Produced by Turgut Dincer, Chris Pinfield, and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) Transcriber's Note: Apparent typographical errors have been corrected. Italics are indicated by _underscores_. Small capitals have been replaced by full capitals. The corrections noted in the Errata section have been incorporated in the text. Two further corrections have also been made: 9/10 in place of 1/10, and 9/10 in place of 6/10, on page 110; and "ex voto" in place of "ex veto" on page 173. A PHILOSOPHICAL ESSAY ON PROBABILITIES. BY PIERRE SIMON, MARQUIS DE LAPLACE. _TRANSLATED FROM THE SIXTH FRENCH EDITION_ BY FREDERICK WILSON TRUSCOTT, PH.D. (HARV.), _Professor of Germanic Languages in the West Virginia University_, AND FREDERICK LINCOLN EMORY, M.E. (WOR. POLY. INST.), _Professor of Mechanics and Applied Mathematics in the West Virginia University; Mem. Amer. Soc. Mech. Eng._ _FIRST EDITION._ FIRST THOUSAND. NEW YORK: JOHN WILEY & SONS. LONDON: CHAPMAN & HALL, LIMITED. 1902. Copyright, 1902, BY F. W. TRUSCOTT AND F. L. EMORY. ROBERT DRUMMOND PRINTER, NEW YORK TABLE OF CONTENTS. PAGE PART I. _A PHILOSOPHICAL ESSAY ON PROBABILITIES._ CHAPTER I. Introduction 1 CHAPTER II. Concerning Probability 3 CHAPTER III. General Principles of the Calculus of Probabilities 11 CHAPTER IV. Concerning Hope 20 CHAPTER V. Analytical Methods of the Calculus of Probabilities 26 PART II. _APPLICATION OF THE CALCULUS OF PROBABILITIES._ CHAPTER VI. Games of Chance 53 CHAPTER VII. Concerning the Unknown Inequalities which may Exist among Chances Supposed to be Equal 56 CHAPTER VIII. Concerning the Laws of Probability which result from the Indefinite Multiplication of Events 60 CHAPTER IX. Application of the Calculus of Probabilities to Natural Philosophy 73 CHAPTER X. Application of the Calculus of Probabilities to the Moral Sciences 107 CHAPTER XI. Concerning the Probability of Testimonies 109 CHAPTER XII. Concerning the Selections and Decisions of Assemblies 126 CHAPTER XIII. Concerning the Probability of the Judgments of Tribunals 132 CHAPTER XIV. Concerning Tables of Mortality, and the Mean Durations of Life, Marriage, and Some Associations 140