| Introduction | |
| Nature of Physical Science | p. 1 |
| Definition of a Material System | p. 2 |
| Definition of Internal and External | p. 2 |
| Definition of Configuration | p. 2 |
| Diagrams | p. 3 |
| A Material Particle | p. 3 |
| Relative Position of two Material Particles | p. 4 |
| Vectors | p. 4 |
| System of Three Particles | p. 5 |
| Addition of Vectors | p. 5 |
| Subtraction of one Vector from another | p. 6 |
| Origin of Vectors | p. 6 |
| Relative Position of Two Systems | p. 7 |
| Three Data for the Comparison of Two Systems | p. 7 |
| On the Idea of Space | p. 9 |
| Error of Descartes | p. 9 |
| On the Idea of Time | p. 11 |
| Absolute Space | p. 12 |
| Statement of the General Maxim of Physical Science | p. 13 |
| On Motion | |
| Definition of Displacement | p. 15 |
| Diagram of Displacement | p. 15 |
| Relative Displacement | p. 16 |
| Uniform Displacement | p. 17 |
| On Motion | p. 18 |
| On the Continuity of Motion | p. 18 |
| On Constant Velocity | p. 19 |
| On the Measurement of Velocity when Variable | p. 19 |
| Diagram of Velocities | p. 20 |
| Properties of the Diagram of Velocities | p. 21 |
| Meaning of the Phrase "At Rest" | p. 22 |
| On Change of Velocity | p. 22 |
| On Acceleration | p. 23 |
| On the Rate of Acceleration | p. 24 |
| Diagram of Accelerations | p. 25 |
| Acceleration a Relative Term | p. 25 |
| On Force | |
| Kinematics and Kinetics | p. 26 |
| Mutual Action between Two Bodies--Stress | p. 26 |
| External Force | p. 26 |
| Different Aspects of the same Phenomenon | p. 27 |
| Newton's Laws of Motion | p. 27 |
| The First Law of Motion | p. 28 |
| On the Equilibrium of Forces | p. 30 |
| Definition of Equal Times | p. 31 |
| The Second Law of Motion | p. 32 |
| Definition of Equal Masses and of Equal Forces | p. 32 |
| Measurement of Mass | p. 33 |
| Numerical Measurement of Force | p. 35 |
| Simultaneous Action of Forces on a Body | p. 36 |
| On Impulse | p. 37 |
| Relation between Force and Mass | p. 38 |
| On Momentum | p. 38 |
| Statement of the Second Law of Motion in Terms of Impulse and Momentum | p. 39 |
| Addition of Forces | p. 39 |
| The Third Law of Motion | p. 40 |
| Action and Reaction are the Partial Aspects of a Stress | p. 40 |
| Attraction and Repulsion | p. 41 |
| The Third Law True of Action at a Distance | p. 42 |
| Newton's Proof not Experimental | p. 42 |
| On the Properties of the Centre of Mass of a Material System | |
| Definition of a Mass-Vector | p. 44 |
| Centre of Mass of Two Particles | p. 44 |
| Centre of Mass of a System | p. 45 |
| Momentum represented as the Rate of Change of a Mass-Vector | p. 45 |
| Effect of External Forces on the Motion of the Centre of Mass | p. 46 |
| The Motion of the Centre of Mass of a System is not affected by the Mutual Action of the Parts of the System | p. 47 |
| First and Second Laws of Motion | p. 48 |
| Method of treating Systems of Molecules | p. 48 |
| By the Introduction of the Idea of Mass we pass from Point-Vectors, Point Displacements, Velocities, Total Accelerations, and Rates of Acceleration, to Mass-Vectors, Mass Displacements, Momenta, Impulses, and Moving Forces | p. 49 |
| Definition of a Mass-Area | p. 50 |
| Angular Momentum | p. 51 |
| Moment of a Force about a Point | p. 51 |
| Conservation of Angular Momentum | p. 52 |
| On Work and Energy | |
| Definitions | p. 54 |
| Principle of Conservation of Energy | p. 54 |
| General Statement of the Principle of the Conservation of Energy | p. 55 |
| Measurement of Work | p. 56 |
| Potential Energy | p. 58 |
| Kinetic Energy | p. 58 |
| Oblique Forces | p. 60 |
| Kinetic Energy of Two Particles referred to their Centre of Mass | p. 61 |
| Kinetic Energy of a Material System referred to its Centre of Mass | p. 62 |
| Available Kinetic Energy | p. 63 |
| Potential Energy | p. 65 |
| Elasticity | p. 65 |
| Action at a Distance | p. 66 |
| Theory of Potential Energy more complicated than that of Kinetic Energy | p. 67 |
| Application of the Method of Energy to the Calculation of Forces | p. 68 |
| Specification of the [Mode of Action] of Forces | p. 69 |
| Application to a System in Motion | p. 70 |
| Application of the Method of Energy to the Investigation of Real Bodies | p. 70 |
| Variables on which the Energy depends | p. 71 |
| Energy in Terms of the Variables | p. 72 |
| Theory of Heat | p. 72 |
| Heat a Form of Energy | p. 73 |
| Energy Measured as Heat | p. 73 |
| Scientific Work to be done | p. 74 |
| History of the Doctrine of Energy | p. 75 |
| On the Different Forms of Energy | p. 76 |
| Recapitulation | |
| Retrospect of Abstract Dynamics | p. 79 |
| Kinematics | p. 79 |
| Force | p. 79 |
| Stress | p. 80 |
| Relativity of Dynamical Knowledge | p. 80 |
| Relativity of Force | p. 81 |
| Rotation | p. 83 |
| Newton's Determination of the Absolute Velocity of Rotation | p. 84 |
| Foucault's Pendulum | p. 86 |
| Matter and Energy | p. 89 |
| Test of a Material Substance | p. 89 |
| Energy not capable of Identification | p. 90 |
| Absolute Value of the Energy of a Body unknown | p. 90 |
| Latent Energy | p. 91 |
| A Complete Discussion of Energy would include the whole of Physical Science | p. 91 |
| The Pendulum and Gravity | |
| On Uniform Motion in a Circle | p. 92 |
| Centrifugal Force | p. 93 |
| Periodic Time | p. 93 |
| On Simple Harmonic Vibrations | p. 94 |
| On the Force acting on the Vibrating Body | p. 94 |
| Isochronous Vibrations | p. 95 |
| Potential Energy of the Vibrating Body | p. 96 |
| The Simple Pendulum | p. 96 |
| A Rigid Pendulum | p. 98 |
| Inversion of the Pendulum | p. 100 |
| Illustration of Kater's Pendulum | p. 100 |
| Determination of the Intensity of Gravity | p. 101 |
| Method of Observation | p. 102 |
| Estimation of Error | p. 103 |
| Universal Gravitation | |
| Newton's Method | p. 105 |
| Kepler's Laws | p. 105 |
| Angular Velocity | p. 106 |
| Motion about the Centre of Mass | p. 106 |
| The Orbit | p. 107 |
| The Hodograph | p. 107 |
| Kepler's Second Law | p. 108 |
| Force on a Planet | p. 109 |
| Interpretation of Kepler's Third Law | p. 110 |
| Law of Gravitation | p. 111 |
| Amended Form of Kepler's Third Law | p. 112 |
| Potential Energy due to Gravitation | p. 113 |
| Kinetic Energy of the System | p. 113 |
| Potential Energy of the System | p. 114 |
| The Moon is a Heavy Body | p. 115 |
| Cavendish's Experiment | p. 116 |
| The Torsion Balance | p. 117 |
| Method of the Experiment | p. 118 |
| Universal Gravitation | p. 119 |
| Cause of Gravitation | p. 120 |
| Application of Newton's Method of Investigation | p. 121 |
| Methods of Molecular Investigations | p. 122 |
| Importance of General and Elementary Properties | p. 122 |
| On the Equations of Motion of a Connected System | p. 123 |
| The Relativity of the Forces of Nature | p. 137 |
| The Principle of Least Action | p. 145 |
| Index | p. 162 |
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