The intellectual development of the world has proceeded under the operation of three Methods. Two of these, identical in their mode of action, but arriving, nevertheless, at widely different results, from the different points at which they take their departure, are not commonly discriminated, but are both included in the technical term _Deductive Method_. The other is denominated the _Inductive_. A brief analysis of these Methods will clear the way for an understanding of the nature of Science, particularly in its application to the subject of History, with which we are at present especially concerned. The earliest evolution of that which has been called Science,--the Mathematics, which we dismiss for the instant, excepted,--took place under the operation of a Method, which, ordinarily confounded with the true Deductive one, is now better known among rigorous Scientists as the Hypothetical or Anticipative Method. This has two modes of expression, one of which consists in the assumption of Laws or Principles, which have not been adequately verified, or in the erection of fanciful hypotheses, as the starting points of reasoning for the purpose of establishing other Facts. The second and most common operation referred to this Method, which is, however, strictly speaking, an imperfect application of the Inductive Method, is _to draw conclusions from Facts which these do not warrant_--sometimes conclusions not related to the Facts, oftener those which, being so related, are a step beyond the legitimate inferences which the Facts authorize, though in the same direction. This results in the establishment of Laws or Principles as true, which are by no means proven, many of which are subsequently found to be incorrect. It is to this operation of the Hypothetical Method that Professor Whewell, who does not discriminate the two, refers when he describes the defect in the physical speculations of the Greek philosophers to have been, 'that though they had in their possession Facts and Ideas, _the Ideas were not distinct and appropriate to the Facts_.' The main cause of defect in the mental process here employed is the tendency of the human mind to generalize at too early a stage of the investigation, and consequently upon a too narrow basis of Facts. This Method characterized the intellectual activity of the race from the earliest beginnings of thought up to a period which is commonly said to have commenced with the publication of the _Novum Organum_ of Lord Bacon. It was of course fruitless of _Scientific_ results, as it was not a Scientific, but an absolutely Unscientific Method, since _certainty_ is the basis of all Science, and since a Method which attempts to deduce Facts from Principles which are not ascertained to be Principles, or Principles from an insufficient accumulation of Facts, cannot insure certainty.