Bagatelle as the inspiration for Galton's Quincunx

Abstract

This paper considers the question of how Francis Galton came to devise the quincunx, a pin-board that simulates the effect of a large number of Bernoulli trials to yield an empirical normal curve. It suggests that the likely inspiration for the design was some variant of bagatelle. The argument forms a small part of an Open University doctoral thesis (May 2005), which revealed the extent of the support Galton received from George Howard Darwin as he developed the concept of statistical regression.

Notes

¹ According to Julian Holland of the Macleay Museum at the University of Sydney, Tisley and his associate, George Spiller, were scientific instrument makers who, at their premises in Brompton Road, ‘sought to capitalize on the expansion of science education in England after 1871’ (Holland 2000).

² The word derives from the Latin quinque, five and uncia, a twelfth. The quincunx was a symbol used by the Romans for five-twelfths of an as, a copper coin. The word had been used in England since the seventeenth century to describe the arrangement of trees in an orchard.

³ In 1892, with the help of Ludwig Boltzmann, the topologist and group theorist, Walther Franz Anton Dyck (1856–1934) organized the first international exhibition of mathematics and physics instruments in Munich, actually postponed to the following year because of a cholera outbreak. The catalogue contains a description in German of the quincunx, submitted by Galton. See Galton. 1892/1994.

⁴ A photograph of the original quincunx was given by Stigler (1986, 277), in which the empirical distribution is more distinctly ‘normal’ than the figure in this article suggests. Part of the problem in capturing the image well is the fact that there is a coating of lead dust on the inside of the glass.

⁵ It took its name from what was originally a ‘trifling’ residence outside Paris, containing a salon de jeu, which in the eighteenth century attracted the gambling fraternity of the French aristocracy.

⁶ The book was published in monthly instalments from March 1836 until November 1837. The reference to bagatelle, in the introductory paragraph of chapter 14, is the earliest in English literature.

⁷ I am advised by David Singmaster that the book went through numerous editions and reprintings, the last as recent as 1969. The description is from the 1833 edition. Note that since the ‘batoon’ would slide up the ‘trunk’ taking the ball with it, the skill lay in pushing just hard enough to persuade the ball to turn under gravity's influence at the optimum point on the rim.

⁸ The numbering on a darts board postdates the sequences on these pin bagatelle boards. It was devised in 1896 by Brian Gamlin, a Bury carpenter.

⁹ This was in the Herbert Spencer Lecture, delivered at Oxford University on 5 June 1907.

¹⁰ Charles Darwin, letter to George Darwin, 24 [February 1859], Cambridge University Library, DAR 210.6:37. The table which cost a little under £54, was installed at Down on the day the letter was written. Hopkins and Stephens were nephews of John Thurston.

¹¹ Charles Darwin, letter to William Erasmus Darwin, 14 [March 1859], Cambridge University Library, DAR 210.6:40.

¹² I am indebted to David Singmaster for finding references to The Rocks of Scilly and Cockamaroo.