Galton's bend: A previously undiscovered nonlinearity in Galton's family stature regression data

In Francis Gallon's 1886 article Regression Towards Mediocrity in Hereditary Stature, Gallon analyzed the heights of 928 adult children and their 205 pairs of parents to illustrate his linear regression model. Although Gallon's data have been recalled frequently to illustrate linear regression and regression toward the mean, no one seems to have noticed that his height data do not fit his model. The purpose of this article is both to reveal this curiosity and to find a possible explanation for its existence using related data from Gallon's colleague Karl Pearson.