A GRAMMAR OF SCIENCE.
The increasing specialization of the sciences and the consequent occupation with the details and technical manipulations of a specialty render it possible for many a student to secure the equipment needed for his immediate activity, with but little appreciation of the general principles that give direction and solidarity to his science, or of the more general and fundamental conceptions which the various sciences and the spirit and progress of science as a whole have in common. The student runs the danger of gaining a certain familiarity with the vocabulary and the usage of the language of science, but of ignoring its grammar. One of the purposes met by Prof. Karl Pearson's 'The Grammar of Science' is to give the serious student an opportunity to acquaint himself with these underlying conceptions—cause and effect and probability, space and time, motion and matter and the composition of the physical and organic worlds. It discusses with him and for him the nature of the knowing process, and demonstrates how the sciences stand—not for a literal copy of reality, but represent a special abstraction and construction on the basis of experience, which serve the purposes of intelligibility and logical system. A law of nature is not an objective reality, but "a résumé in mental shorthand, which replaces for us a lengthy description of the sequences of our sense-impressions. Law in the scientific sense . . . owes its existence to the creative power of his [man's] intellect." Science is thus not the mere reflection of perceptual experience, but is dependent for its advance quite as much upon the formation of appropriate conceptions by the exercise of insight and a keen logical analysis and synthesis. Hence, the importance of the imagination as a requisite for scientific discovery, which leads Professor Pearson to regard Darwin and Faraday as superior in this quality to the best of the poets and novelists. Not only the content of the sciences but the spirit and the means that guide its advance form part of the grammar of science. The nature of the scientific method, the appreciation that the scope of science is really coincident with the scope of verifiable knowledge; that science represents a mode of approach and of inquiry, and that the scientist or the scientifically-minded individual is characterized by a definite logical attitude, by a manner of entering into relation with his surroundings and of dealing with reality; that science discountenances attempted short-cuts and inspired revelations, or guesses of the riddles of existence; that it avoids metaphysic and impractical speculation; that it justifies its existence and the energies which are expended on its behalf by the mental training it provides in education, by its illumination of the problems of life and society, by the practical benefits it confers in the various fields of human activity, as well as by the gratification it yields to some of the most permanent and most worthy of our intellectual and æsthetic impulses—these and other propositions are ably and interestingly presented and constitute an essential portion of this very stimulating and clarifying volume. The success of the work is attested by the appearance of this second edition; the chief addition consists of a discussion of the quantitative method as applied to biological phenomena, which the readers of others of the author's works will recognize as one of his favorite subjects of investigation.
THE TEACHING OF ELEMENTARY MATHEMATICS.
The book with the above title, by David Eugene Smith, principal of the