BY THE SAME AUTHOR. MEASUREMENT CONVERSIONS (English and French). 43 By Prof. "The work is INVALUABLE "-Colliery Guardian. "Ought to be in EVERY office where even occasional conversions are required. Prof. SMITH'S TABLES form very EXCELLENT CHECKS on results. . . USEFUL and good set of diagrams."-Electrical Review. ... A VERY MANUALS INDISPENSABLE FOR THE ENGINEER. By W. J. MACQUORN RANKINE, C.E., LL.D., F.R.S., Thoroughly Revised by W. J. MILLAR, C.E., Late Sec. to the Inst. of Engineers and Shipbuilders in Scotland. RANKINE'S APPLIED MECHANICS. FOURTEENTH EDITION. 12s. 6d. EDITION. 12s. 6d. FOURTEENTH 12s. 6d. RANKINE'S MACHINERY AND MILLWORK. SEVENTH EDITION. RANKINE'S USEFUL RULES FOR ENGINEERS. With Appendix for Electricians by Prof. A. JAMIESON, M.I.El.E. SEVENTH EDITION. 10s. 6d. RANKINE'S MECHANICAL TEXT-BOOK: A Simple Introduction to the Study of Mechanics. FOURTH EDITION. 9s. With PROFESSOR RANKINE'S MISCELLANEOUS SCIENTIFIC PAPERS. **For other STANDARD WORKS see Technical Catalogue at the end of this volume. LONDON: CHARLES GRIFFIN & Co., Ltd., Exeter St., Strand. FOR 70854 ENGINEERS AND PHYSICISTS: INTEGRATION AND DIFFERENTIATION, WITH CLASSIFIED REFERENCE TABLES OF INTEGRALS AND METHODS OF INTEGRATION. BY PROF. ROBERT HSMITH, ASSOC. M.I.C.E., M.I.M.E., M.I.EL.E., M.FED.I.MIN.E., WH. SCH., MEM. ORDER MEIJI. WITH DIAGRAMS. LONDON: CHARLES GRIFFIN AND COMPANY, LTD, EXETER STREET, STRAND. 1897. [All rights reserved.] PREFACE. THIS work aims at the presentation of two leading features in the study and application of the higher mathematics. In the first place, the development of the rationale of the subject is based on essentially concrete conceptions, and no appeal is made to what may be termed rational imagination extending beyond the limits of man's actual physical and physiological experience. Thus no use is anywhere made of series of infinite numbers of things or of infinitely small quantities. The author believes that the logical development is both sound and complete without reference to these ideas. In the second place, a set of Eleven Classified Tables of Integrals and Methods of Integration have been arranged in such manner as seemed best adapted to facilitate rapid reference, and thus relieve the mind engaged in practical mathematical work of the burden of memorising a great mass of formulas. This part of the work has involved very considerable labour. The germ of it is twenty-five years old in the author's manuscripts, but for the extensive and able development of it to its present form he is indebted to the cooperation of Mr R. F. Muirhead, M.A., B.Sc. (Glasgow), B.A. (Cambridge), formerly Clark Fellow of Glasgow University and Lecturer on Mathematics at Mason College. It is hoped that these Tables may prove of great service to physicists and engineers engaged in new applications of science. In the preparation of these Tables assistance has been obtained from |