Stephenson's "Hutcheson Bridge" at Glasgow, which is one of the best specimens of the segmental arch, together with many others, have supplied me with a variety of problems for illustration. Very many elucidatory examples, and, for the most part, manageable without a profound knowledge of the higher mathematics, have been interspersed at their proper places throughout the whole course of my work, and the numerous solutions which I have given at full length will, I trust, contribute to the instruction of students desirous of progressing in studies of this nature. The want of a small and compendious volume for the use of students of military and civil engineering has been of late greatly felt, especially since the highest educational authorities have introduced these branches of study into the programme of the examinations for engineer and artillery officers. To supply this want is the main motive that has impelled the author to draw up the present treatise. Having said thus much of the plan and nature of this treatise, the author feels himself called upon to acknowledge his obligation to the writers, English and Foreign, whose works he has chiefly consulted, and to which reference is made in this work. A list of these works is here subjoined : Cours de Mécanique Appliquée (1859): M. Bresse. Strength of Timber: P. Barlow. On Wrought Iron Bridges (1858): J. H. Latham. Résistance des Matériaux (1857): M. Morin. Cours de Mécanique Appliquée (1858): M. Mahistre. Treatise on the Arch (1858): Captain Woodbury, of the On the Strength of Materials and on Bridges (German, 1858): Applied Mechanics (German): M. Weisbach. The author has derived much aid from the valuable suggestions of Professor Sylvester, without whose kind encouragement this treatise would not have been undertaken. His thanks are also due to his esteemed friend Mr. W. Finley, late of Durham, a mathematician and profound linguist, for many important recommendations and references to foreign scientific publications. July, 1861. PREFACE. CONTENTS. Elementary fibres. Different kinds of resistance. Resistance to extension, to compression, to flexion, to torsion, to sliding Resistance of a cylindrical steam boiler (See another investigation in Appendix.) Thickness of metal of cylindrical steam boilers. Resistance of the base of a cylindrical steam boiler Beam fixed at one extremity in a horizontal position and loaded at the other 43 Beam fixed at one extremity in a horizontal position and uniformly loaded . 43 Beam supported at its extremities and loaded at a point between the |