Few people nowadays would be found to share Mill's belief. It is just because we feel ourselves unable to deduce with any 'approach to certainty' the effect of circumstances upon character, that we all desire to obtain, if it is possible, a more exact idea of human variation than can be arrived at by thinking of mankind 'in the average or _en masse_.' Fortunately the mathematical students of biology, of whom Professor Karl Pearson is the most distinguished leader, are already showing us that facts of inherited variation can be so arranged that we can remember them without having to get by heart millions of isolated instances. Professor Pearson and the other writers in the periodical _Biometrika_ have measured innumerable beech leaves, snails' tongues, human skulls, etc. etc., and have recorded in each case the variations of any quality in a related group of individuals by that which Professor Pearson calls an 'observation frequency polygon,' but which I, in my own thinking, find that I call (from a vague memory of its shape) a 'cocked hat.' Here is a tracing of such a figure, founded on the actual measurement of 25,878 recruits for the United States army. [Illustration: [Transcriber's Description: A line graph of number of recruits vs. height. The horizontal axis is AC, and the line itself is ABC, which is roughly normal.]] The line _ABC_ records, by its distance at successive points from the line _AC_, the number of recruits reaching successive inches of height. It shows, e.g. (as indicated by the dotted lines) that the number of recruits between 5 ft. 11 in. and 6 ft. was about 1500, and the number of those between 5 ft. 7 in. and 5 ft. 8 in. about 4000.[40] [40] This figure is adapted (by the kind permission of the publishers) from one given in Professor K. Pearson's _Chances of Death_, vol. i. p. 277. For the relation between such records of actual observation and the curves resulting from mathematical calculation of known causes of variation, see _ibid._, chap, viii., the paper by the same author on 'Contributions to the Mathematical Theory of Evolution,' in vol. 186 (A) of the _Royal Society's Philosophical Transactions_ (1896), and the chapters on evolution in his _Grammar of Science_, 2nd edition. Such figures, when they simply record the results of the fact that the likeness of the offspring to the parent in evolution is constantly inexact, are (like the records of other cases of 'chance' variation) fairly symmetrical, the greatest number of instances being found at the mean, and the descending curves of those above and those below the mean corresponding pretty closely with each other. Boot manufacturers, as the result of experience, construct in effect such a curve, making a large number of boots of the sizes which in length or breadth are near the mean, and a symmetrically diminishing number of the sizes above and below it.