HUMAN FACULTY 283
Then, through the courtesy of Mr. Muir, the Chief Examiner at the Education Office, I was allowed to examine a large number of results from the Civil Service Examinations, and found that the average value of the first prize should be ,174.. Taking groups of 5o cases, each group gave that value pretty closely, no one differing as much as 64 from it.
The subject has since been generalised and discussed in Biometrika with far more mathematical skill than I possess, by both Professor Karl Pearson and Mr. W. F. Sheppard (a former Senior Wrangler), with practically the same result, so that if only two prizes are to be given, whatever be the character of the competition, and whatever the number of candidates, the first prize should in round numbers be three times the value of the second.
Professor Max Miiller had, in a work dated 1886 or 1887, laid an exaggerated stress, as I considered, on language as a means of thought, upon which I wrote some remarks in Nature , entitled " Thought without Words," which led to a short newspaper controversy, June 2, between us two. My point was that I myself thought hardest when making no mental use of words. Professor Max Muller's definitions of what 'he considered "words" seemed to me to vary, and therefore to be elusive, so I did not and will not pursue the matter farther.
I t led, however, to the idea of an experiment that seemed worth making, which I described  as "Arithmetic by Smell." When we propose to add, and hear the spoken words "two" and "three," we