August 21, 1884] 



NA TURE 



5§3 



of two consecutive pairs, and serves to connect the pairs 

 so that the whole mechanism ma)- be described as a 

 chain, of which the parts form the links. Such a series 

 of connected pieces is called a kinematic chain." It is in 

 this mode of regarding the component parts of a machine 

 and in the consequences that flow from it that the pecu- 

 liarities of the modern system consist. A valuable feature 

 of this work is the series of curves of velocity given for 

 different mechanistic combinations, especially those de- 

 rived from the slider-crank chain. The special use of 

 such curves is that the varying motion of different parts 

 is exhibited to the eye, which is thus enabled to realise 

 its changes during the cycle in a complete way which 

 would otherwise be difficult, if not impossible. Of the 

 large and intricate subject of the Teeth of Wheels only a 

 sketch is given, which a student would need to supplement 

 by extensive reference to other books in order to under- 

 stand. 



In the Part on the Dynamics of Machines we find the 

 chapter on " The Dynamics of the Steam-Engine" the 

 best in the book. The mode of constructing curves of 

 crank effort of two kinds is shown, and the results given 

 in different cases for two cranks at right angles and for 

 three cranks at angles of 120°, and these curves are used 

 to determine the fluctuation of energy in a complete revo- 

 lution. This last is expressed in terms of the total energy 

 as a fraction which, in the case of a three-throw crank 

 with connecting rod equal in length to six cranks is as 

 low as -0084. A method is afterwards given by which to 

 obtain similar results from any indicator diagram. 



The chapter on Friction contains a complete rfowne of 

 modern experiments on friction with an investigation by 

 both exact and approximate methods of the efficiency of 

 mechanism when friction is considered. 



The Principle of Work is assumed throughout the book, 

 being regarded as " a fundamental mechanical principle 

 continually verified by experience, and a great many 

 results are thus arrived at in the simplest way. One very 

 interesting example is got by applying this principle (in 

 the form known as the principle of virtual velocities) to 

 the determination of the bending moment in the case of a 

 loaded beam. Nowhere has the author been more suc- 

 cessful in his simple mathematical treatment than in the 

 chapters which deal with the strength and deflection of 

 beams, and the power possessed by a combination of the 

 mathematical and the graphical methods could hardly be 

 shown more strongly than by the proof, given without the 

 use of the calculus, of the most general form of Clapeyron's 

 Theorem of Three Moments. 



The fundamental theorems of the theory of elasticity 

 are presented in an equally simple and elementary way. 

 In describing the behaviour of matter strained beyond 

 the elastic limit, a brief account is given of the mode of 

 rupture of different classes of bodies when loaded so as to 

 exceed that limit, and the information here furnished, as 

 in all the other descriptive parts of the book, is brought 

 up to the level of our present experimental knowledge. 



The concluding chapters treat of the transmission and 

 conversion of energy by fluids, and contain a brief 

 account of the ordinary propositions in hydraulics and 

 pneumatics, together with the outlines of the theories of 

 hydraulic motors and of heat-engines. The flow of liquids 

 and gases through pipes is also dealt with. 



The aim of the book excludes any detailed description 

 of machines, although the drawings of machines are, as a 

 rule, working drawings, the desire being to elucidate the 

 principles and theory of machines in general, but inci- 

 dentally much valuable descriptive matter is introduced, 

 and the illustrations are in all cases derived from actual 

 machines and structures. Thus, among other valuable 

 topics of practical interest we have an exposition of the 

 theory of fly-wheels, centrifugal regulators, dynamometers, 

 the balancing of machines, and of impact, this last being 

 illustrated, amongst other examples, by the action of a 

 gust of wind on a vessel. 



At the end of each chapter we find a selection of well 

 devised and admirable examples, most of them so framed 

 as either by way of illustration to bring into prominence 

 particular parts of the text or to show the influence in 

 special cases of modifying causes. This collection, which 

 must have taken much time and trouble to prepare, is by 

 no means the least useful part of the book, the value of 

 which is yet further increased by the full list of authorities 

 for reference which is appended to each chapter, which 

 will assist the student in extending his studies in any 

 special direction. 



This book may be recommended not only for the 

 admirable mode of treatment of that which it contains, 

 but also for the exclusion of that which does not find a 

 place there. The same knowledge of the needs of a 

 reader beginning the study of applied mechanics which 

 has led to the selection and arrangement of the topics 

 introduced, has led to the omission of other parts which, 

 though useful and interesting in themselves, are not 

 necessary to be mastered on a first approach to the sub- 

 ject. We could wish that the proofs had been more 

 carefully revised, so that a number of, for the most part 

 trifling, though tiresome, errata might have been cor- 

 rected. A careful perusal of the volume leads us to 

 express almost unqualified praise of this latest addition 

 to the English literature of applied mechanics. 



J. F. Main 



OUR BOOK SHELF 



Graphic and Analytic Statics in Theory and Comparison. 



By Robert Hudson Graham, C.E. (London : Crosby 



Lockwood and Co., 1884.) 

 This is an extensive treatise for the use of engineers, the 

 distinguishing feature of it being that graphic and analytic 

 methods are both employed. The first part (30 pp.) deals 

 with the principles of graphic statics, and contains some 

 well-chosen examples of the beautiful method of reciprocal 

 figures. The second part (50 pp.) treats of the stresses of 

 roofs and bridge structures, both methods being employed. 

 The third part (290 pp.), which for some reason is called 

 comparative statics, consists of eight chapters, the sub- 

 jects of which are direct stress (elongation of bars, &c), 

 couples, composition of forces, centre of gravity, moments, 

 straight beams and girders, solid girders in equilibrium, 

 and wind pressures. Throughout the book there are 

 interspersed collections of valuable exercises with their 

 results. 



The most manifest defect of the work is a prevailing 

 inaccuracy of expression. With such a subject this is 

 quite inexcusable, and is sure to be found excessively 

 trying to the patience of a student. It is not at all due to 

 want of mathematical knowledge on the author's part, so 

 that, as might be expected, he is perfectly unconscious of 

 it. Ludicrously so indeed ; for in the preface he tells us 



