In his great work, the Théorie Analytique des Probabilités (which may he supposed to embody the author's latest and most matured views respecting that abstruse and difficult subject), Laplace reduces the fundamental principles of the whole doctrine of probabilities (both direct and inverse) to four comprehensive propositions. The four “Principes” of Laplace are extremely well adapted to show how important is the part, in that doctrine, which belongs to the indirect or inverse branch of it; and I know of no means better calculated to throw light upon the subject of this article than the course which I propose in the present section to follow, namely, to illustrate each “Principe” by an example relating to a coin falling head a certain number of times in succession.