CALCULATIONS FOR ENGINEERS AND FIREMEN. RELATING TO THE STEAM ENGINE, THE STEAM BOILER, HAW COMPRISING THE ELEMENTS OF MECHANICAL PHILOSOPHY, MENSURATION, AND FOR REFERENCE, TABLES OF SQUARES AND CUBES, SQUARE AND BY N. HAWKINS, M. E., HONORARY MEMBER NATIONAL ASSOCIATION OF STATIONARY ENGINEERS THEODORE AUDEL & CO., PUBLISHERS, 63 FIFTH AVENUE, NEW YORK CITY. INTRODUCTION. "I would give a thousand dollars if I knew the principles upon which my engine works." 66 This was the remark of a western engineer made to a gentleman who was admiring the performance of the steam plant under the charge of the former. "I can attend to every necessary thing about my whole apparatus; engine, boilers, pumps, pipes, and do all that is expected of an engineer, but I don't know why the steam does its work, and I would give a thousand dollars to know." This work is prepared for those who, like the engineer whose words are quoted, wish to know, and are willing to pay the cost, in money and study. Abraham Lincoln once said, in the early days of his opening manhood, with the warm enthusiasm characteristic of his noble mind, "That man who furnishes me with a good book is my best friend;" at the age of 18 he was the proud owner of six volumes. The desire has been strong indeed, in the mind of the author, while compiling this work, upon a single page of which, at times, several days have been spent, that it might come to many aspiring men, with the same potent good, as the few books which Abraham Lincoln had access to in his early struggling days. In the wide expanse of mathematics it has been a task of the utmost difficulty for the author to lay out a road that would not too soon weary or discourage the student; if he had his wish he would gladly advance step by step with his pupil, and much better explain, by word and gesture and emphasis, the great principles which underlie the operations of mechanics; to do this would be impossible, so he writes his admonition in two short words: In case of obstacles, "GO ON." If some rule or process seems too hard to learn, go around the difficulty, always advancing, and, in time, return and conquer. One thing of importance may here be said. The value of a teacher or instructor cannot be overestimated. Men were not made to do their work alone; they are created so that they need assistance and encouragement in every direction except downwards; to be helped and to help is the universal law. In no profession more than steam engineering does this law hold truer, and while the editor has written down the hard problems he has all the time, while making them as plain as possible to do so, had the secret wish that the learner might have at his side, when the book came to him, a kind and generous tutor, who could, and cheerfully would, go with him over the untravelled road. There is a single unique Book in the world, two thousand years compiling, of which it is said that no person can be called foolish who diligently peruses its pages; so the author's topmost wish has been now to prepare a book so elementary and yet so wide in its scope that no engineer or fireman could justly be called ignorant who had carefully studied and become familiar with its pages. We quote for a motto "Education does not consist merely in storing the head with materials; that makes a lumber room of it; but in learning how to turn those materials into useful products; that makes a factory of it; and no man is educated unless his brain is a factory, with storeroom, machinery and material complete." Hence in arranging the materials of this work, the author has aimed to give it a certain completeness and harmony with itself, from beginning to end; to make it "a factory, with |