Mathematical Demography

1. Front Matter

   Pages I-XI

   PDF

2. The Life Table

   1. Front Matter

      Pages 1-5

      PDF

   2. Tables of Annuity Values Which Were Sanctioned by the Roman Law for the Purposes of the Lex Falcidia

      • C. F. Trenerry

      Pages 7-9

   3. Natural and Political Observations Mentioned in a Following Index, and Made Upon the Bills of Mortality

      • John Graunt

      Pages 11-20

   4. An Estimate of the Degrees of the Mortality of Mankind

      • Edmund Halley

      Pages 21-26

   5. A Treatise on the Valuation of Annuities and Assurances on Lives and Survivors

      • Joshua Milne

      Pages 27-34

   6. Statistical Applications of the Mortality Table

      • George King

      Pages 35-38

   7. Formal Treatment of Aggregate Mortality Data

      • Wilhelm Lexis

      Pages 39-41

   8. A Short Method for Constructing an Abridged Life Table

      • Lowell J. Reed, Margaret Merrell

      Pages 43-51

   9. Short Methods of Constructing Abridged Life Tables

      • T. N. E. Greville

      Pages 53-60

   10. Life Tables for Natural Populations of Animals

       • Edward S. Deevey Jr.

       Pages 61-74

3. Stable Population Theory

   1. Front Matter

      Pages 75-77

      PDF

   2. An Illustration of Population Growth

      • Johann Peter Süssmilch

      Pages 79-82

   3. A General Investigation into the Mortality and Multiplication of the Human Species

      • Leonard Euler

      Pages 83-91

   4. Relation Between Birth Rates and Death Rates

      • Alfred J. Lotka

      Pages 93-95

   5. A Problem in Age-Distribution

      • F. R. Sharpe, Alfred J. Lotka

      Pages 97-100

   6. The Stability of the Normal Age Distribution

      • Alfred J. Lotka

      Pages 101-107

   7. Resolving a Historical Confusion in Population Analysis

      • Paul A. Samuelson

      Pages 109-129

   8. On the Integral Equation of Renewal Theory

      • William Feller

      Pages 131-156

   9. A New Method for Calculating Lotka’s r—The Intrinsic Rate of Growth in a Stable Population

      • Ansley J. Coale

      Pages 157-160

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.

• Calculation
• Demografie
• Demographie
• Mathematica
• START
• calculus
• demography
• development
• equation
• function
• mathematics
• mortality
• stochastic processes
• theorem

• Center for Population Studies, Harvard University, Cambridge, USA

  David P. Smith, Nathan Keyfitz

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