THE PRINCIPLES OF MECHANICAL PHILOSOPHY APPLIED TO INDUSTRIAL MECHANICS: FORMING A SEQUEL TO THE AUTHOR'S "EXERCISES ON MECHANICS AND NATURAL PHILOSOPHY." BY THOMAS TATE, F.R.A.S., OF KNELLER TRAINING COLLEGE, TWICKENHAM; LATE MATHEMATICAL PROFESSOR AND LECTURER ON CHEMISTRY IN THE NATIONAL SOCIETY'S TRAINING COLLEGE, BATTERSEA. AUTHOR OF "THE PRINCIPLES OF THE DIFFERENTIAL AND INTEGRAL CALCULUS"; 66 THE PRINCIPLES OF GEOMETRY AND MENSURATION, ETC." ETC. ETC. LONDON: LONGMAN, BROWN, GREEN, AND LONGMANS. ΤΟ G. TATE, F. G. S., PRESIDENT OF THE BERWICKSHIRE NATURALISTS' CLUB, SECRETARY OF THE ALNWICK SCIENTIFIC INSTITUTION, ETC. DEAR BROTHER, THIS Work I inscribe to you as a tribute of esteem and affection, and as a memorial of those joyous days of our youth, when, hand in hand, we were engaged in the disinterested pursuit of knowledge. That the evening of your life may be as serene and happy as its meridian has been active and useful, is the earnest wish of Your affectionate Brother, Kneller Hall, Isleworth, February, 28. 1853. THOMAS TATE. PREFACE. THE present work is intended to give a concise yet comprehensive exposition of the principles of mechanical philosophy, as applied to industrial mechanics. With the view of rendering the subject instructive to practical engineers and teachers, the investigations are, for the most part, conducted on algebraic and geometrical principles, and numerous applications and illustrations are given throughout the work. With respect to the importance of industrial mechanics, as a branch of national education, Professor Moseley observes, in his report on the Hydraulic machines of the Great Exhibition : "In reporting upon the hydraulic machines exhibited, it is impossible to refrain from adverting to the general neglect of those elementary principles of scientific knowledge on which the perfection of such machines always depends, and in some cases, their whole usefulness, in an economical point of yiew. The Exhibition affords positive evidence of the sacrifice of a large amount of capital, and of much mechanical ingenuity, due simply to the ignorance of certain acknowledged principles of hydraulic science. In adverting to this fact, the jury cannot but observe that the success with which the principles of mechanical science, in their application to practical questions, are beginning to be cultivated in France, |