Page:Popular Science Monthly Volume 20.djvu/293

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an excellent sign of the times, as it becomes an index of activity in the field of experimental work. But these little manuals of practice are generally prepared with no other view than to serve as convenient helps in manipulation, and arc but rarely steps in a broad, well-defined educational plan. The little book before us is of a different character, and has its place as part of a comprehensive system of biological study.

Professor Martin, who has charge of biology in Johns Hopkins University, has organized his department of teaching on a rational basis, and this book is the first installment of a series of small hand-books which has had its origin in his experience and necessities as a teacher. His theory of the method of study, which is hardly new, but has not been before reduced to a working system, is that students should first acquire some general idea of the elements and relations of their subject before concentrating study upon special divisions of it. In accordance with this idea, he some years ago, in connection with Professor Huxley, issued a volume called "Practical Biology," which was designed to introduce students to this science by observations of the structure and life-history of a number of typical plants and animals. It assumed that there is properly a science of living beings, as such, quite apart from any division of them into animals and plants. The course of study prescribed was experimental and thorough, and designed to lay a firm foundation for the further pursuit of the subject. Being thus grounded in general biology, the student is prepared to take up botany, or animal anatomy and physiology, and proceed with them to the greatest advantage. The present hand-book comes in at this point when it is proposed to enter upon the scientific investigation of vertebrates, and it shows him "how to dissect a chelonian." The Chelonia are reptiles of the tortoise kind, and among these Professor Martin selects the Red-bellied Slider Terrapin for dissection, and adapts his book to the details of its structure. But, if students can not find this species, Professor Martin says that it is quite as well, and even in some respects better, to obtain species slightly different from the one described; the attention of students being kept more alert when they find they can not altogether rely on the description in the book, but have to look at everything carefully for themselves.

The present monograph will shortly be followed by two others, containing directions for the dissection of a pigeon and a rat, both of which are nearly ready for publication. The series will ultimately include a bony and a cartilaginous fish, a lizard, and one of the large-tailed amphibia, and when completed the series will form a Hand-book of Vertebrate Dissection.

Algebra for Schools and Colleges. By Simon Newcomb, Professor of Mathematics, U. S. Navy. New York: Henry Holt & Co. 1881. Pp. 454. Price, $1.90.

A characteristic of this book is that, for the convenience of teachers, it is divided into two parts: the first adapted to well-prepared beginners, and comprising about what is commonly required for admission to college; and the second designed for the more advanced general student.

In the preparation of his work, Professor Newcomb recognizes two important principles in education which are much overlooked, and are novelties in their application to algebra. The first is that, in the acquisition of knowledge, an idea can not be very fully grasped by the youthful mind unless it is presented under a concrete form. This requires that, whenever possible, an abstract idea should be embodied in some visible representation, and all general theorems presented in a variety of special forms. In accordance with this principle, numerical examples of nearly all algebraic operations and theorems have been given. Algebraic operations with pure numbers are made to precede the use of symbols, and the latter are introduced only after the pupil has had a certain amount of familiarity with the distinction between algebraic and numerical operations. The second principle is the importance of time in mental processes. All mathematical conceptions require time to become ingrafted upon the mind, and the greater their abstruseness the more time is needed. The author is of the opinion that the backward state of mathematical instruction in this country, as compared with Europe, is due to a neglect of