Studies of Pallas in the Early Nineteenth Century: Historical Studies in Asteroid Research

484 Pages·2017·21.29 MB·English

by  Clifford J. Cunningham (auth.)

Clifford J. Cunningham
Studies of
Pallas in
the Early
Nineteenth
Century
Historical Studies
in Asteroid Research
Second Edition
Studies of Pallas in the Early Nineteenth Century
Clifford J. Cunningham
Studies of Pallas in the Early
Nineteenth Century
Historical Studies in Asteroid Research
Second Edition
123
Clifford J.Cunningham
Fort Lauderdale, FL
USA
This book was originally self-published in softcover in 2004 by the author and was called
ThePallasProblem.Inthisneweditionitissubstantiallyrevisedwithmuchnewmaterialand
new translations.
ISBN978-3-319-32846-1 ISBN978-3-319-32848-5 (eBook)
DOI 10.1007/978-3-319-32848-5
LibraryofCongressControlNumber:2016948619
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Preface
In his treatise On the Problem of the Historian, Wilhelm von Humboldt states his
views succinctly. “The problem of the historian is to tell what actually happened.
Themoreexactlyandcompletelyhesucceeds,themoreperfectlyhehassolvedthat
problem.” In the three books of this series to date, I have tried to put Humboldt’s
precept into practice.
First,bypublishingallofthelettersandscientificpapersdealingwithCeresand
Pallas, the reader can examine exactly what was being thought and written by all
the eminent astronomers of the time. Most of these letters have never been pub-
lished before, and this is the first time they have ever appeared in English. Also,
William Herschel’s first two studies of Ceres and Pallas are given, along with an
analysis of vicious contemporary critiques, one of which equated his work with
evil.
Second,thisbookisdeeplygroundedinphilosophytoestablishtheconceptsand
ideasthatmotivatedtheresearchandidealsofthoseastronomers.Forexample,ina
study of the Paris Institute prize for a study ofPallas’ orbit, Ishow why a mindset
existed that led eminent scientists to think that all problems were solvable. Prizes
offered by the academies of Paris and Berlin are surveyed to put the Pallas prize
question in context. Other issues are related to such diverse philosophical discus-
sions as Rene Descartes’ Optics; John Locke’s writing on language and ideas;
Joseph Priestley’s psychology of association; theories of reference to explore
J.-J.Lalande’sinsistenceonabjuringclassicalnamesfornewplanetarydiscoveries;
gap theory by Adam Smith; David Hume’s principle of resemblance; the concepts
ofanachronism,analogyanddoubt;ThomasYoung’sanalysisofhypothesisversus
theory; Christian Wolff’s deductive reasoning as applied to planetary distances;
the theoretical and linguistic systems of Pierre Duhem; the intellectual antecedents
of Laplace’s concept of Intelligence in a deterministic cosmos; and the school of
Scottish Common Sense Realism. The study of aesthetics by Francis Hutcheson,
fatheroftheScottishEnlightenment,isusedtorelatetheconceptsofharmonyand
proportion that stretched from Pythagoras to Johannes Kepler to Capel Lofft. The
relationships between Giuseppe Piazzi (discoverer of Ceres), the muse Urania,
Apollo’s lyre and the music of spheres are explored in part through a Latin poem
v
vi Preface
by Tycho Brahe. This book shows how Pallas wrote the final movement to the
symphony of celestial harmony.
The‘geometricbeam’perceivedatthegreatLibraryinAlexandriabytheRoman
traveler Ammianus Marcellinus illuminates this story of Pallas. The geometrical
structure of space is shown to be fundamental in understanding how the orbit of
Pallaswasdeterminedandstudied.ThisisexaminedthroughtheworkdonebyCarl
Gauss and others on the perturbations Pallas is subjected to. As the nineteenth
century Prussian military theorist Carl von Clausewitz observed: “Although our
intellect always longs for clarity and certainty, our nature often finds uncertainty
fascinating.” Nowhere is this human fascination more evident than in the work on
perturbation theory. Even the glittering allure of a gold prize from the Paris
Academywas notsufficientincentive tofullysolve theprobleminanagethathad
no recourse to computational tools. All the literature dealing with the gold prize is
presented in this book for the first time, as well as a unique solution to the Gauss
anagram, a method Gauss used to ensure the priority of his remarkable orbital
discovery about Pallas. His Latin treatise on Pallas is also published here for the
first time in English.
The chance that there was an unobserved planet between Mars and Jupiter led
BaronvonZachtoorganizeasearchforitin1800.Chanceofadifferentfeather,in
theformofprobabilitytheory,isanothermajorelementofthisbookasastronomers
and mathematicians sought to elucidate the orbits and origin of the asteroids.
Thisbookopenswiththelong-forgottenfactthattheorbitalelementsofaplanet
between Mars and Jupiter were first printed in 1681. The missing planet idea that
animated astronomers from Kepler to Zach is the perfect example of what
the British historian of science A. Rupert Hall (1962a: 188) meant when he said,
“The history of science derives its coherence less from the temporal succession of
events than from the continuity of ideas.” He went on to say that “while not
neglecting the work of the scientist’s hands the historian has to look more deeply
forthethoughtthatguidedthatworkandgaveitatheoreticalstructure.”Thisbook,
thoroughly revised and updated from its first edition in 2004, examines both the
thoughtandtheoreticalstructurecreatedbytheastronomersandmathematiciansin
the early nineteenth century as they grappled with the existence of not just one
missing planet but two.
Fort Lauderdale, FL, USA Clifford J. Cunningham
Acknowledgments
Asalwaysgreatthanksgotomytranslatorsforprovidingarichharvestoforiginal
material rendered into English: Telse Wokersien (German and French text); James
Lequeux(Frenchtext);ChristopherGordonandRogerCeragioli(Latintext);Piero
Sicoli (Italian text).
Thanks to my dear friend the late A.C. Addington for his genealogical diagram
in Chap. 4. David Glynn for his unique explanation of the Gauss anagram. John
RamseyandBobMunmanfortheirexpertiseinclassicalhistory,andAriBelenkiy
in mathematics. The paper by Tittel was provided by Andras Holl of Konkoly
Observatory, Budapest. Valuable contributions were also made by Magda Vargha
of Budapest and Paul Feldman of the National Research Council of Canada.
InadvertentlycertainpassagesinDiscoveryoftheFirstAsteroid,Ceres,werenot
properlyattributed.Theparagraphonpg.66beginningwith“Thevariousthemes”
is from an anonymous review in Der neue Teutsche Merkur (1802) vol. 2, no. 6.
(June1802),135–48.Thepassageattheendofpg.66,beginningwith“Allthese”
and which is in quotes, is a personal communication from Doug Stott. The phrase
on pg. 66 “was quite the sensation just after the turn of the century” also should
have been attributed to Stott.
IllustrationsunlessotherwisecreditedarecourtesyofWikimediaCommons.The
attributionoftheportraitofMaskelynegivenintheDiscoveryoftheFirstAsteroid,
Ceres is not secure, but the image of Maskelyne given in this book is definitive.
Variousportionsofthisbookandtheotherbooksinthisseriesderivedirectlyfrom
my unpublished PhD thesis at the University of Southern Queensland. The next
bookintheserieswilldealwiththediscoveryandearlystudyoftheasteroidsJuno
and Vesta.
vii
Contents
1 A Disturbing Inclination. ..... .... .... .... .... .... ..... .... 1
Bernoulli and the First Orbital Properties of Ceres in 1681. ..... .... 1
The End of Heavenly Harmony: The Perturbations of Pallas .... .... 4
The Temple of Natural Philosophy... .... .... .... .... ..... .... 7
The Orbit of Pallas and the Geometrical Structure of Space..... .... 11
The Mass of Jupiter . .... ..... .... .... .... .... .... ..... .... 16
Laplace and the Grand Inequality.... .... .... .... .... ..... .... 19
References. .... .... .... ..... .... .... .... .... .... ..... .... 20
2 The Great Probability Debate . .... .... .... .... .... ..... .... 23
The Legacy of Leibniz ... ..... .... .... .... .... .... ..... .... 23
The Most Delicate of Mathematical Theories ... .... .... ..... .... 28
The Historical Development of Probability. .... .... .... ..... .... 30
Equipossibility.. .... .... ..... .... .... .... .... .... ..... .... 35
Analogy and Probability.. ..... .... .... .... .... .... ..... .... 37
The Origin of the Asteroids and the Twilight of Probability..... .... 38
The Invention of Least Squares.. .... .... .... .... .... ..... .... 43
Gauss and Laplace: The Mathematical Link .... .... .... ..... .... 47
References. .... .... .... ..... .... .... .... .... .... ..... .... 49
3 The Gold Medal ... .... ..... .... .... .... .... .... ..... .... 53
Astronomy and the Republic of Letters.... .... .... .... ..... .... 53
Rivalry ... .... .... .... ..... .... .... .... .... .... ..... .... 59
Reason and the Axiom of Solvability. .... .... .... .... ..... .... 60
The Berlin Academy Prize ..... .... .... .... .... .... ..... .... 65
The Paris Academy Prize . ..... .... .... .... .... .... ..... .... 67
The Pallas Prize .... .... ..... .... .... .... .... .... ..... .... 70
The Prize Is Doubled .... ..... .... .... .... .... .... ..... .... 73
The Prize and the Perturbation Calculations: A Timeline .. ..... .... 76
Lalande and the Asteroids. ..... .... .... .... .... .... ..... .... 76
ix
x Contents
The Lack of Theoretical Work in England . .... .... .... ..... .... 78
Scottish Common Sense Realism: Brougham, Stewart, and Reid . .... 81
Contemporary Views on the State of Astronomy in Great Britain. .... 83
References. .... .... .... ..... .... .... .... .... .... ..... .... 89
4 The Gauss Anagram.... ..... .... .... .... .... .... ..... .... 93
The Origin of the Anagram..... .... .... .... .... .... ..... .... 93
Concinnity. .... .... .... ..... .... .... .... .... .... ..... .... 95
The Solution of the Gauss Anagram.. .... .... .... .... ..... .... 97
Gauss and the Royal Society.... .... .... .... .... .... ..... .... 98
Gauss gives up . .... .... ..... .... .... .... .... .... ..... .... 100
The Royal Patrons... .... ..... .... .... .... .... .... ..... .... 102
References. .... .... .... ..... .... .... .... .... .... ..... .... 103
5 Hypothetical Planets .... ..... .... .... .... .... .... ..... .... 105
Ludwig’s Star .. .... .... ..... .... .... .... .... .... ..... .... 105
Vidal’s Planet .. .... .... ..... .... .... .... .... .... ..... .... 105
Olbers’ Giant Planet . .... ..... .... .... .... .... .... ..... .... 108
Huth’s Moving Star.. .... ..... .... .... .... .... .... ..... .... 108
Cassini’s Planet of 1668 .. ..... .... .... .... .... .... ..... .... 111
Cacciatore’s Planet .. .... ..... .... .... .... .... .... ..... .... 112
References. .... .... .... ..... .... .... .... .... .... ..... .... 114
6 New Planets: The Transition from 1745 to 1804... .... ..... .... 115
The Planetary Gap... .... ..... .... .... .... .... .... ..... .... 115
A Wild and Romantic Idea..... .... .... .... .... .... ..... .... 118
Olbers’ Asteroid Lectures . ..... .... .... .... .... .... ..... .... 126
The First Lecture (October 25, 1802) . .... .... .... .... ..... .... 127
The Second Lecture (Late 1803). .... .... .... .... .... ..... .... 134
Hypothesis and Theory... ..... .... .... .... .... .... ..... .... 141
Lalande’s Planetary Nomenclature ... .... .... .... .... ..... .... 143
Pallas: Chemistry in 1803. ..... .... .... .... .... .... ..... .... 145
References. .... .... .... ..... .... .... .... .... .... ..... .... 147
7 The Olbers Letters . .... ..... .... .... .... .... .... ..... .... 149
Introduction to the Letters. ..... .... .... .... .... .... ..... .... 149
Magnitudes of Ceres of Pallas .... .... .... .... .... ..... .... 149
Mutual Orbital Properties of Ceres and Pallas... .... .... ..... .... 151
The Letters .... .... .... ..... .... .... .... .... .... ..... .... 152
References. .... .... .... ..... .... .... .... .... .... ..... .... 156
8 The Gauss Letters.. .... ..... .... .... .... .... .... ..... .... 157
References. .... .... .... ..... .... .... .... .... .... ..... .... 214
9 The Harding Letters.... ..... .... .... .... .... .... ..... .... 215
References. .... .... .... ..... .... .... .... .... .... ..... .... 233
Contents xi
10 Herschel’s Asteroids .... ..... .... .... .... .... .... ..... .... 235
Herschel’s First Paper of 1802: Ceres. .... .... .... .... ..... .... 235
Herschel’s Second Paper of 1802: Ceres and Pallas .. .... ..... .... 237
Observations on the Two Lately Discovered Celestial Bodies.... .... 237
The Definition of an Asteroid... .... .... .... .... .... ..... .... 248
Critiques of Herschel’s Paper on Ceres and Pallas ... .... ..... .... 251
Two Ladies and a Comet . ..... .... .... .... .... .... ..... .... 260
Thomas Kuhn’s Paradigm Shift.. .... .... .... .... .... ..... .... 267
References. .... .... .... ..... .... .... .... .... .... ..... .... 268
11 Scientific Papers ... .... ..... .... .... .... .... .... ..... .... 271
References. .... .... .... ..... .... .... .... .... .... ..... .... 410
12 Gauss: The Great Asteroid Treatises.... .... .... .... ..... .... 411
References. .... .... .... ..... .... .... .... .... .... ..... .... 447
Appendix A... .... .... .... ..... .... .... .... .... .... ..... .... 449
Appendix B... .... .... .... ..... .... .... .... .... .... ..... .... 467
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 473