Elementary geometrical statics

It has long been my firm conviction that the teaching of Elementary Statics would gain in clearness and educational value by a more general use of geometrical methods. The fundamental propositions of the subject are essentially geometrical, but it is usual for the beginner to abandon the direct use of the geometrical methods in favour of the analytical formulae to which they give rise. This is a pity. Mathematical formulae fail to appeal to the eye with the direct force of a geometrical figure, and the power and neatness of the geometrical methods are unquestionable. The practical engineer makes considerable use of Graphic Statics, but the subject has been much neglected in this country, and there seems to be no book which leads up by easy stages to the mastery of a subject at once interesting and instructive, and which can be systematically dealt within a scientific manner. In most recently published text-books on Elementary Statics, an attempt is made to deal with the subject of Graphic Statics in a short chapter or a few articles, but the matter is worthy of better treatment, and there seems to be a growing need for some such volume as the present, which deals with Geometrical Statics alone. The book is essentially an elementary one, and is intended to prepare the way for such works as Major Clarke's Graphic Statics or Professor Hoskins' Elements of Graphic Statics.

Rather against the advice of friends, I have not attempted to write a treatise independent of existing text-books. My wish is to supplement, not to compete with, such. Hence the Principle of Transmissibility of Force and the Parallelogram of Forces have been assumed, and a direct plunge taken into the geometrical aspect of the subject. For the groundwork and, later on, for an exposition of the Laws of Friction, the student is referred, by permission, to Professor Loney's Elements of Statics.

In preparing this work, I have consulted most available English books which bear upon the subject, and, in particular, Professor Hoskins' Elements of Graphic Statics. The method of lettering the diagrams is the extension of Bow's notation adopted in that volume.

Each chapter concludes with a number of worked-out examples, which are followed by a set of exercises for the student. Each set contains a collection of numerical examples, followed, in most cases, by others of a more general kind, which are intended to be worked with the aid of elementary pure geometry. The numerical examples are designed primarily for solution by means of accurately drawn figures; a careful worker, however, can in the more simple cases obtain fairly accurate results by freehand drawing, while the student of Trigonometry can calculate the lengths of the lines of his force diagram, and thus obtain accurate solutions.

I may claim most of the examples as my own original problems, accumulated during the last six years while teaching the subject to Woolwich pupils. Those which are not original are taken, for the most part, from recent examination papers set to candidates for admission to the Royal Military Academy.

The figures have, in most cases, been reduced in size from my original drawings, so as to admit of space diagram and force diagram being placed side by side on the same page. Those, however, which constitute the answers to numerical questions, are reproduced, in general, on the scale in which they were originally drawn. This has, in some cases, necessitated corresponding figures being placed on different pages facing each other. Attention is drawn to the numbering of the figures. Corresponding to the space diagram 108, we have the force diagram 108a, etc.

Any corrections or suggestions for improvement from either teachers or students will be most thankfully received. I have spared no pains in working out the answers to the examples, and hope that no serious errors will be found to have escaped correction.