Now Ready. 401 pp. Globe 8vo. 3s. 6d. ELEMENTARY PRACTICAL MATHEMATICS BY FRANK CASTLE, M.I.M.E. MECHANICAL LABORATORY, ROYAL COLLEGE OF SCIENCE, LONDON Adapted to the New South Kensington Syllabus London MACMILLAN AND CO., LIMITED NEW YORK: THE MACMILLAN COMPANY EXTRACT FROM PREFACE THE inability of artizan students to profit by much of the technical instruction given in polytechnics and similar institutes is largely due to insufficient preliminary training in Mathematics, for without a fair knowledge of this subject little or no real progress can be made in any branch of Physical Science. Notwithstanding this, classes in pure Mathematics are neither popular nor well attended by students of the industrial class. Even the enthusiastic apprentice seems to find it difficult to connect the instruction usually given in arithmetic, algebra, and geometry with the work of the shop or factory. A number of attempts have been made to remedy this state of affairs. Classes in Technical and Workshop Arithmetic, Machine Calculations, Mensuration, and similar subjects have been started in many centres. The latest attempt to interest and benefit the "practical man" is the syllabus of Practical Mathematics issued by the Department of Science and Art. Judging from the Examination paper of May last, and the lectures delivered by Prof. Perry, F.R.S., to working men and to science teachers, the object of the course is to show the student how to prove and verify truths by experiment instead of arriving at elementary results through the ordinary processes of Euclid and other academic authorities. Abstract reasoning is to be relegated to the background, and concrete facts are to form the basis of the student's work. The syllabus of Practical Mathematics, to which reference has been made, is so extensive in its scope that it is difficult to deal satisfactorily with all the points in it in a text-book such as the present. The course of study outlined in the following pages will consequently be found more than can be undertaken by backward students in one session. In such cases the plan of completing the course in two years may reasonably be adopted. CONTENTS CHAPTER I.-Measurement. Units of Length. CHAPTER II.-Units of Area and Volume. Density. Relative Density Principle of Archimedes. CHAPTER III.-Time and its measurement. Angular measurement; Degrees, Radians. Geometrical construction. CHAPTER IV.-Arithmetic. 66 x and ÷ "; Signs of Operation: G.C.M.; L.C.M.; Vulgar Fractions; Decimals. CHAPTER V.-Involution and Evolution. Simple Application of Arithmetical Rules. CHAPTER VI.-Algebra. Addition, Subtraction, Multiplication, and Division. Simple Operations. Factors. Simplification of Algebraical Expressions. Indices. CHAPTER VII.-Measures and Multiples. H.C.F. and L.C.M. Fractions. CHAPTER VIII.-Simple Equations. Simultaneous Equations. CHAPTER IX.-Graphic Methods. Scales and their use. Graphic Arithmetic. CHAPTER X.-Labour-saving Methods: Logarithms. Multiplication, Division, Involution and Evolution by Logarithms. and Tangent. CHAPTER XII.-Labour-saving Methods. The Slide Rule. CHAPTER XIII.-Arithmetical progression. Geometrical progression, Geometric Mean and Arithmetic Mean. Simple Interest. Compound Interest. Discount. CHAPTER XIV.-Orthographic Projection. True lengths and inclinations of lines referred to two and three Co-Ordinate Planes. CHAPTER XV.-Mensuration, Plane Figures, and Right-Angled Triangles. Areas of Rectangle, Parallelogram, Triangle, Rhombus, Hexagon, Quadrilateral, Trapezoid, Circle. Circumference and Area of Circle. Sector of Circle. Area of Annulus. Ellipse. CHAPTER XVI.-Simpson's Rule. CHAPTER XVII.-Mensuration. Solids. Areas, Volumes and Weights of Prisms (right and oblique)._Cylinder, Hollow Cylinder, Pyramid, Cone, Frustum of Pyramid, Frustum of Cone, Guldin's Theorem. Surface and Volume of Sphere, Cylinder, Ring, Fly-wheel. CHAPTER XVIII.-Linear Motion. Momentum. Force. Mass. Work. Energy (Potential and Kinetic). CHAPTER XIX.-The Specification of Vectors. Polygon of Forces. Funicular Polygon. Graphic conditions of Equilibrium. Moments of Force. Parallel Forces. Bending Moment. Centre of Gravity. Roof Trusses. Moment of Inertia. CHAPTER XX.-Use of Squared Paper. Plotting. Inch-Centimetres. Simple Machines. Area of Diagram to represent work done by a Force. Work done by a Variable Force. Compression of Springs. Stress, and Strain. Modulus of Elasticity. Indicator Diagrams. CHAPTER XXI.-Evaluation of Algebraic and Trigonometrical Formulae. EXAMINATION QUESTIONS. ANSWERS. INDEX. PRESS OPINIONS BOARD TEACHER.-"Just the book for those taking this new division of Science Subject V." BUILDER." It undoubtedly summarises in an excellent manner many branches of mathematics and shows how these may be adapted to the requirements of every day work. May be said to contain all the information ordinarily required by the mechanic." SECONDARY EDUCATION.—"The course embraces exactly what is requisite for students who desire to derive the full benefit of a course of instruction in technical work applicable to trades and industries. The book is admirably arranged. The diagrams are clear, and the examples numerous... Every school teacher ought to have it as a guide to more practical methods in teaching." SCHOOL WORLD.-"Sure to command a good sale. Fortunately it deserves this on its own merits. . . . Many of the subjects dealt with by the author might be introduced with great advantage into a school course; and his book deserves the careful attention of teachers from this point of view." Now Ready. Globe 8vo. Price 2s. 6d. A SCHOOL ARITHMETIC BY R. F. MACDONALD HEADMASTER OF CHILDERIC ROAD BOARD SCHOOL, LONDON THIS BOOK IS INTENDED SPECIALLY FOR USE IN HIGHER GRADE AND ORGANISED SCHOOLS OF SCIENCE London MACMILLAN AND CO., LIMITED NEW YORK: THE MACMILLAN COMPANY A HEADMASTER writes:-"I must congratulate you on bringing out such an excellent and useful work. I am very pleased with it and I shall be very surprised if it does not meet with almost universal acceptance in higher schools. I am particularly struck with the number, variety, and the general style of examples-these will prove a boon to teachers. I gave an examination in Arithmetic to my school this week and picked out all the examples from your book—the Assistants thought the examples given exceedingly fair and straightforward. CHAPTER I. ELEMENTS—Units-Numbers-Figures-Notation-Roman Notation-Exercises in Numeration and Notation, I., II. II. SIMPLE RULES.-Addition-Proofs-Exercise III.-Subtraction -Methods-Proofs-Exercise IV.-Multiplication-Tables- III. COMPOUND RULES. - British System - Tables Reduction Exercises IX., X.-Addition-Exercise XI.-Subtraction – Exercise XII.-Multiplication-Exercise XIII.-Mensuration -Area-Volume-Duodecimals-Exercise XIV.-DivisionExercise XV.-Mensuration-Exercise XVI.-Miscellaneous Exercises XVII. IV. NUMBERS.-Kinds-Factors-Divisibility of Numbers-Series of Numbers-Exercise XVIII.-Highest Common FactorExercise XIX.-Multiples-L.C.M.-Exercise XX. V. VULGAR FRACTIONS.-Equal Parts-Forms--Reduction-Exercise XXI.—Comparison-Exercise XXII.—Addition-ExerciseXXIII. - Subtraction - Exercise XXIV. Multiplication Exercise XXV.-Division-Rule of Signs-Exercise XXVI.— Compound Reduction-Exercise XXVII., XXVIII.-Miscellaneous Exercises XXIX. VI. DEMICALS.-Notation-Reduction-Exercises XXX., XXXI.— Addition-Decimal System of Coinage-Metric System-Exercise XXXII.-Subtraction-Exercise XXXIII.-Multiplication -Contraction-Exercise XXXIV.-Division-Exercise XXXV. - Reduction- Exercise XXXVI., XXXVII. - Miscellaneous Exercises XXXVIII. VII. PRACTICE. -Ratio-Aliquot Parts-Bills and Invoices-Exercises XXXIX., XL., XLI., XLII. VIII. PROPORTION. Ratio - Simple Proportion-Exercises XLIII., IX. PERCENTAGES. The Standard " Clocks - Exercise per centum Examples Brokerage, Gain, Loss, Prime Cost, Selling Price, etc. Exercises L., LI., LII., LIII.-Mixed Exercises LIV. X. INTEREST.- Examples of Methods - Exercise LV.- Principal, Rate, Time-Exercise LVI.-Compound Interest—Examples— Exercise LVII. XI. DISCOUNT.-Bankers' and True Discount-Examples-Exercises LVIII., LIX., LX. XII. STOCKS.-Shares-Examples-Exercises LXI., LXII., LXIII. XIII. ROOTS. -Square Root-Examples - Mensuration - Mean Proportion, etc.-Surds-Exercise LXIV.-Cube Root-Examples -Horner's Method-LXV. XIV. EXAMINATION PAPERS. ANSWERS. |