in case of other stromatolites is problematic.
At present solar tides are so small that they cannot cause
significant
decrease in distance between the Earth and the Sun. Bulawayan
stromatolite
could indicate that solar tides were larger in past than at present.
In addition there is missing experimental data concerning about the
rotation
of the Sun on the geologic time scale. One possibility is that just
when the
Sun condenceded from interstellar gas it must have rotated much
faster than
the present one, so the rotation rate of the Sun has possibly slowed
down on
the geologic time scale from its maximum value (about 3 present
hours,
Runcorn 1967) to the present value (about 27 solar days). It remains
partly
open how fast this slowing has happened and what role an expanding
solar
corona had when interacting with the strong solar wind to this
slowing. There
are several models of the formation of Sunlike stars (see for
example: Lada
and Shu 1990, Schatzman 1960).
The Sun does not rotate rigidly like Earth; this is because the Sun
is
gaseous throughout. The polar regions of the photosphere take 37 days
to
rotate once with respect to the distant stars, whereas the equator
takes
26 days. As observed from Earth, which is moving around the Sun, the
corresponding synodic periods are 41 and 27 days. It is possible that
the
non-rigid rotation of our Sun is caused by rapid rotation of the
solar
interior, which would lead to a shear stress, and swifter rotation,
at the
equator of the visible surface (The Encyclopaedia of Astronomy 1977).
The assumption that Sun's mass has remained constant along the
whole
geologic time scale is not consistent at all time points with the
point of
view that at the creation phase and at so called T-Tauri phase
changes of
the Sun's mass could have been be significant (Runcorn 1967, Lada and
Shu
1990).
Some chaotic oscillation possibly exists in internal prosesses of
the
Earth on the geologic time scale which may have significant influence
on
Earth's rotation (see for example: Powell 1991). And the geology of a
Earth
size planet without a Moon seems to be quite different than Earth's
geology
(see for example: Reports of Venus Geology 1991).
Lastly there remains to be investigated in future somewhat open
question
of tidal density wave interactions, caused by our spiral galaxy Milky
Way or
by around Milky Way rotating Large and Small Magellanic Cloud
galaxies, with
the Sun, with our Planetary System and with the Earth-Moon system.
Distances of these two neigbour galaxies from the Milky Way is
possible
oscillatory in nature and main trend is decreasing on the geologic
time scale.
It has been estimated that these distances have decreased about 50
percent
in 10 billion years. Decreasing rotation period of these neigbour
galaxies is
about 500 million years at present (see for example: Dekker 1976,
Yuan and
Cheng 1989, 1991, The Cambridge Atlas of Astronomy 1985, Binney
Tremaine 1987).
REFERENCES CITED:
1. Allen, C.W., 1973.
Astrophysical Quantities.
3 edition, University of London, The Athlone Press.
2. Berry, W. B. N., Barker, R. M., 1975 a.
Growth Increments in Fossil and Modern Bivalves.
In:
Rosenberg, G. D., Runcorn, S. K. (Editors), 1975.
Growth Rhythms and the History of the Earth's Rotation.
Willey Interscience, New York, Pages 9-24.
3. Binney, J. and Tremaine, S, 1987.
Galactic Dynamics.
Princeton University Press, Princeton, New Jersey,
Pages 17 and 428-431.
4. The Cambridge Atlas of Astronomy, 1985.
Cambridge University Press and Newnes Books.
Printed in France 1985.
5. The Cambridge Encyclopaedia of Astronomy, 1977.
Jonathan Cape thirty Bedford Square London.
6. The Cambridge Encyclopaedia of Earth Sciences, 1982.
Cambridge University Press.
7. Dekker, E., 1976.
Spiral structure and the dynamics of galaxies.
Physics Reports (Section C of Physics Letters), Volume 24,
Number 5, April 1976, North-Holland Publishing Company, Pages
315-389.
8. Eicher, D. L., 1976.
Geologic Time.
2nd edition, Prentice / Hall International, Inc., London 1976,
Figure
on page 117.
9. Halberg, F. and Conner, R. L., 1961.
Proc. Minn. Acad. Sci., Volume 29, Pages 227-239.
10. Jones, C. B., 1981.
Periodicities in stromatolite lamination from Early Proterozoic
Hearne Formation, Great Slave Lake, Canada.
Palaeontology, Volume 24, Part 2, Pages 231-250.
11. Kulp, J. L., 1961.
Geologic Time Scale.
Science, N.Y., Volume 133, pages 1105-1114.
12. Lada, C. J. and Shu, F. H., 1990.
The Formation of Sunlike Stars.
Science, Volume 248, Number4, Pages 564-572, May 1990.
13. Mohr, R. E., 1975.
Measured periodicities of the Biwabik (Precambrian) stromatolites
and their geophysical significance.
In:
Rosenberg, G. D. and Runcorn, S. K. (Editors), 1975.
Growth Rhythms and The History of the Earth's Rotation.
Wiley Interscience, New York, Pages 43-55.
14. Munk, W. H., and MacDonald, G. L. F., 1960.
The Rotation of the Earth.
Cambridge University Press, London, Page 250, 323 pages.
15. Pannella, G., MacClintock, C. and Thompson, M., 1968.
Paleontological evidence of variation in length of synodic month
since Late Cambrian.
Science, Volume 162, Pages 792-796. Washington, D.C.
16. Pannella, G., 1972 a.
Paleontological Evidence on the Earth's Rotational History
Since the Early Precambrian.
Astrophys. Space Science, Volume 16, Pages 212-237.
17. Pannella, G., 1972 b.
Precambrian stromatolites as paleontological clocks.
Twenty-Fourth International Geological Congress, Section 1, Pages
50-57.
18. Pannella, G., 1976.
Tidal Growth Patterns in Recent and Fossil Mollusc Bivalve
Shells:
a Tool for the Reconstruction of Paleotides.
Naturwissenschaften, Volume 63, Pages 539-543.
19. Powell, C. S., 1991.
Trends in geophysics: Peering Inward.
Scientific American, Pages 72-81, June 1991.
20. Reports of Venus Geology, 1991.
(Geology of Earth size planet without a Moon).
Science, Volume 252, Pages 247-312.
21. Rosenberg, G. D., Runcorn, S. K. (Editors), 1975.
Growth Rhythms and the History of the Earth's Rotation.
Willey Interscience, New York, 559 pages.
22. Runcorn, S. K. (Editor), 1967.
International Dictionary of Geophysics.
-Absolute Time Data From Palaeontology, Pages 1-2, Volume 1.
-Sun, Origin of, Pages 1484-1487, Volume 2.
Pergamon Press Ltd., London, Volumes 1 and 2.
24. Schatzman, E., 1960.
Special Tech. Rept. Number 3, Mt. Wilson and Palomar Obs.
25. Schopf, J. William, (Editor), 1983.
Earth's Earliest Biosphere. Its Origin and Evolution.
Princeton University Press, Princeton, New Jersey.
26. Scrutton, C. T., ( 1964 ) 1965.
Periodicity in Devonian Coral Growth.
Palaeontology, Volume 7, Part 4, Pages 552-558, Plates 86-87.
27. Scrutton, C. T., 1970.
Evidence for a monthly periodicity in the growth of some corals.
In:
Runcorn, S. K. (Editor), 1970.
Paleogeophysics.
Academic Press, London, Pages 11-16.
28. Scrutton, C. T., 1978.
Periodic Growth Features in Fossil Organisms and the Length of
the Day
and Month.
In:
Brosche, P. and Sundermann, J. (Editors), 1978.
Tidal Friction and the Earth's Rotation.
Springer-Verlag, New York. 241 pages, Pages 154-196.
29. Vanyo, J. P. and Awramik, S. M., 1985.
Stromatolites and Earth-Sun-Moon Dynamics.
Precambrian Research, volume 29, page 121.
30. Wells, J. W., 1963.
Coral Growth and Geochronometry.
Nature, London, Volume 197, pages 948-950.
31. Wells, J. W., 1970.
Problems of Annual and Daily Growth-rings in Corals.
In:
Runcorn, S. K. (Editor), 1970.
Paleogeophysics.
Academic Press, London, Pages 3-9.
32. Wilhelms, D. E., McCauley, J. F., Trask, N. J., 1987.
The Geologic History of the Moon.
United States Goverment Printing Office, Washington.
33. Williams, G. E., 1989.
Precambrian Tidal Sedimentary Cycles and Earth's Paleorotation.
EOS, volume 70, number 3, pages 40-41.
34. Yuan, C. and Cheng, Y., 1989.
Resonance excitation of spiral density waves in a gaseous disk.
1. A. Linear theory.
Astrophysical Journal, volume 340, Page 216-240, (Paper 1).
35. Yuan, C. and Cheng, Y., 1991.
Resonance excitation of spiral density waves in a gaseous disk.
2. A. Nonlinear theory and application to the 3 kiloparsec arm.
Astrophysical Journal, volume 376, Pages 104-114, (Paper 2).
I would like to acknowledge Neil Jackson for his help in
translating
the text. I took this task to myself as a calendar maker's question.
(See: sci.astro, number=3D 5431, name=3D New Calendar)
I have sent earlier version of this work also 27.11.1991 to the
Geology
magazine (Geological Society of America, 3300 Penrose Place, P.O. Box
9140,
Boulder, Co 80301, U.S.A).
I sent this work is also 10.12.1991 to sci.astro (number=3D 5394,
name=3D
Ancient Time Formula) for criticism.
I would be grateful of suggestions and criticism of C(T)'s and
P(T)'s
formulas and their possible connections.
Kiiminki 16.12.1991
Hannu Poropudas
.
|
|
| User: "Hannu Poropudas" |
|
| Title: Re: Using Coral as a Clock (Update 30.4.2007) |
01 May 2007 08:46:27 AM |
|
|
Please forgive me I forgot to update calculated values in the table.
I put correct update below. (The text is made by the WORD program.)
Hannu
My Updating Notes (30.4.2007):
I=2E The coefficient of the asymptotic straight line for the month
formula is
-7
about 3.53 * 10 from my calculations (1, Allen 1973) and the
little
uncertain period of oscillation about this line is roughly
4
429.4 * 10 centuries from (Pannella MacClintoc and Thompson 1968).
-7 4
P(T) =3D 29.53 - 3.53 * 10 * ( 1 - e*sin ( 2 P T / (429.4 * 10 )))*
T
P(T)=3D number of mean solar days per synodic month at a
certain
point T of time
0 <=3D e <=3D 1, (e =3D 1 in first approximation, e =3D 0 in seco=
nd
approx.)
P =3D 3.14159 radians
(This month formula is not used because it is still under testings.
Existence of this oscillation is needed to be confirmed with more
complete
fossil data and with more accurate age determinations.)
(The coefficient is 2.60 * 10^(-7) from (Scrutton 1978) and 4.29 *
10^(-7)
from (Pannella MacClintoc and Thompson 1968) and 3.50 * 10^(-7) from
(Scrutton 1964, 1970, Kulp 1961).)
II.
(In the text wrong word "speeds up" is corrected to "slows down".)
III.
The depositional age of the Gunflint Formation is
1878.3 Ma +- 1.3 Ma (2) (The sample YPM-IP-28510 & YPM-IP-28511
is only complete test point of stromatolites.)
MAINLY PANNELLA'S STROMATOLITE DATA:
TABLE 9
MAINLY PANNELLA'S STROMATOLITE DATA:
4
1. =3D T / 10 (centuries)
2. =3D calculated value from the first time formula (days/year)
3. =3D calculated value from the second time formula (days/year)
7. =3D experimental value (Pannella 1972 a).
9. =3D the code of the fossil specimen
10. =3D Highest count=3D(days/month)?, (Pannella 1972 a and Pannella
1972 b).
11. =3D Mode=3D(days/(month/4))-(days/(month/2))-(days/month) ?,
(Pannella 1972 a and Pannella 1972 b ).
12. =3D Tidal cycles per year =3D (months/year) ?,
(Pannella 1972 a and Pannella 1972 b).
U =3D Upper, M =3D Middle, L =3D Lower.
YPM-IP =3D The collection of Division of Invertebrate Paleontology,
Peabody Museum, Yale University
1. 2. 3. 7. 10. 11. 12. 9.
----------------------------------------------------------------------------
-1878 516.83 580.71 504-546 39 18-36 14 YPM-IP-28510
YPM-IP-28511
=20
----------------------------------------------------------------------------
(Note. 1. Error limits =3D +-1.3*10^4, 12. 28 fortnights per tropical
year?,
14 synodic months per tropical year?)
----------------------------------------------------------------------------
-(2715- 567.65 741.90 41 10-20-40 UCLA-BUL-7
-2672)(565.50) (731.79) (=3D P.P.R.G.
253)
=20
----------------------------------------------------------------------------
(Note. 1. -(2715 +- 15)*10^4, (2672 +-12)*10^4, 2.,3. 567.65 and
741.90
corresponds to T =3D -2715*10^4 centuries and 565.50 and 731.79
corresponds
to T =3D -2672*10^4 centuries, 7. 504=3D14*36, 546=3D14*39.)
Somewhat uncertain data about UCLA-Bul-7 (The sample
UCLA-Bul-7 is a incomplete test point. I recall that possible
"year" marks were not found by Pannella (Pannella 1972 a, b)):
A=2E Huntsman limestone stromatolites of MacGregor belong in the
Upper Bulawayan Greenstones (3)(if I can rely on J.F.Wilson, this
needs still to be confirmed):
"J.F.W.'s correlations across the greenstone belts also allow the
rationalization of the known occurrences of Rhodesian Archean
stromatolites which now number five (Fig.1).
All of these occur in the Upper Greenstones. ... Three occur in
limestones
above the tholeiitic pile; one at Belingwe, one south-east of
Redcliff ...
and one the Huntsmann limestone stromatolites of MacGregor, some
60 km north of Bulawayo."
B=2E Age of the Upper Bulawayan Greenstones (4) (this needs still to
be confirmed with more local age data):
"Timespan of deposition of Upper Bulawayan Greenstones is
2715 Ma +- 15 Ma (Iron Mask Formation, ZIM-74)- 2672 Ma +- 12 Ma
(Harare-Shamva greenstone sequence ,,Black Cat porphyry", ZIM-29)"
(The Stromatolite UCLA-Bul-7 (found by K.A. Kvenvolden from one
tailings
of pile of Huntsman Limestone Quarries) could be a little older than
this
age, because it could originate little below Upper Bulawayan
Greenstones in Huntsman Limestone Quarries (5)?)
C=2E About geology of the Bulawayan Supergroup is in the reference (6)
written by M.D. Prendergast.
References:
1=2E Poropudas Hannu, 1996.
Harrastelijan ajatuksia p=E4iv=E4n, kuukauden ja vuoden pituudesta
muinaisina aikoina.
Geologi, 4-5/1996, Pages 92-96.
2=2E Fralick Philip, Davis Don W., and Kissin Stephen A. 2002.
The age of the Gunflint Formation, Ontario, Canada:
single zircon U-Pb age determinations from reworked volcanic ash.
Can. J. Earth Sci. vol. 39: 1085-1091.
3=2E Wilson, J.F. et al, 1978.
Granite-greenstone terrain of the Rhodesian Archean craton.
Nature, vol. 271, 1978, 23-27.
4=2E Jelsma,H.A., Vinyu,M.L., Valbracht,P.J., Davies,G.R.,
Wijbrans,J.R., Verdurmen,E.A.T., 1996.
Constraints on Archean crustal evolution of the Zimbabwe craton:
a U-Pb zircon, Sm-Nd and Pb-Pb whole rock isotope study.
Contrib. Mineral Petrol. (1996) 124: 55-70.
5=2E Bond,G., Wilson,J.F. & Winall,N.J., 1973.
Age of the Huntsman Limestone (Bulawayan) Stromatolites.
Nature 244, 275-276. (the map of the Huntsman Limestone Quarries).
6=2E Prendergast,M.D., 2004.
The Bulawayan Supergroup: a late Archean passive margin-related
large igneous province in the Zimbabwe craton.
Journal of the Geological Society, London, Vol. 161,
2004, pp. 431-445. Printed in Great Britain.
.
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