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This volume is an effort to bring together important contributions to the mathe matical development of demography and to suggest briefly their historical context. We have tried to find who first thought of the several concepts and devices commonly used by demographers, what sort of problem he was facing to which the device or concept seemed the solution, and how his invention developed subsequently in the hands of others. Historically, the book starts with a Roman table of life expectancies from the third century a. d. about which we know little, and with John Graunt's explora tions in an area that was still popularly suspect when he wrote in 1662. These are followed by the astronomer Halley, who looked into the field long enough to invent the life table and to notice that Their Majesties would take a sizeable loss on the annuity scheme they had just launched; and by Euler, who was first to devise the formulas of stable population theory and to apply them to filling gaps in data To these we add the handful of further contributions in the 19th century and many pieces from the explosion of contributions that began in this century with Lotka. We doubt that we have managed to trace everything back to its ultimate beginning, and suspect that our nominees in some cases have been anticipated by predecessors who will be turned up by other students.
The Life Table.- 1. Tables of Annuity Values Which Were Sanctioned by the Roman Law for the Purposes of the Lex Falcidia.- 2. Natural and Political Observations Mentioned in a Following Index, and Made Upon the Bills of Mortality.- 3. An Estimate of the Degrees of the Mortality of Mankind.- 4. A Treatise on the Valuation of Annuities and Assurances on Lives and Survivors.- 5. Statistical Applications of the Mortality Table.- 6. Formal Treatment of Aggregate Mortality Data.- 7. A Short Method for Constructing an Abridged Life Table.- 8. Short Methods of Constructing Abridged Life Tables.- 9. Life Tables for Natural Populations of Animals.- Stable Population Theory.- 10. An Illustration of Population Growth.- 11. A General Investigation into the Mortality and Multiplication of the Human Species.- 12. Relation Between Birth Rates and Death Rates.- 13. A Problem in Age-Distribution.- 14. The Stability of the Normal Age Distribution.- 15. Resolving a Historical Confusion in Population Analysis.- 16. On the Integral Equation of Renewal Theory.- 17. A New Method for Calculating Lotka’s r—The Intrinsic Rate of Growth in a Stable Population.- 18. The Fundamental Theorem of Natural Selection.- 19. How the Age Distribution of a Human Population is Determined.- 20. On the Reproduction of Organisms with Overlapping Generations.- 21. The Population Consequences of Life History Phenomena.- Attempts at Prediction and the Theory they Stimulated.- 22. The Probability of a Cessation of the Growth of Population in England and Wales during the Next Century.- 23. An Empirical Method for Calculating Future Population.- 24. Population Waves.- 25. On the Generation and Growth of a Population.- 26. On the Use of Matrices in Certain Population Mathematics.- 27. Matrix Representation of Changes in the Active Population.- 28. Weak Ergodicity.- 29. Ergodic Properties of Populations I: The One Sex Model.- Parameterization and Curve Fitting.- 30. On the Nature of the Function Expressive of the Law of Human Mortality.- 31. On the Law of Mortality.- 32. Calculation of Model Tables.- 33. Estimates of Fertility and Mortality Based on Reported Age Distributions and Reported Child Survival.- 34. Methods of Analysis and Estimation.- 35. Nuptiality, Fertility, and Reproductivity.- 36. Model Fertility Tables: Variations in the Age Structure of Childbearing in Human Populations.- 37. A Note on the Law of Population Growth.- 38. On the Rate of Growth of the Population of the United States since 1790 and its Mathematical Representation.- 39. The Measurement of Population Distribution.- Probability Models of Conception and Birth.- 40. First Investigations on the Fecundability of a Woman.- 41. Theoretical Basis of Measures of Natural Fertility.- 42. A Note on the Structure of a Stochastic Model.- 43. On the Time Required for Conception.- Branching Theory and Other Stochastic Processes.- 44. On the Probability of the Extinction of Families.- 45. Extinction Probabilities in Branching Processes.- 46. Stochastic Processes and Population Growth.- 47. An Age-Dependent Birth and Death Process.- 48. On the Use of the Direct Matrix Product in Analyzing Certain Stochastic Population Models.- Cohort and Period, Problem of the Sexes, Sampling.- 49. Aspects of Recent Trends in Marriage in England and Wales.- 50. The Relations between Male and Female Reproduction Rates.- 51. The Measurement of Reproductivity.- 52. Stochastic Processes and Population Growth.- 53. Population Growth of the Sexes.- 54. On Future Population.- 55. The Standard Deviation of Sampling for Life Expectancy.- 56. Probability Distributions of Life Table Functions.- References.- Author Index.