To reach the kernel of the matter at once, the reader must note that the fallacy consists in neglecting to consider that in dealing with astronomers or with great men, or with persons of eminence of the nineteenth century, one is dealing with a group which is already carefully selected, _and the selection of which inevitably involves the attainment of a certain age_. The result is that we are not dealing with average persons as regards longevity, but with persons who in the very nature of things have already reached a certain period of maturity. No one can become a poet, or a novelist, or a painter, or a philosopher, or a commander or a statesman unless he lives at least a sufficient number of years to acquire the development of an adult, and to have the opportunity of developing his abilities and distinguishing himself. If great men were great from their infancy, and if we had the means of ascertaining this fact, then, and only then, would the method used be correct. It is ordinarily stated that the average duration of life is somewhere between thirty-three and forty years, and Mr. Thayer considers that in the present century it has moved forward towards the latter figure. What this means is that if we were to keep a record of the age at death of all Americans who are to be born within the first ten years of the coming century, we should find that their average age at death would be some thirty odd years. But this number can by no means be used as a standard with which to compare the average age at death of men of distinction, or indeed of any other class of men selected according to a standard which involves on their part the attainment of mature years. If we were investigating the longevity of twins, or of persons with supernumerary toes, or indeed of persons possessing any quality which one could detect in new-born infants, and if we could determine the average life-period of this class of persons and find that it markedly exceeded the average of the entire community, we should be entitled to conclude that twins, or persons who have supernumerary toes, are blessed with a greater longevity than the average man. But so long as men who are to acquire distinction bear no traces upon them of this power until they exhibit their powers and actually gain distinction, it is obvious that we are concerned with their longevity only from that moment when they have entered, or have become promising candidates for that class of selected individuals whose longevity we are investigating. Proceeding on this basis, I tried to determine the age at which, on the average, men of genius had accomplished a work sufficient to entitle them to be so denominated. This investigation was instigated by Mr. C. S. Peirce, then in charge of courses in logic at the Johns Hopkins University. Under his leadership a small company, of whom I was one, proposed to study certain traits of great men, and for this purpose we tried to select the three hundred greatest men