Chapter I: Preface

I here present the revised edition of a course of lectures on Experimental Mechanics which I delivered in the Royal College of Science at Dublin eighteen years ago. The audience was a large evening class consisting chiefly of artisans.

The teacher of Elementary Mechanics, whether he be in a Board School, a Technical School, a Public School, a Science College, or a University, frequently desires to enforce his lessons by exhibiting working apparatus to his pupils, and by making careful measurements in their presence.

He wants for this purpose apparatus of substantial proportions visible from every part of his lecture room. He wants to have it of such a universal character that he can produce from it day after day combinations of an ever-varying type. He wishes it to be composed of well-designed and well-made parts that shall be strong and durable, and that will not easily get out of order. He wishes those parts to be such that even persons not specially trained in manual skill shall presently learn how to combine them with good effect. Lastly, he desires to economize his money in the matters of varnish, mahogany, and glass cases.

I found that I was able to satisfy all these requirements by a suitable adaptation of the very ingenious system of mechanical apparatus devised by the late Professor Willis of Cambridge. The elements of the system I have briefly described in an Appendix, and what adaptations I have made of it are shown in almost every page and every figure of the book.

In revising the present edition I have been aided by my friends Mr. G. L. Cathcart, the Rev. M. H. Close, and Mr. E. P. Culverwell.

ROBERT S. BALL.

OBSERVATORY, CO. DUBLIN,
_3rd August, 1888_.

TABLE OF CONTENTS.

LECTURE I.
_THE COMPOSITION OF FORCES._
PAGE
Introduction.—The Definition of Force.—The
Measurement of Force.—Equilibrium of Two
Forces.—Equilibrium of Three Forces.—A Small
Force can sometimes balance Two Larger Forces 1

LECTURE II.
_THE RESOLUTION OF FORCES._

Introduction.—One Force resolved into Two
Forces.—Experimental Illustrations.—Sailing.—One
Force resolved into Three Forces not in the
same Plane.—The Jib and Tie-rod 16

LECTURE III.
_PARALLEL FORCES._

Introduction.—Pressure of a Loaded Beam on its
Supports.—Equilibrium of a Bar supported on
a Knife-edge.—The Composition of Parallel
Forces.—Parallel Forces acting in opposite
directions.—The Couple.—The Weighing Scales 34

LECTURE IV.
_THE FORCE OF GRAVITY._

Introduction.—Specific Gravity.—The Plummet and
Spirit-Level.—The Centre of Gravity.—Stable and
Unstable Equilibrium.—Property of the Centre of
Gravity in a Revolving Wheel 50

LECTURE V.
_THE FORCE OF FRICTION._

The Nature of Friction.—The Mode of
Experimenting.—Friction is proportional to
the pressure.—A more accurate form of the
Law.—The Coefficient varies with the weights
used.—The Angle of Friction.—Another Law of
Friction.—Concluding Remarks 65

LECTURE VI.
_THE PULLEY._

Introduction.—Friction between a Rope and an
Iron Bar.—The Use of the Pulley.—Large and
Small Pulleys.—The Law of Friction in the
Pulley.—Wheels.—Energy 85

LECTURE VII.
_THE PULLEY-BLOCK._

Introduction.—The Single Movable Pulley.—The
Three-sheave Pulley-block.—The Differential
Pulley-block.—The Epicycloidal Pulley-block 99

LECTURE VIII.
_THE LEVER._

The Lever of the First Order.—The Lever of the Second
Order.—The Shears.—The Lever of the Third Order 119

LECTURE IX.
_THE INCLINED PLANE AND THE SCREW._

The Inclined Plane without Friction.—The Inclined
Plane with Friction.—The Screw.—The
Screw-jack.—The Bolt and Nut 131

LECTURE X.
_THE WHEEL AND AXLE._

Introduction.—Experiments upon the Wheel and
Axle.—Friction upon the Axle.—The Wheel
and Barrel.—The Wheel and Pinion.—The
Crane.—Conclusion 149

LECTURE XI.
_THE MECHANICAL PROPERTIES OF TIMBER._

Introduction.—The General Properties of
Timber.—Resistance to Extension.—Resistance to
Compression.—Condition of a Beam strained by a
Transverse Force 169

LECTURE XII.
_THE STRENGTH OF A BEAM._

A Beam free at the Ends and loaded in the Middle.—A
Beam uniformly loaded.—A Beam loaded in the
Middle, whose Ends are secured.—A Beam supported
at one end and loaded at the other 188

LECTURE XIII.
_THE PRINCIPLES OF FRAMEWORK._

Introduction.—Weight sustained by Tie and
Strut.—Bridge with Two Struts.—Bridge with Four
Struts.—Bridge with Two Ties.—Simple Form of
Trussed Bridge 203

LECTURE XIV.
_THE MECHANICS OF A BRIDGE._

Introduction.—The Girder.—The Tubular Bridge.—The
Suspension Bridge 218

LECTURE XV.
_THE MOTION OF A FALLING BODY._

Introduction.—The First Law of Motion.—The Experiment
of Galileo from the Tower of Pisa.—The Space
is proportional to the Square of the Time.—A
Body falls 16' in the First Second.—The Action
of Gravity is independent of the Motion of the
Body.—How the Force of Gravity is defined.—The
Path of a Projectile is a Parabola 230

LECTURE XVI.
_INERTIA._

Inertia.—The Hammer.—The Storing of Energy.—The
Fly-wheel.—The Punching Machine 250

LECTURE XVII.
_CIRCULAR MOTION._

The Nature of Circular Motion.—Circular motion in
Liquids.—The Applications of Circular Motion.—The
Permanent Axes 267

LECTURE XVIII.
_THE SIMPLE PENDULUM._

Introduction.—The Circular Pendulum.—Law connecting
the Time of Vibration with the Length.—The Force
of Gravity determined by the Pendulum.—The Cycloid 284

LECTURE XIX.
_THE COMPOUND PENDULUM AND THE
COMPOSITION OF VIBRATIONS._

The Compound Pendulum.—The Centre of Oscillation.—The
Centre of Percussion.—The Conical Pendulum.—The
Composition of Vibrations 299

LECTURE XX.
_THE MECHANICAL PRINCIPLES OF A CLOCK._

Introduction.—The Compensating Pendulum.—The
Escapement.—The Train of Wheels.—The Hands.—The
Striking Parts 318

APPENDIX I.

The Method of Graphical Construction 339
The Method of Least Squares 342

APPENDIX II.

Details of the Willis Apparatus used in illustrating
the foregoing lectures 345

INDEX 355

EXPERIMENTAL MECHANICS.

LECTURE I.
_THE COMPOSITION OF FORCES._

Introduction.—The Definition of Force.—The
Measurement of Force.—Equilibrium of Two
Forces.—Equilibrium of Three Forces.—A Small
Force can sometimes balance Two Larger Forces.