XXXVII. Mutual Action between Two Bodies-Stress XXXIX. Different Aspects of the same Phenomenon XLI. The First Law of Motion......................................................... XLV. Definition of Equal Masses and of Equal Forces... XLVII. Numerical Measurement of Force XLVIII. Simultaneous Action of Forces on a Body... L. Relation between Force and Mass LV. Action and Reaction are the Partial Aspects of a 33 33 34 PAGE 34 35 36 LVI. Attraction and Repulsion LVII. The Third Law True of Action at a Distance...... 48 CHAPTER IV. ON THE PROPERTIES OF THE CENTRE OF MASS OF A MATERIAL LIX. Definition of a Mass-Vector... LX. Centre of Mass of Two Particles.......................................................... 49 50 50 51 LXIII. Effect of External Forces on the Motion of the Centre of Mass...... 52 LXII. Momentum Represented at the rate of Change of LXIV. The Motion of the Centre of Mass of a System is .................. LXV. First and Second Laws of Motion LXVIII. Definition of a Mass-Area ....... ..... LXX. Moment of a Force about a Point LXXIII. Principle of Conservation of Energy LXXIV. General Statement of the Principle of the Con- LXXV. Measurement of Work....... LXXVIII. Oblique Forces....... .... LXXXIX, Kinetic Energy of Two Particles Referred to LXXX. Kinetic Energy of a Material System Referred LXXXI. Available Kinetic Energy LXXXII. Potential Energy.. LXXXIII. Elasticity LXXXIV. Action at a Distance LXXXV. Theory of a Potential Energy more Complicated LXXXVI. Application of the Method of Energy to the Cal- LXXXVII. Specification of the Direction of Forces............ vii PAGE 74 XC. Variables on which the Energy Depends........... 75 XCII. Theory of Heat....... XCIII. Heat a Form of Energy. ............. XCIV. Energy Measured as Heat...................................................... XCV. XCVI. History of the Doctrine of Energy.. CVII. Matter and Energy........ CVIII. Test of a Material Substance...... CIX. Energy not Capable of Identification.... CX. Absolute Value of the Energy of a Body Un- known ARTICLE CXI. Latent Energy. CXII. A Complete Discussion of Energy would include CHAPTER VII. THE PENDULUM AND GRAVITY. CXIII. On Uniform Motion in a Circle........... CXIV. Centrifugal Force CXVI. On Simple Harmonic Vibrations PAGE 94 95 95 96 97 ..... 97 CXVII. On the Force Acting on the Vibrating Body...... 98 CXIX. Potential Energy of the Vibrating Body CXX. The Simple Pendulum CXXI. A Rigid Pendulum........ CXXII. Inversion of the Pendulum CXXIII. Illustrations of Kater's Pendulum 98 99 100 101 103 104 104 105 CXXIV. Determination of the Intensity of Gravity.. CXXV. Method of Observation CXXVI. Estimation of Error........... CXXX. Motion about the Centre of Mass....................................................... 109 CXXXV. Interpretation of Kepler's Third Law........ CXXXVII. Amended Form of Kepler's Third Law CXXXVIII. Potential Energy due to Gravitation CXL. Potential Energy of the System 113 113 CXLVII. Application of Newton's Method of Investigation 124 124 CXLIX. Importance of General and Elementary Properties 125 MATTER AND MOTION. CHAPTER 1: INTRODUCTION. ARTICLE I.-NATURE OF PHYSICAL SCIENCE. PHYSICAL SCIENCE is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events. The name of physical science, however, is often applied in a more or less restricted manner to those branches of science in which the phenomena considered are of the simplest and most abstract kind, excluding the consideration of the more complex phenomena, such as those observed in living beings. The simplest case of all is that in which an event or phenomenon can be described as a change in the arrangement of certain bodies. Thus the motion of the moon may be described by stating the changes in her position relative to the earth in the order in which they follow one another. In other cases we may know that some change of arrangement has taken place, but we may not be able to ascertain what that change is. Thus when water freezes we know that the molecules or smallest parts of the substance must be arranged differently in ice and in water. We also know that this arrangement in ice must have a certain kind of symmetry, because the ice is in the form of symmetrical crystals, but we have as yet no precise knowledge of the actual arrangement of the molecules in ice. But whenever we can completely describe the change of arrangement we have a knowledge, perfect so far as it extends, of what has taken place, though we may still have to learn the necessary conditions under which a similar event will always take place. Hence the first part of physical science relates to the relative position and motion of bodies. ARTICLE II.-DEFINITION OF A MATERIAL SYSTEM. In all scientific procedure we begin by marking out a certain region or subject as the field of our investigations. To this we must confine our attention, leaving the rest of the universe out of account till we have completed the investigation in which we are engaged. In physical science, therefore, the first step is to define clearly the material system which we make the subject of our statements. This system may be of any degree of complexity. It may be a single material particle, a body of finite size, or any number of such bodies, and it may even be extended so as to include the whole material universe. ARTICLE III.-DEFINITION OF INTERNAL AND EXTERNAL. All relations or actions between one part of this system and another are called Internal relations or actions. Those between the whole or any part of the system and bodies not included in the system are called External relations or actions. These we study only so far as they affect the system itself, leaving their effect on external bodies out of consideration. Relations and actions between bodies not included in the system are to be left out of consideration. We cannot investigate them except by making our system include these other bodies. ARTICLE IV.-DEFINITION OF CONFIGURATION. When a material system is considered with respect to the relative position of its parts, the assemblage of |