CONTENTS.

PREFACE

CHAPTER I. KINEMATICS

Division of the subject, §§ 1-3.

Velocity, SS 4-7.

Composition and Resolution of Velocities, §§ 8-II.

Acceleration, §§ 12-17.

Hodograph, § 18.

Moment of Velocity, §§ 19-22.

Motion of a point deduced from the given acceleration, § 23.

Relative Velocity and Acceleration, §§ 24-31.

Angular Velocity and Acceleration, §§ 32-35.

Velocity and Acceleration relative to Moving Axes, §§ 36—38.

EXAMPLES

PAGES

vii-x

1-29

29-32

CHAPTER II. LAWS OF MOTION

33-49

Definitions of Mass, Density, Particle, Force, Momentum,

Vis Viva, Kinetic Energy, Measure of Force, Compo-

nent of Force, &c. &c. §§ 39-52.

Definition, and Properties, of Center of Inertia, § 53.

Definition of Moment of Momentum, § 54.

Definition of Work done by a force, and consequences of the

definition, §§ 55, 56.

Definition of Potential Energy, § 57.

Newton's Laws of Motion, with their consequences-as
Measure of Time, Parallelogram of Forces, Conservation
of Momentum and of Moment of Momentum, &c.
$$ 58-67.

Scholium to the Third Law, with its interpretation. D'Alem-
bert's principle, Horse-power, Conservation of Energy
in Ordinary Mechanics, §§ 68-70.

Conservation of Energy, Impossibility of Perpetual Motion,
Joule's experimental results, §§ 71-73".

PAGES

Force varying according to different powers of the distance,

Force constant in direction, but not in magnitude, §§ 114—121.

Newton's investigation of the motion of a luminous corpus-

General Equations, §§ 123, 124.

Force proportional to the distance, § 125.

Polar Form of General Equations, and consequences, §§ 126

-135.

Properties of Apses, §§ 136-139.

Orbits under the Law of Gravitation, §§ 140-149.

EXAMPLES

CHAPTER VI.

ELLIPTIC MOTION

Definitions and immediate deductions, §§ 150-153.

The Direct Problem, § 154.

The Inverse, or Kepler's, Problem, §§ 155–161.

Orbit Parabolic, or Elliptic and of great excentricity, §§ 162

-164.

Lambert's Theorem, §§ 165, 166.

EXAMPLES

50-70

70-75

76-95

95-100

101-122

122-138

139-155

155-157

PAGES

CHAPTER VII. CONSTRAINED MOTION

Preliminary remarks on Constraint, § 167.

Motion on Smooth Plane Curve, Cycloidal and Common

Pendulum, &c. Direct Problem, §§ 168-178.

158-212

Inverse Problems-Common Brachistochrone, &c. §§ 179–183.

Central Force, §§ 184, 185.

Constraint by Tortuous Smooth Curve, § 186.

Tautochrone, §§ 187, 188.

Brachistochrone, §§ 189, 190.

Motion on Smooth Surface, §§ 191-194.

Particular Case-Conical Pendulum, §§ 195-199.

Double Pendulum, § 200.

Brachistochrone on Smooth Surface, § 201.

Constraint by String attached to a moving Point, §§ 202-204.

Constraint by Smooth Tube in motion, §§ 205-210.

Constraint by Rough Curve, §§ 211, 212.

Constraint by Rough Surface, § 213.

EXAMPLES

CHAPTER VIII.

212-227

MOTION IN A RESISTING MEDIUM. 228-245

General Statement of the Problem, § 214.

Rectilinear Motion with various applied forces and various

laws of resistance-Terminal Velocity, &c. §§ 215-218.

Curvilinear Motion, under various laws of resistance and

various forces. Approximate determination of path of

projectile with low trajectory, $$ 219-223.

Inverse Problems, §§ 224-228.

Equation to Central Orbit in resisting medium, § 229.

EXAMPLES

CHAPTER IX. GENERAL THEOREMS

Constraint perpendicular to direction of motion, §§ 330-232.

All central forces have a potential, § 233.

Conservation of Energy, and Equipotential Surfaces, S$ 234,

235.

Inverse Problem as to conservative forces, § 236.

Deductions from Conservation of Energy, S$ 237-240.

Least, or Stationary, Action, § 241-248.

Varying Action, SS 249-258.

245-251

252-284

Preliminary Remarks, Coefficient of Restitution, § 271.

Direct Impact of Spheres, SS 272, 273.

Impact of Sphere on Fixed Surface, § 274.

Impact of Smooth Spheres generally, Apparent Loss of

Energy, § 275, 276.

Impulsive Tension in Chain, §§ 277-282.

Continuous Series of Indefinitely Small Impacts, §§ 283-285.

EXAMPLES

CHAPTER XI. DISTURBED MOTION

Explanation of Instantaneous Orbit, Parameters, &c. § 286.

Cycloidal Pendulum disturbed, §§ 291–298.

General Principle, §§ 287-290.

Projectile disturbed by Resistance, § 299.

Disturbed Planet, § 300.

Planet and Projectile disturbed by Impact, § 301.

EXAMPLES

302-306

307-323

323-325

CHAPTER XII. MOTION OF TWO OR MORE PARTICLES 326-346

I. Free Motion. General Equations, §§ 303, 304.

Conservation of Momentum, § 305; of Moment of Momen.

tum, § 306, of Energy, § 307.

Particular Case of Two Particles only, $$ 308–312.

II. Constrained Motion. Conditions of Constraint, § 313.

Two particles, in space, connected by inextensible string,

§ 314.

String constrained by pulley, § 315.

Chain slipping over pulley, § 316.

Two particles, one resting on a plane, connected by inexten-

sible string passing over pulley, § 317.

Two particles, resting on inclined planes, connected by rigid

rod, § 318.

A. On the integration of the equations of motion about

C. General property of free path and brachistochrone for
any force whose direction is constant.

D.

E.

Of two curves, convex upwards, joining two points in

a vertical plane, the inner is described in less time

than the outer.

Inverse problem-To find the equation to the con-
straining curve when the time of descent, to the
lowest point, through any arc, is given as a func-
tion of the vertical height fallen through.

PAGES

346-349

349, 350

351-363