NATURE 



41 



THURSDAY, NOVEMBER 16, 1871 



NEW WORKS ON MECHANICS 



Lehrbuch der Mechaiiik in elemcntarer Darstelliing init 

 Uebnngen uni Anwcndmigen atif Maschinen mid Bait- 

 Constructionen. Von Ad Wernicke. Vol. I. (Braun- 

 schweig, 1871. London : Williams and Norgate.) 



Lehrbuch der physikalischen Mcchanik. Von Dr. Hein- 



rich Buff. Vol. I. (Braunschweig, 1871. London : 



Williams and Norgate.) 

 An Elementary Course of Theoretical and Applied 



Mechanics. By Richard Wormell. Second Edition. 



(London, 1871. Groombridge and Sons.) 



WERNICKE'S work is intended for pupils in the 

 Prussian industrial schools [Ge-wcrbeschnlen). The 

 first volume treats of Statics and Dynamics, leaving Hydro- 

 mechanics for the second. According to the preface, 

 students reading this work should be acquainted with 

 elementary mathematics, including co-ordinate geometry, 

 while a knowledge of the differential calculus is not 

 required. From an English point of view, it is not de- 

 sirable to draw the line between co-ordinate geometry and 

 the calculus. Even in our universities, not twenty per 

 cent, of the students are acquainted with co-ordinate 

 geometry. It is to be regretted that the proportion is so 

 small ; that it is so, is due to the present preposterous 

 system of classical education, that relic of the middle ages 

 which is the bane of our schoolboy days. Almost all 

 English students, however, who learn co-ordinate geo- 

 metry, generally study both the differential and integral 

 calculus before commencing mechanics. Now intelligent 

 pupils like a te.\t-book of mechanics in which they find 

 scope for exercising all their mathematical knowledge ; 

 hence it would appear that for English purposes the line 

 is drawn either too high or too low. 



As to the manner in which Wernicke has executed his 

 task, it would be hard to speak too favourably ; and not- 

 withstanding the point we have raised, we should hail an 

 English translation as a valuable addition to our standard 

 works on mechanics. One of the best features in the 

 book is that it presents theoretical and practical mechanics 

 not as two distinct subjects, but in that degree of com- 

 bination which naturally belongs to them. 



The first volume of Wernicke's work consists of 500 

 octavo pages, and is divided into three parts. Part I. 

 discusses the Kinematics of a mathematical point, 

 the inquiry being principally confined to space of two 

 dimensions. The symbol j is here and throughout the 

 work used to denote an acceleration : for example, jx is 

 the acceleration parallel to the axis of x. This notation (un- 

 familiar to English readers) has obvious advantages when 

 the more appropriate language of the differential calculus 

 cannot be employed. About fifty examples, many of a 

 practical character, are appended to Part I. Among them 

 is found (Ex. 31) a problem virtually requiring the inte- 

 gration of x^. The solution given is necessarily round- 

 about and cumbrous, owing to the restraint which the 

 author has imposed upon his use of mathematics. It 

 may, indeed, be questioned whether a student who is 

 not acquainted with the integral calculus could really 



VOL. V. 



profit by a solution which is merely the integral calculus 

 ground down and spoiled. 



Part II. is upon the Mechanics of a material particle. 

 We notice here small points in the diagrams which must 

 be useful to the learner. Thus, in a figure where the 

 length of a line is denoted by a symbol, the extremities of 

 a bracket indicate the extremities of the line. Those who 

 use the black-board in teaching will appreciate the 

 advantage of this detail. Take, for example, Fig. 54, 

 which refers to motion in an ellipse about a force in the 

 focus. In this part and the examples appended, the usual 

 proportions relating to the statics and dynamics of forces 

 applied at a single point will be found. 



The third part, which treats of the mechanics of a 

 rigid body, occupies four-fifths of the volume. Chap. I. 

 discusses the Composition and Equilibrium of Forces in 

 space ; some of the examples require a good deal of 

 honest nu.merical work, others are well-known questions 

 not involving friction. Chap. II. ison the Centre of Gravity ; 

 in this we do not notice much that is unusual, except 

 the excellence of the illustrations. The examples contain 

 problems on the centre of gravity of various useful areas 

 and volumes, the theory of the arch, and many other sub- 

 jects. 



In Chap. III. we have a treatise upon Friction. We 

 miss here an actual description and discussion of a series 

 of experiments from which the laws of friction are estab- 

 lished. This omission is to be regretted, because the 

 laws are only appro.ximate, and it is important for the 

 pupil to have materials presented to him from which he 

 can form his own estimate of their correctness. Intelli- 

 gent pupils v.'ould have been pleased to find how true the 

 laws are on the whole, and interested in noting the dis- 

 crepancies. No good opportunity for introducing and 

 discussing the results of experiments should have been 

 lost in a work of this kind. With this exception, the 

 force of friction has been treated in a manner worthy of 

 its importance ; we find its effect upon the various me- 

 chanical powers, upon toothed wheels and brakes, and in 

 many other cases, treated in an excellent manner. Chap. 

 IV., on the Motion of a rigid body, very properly com- 

 mences with the exquisite kinematical theorems of 

 Poinsot. D'Alembert's principle follows, and also a table 

 of moments of inertia, which will be found a useful aid in 

 recollecting these troublesome quantities. 



Chap, v., on Elasticity and Rigidity, is certainly the best 

 chapter in the book. Problems connected with the deflec- 

 tion of a beam are among the most interesting questions 

 of mechanics. We have here an exceedingly careful dis- 

 cussion of this subject, not too much encumbered with 

 formula?. A large number of examples thoroughly worked 

 illustrate this chapter. Every teacher of applied mechanics 

 will find these examples invaluable ; they are far better 

 than those on the same subject in any other book with 

 which we are acquainted. 



Finally, in estimating the merits of this work, we must 

 recollect that it is a manual for class instruction ; it is not, 

 nor does it profess to be, a comprehensive and original 

 treatise, like the great work of Weisbach. 



Buff's work, of which the first volume is before us, is of 

 somewhat different character to that of Wernicke. It 

 bears the same marks of painstaking thoroughness which 

 characterise the better class of German works on science. 



