December 15, 1904] 



NA TURE 



M9 



English books, followed by a discussion of all the 

 ordinary simple machines — with this difference, that 

 Herr Stephan's figures are much better than those of 

 our text-books. Then follows a discussion of friction, 

 in which, although the author almost invariably solves 

 his problems by introducing the normal force N and 

 the friction mN, he does not omit to point out the 

 utility of the total resistance and the angle of friction. 

 He underestimates this utility, however, in solving a 

 simple problem by the N and ^uN method, and in his 

 final results (p. iiS) substituting the angle of friction 

 — a process which simply obscures the merit of the 

 second (and much shorter) method — with the remark 

 that the example shows the advantage which the intro- 

 duction of the angle of friction "occasionally offers." 

 The truth is that in the hands of a skilful student the 

 geometrical method founded on the employment of the 

 angle of friction and the total resistance is almost 

 always more neat, direct, and simple than the 

 analytical, or N and mN, method. It can be conceded, 

 however, that for engineering students, and technical 

 students generally, this analytical method is the safer, 

 although the longer, and requires less of the esprit 

 mathhnatique. The nature of rolling resistance, 

 which seldom finds mention in our English books, is 

 well explained and illustrated by several applications 

 (pp. 147, S:c.). Indeed, the whole of Herr Stephan's 

 treatment of the machines (screw presses, cranes, 

 friction band-brakes, &c.) commonly discussed is excel- 

 lent, and occupies a very large part of the treatise ; it 

 is, in fact, the best and most useful portion of the book. 



The only kind of catenary treated of in this volume 

 is the parabola of suspension bridges, to which only 

 two pages and two illustrative examples are devoted. 

 Doubtless the subject will receive more consideration 

 in some subsequent volume. 



Herr Stephan is very careful to avoid errors in his 

 figures, and to represent the lines of action of three 

 forces when they keep a body in equilibrium as meet- 

 ing in a point — a very elementary condition not always 

 observed in our text-books. Once, however, he over- 

 looks this necessity, and represents the lines of action 

 of three forces acting on a bar in a framework (Fig. 

 164) as forming a triangle of very respectable area. 



In the section dealing with the equilibrium of frame- 

 works of jointed bars, he directs attention to the obvious 

 fact, which is not usually mentioned in our books, that 

 even if the bars are loaded throughout their lengths 

 (by their own weights or otherwise) the stresses can 

 be calculated by taking any of the bars as unloaded 

 and weightless, and then superposing the calculated 

 results (p. ig7). This simple principle he applies in a 

 special case, and it is one which on many occasions 

 might be employed with great advantage. 



The last hundred pages are devoted to kinetics of an 

 elementary kind — including the theory of direct 

 collision of spheres, the compound pendulum, &c. — 

 together with a section on the moments of inertia of 

 various figures and solids. There is no mention made 

 of the very simple and useful rule that a triangular 

 area can be replaced by three equal particles placed at 

 the middle points of its sides — a rule which saves an 

 enormous amount of trouble in the calculation of 

 NO. 1833, VOL. 71] 



moments of inertia for all plane areas bounded by 

 right lines. In the absence of this simple rule, a pon- 

 derous application of the integral calculus is the only 

 refuge of the student. A somewhat similar " particle 

 rule " saves reams of ponderous calculus work in 

 hydrostatics ; but these rules are not widely known. 



Herr Stephan very properly makes short work of 

 D'Alembert's principle, deducing it directly from 

 Newton's axioms ii. and iii., so that, although he 

 employs the term " centrifugal force," he is careful, 

 except in one instance, to show that it is a force exerted 

 6y, and not on, a moving particle. The exceptional 

 instance occurs at p. 281, where he is calculating the 

 tension in a driving belt which passes over the surfaces 

 of two revolving cylinders. Here he speaks of a small 

 element of the band as " experiencing " a centrifugal 

 force, which is duly represented, in the usual way, by 

 a centre-flying arrow. His subsequent teaching, how- 

 ever, removes the erroneous notion herein contained. 



The book is wonderfully well printed and illustrated, 

 as well as free from mistakes. On p. 15 " Punkte " 

 should clearly be " Krrifte," and on p. 187 the reference 

 should be to Fig. 131 and not to Fig. 135. The theory 

 is illustrated by nearly 200 examples. 



To all students who desire to attain a real and! 

 physical conception of the subject Herr Stephan's work 

 can be very strongly recommended. 



George M. Minchin. 



OUR BOOK SHELF. 

 Machine Drawing. By Alfred P. Hill. Pp. 83- 

 (London : P. S."King and Son, 1904.) Price 2s. 6d. 



net. 

 In this text-book the author presents a course of in- 

 struction which he considers suitable for students 

 attending elementary drawing classes who are unable 

 to spare more than one evening per week, and whose 

 technical training is thus confined to the one subject of 

 machine drawing. Three dozen plates are given, 

 affording a choice of examples to be copied to scale 

 from the dimensions figured, some of which are pro- 

 portional dimensions covering a range of sizes. Accom- 

 panying the plates are descriptive accounts of the 

 construction and uses of the machine parts drawn, 

 with sets of questions founded thereon. At intervals, 

 where space is available, formulae and physical data 

 are introduced and used in making calculations illus- 

 trating machine design. This crude attempt to teach 

 applied mechanics along with elementary machine 

 drawing seems to us a mistake, as, in the 

 absence of a knowledge of mechanical principles, such 

 formulae as are given become mere rules of thumb, and 

 any attempt to apply them independently cannot fail 

 to be disastrous, as, for instance, in the author's 

 method of estimating the limiting speed of a fly.-wheel 

 on p. 42. The time wasted on these premature cal- 

 culations might very profitably be spent with rule, 

 callipers, and squared paper, in measuring and making 

 careful and complete dimensioned sketches of actual 

 machine parts, and so cultivating the habit of .closely 

 and accurately observing constructional details. 



Errors abound throughout the book. The author is 

 not a safe guide even in such a small detail as the 

 projection of a hexagonal nut, while his statement on 

 p. 44 that " heat and work are mutually contro- 

 vertible " is a fair index of the scientific value of the 

 work. The volume is somewhat redeemed bv a few 



