Our examination of the Methods in use thus far in our past search after knowledge has developed these facts:--that prior to an era which is commonly said to commence with Bacon, the Method of intellectual investigation was _mainly_ by attempting to proceed from Principles to Facts, and that the attempt exhibits three distinct phases: one, in which the Induction stage is so simple and so short as to be instinctively and correctly performed by all people, and the Deductive stage at once reached--this furnishes the Mathematics, the only Science in which hitherto the _true_ Deductive Method has prevailed; a second, in which Principles are assumed to reason from, without any previous effort at Induction, such as existed, being unconsciously made from the supposed Facts or Knowledge which the mind was in possession of; and a third, in which Facts were collected, classified, and Induction therefrom as a basis of further investigation attempted, but in which the Laws or Principles assumed as established by the Facts were not rigorously and accurately derived from Facts; or, in other words, in which the Facts were not strictly used for the purpose of deriving from them just such Laws or Principles only as they actually established, but were wrenched to the attempted support of Laws, Principles, or Ideas more or less fanciful or unrelated to the Facts. These two last phases are included in what is known among Scientists as the Anticipative or Hypothetical Method; while the three phases are commonly undiscriminated and collectively termed the Deductive Method. It was also developed that the results of this period of intellectual activity were fruitless of definite Scientific achievements, _except so far as the true Deductive Method_ had been employed. It was furthermore seen that since Bacon's time, the opposite Method of procedure, namely, from Facts to Principles, has been chiefly in vogue; that under its impulse distinctness and clearness have been brought to pervade those stores of knowledge which were already in our possession, thus fulfilling _one_ of the requisites of a perfect Scientific Method, while, however, the other necessary requirement, that of furnishing a _certain_ guide to future discoveries, has been only proximately attained by it.