Synopses & Reviews
ON THE l . STR, ENGTII OF iMAl1ER, 1ALS, WORKS BY T, TArlE, OF KNELLER TRAINING COLLEGE, TWICKENHAM, LATE MATHENATICAL PROFESSOR AND LECTURER OX CAEMIBTY IN THE NATIONAL SOCIETYS TRAINING COLLEGE, BAITERSEA. I. A TREATISE ON THE FIRST PRINCIPLES OF ARITHMETIC, dedped for the use of Teachers and nfonitors in Elementary Schools. New Edition, with Addtlona and Improvements. 12x110. Price 1s. 6d. 11. ALGEBRA MADE EASY. Chiefly intended for the use of Schools. New Edition. 121110. Price 2s. 111. EXERCISES ON DTECHANICS AND NATURAL PHIIdOSOPHY or an easy Introduction to Engineering, for theuseof Schools andprivate Students containing varinus ApplIcatlonsof the Principle of Work the Theory of the Steam-Englne. with simple Machines Theorems and Problems on Accumulated Work the Equilibrium of Structure. with the Theory of the Arch the Pressure and Efflux of Fluids Calculations on Railway Cuttings, c. c. New Edition. 121110. Price . v. I v. THE PRINCIPLES OF GEOMETRY, MENSURATION, TRTGONO METRY LAND-SURVEYING AND LEVELLING. containin familiar Demonatrations and lllus rationosf the most impdrtant Propositions In huclids fernents. P roofs of all the useful Rules and Formulse in Mensuration and Trigonometry. with their Ap lication to the Solution of Practical Problems In Estimation, Surveying, and Railway n eering. New Edition, corrected. 12mo. with 317 Woodcuts. Price 3s. Gd. v. THE FIRST THREE BOOKS OF EUCLIDS ELEMENTS OF GEOMETRY, from the Text of Dr. 1Losanr S wsoxt, o gether with various useft11T heorems and Problems, as Geomctrlcal exercise on each Book Second Edltlon. 1 2mo. Price Is. W. VI. THE PRINCIPLES O F T H E DIFFERENTIAL AND INTEGRAL CALCULUS, simplified an4 applied to the Solutionofvarious useful Problemsin Mathematics and Mechanics. 12mo. Price 4s. M. VII. OUTLINES OF EXPERIMENTAI, CHEMISTRY being a familiar Introduction to the Science of Agriculture designed for the use of Schoolr and Schoolmasters. Price 18. Gd. VIII. ON THE STRENGTH OF IHATERIALS containing various Original and Uaeful Fonnulse, specially applied to Tubular Bridges, Wrought Iron and Cast Iron Beams, c. 8vo. I X. THE ELEMENTS OF MECHANIS3f. 12mo. With Numerous Woodcuts. Shortly will be published. X. A TREATISE ON FACTORIAL ANALYSIS AND THE SUMMATION OF SERIES. 8vo. Price 4s. Published by G. BELL, 186. Fleet Streef. LONDON LONGMAN, BROWN, GREEN, AND LONGMANS. ON THE STRENGTH OF BIIIBTERIALS COiYTAlNINo VARIOUS ORIGINAL AND USEFUL FORMULA, GPLCIALLY APPLIED TO TUBULAR BRIDGES, WROUGHT IRON AND CAST IRON BEAMS, ETC, AUTHOR OF TliE PnlNClPLEH OF THE DIFFERENTIAL AND INTEGRAL CALCLZUB, FACTORIAL ANALYRIR. ETC LONDON PRINTED FOR LONGAIAN, BROWN, GREEN, AND LONGMANS, PATERNOSTER-ROW. 1850. . ONDON sro r. r sr oon n n s d Slrna, Hcw alreet-Square. I N T R O D U C T I O N . THE railway system in this country has recently given rise to a new and important principle of const, ruction, -that of tubular beams and the facts elicited by t. he experiments made on this subject have placed i11 the hands of the mathematician new and valuable data relative to the strengt, h of materials. Mathematicians had long known, that in order to attain the condition of maximum strength, with a given amount of material, in a beam subjected to transverse strain, the material in the section should be so distributed, that when it is about to yield by the force of compression on the upper side of the beam, it should at the sametime be upon the point of yielding to that of extension on the under side. If the resistance of the material to compression were in all cases equal to the resistance which it presents to extension, then it is obvious that the form answering to maximum strength vouldb e that in which the material mould be equally accumulated towards the upper and under sides of the beam. Rut this is not generally the case...