Page:Popular Science Monthly Volume 20.djvu/294

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this principle. he says: "Let us take, for instance, the case of the student commencing the calculus. On the system which was so universal among us a few years ago, and which is still widely prevalent, he is confronted at the outset with the number of entirely new conceptions, such as those of variables, functions, increments, infinitesimals, and limits. In his first lesson he finds these all combined with a notation so entirely different from that to which he has been accustomed, that before the new ideas and forms of thought can take permanent root in his mind he is through with the subject, and all that he has learned is apt to vanish from his memory in a few months. To meet this difficulty, the author has not scrupled to deviate from strict logical order to introduce the more advanced conceptions, disguised, perhaps, under some simple form at the earliest practicable period in the course. Some familiarity with ideas is thus acquired before their more formal enunciation. The practical feature of the work subsidiary to this principle consists in subdividing each subject as minutely as possible, and exercising the pupil on the details preparatory to combining them into a whole. Exercises in the use of algebraic language have been made to precede any solution of problems. In general, each principle which is to be presented or used is stated singly, and the pupil is practiced upon it before proceeding to another."

These features of the work certainly conform to sound educational philosophy, and they justify the conclusion that it has been executed throughout in a similar spirit. Professor Newcomb's reputation as a mathematician will be sure to commend his work to the favorable regard of teachers, and experience with it will test the fidelity with which he has applied the principles we have referred to, and others of perhaps equal importance which we have not space to notice.

Man's Origin and Destiny, sketched from the Platform of the Physical Sciences. By G. P. Lesley, State Geologist of Pennsylvania. Boston: George 11. Ellis. Pp. 442.

The chief portion of this volume was prepared as a series of lectures, and delivered at the Lowell Institute, Boston, in 1866. They were published in a volume under the present title in 1868, and, the work continuing to be called for, some slight corrections were made in the plates, and a new edition is now issued, to which six more lectures are added.

It was the author's aim in his lectures "to attempt to show how far the sciences) as they are now advanced, succeed in throwing light upon the early history of our race"; or "to stimulate one class of minds by certain new suggestions respecting the correlation of the physical sciences with the history of mankind." His book is in no sense the systematic exposition of a theory which he claims as his own, but is rather a free, discursive interpretation and criticism of some of the leading doctrines and tendencies of modern scientific thought. The purpose and quality of the work are sufficiently indicated in the following prefatory passage: "The author never contemplated anything beyond a general sketch of the present bearings of science upon the vexed question of the origin and early history of man. But the question has many subdivisions. He intended the several lectures to be separate sketches of those subdivisions of the field of discussion—mere introductions to their proper study. His views are stated, therefore, in round terms. Nothing is closely reasoned out. Much is left to the logical instinct, and more to the literary education, of the reader. Reference is everywhere made to the sources of information within easy reach of all. Even the style of an essay has been avoided. The book is merely a series of familiar conversations upon the current topics of interest in the scientific world."

We have gone through Mr. Lesley's book with interest and profit—pleased with its brilliant and forcible passages, which are frequent; instructed by its learning and its abounding facts, and stimulated by its incisive observations and its forcible arguments. But the work is strongly stamped with the author's individuality, and its supplementary chapters especially, fresh and breezy as they are, contain various opinions to which we find it impossible to subscribe. The view taken of sociology, in the lecture on "The Social Destiny of the Race," appears to us inadequate and not up to the times; and in the lecture on "The Future