HANDBOOK OF ENGINEERING MATHEMATICS - 1920 - AUTHORS PREFACE - IN the present edition, the handbook has been revised to include a number of additions to the mathematical sections and to the tables of mathematical functions, and the values of physical and chemical constants have been revised to agree with recent investigation. The authors are especially indebted to Professor W. D. Ennis of the United States Naval Academy, Annapolis, for a critical reading of the revised manuscript and for valuable suggestions and for the section on aeronautics which has been contributed by Professor Ennis also to Professor Ernst J. Berg and John N. Vedder of Union College for advice in connection with certain sections. The authors wish to express their thanks to Professors Irving P. Church, G. A. Goodenough, and William A. Granville, who have kindly given permission for the use of special material, tables, and constants from their works, and to whom proper credit is given where such material appears. TABLE OF CONTENTS PAGE ALGEBR . A .. ......................................... I Exponents ....................................... I Binomial theorem ................................. 2 Proportion ....................................... 2 Progressions ..................................... z Logarithms ...................................... 4 Series ........................................... 6 . Complex imag . v naryq uantities ...................... 9 GEOMETR .. Y . ........................................ 12 Planefigures ..................................... 12 Solids ........................................... 14 PLANET RIGONOMET .. R . Y .. ........................... 15 Numerical values ................................. 16 Trigonometric formulae ............................. I 7 . Plane triangles ................................... 19 SPHERICATLR IGONOMET .. R .. Y . ......................... 21 Formulae ....................................... 21 Application to navigation .......................... 22 PLANEA NALYTIGCE OMETR .. Y .. ........................ 24 Straightline ...................................... 24 Rectangular and polar coordinates .................. 26 Circle ............................................ 26 Parabola ........................................ 27 Ellipse .......................................... 29 Hyperbola ........................................ 29 v vi TABLE OF CONTENTS Cyclid ........................................... Epicycloid ....................................... Cardioid ......................................... Hypocycloid ..................................... Catenary ........................................ Higher plane curves ............................... SOLID. A NALYTIGC EOMETR . Y .. ......................... Direction cosines ................................. Plane ........................................... Straight line ..................................... CALCULU . S . .......................................... Application of differential calculus .................. Formulz of differential calculus .................... Maxima and minima .............................. Taylors and Maclaurins series .................... Application of integral calculus ..................... Curve tracing .................................... Methods of integration ............................ Table of . integrals ................................. HYPERBOLFIUCN CTIO .. N .. S . ............................