May 1 6, 1889] 



NATURE 



51 



operations of the same character required by the engineer, 

 shipbuilder, or constructor in general, that the graphic 

 method takes the lead once the calculator has got his 

 mental operations thought out, and his instruments in good 

 order; for which purpose Chapter I., on instruments, gives 

 valuable hints and information. 



Chapter II. explains succinctly the plan of the book in 

 its applications to graph-arithmetic. Chapter III. ; graph- 

 algebra. Chapter IV. ; grapho-trigonometry and mensura- 

 tion, Chapter V., &c., and lastly, grapho-dynamics, 

 experimental and mathematical tabulation. 



It is in the later chapters that the full power of the 

 graphic method is developed, but in the earlier chapters 

 the student is exercised by well-chosen practical examples 

 in the mental operations and manipulation required in 

 the advanced processes. The student of ordinary mathe- 

 matical processes will find here graphic solutions of geo- 

 metrical loci, and the solution of quadratic, cubic, and 

 other algebraical and trigonometrical equations, illus- 

 trated by carefully-drawn diagrams in the atlas of 

 plates. But the author appears to underrate the value 

 of the planimeter on p. 63, in its application to the evalua- 

 tion of the irregular areas encountered in indicator dia- 

 grams, shipbuilding, and railway engineering. 



In Chrystal's " Algebra," the importance of the graphic 

 solution in integers of the loci represented by indeter- 

 minate equations of the first and second degree is pointed 

 out ; and in the present work the graphic solution of the 

 general quadratic and cubic equations by means of acare- 



fully-drawn curve, y = ' , or y = — .and its intersec- 

 10 -^ 100' 



tions with a straight line, is also developed, and illustrated 



in the Atlas of Diagrams. • . 



■ The logarithmic curve, y = t", or lo>^^, would also be 



useful for the graphic solution of transcendental equations 



of the form — 



\a^ -\- D.v + F = o, 



required in the problem of the hydraulic buffer. 



Again, in trigonometry, the solution of the equation — 



a cos ^ + ^ sin ^ = ^, 



or the summations 2 cos (a -}- «/3) or 2' sin (a -f ;//3) by a 

 graphical method, or drawing Lissajous's figures graphic- 

 ally, would tend to impart freshness to a subject at 

 present running in a narrow dry rut. Paper ruled into 

 small squares of centimetres and millimetres, suitable for 

 graphic methods, can be obtained in Germany, of Carl 

 Schleicher and Schiill in Diiren, for instance. 



It is curious to notice that the fresh and original ideas 

 and treatment of elementary mathemathical subjects due 

 to Maxwell and Clifford are to be found embodied and 

 adopted only in practical and technical treatises, such as 

 the present work. Elementary mathematical treatises are 

 in danger of becoming as dry and orthodox as a religious 

 creed : examiners, on the one hand, are forbidden to set 

 ideas out of the groove of a few antiquated text-books ; and 

 examinees, on t'he other hand, dare not allow themselves 

 to learn new ideas and methods, for fear of finding them- 

 selves at a disadvantage with old-fashioned examiners. 



Some reflections on p. i8i of the present work on the 

 radiant-energy-carrying ether show, however, that the 

 author allows himself occasionally to indulge in the 



purely abstract speculations dear to SirW. Thomson and 

 Mr. Macfarlane Gray. 



Chapter IX., on the " Kinematics of Mechanisms," 

 covers much the same ground as Kennedy's " Mechanics 

 of Machinery," and follows Reauleaux's treatment in his 

 " Kinematik." Chapter X., on "Static Structures, Frames, 

 or Linkages," and Chapter XI., on " Flat Static Structures, 

 containing Beam-Links," contain the applications of the 

 graphic method to problems most commonly encountered 

 by the practical designer. 



The consideration of" Solid Static Structures" in Chap- 

 ter XII. follows very usefully as a check upon the in piano 

 treatment of the subject in the two preceding chapters. 

 The failure of many very scientifically-designed bridges 

 in America has shown that it is not sufficient to treat the 

 beam in elevation only, as if it was a vertical plane struc- 

 ture ; but that the torsional rigidity is of importance 

 whenever the load is applied in the least degree 

 eccentrically. 



A glossary of special terms and symbols is inserted 

 at the beginning, containing without redundancy the 

 new terminology useful in this subject ; and an index 

 completes the work, in which we should like to have seen 

 a complete list of books in English bearing on this and 

 kindred subjects, such as Cotterill's " Applied Mechanics,' 

 Eagles's " Constructive Geometry," Clarke's " Graphic 

 Statics," Wormell's "Plotting, or Graphic Arithmetic"; 

 also McLay's articles on " Geometrical Drawing," now 

 appearing in the Practical Engineer. 



The author promises a second part dealing with "The 

 Distribution of Stress and Strain," " The Strength, 

 Stiffness, and Design of Beams and Struts," " Economy 

 of Weight in Structures," " Stresses in Redundant Struc- 

 tures," " Statics and Dynamics of Machines," " Frictional 

 Efficiency," " Governors and Fly-wheels," " Valve Gears," 

 " Practical Thermodynamics of Furnaces, Boilers, and 

 Engines," " Hydrostatics and Hydrokinetics of Ships and 

 Hydraulic Machines"— all subjects of great practical and 

 theoretical interest, to which we shall look forward with 

 much pleasure. A. G. Greenhill. 



THE CHEMICAL ANALYSIS OF IRON. 

 The Chemical Analysis of Iron. By Andrew Alexander 

 Blair. (London : .Whittaker and Co. Philadelphia : 

 J. B. Lippincott, 1888.) 



OF all the branches of quantitative analysis practised 

 for the control of industrial processes, none is of 

 greater importance than that which concerns iron. The 

 precise relationship of chemical composition to mechan- 

 ical properties is by no means fully ascertained ; but a 

 great deal of excellent work has been done in this 

 direction, and we know in several cases the kind of 

 variation in physical properties which is, cceteris paribus, 

 to be expected to accompany a variation in the quantity 

 of one constituent. We know, moreover, how extra- 

 ordinarily great this physical change may be, com- 

 pared with the change in composition. When we reflect 

 that a quantity, which in most other technical analyses 

 is within the error of experiment, may become the 

 criterion by which an iron is appraised, we must recog- 

 nize the necessity of accurate methods of analysis for 

 this particular commodity. 



