Contents
Introduction  1
PART ONE
The Development of Mathematical Statistics in Astronomy and Geodesy before 1827  9
1. Least Squares and the Combination of Observations 11 Legendre in 1805
12
Cotes's Rule 16
Tobias Mayer and the Libration of the Moon 16
Saturn, Jupiter, and Euler 25
Laplace's Rescue of the Solar System 31
Roger Boscovich and the Figure of the Earth 39
Laplace and the Method of Situation 50
Legendre and the Invention of Least Squares 55
2. Probabilists and the Measurement of Uncertainty 62
Jacob Bernoulli 63
De Moivre and the Expanded Binomial 70
Bernoulli's Failure 77 De Moivre's Approximation 78
De Moivre's Deficiency 85
Simpson and Bayes 88
Simpson's Crucial Step toward Error 88
A Bayesian Critique 94
3. Inverse Probability 99
Laplace and Inverse Probability 100
The Choice of Means 105
The Deduction of a Curve of Errors in 1772-1774 109
The Genesis of Inverse Probability 113
Laplace's Memoirs of 1777-1781 117
The Error Curve of 1777 120
Bayes and the Binomial 122
Laplace the Analyst 131
Nonuniform Prior Distributions 135
The Central Limit Theorem 136
4. The Gauss -Laplace Synthesis 139
Gauss in 1809 140
Reenter Laplace 143
A Relative Maturity: Laplace and the Tides of the Atmosphere 148
The Situation in 1827 157
PART TWO
The Struggle to Extend a Calculus of Probabilities to the Social Sciences 159
5. Quetelet's Two Attempts 161
The de Keverberg Dilemma 163
The Average Man 169
The Analysis of Conviction Rates 174
Poisson and the Law of Large Numbers 182
Poisson and juries 186
Comte and Poinsot 194
Cournot's Critique 195
The Hypothesis of Elementary Errors 201
The Fitting of Distributions: Quetelismus 203
6. Attempts to Revive the Binomial 221
Lexis and Binomial Dispersion 222
Arbuthnot and the Sex Ratio at Birth 225
Buckle and Campbell 226
The Dispersion of Series 229
Lexis's Analysis and Interpretation 233
Why Lexis Failed 234
Lexian Dispersion after Lexis 237
7. Psychophysics as a Counterpoint 239
The Personal Equation 240
Fechner and the Method of Right and Wrong Cases 242
Ebbinghaus and Memory 254
PART THREE
A Breakthrough in Studies of Heredity 263
8. The English Breakthrough: Galton 265
Galton, Edgeworth, Pearson 266
Galton's Hereditary Genius and the Statistical Scale 267
Conditions for Normality 272
The Quincunx and a Breakthrough 275
Reversion 281
Symmetric Studies of Stature 283
Data on Brothers 290
Estimating Variance Components 293
Galton's Use of Regression 294
Correlation 297
9. The Next Generation: Edgeworth 300
The Critics' Reactions to Galton's Work 301
Pearson's Initial Response 302
Francis Ysidro Edgeworth 305
Edgeworth's Early Work in Statistics 307
The Link with Galton 311
Edgeworth, Regression, and Correlation 315
Estimating Correlation Coefficients 319
Edgeworth's Theorem 322
10. Pearson and Yule 326
Pearson the Statistician 327
Skew Curves 329
The Pearson Family of Curves 333
Pearson versus Edgeworth 338
Pearson and Correlation 342
Yule, the Poor Law, and Least Squares: The Second Synthesis 345
The Situation in 1900 358
Appendix A. Syllabus for Edgeworth's 1885 Lectures 363
Appendix B. Syllabus for Edgeworth's 1892  Newmarch Lectures 367
Suggested Readings 370
Bibliography 374
Bibliography
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