'Sur l'homme': the astronomers' law of error applied to people

1835 Number and measure method

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A device in which the astronomers' error curve, describing the scatter of measurements of a single star, is applied to a living population: the scatter of height, weight and chest circumference among thousands of people falls around an 'average man' along the same curve as errors of observation.

The device was proposed in 'Sur l'homme' (1835) by the Belgian Adolphe Quetelet, astronomer of the Brussels Observatory, who had studied probability under Laplace and Fourier. The regularity of the numbers of births, marriages and crimes he called 'social physics'.

This is a method rather than a concept: what was new was the procedure, to count a living population the way astronomers counted a series of measurements. On the map it is an adapter: the same curve reaches Maxwell's theory of gases through Herschel's review, and the study of heredity through Galton.

Why this date

The date is that of the first edition: A. Quetelet, 'Sur l'homme et le développement de ses facultés, ou Essai de physique sociale', 2 vols, Paris, Bachelier, 1835. Year and content are confirmed by the MacTutor article (O'Connor and Robertson, 2006) and by Eknoyan's abstract (2008). Quetelet's separate papers on the propensity to crime appeared from 1831, but the axis takes the book, where the 'average man' and the application of the error curve to height and weight are set out in full.

What it grew from

• The method of least squares

  influenced · Confidence: medium

  The error curve with which astronomers and surveyors described the scatter of measurements (Gauss, Legendre) was in Quetelet applied for the first time not to errors of observation but to the scatter of traits in a human population. Brush states outright that the law discovered by Adrain and Gauss was 'extensively applied by Quetelet'. The link is drawn as "influenced" rather than as a prerequisite: Quetelet did not use the method of least squares itself, he took the error distribution from the same tradition.

  Dispute: Brush's sentence asserts the Gauss-Quetelet link in passing, inside a statement about Maxwell; no separate historian's study analysing what exactly Quetelet took from the error theory of Gauss and Laplace, and what from Laplace's demographic work, was read here. The core node least_squares is the method of least squares, not the error distribution as such, so the link is called "influenced" and the confidence is medium.

  Link sources

  • Stephen G. Brush, History of the Kinetic Theory of Gases (Storia della Scienza, vol. 7, ch. 44) (2004) Verified 20 Sep 2026

    The crucial step was his translation of the 'normal distribution law' or 'law of errors,' discovered by Adrain and Gauss and extensively applied by Quetelet, into a distribution law for molecular velocities.

  • J. J. O'Connor, E. F. Robertson, Adolphe Quetelet, MacTutor History of Mathematics Archive, University of St Andrews (2006) Verified 20 Sep 2026

    Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

What grew out of it

• Kinetic theory of gases and statistical mechanics

  influenced · Confidence: high

  In 1860 Maxwell obtained the distribution of molecular velocities by carrying into physics the normal law which had until then been applied to people: Brush calls this the crucial step and states outright that the formula was borrowed from the social sciences, where Quetelet had applied it extensively. It is the same branch that leads from Quetelet to Galton, only turned towards physics.

  Dispute: Historians differ over whether Maxwell read Quetelet himself or got the same idea from John Herschel's review of Quetelet's 'Letters on the theory of probabilities' (Edinburgh Review, July 1850). Porter (The Rise of Statistical Thinking, 1986), and several authors following him, trace Maxwell's acquaintance with the procedure to Herschel's review; Herschel is not mentioned in the chapter of Brush cited here. For the map this does not change the direction of the link, but it means the transmission went through an intermediary.

  Link sources

  • Stephen G. Brush, History of the Kinetic Theory of Gases (Storia della Scienza, vol. 7, ch. 44) (2004) Verified 20 Sep 2026

    To describe this distribution he borrowed a mathematical formula from the social sciences. The crucial step was his translation of the 'normal distribution law' or 'law of errors,' discovered by Adrain and Gauss and extensively applied by Quetelet, into a distribution law for molecular velocities.

  • J. C. Maxwell, Illustrations of the Dynamical Theory of Gases, Philosophical Magazine 19-20 (1860) Verified 20 Sep 2026

    the velocities are distributed among the particles according to the same law as the errors are distributed among the observations in the theory of the 'method of least squares.'

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

  Further reading

  Not evidence: these carry no quotation and support nothing we wrote. They are books and scans to read next.

  • Porter T. M. «The Rise of Statistical Thinking, 1820-1900», Princeton University Press (1986)

• Regression to the mean and correlation: heredity as statistics

  influenced · Confidence: high

  Galton learned of the application of the 'Law of Error' to anthropometric measurements, height and chest circumference, precisely from Quetelet's work, which reached him through the writings of Spottiswoode and Herschel: so Chatterjee writes. Stigler specifies the mechanism: Spottiswoode used Quetelet's own procedure to fit a normal curve to the orientation of mountain ranges, and it was this work that first turned Galton to the normal law of error.

  Dispute: In his autobiography of 1908 Galton himself traced his acquaintance with the law of error to Spottiswoode rather than to Quetelet and, in Tankard's words, 'tended to minimize Quetelet's influence on him'. Stigler, quoting the same autobiographical reference, remarks that it speaks more for the keenness of Galton's eye than for the quality of Spottiswoode's work. Moreover Galton departed from Quetelet in substance: Quetelet's 'average man' is a type from which deviations are errors, whereas for Galton variation itself is the object of measurement.

  Link sources

  • Shoutir Kishore Chatterjee, Statistical Thought: A Perspective and History, Oxford University Press, 286 (2003) Verified 25 Sep 2026, quotation assembled from fragments

    Galton became acquainted with Quetelet's use of the 'Law of Error' for describing the variation of anthropometric measurements like those on height and chest circumference...through the writings of Spottiswoode and Herschel

  • Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty before 1900, Harvard University Press, 219 (1986) Verified 25 Sep 2026

    Spottiswoode attempted to use Quetelet's own procedure to fit a normal curve to the distribution of direction of orientation of eleven mountain ranges to see whether they corresponded to a common "type."

  • Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty before 1900, Harvard University Press, 219 (1986) Verified 25 Sep 2026

    this work of Spottiswoode that caught his eye and first interested Galton in the normal law of error (Galton, 1908, p. 304)

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong. "Assembled from fragments" means the words do not stand together on the page: we found each fragment separately and joined them with an ellipsis.

• Pearson's correlation coefficient and the chi-square test

  influenced · Confidence: medium

  Pearson built his statistics in direct argument with the conviction that every distribution must be normal, and that conviction Magnello traces to Quetelet's determinism. Hence the family of skew curves and the goodness-of-fit test: Pearson looked for a way of describing data without forcing them into the normal curve, 'as Galton and Quetelet had done'.

  Dispute: This is influence by opposition: Magnello describes Quetelet as the source of a view that Pearson was overcoming, not as the source of his method. The text read does not assert that Pearson read Quetelet directly, hence the medium confidence.

  Link sources

  • M. Eileen Magnello, Karl Pearson and the Origins of Modern Statistics: An Elastician becomes a Statistician, The Rutherford Journal 1 (2005) Verified 20 Sep 2026

    The Belgian statistician, Adolphe Quetelet (1796-1874) attached so much significance to the normal curve because of his belief in determinism, which meant that there was an ideal statistical mean value and that the normal curve was the ideal curve, since it followed the law of errors; hence, all the variation around the mean had to conform to this curve. That Pearson would go on to create a new type of statistics was to a large extent in response to the unshakable conviction, held by so many vital statisticians, mathematicians and philosophers, that the normal distribution was the only feasible distribution for the analysis and interpretation of statistical data.

  • M. Eileen Magnello, Karl Pearson and the Origins of Modern Statistics: An Elastician becomes a Statistician, The Rutherford Journal 1 (2005) Verified 20 Sep 2026

    Pearson wanted to find another way to interpret the data without trying to normalise it, as Galton and Quetelet had done.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

Node sources

• J. J. O'Connor, E. F. Robertson, Adolphe Quetelet, MacTutor History of Mathematics Archive, University of St Andrews (2006) Verified 5 Oct 2026

  He gained world-wide fame in 1835 when he published Sur l'homme et le developpement de ses facultés, essai d'une physique sociale.

• J. J. O'Connor, E. F. Robertson, Adolphe Quetelet, MacTutor History of Mathematics Archive, University of St Andrews (2006) Verified 5 Oct 2026

  Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale he presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve.

• J. J. O'Connor, E. F. Robertson, Adolphe Quetelet, MacTutor History of Mathematics Archive, University of St Andrews (2006) Verified 5 Oct 2026

  In December 1823, he went to Paris to study astronomy at the Observatory there. He learnt astronomy from Arago and Bouvard and the theory of probability under Joseph Fourier and Pierre Laplace.

• Garabed Eknoyan, Adolphe Quetelet (1796-1874): the average man and indices of obesity, Nephrology Dialysis Transplantation 23 (1), 47-51 (2008)

  His principal work, ‘A Treatise of Man and the development of his faculties’ published in 1835 is considered ‘one of the greatest books of the 19th century’.

"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

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