contrasted with deduction, but that induction is simply an inverse employment of deduction. Within the last century a reaction has been setting in against the purely empirical procedure of Francis Bacon, and physicists have learned to advocate the use of hypotheses. I take the extreme view of holding that Francis Bacon, although he correctly insisted upon constant reference to experience, had no correct notions as to the logical method by which, from particular facts, we educe laws of Nature. I endeavor to show that hypothetical anticipation of Nature is an essential part of inductive inquiry, and that it is the Newtonian method of deductive reasoning, combined with elaborate experimental verification, which has led to all the great triumphs of scientific research.
"In attempting to give an explanation of this view of scientific method, I have first to show that the sciences of number and quantity repose upon and spring from the simpler and more general science of logic. The theory of probability, which enables us to estimate and calculate quantities of knowledge, is then described, and especial attention is drawn to the inverse method of probabilities, which involves, as I conceive, the true principle of inductive procedure. No inductive conclusions are more than probable, and I adopt the opinion that the theory of probability is an essential part of logical method, so that the logical value of every inductive result must be determined consciously or unconsciously, according to the principles of the inverse method of probability.
"The phenomena of Nature are commonly manifested in quantities of time, space, force, energy, etc.; and the observation, measurement, and analysis of the various quantitative conditions or results involved, even in a simple experiment, demand much employment of systematic procedure. I devote a book, therefore, to a simple and general description of the devices by which exact measurement is effected, errors eliminated, a probable mean result obtained, and the probable error of that mean ascertained. I then proceed to the principal, and probably the most interesting, subject of the book, illustrating successively the conditions and precautions requisite for accurate observation, for successful experiment, and for the sure detection of the quantitative laws of Nature. As it is impossible to comprehend aright the value of quantitative laws without constantly bearing in mind the degree of quantitative approximation to the truth probably attained, I have devoted a special chapter to the theory of approximation, and, however imperfectly I may have treated this subject, I must look upon it as a very essential part of a work on scientific method.
"It then remains to illustrate the sound use of hypothesis, to distinguish between the portions of knowledge which we owe to empirical observation, to accidental discovery, or to scientific prediction. Interesting questions arise concerning the accordance of quantitative theories and experiments, and I point out how the successive verification of an hypothesis by distinct methods of experiment yields conclusions approximating to but never attaining certainty. Additional illustrations of the general procedure of inductive investigations are given in a chapter on the 'Character of the Experimentalist,' in which I endeavor to show, moreover, that the inverse use of deduction was really the logical method of such great masters of experimental inquiry as Newton, Huyghens, and Faraday.
"The application of scientific method cannot be restricted to the sphere of lifeless objects. We must sooner or later have strict sciences of those Mental and Social phenomena which, if comparison be possible, are of more interest to us than purely material phenomena. But it is the proper course of reasoning to proceed from the known to the unknown—from the evident to the obscure—from the material and palpable to the subtile and refined. The physical sciences may therefore be properly made the practice-ground of the reasoning powers, because they furnish us with a great body of precise and successful investigations."
It is thus evident that the plan of Prof. Jevons's work involves a thorough handling of the most recent questions that have been raised in science and philosophy, and an examination of it will show that he has carried out his project in an able and independent manner. We publish a portion of his
