by Russell McNeil, PhD

Author also of: The Meditations of Marcus Aurelius: Selections Annotated and Explained

TheMechanism of the Heavenswas the first english language "rendition" of Pierre Simon Laplace's five volumeMécanique céleste.In this work Somerville, who was later known for her predition of the then undiscovered planets Neptune and Pluto, introduced continental mathematics to english speaking readers for the first time This led to a revolution in mathematics in the UK, beginning at Cambridge University where theMechanism of the Heavensbecame a standard text in courses on higher mathematics.

This second edition ofMechanism of the Heavensis designed to address not only its scarcity, but several deficiencies in the first edition. These include the correction of 140 reported errata and a significant number of unreported errata in the 1831 edition. The unreported errata include obvious printing errors such as page repeats, mislabeled chapters, and obvious printing related mathematical errata. All changes to the text have been clearly identified and the original expressions included in notes at the end of each chapter. We have made no attempt to challenge the mathematical integrity of this work. TheCritical Reviewswritten in 1832 and included in this second edition clearly document the importance of the original text in altering the trajectory of 19th century mathematics in the English speaking world. This annotated second edition includes short biographies of numerous 19th century mathematicians and scientists referred to in the first edition (most of whom were known to Somerville). New non-mathematical annotatedForewordsto each of the four Books ofMechanism of the Heavensare drawn exclusively from Somerville's own clear writing on selected topics in Celestial Mechanics published in the 10th and final edition of her popular textOn the Connexion of the Physical Sciences(1877). Somerville, who was completely self taught, was considered as one of only a handful of english speaking mathematicians able to undertake this work and was praised lavishly by many of the leading scientists, mathematicians and other intellectuals of her day including James Clerk Maxwell, Charles Darwin, Michael Faraday, Sir Charles Lyell and John Stuart Mill. The work is divided into four major books onDynamics,Universal Gravitation,Lunar Theory, and TheSatellites of Jupiter. The substantialPreliminary Dissertationtogether with the newForewordsto each book provide the non-technical reader sufficient background to appreciate the significance of this work. The appendicies include four contemporary critical reviews, a revised subject index and a new name index.

The editor is indebted to the assistance provided by Somerville College, Oxford, during the research phase of this project. College Librarian and Archivist Ms. P. Adams was generous in providing advice and materials. College Secretary Ms. Norma MacManaway and Ms. Anne Wheatley provided access to College resources and accommodation and Mr. Chris Bamber provided computer assistance. I would also like to extend my appreciation to Professor A. Morpurgo Davies for additional direction. The archivists, librarians and staff of the Bodleian Library, Oxford, were especially helpful and generous in answering many questions and providing free access to the Mary Somerville Collection and related documents. The more than 5,000 items in that Collection were sorted and catalogued by Elizabeth Chambers Patterson beginning in 1967. That archival work culminated in the publication in 1983 of her extraordinarily thoroughMary Somerville and the Cultivation of Science 1815-1840, an invaluable source for students of Mary Somerville. Cambridge University Press has also released a new publication on Somerville by Kathryn A. Neeley. This important workMary Somerville : Science, Illumination, and the Female Mindoffers new insight on the character of this extrordinary 19th century intellectual.

Russell McNeil, Ph.D.

Department of Physics, Engineering and Astronomy and,

Department of Liberal Studies

Malaspina University College

Mechanism of the Heavens (1831)

"All my other books will soon be forgotten, by this my name will be alone remembered..."

Mary Fairfax Greig Somerville

Foreword to the Second Edition

Read the Original Critical Reviews of

ISBN 1-896886-36-1

(816 p. in 61 pdf files)

Somerville Portrait and Copyright Information p. ii

1st Edition Dedication by Mary Somerville (July 21st, 1831) p. iii

2nd Edition Dedication by Russell McNeil (September 1st, 2001) p. iv

Table of Contents (print version) p. v-xvi

Acknowledgements (2nd Edition) p. xvii-xviii

Foreword to the 2nd Edition p. xix-xxvi

Glossary of Symbols and List of Images p. xxvii-xxx

Somerville Introduction - Physical Astronomy p. 41-43

Chapter I Definitions, Axioms, etc. p. 65-78

Chapter II Variable Motion p. 79-110

Chapter III On the Equilibrium of a System of Bodies p. 111-126

Chapter IV Motion of a System of Bodies p. 127-140

Chapter V The Motion of a Solid Body of any Form Whatever p. 141-168

Chapter VI On the Equilibrium of Fluids p. 169-176

Chapter VII Motion of Fluids p. 177-205

Foreword to Book II - Universal Gravitation p. 207-218

Chapter I Progress of Astronomy p. 219-223

*NASA Image of Venus* p. 224

Chapter II On the Law of Universal Gravitation, Deduced from Observation p. 225-240

Chapter III On the Differential Equations of the Motion of a System of Bodies p. 241-253

*NASA Image of Mars* p. 254

Chapter IV On the Elliptical Motion of the Planets p. 255-285

*NASA Image of Saturn* p. 286

Chapter V Theory of the Perturbations of the Planets p. 287-328

Chapter VI Secular Inequalities in the Elements of the Orbits p. 329-370

Chapter VII Periodic Variations in the Elements of the Planetary Orbits p. 371-376

Chapter VIII Perturbations of the Planets in Longitude, Latitude, and Distance p. 377-386

Chapter IX Second Method of Finding the Perturbations of the Planets p. 387-409

*NASA Image of Jupiter* p. 410

Chapter X The Theory of Jupiter and Saturn p. 411-429

*NASA Image of The Sun* p. 430

Chapter XI Inequalities Occasioned by the Ellipticity of the Sun p. 431-434

Chapter XII Perturbations of the Planets Occasioned by their Satellites p. 435-437

*NASA Image of Uranus* p. 438

Chapter XIII Data for Computing the Celestial Motions p. 439-452

Chapter XIV Numerical Values of the Perturbations of Jupiter
p. 453-497

*NASA Image of Moon* p. 498

Chapter I Lunar Theory p. 509-550

Chapter II Numerical Values of the Coefficients p. 551-572

Chapter III Inequalities from the Form of the Earth p. 573-578

Chapter IV Inequalities from the Action of the Planets p. 579-586

Chapter V Effects of the Secular Variation in the Plane of the Ecliptic p. 587-590

Chapter VI Effects of an Ethereal Medium on the Motions of the Moon p. 591-602

Chapter I Theory of Jupiter's Satellites p. 611-650

Chapter II Perturbations of the Satellites in Latitude p. 651-670

Chapter III Numerical Values of the Perturbations p. 671-701

Chapter IV Eclipses of Jupiter's Satellites p. 703-727