282 



THE POPULAR SCIENCE MONTHLY 



this principle. lie 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 con- 

 fronted at the outset with the number of 

 entirely new conceptions, such as those of 

 variables, functions, increments, infinitesi- 

 mals, and limits. In his first lesson he finds 

 these all combined with a notation so en- 

 tirely 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 enunci- 

 ation. The practical feature of the work 

 subsidiary to this principle consists in sub- 

 dividing each subject as minutely as possi- 

 ble, 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 math- 

 ematician will be sure to commend his work 

 to the favorable regard of teachers, and ex- 

 perience with it will test the fidelity with 

 which he has applied the principles we have 

 referred to, and others of perhaps equal im- 

 portance which we have not space to notice. 



Man's Oric.in and Destiny, sketched from 

 THE Platform of ihe Physical Sciences. 

 By G. P. Lesley, State Geologist of 

 Pennsylvania. Boston: George 11. Ellis. 

 IV- 142. 



The chief portion of this volume was 

 prepared as a scries of lectures, and deliv- 

 ered at the Lowell Institute, Boston, in 1866. 

 They were published in a volume under the 



present title in 1S68, and, the work continu- 

 ing 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 throw- 

 ing 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 the- 

 ory which he claims as his own, but is rather 

 a free, discursive interpretation and criti- 

 cism 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 pref- 

 atory passage : " The author never contem- 

 plated anything beyond a general sketch 

 of the present bearings of science upon the 

 vexed question of the origin and early his- 

 tory of man. But the question has many 

 subdivisions. He intended the several lect- 

 ures to be separate sketches of those sub- 

 divisions 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 th2 

 literary education, of the reader. Reference 

 is everywhere made to the sources of infor- 

 mation within easy reach of all. Even the 

 style of an essay has been avoided. The 

 book is merely a series of familiar conver- 

 sations 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 in- 

 cisive observations and its forcible argu- 

 ments. But the work is strongly stamped 

 with the author's individuality, and its sup- 

 plementary 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," ap- 

 pears to us inadequate and not up to the 

 times ; and in the lecture on " The Future 



