**The elements of statics and dynamics - **part 1 Statics

The book has been somewhat altered, and I hope improved, for this edition, and the type entirely re-set. Graphic solutions have been introduced much earlier, and more use has been made of graphic methods throughout the book. More experimental work has also been introduced.

The chapter on Work has been placed earlier, and much greater stress has been laid upon the Principle of Work. Sundry somewhat long analytical proofs have been relegated to the last chapter, and here I have not scrupled to introduce alternative proofs involving the use of the Differential Calculus. For ten of the new figures in this book, I am much indebted to the kindness and courtesy of Dr R. T. Glazebrook, who allowed me to use the blocks prepared for his Statics. Most of these figures have the additional merit of having been drawn from actual apparatus in use at the Cavendish Laboratory at Cambridge.

1. A Body is a portion of matter limited in every direction. 2. Force is anything that changes, or tends to change, the state of rest, or uniform motion, of a body. 3. Rest. A body is said to be at rest when it does not change its position with respect to surrounding objects. 4. Statics is the science that treats of the action of forces on bodies, the forces being so arranged that the bodies are at rest. The science which treats of the action of force on bodies in motion is called Dynamics. In the more modern system of nomenclature which is gradually gaining general acceptance, the science which treats of the action of force on bodies is called Dynamics, and it has two subdivisions. Statics and Kinetics, treating of the action of forces on bodies which are at rest and in motion respectively. 5. A Particle is a portion of matter which is in- definitely small in size, or which, for the purpose of our investigations, is so small that the distances between its different parts may be neglected.

### Contents:

I. Introduction 1

II. Composition and Resolution of Forces . . 8

III. Composition and Resolution of Forces (continued) 29

IV. Parallel Forces 47

V. Moments 58

VI. Couples 75

VII. Equilibrium of a rigid body acted upon by

three forces in a plane .... 84

VIII. General conditions of equilibrium of a rigid

BODY acted on BY A SYSTEM OF FORCES IN

ONE PLANE . 97

IX. Centre of Gravity 119

Centre of gravity of a Triangle, Tetrahedron,

etc 123

General formulae for the determination of the

centre of gravity 129

X. Centre of Gravity (continued).

Properties of the centre of gravity . . . 149

Stable and unstable equilibrium . . . 153

Stable and unstable equilibrium . . . 153

XI. Work .... 163

XII. Machines 171

I. The Lever 174

11. Pulleys and Systems of Pulleys . . 180

III. The Inclined Piano . . . .196

IV. The Wheel and Axle . . . .203

Weston's Differential Pulley . . 207

Weston's Differential Pulley . . 207

V. The Common Balance .... 209

VI. The Steelyards 218

VII. The Screw 224

XIII. Friction 232

Laws of Friction 233

Equilibrium on a Rough Inclined Plane . . 241

The efficiency of machines ..... 246

Machines with friction 248

XIV. Problems with Friction 260

XV. ]\IlSCELLANEOUS.

Smooth Hinges 274

Funicular Polygon 279

Tensions of Elastic Strings .... 282

Graphic Constructions. Link and Force Poly-

gons 286

Graphic Constructions. Link and Force Poly-

gons 286

XVI. Some Additional Propositions .... 297

Formal proof of the Parallelogram of Forces. 297

Centre of gravity of a Circular Arc, and of a

Centre of gravity of a Circular Arc, and of a

Sector and Segment of a Circle . . 301

Centre of gravity of a Zone of a Sphere. 305

Centres of gravity of a Hollow and a Solid

Centres of gravity of a Hollow and a Solid

Hemisphere 308

Virtual Work 310

Roberval's Balance 314

Easy Miscellaneous Examples 318

Harder miscellaneous Examples 320

Answers . .

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