A treatise on statics with applications to physics

It has been thought desirable to bring out the third edition of this work in two volumes, because experience proved that the previous edition contained more than was suitable to the wants of the great majority of students who reach the standard of Undergraduate Honours in Mathematics.

The reception of the work in the Universities at home and abroad, has made me desirous of rendering it more deserving of the favour accorded to it by high class students. Accordingly, I determined to reserve for the second volume the more advanced portions of the previous work (those dealing with Non-Coplanar Forces, Attractions, and the Theory of Strain and Stress), and, while greatly extending these portions, to introduce such fresh applications of the subject as would in the work really useful to those, for example, who aim at distinction in the Mathematical Tripos.

With regard to the first volume, little needs to be said. It is meant for those who attain the standard of Undergraduate Honours and Scholarships, but do not desire to compete for higher distinctions. Within this range it will, I think, be found tolerably complete. A re-arrangement of the order of treatment in the previous edition has been made. At an early stage in the shnlrrit's reading I endeavour to make him familiar with graphic methods both in practice and in theory.

To this end, attention has been directed to the solution, by graphic construction, of several classes of equations to which we are led in seeking for positions of equilibrium equations, the accurate solution of which would be impossible, and the approximate solution of which by the ordinary analytical methods would be attended with great trouble. Experience has proved to me that this is a most valuable aid in producing in the mind of the student a knowledge of the nature of dynamical problems, and an interest which cannot be evoked by symbols and equations alone.

Indeed, it will be observed that graphic methods figure more largely in this edition, all through, than in the previous one notably in the general discussion of Funicular Polygons in Chapter V. This is a branch of elementary Statics to which too little attention is paid; but it is both valuable and full of elegance.

The second volume opens with a long chapter on Non- Coplanar Forces, in which I have given an exposition of Dr. Pall's Theory of Screws, so far as it relates more particularly to the Statical branch of Dynamics. It will be observed that, while following Dr. Ball's method of treatment very closely, I have departed from it in some instances. To prevent misconception, I may say that my reason for doing so is simply the fact that students of any branch of science derive great benefit by looking at it from several different points of view.

In this chapter the general conditions of equilibrium are illustrated by examples of the same character as those employed so largely in the chapters dealing with the Coplanar Forces my object being to avoid mere generalities in symbols.

The chapter on Astatic Equilibrium is founded on a paper which I published on the subject a few years ago. Now that students of the works of Hamilton, Tait, and Clerk-Maxwell are so numerous in the Universities, no apology is necessary for the treatment of this subject by elementary Quaternions.

The part of this volume dealing with Attractions and the general theory of Potential in Electricity and Magnetism has been much enlarged; and it will be in its present condition. I hope, a valuable assistance to the student of the great and enduring works of Thomson and Tait, and Clerk-Maxwell.

The subject-matter of tins second volume differing very greatly from that of the first, a few words with regard to the manner in which I have treated it seem to be necessary.

The reader will observe that in the Chapter dealing with Virtual Work, I have ventured to reject the term ‘Generalised Component of Force,’ and to replace it by the term ‘Work Coefficient,’ the former term being, to my mind, open to the objection of conveying an erroneous idea with regard to the nature of the thing defined.

In the Chapter on Attractions the great object which I have constantly kept in view has been the fixing of a definiteness of idea in the mind of the student with regard to the various physical magnitudes which are represented by symbols in our equations. To this end, I have explicitly adopted the C. G. S. system, and I have introduced a sufficient number of numerical illustrations in which Forces and Potentials are definitely presented as so many Dynes and so many Ergs per gramme. The C. G. S. system stands pre-eminent for its extreme simplicity; and when once the student of Mathematical Physics learns how to make a real working use of its units - to recognise, without mental effort and as a mere matter of course, that his symbol, p, for volume-density always means so many grammes per cubic centimetre; that his symbol, X, for force-intensity means so many dynes per gramme; and so on - he will never experience any difficulty in altering the values of fundamental numerical constants to suit the units of mass, time, and length which are adopted in any other system. In the calculation of Attractions - and especially in the domains of Electricity and Magnetism - the ever present notion of a concrete reality corresponding to every algebraic symbol is of immense importance. Indeed, without this definiteness of idea, no knowledge of the slightest value can exist.