FeBKL AKY 24, I'JOo.] 



SCIENCE. 



303 



the book will doubtless prove effective in the 

 hands of a teacher who is in sympathy with 

 the methods and point of view of its author. 



Stephan's book is admirable for the sim- 

 plicity with which elementary principles and 

 methods are presented. If written in English 

 it would probably find favor with many teach- 

 ers in America who desire a text-book not pre- 

 supposing calculus. It should be said, how- 

 ever, that while calculus notation is not em- 

 ployed by Stephan, he does employ the concep- 

 tions of both differential and integral calculus. 

 The fundamental conceptions of the calculus 

 are, of course, necessarily employed in any 

 sound presentation of the principles of me- 

 clijinics, and it may be doubted whether real 

 simplicity is gained by avoiding its notation. 



The three books are all designed for stu- 

 dents of engineering, and each aims to be 

 practical by including many numerical exer- 

 cises and illustrative examples of the kind 

 met in engineering practise, but each is a text- 

 book of theoretical, rather than applied, me- 

 chanics. All have much the same scope, cov- 

 ering the statics, kinematics and kinetics of 

 particles and of rigid bodies. Two of the 

 books — those of Maurer and Stephan — agree 

 somewhat closely in order of treatment, be- 

 ginning with statics and following with kine- 

 matics and kinetics. Ziwet, on the other 

 hand, begins with geometry of motion and 

 kinematics, follows with an introduction to 

 dynamics (statics being treated as a special 

 case) and concludes with kinetics. In all the 

 treatment is mainly restricted to the simpler 

 force systems and the simpler cases of motion. 

 Of the three books that of Stephan is the most 

 elementary in treatment, while that of Ziwet 

 would probably be the most difficult reading 

 for the average student beginning the subject 

 in its usual place in a course in engineering. 



As features of Maurer's book may be men- 

 tioned the emphasis everywhere given to the 

 vector nature of the quantities dealt with, the 

 parallel treatment of graphical and analytical 

 methods in statics, the admirable chapter on 

 work and energy, and the satisfactory treat- 

 ment of the subject of units. Professor Ziwet 

 also gives prominence to vector notions, and 

 also includes graphical methods in statics. 



though less fully than Maurer. His book con- 

 tains no systematic presentation of the theory 

 of energy, though the main features of the 

 theory may be gathered from detached pas- 

 sages. His treatment of kinematics and kin- 

 etics is throughout more elaborate on the 

 theoretical side than that of Maurer or of 

 Stephan, and more use is made of general 

 analytical methods. Stephan does not use 

 the language of vectors. In statics he makes 

 free use of graphical methods, but does not 

 give the student the aid which comes from 

 the use of Bow's notation for the designation 

 of forces. His treatment of kinematics and 

 of kinetics is relatively brief, and only the 

 merest introduction to the theory of energy is 

 given, potential energy not being mentioned. 



Dimensional equations and the theory of 

 units are explained by both Maurer and Ziwet, 

 the former devoting to this subject an ap- 

 pendix of six pages. In Professor Ziwet's 

 book (Art. 58) occurs an erroneous illustra- 

 tion which is likely to confuse the student: 

 ' * * * we have of course the proportion : 30 

 miles an hour is to one mile an hour as 44 

 feet per second is to one foot per second.' 

 Both gravitational and kinetic systems of 

 units are explained in each of the three books. 

 The simple treatment of the engineers' kinetic 

 system adopted by Maurer and Stephan should 

 effectually clear away the traditional haziness 

 surrounding the equation to = W/g. The 

 unit mass is taken as a derived unit, and de- 

 fined as the mass to which the gravitation 

 unit force (the pound-force or kilogram-force) 

 gives unit acceleration; this unit mass is thus 

 equal to g pounds or g kilograms, and the 

 equation expresses the reduction from one 

 unit mass to another. The usefulness of a 

 name for the unit thus defined will be agreed 

 to even by those who hesitate to adopt the 

 names geepound and geeJcilogram suggested by 

 Maurer. 



In considering the general question as to 

 the best method of presenting the fundamental 

 principles of mechanics in an elementary text- 

 book, two requirements must be kept in view, 

 soundness and intelligibility. Critics are by 

 no means agreed as to what constitutes a 

 sound formulation of the laws of motion. 



