Chemistry and Physics. 113 



and the answers are given with but few exceptions. The text- 

 figures and type are clear and emphasis is indicated by the judi- 

 cious use of italics. Also, at the close of the volume, some useful 

 numerical data and an index are given. The book is doubtless 

 admirably adapted to the needs of British students but it gives 

 the impression of being too extensive and detailed for the require- 

 ments of most colleges in the United States. h. s. u. 



8. An Elementary Treatise on Calculus; by William S. 

 Franklizst, Barry MacNutt and Rollix L. Charles. Pp. x, 

 294, with 179 figures. South Bethlehem, 1913 (The Authors). — 

 Teachers of physics often find that students who can apply with 

 ease the operations of the calculus to the solution of formal, 

 analytical questions are altogether at sea when it becomes neces- 

 sary to work out even a simple problem of a practical nature. 

 The authors have not only experienced this difficulty but they 

 have written and printed a book which is especially designed to 

 meet the exigencies of the case. In view of the apparently radi- 

 cal and unorthodox nature of the text the volume has not yet 

 been given to a publishing house but has been printed tentatively 

 in order to find out whether a widespread need for reform is felt 

 by other successful teachers of the subject. 



The guiding principle of the presentation is expressed as fol- 

 lows: " We believe that the most important thing in the teaching 

 of calculus is to lead the student to a clear understanding of 

 principles." " Therefore our chief endeavor has been to develop 

 the subject as simply and as directly as possible." This has been 

 accomplished by teaching the student to think clearly about the 

 meanings of the operations which he performs and not to effec- 

 tively treat the calculus as a mathematical game which is played 

 with symbols according to certain rules and regulations. For 

 illustration, the subject of integration is introduced by calling 

 attention to the fact that such familiar instruments as cyclom- 

 eters and watt-hour meters are integrating machines. A dis- 

 cussion of the Amsler planimeter is then followed by an example 

 of " integration by steps " in connection with a speed-time curve 

 of an electric car. After nine pages of this kind of prepara- 

 tion the subject of algebraic integration is begun. The definition 

 of a differential equation is wisely presented as early as page 31. 

 Chapter VII (pp. 168-189) deals with " Some Ordinary Differen- 

 tial Equations" and chapter VIII (pp. 190-209) is entitled "The 

 Partial Differential Equation of Wave Motion." The final chap- 

 ter (IX, pp. 210-253) is on "Vector Analysis." There are three 

 appendices comprising respectively problems, a table of integrals, 

 and a commentated list of some important books on mathematical 

 theory. To sum up, this text amounts to a homogeneous mixture 

 of the calculus, differential equations, vector analysis, physics, 

 and, above all, common sense. At present there are a great many 

 errors in the numerical answers to the problems but these will 

 doubtless be eliminated before final publication. The only way 

 to get a correct idea of the contents of this admirable book is to 

 procure a copy and read it entirely through, as the reviewer has 

 done. h. s. u. 



Am. Jour. Sci.— Fourth Series, Vol. XXXVII, No. 217.— January, 1914. 



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