Author: Hannu K. J. Poropudas Title: Using Coral as a Clock APPROXIMATE ANCIENT TIME FORMU

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=============================================================================== Author: Hannu K. J. Poropudas Title: Using Coral as a Clock =============================================================================== APPROXIMATE ANCIENT TIME FORMULA BASED ON FOSSIL DATA Hannu K. J. Poropudas (R&D Engineer, Nokia Telecommunications) (E-Mail Address: poropuda@tnclus.tele.nokia.fi) 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) - 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 850 (+ 50) 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) = --------------------- 1 + C(T)* T N(T) = Number of mean solar days in tropical year at the point T T = time in uniform centuries M = 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 = 1 + ----- * ----- * T = 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 = T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C*(N2T1-N1T2)/(T2-T1) B = (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 = 2,46 * 10 and B = 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 = 2,28 * 10 and B = 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) = T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C(T)*(N2T1-N1T2)/(T2-T1) B(T) = (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 speeds up 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) = 29,53 - 2,60 * 10 * ( 1 - e*sin ( 2 P T / (429,4 * 10 )))* T P(T)= number of mean solar days per synodic month at a certain point T of time 0 <= e <= 1, (e = 1 in first approximation) P = 3,14159 radians (This month formula is not used because it is still under testings). 4 If dT = + 5 * 10 centuries and dN = + 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 = 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) = 42 + 11 (coral data) Earth Earth-Moon - = 46 + 8 (bivalve data) - = 51 + 5 (modern astronomical data) - = 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. = T / 10 (centuries) 2. = calculated value from the first time formula (days/year) 3. = calculated value from the second time formula (days/year) 7. = experimental value (days/year), (Wells 1963). 8. = era (end time). 1. 2. 3. 7. 8. ------------------------------------------------------------------------ 0 365,24 365,24 365,24 Cenozoic ------------------------------------------------------------------------ - 65 370,95 370,89 371 Cretaceous ------------------------------------------------------------------------ -135 377,07 377,07 377 Jurassic ------------------------------------------------------------------------ -180 381,00 381,10 381 Triassic ------------------------------------------------------------------------ -230 385,34 385,63 385 Permian ------------------------------------------------------------------------ -280 389,67 390,22 390 Pennsylvanian ------------------------------------------------------------------------ -310 392,26 393,01 393 Mississippian ------------------------------------------------------------------------ -345 395,27 396,28 396 Devonian ------------------------------------------------------------------------ <-405 400,42 401,96 >400 ------------------------------------------------------------------------ -405 400,42 401,96 402 Silurian ------------------------------------------------------------------------ -425 402,14 403,88 Ordovician ------------------------------------------------------------------------ -500 408,53 411,15 412 Cambrian (the fossil can be older) ------------------------------------------------------------------------ -600 416,99 421,08 424 Precambrian (no fossil evidence) ------------------------------------------------------------------------ -390- 399,14- 400,53->400 Devonian (The Cambridge Atlas of) -400 400,00 401,48 Astronomy 1985, p.55 and p.54) ------------------------------------------------------------------------ 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. ------------------------------------------------------------------------- Pensylvanian Caninia 385 day layers ------------------------------------------------------------------------- Pennsylvanian Lophophyllidium 390 day layers ------------------------------------------------------------------------- Middle-Devonian Heliophyllum halli usually about 400 day layers, (13 annual growth increments) ranging between extremes of 385 Eridophyllum archiaci and 410 Favosites ------------------------------------------------------------------------- Lower-Silurian Holophragma calceoloides ------------------------------------------------------------------------- Cambrian An estimation= 21-hr Cambrian day (Munk MacDonald 1960). Era 2. Sample 2. Data 2. ------------------------------------------------------------------------- Mississippian Lithostrontion 398 day layers. ------------------------------------------------------------------------- Mississippian Lophophylldium 380 and 390 day layers. ------------------------------------------------------------------------- Middle-Devonian Heliophyllum halli average of 398 with a range from Eridophyllum archiaci 385 to 405. (Fig. 3.) Cylindrophyllum Favosites ------------------------------------------------------------------------- Middle-Silurian Holophragma calceoloides. (Fig. 1. and 2.) ------------------------------------------------------------------------- Middle Silurian Ketophyllum about 400 day layers. ------------------------------------------------------------------------- Upper Ordovician Streptelasma about 412 day layers. ------------------------------------------------------------------------- Cambrian Escherichia coli An estimation = 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. = experimental value (days/year), (Eicher/Wells 1976). 1. 2. 3. 7. 8. ------------------------------------------------------------------------ 0 365,24 365,24 365,24 Cenozoic ------------------------------------------------------------------------ - 65 370,95 370,89 371 Cretaceous ------------------------------------------------------------------------ -136 377,16 377,16 377 Jurassic ------------------------------------------------------------------------ -190 381,87 382,00 382 Triassic ------------------------------------------------------------------------ -225 384,91 385,18 385 Permian ------------------------------------------------------------------------ -280 389,67 390,22 390 Pennsylvanian ------------------------------------------------------------------------ -325 393,55 394,41 394 Mississippian ------------------------------------------------------------------------ -345 395,27 396,28 396 Devonian ------------------------------------------------------------------------ -395 399,57 401,00 401 Silurian ------------------------------------------------------------------------ -435 402,99 404,84 405 Ordovician ------------------------------------------------------------------------ -500 408,53 411,15 412 Cambrian ------------------------------------------------------------------------ -570 414,46 418,07 421 Precambrian ------------------------------------------------------------------------ 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. = experimental value (days/year), (Vanyo Awramik 1985). 1. 2. 3. 7. ------------------------------------------------------------------------ -850 437,83 447,19 435 (best) or 454 or 409 or 485 ------------------------------------------------------------------------ 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. = experimental value, Highest count=(days/month) ?,(Jones 1981, Schopf 1983). 8. = experimental value, Mode=(days/(month/2))-(days/month) ?, (Jones 1981, Schopf 1983). 9. = experimental value, Tidal cycles per year=( months/year ) ?, (Pannella 1972 b). 1. 2. 3. 7. 8. 9. ------------------------------------------------------------------------ -1790- 510,60- 567,10- -2170 536,42 629,58 13 ------------------------------------------------------------------------ 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. -- ( )= 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. = T / 10 (centuries),(Schopf 1983) . 7. = experimental value, Highest count=(days/month)?, (Pannella 1972 a). 8. = experimental value, Mode=(days/(month/4))-(days/(month/2))-(days/month)?, (Pannella 1972 a). 9. = experimental value, Tidal cycles per year (months/year)?,(important) 1. 2. 3. 7. 8. 9. ------------------------------------------------------------------------ -2460- 556,33- 693,70- 41 10-20-40 ? -2740 571,69 762,65 ------------------------------------------------------------------------ There are very clear growth layers and time marks in the Bulawayan stromatolite ? (Pannella 1972 a): Mode = 10-20-40 and Highest Count = 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 = Precambrian Paleobiology Research Group. (Schopf 1983 and error limit 32 million years, sample is partially melted). TABLE 7 7. = experimental value, Highest count = (days/month) ?. 8. = experimental value, Mode= (days/(month/4))-(days/(month/2))-(days/month) ?. 9. = experimental value, Tidal cycles per year = (months/year) ?. 1. 2. 3. 7. 8. 9. ------------------------------------------------------------------------ -3556 591,60 1009,77 ------------------------------------------------------------------------ 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. = experimental value, interpreted as (days/month), (Pannella 1972 a and Pannella MacClintock Thompson 1968). 8. = standard deviation in experimental value (days/month) 9. = the code of the fossil specimen 10. = Highest count=(days/month)?, (Pannella 1972 a and Pannella 1972 b). 11. = Mode=(days/(month/4))-(days/(month/2))-(days/month) ?, (Pannella 1972 a and Pannella 1972 b ). 12. = Tidal cycles per year = (months/year) ?, (Pannella 1972 a and Pannella 1972 b ). U = Upper, M = Middle, L = Lower. YPM-IP = The collection of Division of Invertebrate Paleontology, Peabody Museum, Yale University Approximate absolute ages are estimated from Kulp (Kulp 1961). (*) = in reference (Pannella 1972 a) and absolute age determination method different than in reference (Pannella MacClintock Thompson 1968). (**)= Pannella 1972 b. (***)= The well preserved specimen from Belt Supergroup. 1. 2. 3. 7. 8. 9. ---------------------------------------------------------------------------- 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 (*) ---------------------------------------------------------------------------- U- -10 366,12 366,11 29,7 1,05 YPM-IP-28494 (*) 29,4 0,97 26376 (*) 29,8 1,27 28495 (*) ---------------------------------------------------------------------------- M- -17 366,74 366,71 29,4 1,08 28483 (*) ---------------------------------------------------------------------------- -18 366,83 366,80 29,4 0,97 YPM-IP-26376 ---------------------------------------------------------------------------- L- -27 367,62 367,58 29,2 0,99 28482 (*) ---------------------------------------------------------------------------- L- -35 368,32 368,27 29,6 0,97 26377 (*) ---------------------------------------------------------------------------- -40 368,76 368,71 29,6 0,97 YPM-IP-26377 ---------------------------------------------------------------------------- M- -45 369,20 369,14 29,9 0,90 28496 (*) ---------------------------------------------------------------------------- -46 369,29 369,23 30,0 0,88 YPM-IP-26380 ---------------------------------------------------------------------------- L- -50 369,64 369,58 29,4 1,03 28480 (*) ---------------------------------------------------------------------------- L- -54 369,99 369,93 29,6 1,55 28485 (*) ---------------------------------------------------------------------------- U- -58 370,34 370,27 30,0 0,88 26380 (*) ---------------------------------------------------------------------------- U- -70 371,39 371,33 29,7 1,03 26322 (*) ---------------------------------------------------------------------------- -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 ---------------------------------------------------------------------------- U- -70 371,39 371,33 29,8 1,69 28497 (*) 29,6 0,80 11655 (*) ---------------------------------------------------------------------------- -205 383,17 383,36 29,8 1,24 YPM-IP-26803 29,8 1,15 26804 29,3 1,25 26805 ---------------------------------------------------------------------------- M- -220 384,47 384,72 30,0 1,32 26803 (*) 29,4 1,18 26804 (*) 29,4 1,16 26805 (*) ---------------------------------------------------------------------------- -290 390,53 391,15 30,7 0,70 YPM-IP-26383 30,0 0,83 26378 29,9 0,52 26384 ---------------------------------------------------------------------------- -305 391,83 392,54 30,2 1,20 YPM-IP-26323 ---------------------------------------------------------------------------- L- -330 393,98 394,87 30,2 1,20 26323 (*) ---------------------------------------------------------------------------- -340 394,84 395,81 30,3 1,30 YPM-IP-26806 30,5 1,28 26807 ---------------------------------------------------------------------------- M- -360 396,56 397,69 30,5 1,25 26808 (*) 30,2 1,56 28499 (*) ---------------------------------------------------------------------------- -380 398,28 399,58 30,5 1,25 YPM-IP-26808 U- -420 401,71 403,40 29,8 1,40 28505 (*) ---------------------------------------------------------------------------- L- -470 405,98 408,22 30,7 1,60 ? (*) ---------------------------------------------------------------------------- -510 409,38 412,13 31,6 3,15 YPM-IP-13849 ---------------------------------------------------------------------------- MAINLY PANNELLA'S STROMATOLITE DATA: TABLE 9 MAINLY PANNELLA'S STROMATOLITE DATA: 1. 2. 3. 10. 11. 12. 9. ---------------------------------------------------------------------------- -510 409,38 412,13 33 16-31 YPM-IP-13849 ---------------------------------------------------------------------------- -510(**) 409,38 412,13 13 YPM-IP-13849 13 28473 ---------------------------------------------------------------------------- -950(***)446,02 458,19 31 16-31 YPM-IP-28459 ---------------------------------------------------------------------------- -900- 441,94- 452,65- 473,94 499,64 -1300(**) 13 YPM-IP-28459 13 28471/2 ---------------------------------------------------------------------------- -1750 507,73 561,10 39 18-36 YPM-IP-28510 28511 ---------------------------------------------------------------------------- -1800- 511,31- 568,62- 518,34 584,13 -1900(**) 13 YPM-IP-28465 YPM-IP-28513 38 ? (Biwabik, Mohr 1975) ---------------------------------------------------------------------------- -1845- 514,50- 575,52- 548,81 667,16 -2370(**) 13 YPM-IP-28469 13 28468 ? (Great Slave,GSM 77325,Jones,1981) ---------------------------------------------------------------------------- <-2500 556,33 693,70 YPM-IP-28467 (**) ---------------------------------------------------------------------------- <-2800 571,69 762,65 41 10-20-40 BUL-6/BUL-7 ? or UCLA-BUL-7 ---------------------------------------------------------------------------- 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), ( ) = between. ----- THE BIVALVE FOSSIL DATA OF BERRY AND BARKER: TABLE 10 4 1. = T / 10 (centuries), (Kulp 1961, ( )=Berry Baker 1975 a, Fig 2, p. 21) 7. = experimental value, interpreted as (days/month),(Berry Barker 1975 a) 9. = the name of the bivalve fossil specimen, era and formation. 1. 2. 3. 7. 9. ---------------------------------------------------------------------------- 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) ---------------------------------------------------------------------------- -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) ---------------------------------------------------------------------------- -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) ---------------------------------------------------------------------------- -36- 368,41- 368,36- ECOCENE -58 370,34 370,28 (-45) 29,7 Meretrix splendida (Lutetian, Morigny, France) ---------------------------------------------------------------------------- -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) ---------------------------------------------------------------------------- -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) ---------------------------------------------------------------------------- -135- 377,07- 377,07- JURASSIC -180 381,00 381,10 (-160) 29,8 Lima gigantea (Leamington, England) ---------------------------------------------------------------------------- -180- 381,00- 381,10 TRIASSIC -230 385,34 385,63 (-220) 29,8 Septocardia sp. (Luning Formation, Pilot Mountains, Nevada) ---------------------------------------------------------------------------- -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) ---------------------------------------------------------------------------- -345- 395,27- 396,28- DEVONIAN -405 400,42 401,96 (-350) 30,5 Conocardium sp. (Alpena Limestone, Michigan) ---------------------------------------------------------------------------- SCRUTTON'S MIDDLE DEVONIAN CORAL FOSSIL DATA: TABLE 11 7. = experimental values and average, interpreted as (days/month), (Scrutton 1964 and Scrutton 1970) 8. = experimental average, months/year 9. = the code of the fossil specimen and the era. 10. = Number of consecutive bands. 11. = Ridges per band 27 28 29 30 31 32 33 34 35 1. 2. 3. 7. 8. 9. ---------------------------------------------------------------------------- -365- 397,00- 398,16- Middle Devonian -390 399,14 400,53 11. 10. 27 28 29 30 31 32 33 34 35 ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- 13 1 2 3 1 4 2 30,85 12,93 OUM DT2 ---------------------------------------------------------------------------- 8 1 3 2 2 30,9 2 2 30,0 ---- 30,7 12,99 OUM DT3 ---------------------------------------------------------------------------- 16 1 1 8 4 2 30,7 12,99 OUM DT4 ---------------------------------------------------------------------------- 7 1 1 1 2 2 30,15 5 2 2 1 30,8 ---- 30,4 13,12 OUM DT5 ---------------------------------------------------------------------------- 7 4 1 2 30,7 5 2 1 2 31,0 2 1 1 31,0 ---- 30,8 12,95 OUM DT6 ---------------------------------------------------------------------------- 12 2 4 2 1 2 1 31,0 12,87 OUM DT7 ---------------------------------------------------------------------------- 7 1 1 4 1 30,6 13,04 OUM DT8 ---------------------------------------------------------------------------- 9 3 4 1 1 30,0 13,3 OUM DZ32 ---------------------------------------------------------------------------- 8 2 1 2 2 1 29,9 13,34 OUM DZ33 ---------------------------------------------------------------------------- Silurian BM R21668 ---------------------------------------------------------------------------- Cretaceous BM R41812 ---------------------------------------------------------------------------- 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 = Oxford University Museum. BM = 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. = experimental value (months/year), (Williams 1989) 8. = error limit for 7. (months/year) 9. = experimental value (days/month), (Williams 1989) 10. = error limit for 9. (days/month) 11. = experimental value (days/year), (Williams 1989) 12. = error limit for 11. (days/year) 1. 2. 3. 7. 8. 9. 10. 11. 12. ---------------------------------------------------------------------------- -650 421,20 426,15 13,1 0,5 30,5 1,5 400 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= 5431, name= 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= 5394, name= 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

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