(1.) The inquiry which, with its results, I propose to lay before the Society, was suggested by the following passage in the very popular Treatise on Logic by Dr Whately, now Archbishop of Dublin.

“As in the case of two probable premises, the conclusion is not established except upon the supposition of their being both true, so in the case of two (and the like holds good with any number) distinct and independent indications of the truth of some proposition, unless both of them fail, the proposition must be true: we therefore multiply together the fractions indicating the probability of the failure of each—the chances against it—and the result being the total chances against the establishment of the conclusion by these arguments, this fraction being deducted from unity, the remainder gives the probability for it.