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Bauer, Thomas K.; Bender, Stefan; Heining, Jörg; Schmidt, Christoph M.

Working Paper

Brother Sun, Sister Moon: The Lunar Cycle, Sunspots and the Frequency of Births Ruhr economic papers, No. 225 Provided in Cooperation with: RWI - Leibniz-Institut für Wirtschaftsforschung, Essen

Suggested Citation: Bauer, Thomas K.; Bender, Stefan; Heining, Jörg; Schmidt, Christoph M. (2010) : Brother Sun, Sister Moon: The Lunar Cycle, Sunspots and the Frequency of Births, Ruhr economic papers, No. 225, ISBN 978-3-86788-257-6

This Version is available at: http://hdl.handle.net/10419/45314

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RUHR ECONOMIC PAPERS

Thomas K. Bauer Stefan Bender Jörg Heining Christoph M. Schmidt

Brother Sun, Sister Moon: The Lunar Cycle, Sunspots and the Frequency of Births

#225

Imprint

Ruhr Economic Papers Published by Ruhr-Universität Bochum (RUB), Department of Economics Universitätsstr. 150, 44801 Bochum, Germany Technische Universität Dortmund, Department of Economic and Social Sciences Vogelpothsweg 87, 44227 Dortmund, Germany Universität Duisburg-Essen, Department of Economics Universitätsstr. 12, 45117 Essen, Germany Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI) Hohenzollernstr. 1-3, 45128 Essen, Germany Editors Prof. Dr. Thomas K. Bauer RUB, Department of Economics, Empirical Economics Phone: +49 (0) 234/3 22 83 41, e-mail: [email protected] Prof. Dr. Wolfgang Leininger Technische Universität Dortmund, Department of Economic and Social Sciences Economics – Microeconomics Phone: +49 (0) 231/7 55-3297, email: [email protected] Prof. Dr. Volker Clausen University of Duisburg-Essen, Department of Economics International Economics Phone: +49 (0) 201/1 83-3655, e-mail: [email protected] Prof. Dr. Christoph M. Schmidt RWI, Phone: +49 (0) 201/81 49 -227, e-mail: [email protected] Editorial Office Joachim Schmidt RWI, Phone: +49 (0) 201/81 49 -292, e-mail: [email protected] Ruhr Economic Papers #225 Responsible Editor: Thomas K. Bauer All rights reserved. Bochum, Dortmund, Duisburg, Essen, Germany, 2010 ISSN 1864-4872 (online) – ISBN 978-3-86788-257-6 The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors’ own opinions and do not necessarily reflect those of the editors.

Ruhr Economic Papers #225 Thomas K. Bauer, Stefan Bender, Jörg Heining, and Christoph M. Schmidt

Brother Sun, Sister Moon: The Lunar Cycle, Sunspots and the Frequency of Births

Bibliografische Informationen der Deutschen Nationalbibliothek

Die Deutsche Bibliothek verzeichnet diese Publikation in der deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über: http://dnb.d-nb.de abrufbar.

ISSN 1864-4872 (online) ISBN 978-3-86788-257-6

Thomas K. Bauer, Stefan Bender, Jörg Heining, and Christoph M. Schmidt 1

Brother Sun, Sister Moon: The Lunar Cycle, Sunspots and the Frequency of Births Abstract Based on multivariate linear regression models, we analyze the effect of the lunar cycle and the number of sunspots occurring on a particular day on the number of births using social security data and controlling for a number of other potential confounders. The daily number of births between 1920 and 1989 have been calculated from the full sample of individuals who have been registered at least once in the German social security system. While the lunar cycle does not affect the number of births, the number of sunspots has a positive, albeit small effect on the number of births which is decreasing over time. The empirical results may be explained by medical technological progress making natural influences on births less important over time. This interpretation is supported by the results on the intertemporal influence of weekends and holidays on the frequency of daily births. JEL Classification: I12, J13 Keywords: Daily frequency of births; lunar cycle; sunspots November 2010

1 Thomas K. Bauer, RWI, Ruhr-Universität Bochum and IZA, Bonn; Stefan Bender, IAB Nürnberg; Jörg Heining, IAB Nürnberg; Christoph M. Schmidt, RWI, Ruhr-Universität Bochum, IZA, Bonn, and CEPR London. – We thank Christina Grabinger at the IAB for her support in the preparation of the data. – All correspondence to Thomas K. Bauer, RWI, Hohenzollernstr. 1-3, 45128 Essen, Germany, E-Mail: [email protected].

Introduction ƒ› ’‡‘’Ž‡ǡ —‡†—…ƒ–‡† ‘” ‡†—…ƒ–‡†ǡ „‡Ž‹‡˜‡ –Šƒ– –Š‡”‡ ‹• •‘‡–Š‹‰ •‹‹•–‡” ƒ„‘—– –Š‡ ˆ—ŽŽ ‘‘ǤƒŽ‡•ƒ„‘—–‘•–‡”•ǡ™‡”‡™‘Ž˜‡•ǡƒ†˜ƒ’‹”‡•”ƒ‹•‡†„›–Š‡ˆ—ŽŽ‘‘–‘’—”•—‡–Š‡‹” ‡˜‹Ž †‡‡†• •–‹ŽŽ „‡Ž‘‰ –‘ –”ƒ†‹–‹‘ƒŽ ˆ‘ŽŽ‘”‡ǡ ‘– ‘Ž› ‹ ”ƒ•›Ž˜ƒ‹ƒǤ ˜‡ ‘–Š‡”™‹•‡ “—‹–‡ •‘„‡”’‡‘’Ž‡•‘‡–‹‡•„Žƒ‡–Š‡ˆ—ŽŽ‘‘ˆ‘”–Š‡„ƒ†„‡Šƒ˜‹‘”‘ˆ‹†•‘”ˆ‘”•Ž‡‡’Ž‡••‹‰Š–•Ǥ ‡’‘’—Žƒ”ƒ†’‡”•‹•–‡–•—’‡”•–‹–‹‘‡˜‡ƒ‘‰—”•‡•‹‘„•–‡–”‹…•™ƒ”†•Š‘Ž†•–Šƒ––Š‡ Ž—ƒ”…›…Ž‡ƒˆˆ‡…–•–Š‡‘•‡–‘ˆŽƒ„‘”ƒ†–Šƒ–ǡ…‘•‡“—‡–Ž›ǡ–Š‡ˆ—ŽŽ‘‘”ƒ‹•‡•–Š‡—„‡”‘ˆ „‹”–Š•Ǥ ˆ –Š‹• ™‡”‡ ‹†‡‡† –Š‡ …ƒ•‡ǡ ‹– •Š‘—Ž† „‡ ‘ˆ …‘•‹†‡”ƒ„Ž‡ ‹–‡”‡•– ˆ‘” –Š‡ ƒƒ‰‡”• ‘ˆ Š‘•’‹–ƒŽ•ǡ•‹…‡–Š‡–Š‡›…‘—Ž†‡ƒ•‹Ž›ƒ†Œ—•––Š‡•–ƒˆˆ‹‰–‘–Š‡˜ƒ”‹ƒ„Ž‡™‘”Ž‘ƒ†‘……—””‹‰‹ †‹ˆˆ‡”‡–’Šƒ•‡•‘ˆ–Š‡Ž—ƒ”…›…Ž‡Ǥ ‘‰‘–Š‡”‘–‹˜‡•ǡ–Š‹•‹–‡”‡•–Šƒ•‹•’‹”‡†”‡•‡ƒ”…Š‡”•–‘‹˜‡•–‹‰ƒ–‡–Š‡‡ˆˆ‡…–‘ˆ–Š‡Ž—ƒ” …›…Ž‡ƒ†‘–Š‡”ƒ–—”ƒŽ’Š‡‘‡ƒ•—…Šƒ•ǡˆ‘”‡šƒ’Ž‡ǡ’”‡…‹’‹–ƒ–‹‘ǡ–‡’‡”ƒ–—”‡˜ƒ”‹ƒ–‹‘•ǡ ƒ† „ƒ”‘‡–”‹… ’”‡••—”‡ ‘ ’”‡‰ƒ…› ƒ† Žƒ„‘”Ǥ ȋͳȌ ȋʹȌ ȋ͵Ȍ ȋͶȌ ȋͷȌ ȋ͸Ȍ ȋ͹Ȍ ȋͺȌ Ž‘•‡Ž› ”‡Žƒ–‡† ’ƒ’‡”• ƒƒŽ›œ‡†‘–Š‡”’‘–‡–‹ƒŽ‡ˆˆ‡…–•‘ˆ–Š‡Ž—ƒ”…›…Ž‡ǡ•—…Šƒ•–Š‡‡ˆˆ‡…–‘ˆ–Š‡ˆ—ŽŽ‘‘‘ƒ‹ƒŽ „‹–‡•ȋͻȌȋͳͲȌǡ…”‹‡ȋͳͳȌǡƒ†—”‹ƒ”›”‡–‡–‹‘ȋͳʹȌǤŽŽ–Š‡•‡•–—†‹‡•ǡŠ‘™‡˜‡”ǡ‡‹–Š‡””‡Ž›‘”ƒ–Š‡” •ƒŽŽ•ƒ’Ž‡•ǡƒ”‡”‡Žƒ–‡†–‘ƒ•‹‰Ž‡Š‘•’‹–ƒŽ‘”ƒ•‹‰Ž‡”‡‰‹‘‘Ž›ǡ‡”‡Ž›…‘˜‡”ƒ•Š‘”––‹‡ ’‡”‹‘†‘”‡’Ž‘›‘˜‡”Ž›•‹’Ž‡„‹˜ƒ”‹ƒ–‡•–ƒ–‹•–‹…ƒŽ–‡•–•™Š‹…Šƒ”‡’”‘‡–‘‰‡‡”ƒ–‡•’—”‹‘—• ”‡•—Ž–•ǤŠ‡‘˜‡”ƒŽŽ‡˜‹†‡…‡ƒ’’‡ƒ”•–‘„‡‹š‡†ǡ™‹–Š‘•–•–—†‹‡•ˆ‹†‹‰‘‘”ƒ–„‡•–ƒ™‡ƒ ƒ••‘…‹ƒ–‹‘„‡–™‡‡–Š‡Ž—ƒ”…›…Ž‡ƒ†–Š‡ˆ”‡“—‡…›‘ˆ„‹”–Š•Ǥ ƒ–—”ƒŽ ’Š‡‘‡ƒ –Šƒ– Šƒ˜‡ „‡‡ ‹˜‡•–‹‰ƒ–‡† Ž‡•• ‡š–‡•‹˜‡Ž› ƒ”‡ –Š‡ ”‘Ž‡ ‘ˆ ‰‡‘ƒ‰‡–‹… †‹•–—”„ƒ…‡•ƒ†”ƒ†‹ƒ–‹‘‘Š—ƒŠ‡ƒŽ–Š‘—–…‘‡•Ǥš‹•–‹‰‡˜‹†‡…‡‹†‹…ƒ–‡•ǡˆ‘”‡šƒ’Ž‡ǡ –Šƒ–•‘Žƒ”ƒ…–‹˜‹–›‹•…‘””‡Žƒ–‡†™‹–ŠŠ—ƒ…‘…‡’–‹‘•ȋͳ͵ȌȋͳͶȌȋͳͷȌȋͳ͸ȌǡŠ—ƒŽ‹ˆ‡•’ƒȋͳ͹ȌȋͳͺȌƒ† ‘–Š‡”Š‡ƒŽ–Š‘—–…‘‡˜ƒ”‹ƒ„Ž‡•ȋ•‡‡ȋͳ͵Ȍˆ‘”ƒ”‡˜‹‡™ȌǤ Š‹• ’ƒ’‡” ‡šƒ‹‡• –Š‡ ‡ˆˆ‡…– ‘ˆ –Š‡ Ž—ƒ” ƒ† •‘Žƒ” …›…Ž‡ ‘ –Š‡ †ƒ‹Ž› ˆ”‡“—‡…› ‘ˆ „‹”–Š• ‹

‡”ƒ› —•‹‰ ƒ Žƒ”‰‡ †ƒ–ƒ •‘—”…‡ …‘˜‡”‹‰ –Š‡ „‹”–Š ›‡ƒ”• ˆ”‘ ͳͻʹͲ –‘ ͳͻͻͲǤ ‡ ‡’Ž‘› —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ƒƒŽ›•‹• ‹ ‘”†‡” –‘ ƒ……‘—– ˆ‘” …‘ˆ‘—†‹‰ ˆƒ…–‘”•ǡ •—…Š ƒ• •‡ƒ•‘ƒŽ ƒ†™‡‡Ž›„‹”–Š’ƒ––‡”•ƒ•™‡ŽŽƒ•–Š‡‡ˆˆ‡…–‘ˆ’—„Ž‹…Š‘Ž‹†ƒ›•Ǥ

Data and Methods ‡—•‡–Š‡ˆ—ŽŽ•ƒ’Ž‡‘ˆ–Š‡ ‡”ƒ‡’Ž‘›‡–”‡‰‹•–‡”Ȃƒƒ†‹‹•–”ƒ–‹˜‡†ƒ–ƒ•‡–…‘˜‡”‹‰ ƒŽŽ’‡”•‘•™‹–Š ‡”ƒƒ–‹‘ƒŽ‹–›™Š‘Šƒ˜‡’ƒ‹†•‘…‹ƒŽ•‡…—”‹–›…‘–”‹„—–‹‘•ˆ‘”ƒ–Ž‡ƒ•–‘‡ †ƒ› †—”‹‰ –Š‡ ’‡”‹‘† ˆ”‘ ͳͻ͹ͷ –‘ ʹͲͲͺ ƒ† †‡•…”‹„‡† ‹ †‡–ƒ‹Ž „› ȋͳͻȌǤ ‡ ‡š…Ž—†‡† ˆ‘”‡‹‰‡”•ˆ”‘–Š‡ƒƒŽ›•‹•„‡…ƒ—•‡–Š‡›•Š‘™ƒ—ƒ–—”ƒŽ…Ž—•–‡”‹‰‘ˆ„‹”–Š†ƒ›•ƒ–•’‡…‹ˆ‹… †ƒ›•ǡ•—…Šƒ•–Š‡ˆ‹”•–†ƒ›‘ˆ‡ƒ…Š‘–ŠǤ ”‘–Š‹••ƒ’Ž‡™‡—•‡–Š‡‡šƒ…–„‹”–Š†ƒ›•ˆ‘”‘”‡ –Šƒ ͸ͳǤͶ ‹ŽŽ‹‘ ‹†‹˜‹†—ƒŽ• –‘ …ƒŽ…—Žƒ–‡ –Š‡ —„‡” ‘ˆ „‹”–Š• ‘ ‡ƒ…Š †ƒ› ‹ –Š‡ ’‡”‹‘† ˆ”‘ ͳͻʹͲ –‘ ͳͻͺͻǡ ’”‘˜‹†‹‰ —• ™‹–Š ƒ –‘–ƒŽ ‘ˆ ʹͷǡͷ͸ͺ ‘„•‡”˜ƒ–‹‘•Ǥ ‡ ‡”‰‡† –Š‹• †ƒ–ƒ ™‹–Š –Š‡ †ƒ‹Ž› —„‡” ‘ˆ •—•’‘–•ǡ ‘„–ƒ‹‡† ˆ”‘ –Š‡ ™‡„’ƒ‰‡ ‘ˆ –Š‡ ‘Žƒ” ˆŽ—‡…‡• ƒ–ƒ ƒŽ›•‹• ‡–‡” ȋŠ––’ǣȀȀ•‹†…Ǥ‘ƒǤ„‡Ȁ•—•’‘–Ǧ†ƒ–ƒȀ†ƒ‹Ž›••Ǥ’Š’Ȍǡ ƒ† ™‹–Š ‹ˆ‘”ƒ–‹‘ ‘ –Š‡ Ž—ƒ” …›…Ž‡ǡ ‘„–ƒ‹‡† ˆ”‘ –Š‡ Š‡ —‹…Š •–”‘ ”…Š‹˜‡ ȋŠ––’ǣȀȀ™™™ǤƒƒǤŠǤ†‡Ȁ–ƒ”ƒ–‡Ȁ‘†’Šƒ•‡ǤŠ–ŽȌǤ  –‘–ƒŽǡ ‘—” •ƒ’Ž‡ ’‡”‹‘† …‘˜‡”• ƒ„‘—–ͺ͸͸”‡’‡–‹–‹‘•‘ˆ–Š‡Ž—ƒ”…›…Ž‡Ǥ 4

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Figure 1:ƒ‹Ž›—„‡”‘ˆ•—•’‘–•ǡͳͻʹͲȂͳͻͺͻ

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Figure 2:ƒ‹Ž›—„‡”‘ˆ„‹”–Š•

Year

 ‹‰—”‡ͳ•Š‘™•–Š‡—„‡”‘ˆ•—•’‘–•ˆ‘”‡˜‡”›†ƒ›…‘˜‡”‡†„›–Š‡†ƒ–ƒǤ –…Ž‡ƒ”Ž›•Š‘™•–Š‡ ™‡ŽŽ†‘…—‡–‡†ͳͳǦ›‡ƒ”…›…Ž‡‘ˆ•—•’‘–•ǡ†‘—„Ž‡Ǧ’‡ƒ‹‰ˆ‘”ƒ„‘—––Š”‡‡›‡ƒ”•‹‡˜‡”›…›…Ž‡Ǥ ȋʹͲȌŠ‡ƒ˜‡”ƒ‰‡†ƒ‹Ž›—„‡”‘ˆ•—•’‘–•‹‘—”†ƒ–ƒ‹•͸͸ǡ”ƒ‰‹‰ˆ”‘‘•—•’‘–•‘ʹͷͺͻ 5

†ƒ›•–‘ƒƒš‹—‘ˆ͵ͷͷ•—•’‘–•‘……—””‹‰‘–Š‡ʹͶ–Šƒ†ʹͷ–Š‘ˆ‡…‡„‡”ͳͻͷ͹Ǥ ‹‰—”‡ʹ †‡’‹…–• –Š‡ †‡˜‡Ž‘’‡– ‘ˆ –Š‡ —„‡” ‘ˆ †ƒ‹Ž› „‹”–Š• ‹ ‘—” •ƒ’Ž‡ ’‡”‹‘†Ǥ – •Š‘™• –Š‡ ‹…”‡ƒ•‹‰ —„‡” ‘ˆ „‹”–Š• —–‹Ž ͳͻͶͲǡ –Š‡ †”‘’ ‹ „‹”–Š• ƒ– –Š‡ ‡† ‘ˆ ‘”Ž† ƒ” ǡ –Š‡ ‹…”‡ƒ•‹‰ˆ‡”–‹Ž‹–›–Š‡”‡ƒˆ–‡”ǡ…—Ž‹ƒ–‹‰‹–Š‡„ƒ„›„‘‘‹–Š‡ͳͻ͸Ͳ•ǡƒ†ˆ‹ƒŽŽ›–Š‡†”‘’‹ –Š‡—„‡”‘ˆ„‹”–Š•ƒ••‘…‹ƒ–‡†ǡƒ‘‰‘–Š‡”•ǡ™‹–Š–Š‡‹˜‡–‹‘‘ˆ–Š‡‘”ƒŽ…‘–”ƒ…‡’–‹˜‡’‹ŽŽǤ Š‡‡ƒ—„‡”‘ˆ†ƒ‹Ž›„‹”–Š•‹‘—”•ƒ’Ž‡‹•ʹͶͲͲǡ”ƒ‰‹‰ˆ”‘ƒ‹‹——„‡”‘ˆͺʹ͵ –‘ƒƒš‹——„‡”‘ˆͷʹͷͲǤ ‘†‡–‡”‹‡–Š‡‡ˆˆ‡…–‘ˆ–Š‡Ž—ƒ”ƒ†•‘Žƒ”…›…Ž‡‘–Š‡ˆ”‡“—‡…›‘ˆ„‹”–Š•ǡ™‡‡•–‹ƒ–‡Ž‹‡ƒ” —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ‘†‡Ž• „› ‘”†‹ƒ”› Ž‡ƒ•– •“—ƒ”‡• —•‹‰ –Š‡ Ž‘‰ƒ”‹–Š ‘ˆ –Š‡ †ƒ‹Ž› —„‡”‘ˆ„‹”–Š•ƒ•†‡’‡†‡–˜ƒ”‹ƒ„Ž‡ƒ†–Š‡Ž‘‰ƒ”‹–Š‘ˆ–Š‡—„‡”‘ˆ•—•’‘–•ƒ•™‡ŽŽƒ•ƒ •‡”‹‡•‘ˆ†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š”‡‡‘ˆ–Š‡ˆ‘—”•–ƒ–‡•‘ˆ–Š‡Ž—ƒ”…›…Ž‡ȋ‡™‘‘ǡ ˆ‹”•–“—ƒ”–‡”ƒ†ˆ—ŽŽ‘‘ǡ™‹–ŠŽƒ•–“—ƒ”–‡”ƒ…–‹‰ƒ•”‡ˆ‡”‡…‡‰”‘—’Ȍƒ•‡š’Žƒƒ–‘”›˜ƒ”‹ƒ„Ž‡•Ǥ  –Š‡ —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ‘†‡Ž• ™‡ ƒŽ•‘ …‘–”‘Ž ˆ‘” ƒ —„‡” ‘ˆ ’‘–‡–‹ƒŽ …‘ˆ‘—†‹‰ ˆƒ…–‘”•Ǥ –ƒ’’‡ƒ”•–‘„‡‹’‘”–ƒ–ǡˆ‘”‡šƒ’Ž‡ǡ–‘–ƒ‡’‘–‡–‹ƒŽ‡ˆˆ‡…–•†—‡–‘–Š‡…Ž—•–‡”‹‰‘ˆ ‹†—…‡† Žƒ„‘”• ƒ† ‡Ž‡…–‹˜‡ Ǧ•‡…–‹‘• ‘ ’ƒ”–‹…—Žƒ” †ƒ›• ‘” ™‡‡‡† ‡ˆˆ‡…–• ‹–‘ ƒ……‘—–Ǥ ȋʹͳȌ Š‡‘†‡Ž–Š‡”‡ˆ‘”‡‹…Ž—†‡•ƒ•‡”‹‡•‘ˆ†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š‡†ƒ›‘ˆ–Š‡™‡‡ǡ ™‹–Š ‡†‡•†ƒ› „‡‹‰ –Š‡ ”‡ˆ‡”‡…‡ ‰”‘—’ǡ ƒ• ™‡ŽŽ ƒ• †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• ˆ‘” –Š‡ ‘•– ‹’‘”–ƒ– ‡”ƒŠ‘Ž‹†ƒ›•Ǥ‡ˆ—”–Š‡”‹…Ž—†‡ƒ•‡”‹‡•‘ˆ‹†‹…ƒ–‘”˜ƒ”‹ƒ„Ž‡•ˆ‘”–Š‡‘–Š‘ˆ „‹”–Š ƒ• ™‡ŽŽ ƒ• ͸ͻ †—‹‡• ˆ‘” –Š‡ ”‡•’‡…–‹˜‡ ›‡ƒ”• ‘ˆ „‹”–Šǡ–‘ …‘–”‘Ž ˆ‘” ’‘–‡–‹ƒŽ •‡ƒ•‘ƒŽ ’ƒ––‡”•™‹–Š‹ƒ’ƒ”–‹…—Žƒ”›‡ƒ”ƒ•™‡ŽŽƒ•–Š‡Ž‘‰Ǧ–‡”†‡˜‡Ž‘’‡–‘ˆˆ‡”–‹Ž‹–›‹‘—”•ƒ’Ž‡ ’‡”‹‘†Ǥ

Results ‘šǦŽ‘–• ȋʹʹȌ ‘ˆ –Š‡ ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ –Š‡ Ž‘‰ƒ”‹–Š ‘ˆ †ƒ‹Ž› „‹”–Š• ƒ† –Š‡ Ž—ƒ” …›…Ž‡ ȋˆ‹‰—”‡͵Ȍ ‹†‹…ƒ–‡ –Šƒ– –Š‡”‡ ‹• ‘ ‡˜‹†‡– ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ –Š‡ ‘‘’Šƒ•‡• ƒ† –Š‡ —„‡”‘ˆ„‹”–Š•ǤŠ‡’”‡†‹…–‡†”‡Žƒ–‹‘•Š‹’ȋƒ†ƒͻͷΨ…‘ˆ‹†‡…‡‹–‡”˜ƒŽȌ„‡–™‡‡–Š‡†ƒ‹Ž› —„‡” ‘ˆ „‹”–Š• ƒ† –Š‡ †ƒ‹Ž› —„‡” ‘ˆ •—•’‘–• ”‡•—Ž–‹‰ ˆ”‘ ƒ „‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ –‘‰‡–Š‡”™‹–Šƒ•…ƒ––‡”’Ž‘–‘ˆ–Š‡–™‘˜ƒ”‹ƒ„Ž‡•‹••Š‘™‹ˆ‹‰—”‡ͶǤ›…‘–”ƒ•––‘–Š‡Žƒ…‹‰ ƒ••‘…‹ƒ–‹‘ ™‹–Š –Š‡ Ž—ƒ” …›…Ž‡ –Š‡”‡ ‹• ƒ •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ– ’‘•‹–‹˜‡ ƒ••‘…‹ƒ–‹‘ „‡–™‡‡ –Š‡–™‘˜ƒ”‹ƒ„Ž‡•Ǥ  ‘”†‡” –‘ ‡š’Ž‘”‡ ™Š‡–Š‡” –Š‡ ƒ••‘…‹ƒ–‹‘ „‡–™‡‡ –Š‡ —„‡” ‘ˆ „‹”–Š• ƒ† –Š‡ Ž—ƒ” ƒ† •‘Žƒ” …›…Ž‡ †‘…—‡–‡† ‹ ˆ‹‰—”‡•͵ ƒ† Ͷ ƒ”‡ …‘ˆ‹”‡† ™Š‡ …‘–”‘ŽŽ‹‰ ˆ‘” ‘–Š‡” ’‘–‡–‹ƒŽ …‘ˆ‘—†‹‰ ˆƒ…–‘”• ˆ‘” –Š‡ —„‡” ‘ˆ „‹”–Š•ǡ –ƒ„Ž‡ͳ •Š‘™• –Š‡ ”‡•—Ž–• ˆ”‘ —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘‘†‡Ž•ˆ‘”‘—”ˆ—ŽŽ•ƒ’Ž‡‘ˆ„‹”–Š•„‡–™‡‡ͳͻʹͲƒ†ͳͻͺͻȋ…‘Ž—ȋͳȌȌƒ•™‡ŽŽƒ• –Š‡•—„•ƒ’Ž‡‘ˆ„‹”–Š•‘……—””‹‰„‡–™‡‡ͳͻʹͲƒ†ͳͻͶͻǡͳͻͷͲƒ†ͳͻ͸ͻǡƒ†ͳͻ͹Ͳƒ†ͳͻͺͻ ȋ…‘Ž—•ȋʹȌ –‘ ȋͶȌȌǤ Š‡ ‡•–‹ƒ–‹‘ ”‡•—Ž–• …‘ˆ‹” –Š‡ ‡š’Ž‘”ƒ–‘”› •–ƒ–‹•–‹…ƒŽ ƒƒŽ›•‹• ‘ˆ ˆ‹‰—”‡•͵ ƒ† ͶǤ Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• ‘ˆ –Š‡ –Š”‡‡ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• †‡•…”‹„‹‰ –Š‡ Ž—ƒ” …›…Ž‡ ƒ”‡ ‘– •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ–Ž› †‹ˆˆ‡”‡– ˆ”‘ œ‡”‘ ˆ‘” ƒ› ’‡”‹‘† …‘•‹†‡”‡†Ǥ ……‘”†‹‰ –‘ –Š‡ ”‡•—Ž–• ‘ˆ –Š‡ ƒ’’”‘’”‹ƒ–‡ Ǧ–‡•–ǡ –Š‡ —ŽŽ Š›’‘–Š‡•‹• –Šƒ– –Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• ‘ˆ –Š‡•‡ –Š”‡‡ ˜ƒ”‹ƒ„Ž‡• ƒ”‡ Œ‘‹–Ž› œ‡”‘ ‹• ‘– ”‡Œ‡…–‡† ˆ‘” ƒ› ‘ˆ –Š‡•‡ •ƒ’Ž‡• ƒ– …‘˜‡–‹‘ƒŽŽ‡˜‡Ž•‘ˆ•‹‰‹ˆ‹…ƒ…‡Ǥ  6

6.5

Logarithm of Number of Births 7 7.5 8

8.5

Figure 3:‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š•ƒ†‘‘’Šƒ•‡•

New Moon

First Quarter

Full Moon

Last Quarter



6.5

Logarithm of Number of Births 7 7.5 8

8.5

Figure 4:‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š•ƒ†—•’‘–•

0

1

2 Number of Sunspots (in 100)

3

4

 



7

Table 1: ‡‰”‡••‹‘‡•—Ž–•Ǣ‡’‡†‡–ƒ”‹ƒ„Ž‡ǣ‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š• ‘Ž— ƒ’Ž‡

ȋͳȌ ŽŽ‡ƒ”•

ȋʹȌ ͳͻʹͲǦͳͻͶͻ

ȋ͵Ȍ ͳͻͷͲǦͳͻ͸ͻ

ȋͶȌ ͳͻ͹ͲǦͳͻͺͻ

—„‡”‘ˆ—•’‘–•

ͲǤͲͲ͵ͳȗȗ ȋͲǤͲͲͳͷȌ

ͲǤͲͲ͸ͺȗȗȗ ȋͲǤͲͲʹͶȌ

ͲǤͲͲͲͺ ȋͲǤͲͲͳͷȌ

ͲǤͲͲͲͺ ȋͲǤͲͲͳ͹Ȍ

ǦͲǤͲͲͲͷ ȋͲǤͲͲͳ͵Ȍ ǦͲǤͲͲͲͳ ȋͲǤͲͲͳ͵Ȍ ǦͲǤͲͲͳ͵ ȋͲǤͲͲͳ͵Ȍ

ǦͲǤͲͲͳͷ ȋͲǤͲͲʹͲȌ ǦͲǤͲͲͳ͹ ȋͲǤͲͲʹͲȌ ǦͲǤͲͲͳͳ ȋͲǤͲͲʹͲȌ

ǦͲǤͲͲͳͲ ȋͲǤͲͲͳͷȌ ǦͲǤͲͲͲͻ ȋͲǤͲͲͳͷȌ ǦͲǤͲͲʹͶȗ ȋͲǤͲͲͳͷȌ

ͲǤͲͲͳ͵ ȋͲǤͲͲͳ͸Ȍ ͲǤͲͲ͵Ͳȗ ȋͲǤͲͲͳ͸Ȍ ͲǤͲͲͲʹ ȋͲǤͲͲͳ͸Ȍ

ǦͲǤͲͶͷͷȗȗȗ ȋͲǤͲͲͳ͹Ȍ ǦͲǤͲͲͺͺȗȗȗ ȋͲǤͲͲͳ͹Ȍ ǦͲǤͲͲͲͶ ȋͲǤͲͲͳ͹Ȍ ͲǤͲͳͲͲȗȗȗ ȋͲǤͲͲͳ͹Ȍ ͲǤͲͳ͸ͻȗȗȗ ȋͲǤͲͲͳ͹Ȍ ǦͲǤͲͳͺ͸ȗȗȗ ȋͲǤͲͲͳ͹Ȍ

ͲǤͲͶ͹͸ȗȗȗ ȋͲǤͲͲʹ͸Ȍ ǦͲǤͲͳͳͶȗȗȗ ȋͲǤͲͲʹ͸Ȍ ǦͲǤͲͳ͹͵ȗȗȗ ȋͲǤͲͲʹ͸Ȍ ͲǤͲͳ͹͸ȗȗȗ ȋͲǤͲͲʹ͸Ȍ ͲǤͲͳ͸ͳȗȗȗ ȋͲǤͲͲʹ͸Ȍ ͲǤͲʹ͹͸ȗȗȗ ȋͲǤͲͲʹ͸Ȍ

ǦͲǤͲʹ͵͵ȗȗȗ ȋͲǤͲͲͳͻȌ ǦͲǤͲͲʹ͸ ȋͲǤͲͲͳͻȌ ǦͲǤͲͲʹ͸ ȋͲǤͲͲͳͻȌ ͲǤͲͳͳͻȗȗȗ ȋͲǤͲͲͳͻȌ ͲǤͲͳͻͶȗȗȗ ȋͲǤͲͲͳͻȌ ͲǤͲͳͲͶȗȗȗ ȋͲǤͲͲͳͻȌ

ǦͲǤʹͲ͹Ͷȗȗȗ ȋͲǤͲͲʹͳȌ ǦͲǤͲͳͳͳȗȗȗ ȋͲǤͲͲʹͳȌ ͲǤͲʹ͹ʹȗȗȗ ȋͲǤͲͲʹͳȌ ǦͲǤͲͲʹͺ ȋͲǤͲͲʹͳȌ ͲǤͲͳͷͺȗȗȗ ȋͲǤͲͲʹͳȌ ǦͲǤͳͳ͸͸ȗȗȗ ȋͲǤͲͲʹͳȌ

ͲǤͳʹͳͲȗȗȗ ȋͲǤͲͲͻͲȌ ǦͲǤͲ͵ͷͶȗȗȗ ȋͲǤͲͲͶ͹Ȍ ǦͲǤͲʹ͸ͻȗȗȗ ȋͲǤͲͲͷ͵Ȍ ǦͲǤͲͶʹͲȗȗȗ ȋͲǤͲͲͷͶȌ ǦͲǤͲ͵ʹ͵ȗȗȗ ȋͲǤͲͳͲʹȌ ͲǤͲͲͳͶ ȋͲǤͲͳͲͲȌ ǦͲǤͲͲ͹ͻ ȋͲǤͲͲ͹ͶȌ ͸Ǥͻ͹ͳͷȗȗȗ ȋͲǤͲͲͶͶȌ ͲǤ͵ͻ ȏͲǤ͹͸ͳͲȐ ʹͷǡͷ͸ͺ ͲǤͻͷ͸ͻ

ͲǤͳͳͲͲȗȗȗ ȋͲǤͲͳ͵ͷȌ ǦͲǤͲͲͲͷ ȋͲǤͲͲ͹ͳȌ ǦͲǤͲͲͲʹ ȋͲǤͲͲͺͲȌ ͲǤͲʹͶͶȗȗȗ ȋͲǤͲͲͺͳȌ ͲǤͲ͵͵ͻȗ ȋͲǤͲͳͻ͹Ȍ ͲǤͲ͵ͳͻ ȋͲǤͲʹʹͷȌ ͲǤͲͲ͹Ͷ ȋͲǤͲͳ͹ͺȌ ͸ǤͻͷͲͶȗȗȗ ȋͲǤͲͲͷͲȌ ͲǤʹͻ ȏͲǤͺ͵͵ͺȐ ͳͲǡͻͷͺ ͲǤͻͷͷʹ

ͲǤʹͳ͹ͳȗȗȗ ȋͲǤͲͳͲͲȌ ǦͲǤͲʹͷͻȗȗȗ ȋͲǤͲͲͷʹȌ ǦͲǤͲͳͻʹȗȗȗ ȋͲǤͲͲͷͻȌ ǦͲǤͲʹͶͺȗȗȗ ȋͲǤͲͲ͸ͲȌ ǦͲǤͲͳͻʹȗ ȋͲǤͲͳͲͳȌ ͲǤͲʹ͸ͺȗȗȗ ȋͲǤͲͳͲͲȌ ͲǤͲͲ͸ͷ ȋͲǤͲͲ͹ͶȌ ͹Ǥͻͻ͹ͳȗȗȗ ȋͲǤͲͲ͵͵Ȍ ͲǤͻ͵ ȏͲǤͶʹͷ͸Ȑ ͹ǡ͵Ͳͷ ͲǤͺͺͷͶ

ͲǤͲͶʹ͹ȗȗȗ ȋͲǤͲͳͲͺȌ ǦͲǤͲͻ͸͸ȗȗȗ ȋͲǤͲͲͷ͸Ȍ ǦͲǤͲ͹ͷͳȗȗȗ ȋͲǤͲͲ͸ͶȌ ǦͲǤͳͷͻͶȗȗȗ ȋͲǤͲͲ͸ͶȌ ǦͲǤͳͲ͸͹ȗȗȗ ȋͲǤͲͳͲͻȌ ǦͲǤͲ͸ʹͳȗȗȗ ȋͲǤͲͳͲͺȌ ǦͲǤͲ͵͸ʹȗȗȗ ȋͲǤͲͲ͹͸Ȍ ͹ǤͷʹͲʹȗȗȗ ȋͲǤͲͲͶͶȌ ͳǤͶͻ ȏͲǤʹͳ͸ͶȐ ͹ǡ͵Ͳͷ ͲǤͺͻ͵ͺ

Moonphases ‹”•–—ƒ”–‡” —ŽŽ‘‘ ƒ•–—ƒ”–‡” Weekdays —†ƒ› ‘†ƒ› —‡•†ƒ› Š—”•†ƒ› ”‹†ƒ› ƒ–—”†ƒ› Holidays ‡™‡ƒ” ƒ•–‡” ‘™—†ƒ› Š”‹•–ƒ• •…‡•‹‘ƒ› ƒ„‘—”ƒ› ƒ–‹‘ƒŽƒ› ‘•–ƒ–  ȋ ‹”•–—ƒ”–‡”α —ŽŽ‘‘αƒ•–—ƒ”–‡”αͲȌ ȏ”‘„δ Ȑ „•‡”˜ƒ–‹‘• †Œ—•–‡†ʹ 



‘–‡•ǣ–ƒ†ƒ”†‡””‘”•‹’ƒ”‡–Š‡•‡•Ǣȗȗȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž ‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆͳΨǢȗȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆ ͷΨǢȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆͳͲΨǤŽŽ”‡‰”‡••‹‘• ‹…Ž—†‡ ‡Ž‡˜‡ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• ‹†‹…ƒ–‹‰ –Š‡ ‘–Š ƒ† ƒ •‡”‹‡• ‘ˆ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š‡›‡ƒ”‘ˆ„‹”–ŠǤ

› …‘–”ƒ•– –‘ –Š‡ Ž—ƒ” …›…Ž‡ǡ –Š‡ •‘Žƒ” …›…Ž‡ •Š‘™• ƒ •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ– ’‘•‹–‹˜‡ǡ ƒŽ„‡‹– •ƒŽŽ ‡ˆˆ‡…– ‘ –Š‡ —„‡” ‘ˆ „‹”–Š•Ǥ ……‘”†‹‰ –‘ –Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡– ‹ …‘Ž—ȋͳȌ ‘ˆ –ƒ„Ž‡ͳǡ–Š‡‘……—””‡…‡‘ˆ•‘‡͸Ͳƒ††‹–‹‘ƒŽ•—•’‘–•ǡƒ’’”‘š‹ƒ–‡Ž›‘‡•–ƒ†ƒ”††‡˜‹ƒ–‹‘‹ –Š‡†‹•–”‹„—–‹‘‘ˆ•—•’‘–•ǡ‹…”‡ƒ•‡•–Š‡—„‡”‘ˆ„‹”–Š•„›ƒ„‘—–ͲǤͲͲʹΨ‘”Ȃ‡˜ƒŽ—ƒ–‡†ƒ– –Š‡ƒ˜‡”ƒ‰‡†ƒ‹Ž›—„‡”‘ˆ„‹”–Š•Ȃ„›ƒŽ‘•–ͷ„‹”–Š•Ǥ‘•–‹’‘”–ƒ–Ž›ǡ–Š‹•‡ˆˆ‡…–ƒ’’‡ƒ”•–‘ 8

†‡…”‡ƒ•‡‘˜‡”–‹‡ǤŠ‹Ž‡ƒ‘‡Ǧ•–ƒ†ƒ”†Ǧ†‡˜‹ƒ–‹‘‹…”‡ƒ•‡ ‹ –Š‡—„‡”‘ˆ•—•’‘–•”ƒ‹•‡† –Š‡†ƒ‹Ž›—„‡”‘ˆ„‹”–Š•‘ƒ˜‡”ƒ‰‡„›‘”‡–ŠƒͲǤͲͲͶΨ„‡ˆ‘”‡ͳͻͷͲǡ–Š‡‡ˆˆ‡…–†‡…”‡ƒ•‡†–‘ Ž‡••–ŠƒͲǤͲͲͲͷΨƒˆ–‡”ͳͻͷͲǡ‘–‡˜‡„‡‹‰•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘‹–Š‡ Žƒ–‡”’‡”‹‘†ǤŠ‡•‡”‡•—Ž–••—‰‰‡•––Šƒ––Š‡”‡‹•ƒƒ–—”ƒŽ‹ˆŽ—‡…‡‘ˆ–Š‡•—‘–Š‡ˆ”‡“—‡…›‘ˆ „‹”–Š•ǡ „—– –Šƒ– –Š‹• ‡ˆˆ‡…– Šƒ• †‹•ƒ’’‡ƒ”‡† ƒ• ‡†‹…ƒŽ –‡…Š‘Ž‘‰‹…ƒŽ ’”‘‰”‡•• ‹…”‡ƒ•‹‰Ž› ™‹†‡‡†–Š‡‰›‡…‘Ž‘‰‹…ƒŽ’‘••‹„‹Ž‹–‹‡•–‘…‘–”‘Ž–Š‡–‹‹‰‘ˆ„‹”–Š•Ǥ Š‹•‹–‡”’”‡–ƒ–‹‘‹••—’’‘”–‡†„›–Š‡”‡•—Ž–•ˆ‘”–Š‡‘–Š‡”ˆƒ…–‘”•†‡–‡”‹‹‰–Š‡ˆ”‡“—‡…›‘ˆ „‹”–Š•Ǥ ˜‡”ƒŽŽǡ „‹”–Š• ƒ’’‡ƒ” –‘ „‡ Ž‡•• Ž‹‡Ž› ‘ ™‡‡‡†• ƒ• ™‡ŽŽ ƒ• Š‘Ž‹†ƒ›• ȋ…‘Ž—ȋͳȌ ‘ˆ –ƒ„Ž‡ͳȌǤ Š‡”‡ ‹•ǡ Š‘™‡˜‡”ǡ ƒ ”‡ƒ”ƒ„Ž‡ ‹–‡”–‡’‘”ƒŽ ’ƒ––‡”Ǥ Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• •—‰‰‡•––Šƒ–„‹”–Š•ƒ–™‡‡‡†•„‡…ƒ‡•—„•‡“—‡–Ž›Ž‡••Ž‹‡Ž›‘˜‡”–‹‡Ǥ ‘”‡šƒ’Ž‡ǡ„‡ˆ‘”‡ ͳͻͷͲ •‘‡ ͶǤ͸Ψ ‘”‡ „ƒ„‹‡• Šƒ˜‡ „‡‡ „‘” ‘ —†ƒ›• –Šƒ ‘ ‡†‡•†ƒ›•ǡ ™Š‹Ž‡ ‹ –Š‡ ͳͻ͹Ͳ•ƒ†ͳͻͺͲ••‘‡ʹͲǤ͹Ψˆ‡™‡”„ƒ„‹‡•Šƒ˜‡„‡‡„‘”‘—†ƒ›•–Šƒ‘‡†‡•†ƒ›•Ǥ •‹‹Žƒ”’ƒ––‡”ƒ’’‡ƒ”•ˆ‘”ƒ–—”†ƒ›•ƒ†‘•–‘ˆ–Š‡Š‘Ž‹†ƒ›•ǤŠ‹Ž‡ʹǤͶ؏‘”‡„ƒ„‹‡•Šƒ˜‡ „‡‡ „‘” ‘ Š”‹•–ƒ• –Šƒ ‘ ƒ˜‡”ƒ‰‡ „‡–™‡‡ ͳͻʹͲ ƒ† ͳͻͶͻǡ ƒŽ‘•– ͳ͸Ψ ˆ‡™‡” „ƒ„‹‡• Šƒ˜‡„‡‡„‘”‘Š”‹•–ƒ•–Šƒ‘ƒ˜‡”ƒ‰‡„‡–™‡‡ͳͻ͹Ͳƒ†ͳͻͺͻǤ‰ƒ‹–Š‹•†‡˜‡Ž‘’‡– ƒ›„‡‡š’Žƒ‹‡†„›‹’”‘˜‡†’‘••‹„‹Ž‹–‹‡•‘ˆ‡†‹…ƒŽ–”‡ƒ–‡–ǡ‹…”‡ƒ•‹‰–Š‡‘’–‹‘•–‘ƒ˜‘‹† „‹”–Š•ƒ–†ƒ›•™‹–Šƒ”‡Žƒ–‹˜‡Ž›Ž‘™•–ƒˆˆ‹‰ƒ–‘„•–‡–”‹…™ƒ”†•Ǥ Š‡”‡•—Ž–•ˆ‘”–Š‡†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•†‡•…”‹„‹‰–Š‡‘–Šƒ†›‡ƒ”‘ˆ„‹”–Šǡ™Š‹…Šƒ”‡‘– •Š‘™ ‹ –ƒ„Ž‡ͳ „—– ƒ”‡ ƒ˜ƒ‹Žƒ„Ž‡ ˆ”‘ –Š‡ ƒ—–Š‘”• —’‘ ”‡“—‡•–ǡ ƒ”‡ ‹ ƒ……‘”†ƒ…‡ ™‹–Š ‡š‹•–‹‰ ‡˜‹†‡…‡Ǥ ’‡…‹ˆ‹…ƒŽŽ›ǡ „‹”–Š ˆ”‡“—‡…‹‡• ‹ ‘—” †ƒ–ƒ •Š‘™ –Š‡ —•—ƒŽ •‡ƒ•‘ƒŽ ’ƒ––‡”ǡ „‡‹‰‘”‡Ž‹‡Ž›ƒ––Š‡„‡‰‹‹‰‘ˆ–Š‡›‡ƒ”•–ƒ”–‹‰‹ ‡„”—ƒ”›ƒ†Ž‡••Ž‹‡Ž›‹‹†•—‡” ƒ† ƒ– –Š‡ ‡† ‘ˆ –Š‡ ›‡ƒ”Ǥ —”–Š‡”‘”‡ –Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• ‘ˆ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• †‡•…”‹„‹‰–Š‡›‡ƒ”‘ˆ„‹”–Š”‡ˆŽ‡…––Š‡‘˜‡”ƒŽŽ†‡˜‡Ž‘’‡–‘ˆ„‹”–Š”ƒ–‡•‹ ‡”ƒ›™‹–ŠŽ‘™‡” ”ƒ–‡•‹–Š‡‰”‡ƒ–†‡’”‡••‹‘‹–Š‡ͳͻʹͲ•ƒ†–Š‡„ƒ„›„‘‘‹–Š‡ͳͻ͸Ͳ•Ǥ ‹ƒŽŽ›ǡ –Š‡ ‡š’Žƒƒ–‘”› ’‘™‡” ‘ˆ ‘—” ”‡‰”‡••‹‘ ‘†‡Ž †‡…”‡ƒ•‡• ‘˜‡” –‹‡ ƒ† Š‡…‡ǡ ƒŽ•‘ •—’’‘”–• ‘—” ‹–‡”’”‡–ƒ–‹‘ –Šƒ– ‹’”‘˜‡† ‡†‹…ƒŽ –‡…Š‘Ž‘‰› †‡…”‡ƒ•‡ –Š‡ ‹’ƒ…– ‘ˆ ƒ–—”ƒŽ ˆƒ…–‘”• †‡–‡”‹‹‰ –Š‡ —„‡” ‘ˆ „‹”–Š•Ǥ Š‹Ž‡ –Š‡ ƒ†Œ—•–‡† ʹ ‹†‹…ƒ–‡• –Šƒ– ™‡ ƒ”‡ ƒ„Ž‡ –‘ ‡š’Žƒ‹‘”‡–ŠƒͻͷΨ‘ˆ–Š‡˜ƒ”‹ƒ–‹‘‘ˆ‘—”†‡’‡†‡–˜ƒ”‹ƒ„Ž‡ˆ‘”’‡”•‘•„‘”„‡ˆ‘”‡ͳͻͷͲǡ –Š‡ •ƒ‡ ‘†‡Ž ‡š’Žƒ‹• ‘Ž› ƒ„‘—– ͺͻΨ ‘ˆ –Š‡ ˜ƒ”‹ƒ–‹‘ ‘ˆ –Š‡ —„‡” ‘ˆ †ƒ‹Ž› „‹”–Š• ‹ –Š‡ ͳͻ͹Ͳ•ƒ†ͳͻͺͲ•Ǥ

Discussion ‘ˆ‹”‹‰ ‡š‹•–‹‰ ‡˜‹†‡…‡ ˆ‘” ‘–Š‡” …‘—–”‹‡•ǡ –Š‡ ˆ”‡“—‡…› ‘ˆ „‹”–Š• ‹ ‡”ƒ› †‘‡• ‘– •‡‡–‘„‡”‡Žƒ–‡†–‘–Š‡Ž—ƒ”…›…Ž‡Ǥ‘™‡˜‡”ǡ„‹”–Š•ƒ”‡ƒ’’ƒ”‡–Ž›”‡Žƒ–‡†•‹‰‹ˆ‹…ƒ–Ž›–‘–Š‡ —„‡”‘ˆ•—•’‘–•ǡ‡˜‡–Š‘—‰Š‹“—ƒ–‹–ƒ–‹˜‡–‡”•–Š‡‡ˆˆ‡…–‘ˆ–Š‡•‘Žƒ”…›…Ž‡‘„‹”–Š•‹• •ƒŽŽǤ ‡…‡ǡ ™Š‹Ž‡ ‘—” ”‡•—Ž–• ƒ› Š‡Ž’ ™ƒ”†‹‰ ‘ˆˆ –Š‡ …‘‘ •—’‡”•–‹–‹‘• ”‡‰ƒ”†‹‰ –Š‡ ‡ˆˆ‡…–• ‘ˆ –Š‡ Ž—ƒ” …›…Ž‡ǡ ‘—” ”‡•—Ž–• ƒ› •—’’‘”– ‘–Š‡”ǡ ƒŽ„‡‹– Ž‡•• …‘‘ „‡Ž‹‡ˆ• ƒ„‘—– –Š‡ ‹ˆŽ—‡…‡‘ˆ–Š‡•—‘Š—ƒˆ‘”–—‡Ǥ —”‡’‹”‹…ƒŽƒƒŽ›•‹•ƒ‡••–”‘‰‡ˆˆ‘”–•–‘ƒ˜‘‹†–Šƒ–™‡Œ—•–‡ƒ•—”‡ƒ•–ƒ–‹•–‹…ƒŽƒ”–‹ˆƒ…–Ǥ ‡ —•‡ ƒ Š—‰‡ •ƒ’Ž‡ …‘˜‡”‹‰ ƒŽ‘•– –Š‡ ‡–‹”‡ ‡”ƒ ’‘’—Žƒ–‹‘ „‘” „‡–™‡‡ ͳͻʹͲ ƒ† ͳͻͺͻǤ‡…‡ǡ„‹ƒ•‡†‡•–‹ƒ–‹‘”‡•—Ž–•†—‡–‘•ƒ’Ž‡•‡Ž‡…–‹‘’”‘„Ž‡•†‘‘–ƒ’’‡ƒ”–‘„‡ƒ ’”‘„Ž‡Ǥ Ž•‘ǡ „› —•‹‰ —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ƒƒŽ›•‹• –Šƒ– …‘–”‘Ž• ˆ‘” ƒ ˜ƒ•– —„‡” ‘ˆ 9

’‘–‡–‹ƒŽ…‘ˆ‘—†‹‰ˆƒ…–‘”•ǡ™‡–”›–‘ƒ˜‘‹†’”‘„Ž‡•‘ˆ•’—”‹‘—•”‡‰”‡••‹‘Ǥ‡˜‡”–Š‡Ž‡••ǡ™‡ ƒ› Šƒ˜‡ ‹••‡† •‘‡ ’‘–‡–‹ƒŽ ‘–Š‡” †‡–‡”‹ƒ–• ‘ˆ –Š‡ †ƒ‹Ž› ˆ”‡“—‡…› ‘ˆ –Š‡ —„‡” ‘ˆ „‹”–Š•–Šƒ–‹‰Š–„‡…‘””‡Žƒ–‡†™‹–Š–Š‡—„‡”‘ˆ•—•’‘–•Ǥ˜‡–Š‘—‰Š…‘•‹•–‡–•…‹‡–‹ˆ‹… ”‡•—Ž–•ƒ”‡•–‹ŽŽ‹••‹‰ǡ‹–ƒ›„‡–Š‡…ƒ•‡–Šƒ–•—•’‘–•‹ˆŽ—‡…‡–Š‡…Ž‹ƒ–‡ǡ‹Ǥ‡Ǥ–‡’‡”ƒ–—”‡ǡ Š—‹†‹–› ‘” „ƒ”‘‡–”‹… ’”‡••—”‡Ǥ ‘ –Š‡ ‡š–‡– –Šƒ– –Š‡•‡ ˜ƒ”‹ƒ„Ž‡• ƒŽ•‘ ƒˆˆ‡…– „‹”–Š•ǡ ‘—” ‡’‹”‹…ƒŽ”‡•—Ž–•ƒ›„‡„‹ƒ•‡†Ǥ˜‡”ƒŽŽǡ‘—””‡•—Ž–••—‰‰‡•––Šƒ–ˆ—”–Š‡”•–ƒ–‹•–‹…ƒŽƒ†‡†‹…ƒŽ ‹˜‡•–‹‰ƒ–‹‘•‘ˆ–Š‡†‡–‡”‹ƒ–•‘ˆ„‹”–Š••Š‘—Ž†…‘…‡–”ƒ–‡‘”‡‘–Š‡•‘Žƒ”ƒ†‘–‘–Š‡ Ž—ƒ”…›…Ž‡Ǥ —” ”‡•—Ž–• …‘˜‡› –™‘ ‡••ƒ‰‡•ǡ ‘‡ ‹•–‹‰ƒ–‹‰ Š‘’‡ ‹ Š—ƒ ’”‘‰”‡•• ƒ† –Š‡ ‘–Š‡” ‡Žƒ…Š‘Ž›Ǥ‘•–‹’‘”–ƒ–Ž›ǡ™‡ˆ‹†ƒ’Ž‡”‡ƒ•‘–‘•–”‡‰–Š‡‘—”…‘ˆ‹†‡…‡‹‘†‡”‡”ƒ Š‡ƒŽ–Š •›•–‡•Ǥ ƒ–—”ƒŽ ’Š‡‘‡ƒǡ ‹– ‹• –”—‡ǡ •Šƒ’‡ Š—ƒ ‡š’‡”‹‡…‡ ‹ ˆ—†ƒ‡–ƒŽ ™ƒ›•ǡ ‡˜‡ ‹ˆŽ—‡…‹‰ –Š‡ †ƒ› ‘ˆ „‹”–ŠǤ ‹…‡ ‹ ‘†‡” •‘…‹‡–‹‡• Š‡ƒŽ–Š …ƒ”‡ ‹• •›•–‡ƒ–‹…ƒŽŽ› ‘”‰ƒ‹œ‡† ƒ……‘”†‹‰ –‘ –Š‡ ™‘” ™‡‡ǡ ™‹–Š Ž‘™‡” •–ƒˆˆ‹‰ ‘ˆ Š‘•’‹–ƒŽ• ‘ ™‡‡‡†•ǡ –Š‡ †‹˜‡”‰‡…‡„‡–™‡‡ƒ–—”‡ƒ†Š—ƒ‘”‰ƒ‹œƒ–‹‘…‘—Ž†‰‡‡”ƒ–‡’”‘„Ž‡•Ǥ‘–Š‡”•™Š‘ƒ”‡ ˆ‘ŽŽ‘™‹‰ƒ–—”‡ǯ•…‘—”•‡™Š‹…Šƒ–Ž‡ƒ•––‘•‘‡‡š–‡–‹•‹ˆŽ—‡…‡†„›–Š‡•‘Žƒ”…›…Ž‡ǡƒ†‰‘ ‹–‘ Žƒ„‘” ‘ ƒ ™‡‡‡†ǡ ‹‰Š– ”‡…‡‹˜‡ Ž‡•• ‘„•–‡–”‹… ƒ––‡–‹‘ǡ •‹…‡ Š‘•’‹–ƒŽ •–ƒˆˆ‹‰ ‹• ‰‘˜‡”‡†„›Š—ƒ”—Ž‡•‹•–‡ƒ†Ǥ—–ƒ––Š‡•ƒ‡–‹‡ƒ•–Š‡‘”‰ƒ‹œƒ–‹‘‘ˆŠ‡ƒŽ–Š•›•–‡•Šƒ• ƒ†ƒ’–‡†–‘–Š‡†‡ƒ†•‘ˆƒ‘†‡”‡…‘‘›ǡ–‡…Š‘Ž‘‰‹…ƒŽ…ƒ’ƒ…‹–‹‡•Šƒ˜‡‹’”‘˜‡†‹•–‡’ǡ ƒ†–Š‡‹ˆŽ—‡…‡‘ˆ–Š‡•‘Žƒ”…›…Ž‡‘–Š‡–‹‹‰‘ˆ„‹”–Š•Šƒ•‡ˆˆ‡…–‹˜‡Ž›„‡‡‡Ž‹‹ƒ–‡†Ǥ—–ƒ• —…Šƒ•™‡‹‰Š–…‡Ž‡„”ƒ–‡–Š‡‡ˆˆ‡…–‹˜‡ƒ†‡“—‹–ƒ„Ž‡–”‡ƒ–‡–™Š‹…Š‘†‡”Š‡ƒŽ–Š•›•–‡• ‘ˆˆ‡”–Š‡‹”…Ž‹‡–•ǡ–Š‹•…‘…Ž—•‹‘†‘‡•‘–Œ—•–‹ˆ›ƒ—“—ƒŽ‹ˆ‹‡†ƒ’‘–Š‡‘•‹•‘ˆ’”‘‰”‡••Ǥ‡––‡” Š‡ƒŽ–Š …ƒ”‡ †‡Ž‹˜‡”›ǡ ‹– •‡‡•ǡ ‹• —ƒ˜‘‹†ƒ„Ž› ƒ……‘’ƒ‹‡† „› Ž‘•‹‰ ›‡– ƒ‘–Š‡” ˆƒ…‡– ‘ˆ –Š‡ †‹˜‡”•‹–›‘ˆŠ—ƒ‡š‹•–‡…‡Ǥ

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References

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