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LX. Notices respecting New Books. 



An Elementary Treatise on Rational 31echanics. By the Rev. 



John Kerr, M.A. Glasgow : William Hamilton [1867], pp. 295. 

 rpHIS work is designed for the use of those students of natural 

 -*- philosophy " who have no time for the higher mathematics," 

 the use of the higher mathematics being avoided by a free employ- 

 ment of limits and infinitesimals wherever required. Such is the 

 author's account of the book ; and we may add that even when the 

 student has time and inclination to master the higher mathematics, 

 the best introduction to the Calculus is a work in which detached 

 questions are treated by limits — such as the early sections of the 

 ' Principia,' &c. 



The present treatise contains a very comprehensive view of ele- 

 mentary mechanics, and discusses several subjects not generally 

 contained in books of this class, such as vis viva, central forces, and 

 the motion of a rigid body round a fixed axis. The latter of these is a 

 very valuable addition to the usual course, though the subject cannot 

 be fully treated in an elementary work ; e. g. it is scarcely possible 

 to discuss the pressure on the axis of the revolving body by elemen- 

 tary mathematics only. The work is illustrated by a large number 

 of well-selected examples ; and a student who thoroughly masters 

 its contents will have an excellent knowledge of the subject. 



It is liable to what in the case of an elementary treatise is a some- 

 what serious objection : it is abstruse ; by which we mean that the 

 inherent difficulty of the subject is increased by the order in which 

 the parts are arranged, and in some cases by the way in which they 

 are stated. It would require a detailed examination of the book to 

 show this ; we will mention just one instance. The learner is in- 

 troduced to every combination of forces acting on a point before he 

 comes to the first example ; whereas in practical teaching it is far 

 the best method to familiarize the learner with the cases of three 

 forces in equilibrium before letting him go further. This we believe 

 to be the most serious obstacle to the usefulness of the work ; and 

 this will be overcome by any learner who has sufficient energy to 

 avail himself of the author's caution: — " In using this treatise the 

 beginner will find it essential to secure his ground very carefully as 

 he proceeds." 



We would invite Mr. Kerr's attention to a point which in our 

 opinion he should reconsider in case a new edition of his work be 

 called for : we mean his use of the term " force of inertia," which 

 occurs several times, and which we suppose to be a translation of 

 the old term " vis inertia?." The objection to the term is that, force 

 being defined in the usual way (p. 1), "force of inertia" is not a 

 force at all. Now, though Mr. Kerr must be well aware of this, 

 what he says on the subject is highly calculated to mislead the 

 learner on a fundamental point. Thus, in the note headed " Illus- 

 trations of Force," we have apparently as different examples of force, 

 muscular effort, force of gravity, force of inertia, force of elasticity 

 (p. 287). So, again, on page 183 we find that "when a train 



