REVIEWS. 
Mathematics for Engineers, Part II.; by W. N. Rose, B.Sc. Pp. xiv., 419. 
London, Chapman and Hall Ltd. 1920. Published price, 13s. 6d. ‘This book 
is the second yolume of a comprehensive and practical treatise on the subject 
of mathematics for engineers. ‘The first part dealt with Mensuration, Graphs, 
Advanced Algebra, Plane Trigonometry, Plotting of Curves, &c. With the excep- 
tion of Chapters on Spherical Trigonometry and Mathematical Probability, 
the second part is devoted to the study of the calculus, both differential and 
integral. Though the treatise is based upon algebraic principles, much atten- 
tion has been paid by the author to graphic interpretation. Thus from the 
commencement the connexion between the rate of change of a quantity and the 
slope of a curve is clearly demonstrated, and this correlation of the algebraic 
and graphic methods is continued through all the stages of the development of 
the subject. 
In Chapter 1, the conception of “limiting values,” which was mentioned — 
briefly in Part I’ of the book, is further discussed, and two methods of graphic 
differentiation are given. The various rules for the differentiation’ of . both 
algebraic and trigonometrical functions are explained in detail in Chapter 2, 
while Chapter 3 explains the rules for the differentiation of a function, 
the product of functions, &¢., and furnishes an introduction to partial 
differentiation. Interesting and valuable examples of the practical applications 
of differentiation are given in Chapter 4, and special attention is paid to the . 
determination of maximum and minimum yalues. The use of ERA ‘Theorem 
in cases of interpolation from steam tables is demonstrated. 
Chapters 5 and 6 contain the rules required for the integration of functions 
occurring in engineering theory and practice. At this stage also the reduction 
formule are introduced, and mention is made of the Gamma function and its 
uses: Examples of the application of the rules of integration are given in 
Chapter 7, and special features of this Chapter are the graphic method for 
fixing the position of the centroid vertical, and the evaluation of moments of 
inertia. The following Chapter deals with the utility of polar co-ordinates, and 
illustrations are given of their practical value by the inclusion of examples on 
the candle-powers of lamps and the employment of the Rousseau: diagram to 
find the mean spherical candle-power. The methods of solution of common 
types of differential equations are lucidly explained, and Chapter 10, with its 
applications of the calculus to problems encountered in* the study of thermo- 
dynamics, strength of materials, applied mechanics, electricity and hydraulics, 
provides saree dtre illustration of the need of a sound knowledge of the subject 
to the engineer desirous: of equipping himself at all. points. 
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