Chapter 3. Probability of Events and of Their Causes: The Origin of Statistical Inference

Chapters in this book

1. Frontmatter i
2. Content v
3. Preface vii
4. Acknowledgment xi
5. PART I: EARLY CAREER, 1768-1778
6. Chapter 1. Youth, Education, and Election to the Academy 3
7. Chapter 2. Finite Differences, Recurrent Series, and Theory of Chance 7
8. Chapter 3. Probability of Events and of Their Causes: The Origin of Statistical Inference 13
9. Chapter 4. Universal Gravitation 29
10. Chapter 5. Distribution of Comets 38
11. Chapter 6. Partial Differential Equations, Determinants, and Variation of Constants 44
12. Chapter 7. The Figure of the Earth and the Motion of the Seas 51
13. PART II: LAPLACE IN HIS PRIME, 1778-1789
14. Chapter 8. Influence and Reputation 67
15. Chapter 9. Variation of Constants, Differential Operators 70
16. Chapter 10. Probability Matured 72
17. Chapter 11. Generating Functions and Definite Integrals 86
18. Chapter 12. Population 93
19. Chapter 13. Determination of the Orbits of Comets 96
20. Chapter 14. Lavoisier and Laplace: Chemical Physics of Heat 101
21. Chapter 15. Attraction of Spheroids 109
22. Chapter 16. Planetary Astronomy 124
23. PART III: SYNTHESIS AND SCIENTIFIC STATESMANSHIP
24. Chapter 17. The Revolution and the Metric System 149
25. Chapter 18. Scientific Work in the Early Revolution 156
26. Chapter 19. Exposition du système du monde 166
27. Chapter 20. A Scientific Eminence 176
28. Chapter 21. Traité de mécanique céleste 184
29. PART IV: LAPLACIAN PHYSICS AND PROBABILITY
30. Chapter 22. The Velocity of Sound 199
31. Chapter 23. Short-Range Forces 203
32. Chapter 24. The Laplacian School 209
33. Chapter 25. Theory of Error 216
34. Chapter 26. Probability: Théorie analytique and Essai philosophique 224
35. Chapter 27. Loss of Influence 243
36. Chapter 28. The Last Analysis 250
37. PART V: THE LAPLACE TRANSFORM
38. Chapter 29. Laplace's Integral Solutions to Partial Differential Equations 259
39. Conclusion 271
40. Abbreviations 280
41. Bibliography 281
42. Index 319