Text-Book Mechanics: With Numerous Examples

From the author's Preface: THE science of mechanics, as all other departments of physical science, has made great advances in recent years. In this book I have endeavored to unfold the principles of modern mechanics systematically, and also to call the attention of the student to the more useful applications of the subject. It has long seemed to me that the more practical parts might with advantage be presented to the beginner at least as fully as the more abstract, and that, too, without any sacrifice of scientific precision. The book is so arranged that the student, whether intending to make a specialty of engineering, physics, or astronomy, can branch out in his special direction without difficulty. It has been the aim to make the examples as practical as possible. Thus while writing the Strong locomotive (No. 444) was brought out by the L. V. R. E. Co., and the Westinghouse air-brake tests (1887) were being made. Many problems founded on these and other mechanisms have been introduced. It has been the aim also to make the examples typical. Instead of making them mere numerical illustrations of formulas, the idea has been to encourage independent thought. In many cases different methods of solution have been indicated to encourage the student to trust rather to an independent investigation than to an answer so called. Considerable attention has been paid to the graphical method of solution, guarding, however, against making it a "complicated weapon with which one can attack all sorts of problems which are more easily solved in other ways." In several applications of the subject approximate formulas are of the utmost importance, and many such formulas are here developed. In all cases the rigorous formula has been given first, and the approximate deduced from it. In this ay the degree of approximation can be estimated. As regards the nomenclature of mechanics, I have endeavored to be modern and at the same time conservative. One or two terms have been introduced, the better to illustrate the second law of motion and the appropriateness of the expression moment of inertia. The words weight and pound have been used in the double sense employed in ordinary life. No confusion need arise from this, as the context is always sufficient to show the sense intended. (See p. 40.) Other departures from the traditional treatment will be noticed. Thus the usual chapter on the Mechanical Powers has been emitted, though the "Powers" themselves have been discussed in their proper places. All dynamical equations have been expressed in terms of the absolute units. By doing this it has been possible to ignore the expression w = mg, the source of so much confusion in dynamics. The Calculus has been used in all cases where its use is attended with marked advantage. In the earlier chapters two parallel courses are given, one with and one without Calculus. This I think an advantage in that it shows the student the oneness of what are called elementary and analytical mechanics. If thought advisable, a course may easily be selected into which no Calculus enters.