The author began by some remarks upon the expression or . Where p represents the a priori probability of an event attested by a witness whose veracity, or the ratio of whose true assertions to the number of all his assertions is, v. He observed that U, or the ultimate probability of the asserted fact, depended upon the accuracy of the numerical value given to v, and that men have never such knowledge of their neighbours' antecedents, as to assume this value with anything like an approximation to the truth.