The subject matter of this book was first broached in the brain of Leibniz, who, in the dissertation, written in his twenty-third year, on the mode of electing the kings of Poland, conceived of Probability as a branch of Logic. A few years before, “un problème,” in the words of Poisson, “proposé à un austère janséniste par un homme du monde, a été l'origine du calcul des probabilités.” In the intervening centuries the algebraical exercises, in which the Chevalier de la Méré interested Pascal, have so far predominated in the learned world over the profounder enquiries of the philosopher into those processes of human faculty which, by determining reasonable preference, guide our choice, that Probability is oftener reckoned with Mathematics than with Logic. There is much here, therefore, which is novel, and, being novel, unsifted, inaccurate, or deficient. I propound my systematic conception of this subject for criticism and enlargement at the hand of others, doubtful whether I myself am likely to get much further, by waiting longer, with a work, which, beginning as a Fellowship Dissertation, and interrupted by the war, has already extended over many years.