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408   Life and Letters of Francis Galton

Those who recognise the relative mercy of the long drop may wonder why capital punishment has not been still further modified in the direction of scarcely less painful, but more seemly, methods of disposing of the socially abhorrent.

Galton further contributed a letter to the discussion on " Corporal Punishment "which developed in the Times in 1898. He considered that the writers on the subject had overlooked two important points

"The first is, the worse the criminal the less sensitive he is to pain, the correlation between the bluntness of the moral feelings and those of the bodily sensations being very marked. The second relates to the connection between the force of the blow and the pain it occasions, which

do not vary at the same rate, but approximately, according to Weber's law, four times as heavy a blow only producing about twice as much pain. In a Utopia the business of the Judge would be confined to sentencing the criminal to so many units of pain in such and such a form, leaving it to anthropologists skilled in that branch of their science to make preliminary experiments and to work out tables to determine the amount of whipping or whatever it might be that would produce the desired results. Really these latter considerations might even now be made the subject of a solid scientific paper of no small interest, but they cannot be more than hinted at in a short letter like this, which has to be written in non-technical language."

The unit of pain-quite apart from corporal punishment-seems no more incapable of measurement than a unit of intelligence. The threshold of the sensation of pain might be determined in a number of ways, and then correlated with other mental and physical characters of the individual. Like all Galton's writings, this brief letter suggests unexhausted fields for the persistent and cautious investigator.

Galton's fertility of statistical ideas may be further illustrated by two papers, one belonging to 1894 when he was seventy-two years of age, and the other written fifteen years later when he was 87. The first was contributed to the Proceedings of the Royal Society' and deals with the important problem of the fertility of marriages according to the ages of father and mother. The fertility is measured by percentage of families which have a child when the husband and wife are of the given ages. If a chart be formed of which one variate is age of father, the second age of mother, and the percental offspring be inscribed for each pair of ages, then Galton proposes to represent the loci of equal percentages by contours, which he terms isogens. By a fairly simple, if somewhat rough process he constructs these isogens for KOrOsi's Budapest data, and we reproduce them below.

The diagram indicates that the form of the isogens as long as the husband is older than the wife is very closely a system of straight equidistant and diagonal lines. As a result of this Galton concludes that the fertility of a husband of age a$ and a wife of age aW will be closely given by

P=93-al. -a,,

provided that (i) the wife is not older than the husband, and_ (ii) she is not less than 23 nor (iii) more than 40 years of age.

' Vol. Lv, pp. 18-23. "Results derived from the Natality Table of Korosi by employing the method of Contours or Isogens."