THE NATURE OF MATTER AND ELECTRICITY THE NATURE OF MATTER AND ELECTRICITY AN OUTLINE OF MODERN VIEWS BY DANIEL F. COMSTOCK, S.B., Ph.D., ENGINEER AND ASSOCIATE PROFESSOR OF THEORETICAL PHYSICS IN THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY AND LEONARD T. TROLAND, S.B., A.M., Ph.D., INSTRUCTOR IN HARVARD UNIVERSITY ILLimPATED NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLACE 1917 COPYRIGHT, 1917 BY D. VAN NOSTRAND COMPANY THE-PLIMPTON-PRESS NORWOOD-MASS-U'S'A PREFACE This book attempts to give in broad, schematic form the conception of the structure of the material universe which has developed in the minds of modern students of physical science. The treatment of the subject which is here offered is radically elementary, and is intended to be "popular" if not "literary" in its style. But, although elementary, it omits none of the salient general ideas, whether these belong primarily to the sciences of chemistry, electricity, optics, or heat. It is characteristic of the modern standpoint that it permits a blending of all of the physical sciences into a single world view, which grows in unity with the years, and with study. A glance at the table of contents of the present volume will reveal what may seem to the uninitiated reader a very heterogeneous assemblage of topics, but it is the hope of the writers that a perusal of the book its eh* will give a sense of the profound inner unity of all of these outwardly various matters. It is the belief of the authors that a book of this nature, written in the light of the most recent discoveries, will find a welcome amongst the scientific laity, as well as with scientific or philosophic workers in general whose special fields are perhaps somewhat removed from that of theoretical physics. At the moment of writing there is no book available dealing with the whole modern theory of matter and energy in either an elementary or an advanced fashion, and treating it as a unit. Many [v] 3G7522 PREFACE admirable treatises on portions of the field are of course obtainable. For a considerably more advanced, yet not very difficult, discussion the reader is referred to three books which together cover the ground fairly thoroughly, o/z., The sixth edition of Nernst's "Theoret- ical Chemistry," the second of Campbell's "Modem Electrical Theory," and Rutherford's "Radio-active Substances and their Radiations." Specific references to other works are given at the end of each Section of Part n of the present book. Something must be said in explanation of the arrange- ment of the book. It consists of two parts, the first giving a rapid survey of the entire subject, outlining the fundamental conceptions and emphasizing then* most significant applications only, while the second retraces the same general field in a slower and less connected way, in order to consider details omitted hi the more cursory treatment. The second part is divided into fifty- six sections, each of which is numbered and referred to by its number in the appropriate connection in Part I. The book may be read in various ways according to the purposes or pleasure of the reader. If he is interested only to acquaint himself with the fundamentals of the modern theory through a quick, general sketch he may read Part I continuously and omit Part n altogether. If, on the other hand, he is already familiar with these essentials he may prefer to reverse the procedure and omit Part I. Part II although definitely divided by topics nevertheless forms a fairly continuous discussion. In general, however, the best method of using the book will probably be to read both of the sections in parallel, refer- ring to each Section in Part n as its number appears in the text of the first part. It is believed that this method of study will encourage the type of attitude which is re- [vi] PREFACE quired to give the subject the greatest clearness in the reader's mind. It is obvious that the structure of Part n permits its ready use for purposes of special reference, such as may arise, for example, in connection with school courses in elementary physics and chemistry. The basis of Part I is to be found in a series of articles contributed in 1911 by D. F. Comstock to the " Science Conspectus," the journal of the Massachusetts Institute of Technology Society of Arts. Somewhat to his surprise, there was a wide demand from various sources for fur- ther copies of these articles, and hence it seemed worth while to publish them in book form, together with a more complete discussion of the same subject. The articles have been amplified and brought up to date by their original author. At Professor Comstock's suggestion, I undertook the writing of Part II, which provides the more elaborate treatment just mentioned. L. T. TROLAND Boston, Mass. CONTENTS PART I A BRIEF OUTLINE OF THE MODERN THEORY OF MATTER, ELECTRICITY AND ENERGY. (BY D. F. COMSTOCK) I. INTRODUCTORY II. THE ULTIMATE REALITIES HI. ATOMS AND THEIR BEHAVIOR 2 Their Size; Their Shape; The Different Kinds of Atoms; The Tendency Shown by Atoms to Form Groups; Elements and Compounds; Chemical Ac- tion; Permanence of the Atom; General Forces of Attraction Between Atoms and Between Groups of Atoms. IV. THE NATURE OF HEAT AND ALLIED PHE- NOMENA 11 The Motion of the Molecules; Molecules are Per- fectly Elastic; Solid, Liquid and Gas, The Causes of Their Differences; The Brownian Movement and the Visibility of Heat Motion ; A Model of a Liquid ; A Model of a Solid; How Friction Causes Heat; Why " Evaporation Cools "; The " Absolute Zero "; The Heat Energy in Bodies. V. THE ELECTRON AND ITS BEHAVIOR 21 Its Size; Its Weight; Its Shape and Structure; The Two Electricities; Both Kinds of Electricity Abun- dant hi all Bodies; Electrons Negatively Charged; Atoms and Electricity; Negative Charge means " Too el*: CONTENTS Many" Electrons, Positive Charge "Too Few"; The Electric Current; The Action of a Battery or Dynamo; "Free Electrons"; The "Evaporation" of Electrons. VI. ELECTRONS, CHEMICAL ACTION, AND LIGHT . 27 Electrons and Chemical Action; Electrons and Light; The Absorption of Electric Waves; The Reflection of Electric Waves; The Speed of Electric Waves in Different Bodies. VH. ELECTRONS AND MAGNETISM ........ 32 The Connection of Electricity with Magnetism; The Deflection of Electrons Caused by Magnetism; The Action of a Dynamo; Permanent Magnetism; The Effect of Magnetism on Light. RADIO-ACTIVITY ................ 34 The Three Rays; The Beta Rays; The Alpha Rays; The Gamma Rays; The Cause of Radio- Activity; Successive Disruptions of the Atoms of Radio-Active Substances; Radio- Activity not a Chemical Change; Intra- Atomic Energy; The Quantity of Intra- Atomic Energy; The Radio-Active Elements; Are all of the Elements Radio-Active? The Evolution of the Ele- ments. IX. THE STRUCTURE OF THE ATOM ....... 41 General Principles; Evidence for Orderly Structure in the Atom ; Spectral Lines. X. RECENT DISCOVERIES CONCERNING ATOMIC STRUCTURE AND RADIATION ....... 43 Recent Advances Concerning the Atom; Atomic Numbers; The Quantum Theory; The Similarity of all Forms of Radiant Energy; X Rays. XL ATOMS AND LIFE ......... . ..... 60 CONTENTS PART II AN APPENDIX TO PART I, CONSISTING OF FIFTY-SIX SECTIONS, EACH DISCUSSING IN FURTHER DETAIL SOME PROBLEM MORE BRIEFLY TREATED IN PART I. (BY L. T. TROLAND) 1. THE SOURCES OF THE MODERN THEORY OF MATTER 62 A brief statement of the history of the subject. 2. METHODS OF DETERMINING ATOMIC SIZES . . 63 The thickness of the thinnest known films of matter; Calculations based on the volume occupied by the atoms, on chemical deposition caused by the electric current, on the speed of ions, heat conduction, etc.; Agreement of the differently obtained results amongst themselves. 3. ATOMS, COLLOIDS AND THE MICROSCOPE ... 68 Can atoms be seen? Nature of Colloids. 4. THE SHAPE OF ATOMS 60 Atoms probably spherical; Means of showing this; The " solar system " idea of the atom. 6. SPECIES OF ATOMS; ATOMIC WEIGHTS, AND ATOMIC VOLUMES 62 Table of the elements, their symbols, atomic weights, general properties, and dates of discovery; Table of the radio-active atoms; Methods of ascertaining the relative weights of atoms, from chemical analysis, from the volumes occupied by gases ; How the volume of an atom is related to its weight, [xi] CONTENTS 6. THE PERIODIC TABLE OF THE ELEMENTS. . . 68 Systematic resemblances between different elements; The principle of the Periodic Table, "families" and "series" of elements; Our knowledge of elements as yet undiscovered; Defects in the Periodic System; The probable meaning of the system; Prout's Hypothe- sis: Helium and the Nucleus Theory; Isotopes; Meta- neon; The Table itself. 7. THE ARRANGEMENT OF THE ATOMS IN THE MOLECULE 76 The multitudinous compounds of carbon; " Isomers " and structural formulae ; Proof that our conceptions of molecular structure are correct in the case of " ben- zene," as an example; Molecules of single elements; How the shape of crystals depends on that of the mole- cules composing them. 8. THE PHYSICAL PROPERTIES OF COMPOUND SUBSTANCES 86 What determines these properties; Meaning of color; Individuality of molecules ; Allotropism ; Recent ideas concerning the basis of chemical individuality. 9. CONCERNING CHEMICAL EQUATIONS 90 The types of chemical change and the way in which the chemist represents them. 10. THE FORCES OF ATTRACTION WITHIN BODIES . 91 Probable relation between gravitation and the attrac- tion between individual molecules and atoms; De- pendency of the forces of cohesion, etc., upon those of chemical affinity, and of the latter upon the forces within the atom itself. 11. "THE KINETIC MOLECULAR THEORY" ... 92 The nature of this theory and the ideas it is based on ; The idea of probability and the use of averages in mo- lecular physics ; Individuality in the molecular world. [xii] CONTENTS 12. THE SPEEDS OF MOLECULAR MOTION 94 The temperature of a body is proportional to the " ki- netic energy " of its molecules ; Relative speeds of heavy and of light molecules at the same temperature ; The actual calculated speeds of certain molecules. 13. THE AVERAGE DISTANCE TRAVERSED BY A GAS MOLECULE BETWEEN IMPACTS 97 Definition of "mean free path" in a gas; Properties of a gas affected by size of this path; Its length about one one-millionth of an inch under ordinary conditions. 14. DIFFUSION 99 Its cause and mechanism. 16. SOUND 101 The structure of a sound-wave ; How it is set up and how it travels; Similarity between sound- and heat- waves. 16. LATENT HEATS 102 Explanation of the fact that heat disappears when a body melts or vaporizes. Why solids soften when heated; Cause of the " surf ace tension" of liquids; The mechanism of evaporation. 17. THE "CRITICAL" AND BOILING POINTS OF LIQUIDS 106 Definition of the "critical point" of a liquid; Change in latent heats and surface tension near critical point and reason therefor; What "boiling" means on the molecular theory. 18. THE SIMPLE LAWS OF GASES AND OF SOLU- TIONS 106 Why the pressure exerted by a gas increases with its degree of confinement, and with rise in temperature, the laws of Boyle and of Charles; Absolute Zero and the [xiii] CONTENTS principle of Gay-Lussac; Explanation of the law of Avogadro ; Effect of volume of the molecules and their mutual attractions upon the laws of gases, the formula of Van Der Waals. 19. OSMOTIC PRESSURE 108 Why dissolved substances obey the same general laws as gases. 20. HEAT CONDUCTION 109 The cause of differences in the heat conductivity of solids, liquids and gases; The part played by "free electrons " in the conduction of heat. 21. THE BROWNIAN MOVEMENT AND ITS MEAS- UREMENT 110 Method of studying the Brownian movement; Specific results verifying the kinetic molecular theory. 22. THE SOLID AND CRYSTALLINE STATES 112 The difference between crystalline and "amorphous" bodies; The crystal as the unit of structure of matter just above the molecule ; Crystal structure as studied by X rays; Liquid crystals. 23. VAPOR PRESSURE AND THE LAW OF DISTRI- BUTION OF MOLECULAR SPEEDS 115 Although for a given temperature all of the molecules do not move at the same speed, most of them tend to have at least approximately the average speed for all; How this fact explains the manner in which the rapidity of evaporation of liquid increases with temperature; Similarly with respect to the pressure exerted by the resulting vapor ; Why a liquid and its vapor maintain the same temperature in spite of the "cooling effect of evaporation." CONTENTS 24. HEAT ENERGY AND SPECIFIC HEATS 118 Definition of the "total heat energy" of a body, and of "specific heat"; Du Long and Petit's law of "atomic heats " and its explanation; Explanation of the constant relation between the atomic heats of solids and of gases; Deviations from these rules and their probable signifi- cance. 25. THE DISCOVERY AND MEASUREMENT OF THE ELECTRON 120 J. J. Thomson's work on the "cathode rays"; How Thomson determined the mass and charge of the elec- tron; Counting electrons by the use of a fog; How the size of the electron can be calculated; Its substance and its structure. 26. THE IMPORTANCE OF ELECTRICAL FORCES IN NATURE 126 All physical events probably determined by such forces in the last analysis. 27. THE REACTIONS OF ELECTRONS AND CHARGED ATOMS 125 Definition of an "ion," and how ions are produced; Energy required to drag an electron from an atom; How electrons and ions of different kinds act on one another; Rules for such action. 28. SOME EFFECTS CONNECTED WITH THE ELEC- TRICAL CURRENT 129 The "Hall Effect," why magnetism deflects an electric current; Nature of electrical "resistance"; Signifi- cance of "amperage " ; Why the best electrical conduc- tors are also the best heat conductors, and why metals are in general superior to other substances hi these respects ; The motion of electrons in a wire is opposite in direction to the "current." 29. ELECTRICAL CONDUCTION IN GASES AND LIQUIDS 131 Ions carry electricity in these substances; Nature of electro-chemical action, or " electrolysis." CONTENTS 30. THE ELECTRICAL TRANSMISSION OF POWER. . 133 Mechanism of this transmission. 81. THERMO-ELECTRICITY 133 The various "affinities" of different substances for electrons; the operation of a "thermopile" explained on the electron theory; The elements arranged in order of their affinities for electrons. 32. CHEMICAL AFFINITY 136 Electro-negative and electro-positive elements; Ions and electrons in chemical action; Electro-negativity or positivity only a relative conception; How atoms of the same species can be attracted electrically; Nature of chemically "inert" elements. 33. SOLUTION AND ELECTRICAL DECOMPOSITION. 139 How water can "ionize" substances which dissolve in it; Definition of "electrolytic dissociation"; Motion of the ions in a solution under the influence of electrical force; How it is proven that water dissociates dis- solved substances, effect on boiling and freezing points. 34. CHEMICAL VALENCY 141 Definition and cause of valency. 35. CHEMICAL ACTION 142 The complexity of the changes involved in chemical action; Chemical change depends on the chance col- lision of molecules; Explanation of the fundamental "law of chemical mass action" on this basis; Rever- sible and irreversible chemical processes; Chemical equilibrium and its kinetic nature. 36. EFFECTS AND CONDITIONS OF CHEMICAL CHANGE 144 Heat and chemical change; How electric current and light can be generated by chemical action; Nature of "chemical energy." CONTENTS 37. LIGHT WAVES AND LINES OF ELECTRICAL FORCE 146 Present status of the "aether" theory; Definition and nature of a line of electrical force; Formation of "kinks" in such lines; Light not a continuous wave- motion. 38. THE ZEEMAN EFFECT 149 General nature of the theory of the effect, and results of its application to the phenomena; The Stark Effect. 39. THE CONDITIONS UNDER WHICH LIGHT IS PRODUCED 150 Temperature radiation; Why the light from a glowing body is whiter the hotter the body; The law connect- ing wave-length and energy of emitted light with tem- perature, and its general explanation in terms of the electron theory ; The emission of light by gases ; loni- zation and the production of "line spectra"; Spectral "series." 40. THE GAMUT OF ELECTRICAL WAVES 155 The complete spectrum, including all electrical waves; Position of visible light, "ultra-violet," "infra-red," heat, "Hertz waves," X rays, etc., in this spectrum; Velocity of light; Actual lengths and frequencies of light and other electrical waves. 41. COLOR AND THE ABSORPTION AND REFLEC- TION OF LIGHT 157 How color is produced by absorption; Explanation of the "selective absorption" of light; Basis of the sen- sations of color; Production of color by reflection. 42. THE REFRACTION OF LIGHT 159 How a column of light is bent in passing from air into glass; Definition of "dispersion" and statement of the law governing it; Relation between the index of refraction of a substance and its "dielectric capacity." [xvii] CONTENTS 43. ROWLAND'S EXPERIMENT 161 How it was shown that the motion of an electrical charge causes magnetism. 44. THE DEFLECTION OF MOVING ELECTRONS BY A MAGNET 162 How the experiment is performed. 46. ALL BODIES ARE MAGNETIC 163 The two kinds of magnetism; How permanent magnet- ism is possible. 46. THE RADIO-ACTIVE SUBSTANCES 165 The Work of Becquerel and the Curies; The "Radium series"; The law of decay of radio-active substances; Their position in the Periodic Table. 47. HOW THE RAYS FROM RADIUM ARE STUDIED . 168 The differential effect of magnetism on the rays ; Pene- trating power of the beta rays. 48. HOW RUTHERFORD PROVED THE ALPHA RAYS TO BE HELIUM ATOMS 169 Description of the experiment. 49. THE NATURE OF THE GAMMA RAYS 170 Relation of the gamma rays to the beta rays and the disruption of the radio-active atom ; Secondary gamma rays. 60. THE ENERGY OF THE ATOM 172 The great stability of the atom; Relation of intra- to inter-atomic forces and energies. 51. THE RADIO-ACTIVITY OF POTASSIUM 173 The work of Campbell. [xviii] CONTENTS 62. INORGANIC EVOLUTION 173 The variability of the line spectra of the elements; The spectra shown by the hottest stars are the most imper- fect; Lockyer has shown that the very hottest stars con- tain only the simplest elements; Meaning of these facts. 53. THEORIES OF THE STRUCTURE OF THE ATOM . 174 Thomson's theory and its partial explanation of the mystery of the Periodic Table; The modern "Nucleus Theory " ; The empirical basis of this latter theory ; The number of electrons in the atom; Isotropism; Atomic numbers ; The hydrogen atom, its constitution and the basis of its line spectrum as deduced from the " Quan- tum Theory " of light. 54. THE QUANTUM THEORY OF RADIANT ENERGY . 182 The nature of the theory; The photo-electric effect; The relation between the "frequency" and energy of light quanta; The conditions of the absorption and emis- sion of quanta; The explanation of the low values of specific heats near absolute zero temperature ; Planck's original reason for propounding the theory; The broad significance of the theory; The doctrine of entropy and its basis in the theory of probabilities; Entropy and radiation. 65. X RAYS AND THEIR MEASUREMENT 189 The origin and nature of X rays; Characteristic X rays; Why Xrays penetrate "opaque" bodies; The cor- puscular properties of X rays; The reflection and "diffraction" of X rays by crystals; New light on crystal structure. 66. LIFE AND CATALYSIS 193 Vital phenomena are consistent with an explanation in terms of atoms, molecules and electrons. INDEX 196 [xix] ILLUSTRATIONS Page Sir Joseph J. Thomson Frontispiece Fig. 1. The Relative Sizes of Atoms and Molecules ... 3 Fig. 2. Relative size of Molecules and Visible Particles . 4 Fig. 3. Water Molecules Facing page 4 Fig. 4. Molecules of Steam 6 Fig. 5. Atoms of a Liquid 6 Fig. 6a. Formulae of some Common Organic Compounds . . 8 Fig. 6b. Formula of an Azo-dye 9 Fig. 7. Atoms of a Solid Facing page 10 Fig. 8. Gas Molecules 12 Fig. 9. Vapor Molecules at the Surface of a Liquid .... 15 Fig. 10. The Constitution of a Simple Molecule 28 Figs, lla, b. The Radio-Active Elements and their Relation- ships and Rays 36, 37 Fig. 12. Five Isomeric Hydrocarbons having the Constitution C 6 H 14 79 Figs. 13a, b. Benzene and its Chlorine Derivatives .... 81, 82 Fig. 14. Models of Tartaric Acid Molecules 84 Fig. 15. Crystals of "Right" and "Left" Tartaric Acids . . 86 Fig. 16. Diffusion Paths 100 Fig. 17. "Distribution Curve" for Molecular Speeds ... 116 Fig. 18. Vacuum Tube to show the Action of the Cathode Rays 121 Fig. 19. How the Cathode Rays May be Bent by a Magnet . 122 Fig. 20. The Forces Acting Between Ions, Atoms and Electrons 127 Fig. 21. A Thermo-Electric Circuit 134 Fig. 22. Showing the Manner in which Two Neutral Aggre- gates of Electrical Particles may attract eath other. 138 Fig. 23. To Show how Radiation is Produced by Stopping the Motion of an Electrical Particle 148 ILLUSTRATIONS Fig. 24. The Zeeman Effect 160 Fig. 26. Curve Showing the Relative Intensities of Radiation of Different Wave Lengths Emitted by Solid Bodies at Various Temperatures 153 Fig. 26. The Direction of the Magnetic Forces about a Moving Electrical Charge 162 Fig. 27. Structural Plan of a Simple Crystal 192 PLATES I. Line Spectrum of Iron Facing page 42 n. Cavendish Gravitation Apparatus .... " " 92 in. Thomson Cathode Ray Tube " " 122 IV. The Deflection of Cathode Rays by a Magnet. " " 162 V. Coolidge X Ray Tube " " 190 [xxii] PART I A BRIEF OUTLINE OF THE MODERN THEORY OF MATTER, ELECTRICITY, AND ENERGY CHAPTER I INTRODUCTORY During the last two decades there has been a very great advance in our knowledge of the ultimate constitu- tion of matter. (1) The older ideas which prompted the contemptuous phrase " gross matter" are inadequate to represent the extraordinary complexity and delicacy of structure which have since been revealed. The end is of course not yet, but throughout all this advance there has been singularly little in former ideas which had to be considered totally wrong. They were right as far as they went, although insufficient, and so it proba- bly is with our present ideas respecting the structure of things; they will doubtless appear crude in the light of future knowledge but in a general way they are proba- bly right as far as they go, and hence are worthy of our attention. CHAPTER H THE ULTIMATE REALITIES According to the modern theory of matter all bodies are complex structures composed of small particles called NOTE: The full-face numbers inserted in the text at various points refer to the Sections of Part II in which related subjects are discussed (see Preface), or in which further details are given on the same subject. [1] ATOMS AND THEIR BEHAVIOR [Chap. IE atoms, together with still smaller particles known as electrons. If, therefore, we were familiar with the laws of action of atoms and electrons we should understand completely all the physical phenomena in nature. The atom, as we shall see later, is a much more complex structure than the electron, so that atoms and elec- trons are not quite on a par as regards classification, except from the introductory point of view, from which we begin discussion. As a third fundamental entity, there should be men- tioned the energy associated with atoms and electrons, but for the present this will be left out of consideration. CHAPTER HI ATOMS AND THEIR BEHAVIOR Size. Atoms are minute particles each about one three-hundred-millionth of an inch in diameter (2). If the earth were made up of base-balls it would be a fair model of a drop of water made up of atoms. The most powerful microscope known, used under the best condi- tions, would enable us to see an object approximately two hundred atoms in width. Single atoms are, there- fore, totally invisible, and their properties cannot be found out by direct inspection (3). Shape. Not much is known as regards the shape of the atoms, but in general they behave as if they were not very far from spherical (4). Different Kinds. We are now acquainted with about one hundred different kinds of atoms, that is, different species. The individual atoms in each species are, how- ever, exactly alike, or have so nearly the same properties that under most conditions there is no difference in the [2] Chap. HI] SPECIES OF ATOMS action of the individuals. Atoms of different kinds differ in size and still more in weight. At present there is no agreement as to the difference in size of the various kinds of atoms. On the basis of certain calculations from coefficients of expansion, some Fig. 1 THE RELATIVE SIZES OF ATOMS AND MOLECULES This diagram is intended to give an idea of the relative magnitudes of atoms and molecules. However, the drawings are only symbolic, as the dimensions have been calculated on the assumption that the mole- cules are spherical, which cannot be strictly true. It will be noticed that the smallest atom (that of hydrogen) differs only slightly in size from the largest atom (that of uranium). The starch molecule is probably one of the largest which exists and it will be seen that, according to the diagram, it is very much larger than the largest atom or than the mole- cule of sugar. The relative weights of the particles represented are as fol- lows: Hydrogen, 1; Uranium, 239; Sugar, 366; and Starch, not accu- rately known but probably about 25,000. A molecule of ordinary alcohol weighing 46, would be slightly larger than the uranium atom. investigators believe that the sizes of the different kinds of atoms are in the same order as their weights. Ac- cording to this view, therefore, the lightest atom, hydro- gen, is also the smallest; and the heaviest atom, uranium, is also the largest. The atom of uranium is about 240 times as heavy as the atom of hydrogen, whereas it has [3] ATOMS AND THEIR BEHAVIOR [Chap. HI only about two and one-half times as great a diameter. If this view is correct, we might represent an atom of hydrogen by a wooden ball the size of a pea, and an atom of uranium by a lead ball the size of a cherry. Representatives of all of the other atomic species would then be arranged in a complete series from the small wooden ball to the large lead one. Fig. 2 RELATIVE SIZE OF MOLECULES AND VISIBLE PARTICLES The molecule represented in this diagram is the starch molecule of Figure 1, very much reduced in scale. It is not certain that the starch molecule is the largest which exists, but it is very far from being the smallest. The microscopic particle which is represented is the small- est which can actually be seen under the most powerful microscope. Particles nearly as small as the starch molecule can be seen indirectly by means of the ultra-microscope. (See Section 3.) Although the individual atoms of one kind are, with certain modern reservations, all alike, those of different species have decidedly different properties, and this difference hi property is what gives variety to the phys- ical world as we see it. The atoms of one species are [4] Chap. IH] MOLECULES so definite, unique, and characteristic in their actions and properties that they give one the impression of a delicacy and complexity of structure suggestive, almost, of the complexity of personality. There are subtle resem- blances between one species and another with regard to one -property, and marked differences with regard to another (6). Hence one should be very careful to realize that when, for reasons of analogy, we represent an atom as a ball of wood or a ball of lead we are representing it only in the vaguest general way, and are totally ignoring its complexity and individuality. Tendency to Form Groups (Molecules). Atoms tend to form groups known as molecules. The atoms in a mole- cule adhere with considerable force and some molecules can be broken up only with the greatest difficulty. These groups have a definite individuality and unless acted on from the outside they are apparently permanent. The same atoms may be grouped into quite different molecules just as the same bricks may be used to build a church or a jail, or the same letters used to form altogether different words. The individuality of a molecule is per- haps best appreciated by thinking of the individuality of a word. A word, though consisting solely of letters, has a definite unity of its own. A molecule made up of atoms is just as definite an aggregate (7). As a help toward a concrete conception two drawings are given in Figures 3 and 4. The first represents sym- bolically water molecules, each consisting of two hydro- gen atoms and one oxygen atom, in the closely crowded state known as liquid, and the second the same mole- cules in the more dispersed state known as vapor (steam). Elements and Compounds. When the atoms making up the molecules of a substance are all alike, that is when [6] ATOMS AND THEIR BEHAVIOR [Chap, m they belong to the same species, the substance is called an "element." An element, therefore, is composed of only one kind of atom. A compound is a substance the molecules of which are made up of more than one kind of atom. Figure 5 represents symbolically a liquid element, Figure 3 a liquid compound. "Oxygen," "hydrogen," "carbon," "lead," "copper," are names of some of the elements, and they are, therefore, names of atomic species. "Water," "salt," "sugar," and "carbon-dioxide" are names of compounds, and hence are the names of molecular species. The water molecules in Figure 3 are seen to consist of one large atom and two smaller ones in a group. The large atom is an oxygen atom. The two smaller ones are hydrogen atoms and the group as a whole is a water molecule. It is therefore true to say that a water mole- cule is the smallest particle of water that it is possible to have, for if it is further broken up it is no longer water. These drawings are in no sense other than symbolic. As a moment's thought will show, thousands upon thousands of different kinds of molecules are known. Some, such as the water molecule, are relatively simple and composed of a few atoms, and some, such as the sugar molecule, are very complex. (See Figure 6.) In the par- ticular case of the sugar molecule the number of atoms is forty-five. A small crystal of "granulated" sugar is, therefore, a solid mass consisting of hundreds of millions of sugar molecules, that is hundreds of millions of definite, co- herent groups of atoms, each group containing twelve atoms of carbon, twenty-two of hydrogen, and eleven of oxygen. [63 Chap. IH] CHEMICAL ACTION The definiteness of molecular structure must not be forgotten. One of these sugar molecules might be com- pared to a word of forty-five letters, for if a single atom were removed from the group, or if a single atom had its position markedly changed, the group might still be a molecule, but it would not be a molecule of sugar, and a vast mass of such modified molecules would not make up a crystal having the same properties as the one with which we started (8). Chemical Action. Chemical action is the name given to the process in which the groups known as molecules are either formed or destroyed. When a substance is burned or when an acid "eats" a metal the action in- volves the formation of new molecules, because of the re- arrangement of the atoms, and therefore the production of new substances. By an inspection of Figure 3 it will be clear that if two of the "large " oxygen atoms could be separated from their respective water molecules, to re- combine as represented in Figure 8, there would be left behind, four of the "small" hydrogen atoms of Figure 3 (two from each decomposed molecule), and these would adhere in twos and would form two hydrogen molecules. When thousands of molecules were thus broken up the complete process would be called the decomposition of water into oxygen and hydrogen. It is easily accom- plished in the laboratory. It is clear that when complex molecules are present it is possible for the rearrangement which takes place to be very complicated indeed. There are often, also, several possibilities of rearrangement, each resulting in a dif- ferent set of substances as a final outcome. Outside conditions such as temperature, pressure, etc., have marked effects on the results of chemical reactions. Chemical action, therefore, always implies the break- [7] ATOMS AND THEIR BEHAVIOR [Chap. HI H H Ethyl Alcohol H C C O H H Acetic Acid H C C= O O-H H H-C-O-H H O C H Grape Sugar H O C H (dextrose) H C O H H O C-H 0=C H Fig. 6a FORMULA OF SOME COMMON ORGANIC COMPOUNDS NOTE. The formula of ordinary cane sugar (or saccharose) is not definitely established, but probably consists of two groups of atoms similar to that for dextrose, combined with a molecule of water. [8] Chap. IIT| COMPLEX MOLECULES O H H H H H H c c U U /. \ / .\ S \ S \ H-C C C-N=N-C C-C C-N= c c x c=/ x c=c x Y A A A A H O=S=O i Na H H C H H H H U A A =K-/ Vp-f-/ V % C-H C=C X H-C C C-H A o=s=o o c-c I Na O S C C O H \ / Na O C= C H C C H C=C HH Fig. 6b FORMULA OF AN AZO-DYE ATOMS AND THEIR BEHAVIOR [Chap. HI ing up or forming of molecules, and in general it means both (9). Permanence of the Atom. Although every one of the thousands of "chemical reactions" which are daily going on hi the world involves the formation or decomposition of molecules, no way has yet been found to change an atom of one species into one of another species. To find such a way was the hope of the alchemists but it was never realized. We shall see later that the atoms are probably not absolutely permanent but that the mysterious forces which preserve their integrity are so much greater than the forces which hold them together in molecules, that as yet it has not been found possible to shatter them artificially. The atoms have great family attraction and it is the business of the chemist to make use of this attraction in the service of man, but the instinct, we might say, of self- preservation is so vastly greater hi the atom than its group-forming tendency, that although it submits to the breaking of family ties it will not allow its own individual- ity to be tampered with. To state that it will never be possible to break up atoms artificially would of course be folly, but we can say at present with considerable certainty that the disruption of atoms must involve forces of an entirely different magnitude from those called " chemical," which are associated with the breaking up of molecules into atoms. We shall see later that there appears to be going on in nature a spontaneous decomposition of the atoms of radium and certain other substances, but thus far it has been found quite impossible artificially to influence this spontaneous disruption to the slightest degree, and there- fore although we might call the process " natural al- [10] . -i^. ^aafc lip -, III *** ' Chap. IV] MOLECULAR MOTION chemy" it cannot be called alchemy in the ordinary sense of the word. General Forces of Attraction. Just as atoms have forces of attraction which hold them together in mole- cules, so molecules attract each other and tend to form the large aggregates which we call " objects." These forces are in general weaker than the forces between the atoms (10). They are great enough, however, to account for the relatively strong cohesion of solid bodies and the weaker cohesion of liquids. CHAPTER IV THE NATURE OF HEAT AND ALLIED PHENOMENA The Motion of the Molecules. It is now believed, and the odds amount almost to certainty (11), that all atoms of all substances are in ceaseless motion to and fro. This motion is what we call the heat of a body. 1 The more violent the motion the hotter the body (12). It is perhaps a pity that the motion picture art is not de- veloped to a point which would enable us to embody this violent vibration in the accompanying figures, so we must request imagination to aid incompetent art and to endow every atom or molecule of Figures 3 to 8 with a rapid motion; a motion which, like the modern idea of freedom, is limited only by the equal rights of all the other atoms. Thus in the liquid and solid states (Figures 3, 5 and 7) the crowding is so close that "the rights of others" 1 Strictly speaking, it is the energy of the atomic or molecular motion which constitutes the heat of a body. The distinction between atoms, molecules and electrons is not important when heat phenomena are being described in a general way since it is probable that all of the particles share in the motion. [11] HEAT PHENOMENA [Chap. IV allow only vibration through a very limited distance, while in the gaseous state (Figures 4 and 8), the motion consists of a straight line flight until by chance there is an encounter with another molecule. When this occurs there is a rebound and then another flight. The distance between the molecules is so small and their speed is so large that literally billions of these impacts are occurring every second in even a cubic inch of gas (13). Molecules Have No Friction. It is necessary in order that this motion should continue indefinitely that the atoms or molecules l be considered frictionless. At first sight this seems an improbable hypothesis, but when the nature of friction is understood from the present point of view the assumption is seen to be justified. A number of billiard balls put on a table and set going would bound to and fro for a short time and gradually come to a stop, but this is because at every impact part of the energy of the balls' motion is wasted in the form of heat, that is, the balls are actually a trifle warmer after striking each other than before. Now from the present point of view, as we have just seen, "warmer" means more rapid molecular motion, so that the billiard balls gradually slow down and stop because their motion is gradually transformed into the invisible motion of the molecules which compose them and surrounding objects. Thus friction exists between visible objects solely because of the existence of the molecules which go to make them up, these molecules absorbing the motion. From this it is clear that for two molecules to waste energy in impact after the manner of two billiard balls, 1 The argument here presented applies strictly only to the " ultimate particles " of matter, whatever these may be. How- ever, no very important inaccuracy can result from identifying these ultimate particles with atoms, molecules and electrons. [12] I I f Chap. IV] MOLECULES AND FRICTION it would be necessary for them to be composed of still smaller "molecules." Hence, the ultimate particles themselves cannot possess friction in the ordinary sense. As a matter of fact we shall see later that molecules do lose energy, not in a way similar to the friction of large objects, but by radiating it in the form of heat waves. An analogy for this radiation of energy may still be found among billiard balls, for if they, the table, the cushions against which they strike, and the air around, were all perfectly elastic and frictionless, the balls when set going would keep then* motion for a far greater time than they actually do, but they would not continue to move indefi- nitely. This is because at each impact between two balls there would still be a sound, the "crack" with which we are all familiar, and this would carry energy away. This loss of energy by sound is vaguely similar to the radiation of heat energy by the molecules of a substance (15). Solid, Liquid and Gas. All substances which do not decompose (that is, all substances the molecules of which do not break up) on heating, are capable of existing in three states, the solid, the liquid and the gaseous. A solid when heated above its melting point becomes a liquid and a liquid through the process of evaporation or boiling changes into a gas. It is also possible, at cer- tain temperatures and pressures, for a solid to pass directly into the gaseous state and vice versa. From the present point of view the cause of these changes is readily seen. We have said that heating a body means increasing the violence of its internal vibra- tion. Now it is easy to imagine that when in a solid sub- stance this vibration comes to exceed a certain amount the atoms or molecules will no longer be able to adhere in orderly arrangement but will be forced farther apart [13] HEAT PHENOMENA [Chap. IV by the motion and, although not completely out of the influence of each other's attraction so that they become totally dispersed, still are so far apart that they wander about at random, like the frantic members of a mob. Under these circumstances rigidity no longer exists and the substance is liquid (16). When the vibration gets still more violent, i.e., when the liquid is further heated, the number of molecules at the surface of the liquid which escape into the surrounding region becomes very large. The molecules which escape do so because amid the random vibration they happen to have a speed sufficient to carry them up beyond the at- traction of the other molecules of the liquid. These molecules in the space above the liquid constitute a gas (17). In the case of a solid or liquid the heat motion takes place through a very short distance and is then reversed, and therefore we may speak with propriety of the motion as a "vibration" of the molecules or atoms. In the case of a gas, however, the motion is different, each molecule travelling practically in a straight line until by chance it encounters another flying molecule. In such a gas as air (which is mainly a mixture of oxygen gas and nitrogen gas) a molecule travels on the average through a distance several hundred times its own diameter before it strikes another (14). The existence of this atomic and molecular motion is at the very heart of the modern conception of matter. A somewhat extended analogy will, therefore, not be out of place. Suppose that into a room are thrown at high speed, through an open door, ten thousand tennis balls, and that the door is then closed. It is clear that the balls will for a time bound back and forth among themselves, striking [14] Chap. IV] MODEL OF A GAS the walls and each other. If, now, we make the ideal assumption that the walls of the room and the balls are perfectly elastic, that is, that there is no energy lost at any of the impacts, it is clear that the bouncing of the / A A- -& - / \ -x ' \ A . >' \ l'\ \ ! A * Fig. 9 VAPOR MOLECULES AT THE SURFACE OF A LIQUID As explained in the text, the vapor which rises from the surface of any liquid consists in molecules which are shot through the film of surface attraction. Slow-moving molecules may penetrate the liquid surface but be returned to it once more by the forces of attraction. Fast-moving molecules, however, may escape permanently. The paths described by molecules of both sorts are illustrated above. A is the limit at which the attraction ceases to be effective for a molecule moving sufficiently fast to reach this line. B is the liquid surface. balls will go on indefinitely. Such a room with the balls will represent in a general way a small vessel filled with a gas. 1 Some of the well-known properties of gases follow in the simplest way from a consideration of the above model of a gas. It is obvious that the walls of the room will be 1 The analogy here given may appear crude, but an actual model on the general principle outlined, using small steel balls, has been constructed by Professor Northrup of Princeton. When in action, this model exhibits all of the fundamental properties and laws of gases. [16] HEAT PHENOMENA [Chap. IV bombarded by the flying tennis balls. The walls will, therefore, feel a thrust, that is, they will have an outward pressure acting upon them. This corresponds to the well- known pressure of any gas confined in a closed vessel. Moreover, this pressure due to bombardment will be greater if the speed of the flying balls is greater, and hence in the case of a gas we should expect the pressure to increase with the temperature, that is, with the aver- age energy of motion of a molecule. It is a well-known fact that the pressure of a gas does increase in this way (18), (19). Again, returning to our model, it seems fairly reason- able to suppose (and can, in fact, be proved mathemati- cally) that if the balls hi one hah* of the room have on the average a higher speed than the balls in the other half, there will be a gradual slowing down of the one and a speeding up of the other until all of the balls have the same average speed. This corresponds to the gradual equalization of temperature which goes on in any vessel containing a gas, when at the start one part of the gas is at a higher temperature than another. This transmission of energy in a gas is what is called heat conduction (20). The Brotonian Movement and the Visibility of Heat Motion. If one of the tennis balls above mentioned were much larger and heavier than the rest it would be found to move on the average much more slowly. In the case of a gas, therefore, heavy molecules move on the average more slowly than light ones. As we pass to heavier and heavier molecules or to larger and larger particles of some foreign substance immersed in the gas, the average motion of the particles considered becomes less and less, until it disappears into the imperceptible. Now the ques- tion arises whether it might not be possible to detect the motion of particles so large that they could be seen with [16] Chap. IV] MODEL OF A LIQUID a microscope. If this were possible we could obtain a direct view of the heat motion of the gas, for although we should not be able to see the motion of single molecules we could see the closely related motion of a very much larger particle. Now, as a matter of fact, this continuous random motion of all very small solid particles floating hi a gas or a liquid is a well-known phenomenon and is called the Brownian Movement. It is so common that biologists have to learn to distinguish between the life-motions of bacteria which they are examining under the micro- scope and the "Broionian movements" which the bacteria have in common with all other small particles. This Brownian movement is an extraordinary veri- fication of modern ideas of heat for the verification goes farther than was stated above. It has recently been shown that the motion observed under the micro- scope is not only of the same *W but also of the same magnitude as that which is predicted mathematically from molecular considerations (21). A Model of a Liquid. If we imagine the above men- tioned tennis balls to have then- average motion slowly diminished, and if we remember that in order to repre- sent molecules the balls must have a slight attraction for each other, it will be clear that finally the balls will no longer fill the room as they did before but will divide themselves into two groups. There will be a layer of balls on the floor adhering more or less closely together, al- though still vibrating among themselves, and above this layer there will be flying at random the balls which we have already taken to represent a gas. The layer on the floor might be a foot or two thick, depending on the num- ber of balls present, and they would give us the impres- sion of a ceaselessly squirming mass. [17] HEAT PHENOMENA [Chap. IV This dense layer of agitated balls on the floor repre- sents the surface of the liquid and the flying balls in the remainder of the room represent the gas or vapor which always exists above any liquid confined in a closed vessel. It will be clear hi a general way from this model why "heat expands" in the case of a liquid, for as the violence of vibration increases (and this corresponds to a rise in temperature) the closely adhering balls representing the liquid will, on the average, be forced farther apart and the total volume of balls will appear to fill more space. In a few rare cases a liquid expands on being cooled. In these cases we must imagine that the molecules are not simple spheres but have more complicated shapes. A change in temperature may therefore result in a different fitting together and unexpected volume changes. A Model of a Solid. The model above discussed probably represents the truth in a general way as re- gards a liquid, a gas, and the relation between the two, but we cannot be so sure in the case of a solid. The tennis balls, if they are to represent molecules, must not be perfectly spherical. Let us suppose them to be egg-shaped. Let us suppose too that the internal motion of the balls on the floor be diminished more and more and that after a while there is a tendency to form orderly arrangements which persist. They will still be vibrating somewhat, but if one of the balls has its sharper end turned in one direction at present, it will be turned hi the same direction at a later period. It is as if a net-work of elastic threads fastened the balls together. They are still capable of vibrating to and fro, but any individual maintains permanently a certain position in the total mass. [18] Chap. IV] COOLING AND HEATING EFFECTS Such a model probably corresponds to a substance in the solid state, although, as has been said, this is not certain at present. There may be some other subtle difference between a liquid and a solid, but this is per- haps the principal one. One reason why we are not very sure that permanent orderly arrangement is the only difference between a solid and a liquid is because of the existence of orderly arrangement within liquids. Liquid crystals, as they are called, are known to exist and certainly are of extreme interest and importance (22). How Friction Causes Heat. It will be clear from the above considerations why the rubbing of one surface on another invariably causes heat. The molecules of both bodies are "stirred up" as it were, so that the violence of vibration is increased and this corresponds to a rise in temperature. The energy required to increase the vi- bration of the molecules comes from the work done in the rubbing. Why " Evaporation Cools." - That the evaporation of a liquid has a cooling effect is well known to everyone. Boys detect the direction of the wind by noticing the coolness of one side of a wet finger. From the above consideration the reason for this cooling effect is not difficult to imagine. From the surface of a liquid, mole- cules are constantly passing away to become part of the surrounding vapor. In the course of the random motion which a molecule at the surface of a liquid undergoes it may at certain times, as has been said, attain sufficient speed to enable it to break away from the attraction of its neighbors. (See Figure 9.) Since the deserters will always be molecules which at the moment possess greater speeds than the average, the liquid by evaporation is constantly losing some of its fastest moving particles. Such selective action will result in a gradual decrease in [19] HEAT PHENOMENA [Chap. IV the average speed of those that remain. This corre- sponds to a cooling of the liquid (23). The "Absolute Zero." It has been said that from the modern point of view the violence of molecular or atomic vibration corresponds to the temperature of a body. Now if we imagine a body to be cooled indefinitely it is clear that sooner or later we should reach a point at which all vibration would have ceased, that is, when the molecules and atoms of a body would simply be packed together in an absolutely inert mass. Such a point would correspond to a temperature below which it would be impossible to go, because it is obviously impossible to have less vibration than no vibration. There are ways (see Section 18) of calculating in terms of degrees Fahrenheit this lowest conceivable tempera- ture although it cannot be completely attained in practice. It is approximately 459 below zero. This temperature is called "the absolute zero" and corresponds to the ab- sence of all heat. "Heat" and "cold" are consequently not symmetrical terms. "Heat" is molecular motion. "Cold" is the absence of molecular motion, that is, the absence of heat. It is therefore wrong to speak of "adding cold" to a body. We should say, "taking heat away." The value of ice in a refrigerator consists in the fact that it absorbs large quantities of heat from the objects put near it and not that it "gives out cold." The Heat Energy in Bodies. From the above con- siderations it follows that all bodies at room-temperature possess enormous quantities of heat and what we call a "hot body" is distinguished from a "cold body" by the fact that the first has a higher temperature than the hu- man body, and that the second has a lower temperature (24). [20] Chap. IV] HEAT ENERGY It may be worth stating that the amount of heat in a glass of water at ordinary temperatures corresponds to an amount of energy which, if utilized mechanically, would be sufficient to raise this water to a distance of thirty miles or more above the ground. Practically the same would be true of a piece of ice, since its total heat is only a little less than that of the water. It may also be worth mentioning that in the last few years temperatures have been reached in the laboratory which are only two or three degrees above the absolute zero. At such low temperatures some of the properties of matter, as we shall see later (Part II, Section 54), undergo remarkable modifications. CHAPTER V THE ELECTRON AND ITS BEHAVIOR We are now ready to consider the second fundamental entity, namely the electron. To quote from the first chapter, " according to the modern theory, all bodies are complex structures composed of small particles called atoms and still smaller particles known as electrons." So far as we know, all electrons are exactly alike. In this respect, therefore, they differ greatly from atoms, which, it will be remembered, exist in about a hundred different varieties. Size. In size the electron is very much smaller than the atom. The exact size is not known but it has a di- ameter of about one one-hundred-thousandth that of an atom. This means that if the average atom be repre- sented by a sphere one hundred yards in diameter, the electron, on the same scale, would be about the size of a pin-head. In other words, a large office building is not [21] THE NATURE OF THE ELECTRON [Chap. V large enough to represent an atom if a pin-head is to represent an electron. Weight. The electron is much lighter than any known atom although hi proportion to its size it is much heavier. Although the atom is enormously larger than the electron, the lightest atom, namely that of hydro- gen, is only about two thousand times as heavy as an electron. 1 A short calculation shows, therefore, that the " density" of the electron is a million million times that of the atom. The minuteness of the electron may seem almost in- credible, but careful research leads almost inevitably to the conclusions stated, and the scientist must report what he finds. Shape and Structure. Practically nothing is known as to the shape or structure of the electron. There are indications, however, that it is spherical in shape and symmetrical hi every way (25). The Two Electricities. It will be remembered by those whose physics is not too distantly lost in the past that there are two "kinds" of electricity, " positive" and "negative." If a body is charged with electricity of one kind it repels all bodies having a similar charge and attracts all those having an opposite charge. In the familiar terms: "like charges repel each other; unlike charges attract each other." The attraction of unlike charges is the common phenomenon noticed when in cold weather a recently used comb is held near bits of paper. At present it seems not improbable that most of the phenomena in nature are due, in the last analysis, to electric attractions and repulsions (26). 1 Strictly speaking it is the " mass" and not the weight that we refer to, but the term " weight" is in common use and of proper implication. [22] Chap. V] NEGATIVE AND POSITIVE ELECTRICITY Both Kinds of Electricity Abundant in all Bodies. All bodies seem to possess enormous quantities of both positive and negative electricity, but usually it is in exactly equal amounts, so that one kind neutralizes completely the effect of the other and no electricity seems to be present. Charging a body with electricity is then to be considered as merely disturbing this balance by taking away or add- ing to the body a small amount of one kind of electricity. We shall see later that the electricity added or taken away appears hi the light of modern theory always to be the negative. Electrons Negatively Charged. Each electron has a negative charge of electricity and this charge, consider- ing the size of the particle, is very great. Electrons are therefore, attracted towards all positive charges of elec- tricity and at the same time repel each other strongly. Modern research has made it probable that not only do electrons always possess a negative charge but negative electricity exists only in the form of electrons. That is, negative electricity and electrons are inseparable and the only way to give a body a negative charge is to put electrons on it or hi it. Atoms and Electricity. Since all bodies are made up of atoms, charging a body with electricity is the same as charging some of its atoms with electricity. Speaking now of " atoms" instead of " bodies," it follows from the above that no atom can be charged with negative electricity without putting one or more electrons on it. Each ordinary atom contains a number of electrons and enough positive electricity to exactly balance the negative electricity of the electrons. At present it appears that the positive electricity never leaves the atom, whereas elec- trons allow themselves to be taken away from or added to the atom with relative ease. [23] NATURE OF THE ELECTRON [Chap. V Negative Charge "Too Many" Electrons; Positive Charge " Too Few." - Since it is probable that only negative electricity in the form of electrons is movable, an atom can be charged positively only by taking away some of the electrons which it normally possesses. This allows the positive charge of the atom (which it has perpetually) to predominate and produces the same effect as if posi- tive electricity had been added to it. Thus briefly, an atom contains normally a certain number of electrons and also positive electricity enough to neutralize exactly their negative charges. The atom is then "uncharged." If an electron is added to the atom from the outside there will be more negative electricity than positive and the atom will have a " negative charge" (27). The Electric Current. The attraction which an atom has for an electron varies greatly with the different species of atoms. The atoms of the so-called metals exert only a relatively weak attraction on electrons, whereas the attraction of the "non metals" appears to be greater. In a metal, therefore, it will be relatively easy to move electrons from place to place. When a stream of electrons is caused to move through the body of such a substance we have an electric current. From the modern point of view, therefore, an electric cur- rent in a wire is a stream of electrons moving through the relatively large spaces between the atoms or through the atoms themselves (28). The electrons forming the electric current move very slowly, perhaps only several inches a minute, but they move in enormous numbers. This speed must not be confused with the so-called " speed of electricity *' The far greater " speed of electricity" is due to the fact that the impulse is passed on very rapidly from electron to electron, so that when the electrons at the near end of [24] Chap. V] THE ELECTRIC CURRENT a hundred mile wire are set moving those at the distant end are caused to take up the motion a very small frac- tion of a second later. Briefly, the actual speed of the electrons is very slow, but the rate of transmission of motion from electron to electron is very great. The action is closely similar to what follows when one end of a long rope is pulled. The impulse which results in the movement of the other end travels with much greater speed than the rope itself commonly attains. In the electrical case, the impulse to move travels with the speed of light, i.e., one hundred and eighty-six thou- sand miles a second, whereas the electrons themselves (i.e., the true electricity) move only a small fraction of an inch a minute. The Action of a Battery or Dynamo. Since it appears probable that electricity in its movable state always con- sists of one or more electrons, it is clear that no machine or device of any kind can produce electricity (29). What it does is to drive electricity. Hence a battery might be called "an electricity pump" or perhaps even "an elec- tron pump." Because of the chemical action taking place within the battery it is enabled to force electrons out through its negative terminal, and these electrons flow through the wires of the outside circuit and re-enter the battery again through the positive terminal. We pay a lighting company, therefore, not for "elec- tricity" but for electrical energy. Nor is electricity "used up" when the current passes through the fila- ment of an incandescent lamp. Precisely as many elec- trons leave the filament as enter it, but the stream as it passes through tends to set the atoms hi more violent vibration, and so heats or maintains the temperature of the filament. The electric transmission of power is thus closely [25] NATURE OF THE ELECTRON [Chap. V analogous to the transmission of power by compressed air. We must stipulate, to improve the analogy, that the compressed air when "used" at the far end of the pipe- line be not set free, but returned by another pipe to the air compressor. Under these conditions, if the action goes on for a long enough time, the same air will go several times around the circuit. Ah* is not consumed, nor is it manufactured. It is simply compressed, that is, pumped around the circuit. The " consumer" who pays for compressed air under these circumstances gets value because the air comes to him at a high pressure and he sends it back at a low pressure. He has consumed energy and not air. The difference in ah* pressure in the pipes corresponds to the " voltage" of an electric transmission line (30). " Free Electrons" It has been said that the atoms of different elements seem to have different attractions for electrons. Recent experiments have made it probable that the so-called "positive" elements, including the metals, have a relatively weak attraction and the negative elements, such as sulphur, a powerful one. Many elec- trical phenomena probably owe their existence to this fact. It is doubtless owing to this difference, for example, that metals conduct electricity so readily, whereas sub- stances like sulphur do not. We must suppose that the atoms of a metal have such a weak attraction for electrons that a vast number of the latter are in a practically free state throughout the body of the metal and are thus capable of being moved readily by any outside electric forces. This ease of movement makes the substance a good conductor. Atoms of such elements as sulphur, on the other hand, possess such great attraction for elec- trons that most of them are held tight in the atoms and [26] Chap. VI] FREE ELECTRONS cannot be moved easily from one place to another within the substance. This makes the material a "poor con- ductor," or, as we say, a "good insulator." There is good reason for believing that the electrons within a conductor act as regards heat motion as if they were small atoms, that is, they take part with the atoms or molecules hi the random vibration which appears to con- stitute the heat of a body. The "Evaporation" of Electrons. If electrons exist in large numbers within the substance of a metal it might be expected that if a metal were heated hot enough some of these would be given off into the surrounding space, after the manner in which a liquid loses molecules by evaporation. In fact this is found by experiment to be the case. The emission of electrons appears to be in every way analogous to the evaporation of a liquid (31). CHAPTER VI ELECTRONS, CHEMICAL ACTION, AND LIGHT Electrons and Chemical Action. It seems probable that the forces involved in chemical affinity are electrical in character, that is, the atoms which form the groups known as molecules are held together by electric attrac- tion. Thus a molecule of hydrochloric acid is composed of one atom of hydrogen and one atom of chlorine, and the two cling together, probably because the chlorine atom has a negative charge, while the hydrogen atom has a positive one, and "unlike charges attract each other." When hydrogen gas and chlorine gas are put together in a vessel, heat and even light will cause them to combine suddenly and to form hydrochloric acid. That is, each atom of one kind becomes attached to one of the other [27] ELECTRONS AND LIGHT [Chap. VI Fig. 10 kind, forming a molecule of the new "compound," hydrochloric acid. We are on rather treacherous ground at this point, but we shall probably be not far wrong if we picture the mechanism of the process of union somewhat as follows. The light or heat detaches from some of the atoms a few electrons and these bound about at random between the molecules of the two sepa- rate gases. A very important fact then makes itself felt. As was said in the last chap- ter, different kinds of atoms have very different attrac- tions for electrons, and, hi the present case, the attrac- tion of the chlorine atoms is vastly greater than that of the hydrogen. Thus it will happen before long, since a few new electrons are being detached constantly, that every chlorine atom has one electron too many while every hydrogen atom has one electron too few. This means, of course, that each of the former attains a negative charge, and each of the latter a positive one. The remainder of the process consists in the attraction, and permanent combination in twos, of these atoms of unlike charge to form the groups which we call hydrochloric acid mole- cules (32), (33), (34). This theory of chemical action is not certain as yet but is worth mentioning. It is to be noticed that some kind of disturbance, in the above case heat or light, is necessary to keep up the [28] THE CONSTITUTION OF A SIMPLE MOLECULE The molecule which is symbolically represented above is one of hydro- chloric (muriatic) acid. As shown, it is made up of one atom of hydro- gen, //, combined with one atom of chlorine, CL The former bears a positive electrical charge, and the latter an equal negative charge. It is the attraction between these op- posite charges which is supposed to hold the molecule together. When the charged atoms are separated, as in "electrolytic dissociation" (see text), they form hydrogen and chlo- rine "ions." Chap. VI] ELECTRONS AND CHEMICAL ACTION supply of "free electrons." We see, therefore, that were there no heat or light, or were the intensity of these below a certain limit, depending on the nature of the substances, we could get no chemical action (35). This inertness would probably be a property of all sub- stances in the dark at the so-called absolute zero of temperature (36). Atoms, Electrons and Light. There is good reason for believing that light-waves are electrical hi character. There seems to be no fundamental difference between light-waves and the electric waves used in wireless teleg- raphy, except that the latter are very much "longer" and the vibration is very much slower than in the former case. Light-waves and "wireless" waves are thus re- lated in the same way that a high-pitched sound is related to one of low pitch. "Wireless" waves (i.e., "Hertz" waves) are always produced by causing a charge of electricity to oscillate to and fro. According to the prevailing view, waves are thus set up hi the "ether of space " in a manner somewhat similar to the way sound-waves are set up by a vibrating bell (37). Since an oscillating charge is thus the cause of these waves it seems reasonable to ask what electric charge is responsible for the closely similar but vastly more rapid waves of light. This question has been asked, and an- swered by studying the effect of a powerful magnet on various sources of the vibrating charges within the glow- ing body which must be held responsible for the light- waves emitted. Results obtained by a distinguished Dutch scientist lead to the conclusion that the charge is that of the electron. Here again, therefore, we are thrown back on the same fundamental entity (38). The "radiant heat" from the sun is also of this electric- [29] ELECTRONS AND LIGHT [Chap. VI wave type of vibration so that the sun must be considered a light and heat radiator because of the vast number of vibrating electrons which it contains. To sum up: according to the modern wave theory, whenever an electric charge, whether this charge be that of one electron or many, vibrates back and forth, it radiates electrical waves which go out in all directions in space (39). If the oscil- lation is very slow they are called Hertzian waves, or "wireless" waves. If the oscillation is more rapid they are in general termed " heat-waves," and if the vibration is still more rapid the waves are capable of affecting the retina of the eye, and are called " light-waves " (40). All of these waves can be absorbed, refracted and reflected. They all transmit energy and hence are capable of heating any body which absorbs them. The Absorption of Electric Waves. The mechanism of the absorption of electric undulations is to be thought of as follows. As a sound-wave which is emitted from a vibrating body tends to set any body which it strikes into a similar vibration, so an electric wave which is emitted by an oscillating electric charge tends to set vibrating the electric charges within the body which it strikes. If these charges are so conditioned that they are capable of responding easily to the particular rapidity of vibration which thus strikes them, they will be set into violent vibration at the expense of the energy of the entering wave. This vibration ultimately becomes the random motion of heat. Since absorption is apparently due to motion of the electrons which a body contains, it follows that opaque- ness in bodies must be ascribed to this electron mobility. It is probable that if the electric charges within a body could be held fixed, the latter would be transparent to any electric wave. [30] Chap. VI] PROPERTIES OF ELECTRIC WAVES The Reflection of Electric Wanes. When the electrons within a body are set into vibration by an impinging light-wave they will, of course, act as radiators of new light-waves, and if the body has a flat surface those emitted from the electrons near the surface will join to form a definite single wave which travels back in an opposite direction to that of the entering one. This constitutes the reflected wave, which exists in general whenever light strikes a flat surface. The reflected wave may be almost as strong as that entering or it may be very weak, but except hi ideal cases it always exists. Whether the surface is flat or not there will always be reflection, but if the surface has a certain degree of flat- ness the reflection will not be "diffuse" like that from a white-washed wall, but will be regular, like that from a mirror (41). The Speed of Electric Waves in Different Bodies. It is a generally accepted fact that all electric waves whether they correspond to light, heat or Hertzian waves, travel with the same speed in empty space, but with different speeds in material bodies. The explanation of this is that all material bodies contain electrical charges and that the wave which passes through the body is a complex resultant of the original entering wave and the secondary waves which are set up when the charges oscillate in response to the entering wave. This complex resulting wave, although it has the same vibration frequency as the original one, is altogether differently conditioned and it can be shown mathematically that it will not travel with the same speed (42). [31] CHAPTER VH ELECTRONS AND MAGNETISM The Connection of Electricity with Magnetism. It is a well-known fact that magnetism always exists in the region surrounding a wire carrying an electric current. Since the trend of modern theory is towards the conclu- sion that an electric current always consists in the bodily movement of electrons or atoms, we must suppose mag- netism to accompany invariably the motion of electric charges, and indeed this has been found to be true (43). Any magnetic effect can best be magnified by winding the wire which is to carry the electric current around a piece of iron in the same general way that thread is wound upon a spool. The wire must, of course, be in- sulated so that the various turns do not touch each other. Such an iron spool may become a strong magnet when a current of electricity is sent through the wire surround- ing it. This is the principle at the basis of the action of the ordinary electric motor. The electric car is kept moving because the current which enters through the trolley wire, and leaves through the track, passes through a wire wound on a similar spool, and the spool (then a magnet) through its attraction sets rotating other pieces of iron which are attached to the wheels of the car. Deflection of Electrons Caused by Magnetism. It can be shown that if an electric charge is caused to move rapidly past the end of a magnet, the charge tends to be de- flected sidewise. This lateral deflection of electrons in a so-called " magnetic field" corresponds to one of the fundamental relations between electricity and magnetism, [32] Chap. VII] ELECTRONS AND MAGNETISM and by its means we have an important method of " gen- erating" an electric current, i.e., of moving electrons. Suppose for instance that a piece of wire is moved rapidly through a magnetic field, that is, near a magnet. The piece of wire in common with all conductors contains countless easily moved electrons, and when the wire is moved through the field the deflecting force mentioned above causes them to be pushed towards one end of the wire, If the latter is held in the proper position (44). The Action of a Dynamo. The ordinary dynamo or electric generator, as it is often called, is a machine for moving wires rapidly through a magnetic field, and for collecting the electric current which is set up by the de- flecting forces above mentioned. Such a machine has, of course, to be run by some outside source of power such as a steam-engine, or a water-wheel. Permanent Magnetism. The familiar type of magnet which is not maintained by means of an electric current, the small red-painted horse-shoe magnet of the toy-shops, for example, is called technically a " permanent magnet." It is probable that the ultimate cause of magnetism in this case is quite similar to that in the case of the spool before mentioned. In the latter, electrons circulate in a helix around the outside of a large piece of metal, and in the former, although there is no circulation of electrons around any visible path, helical or circular, still such paths probably exist within the molecules of the iron which forms the permanent magnet. According to the present belief, the electrons within a piece of magnetized iron do not move in a wholly random fashion, but have what we might call a " helical prejudice," and perhaps even re- volve in circles within the molecules themselves. It is now generally believed that the cause of magnetism is always the motion of electrical charges (45). [33] RADIO-ACTIVITY [Chap. VHI The Effect of Magnetism on Light. Since the source of the light which an incandescent body emits lies in the vibratory motions of electrons within the body, and since magnetism has a tendency to deflect moving electrons, we should not be surprised to find that certain sources of light when put near a powerful magnet have their emitted light modified in a complicated way. This has been found to be the case, and the results tend to verify the views herein set forth (38). CHAPTER VHI RADIO-ACTIVITY There is a remarkable group of substances which emit rays continuously, without obtaining energy from their surroundings. Radium is, perhaps, the most striking member of this group and it is now known with consider- able surety that in its case the rays would only fall off to about half then* present intensity in two thousand years. This extraordinary action goes under the general name of " radio-activity" and the substances which emit the rays are known as "radio-active substances" (46). The Three Rays. The rays emitted are not all of the same kind, but are composed of three distinct types, each with definite characteristics of its own. It was thought convenient in the beginning to designate these rays by the first three of the Greek letters, and they are therefore known as the alpha rays, the beta rays, and the gamma rays. The Beta Rays. There is now no reasonable doubt that the beta rays consist of a stream of electrons com- ing out of the substance like bullets from a machine gun. The most surprising thing about these rays is the enor- [34] Chap. VHi: RADIUM RAYS mous velocity of the electrons. Their speed is almost equal to that of light, or about one hundred and eighty- six thousand miles a second. This inconceivable velocity is measured indirectly, but by methods which make it almost certain that the result is correct. This speed enables part of the rays to penetrate a plate of metal as thick as an ordinary book cover (47). The Alpha Rays. Within the last few years it has become practically certain that these rays consist of a stream of atoms of the element helium. This surprising fact could certainly not have been predicted when first the rays were discovered. The helium atoms have each a double positive charge ; each atom, that is, has lost two electrons. The atoms of the stream have a velocity of about one-tenth that of light, or about eighteen thou- sand miles per second. This is less than the speed of the beta rays, but it must be remembered that the atom of helium, whose " atomic weight" is four, is about eight thousand times as heavy as an electron, and thus, al- though the helium atoms of the alpha rays are moving more slowly, their energy is much greater than that of the beta ray particles, the electrons (48). This energy is in fact so great that a single "alpha particle," that is, a single atom of helium, when it strikes certain substances, will cause them to phosphoresce (or more properly fluoresce) for an instant over a region large enough to be seen with a lens. This makes visible the effect due to a single atom and gives us the first case in the history of science where any effect caused by one atom has been observed. The Gamma Rays. There has been some dispute as to the ultimate nature of the gamma rays, but it is now practically certain that they do not consist of particles in the ordinary sense, but of impulses similar to those con- [36] RADIO-ACTIVITY [Chap. VHI 1 MB9-fiUNU*J sa (22d) 79j*~ i Mj0-ftww*f2 A o 6.9 Ao<"* kd) V 1 #A0/o-7#ofr/ .}. sla L 3| H K o i PQ B a d g s g w w is 3 S|S "3 3|S CO 3 |>; a 10 "P. ^ 23 Vanadium 51 eo g 10 co w c- 41 Columbium 94 o d g | lie | a i' 8 f2 *}3 H N 1 | 1 - **:? ^J S| S^3 !? w'CS WW 3 & JH fi | | a Q"p w w u 3 "fa Mi sf<5 s CO | g Pa, w w |- o 3 s|s IS ls - 1 CO o 5 s 3 a 3 g o 4J 00 H ^^^ s ^ M o 55*" W * 3 M -h ^ PQ ^5 w [72] Sec. 6] THE PERIODIC TABLE 3 10 &2SS 8 s|J w *" o ! i el 85 Unknown 52 Tellurium 127.6 J 84 Polonium 210 92 Uranium 238.5 J 73 Tantalum 181 83 Bismuth 208 ajg 5 . Sjj ! |1 ! 'I' Ji | 48 Cadmium 112.4 m ^ S 2 a> 88 Radium 226.5 Li | o i 5|8 g| P!S si a ft g. M^ K 9 - n - [73] THE PERIODIC TABLE [Sec. 6 a definite and well-grounded conception of the structure of the hydrogen atom (Cf. Section 53), in accordance with which the latter is composed of a single minute particle of negative electricity an electron and a very much smaller particle of positive electricity about which the electron revolves. Practically the entire mass of the atom is concentrated in the positive "nucleus," as it is called. The more ponderous atoms are supposed to be formed from a larger number of positive and negative particles, according to their respective weights. The positive particles are always condensed into very small nuclei, together with a portion of the electrons, and it is probable that, hi the case of the heavier elements at least, the helium atom is an important secondary unit in the structure of these nuclei. Within the past few years the study of radio-active sub- stances has brought out facts which indicate that the fundamental principle of the periodic table that the chemical properties of an element are determined by its atomic weight is only approximately true. As already mentioned (Section 5, above), radio-active elements isotopes are known which differ in atomic weight but have identical chemical properties. On the other hand, there are elements of the same atomic weight which show radical differences chemically. The explanation of this very important discovery apparently lies in the sugges- tion that the chemical nature of an atom depends not directly upon its weight but upon its electrical structure, which to a limited extent may change practically inde- pendently of the weight. Of this more will be said in the appropriate context. (See Section 53.) Chemical Elements as Atomic Mixtures. The exist- ence of " isotopes" among the radio-elements suggests their presence in other parts of the periodic table. In [74] Sec. 6] ISOTOPES the latter case there appears a possible solution of the difficulty that the majority of the atomic weights are not accurate multiples of that of hydrogen. It is conceivable, even probable, that the chemical elements which we have previously regarded as individual species of matter are in reality only types, or classes, of such individuals, all of the members of a single class being indistinguish- able and non-separable from each other by purely chemi- cal means. In this case the atomic weights given in Table I (Section 5) must represent averages of the rela- tive weights of a number of chemically similar atoms with different masses, which may be present in standard chemical preparations in nearly constant but in unequal amounts. If this is true it is not surprising that our em- pirically determined atomic weights do not have integral values. The above speculations receive support from certain experiments by J. J. Thomson, not depending in any way upon radio-active phenomena, which suggested that the inert atmospheric gas, neon, is really made up of two isotopic constituents, one of atomic weight about 20 and the other (meta-neon) about 22. F. W. Aston, following out this clue, found that by the use of physical methods relying on the relative rates of diffusion of the two components, pure atmospheric neon could actually be separated into two gases of different density. Careful comparisons of samples of lead derived from geologically different sources indicate that this element, also, may be a mixture of isotopes, an idea which is strongly sug- gested by its relation with the radio-active substances. All of these results should be accepted with reserva- tions on account of their novelty, but it must be admitted that they open a vista of new insights into the meaning of the periodic table. [76] MOLECULAR STRUCTURE [Sec. 7 REFERENCES For a detailed discussion of the periodic table see Harry C. Jones, "The Elements of Physical Chemistry" (1902), pp. 18-37. A more popular exposition can be found in R. K. Duncan's "The New Knowledge " (1905), Part H. See also W. Nernst's: "Theoretical Chemistry," Eng. trans. from 6th German ed. (1911), pp. 178-190. On "isotopes," see Frederick Soddy's "The Chemistry of the Radio-Elements" (1915), Part I, pp. 50-56; Part II, complete. Also an article by E. Rutherford: "The Constitution of Matter," Popular Science Monthly, August, 1915. Section 7 THE ARRANGEMENT OF THE ATOMS IN THE MOLECULE Atoms may group themselves to form molecules of almost any conceivable shape. The properties of the substance which such molecules compose seem to depend in large part upon the manner in which the atoms are combined) that is, not only upon the number and nature of the atoms but upon their geometrical arrangement within the molecule. To show what a great variety of substances can be formed by different modes of combination of the same elements it may be stated that about two hundred thou- sand distinct compounds of the element carbon are now known, most of which are with only three other elements : hydrogen, oxygen, and nitrogen. These substances be- long to the class of "organic" compounds, so called for the reason that many of them are essential in the chemical structures and changes of living organisms. There are undoubtedly thousands, if not millions, of specific chemical substances in living bodies which are [76] Sec. 7] STRUCTURAL FORMULAE built up from the same four elements but which have not yet been separated out and analyzed. The element carbon is remarkable on account of the very large number of compounds which it can form, but the other elements also enter into the composition of a great variety of different substances. Each of these substances, organic or inorganic, possesses characteris- tic properties which distinguish it more or less sharply from all other substances. homers and Structural Formulae. That the differ- ences which exist in the properties of substances must depend at least in part upon the arrangement of the atoms within the molecule is proved by the fact that compounds exist which have quite different properties but exactly similar numbers and kinds of constituent atoms. Such cases are quite common in organic chemistry, and the substances involved are known as "isomers." Thus the organic chemist is acquainted with twenty-six different compounds which contain four atoms of carbon, six of hydrogen and three of oxygen, and with one hundred and fifty-seven which are composed of ten atoms of carbon and sixteen of hydrogen. It is customary for the chemist to represent the make- up of a compound by means of a so-called "chemical for- mula" which shows in a simple way the constitution of the molecules of the substance. The formula of water, H 2 O, may be taken as a simple example. This formula states that a molecule of water is made up of two atoms of hydro- gen, H, combined with one atom of oxygen, O. As an example of a more complex formula we may consider that of alcohol, C 2 H 6 O, or that of the coal-tar oil, benzene, C 6 H 6 , in both of which C stands for the element, or the atoms of carbon. There is only one substance which has the formula [77] MOLECULAR STRUCTURE [Sec. 7 H 2 O, so that no confusion can arise as to the meaning of this formula. It always stands for water. However, at least two substances are known which have the formula C2H 6 O, namely ordinary alcohol, and a gas called * 'methyl ether," which is closely similar to the ether employed in surgical operations. It is obvious that if we desired we could write the formula of water as H-O-H, in order to show the probable manner in which the atoms are combined in the molecule, but although this is not required in the case of water it is found necessary hi the case of alcohol, and other substances which have isomers. Such a formula is called "structural" or "graphical" because it is a simple drawing representing the supposed arrangement of the atoms in the molecule of a substance. These formulae can be constructed by studying the chemi- cal relationships which exist between different com- pounds, and when thus evolved they not only enable us to distinguish theoretically between isomers, but also explain the differences which are found hi their properties. However, as we shall see, their utility is not limited to the study of isomerism, for it is obvious that the more exact is our knowledge of the structure of different mole- cules the clearer will be our ideas concerning the changes which are liable to occur in these molecules. A study of the manner hi which alcohol can be built up from its elements leads us to assign to it the structural HH I I formula: H-C-C-O-H. The substance "methyl ether," I i HH on the other hand, which we have mentioned as an isomer H H I | of alcohol, proves to have the formula: H-C-O-C-H. [ 78 ] H H Sec. 7] ISOMERIC COMPOUNDS H H H H H H Normal Hexane H C C C C C C H H H H C C H H | I H Methyldiethyl Methane H C C H H H I H C C H I I H H H H C H H H H Dimethylpropyl Methane H C C C C H H C H H H H H H H H C H H C H I | Dimethylisopropyl Methane H C- C H H C H H C H H H C H H H Trimethylethyl Methane H C C - C H H H C H H C H TT Fig. 12 FIVE ISOMERIC HYDROCARBONS HAVING THE CONSTITUTION C 6 H 14 These chemical formulas represent the supposed structure of the mole- cules of five distinct substances all of which contain the same number of hydrogen and of carbon atoms. [79] MOLECULAR STRUCTURE [Sec. 7 It is easy to see why the decomposition of the two mole- cules thus represented should lead to different results in spite of the fact that identically the same atoms are present in each case. We believe that these formulae give a partial representation of the actual arrangement of the atoms in the molecules of alcohol and methyl ether respectively. Figure 12 gives the graphical formulae of five isomeric hydrocarbons each made up of six atoms of carbon, and fourteen of hydrogen. Although the formulae show certain general resemblances, the five structures are nevertheless quite distinct. The resemblances corre- spond with an actual physical similarity of the sub- stances, which causes them to be grouped in the same general class, but within this class the substances show a perfectly clear chemical individuality. Many other examples of this principle that the nature of a chemical substance depends upon the exact geometric structure of its molecules could easily be found. The "Benzene Ring" - The approximate truth of the representations of the structure of molecules which are given by the structural formulae now in use among chem- ists, is attested by such cases as that of the formula of benzene, the coal-tar oil of which we have spoken above. The six carbon atoms are supposed to be arranged in a molecule of this substance in the form of a ring, and to each of them is attached one of the hydrogen atoms. This formula is shown in Figure 13, (a). Each of the hydrogen atoms in the molecule can be replaced by atoms of other elements, as for example chlorine atoms, and for every new and different molecule thus produced there should exist a correspondingly distinct substance, which [80] Sec. 7] BENZENE DERIVATIVES H H C C H H C C Cl H-C C-H H-C C-H V V C. H C t X \ / \ / \ Cl C C H Cl C C Cl Cl C C H H C C H H C C H H C C Cl V V V i Jl H t t t X \ / \ / \ Cl C C Cl Cl C C Cl Cl C C Cl H C C Cl H C C H H C C H V V V i Fig. 13 a See Fig. 13 b [81] MOLECULAR STRUCTURE [Sec. 7 Cl I: / \ / V / \ H C C Cl H C C H H C C Cl H C C Cl Cl C C Cl Cl C C H V V d, t C, t / \ / \ H C C Cl Cl C C Cl II I II I Cl C C Cl Cl C C Cl \ X V X C C A Fig. 13 b BENZENE AND ITS CHLORINE DERIVATIVES The significance of these formulae is explained in the text. would be known to the chemist as a "chlorine derivative of benzene." Now a moment's study will show that by a simple exami- nation of the ring formula we can predict the number of such derivatives which we shall be able to form, provided the formula is correct. If only one hydrogen atom is replaced there is only one possible compound, (b) Figure 13, since the ring is perfectly symmetrical and hence the structure which is formed is the same no matter which hydrogen atom is disturbed. However, if two, three, or [82] Sec. 7] MOLECULES OF ELEMENTS four hydrogen atoms are replaced there will be three dif- ferent molecular structures corresponding to each of these numbers. This fact is shown in Figure 13 (c) to (k) inclusive. No more than three can be formed, however, in each case. If five or six chlorine atoms are introduced only one compound can be produced corresponding to each number, (1) and (m), respectively, in the Figure. We are thus able to prophesy the possibility of twelve chlorine derivatives of benzene and of no more than twelve. The actual study of this substance in the labo- ratory has revealed the existence of all of these deriva- tives and has proven the impossibility of producing any others. This is a striking verification of the idea that the benzene molecule actually has a ring structure. We have studied this matter of the structure of the molecule in connection with benzene because the formula of this substance is distinctive and is one of the most successful in its applications. However, there are other instances of the same thing which are almost equally striking. Indeed the science of organic chemistry would be practically impossible without the help which is pro- vided by a knowledge of the actual structure of the mole- cules composing the substances with which it deals. The exact structure of the molecule is of less importance hi inorganic chemistry because here the molecules are so much simpler. Molecules of Single Elements. In this connection it may be well to note the fact that the atoms of the elements in the pure state generally unite to form molecules, which are thus made up of two or more atoms of the same kind. Thus hydrogen gas is not composed of free atoms but of hydrogen molecules, each of which contains two atoms of the element. Many simple elements in gaseous form have two atoms hi then* molecules. The vapor of the [83] MOLECULAR STRUCTURE [Sec. 7 metal mercury is distinguished from most elementary gases by the fact that its atoms are uncombined. Some elements, on the other hand, form molecules containing as many as seven similar atoms, and the same element may yield molecules of different sizes under different condi- // Fig. 14 MODELS OF TARTARIC ACID MOLECULES To gain a correct impression from this drawing one should imagine the H and OH circles on the inner portion of each model to be spheres pro- jecting outward from the page, so that the models have a three-dimen- sional form. The letters attached to each black circle stand for the groups of atoms which the circle represents, and the lines connecting the circles indicate the structure of the molecules. It will be observed that these two molecules, which are of "right "and " lef t " tartaric acid respectively, are so constructed that one is the mirror-image of the other. This rela- tionship of structure is offered as an explanation of the similar relationship which exists between the structure of the crystals shown in Figure 15. tions. The various forms of pure sulphur and of phos- phorus the yellow and the red probably correspond to molecules containing different numbers of atoms of these elements. It is possible that the three familiar [84] Sec. 7] MOLECULES AND CRYSTALS forms of the element carbon: charcoal, graphite, and diamond, may be due to the same causes. Molecular and Crystal Structure. The structure of the molecule which is characteristic of a substance is proba- bly closely related with the shape of the crystals which it produces. 1 Nearly all pure substances will take on a characteristic crystalline shape under the right condi- tions. There are certain pairs of sugars compounds of CRYSTALS OF Fig. 15 1 RIGHT" AND "LEFT 1 TARTARIC ACIDS It will be observed that the two crystals represented above are identical inform except for the fact that one is the mirror-image of the other; what is on the right-hand side of one is on the left-hand side of the other. The two crystalline forms represent two different kinds of tartaric acid, but ordinary chemical analysis reveals no difference in their composition. It is supposed that the actual basis of the distinction lies in the fact that the molecules of the two acids differ in the same general way in which the crystals differ. These molecules are symbolized in Figure 14. carbon, hydrogen, and oxygen the molecules of which as represented in their structural formulae, are distin- guished from each other only by the fact that one is the mirror-image of the other. This difference is made clear in the accompanying Figure 14. Now it turns out that when these sugars crystallize, although the crystals do not have the same form as the molecules, they do differ 1 Present-day studies of crystal constitution (see Section 22) show that the atom and not primarily the molecule is the unit of structure. [85] PHYSICAL PROPERTIES [Sec. 8 in the same way in which the molecules differ, i.e., one is the mirror-image of the other. This fact, which is shown by a comparison of Figures 14 and 15, seems to prove quite conclusively that the shape of the crystal depends directly upon that of the molecule. In this connection it is interesting to note that whereas one of these sugars either in the crystalline form or in solution turns polarized light to the left, the other turns it to the right, and in exactly the same proportion. This fact speaks for the truth of the formulae which have been assigned to the compounds. Further considerations with regard to crystal structure will be found in Section 22. REFERENCES An excellent, detailed and not very difficult discussion of "The Constitution of the Molecule," will be found in W. Nernst's " Theoretical Chemistry," English translation from 6th German edition (1911), Book H, Chapter 4, pp. 278-300. Simpler considerations appear in F. J. Moore's " Outline of Organic Chemistry" (1910). Chapter VIII, pp. 147-161, deals with the phenomena of crystal form above mentioned. Section 8 THE PHYSICAL PROPERTIES OF COMPOUND SUBSTANCES Importance of the Internal Molecular Forces. We have asserted in Section 7, above, that the properties of compound substances depend principally upon the man- ner in which the atoms are arranged in the molecule. Strictly speaking, however, we must say that the char- acteristic properties of a substance depend upon the strength and arrangement of the forces of attraction which hold the molecule together. We perceive such qualities of bodies as hardness, elasticity, color, odor, etc., only [86] Sec. 8] COLOR because these bodies bring to bear upon our organs of touch, sight, and smell certain characteristic combina- tions of forces. The nature of these forces must always depend at least in part upon the nature of the forces within and between the molecules of which the body is made up. Hard bodies are those in which the forces which exist between the molecules are very strong and hold them closely together, so that the body cannot be distorted by our touch. An elastic body is one in which the same forces act to restore its original shape, once it has been distorted. Among other characteristic properties of com- pound substances which must be determined by the internal and external forces of the molecule may be mentioned their melting and freezing points, their latent heats of vaporization and of fusion, their dielectric con- stants (or the degree to which they alter the intensity of an electrical field in which they are placed), their optical nature, their surface tension and the pressure exerted by their vapor when in the liquid state, their chemical activ- ity, the forms of then* crystals, then* compressibility, viscosity, magnetic power, etc. In the course of the dis- cussion in both Part I and II, the manner in which these properties are determined by molecular and inter-molec- ular forces will gradually be made clear. Color. The colors of substances depend upon the nature of the light which they absorb and reflect. If a body looks red in white light this means that it absorbs a great deal of green and blue light and reflects a rela- tively large amount of red. This power to absorb one light and to reflect another is known to depend directly upon the strength of the forces which hold the electrons in the molecule, as is explained in Section 41, below. The nature of the elements of which compounds are made up is undoubtedly of the utmost importance in [87] PHYSICAL PROPERTIES [Sec. 8 determining their properties, but it is probable that the elementary atoms are effective primarily through their power to regulate the forces within the compound mole- cules. Thus the blue color of many copper compounds is due to the copper atom common to all. But since this color changes to red or brown when certain well-known changes occur in the forces binding the molecules of such compounds together, we are compelled again to conclude that what may be called the " dynamical (or force) con- stitution of the molecule" is the immediate cause of the physical properties of the corresponding substance. Allotropism. The marked differences which exist between the so-called "allotropic" forms of certain elements (such as carbon; see Section 7) obviously can- not be attributed to differences in the elementary con- stitution of the substances, and hence must be explained in terms of the different arrangement, and degree of ex- haustion, of the same atomic forces. Diamond which is one of the hardest substances known is made up of exactly the same element as charcoal and graphite, which are relatively soft. The Mystery of Chemical Change. Accordingly, re- flection should free us of the mystery which usually attaches to the qualitative modifications of the properties of bodies which occur in chemical changes. Molecules are not merely chance "heaps" of different atoms. They are definite and relatively stable individuals, the natures of which depend, of course, upon the forces latent in the atoms which make them up, but which neverthe- less realize in their own constitution " force patterns" which do not exist elsewhere. Each new atomic com- pound means a new system of such forces, and conse- quently a new substance, possessing an individuality of its own. [88] Sec. 8] CHEMICAL CHANGE Recent developments connected with the study of iso- topism (see Section 6), make it very probable that the principal physical and chemical properties of elementary substances depend directly only upon the number and arrangement of the electrons in the outer shell of an atom. This superficial structure is identical in isotopes, although the inner, nuclear formations differ. Now, there is little doubt that it is the outer or " valency" electrons (Cf. Section 34), which are active, and change their posi- tions, in chemical reactions. Consequently, it is natural, if what has just been said is true, that the properties of compounds should differ radically from those of the ele- ments which go to make them up. Only a relatively small portion of a complex atom is involved in its every- day dealings with the external world. The immediately interesting things about an atom, so to say, are all super- ficial, and are easily modified through intercourse with other atoms. From the point of view of chemistry, it is possible that the atom may be more radically altered in a chemical reaction than in a radio-active transformation, although the latter is fundamental and irrevocable, and the former easily reversible. REFERENCES The details involved in the above discussion will be further con- sidered in subsequent sections in which references will be given to the special topics concerned. For a more detailed general discussion see W. Nernst's "Theo- retical Chemistry" (1911), Book H, Chapter 5, pp. 303-347,. and Norman Campbell's "Modern Electrical Theory," second edition (1913), Chapter XII. A good discussion of color appears in Franklin and MacNutt's "Light and Sound" (1909), Chapter X. See also M. Luckiesh's excellent volume, "Color and its Applications" (1915). [89] CHEMICAL EQUATIONS [Sec. 9 Section 9 CONCERNING CHEMICAL EQUATIONS The chemist is accustomed to represent chemical changes by means of equations, such as the following : H 2 = 2 H + O, which is intended to show how water breaks down into hydrogen and oxygen. The symbols on the left-hand side of the equation represent the substances entering into the reaction, and those on the right-hand side represent its products. The equation above, stands for a chemical change of a purely destructive type. If the direction of the change is reversed, we have: 2 H + O = H 2 O which is a constructive reaction. However, very few chem- ical changes are purely destructive or purely constructive. As a rule, there is simultaneous building up and break- ing down. Thus the actual process which occurs when water is decomposed into hydrogen and oxygen is not so simple as we have represented it in the first equation above, but is more accurately symbolized by the follow- ing relationship: 2 H 2 O = 2H 2 + O 2 This reaction probably goes on in two stages, the first being that indicated in the equation which was originally given, and the second being the combination of the free hydrogen and oxygen atoms thus produced, to form the hydrogen and oxygen molecules, H 2 and O 2 , respectively, which we mentioned in Section 7. However, since the chemist is usually interested in the so-called "end prod- ucts" of a reaction, and since in any case the two lines [90] Sec. 10] FORCES OF COHESION of change are continuous with each other, the reaction is ordinarily written as shown above. Section 10 THE FORCES OF ATTRACTION WITHIN BODIES Everybody is aware of the fact that particles of matter attract each other with a force which is greater the nearer the particles are together. As everyone knows, it is the gravitational attraction between the earth and the bodies upon it which causes the latter to have "weight." Now since all bodies are made up of atoms it follows that the forces of gravity must depend in some way upon attrac- tions which atoms exert u'pon each other, and on account of the fact that the atoms are separated, at least in the case of solids and liquids, by very minute distances we should expect these " inter-atomic" forces to be relatively more powerful than are those of ordinary gravitation. But as far as the atoms are concerned gravitation is only a sample of much more powerful forces, for the former is in all probability a mere residue from the latter. At the present time the nature of the relationship which almost certainly exists between gravitation and the mutual attractions of the atoms is largely a mystery, but strange as it may seem, we are much clearer concerning the connection between atomic and molecular attractions, between "chemical affinity" and the forces of cohesion within bodies. As we have suggested in Section 6, the atoms are probably complex, being made up of ultimate particles which are much smaller than the atoms themselves. On account of the great stability of atoms we must suppose these particles to be held in position by very powerful forces of attraction. These forces, which are probably [91] THE KINETIC THEORY [Sec. 11 electrical, are not perfectly balanced within the atoms and hence tend to be effective in causing them to adhere to each other. Such secondary attraction is probably the basis of what is commonly called "chemical affinity," the force which binds atoms together into molecules. But just as the tendencies of attraction are not wholly exhausted within the atom, so there are residual attrac- tions which remain after the molecule has been formed, and it is these secondary residual forces which underlie the properties of cohesion, elasticity, and rigidity in solids or liquids. Their existence also accounts for cer- tain striking characteristics of gases, as well as of solids and liquids, as we shall see later on in our discussion. It is important that the reader should bear in mind the qualitative identity of these different forces of attrac- tion which operate between the particles of which all bodies are composed, and also the nature of their quanti- tative relationships. REFERENCES On the relation between atomic, chemical and cohesion forces, see Sir Oliver Lodge's book on "Electrons" (1906), Chapter XVI. Also Norman Campbell's " Modern Electrical Theory," second edition (1913), Chapters XII and XIII. Section 11 "THE KINETIC MOLECULAR THEORY" The Nature and Foundations of the Theory. The " proof" of the doctrine that the atoms of all bodies are in constant motion has been given by the so-called " ki- netic molecular theory," hi connection with the results of experiment. This theory may well be described as an application of the laws of mechanics, or " dynamics," to the world of molecules. The fundamental principles [92] Sec. 11] MOLECULES AND PROBABILITY of mechanics are the familiar "laws of motion" of New- ton, and it is a very significant fact that these principles which were first applied successfully to astronomical bodies should apply also to the almost infinitely smaller bodies called molecules. Certain very recent considera- tions tend to limit the applicability of these laws (see Section 54, below), but they certainly apply approxi- mately, and on the average, to a wide variety of molecular happenings. The kinetic theory regards each molecule as an inde- pendent being, endowed with motion and having certain attractions for all other molecules. It then proceeds to investigate the effects which should follow from the presence of a very large number of such molecules in a limited space, making use only of the laws of motion, of geometry, and of arithmetic. Molecular Chances, and Averages. It was shown by Maxwell, who may be considered the founder of the kinetic theory, that most of the laws which govern such a melee of vibrating particles must be "statistical" in character, that is, that they must depend upon the average of a large number of different individual molecular effects. Because of the vast number of molecules which are contained in even a small volume of material sub- stance, these averages are very certain. When a small number of molecules are considered, however, their action proves to be less certain. The modern theory of matter has thus given rise to a branch of inquiry which is often called "statistical mechanics," because it applies the principles of statistical investigation to mechanical problems. These principles are essentially those of "chance" or "probability." We can tell what will happen in the molecular world in about the same way in which we can predict the events [93] MOLECULAR SPEEDS [Sec. 12 which occur in human society, although generally with greater accuracy. It is possible for insurance men to calculate with sufficient accuracy for successful business administration, the number of people who will commit suicide or arson during a given period, or who will be killed in train wrecks or in automobile accidents. With regard to one person nothing definite could in general be foretold, but the greater the number of individuals con- sidered, the more precisely are predictions fulfilled. It is the same in the molecular world, and here the number of individuals involved is vast almost beyond conception, so that statistical prophecies are very reliable. However, what may be called the " individuality of molecular activities" is of great importance in modern physics. The " proof" of the hypothesis of molecular motion to which we have alluded lies in the remarkable corre- spondence which exists between the results of the kinetic theory and the facts of nature as determined by experi- ment, a correspondence which applies both to the statis- tical and to the individual behavior of the molecules. REFERENCES On the kinetic theory, see W. P. Boynton's " Application of the Kinetic Theory to Gases, Vapors, Pure Liquids, and the Theory of Solutions," 1904. Also W. Nernst's "Theoretical Chemistry" (1911), Book H, Chapter n, pp. 197-249. The latter account is perhaps the simpler of the two, and also the more empirical. Section 12 THE SPEEDS OF MOLECULAR MOTION The Molecular Counterpart of " Temperature" The exact temperature of bodies is not directly proportional to the speed at which then* molecules move, but rather depends upon the average energy of molecular motion. [94] Sec. 12] PARTITION OF ENERGY It is a familiar fact that the energy, or " kinetic energy," of a moving body depends not only upon the speed at which it is travelling but also upon its weight or "mass," or if we consider only bodies made up of the same sub- stance upon its size. Other things being equal, the larger a body is the more work must be done to set it in motion or to stop it, once it is moving. It is found by calculation from the laws of motion and by experiment, that the energy of motion, or kinetic energy, of any body is proportional to its mass and to the " square" of its velocity. This measure of energy of motion applies to molecules as well as to visible bodies, and so we must say that if the temperature of a piece of matter is proportional to the average, kinetic energy of its molecules its tempera- ture is proportional to the average square of the speed of these molecules, so that as their speed increases the corresponding temperature increases much more rapidly in proportion. From these considerations, also, it fol- lows that if we have a number of substances at the same temperature the speeds of their respective molecules will on the average, be less the larger (more massive) these molecules are. This must follow because at the same temperature the average energy must be the same re- gardless of the weight of the molecules, and this can only be true if the heavier molecules are moving at lower speeds than are the others. When a large number of atoms or molecules of differ- ent species and weights are mixed together the average energy of each species will be the same as that of any other species. It seems reasonable that this should be the case, for if the average energies were not equal in this way, the different substances making up the mix- ture would be at different temperatures, which is incon- [95] MOLECULAR SPEEDS [Sec. 12 sistent with the well-known fact that all bodies which are in close contact tend to come to the same tempera- ture. As we shall see later (Section 21), even when the vibrating particles are so large as to be visible under the microscope, their average energy of motion is approxi- mately the same as that of the very much smaller molecules. This is one aspect of what is known as the principle of "the equipariition of energy." Actual Molecular Speeds. We have seen in our pre- vious discussion that atoms and molecules differ widely in weight, and since weight and mass are proportional, it follows from what has been said above about the equal- ity of molecular energies of different substances at the same temperature, that the speeds of different molecules and atoms under these conditions will differ a great deal. The average speed of a hydrogen gas molecule at a tem- perature corresponding with the freezing point of water is about one and one-eighth miles a second, that of the mercury vapor molecule at the same temperature is about one-tenth of this, or about six hundred feet a second. The mercury molecule weighs just one hundred times as much as the hydrogen molecule. For the same temperature, molecular speeds vary as the square-roots of the molecular masses. Even the mercury molecule moves at the tremendous speed of four hundred miles an hour. Vast as this may seem, it is as nothing com- pared with the speeds which are attained by molecules and especially by electrons under other conditions which we are to consider at another point hi our discussion (see Section 25, below). The reader should bear in mind the fact that it is the average energy of motion which is constant at a given temperature. The speeds of the individual molecules differ enormously, but the variations in one direction [96] Sec. 13] MEAN FREE PATH balance those in the other so that from the statistical point of view which we have explained in Section 11 there is constancy. REFERENCES For a detailed and simple account of the relations of molecular speeds in the kinetic theory see Chapter III of Part I of O. E. Meyer's " The Kinetic Theory of Gases." A list of concrete values for the speeds of molecules of thirty-one different substances is given on pages 57-58 of the English translation of this work (1899). "Molecular and Atomic Energies" are discussed in Chapter V of Part I. A still simpler discussion will be found in O. D. Risteen's " Mole- cules and the Molecular Theory of Matter" (1895), Chapter II. Section 13 AVERAGE DISTANCE TRAVERSED BY A GAS MOLECULE BETWEEN IMPACTS The "Mean Free Path." Since the molecules of a gas are moving helter-skelter it cannot be expected that the distance passed over by individual molecules between " bounces" will always be the same. However, from what we have said hi Section 11 about the " statistical" nature of the happenings in the molecular world it might be anticipated that on the average this distance would be constant for the same gas under the same conditions. This turns out to be the case, and the distance in ques- tion is known in the kinetic theory as the "mean (or average) free path" of the molecule. The mean free path of a gas molecule under standard conditions is a very important characteristic of the gas on account of the fact that upon its magnitude depend many of the obvious properties of the gas in question. It is clear that, other things being equal, this distance will be greater the smaller the moving molecules and the fewer [97] MEAN FREE PATH [Sec. 13 there are of them in a given volume. In other words the average uninterrupted motion of the molecules is greater the smaller their chances of collision. When the gas is compressed the mean free path is diminished, so that it varies in a direction opposed to that of the change in pressure. Properties Depending on "Mean Free Path." Among other measurable properties of gases which depend upon the magnitude of the mean free path of then- molecules are to be mentioned their natural rates of " diffusion" (see Section 14) and the ease with which they conduct electricity. Any phenomenon which depends upon the rate at which individual molecules can move from one point to another hi the gas body will also depend upon the size of the "mean free path." Electricity is conducted through gases by being carried along bodily on electrons or molecules which move under the influence of the electrical forces exerted by the dynamo or battery. The longer the mean free path, that is the fewer the obstacles which oppose the motion of the electrified molecules, the less the "resistance" which is offered to the passage of the current. This explains why it is that gases under low pressure such as exist in many so-called " vac- uum-tubes" conduct electricity so much better than do the same gases at " atmospheric pressure." For atmospheric gases under ordinary conditions the mean free path is about one one-millionth of an inch in length. In vacuum tubes for the same gases it may be greater than one ten-thousandth of an inch. These mag- nitudes may seem very small, but when we consider the fact that the average gas molecule is only one three- hundred-millionth of an inch in diameter we see that the free movements of the molecules may be relatively large. The mean free path in hydrogen gas is greater [98] Sec. 14] DIFFUSION under the same conditions than that in, say, mercury vapor, for the reason that the molecules of the latter gas are larger than those of the former. Although the length of the mean free path varies inversely as the square of the diameter of the molecules the difference is not very great, owing to the relatively small difference in diameter of the two species of molecules. On account of the great speed of molecular motion, the time intervals between the successive impacts of gas molecules are very minute even in highly rarefied gases. REFERENCES Concerning "Molecular Free Paths and the Phenomena Condi- tioned by Them" consult Part n of Meyer's "The Kinetic Theory of Gases" (1899). Section 14 DIFFUSION One very commonly observed phenomenon which can be accounted for only in terms of the motion of molecules is that of diffusion. The nature of this process is best illustrated by the manner in which odors travel. When a bottle of some pungent liquid is uncorked in one corner of an apartment the molecules of the vapor, which is always present above any liquid, swarm out of the bottle and ultimately spread themselves like insects to all parts of the room. Certain of them strike the sensitive sur- face of the nostrils and produce distinctive sensations of smell. Of course this motion of odoriferous molecules is assisted by the presence of air currents, but these become effective only when diffusion is also possible. The motion of the molecules in diffusion can seldom resemble a "bee line," since no molecule can be ex- pected to travel across the average room without en- DIFFUSION [Sec. 14 countering countless others in its course. Diffusion movements must, therefore, have " jagged" paths, Fig. 16 DIFFUSION PATHS These jagged lines are supposed to be the paths of two gas molecules which are followed for a short period of time. They show quite clearly what is meant by saying that the motion of such molecules is haphazard, but, although the paths are very far from "bee lines," they nevertheless rep- resent a progressive displacement of the molecules from their original positions. It is in this manner that gases diffuse. The paths represented above were of course not obtained by the observation of gas molecules, but they come from a closely related source, viz., the measurements of M. Perrin of the so-called Brownian movement of small particles suspended hi liquids seen under the microscope. As explained in the text the Brown- ian movement follows the same laws as that of molecules in a gas. somewhat like that of a flash of lightning (see Figure 16). On account of the tremendous obstacles which [100] Sec. 15] SOUND ;' /;, ; are opposed to the straightforward motion of the mole- cules, the diffusion of large quantities of a gas or vapor requires long periods of time. Diffusion would not occur at all if it were not for the heat motion of the molecules. REFERENCES On diffusion see Meyer's work already referred to, Chapter HI of Part H. An account of the physical phenomena of diffusion will be found in A. L. Kimball's "The Physical Properties of Gases" (1890), Chapter VI. Section 15 SOUND From the modern point of view sound must be regarded as a molecular phenomenon. Sound is commonly considered to be a species of wave- motion which is set up in the air, or other material sub- stance, by the vibratory motion of the object which is " emitting the sound." Suppose, for example, that a tuning fork is struck. The prongs of the fork are set into rapid vibration and at each of their excursions they push violently against the air molecules which surround them. These molecules are thus thrust away from the fork and communicate their motion to outlying molecules which act in turn upon a third layer of molecules further still from the fork. When the molecules near the fork have conveyed the impulse to the outlying molecules they rebound, just as does a moving billiard-ball which encounters a stationary one under the right conditions. It can be seen that an impulse of this sort will travel out from the source just as a wave of motion passes along a row of standing dominoes, the first of which has been overturned. The gas molecules, however, unlike the [101] LATENT HEATS [Sec. 16 dominoes, return to their original positions when the wave or impulse has passed, and hence are ready for the gen- eration of a second wave, which is occasioned by the second excursion of the prong of the tuning-fork. The result is that a series of " rarefactions and condensations" among the molecules travel out from the tuning-fork and when these impinge upon the ear they cause the sensa- tion of sound. When the prong of the tuning-fork sets the air mole- cules in motion it of course endows them with some of its energy, and it is this energy which is responsible for the stimulation of the ear. The radiation of heat energy from a hot body is different from the radiation of sound energy in several ways. In the first place heat energy may be lost by two distinct processes. A hot body may lose heat energy on account of the fact that the motions of its surface molecules set up similar motions in the molecules of surrounding bodies, or it may lose energy by the generation of "heat waves." These con- stitute true "radiant heat" and do not consist in the motion of molecules, as do sound waves, but rather are closely similar to light, that is electromagnetic waves. REFERENCES An excellent semi-popular work "On Sound," although now an old one, is John Tyndal's book of that name (1888). The first Chapter is especially pertinent. See also Franklin & MacNutt's "Light and Sound" (1909). Section 16 LATENT HEATS It is a well-known fact that when a solid melts, and that when a liquid is vaporized, definite amounts of heat energy are absorbed, the so-called latent heats of fusion and of vaporization. The cause of this absorption of en- [102] Sec. 16] HEAT OF FUSION ergy can be explained in a general way by the molecular theory. The Latent Heat of Fusion. We have said that the molecules of a true solid body are unable to alter their relative positions and hence vibrate ceaselessly about the same centers. In the light of recent studies of the structure of crystals, it seems probable that the mole- cules of a solid are also not free to rotate, and that in a single crystalline unit they all point in the same general direction. This fixity of the molecules is what gives the solid its rigidity, and we must suppose it to be due to the existence of definite forces of attraction existing be- tween them. Any addition to the heat of a body occurs in opposition to these affinities. Melting occurs when the energy of motion acquired by the molecules is sufficient to enable them to break away from the chains of attraction which bind them to their neighbors. When this happens, how- ever, the attraction necessarily reduces the initial speeds of the molecules, because they constantly tend to be dragged back to then* original positions. Since heat consists in the energy of molecular motion, this slowing down of the molecules as they escape from their neigh- bors must mean the disappearance or " absorption" of a certain amount of heat, and this is the latent heat of fusion which we have mentioned above. It is obvious that when the temperature of a body is near the melting point only a relatively small force should be required to distort it, since the forces which hold the molecules hi their places are very much weakened. This consideration explains the increased "malleability" and plasticity which is exhibited by many bodies at high temperatures. When a liquid cools, the forces of attraction again [103] LATENT HEATS [Sec. 16 come into play and as the molecules drop into their posi- tions these forces increase the velocity of their motion, so that the latent heat once more appears in active form. Surface Tension. The molecules of a liquid are free to move anywhere within the liquid but are, for the most part, held within its bounds by a force which may be appropriately designated as the " attraction of the mass." The fact that an attraction of this character exists is proven by the phenomenon of surface tension. All liquids behave as if they were surrounded by a very thin and tightly stretched skin, an effect which is due to the strong attraction exerted upon the surface molecules by those which are underneath. The Latent Heat of Vaporization. The evaporation of a liquid consists in the escape of certain of its mole- cules through this surface film. In order to escape in this way they must move at a velocity sufficient to enable them to overcome the inwardly directed force which exists at the surface. This means that, in general, only the fastest moving molecules can gain their freedom, and even they achieve it at a certain price, namely a reduc- tion of their speed. The action whereby the fastest moving molecules are constantly being removed from the liquid together with this reduction of speed necessarily involves a loss of heat energy. This loss or absorption of heat is called the latent heat of vaporization. Everyone is familiar with the truth that the evaporation of a liquid has a cooling effect, and this effect is to be attributed to the fact that evapora- tion involves the absorption of heat energy. When a vapor molecule returns to the liquid from which it sprang, its speed is increased as it passes through the surface. In this way the latent heat of vaporization is reconverted into energy of molecular motion. [104] Sec. 17] BOILING POINTS REFERENCES Concerning latent heats consult H. C. Jones* "The Elements of Physical Chemistry" (1902), pp. 104-106, 161-162, which, however, does not deal with the molecular explanation of the phenomena. This is discussed, mathematically, hi W. Nernst's "Theoretical Chemistry" (1911), pp. 236-238. An elaborate dis- cussion of surface tension phenomena will be found in the eleventh edition of the Encyclopaedia Britannica under "Capillarity." Section 17 "CRITICAL" AND BOILING POINTS OF LIQUIDS As the temperature of a liquid is increased, a point is finally reached at which the influences of separation due to the movement of its molecules just balance the forces of inter-molecular attraction. This is called the " critical point" of the liquid. Since the film of surface tension which surrounds a liquid is due to the activity of its internal forces of attrac- tion, this film vanishes at the critical point, thus obliter- ating the distinction between the liquid and its vapor. Just below the critical point the latent heat of vaporiza- tion is practically zero, on account of the absence of any effective forces of attraction to be overcome hi separating the molecules. Both the surface tension and the latent heat of vaporization decrease gradually as the tempera- ture rises. Under ordinary conditions the majority of liquids boil at temperatures which are far below their critical points. Since the atmosphere above a liquid exerts a confin- ing pressure upon it, it is impossible for vapor to form within the mass of the liquid until the pressure exerted by the vapor itself is greater than that of the atmosphere. When this point has been reached the production of vapor within the body of the liquid results in the formation of [105] LAWS OF GASES [Sec. 18 bubbles which rise to the surface and break, the familiar phenomenon of boiling. In accordance with this explana- tion it is easy to see why the boiling points of all liquids should be lowered by a decrease in the pressure of the surrounding atmosphere, and raised by an increase in the pressure. REFERENCES On critical and boiling points see A. D. Risteen's "Molecules and the Molecular Theory of Matter" (1895), pp. 80-84. Also Nernst's "Theoretical Chemistry" (1911), pp. 63-67. Section 18 THE SIMPLE LAWS OF GASES AND OF SOLUTIONS Boyle s Law. The relations which exist between the pressure which is exerted by a gas, its temperature, and its state of compression, i.e., its density, are very simple, and are at once accounted for by the molecular theory. The pressure acting upon a vessel which con- tains a gas must obviously become greater when the size of the vessel is decreased, because although the number of molecules remains constant, the frequency with which they strike the sides of the vessel must increase. This is the basis of the well-known law of Boyle, which states that the pressure exerted by a given quantity of gas is inversely proportional to the volume which it occupies. The law can in fact be derived mathematically by con- sidering the action of the moving molecules. Charles Law. When the temperature of a gas in- creases, the molecules move faster, and hence the pres- sure must increase also. It can be shown by a simple calculation that the pressure caused by the bombardment of the sides of the vessel by the flying molecules should be proportional to the average energy of this motion. This [106] Sec. 18] ABSOLUTE ZERO means that the pressure of a gas is directly proportional to its temperature measured in degrees above the " ab- solute zero": the law of Charles. " Absolute Zero." " Absolute zero" is defined as a point of temperature at which the molecules are motion- less and hence as a point at which the gas-pressure is also zero. By measurements upon gases we can find out how much their pressures decrease for each unit of tempera- ture, and if we then divide their pressure at any tem- perature by this amount, we shall learn the number of degrees which must be subtracted from the temperature in question in order to give us the absolute zero. This is the principle of Gay-Lussac. As should be expected, it turns out that the change in pressure for a given change in temperature is approximately the same pro- portion of the total pressure for all gases studied under the same conditions. The Principle of Avogadro. In Section 12 we have discussed the principle according to which all species of molecules at the same temperature have the same aver- age energy of motion, regardless of their other char- acteristics. If this principle is valid the pressure exerted by a given body of gas should be independent of the kind of molecules of which it is made up, and should depend, as we have stated above, merely upon the number of molecules of any sort whatever which are present. From this it follows that if the same vessel is filled successively with different kinds of gas at the same temperature and pressure, the same number of molecules will be present hi each case, or in other words: " equal volumes of all gases under the same conditions of temperature and pressure contain equal numbers of molecules," which is the famous principle of Avogadro. As we have already seen (Section 5, above), it follows [107] OSMOTIC PRESSURE [Sec. 19 from Avogadro's rule that equal volumes of similarly con- ditioned gases should have weights which are in the same proportion as the weights of their respective molecules. This is another consideration which affects the form of the so-called "gas law," a familiar formula which sum- marizes the relationships which we are now discussing. The Formula of van der Waals. It has been shown by experiment that the law of Boyle does not hold for high pressures and low temperatures. The reason for this we have already mentioned in Section 2. It is to be found in the fact that Boyle's law is calculated on the assumption that the molecules are geometrical points, whereas in reality they have a volume of their own, a fact which must affect the ease with which the gas is compressed. Moreover the gas molecules exert an at- traction upon each other which tends to make compres- sion easier at high than at low pressures. The influence of these factors has been summed up in the very accurate gas formula of van der Waals. As pointed out in Section 19, below, the above con- siderations apply, at least approximately, to substances in the dissolved, as well as in the gaseous state. REFERENCES Concerning the laws of gases consult A. D. Risteen's " Mole- cules and the Molecular Theory," pp. 40-58; W. Nernst's 11 Theoretical Chemistry" (1911), pp. 198-201, or G. Senter's " Outline of Physical Chemistry" (1908), Chapter H. Section 19 OSMOTIC PRESSURE When a substance, such as sugar, is dissolved in (say) water, its molecules are separated from each other and wander about among the water molecules. If we neglect [ 108 ] Sec. 20] HEAT CONDUCTION the presence of the latter we may regard the state of the sugar as essentially that of a gas having a density corre- sponding to the concentration of the sugar in the water. Now there is an arrangement by means of which it can be shown that a dissolved substance actually does behave like a gas. Suppose that some sugar solution is placed in a balloon made of a membrane through which water can pass without difficulty, but which is impenetrable to the molecules of sugar. If we now place this balloon in a glass of water it will tend to expand and may even burst. This effect is due to the fact that the sugar molecules hi the course of then* heat vibrations strike the sides of the balloon, and being unable to pass through it as the water molecules do, they tend by their impact to force it outwards. General considerations lead us to believe that the laws of this so-called " osmotic pressure" should be the same as those of gases, and this is shown by measurements to be approximately the case. REFERENCES A popular discussion of the phenomena of osmotic pressure appears in W. C. D. Whetham's "The Recent Development of Physical Science" (1904), pp. 104-124. For more advanced con- siderations, see H. C. Jones' "The Elements of Physical Chemistry" (1902), pp. 179-199. Section 20 HEAT CONDUCTION Evidently, if the molecular theory is true, gases should be better conductors of heat, per unit of mass, than are liquids, since their constituent molecules are more free to change their positions, thus permitting a more rapid mixing of the fast and the slow. For the same reason C109] BROWNIAN MOVEMENT [Sec. 21 liquids should be better conductors than solids. These expectations appear to be borne out by the facts of nature. There seems to be an exception to the rule, however, in the case of metals, which are the best conductors of heat known. This apparent exception is explained, how- ever, by the fact that metals contain vast numbers of u free electrons," particles so small that they can travel about among the molecules of the metal almost as if they were in unobstructed space. Indeed, the metal may be said to contain negative electricity in gaseous form. These minute particles partake of the heat vibration of the molecules, and by their very rapid motion quickly bring the temperature of all parts of a metallic body to a uniform level. Metals are as good conductors as the lightest gases because the mass of an electron is exceed- ingly small, even as compared with that of the hydrogen atom, and hence, in accordance with the equipartition principle (see Section 12) must move faster at the same temperature. Besides this, it is probable that electrons can pass through the body of an atom without being stopped. REFERENCES On the conduction of heat see Meyer's "The Kinetic Theory of Gases," Part H, Chapter IX (trans. 1899). Section 21 THE BROWNIAN MOVEMENT AND ITS MEASUREMENT Perrin's Experiments. The work upon the physics of the Brownian movement is still new. Credit for the ex- perimental side of the investigation belongs largely to the French scientist Jean Perrin, whose methods of measur- ing the movements are exceedingly ingenious. The Brownian particles which were employed by Perrin were produced by the precipitation of alcoholic [110] Sec. 21] BROWNIAN MOVEMENT solutions of various gums by pouring these solutions into water. They varied in size from about one twenty-five- thousandth to one two-hundred-and-fiftieth of an inch in diameter. Their motions were measured by direct ob- servation under the microscope, and also indirectly by means of certain calculations. Perrin was able to show that these minute drops of gamboge and other gums, when made into emulsions with water, behave in every way like the molecules of a gas of enormous molecular weight. This applies to such characteristic processes as average speed, rates of dif- fusion, pressure, etc. Verification of Equipartition of Energy. One very interesting outcome of Perrin's work lies in its remark- able verification of the principle that the average energy of vibration of any species of particle depends only on the temperature of the mass of matter considered and not on the weight or size of the particles themselves (Sec- tion 12). Some of the particles which he studied were many thousand times as large and heavy as the heaviest known atom, and yet their average energy appeared to be substantially identical with that characteristic of all atoms or molecules at the temperature under observa- tion. He was able to prove, moreover, that the particles have an average energy of rotation which is the same as that of their translatory movements, a result in harmony with the demands of theory. Other investigations have shown that the Brownian movement in gases follows the same laws as those which hold among particles suspended in liquids. REFERENCES Perrin's own account of his researches on the Brownian move- ment will be found in "The Brownian Movement and Molecular Reality," translated by F. Soddy (London, 1910). For the most part the book is not difficult reading. [HI] SOLIDS AND CRYSTALS [Sec. 22 Section 22 THE SOLID AND CRYSTALLINE STATES The Crystal as a Unit of Structure. The statement that solid bodies are characterized by an orderly arrange- ment of their molecules implies that all solids are crys- talline. This implication is probably correct hi spite of the fact that chemistry distinguishes between crystalline and the so-called " amorphous" solids. Amorphous, or formless, bodies may be regarded as crystalline bodies in which the crystals are very small. 1 Strong reasons exist for believing that this holds even for the so-called "colloidal" substances, which are usually contrasted with "crystalloids." If this is the true view the arrangement of the mole- cules in the entire mass cannot be quite orderly, but it is probably permanent. When solids are broken the surfaces of fracture generally coincide with the surfaces of the crystals of which they are composed. It would not be wrong to regard an ordinary solid body as a closely packed mass of smaller bodies, the individual crystals, which alone represent the characteristic form of a solid. The crystal thus becomes the unit of solid matter next in order above the molecule. However, there are some perfectly definite crystals which seem to be decompos- able into smaller, similar, crystals without limit. Such a substance, for example, is mica, which crystallizes hi sheets, but no matter how thin a sheet of mica may be, 1 As elsewhere stated, the recently discovered " liquid crystals " introduce a somewhat mysterious element into these considera- tions. It seems probable that in the last analysis liquid crystals will be found to depend on a somewhat different set of forces than do crystals of solids. [112] Sec. 22] CRYSTALS AND X RAYS it is always theoretically possible to split it into two thinner sheets, provided, of course, that the first one is not of molecular thinness. It seems to be characteristic of the molecules which compose the mica to arrange themselves in geometrical planes. Crystal Structure as Studied by X Rays. Very re- cently it has been found that X rays, when reflected from a crystal surface, are broken up into a pattern the nature of which varies with the crystal employed. The principle in accordance with which this pattern is formed is well known, being that of optical diffraction or interference so that from the character of the pattern it is possible to deduce the arrangement of the molecules within the crystal. It appears from these studies, the basis of which will be further discussed in Section 55, below, that the unit of crystalline structure, from a geometrical point of view, at least is not the molecule, but the atom. Crystal form appears to result from an extension of the same architectural principles upon which the molecule is built. The cubical crystal of potassium chloride, for example, seems to be made up of a rectangular lattice-work of alternate potassium and chlorine atoms, placed at equal distances from one another. It is natural that there should be a close similarity between the external shape of the crystal and that of the spatial configuration of its component atoms, but it is not always possible to infer the latter from the former. For instance, the crystal of potassium bromide, which is externally similar to that of the chloride, appears to have atoms not only at the corners of a simple cubical lattice-work, but also in the centers of all of the cube faces. Sodium chloride, or common salt, another cubical crystal, has an even more complex structure. [113] SOLIDS AND CRYSTALS [Sec. 22 Stages Between Solid and Liquid: Liquid Crystals. Of course all conceivable stages exist between the solid and the liquid states. It would be difficult, for example, to say whether such a substance as asphalt under certain conditions of temperature is a solid or a liquid, and ex- periments have shown that even very hard and brittle substances like the crystals of common salt exhibit defi- nite evidence of vaporization, a process usually ascribed only to liquids. Liquid crystals probably depend upon the definite relative arrangement of molecules which may neverthe- less alter then* absolute position. Just as hi the living organism, the actual matter changes as time goes on, although the form remains practically constant. In other words, it is not impossible to conceive a combination of orderly arrangement, such as is demanded by the crystal- line state, with relative freedom of translatory movement of the molecules among themselves, which seems to characterize the liquid state. In ideal solids, however, whatever the arrangement, this movement cannot oc- cur, and motion of the molecules must be exclusively vibratory. It is to be expected that the new X ray method of studying crystalline structure will eventually clear up most of these mysteries, and at the same time throw light upon the very closely related problem of the constitution of the molecule. As yet, only a few simple crystals have been analyzed by this means. REFERENCES On the "Molecular Theory of Solids" see Risteen's " Mole- cules and the Molecular Theory of Matter," Chapter IV. A German work on liquid crystals is: "Die Neue Welt der Flussigen Kristalle," by O. Lehmann (1911). [114] Sec. 23] DISTRIBUTION CURVE On the analysis of crystals by means of X rays, see G. W. C. Kaye's "Xrays" (1914), pp. 168-204; and W. H. and W. L. Bragg's "X Rays and Crystal Structure" (1915). Section 23 VAPOR PRESSURE AND THE LAW OF DISTRIBUTION OF MOLECULAR SPEEDS The "Distribution Curve" of Molecular Speeds. In Section 11 it is said that the behavior of molecules can be studied satisfactorily only by the use of the sta- tistical method. Even at a constant temperature all of the molecules do not move at the same speed; it is the average speed which is constant. However, because of the enormous number of molecules which are contained in any body which we may consider, it is possible to make true statistical statements which give us more detailed information about the state of affairs hi the body than does the mere knowledge of the average velocity of the molecules. Some of the molecules of a body move faster than the average and others move more slowly, but on account of the vast number which are present and the consequent great frequency of their collisions there exists a constant levelling tendency, a continuous redistribution of energy, which tends to make them all approximate the average speed. Theoretical considerations show that in a chaos of molecules such as is contemplated by the kinetic theory there must be far more molecules moving at approximately the average speed than at any other speed, and that the more the speed of a molecule departs from the average the fewer of its kind there must be. This principle is often spoken of as the "a law of distribution of molecular speeds," and it is of the utmost importance in the study [116] VAPOR PRESSURE [Sec. 23 of heat and allied phenomena. As shown in Figure 17, it is mathematically similar to the well-known " curve of chance " with which the reader may be familiar. The Laws of "Vapor Pressure" Evaporation, it has been explained, consists in the escape from the surface Fig. 17 "DISTRIBUTION CURVE" FOR MOLECULAR SPEEDS This curve shows geometrically the relative number of molecules mov- ing at speeds which differ more or less from the average speed. Relative speed is measured from left to right along the horizontal line and relative number along the vertical line. A is the point corresponding with the " average energy " of all of the molecules. It is evident from the dia- gram that there are more molecules moving at approximately this speed than at any other, and that the more any (approximate) speed differs from the average the fewer will be the molecules moving at this speed. This curve is a special case of the so-called "curve of error" which represents a law of the utmost importance in modern physics. of a liquid of certain molecules which move faster than the average. According to the above law of the dis- tribution of molecular velocities, as the temperature of the liquid is increased the number of molecules which escape should increase also, and the exact nature of this increase can be predicted from the law. The vapor above a liquid is a gas, and hence exerts a [116] Sec. 23] VAPOR PRESSURE pressure upon the bodies immersed in it. This pressure must follow the ordinary gas laws which we have dis- cussed in Section 18. Since according to these laws the pressure is proportional to the number of molecules present in a given volume, and since this number increases with the temperature of the liquid, the "vapor pressure," as it is called, should increase with the temperature also, and in a way harmonious with the law of distribution of molecular speeds. Empirical measurements show that the actual rise of the vapor pressure of all liquids is quite closely in accord- ance with the theoretically deduced law. Everybody is acquainted with the general fact that liquids evaporate faster the hotter they are. It might at first be thought that the vapor escaping from a liquid would be at a higher temperature than the liquid itself, because only the fast-moving molecules are able to pass through the surface. However, as we have indicated in Section 16, the speeds of all of these molecules are slowed down under the influence of the film of surface tension. It so happens that this decrease, which stands for the absorption of the latent heat of vaporization of the substance, is of exactly the right magnitude to reduce the average speed of the escaping molecules so that the temperature of the vapor is the same as that of the liquid from which it rises. This can be shown theoretically by a consideration of the law of distribution of molecular speeds. REFERENCES On the "law of distribution" refer to Meyer's work, Chapter in of Part I (see Note 12). A mathematical discussion of vaporization will be found in Chapter VII of H. P. Boynton's "Applications of the Kinetic The- ory, etc." (1904). [117] HEAT ENERGY [Sec. 24 Section 24 HEAT ENERGY AND SPECIFIC HEATS The total heat energy of any body is the sum of the energies of motion of all of its molecules. It can be esti- mated approximately by multiplying the average energy of the molecules by the total number of molecules in the body. When the temperature of a given weight, say one ounce, of a substance is increased one degree, a definite amount of energy has to be added to it in the form of heat. If this amount of energy be divided by the amount re- quired to bring about the same change in an equal weight of water, the quotient is the "specific heat" of the first substance. Atomic Heats. Measurements have shown that the specific heats of different substances vary quite widely, but it was discovered by the French investigators, Du Long and Petit, that if the specific heat of any ele- mentary substance in the solid state be multiplied by its atomic weighty the resulting product is approximately 6, no matter what element is taken. The reason for this striking fact is not far to seek. It is found in the principle that the average energy of motion of any group of molecules is independent of their species (see Section 12). If all atoms at the same temperature have the same energy of motion, then the energy which must be added to their motion to produce a change in temperature must be independent of their species and hence of the nature of the substance involved. Multiplying the specific heat of an element by the atomic weight reduces the meas- ure of heat capacity to terms of number of atoms alone, eliminating the factor of weight. [118] Sec. 24] SPECIFIC HEATS To raise the temperature of a gas it is only necessary to increase the energy of motion of its molecules, but the molecules of solids and liquids are bound together by strong forces of attraction, and when their vibrations are increased, an amount of energy must be utilized in over- coming these forces which is equal to that which enters into the increased motion. Accordingly, the specific heat of a substance in the solid or liquid form should be about twice that in the gaseous form, and this is found to be the case in nature. Now the considerations which apply to elementary substances apply also to compounds, although with less accuracy. When the specific heat of a compound is mul- tiplied by its molecular weight, that is by the sum of the weights of its contained atoms, the product does not vary a great deal from 6, if the substance is in the solid form, or 3, if it is in the gaseous form. However, the variations which do occur are sufficient to require explana- tion, and this must be given in terms of the " force con- stitution" of the molecule of which we have spoken at some length in Section 8. In general, the stronger the internal forces of the compound the higher will be its specific heat, since a large amount of energy will be absorbed in setting the parts of its molecules into relative vibration, if the attractions which hold these parts to- gether are powerful. It is necessary that the atoms should vibrate within the molecule as well as with the molecule as a whole, and the average energy of this internal vibration should be equal to that of the grosser molecular movement. It has recently been discovered that the specific heats of all substances decrease very rapidly at very low tem- peratures, so that at absolute zero they would probably themselves be zero. The exact meaning of this strange [119] THE ELECTRON [Sec. 25 fact is not yet clear, but it seems to be related with the newly suspected atomic nature of radiant, and perhaps all, energy. We shall discuss this matter briefly in Sec- tion 54. REFERENCES The specific heat of gases is discussed on pp. 63-74, of Jones' " Elements of Physical Chemistry" (1902), liquids on pages 106- 110 and that of solids on pp. 162-166. Consult also James Walker's "Introduction to Physical Chem- istry" (1901), Chapter V. On the changes in specific heats which occur at low temperature, see W. Nernst's "Theoretical Chemistry" (1911), pp. 710-716. Section 25 THE DISCOVERY AND MEASUREMENT OF THE ELECTRON Thomson s Determination of the Electronic Mass and Charge. The electron was discovered by J. J. Thomson as the result of a series of epoch-making and very ingen- ious experiments. When an electrical discharge passes through a tube from which the air has been partly ex- hausted it consists, hi part, of a beam of rays which seem to be emitted from the negative pole, or " cathode," of the battery or induction coil. (See Figure 18.) Thomson showed that these so-called "cathode rays" are made up of very minute bodies nearly two thousand times lighter than hydrogen atoms, and moving at a speed which varies with conditions but which is in gen- eral about one-tenth that of light, or about twenty thousand miles a second. Thomson did not determine the size of the electron directly but only its weight, or more strictly speaking its mass. This he was able to do by use of the well-known principle that the more massive a body is, and the higher [120] Sec. 25] CATHODE RAYS its velocity, the greater is the resistance which it offers to change in its state of motion. It was found that the cathode rays could be bent by the action of a magnet, a fact which showed them to bear electrical charges, and by measuring the magnitude of this bend as compared with the strength of the magnet employed, a basis was provided for the calculation of the mass of the moving Fig. 18 VACUUM TUBE TO SHOW THE ACTION OF THE CATHODE RAYS The cathode rays are emitted from the plated and travel away from it In straight lines, a fact which is shown by the character of the shadow, C, cast by the metal cross, B. This shadow appears in the glow which is produced where the rays strike the end of the tube. particles. (See Figure 19.) Measurement of the bend of the rays under the influence of magnetism alone did not permit Thomson to separate the effect of the speed at which the particles were travelling from that due to their mass, but by studying the bend which occurred when electrical as well as magnetic forces were brought to bear upon the rays, he was able to obtain a measure which depends upon the mass and not upon the velocity of the particles. [121] THE ELECTRON [Sec. 25 However, it unfortunately happened that these meas- ures were not independent of the electrical charge borne by the single particles, and consequently he was obliged to devise a method for the determi- nation of this charge. The method which he actually used consisted in a simple measurement of the total amount of electricity carried by a large number of the particles, followed by a determination of the number itself. From these two measurements the quantity of electricity carried by one particle could obviously be calcu- lated. Thomson's procedure It is seen that after the rays enter the large f r finding the number of bulb A they move along a circular path. particles Corresponding to a known charge was exceedingly clever. On account of its charge each of the particles is a center of forces of attraction, so that if they exist hi an atmosphere over-sat- urated with moisture, this moisture tends to condense about the individual particles, each of the latter thus becoming the nucleus [122] Fig. 19 HOW THE CATHODE RAYS MAY BE BENT BY A MAGNET This drawing represents a cross-section of a tube which was employed by J. J. Thomson in the study of the cathode rays. This is due to the presence of a magnet which is placed outside of the bulb in such a way that the lines of magnetic force between the opposite poles of the magnet are perpendicular to the path of the rays. The magnet is omitted from the drawing so that the path of the rays can be clearly shown. However, if it were supposed to be really absent it would be necessary to represent the rays as impinging on the bulb at C instead of at B, which is an electrical condenser for collecting the charge carried by the rays. I I Sec. 25] ELECTRON MAGNITUDES of a small drop of water. The size of the drops of water thus formed can be determined by the rate at which the fog which they compose settles under the pull of gravity. Since it is easy to measure the total amount of water which condenses, the number of droplets in the fog can be calculated from a knowledge of their individual size. Since each droplet corresponds to a single electrical particle the number of droplets gives a measure of the number of such particles which are present, and hence permits the calculation of the charge which they indi- vidually bear. Knowing the amount of electricity carried by each particle in the cathode rays, it is possible to separate the effect of the charge from that of the mass, and hence to ascertain the magnitude of the latter. The most refined measurements of this sort show that the cathode ray particles, which are now called electrons, have a mass which is about one eighteen-hundredth that of the lightest known atom, that of hydrogen. Sources of electrons other than the cathode rays are now available, and the nature of electrons has been satis- factorily proved to be independent of their source. The Size and Shape of the Electron. The size of the electrons is calculated by use of the fundamental laws of electrical action. These laws imply that electrical charges, even when free from all matter in the ordinary sense of the word, possess one of the most characteristic properties of matter, viz., mass or inertia. The laws state, furthermore, a definite relationship between the charge of an electrical particle, its volume, and its mass, such that for a given charge the mass increases as the volume decreases. Since we know the mass and the charge of the electron from the measurements described above, it is possible to calculate the volume. This calculation is [123] THE ELECTRON [Sec. 25 based upon the assumption that the electron is made up of pure negative electricity and of nothing else, i.e., that it contains no "matter," as distinguished from electricity. Although it is difficult to give a direct justification of this assumption it is nevertheless in harmony with all of the analogies of the situation, and is contradicted by none of the facts. Studies in radio-activity have shown that electrons can pass straight through considerable thick- nesses of solid substances and, indeed, through the atoms themselves. This clearly suggests that the electrons are very minute, as is indicated, also, by the calculations. The symmetry of structure of the electron seems to be borne witness to by certain measurements regarding the manner hi which its mass changes with its velocity. It follows from the fundamental electrical laws mentioned above that the electronic mass will increase at high speeds in a way which depends in its details upon the shape and also upon the internal structure of the electron. By calculating the masses which should be effective at different speeds for various probable types of electronic constitution, and then comparing these results with actual measurements we can obtain some idea as to the real shape and structure of the electron. At present the electron is believed to be spherical at low speeds, but it is thought that it becomes more or less flattened hi the direction of motion when it moves at speeds approaching that of light. REFERENCES A considerable number of popular discussions of the electron and its measurement are obtainable. Among these may be men- tioned the following: R. K. Duncan's "The New Knowledge" (1908), Part 3, Chapters III to X, inclusive. Sir Oliver Lodge's "Electrons" (1907), Chapters HI-XIV inclusive. [124] Sec. 26-7] ELECTRICAL FORCES Harry C. Jones' "The Electrical Nature of Matter and Radio- Activity" (1906), Chapters I-III inclusive. E. E. Fournier D'Albe's "The Electron Theory" (1906), Chap- ter XI. Section 26 THE IMPORTANCE OF ELECTRICAL FORCES IN NATURE The meaning of the statement that "most of the phenomena hi nature are due, hi the last analysis, to electrical attractions and repulsions," will become clear to the reader as he proceeds. Part of its significance can be grasped at the present stage of the discussion if one remembers what has been said hi Section 8 about the dependence of the properties of substances upon the nature of their internal forces. There is now little doubt that these forces are electrical. Also, chemical action and all electrical phenomena clearly involve the agency of electrical forces. When we come to study the question of the constitution of the atom we shall see that the phenomena of radio-activity, and the emission and absorption of light, have an electrical origin. REFERENCES See Sir Oliver Lodge's "Electrons" (1907), Chapter XVI. Section 27 THE REACTIONS OF ELECTRONS AND CHARGED ATOMS How Ions are Produced. When an electron is taken from or added to a previously neutral atom or molecule the charged particle which is thus formed is called an "ion" and the process is that of " ionization." Various means of ionization are known. The collision of molecules [125] IONS AND ELECTRONS [Sec. 27 in the course of their heat vibration may sometimes be sufficiently violent to knock electrons out of the molecules. A more effective process of a similar nature, however, lies in the bombardment of a gas with flying electrons or ions, which on account of their speed and the electrical forces which they exert upon the electrons within the gas molecules are able in many cases to bring about a separation of the two. C. T. R. Wilson, by bringing about the condensation of moisture on the ions which are formed, has been able to obtain accurate photographs of the path of the flying a particles from radium through a gas. A powerful electrical field such as that which' exists between the terminals of a sparking induction coil will cause ionization. Light (including X rays), being a form of electrical energy, can also separate elec- trons from the atoms with which they are combined. Ionization is likewise a common accompaniment of chem- ical action, and occurs in many chemical solutions, a fact later to be considered in greater detail (see Section 29). A definite amount of energy is required to force an elec- tron out of any atom, an amount which varies only slightly with the nature of the atom. The differences which exist, however, are sufficiently constant to constitute charac- teristic properties of the elements. The energy of ioniza- tion of a substance can be estimated from the intensity of the electrical field needed to just produce ionization. The Interactions of Ions and Electrons. As explained in Part I an " uncharged " atom contains a certain number of electrons and also positive electricity, enough to neu- tralize exactly their negative charges. If an electron is added to the atom from the outside there will be more negative electricity than positive and the atom will have a " negative charge"; whereas if an electron is taken away from it there will be more positive than negative elec- [126] Sec. 27] FORCES BETWEEN IONS tricity and the atom will have a "positive charge." (7) in Figure 20 shows two uncharged atoms, (4) two negatively charged ones, and (5) two positively charged REPULSION. ELECTRON REPULSIOK STRONG ATTRACTION ONLY WHEN NEAR ELECTRON Fig. 20 THE FORCES ACTING BETWEEN IONS, ATOMS AND ELECTRONS These diagrams represent in a symbolic way the forces which operate between aggregates of electrical charges, of various degrees of complica- tion. The diagrams are explained in the text. ones. It must be borne carefully in mind that these are not pictures of atoms. They are merely symbolic draw- ings, the black dots representing electrons, and the [127] IONS AND ELECTRONS [Sec. 27 "plus sign" representing the positive charge which is inseparable from the atom. It follows of course from the laws of electricity, as re- called to the reader in Chapter V under the heading, "The Two Electricities," that the following statements are true : (a) Two electrons repel each other [see (1), Figure 20]. (b) An electron is repelled by a negatively charged atom (i.e., one which has one electron too many for neutrality (2). (c) An electron is attracted toward a positively charged atom (i.e., one which has one electron too few for neu- trality) (3). ( d) Two negatively charged atoms repel each other (4). (e) Two positively charged atoms repel each other (5). (/) A positively charged atom and a negatively charged atom attract each other (6). There are also two attractions of a different kind, one of which is already familiar to the reader, which do not follow obviously from the fundamental electrical laws. These are : (g) All atoms attract each other, even when they are neutral (7). This is the familiar attraction considered hi Section 10. It explains the cohesion of solids and liquids in spite of the violent heat vibration to which their atoms and molecules are subject. This attraction, unlike the common "electrical" attraction (/), is effective only when the two atoms are very near each other. (h) All uncharged atoms attract electrons (8). This force, like (g), is only effective when the electron is very near the atom. When it is near, however, the force be- comes very great. At greater distances it is very much weaker than the familiar "electrical" forces before mentioned. [128] Sec. 28] HALL EFFECT REFERENCES Concerning ionization, consult "The Electron Theory" by E. E. Fouraier d'Albe, Chapter IV; " Electrons," by Sir Oliver Lodge, Chapter VII; "Modern Theory of Physical Phenomena" by Augusto Righi (1904), Chapter IV. Section 28 SOME EFFECTS CONNECTED WITH THE ELECTRICAL CURRENT The "Hall Effect." It follows from a fundamental law of electrical science that when a moving electron comes under the influence of a magnet its normally straight-line path will be changed to a curve. Hence if the conduction of electricity through solids actually con- sists in the bodily motion of electrons it should be possi- ble to alter the direction of an electric current in a wire by bringing a sufficiently powerful magnet near it. Ex- periment shows that this can be done, the phenomenon being commonly known as the " Hall effect." There are certain stubborn difficulties in connection with the ex- planation of the Hall effect, because the changes are some- times in one direction and sometimes in the other, but it seems highly probable that the phenomenon is due to electron deflection. The Nature of Electrical Resistance. Different metals and substances in general vary widely in their so- called electrical conductivity, or to put it the other way round, they offer varying degrees of "resistance" to the passage of the electrical current. There are various factors which determine the electrical conductivity or resistance of substances. In the first place, it should be clear that the more electrons a substance contains in a given volume the more electrons will move forward when [129] ELECTRIC CURRENT [Sec. 28 an electrical force is applied to it. The "current" or " amperage" is merely the amount of electricity which flows through a certain portion of the wire in a given time, or, hi other words, the number of electrons which pass any fixed boundary. So it is obvious that the more electrons there are free to move the greater will be the current under a given electromotive force or " voltage," and therefore the higher the conductivity of the sub- stance or the lower its resistance. Substances such as hard rubber and porcelain contain almost no free elec- trons and hence are what we call "non-conductors" or "insulators." Metals like copper and silver contain a large number of free electrons and accordingly are "good conductors." Electrical and Thermal Conductivity. In Section 20 the fact is mentioned that the extraordinarily good heat conductivity of metals is accounted for hi terms of the free electrons which they contain. If this is the true explanation it can be shown to follow that, other things equal, those metals which contain the largest number of free electrons will be the best heat conductors. But such metals will also be the best conductors of electricity, and hence it would appear that some sort of proportionality should exist between the power of a substance to conduct heat and its power to conduct electricity. Accurate meas- urements and calculations show that a relationship of this kind holds in nature, and that its quantitative char- acter is hi remarkable accord with the assumptions of the electronic and molecular theories. Besides the number of free electrons in a unit volume of a substance there are other factors which must influ- ence its conductivity. One of these is the "mean free path" of the electrons among the molecules of the sub- stance (see Section 13). Other things being equal, the [130] Sec. 29] ELECTROLYSIS farther an electron can move without striking an atom or another electron the better the substance will conduct both electricity and heat. It is interesting to note the fact that the direction of movement of the electrons in a wire is opposite to the so-called direction of the current, for the reason that the latter is what would be the line of motion of positive electricity if any were moving. The electrons, it will be remembered, are negative. When they move oppositely to positive particles the two produce identical magnetic effects. If electrons had been known when the termi- nology was developed, the conventional direction of the current would probably be the reverse of that now in use. REFERENCES The following references are to simple discussions of the theory of electrical conduction in solids: E. E. Fournier d'Albe's "The Electron Theory," Chapter IV, Section 4. Sir Oliver Lodge's "Electrons," Chapter X. D. F. Comstock: "The Modern Theory of Electric Conduc- tion," in the "Transactions of the American Electro-Chemical Society" (1912), Volume XXI, pp. 41-48. A somewhat mathematical and more detailed account is given by Sir J. J. Thomson in his " Corpuscular Theory of Matter " (1907), Chapters IV and V. Section 29 ELECTRICAL CONDUCTION IN GASES AND LIQUIDS Conduction by Ions; Electrolysis. Metals are not the only substances which are good conductors of electricity. It is a well-known fact that many solutions are excellent conductors, and in this case the conduction involves the motion not of free electrons but of charged atoms or "ions." Some of these moving atoms are negatively [131] CONDUCTION IN GASES [Sec. 29 charged, that is, bear electrons in excess of their normal number, while others are positive and have lost part of their regular complement of electrons. The current through the liquid consists of negative atoms or ions moving in one direction and of positive atoms or ions moving in the opposite direction. Both of these lose then* charges when they come into contact with the "electrodes" by which the current enters and leaves the solution, the former at the positive pole and the latter at the negative pole. This means that atoms of the positively charged substances will collect about the negative pole while those of the negatively charged kind will segregate about the positive electrode. This process is commonly called electrolysis, and will be further dis- cussed at another point. For this type of conduction it is necessary for the liquid to contain ions. (See Section 27.) The conduction of electricity through gases also de- pends upon the presence of ions. Free electrons, however, are often present and active. To the study of phenomena connected with the passage of electricity through gases we owe a great deal of our knowledge of the nature of electrical processes in general, since the conditions here are particularly favorable for observation. REFERENCES On the conduction of electricity through gases see W. C. D. Whetham's "The Recent Development of Physical Science" (1904), Chapter V. Sir J. J. Thomson's great work "The Conduction of Electricity Through Gases" should also be mentioned. On conduction in solutions, see Augusto Righi's "Modern The- ory of Physical Phenomena (1904), Chapter I, and "The Theory of Electrolytic Dissociation," by Harry C. Jones (1900). [132] Sec. 30] ELECTRIC POWER Section 30 THE ELECTRICAL TRANSMISSION OF POWER The analogy between the transmission of power by electricity and by compressed air really amounts to something very close to identity, if the modern view is correct. When air is pumped in at one end of a pipe the air molecules at that end exert an increased force upon the others further along and thus increase the pres- sure throughout the system. Similarly, in an electrical circuit an increase in voltage may be thought of as cor- responding to the introduction of further electrons into that part of the circuit which lies just beyond the dynamo or battery. These repel neighboring electrons and thus the electrical pressure increases all along the circuit. Ordinarily the electrons are confined within the body of the wire just as the air molecules are held within the pipe. Leaks, however, may occur as in the case of compressed air systems as shown by the glow which sometimes surrounds high tension lines at night. The influence of electrons upon each other's motions of course depends in large part upon the enormous elec- trical repulsions which exist between them. This is not so clearly the case with molecules. REFERENCES See E. E. Fournier d'Albe, "The Electron Theory" (1906), Chapter VH. Section 31 THERMO-ELECTRICITY The Principle of the Thermopile. Roughly speaking, the number of free electrons in a substance is a measure of the lack of affinity of its atoms or molecules for elec- trons. The fact that this aftimty varies for different sub- [133] THERMO-ELECTRICITY [Sec. 31 stances has some interesting consequences quite apart from the production of various degrees of electrical con- B ductivity. For example, if two metals the atoms of one of which have a greater affinity for electrons than have those of the other, are placed in contact the former will appro- priate electrons from the latter. This is due to the fact that the " evaporation of elec- trons" from the surface of one of the metals is more rapid than that from the sur- face of the other metal, so that the first gives out to the second more electrons than it receives. Hence the second metal becomes negatively charged, while the first ac- quires a positive charge. If we suppose the two met- als in question to be in the form of horse-shoe shaped wires touching each other at their extremities it can easily be seen that no current of electricity will flow through the circuit which is thus formed, for the reason that the electrical forces which ex- ist at one junction are exactly balanced by those existing at the other junction. Suppose, however, that the latter is heated to a temperature higher [134] Fig. 21 A THERMO-ELECTRIC CIRCUIT This is a symbolic drawing. The circle as a whole represents the complete electrical circuit, the left half being composed of a metal which emits electrons freely and the right half of one which parts with its electrons less easily. If the junctions A and E are both at the same temperature no current will flow, since the tendency to- wards a clockwise current which exists at E is exactly balanced by the opposite tendency existing at A. However, when the junction A is heated these tendencies are no longer exactly in equilibrium and electrons move around the circuit in the direction of the arrows. It is not necessary that the circuit should be made up of equal masses of only two different metals. It may be broken at any point and long wires of any sort of conducting substance introduced without altering its gen- eral principle. Sec. 31] THERMO-ELECTRIC SERIES than that of the former. (See Figure 21.) This will bring about a change in the electrical forces at the point which is being heated, due in part to the fact that the number of electrons thrown off by one metal increases with the temperature faster than the number emitted by the other metal. The electrical equilibrium of the circuit is thus disturbed, and a current will flow, that is, electrons will move from one junction towards the other. This motion of the electrons carries heat energy from the hot to the cold junction so that continued heat- ing and cooling is necessary in order that it should per- sist. This is the principle of the so-called thermopile. The Thermo- Electric Series of the Metals. By studying different thermo-electric circuits of the sort described above we can arrange a series of metals in which by con- tact with a standard metal, each member of the series gives a higher voltage than the member preceding it. It is found that this series has close affinities with another series which is determined by studying the vol- tages generated by the same metals in the form of an ordinary electrical battery. The exact nature of the electro-motive series varies with the temperature, on account of the fact that as different metals are heated the number of free electrons which they contain in a given volume does not necessarily alter in the same way. A sample sequence is represented below: THERMO-ELECTRIC SERIES OF METALS Metal Relative Potential Difference Bismuth' 89 to 97 Nickel 22 German-silver 11.75 Lead Platinum 0.9 Copper - 1.36 Zinc - 2.3 Iron - 17.5 Antimony - 22.6 to - 26.4 Tellurium 502. Selenium 800. Lead is taken as the standard metal. [135] CHEMICAL AFFINITY [Sec. 32 REFERENCES On thermo-electricity, consult: E. E. Fournier d'Albe's "The Electron Theory" (1906), Chapter V. See also: O. W. Richardson's " Aggregates of Electrons," in the " Proceedings of the American Philosophical Society" (1911), volume 50, pp. 347-366, and W. C. D. Whetham's "The Theory of Experimental Electricity" (1912), Chapter VI. On the evaporation of electrons see N. Campbell's "Modern Electrical Theory," second edition (1913), pp. 81-84. Section 32 CHEMICAL AFFINITY Electro-positive and Electro-negative Elements.* Chemi- cal affinity may perhaps be regarded as another expres- sion of the fact that different kinds of atoms have varying degrees of attraction for electrons. It has been known for a long time that the chemical elements could be grouped into three not very sharply defined classes, those which were characteristically electro-positive, those characteristically electro-negative, and those which might be either electro-positive or electro-negative, according to the circumstances. Hydrogen and the metals are the most powerfully electro-positive of the elements, while such substances as oxygen, chlorine, fluorine, etc., are strongly electro-negative. As we have seen, the former lose electrons easily; the latter, on the other hand, ap- propriate with great avidity electrons not their own. It is clear that when a neutral atom of hydrogen, for example, parts with an electron it must become positively charged, and if this electron or another is appropriated by an atom of chlorine, for instance, the latter becomes negatively charged. Positively and negatively charged atoms of this sort will obviously tend to combine, owing [136] Sec. 32] POSITIVE AND NEGATIVE ELEMENTS to the electrical attractions existing between them, and these attractions, it seems probable, constitute chemical affinity. When we study the actual constitution of chemical com- pounds we find that the most common compounds are made up of just such electro-positive and electro-negative components. Common salt, for example, is composed of the strongly positive element sodium, combined with the strongly negative element chlorine. Any Element may be Positive or Negative. However, if we make a table of elements which we suppose to be electro-positive and another of those which we suppose to be electro-negative, we soon discover that, however we may construct the table, exceptions always occur to a rule which states that only atoms of opposite sign com- bine with each other. For a long tune it was thought that the fact that two negative or two positive atoms could combine chemically was a refutation of the electrical theory of chemical affinity, since atoms bearing charges of like sign could only repel each other. The electron theory removes this difficulty, along with others, for any atom can become negatively charged if it can gain an electron, or positively charged if it can lose one, and the same atom may conceivably suffer either of these changes according to the conditions under which it is placed. No two of the elements have the same affinity for negative electricity, and if any two of them are mixed under proper conditions the atoms of the one having the lesser affinity will lose electrons while the atoms of the other will gain them. Mixed with a different element, the same atoms which here gain electrons might lose them, if the element in question were the more strongly electro-negative. In other words, we can speak of the electro-negativity or positivity of the elements in a relative sense only. [137] CHEMICAL AFFINITY [Sec. 32 There is one difficulty which remains outstanding, however, and that is the explanation of the chemical affinity which apparently exists between atoms of the same species. We have al- -f\ ; ' ready mentioned the fact in \ / Section 7 that almost all of _ i , the elements form complex molecules even in the pure state. This implies the exist- i !_. ence of chemical affinity be- i 1 tween atoms of the same / \ kind. Such affinity is prob- ' \+ ably to be explained by the idea that the positive and negative charges within any WHICH TWO NEUTRAL AGGRE- atom are not uniformly dis- throughout it, and OTHER hence that the surface of The two arcs represented in the figure an atom is, SO to Speak. may be thought of as cross-sections through the surfaces of two adjacent mottled. TWO atoms OI the same kind may thus stick to e ether b y electrical attrac - tive components of the other. Taken tion if, as as wholes both atoms are electrically , j . _. rtrt neutral, but at close range powerful represented Ul Figure 22, mutual attractions may still exist be- t hev afe gQ or ; en ted With tween their parts. This diagram must mev ' ' ^ Li not be regarded as an accurate picture fCSpect to each other that of the surface of an atom. the negative mottlings of one coincide with the positive mottlings of the other, and vice versa. The "Inert" Elements. Some of the elements, such as argon, helium, and the like, are chemically inert, that is, they refuse to combine with any other elements. The reason for this probably lies in the fact that they are incapable of becoming permanently ionized, that is, they [138] Sec. 33] SOLUTION have neither a very strong tendency to gain additional electrons or to part with those which they naturally possess, but rather tend to be stable in this respect. We have mentioned the fact in Section 6 that the electrical character of the elements varies with other of their prop- erties according to the law of the periodic table. The inert elements all fall into the same family, and each of them lies between a strongly electro-negative element on one side and a strongly electro-positive element on the other, so that it is perhaps not surprising that they should be neutral. REFERENCES See the reference, already given, to Sir Oliver Lodge's "Elec- trons," Chapter XVI, and Norman Campbell's " Modern Electrical Theory," second edition (1913), Chapter XIII, esp. pp. 340 ff. Section 33 SOLUTION AND ELECTRICAL DECOMPOSITION How Water "Ionizes" Dissolved Substances. It has been asserted in the course of our discussion that the forces of chemical affinity are probably electrical. If this is true, any influence which tends to weaken these forces should cause the molecules to fall apart under the influence of then* heat vibrations. Now all substances possess a property called dielectric capacity, which can easily be measured, but concerning the exact nature of which we need not here trouble our- selves. Suffice it to say that the electrical forces between any given set of charged particles become less as the dielectric capacity of the medium in which they are placed becomes greater. All material bodies have a higher dielectric capacity than has empty space and it would seem that if two bodies rightly selected could come [139] ELECTROLYTIC DISSOCIATION [Sec. 33 into sufficiently intimate contact with each other the large dielectric capacity of the one might bring about a separation of the electrical particles making up the other. Just this intimacy of contact is assured when one of the substances is a liquid and the other is in solution within it. Suppose, for example, that a solid like common salt, the molecules of which are made up of one atom of chlo- rine and one atom of sodium, is dissolved in water. According to our view of chemical affinity, these mole- cules are held together by the attraction which exists between the positively charged sodium atom, Na + and the negatively charged chlorine atom, Cl~. If the prop- erties of the water cause it to weaken this attraction so that the oppositely charged parts of the salt molecules can be knocked apart, the solution will contain free charged atoms, or ions. This process actually occurs with a great many substances which can be dissolved in water. It is called technically "electrolytic dissociation." The Motion of Ions Through a Solution. When so- lutions conduct electricity the current is due to the bodily motion of the ions which have been produced by the splitting up of the molecules of the dissolved substance. We have discussed this matter in Section 29, and have also referred to some of the related phenomena in Sec- tion 2. The electrical dissociation of the molecules of dissolved substances, which can easily be proven by experiment to exist, furnishes us with another striking verification of the idea that chemical affinity depends upon electrical forces. The Effect of lonization on Boiling and Freezing Points. - When any substance is dissolved in a liquid, the boil- ing point of the liquid is raised and its freezing point is lowered to an extent which is approximately proportional [140] Sec. 34] CHEMICAL VALENCY to the number of molecules which have entered into solution. The cause of these changes can be stated in terms of the kinetic molecular theory. The important fact for us to notice here, however, is that when the molecules of the dissolved substance are split up into ions the number of effective molecules is thereby greatly increased, and that if this is the case the effect upon the boiling and freezing points should be greater than would be expected upon the assumption that no such splitting of the molecules occurred. Empirical measurements ap- pear to verify this conclusion, and also show the presence of an abnormally high osmotic pressure (see Section 19) in solutions of electrically dissociated substances. REFERENCES Refer to Nernst's "Theoretical Chemistry" (1911), Book H, Chapter VII, or Talbot and Blanchard's "The Electrolytic Disso- ciation Theory, etc." (1907). W. C. D. Whetham's "The Recent Development of Physical Science" (1904), Chapter IV. A complete book on this subject is Whetham's "Treatise on the Theory of Solutions" (1902). Section 34 CHEMICAL VALENCY It is a well-known fact that the chemical elements combine with each other in proportions which vary with the element which is considered. For example, one atom of chlorine normally combines with only one atom of hy- drogen, while an atom of oxygen usually combines with two of hydrogen. A single carbon atom, on the other hand, will as a rule unite with four hydrogen atoms. The number of hydrogen atoms with which an atom of a given element will combine is called the "valency" of [141] CHEMICAL ACTION [Sec. 35 the element. Some active elements do not combine readily with hydrogen, but these unite with oxygen, the valency or combining power of which is known to be two. The valency of an element is not perfectly constant, but it is nevertheless fairly characteristic. Its magnitude probably depends upon the affinity of the atoms of the element for electrons. The valency of an element hi any specified compound represents the number of electrons which one of its atoms has either gained or lost. REFERENCES See R. K. Duncan's "The New Knowledge" (1908), 166-167, and N. Campbell's "Modern Electrical Theory," second edition (1913), pp. 340-350. Section 35 CHEMICAL ACTION Chemical action is not as straightforward a process as would at first appear, since it must depend upon the random collision of the reacting molecules or atoms. Let us consider carefully a case of chemical combina- tion or " synthesis" and see if we can visualize for it a reasonable mechanism. The Basis of the Law of "Chemical Mass Action." We start with a certain number of atoms of the species A and an equal number of the species B, which are capable of combining with each other in the proportion of one to one. However, they cannot do this unless all of the individual A atoms come into ultimate contact with as many different B atoms. All of the atoms are bounding about at random and colliding with each other like the members of a panic-stricken crowd, and not every colli- sion that occurs is between an A and a B atom. This will [142] Sec. 35] MASS ACTION be especially true after a sufficient number of favorable collisions have occurred, so that the reaction has pro- gressed some distance, for at this time the mixture will contain not only separate A and B atoms but also the AB molecules which have been formed. When these collide with each other and with the atom, no union occurs, so that as the reaction proceeds the number of collisions favorable to chemical combination constantly decreases. It will be observed that this decrease in the number of favorable collisions is caused by a diminution in the number of reactable atoms which are present. Now the rate or "velocity" of any chemical reaction consists in the number of molecules which are formed or decomposed in a given time, and this, in turn, must depend upon the number of collisions occurring in that time. From this it becomes clear that as a reaction proceeds, its velocity should constantly diminish, and it can be shown in fact that at any time this velocity is proportional to the num- ber of active atoms or molecules of each kind which re- main. This is the law of chemical mass action, which is of the utmost importance in the study of chemical change. Chemical "Equilibrium." -The reaction which we have considered above would be complete when each of the A atoms had combined with a separate B atom. It would take a long time for such a reaction to reach com- pletion, for the reason that when nearly all of the atoms had combined, the remaining ones would be separated by a multitude of inert molecules and so would have small chance of encountering each other. However, in reality most chemical changes are reversible, that is, the mole- cules which are formed by the reaction tend to break up again and reproduce the original substances. Thus, most reactions will consist hi two types of change, a forward and a reverse. When the reaction commences, the for- [143] EFFECTS OF CHEMICAL CHANGE [Sec. 36 ward change is the most rapid because there are more molecules to enter into it, but as the reaction progresses the products of this change pile up, and consequently necessitate a constant increase in the reverse reaction. There finally comes a time, of course, when the rates of the two opposite changes are equal so that they balance each other. At this time the " equilibrium point" of the reaction is said to have been reached, and apparently all chemical change has ceased. This appearance is deceiv- ing, however, for beneath the seeming quiet there goes on a ceaseless balanced activity. It is characteristic of the modern view of things to suppose that nearly all cases of seeming rest are hi reality cases of balanced motions. REFERENCES On the law of chemical mass action, see W. Nernst's "Theoret- ical Chemistry" (1911), Book II, Chapter I. Also: G. Senter's "Outline of Physical Chemistry" (1908), Chapter VH. Harry C. Jones' "The Elements of Physical Chemistry" (1902), Chapter IX. Section 36 EFFECTS AND CONDITIONS OF CHEMICAL CHANGE The Heat Produced by Chemical Change. It is a well- known fact that when chemical changes occur, energy is usually liberated in one form or another, most commonly as heat. If atoms are to combine, under the influence of chemical attraction they must first move towards each other hi response to this attraction, and in so doing they must acquire energy of motion. Hence, in general, the temperature of the reacting substances increases in proportion to the strength of the chemical affinities which are active. [144] Sec. 36] CONDITIONS OF CHEMICAL CHANGE The Generation of Light and Electric Current. Chemi- cal change may produce electrical effects if the condi- tions are arranged as in the ordinary "battery," so that charged atoms which are free to move can combine with the atoms of a solid electrical conductor and deposit their charges, so that the conductor as a whole is electri- fied and tends to become the origin of an electrical cur- rent. The production of light by chemical change may be due to the fact that light is caused directly by the vibra- tion of the electrons which are active during the change, or it may be indirectly caused through the rise in tem- perature brought about by the reaction. Conditions Favor ing Chemical Action. Almost all chem- ical changes involve not only the formation of new molecules but also the breaking up of old ones, and since the decomposition of molecules would tend to be favored by the collisions of the molecules in their heat motion, we should expect for this reason alone that the rapidity of a chemical change would increase with the tempera- ture. As mentioned in Part I, the transfer of electrons from one atom to another must also take place more readily at high than at low temperatures, and this, too, aids the reaction. In the case of reaction between gases, high pressures are favorable to chemical reaction, since the more mole- cules there are in a given volume the more frequently they must collide and hence the greater their chances of decomposition and recombination. Another important condition favoring chemical change is the presence of a catalyzer, which is merely some foreign substance capable of accelerating a reaction without being changed itself. The exact general mechanism by which catalysis is produced is not clearly understood, but it is probable that the catalyzer is an ionizing agent of some sort. [145] LIGHT WAVES [Sec. 37 "Chemical energy," which is utilized when coal, for ex- ample, is burned under the boiler of a steam engine, is really the energy of attraction of charged atoms or groups of atoms. Human life and industry, to-day, depend abso- lutely upon the presence and application of this energy. REFERENCES On the energy relationship of chemical change, consult W. Nernst's "Theoretical Chemistry" (1911), Books in and IV. Section 37 LIGHT WAVES AND LINES OF ELECTRICAL FORCE The Present Status of the "ALiher" Experiment shows that light has many of the properties of some sort of wave motion. Since it is difficult to imagine a wave without thinking of some substance hi which it is a wave, physicists have been accustomed up to recent years to assume the existence of an all-pervading aether, the undulations of which constitute light and other similar disturbances. Of late, however, certain very important experimental and theoretical results clustering around what is called the " principle of relativity" have thrown a great deal of doubt upon the existence of the aether, so that it is now advisable to conceive of a light wave in a somewhat different way. The Nature of Electrical Force Lines. Nearly every- one is familiar with the fact that the state of affairs in the space around a body which is charged with elec- tricity can be represented by what are called "lines of electrical force." These lines show in a symbolic fashion how another charged body placed in the space in question would tend to move, or, in other words, what forces would act upon it. It is probable that these lines of force have [146] Sec. 37] * 'KINKS" IN FORCE LINES some counterpart in reality, and recent developments- make it not improbable that electrons and other charged particles of atomic or sub-atomic size are actually centers of radial " tubes of electrical force." "Kinfe" in Electrical Force Lines. It can be shown that lines of electrical force, if they exist, must possess " inertia," that is, that they must offer resistance to changes in their state of motion or rest. In other words they act as regards motion very much like a stiff rope or wire attached to the electron or other charged particle. Hence if the electron is suddenly set into motion or if, when in motion, it is suddenly brought to rest, its lines of force will not accommodate themselves to this change in motion immediately, but will tend to remain at rest or to keep on moving as they did before anything had hap- pened to the electron. This means that every time an electron is slowed down or is speeded up, and every time the direction of its motion is altered, k in k* or curves will be formed in its lines of electrical force. The principle of the formation of these kinks is essentially the same as that of the production of waves in a rope, one end of which is shaken. Just as the waves in the rope move away from their source at a definite speed, so the kinks in the electrical force lines travel away from the electron or other charges, with the speed of light. The formation of such "kinks" is illustrated in Figure 23. If the charge which is under consideration vibrates continuously back and forth, a series of kinks will obvi- ously be formed in its force-lines, and these will con- stitute waves. As a matter of fact light and many other forms of radiation are probably made up of a series of just such kinks or curves. Electrons probably do not vibrate or oscillate as much as we were once inclined to believe. It seems more [147] LIGHT WAVES [Sec. 37 likely, in the light of recent developments, that they move in "jerks," dropping suddenly from one position to another without an ensuing reverse motion. If this Fig. 23 TO SHOW HOW RADIATION IS PRODUCED BY STOPPING THE MOTION OF AN ELECTRICAL PARTICLE The diagram at the left represents a charge of electricity with its radiat- ing lines of forces. We will suppose this charge with its lines to be mov- ing uniformly in the direction indicated by the arrow in the diagram at the right. When the charge is suddenly brought to rest the "lines" have a tendency to continue in motion, and do so until, so to speak, the news of the stopping of the charge has reached them. This "news" travels out- wards from the charge with the velocity of light, along with the "kinks " in the force-lines which result from the discrepancy between the actual and the "expected" position of the charge. These kinks contain electro- magnetic energy and constitute light and other forms of electro-magnetic radiation. Such radiation is produced whenever any change whatsoever occurs in the state of uniform motion of an electrical charge. is true it means that the ordinary laws of motion do not apply without modification to the motion of electrons. This question is further discussed in Section 54. REFERENCES On the electrical theory of light, consult Righi's "Modern The- ory of Physical Phenomena" (1904), Chapter II. The theory of "kinked" force-lines above discussed was first [148] Sec. 38] ZEEMAN EFFECT developed by J. J. Thomson and one of his simplest accounts of it will be found in his "Electricity and Matter" (1904), Chapters I-in inclusive. See also W. C. D. Whetham's "The Theory of Experimental Electricity" (1912), Chapter IX. Section 38 THE ZEEMAN EFFECT The rapidity with which any vibrating body moves back and forth in its path depends upon the magnitude of the forces which are acting upon it. Magnetic forces are known to act upon moving electrically charged bodies and hence we should expect that if there are electrons vibrat- ing or moving in any way within sources of light, the application of a magnet to such a light source would alter the rate of vibration of these electrons. If this occurs, the vibration time, and hence the " wave-length" of the light, must also be changed. From the mathematical theory of electricity it is possible to calculate the exact change which should occur, assuming a vibrating particle of known charge and mass. Conversely, if we know the change hi the character of the light we can estimate the charge and mass of the electrical particle which is emit- ting the light. A very large number of observations have been made on the effect produced by magnetic forces upon the light given off by many different substances in the glowing state. All of these observations show that, certainly in the majority of cases, the vibrating, or otherwise moving, particle is an electron. The alteration of wave-length of the light emitted by a glowing body under the influence of magnetic forces is known to physicists as the "Zeeman effect," after its discoverer Paul Zeeman. (See Figure 24.) [149] LIGHT PRODUCTION [Sec. 39 It has been shown by J. Stark that the mode of vibra- tion of the electrons within an atom can also be modified by the application of a strong electrical field. A B Fig. 24 THE ZEEMAN EFFECT The two lines A and B in 1 are svpposed to be two lines in the spectrum of a luminous element, such as hydrogen or mercury vapor. When a powerful magnet is applied to the glowing element these spectral lines break up into "triplets" or complex groups of triplets, as shown in 2. This is called the Zeeman effect, and in its simplest form is readily ex- plained by the electron theory. REFERENCES See Sir Oliver Lodge's " Electrons" (1907), Chapter XI; E. C. C. Baly's " Spectroscopy " (1905), Chapter XIV, and Norman Camp- bell's "Modern Electrical Theory," second edition (1913), pp. 146-152. Zeeman's own account will be found in his "Researches in Magneto-optics" (1913). Section 39 THE CONDITIONS UNDER WHICH LIGHT IS PRODUCED Temperature Radiation; . The Spectral "Distribution Curve." -There are various special conditions under which material bodies emit light. The one which is most familiar is that of high temperature. We have already stated that the electrons in bodies take part in the heat vibrations along with the atoms and [150] Sec. 39] TEMPERATURE RADIATION molecules, and if this is true they must constantly give off electrical waves. The length of these waves must obviously depend upon the rapidity of the vibrations, and this, in turn, increases with the temperature. Hence, as the temperature of a body containing electrons is raised, the preponderating length of the waves which it gives out should become less. This is exactly what occurs in nature. When a body is being heated the first perceptible radia- tions which it emits are "heat waves." When the body becomes "red hot" it is giving off the longest of the light waves, and "white heat," which every one recognizes to be hotter than "red heat," is only possible when green and blue light have been added to the red. The wave- lengths of the blue and green are much shorter than that of red light. With still further increases in temperature, the radiation begins to include still shorter waves which make up the so-called "ultra-violet" light. On account of the relationship which holds between the temperature of a hot substance and the color of the light which it emits it is possible to get an idea of this tem- perature by means of observations upon the color of the body. The so-called "optical pyrometer" is an instru- ment based upon this principle, which does for very hot bodies what an ordinary thermometer does for cooler ones. As we have seen in Section 23, all of the molecules, and hence all of the electrons, in a body are not moving at the same velocity even if the temperature is throughout what we call "uniform." Some are moving faster and others slower, according to the "law of distribution of molecular speeds," as explained in the Section referred to. Owing to this fact we should not expect the light from a body at a given temperature to be all of the same wave- [151] LIGHT PRODUCTION [Sec. 39 length. Supposing that the particles whose vibrations are responsible for the light are electrons, it is possible to calculate the wave-length of the light corresponding to the " average molecular energy" which is characteris- tic of a given temperature. Since there are more elec- trons moving at a velocity corresponding to approximately this energy than at any other (approximate) velocity, we should expect most of the light to be of (approximately) the calculated wave-length. Measurements verify this expectation and also the idea that the electron is the ac- tual source of the radiation. The form of this " curve of distribution" of energy in the spectrum of a solid at various temperatures is shown in Figure 25. But there are electrons moving at speeds both higher and lower than this "average speed," and hence there should be light to correspond, although such light should be less intense, the further its wave-length departs from that belonging to the "average speed." Observation validates this conclusion also. However, the so-called law of the distribution of light intensities along the spectrum for any given tempera- ture is not exactly what should be expected from the molecular theory, in its ordinary form, and the efforts of physicists to explain its deviation from the expected form have finally culminated in the modern "quantum" theory of light which is discussed in another place (see Section 54). The theory of temperature radiation is based pri- marily upon the conception of a "black body" which is a body absorbing all radiation impinging upon it and showing a minimum of selectivity in its emission of radiation. The Emission of Light by Gases. Gases as well as solids give off light under the right conditions. It is only [152] Sec. 39] DISTRIBUTION CURVES 1650 Fig. 25 CURVES SHOWING THE RELATIVE INTENSITIES OF RADIA- TION OF DIFFERENT WAVE LENGTHS EMITTED BY SOLID BODIES AT VARIOUS TEMPERATURES The numbers along the horizontal scale represent the wave-length of the radiation (light or heat) in thousandths of a millimeter. The vertical scale represents the relative intensity of the radiation. It will be observed that the curves for the higher temperatures (given in degrees Centigrade) have their maxima at points corresponding with shorter waves than those characteristic of the lower temperatures. The meaning of this fact is explained in the text. These curves are those of the so-called "black body radiation." [163] LIGHT PRODUCTION [Sec. 39 when a substance is in the gaseous state that its charac- teristic "spectrum" can be obtained distinctly. It has not generally been considered possible to cause a gas to glow simply by heating it. The reason for this is to be found in the fact that under ordinary conditions gases contain very few free electrons or ions, and that even high temperatures will not produce a sufficient number of these to make the gas luminescent. In order to accomplish this end, it is necessary either to send an electrical current through the gas or to permit chemical action to take place within it. We have seen in Section 27 that both of these conditions favor ioniza- tion. Ions can be formed in a gas only when electrons are " knocked out" of the atoms which make up the gas, and it is the change in the "mode of motion" of the electrons which occurs either when they are being ejected from or when they return to the atoms which gives rise to the glow that accompanies (say) the electrical discharge through the so-called " vacuum tube." The light of the familiar " mercury vapor arc" depends upon the same principle. "Line Spectra" - The light which is given off by glowing gases differs from that emitted by solids hi respect to its " distribution " along the spectrum. Prac- tically all of the energy in the former case is concentrated about certain definite wave-lengths, the positions of which are not only constant for a given gas, but are different for different gases. The "spectrum" of a glowing gas, then, shows a series of "lines" of colored light in place of the continuous rainbow band which is produced when light from a white hot metal is passed through a prism. This special nature of the spectra of substances in the gaseous condition must be attributed to the fact that the electrons in such substances have much less freedom of movement than have those within a metal, so that they [154] Sect. 39] LINE SPECTRA can only execute vibrations of a few definite frequencies, as determined by the structure of the atoms and mole- cules of the substance. The study of the line spectra of the various elements hi gaseous form has shown that in any single element the lines can be arranged into "series," such that the positions of the individual lines hi these series that is, the wave-lengths of the lights composing them can be calculated from relatively simple mathematical for- mulae. The exact nature of these formulae differs from element to element, although it retains important points of identity throughout. It has for some time been recog- nized, on the basis of the Zeeman effect (which we have discussed in Section 38), that the partial cause of this identity lies in the fact that, in all of the cases consid- ered, the light is emitted by electrons. Only recently, however (see Section 53), have physicists been able to suggest a way in which the relatively simple electronic structure attributed to such atoms as that of hydrogen could be consistent with the very complex nature of their line spectra. REFERENCES A complete but elementary discussion of the various forms of electro-magnetic radiation is given in S. P. Thompson's "Radia- tion" (1898). A more modern treatment is the excellent one by N. Campbell in his "Modern Electrical Theory," second edition (1913), Chap- ters IX and X. Section 40 THE GAMUT OF ELECTRICAL WAVES When a beam of white light, such as ordinary sunlight, is passed through a glass prism it is broken up into the so-called prismatic colors, which are arranged in the order [155] GAMUT OF WAVES [Sect. 40 of their wave-length. The shortest waves are repre- sented by the violet light, and the longest by the red. The wave-length of the latter is about twice that of the former. The arrangement of the colors in the spectrum produced by a prism is not such that the distance of each color from the end of the spectrum is proportional to its wave-length. This relationship does hold, however, in what is called a "normal" spectrum. If a spectrum of this latter sort about a yard long could be extended so as to include all known electro-magnetic radiations (among them the Hertzian waves) it would become over five million miles in length. Of those waves which are shorter than light, the most familiar are the so-called "ultra-violet" waves, which lie just beyond the violet end of the spectrum, and the " X rays," which recent experiments indicate to be differ- ent from ordinary light chiefly in the possession of an extremely short wave, or "kink" (see Section 37), about one thousandth that of ultra-violet light. With the "X rays" we have to include the so-called "gamma rays" from radium (see Part I). The existence of these rays can be detected by their chemical effects, for example by their power to produce pictures or shadows on a photo- graphic plate. The waves which are longer than light comprise the so-called "heat rays," which affect our temperature sense, and the Hertz waves," which are employed in wireless telegraphy. All of these waves travel at the same speed hi empty space, D/Z., at the rate of 186,300 miles per second. The length of the shortest visible light wave is about one hundred-thousandth of an inch. The longest Hertzian waves measure over a mile from crest to crest. On ac- [156] Sec. 41] SELECTIVE ABSORPTION count of the tremendous speed at which light travels the highest speed known to science, and perhaps the highest possible speed the rapidity of vibration, or the " frequency" of light as it passes through a fixed point, is extremely great. About eight hundred trillion waves of violet light would pass through such a point in a second. The extreme brevity of the interval of time required for the passage of a single wave of this sort or for the completion of a single oscillation of the generat- ing electron may perhaps be realized better when it is said that one eight-hundred-trillionth of a second is a vastly smaller part of a second than a second is of the whole of historic time (i.e., one two-hundred-and-fifty- billionth). REFERENCES A very popular account of the properties of light is given in " Light, Visible and Invisible" (1910), by Silvanus P. Thompson. Section 41 COLOR AND THE ABSORPTION AND REFLECTION OF LIGHT The "Selective Absorption" of Light. When light passes through a semi-transparent body it always be- comes less intense, on account of the absorption which takes place. If the original light is colorless we generally find that it is more or less colored when it comes out of the body. This is due to the fact that white light is a mixture of lights of many different wave-lengths, and that these lights are not all absorbed hi equal proportions. The reason for this inequality of absorption is to be found in the general explanation of the absorption of [157] COLOR [Sec. 41 light which is given in Part I. A body absorbs only such light as can produce response in its electrons. If the internal forces (see Section 8) of the molecules of a given body permit the electrons which they contain to respond, to an appreciable extent, only to red light, a beam of white light passing through such a body will be colored blue-green, because the red light is removed by absorp- tion and its complementary blue-green is thus left unbalanced. Generally a body will strongly absorb light of several quite different wave-lengths. The Sensations of Color. The basis of the sensations of color is not to be looked for in the nature of light, so much as in the nature of the effects which light produces in the retina of the eye and in the nerves which are con- nected thereto. Physics as such offers no explanation of the fact that light of one wave-length gives us a sensa- tion quality almost wholly different from that produced by light of another wave-length. Neither does it account for the fact that a mixture of lights of many different wave- lengths gives white. These are problems in physiology although their solution is, of course, closely connected with the physics of light. How Color is Produced by Reflection. When light is colored by reflection from the surface of a body, as for example, from a piece of green paper, we must suppose the process to be in reality an absorption phenomenon, since most of the light undoubtedly penetrates the body to a certain extent before it is reflected. It thus passes through a portion of the body in two directions, and dur- ing this passage is subjected to the ordinary conditions of absorption. Bodies differ in their power to reflect light, primarily on account of the fact that the electrons which they contain are not similarly conditioned by their surround- [ 158 ] Sec. 42] REFRACTION ings. The best reflectors will in general be the metals, since these contain free electrons in large numbers. REFERENCES For a semi-popular discussion of color and absorption, refer to "Light" by R. C. Maclaurin, Chapters II and in. See also Franklin and MacNutt's "Light and Sound" (1909), especially Chapter X. A very recent and comprehensive exposition of color problems is that of M. Luckiesh, "Color and Its Applications (1915). Section 42 THE REFRACTION OF LIGHT How Columns of Light are Bent. Light may be thought of as moving in columns or "pencils" the fronts of which are perpendicular to the direction of motion of the light. When the front of a column strikes the surface of a transparent body the edge which meets the surface first must be retarded in its motion if, as is generally the case, light moves slower in the body than it does in empty space. Hence, the edge in question falls behind the other parts of the front and the plane of the front is rotated. Since in general the column will move in a direction at right angles to the plane of the front, the light is bent at the surface of the body. If the column of light strikes the surface at right angles there will be no bending because all parts of the front will hit the surface at the same time. The more acute the angle of impact, the greater will be the bending. This bending of a light column or pencil when it passes through a surface obliquely is called refraction. As is well known, refraction lies at the basis of the effects pro- [159] REFRACTION AND DISPERSION [Sec. 42 duced by all lenses and prisms. To explain the details of the process is beyond the scope of this book, since they are complicated and do not depend in any especially significant way upon the modern theory of matter, but it should be noted that refraction depends solely on the fact that the velocity of light is different inside and out- side of the medium in question. "Dispersion." -The same substance refracts light waves of different lengths to different extents. This produces what is known as dispersion, a process upon which the formation of spectra by prisms is based. It has been shown experimentally that the degree in which a given substance refracts light of any specified vibration period is closely related with the natural period of vibra- tion of the molecules of the refracting substance itself. As the vibration period of the transmitted light approaches that of the substance, the refraction increases enormously, and then changes suddenly. It is this difference in the refractive power of a single substance for different wave- lengths which makes possible the " dispersion" of color, as in the ordinary prismatic spectrum. "Dielectric Capacity" and the "Index of Refraction" The degree to which a substance refracts light of speci- fied wave-length is called its index of refraction for this light, and it has been shown that a definite relation- ship exists between the dielectric capacity of a substance and its index of refraction. (See Section 33 for another connection of dielectric capacity.) For many solids and liquids this relationship is a complicated one when the frequency of the light considered is close to that of the molecules of the substance itself. However, in the case of gases, and if sufficiently long waves are used, for all bodies, the refractive index is found to be proportional to the square-root of the dielectric capacity. [160] Sec. 43] ROWLAND'S EXPERIMENT The dielectric capacity of a body measures the ease with which the electrical components of its molecules undergo temporary separation (without decomposition of the molecule) through the activity of outside electrical forces. In general, the more the particles of a substance respond to the force of a light wave the greater is the effect upon the speed of the wave. Hence it is easy to see why, within the above-mentioned limits, a substance which has a high dielectric capacity should also have in general a high index of refraction. Both refraction and absorption occur to the greatest extent when the frequency of the light which is passing through a body most closely approximates the natural frequency of vibration of the molecules of the substance, since under these conditions the response of these mole- cules is the greatest possible. REFERENCES On refraction and reflection, consult R. C. Maclaurin's "Light," Chapter VI. Section 43 ROWLAND'S EXPERIMENT The fact that a magnetic field is produced by the mo- tion of an electrically charged body was proven by the late Professor Rowland of Johns Hopkins University. Professor Rowland's experiment was a very simple one. Everybody is familiar with the fact that the presence of a magnetic force can always be detected by the deflec- tion which it causes in the position of a compass needle. Some strips of gold-leaf were cemented upon a hard rubber disk, and after they had been charged with elec- tricity the disk was rotated very rapidly. The needle of [161] ELECTRONS AND MAGNETISM [Sec. 44 a delicate compass placed near by showed a distinct deflection, which could only be ascribed to the magnetic forces generated by the motion of the charged strips of gold-leaf. The relation between the direction of the magnetic forces and that of the moving electricity or electric current is shown in Figure 26. Fig. 26 THE DIRECTION OF THE MAGNETIC FORCES ABOUT A MOVING ELECTRICAL CHARGE Magnetic forces exist around every moving electrical charge. If the charge is positive and is moving in the direction of the large arrow the magnetic forces will possess the arrangement and direction indicated by the black circle and its small arrows. If the charge is negative it must move in the opposite direction to produce the same magnetic effect. REFERENCES On the relation between electricity and magnetism, see Oliver Lodge's "Modem Views of Electricity," Chapter VII. Section 44 THE DEFLECTION OF MOVING ELECTRONS BY A MAGNET The principle which is employed in the dynamo for the generation of the electrical current is illustrated in certain modern experiments and observations to which we have already referred in several places. [162] Sec. 45] DIA- AND PARA-MAGNETISM In Section 25 we have mentioned the fact that the so-called cathode rays, which in reality consist of very rapidly moving electrons, are capable of being deflected by a magnet. Where the rays impinge upon the walls of the "vacuum tube" in which they are produced they cause a bright spot of light. If a strong magnet is brought near the tube this spot of light is seen to move. This deflection of the rapidly moving charges in the cathode rays has been very carefully studied and the results embodied in what is believed to be one of the most fundamental and exact of electromagnetic laws; "The Law of the Deflection of Moving Charges in a Magnetic Field." REFERENCES See J. J. Thomson's "The Discharge of Electricity Through Gases" (1898), Chapter on the "Cathode Rays," p. 137; and Oliver Lodge's "Electrons" (1906), Chapters VTH-XIX inclusive. Section 45 ALL BODIES ARE MAGNETIC Dia- and Para-magnetism. One ordinarily thinks of the vast majority of substances as "non-magnetic." Iron and steel seem to be marked out from other bodies by their possession of magnetic powers. As a matter of fact, however, every known substance possesses magnetic properties. There are two kinds of magnetism, dia- and para- magnetism. When a dia-magnetic body is placed in the field of a strong magnet its long axis tends to turn so as to be at right-angles to the direction of the lines of mag- netic force. Para-magnetic bodies, on the other hand, tend to place their long axes parallel to their lines of force. [163] MAGNETISM [Sec. 45 The fact that all bodies have magnetic properties in- dicates from the present point of view that they all contain electrons in motion. Whether a particular body is dia- or para-magnetic probably depends upon the exact way in which the electrons are moving and upon the conditions which limit this motion. Permanent Magnetism. Iron, cobalt and nickel differ from other substances hi their power to acquire strong permanent magnetism. This property may be explained in the following manner. If there are electrons rotating within or about the atoms of a substance, each atom will behave like a very small magnet. But in a visible body there would be so many of these minute magnets with their positive and negative poles pointing "every which way" that the resulting outside effect would be prac- tically nil. In order that such an external effect should be pro- duced it would be necessary for a number of the little magnets to point hi the same general direction, so that the individual influences would be added to, instead of neu- tralizing, each other. To bring the atoms into line in this way an outside magnetic force might be applied, for it is known from experiments with a compass needle that one magnet can cause another to turn upon its axis. It is probably some such reaction of the atomic magnets as this which produces all of the phenomena of dia- and para-magnetism. In the majority of bodies the atoms do not remain in magnetic line when the outside force is removed. But in others they do tend to remain in line and these latter are said to possess permanent magnetism. If magnetization actually does involve a turning of the molecules on then* axes, we should anticipate that a cer- tain amount of the energy which is used in the process [164] Sec. 46] RADIO-ACTIVE ELEMENTS might be converted into heat, since additional motion is imparted to the molecules. This effect can actually be observed in the case of the more magnetic substances, and is at the basis of a troublesome loss of energy in dynamo work technically called " hysteresis." REFERENCES An exhaustive discussion of "Magnetism" by Shelf ord Bidwell will be found in the eleventh edition of the " Encyclopaedia Bri- tannica." For a simple and briefer account see Norman Campbell, loc. cit., Chapter V. Section 46 RADIO-ACTIVE SUBSTANCES The Discovery of the Radio- Elements. The first sub- stance found to be radio-active was uranium. The dis- covery was made by Becquerel in 1896. M. and Mme. Curie, however, soon found that the ore from which uranium was extracted was four times as radio-active as pure uranium itself, and this observation led to the dis- covery of radium, a new chemical element having a radio-activity over a million times greater than that of uranium. Later on the same investigators laid bare fur- ther and even more powerful radio-active bodies: polo- nium and actinium. Another element, thorium, already known to chemists, was found by Schmidt to be radio- active to about the same extent as uranium. "Disintegration Series" A complete list of the radio- active elements is given in Table II of Section 5. Most of the substances named in this table are what may be called " radio-active products," that is, they are bodies which are produced in the course of radio-activity. Ra- dium, for example, apparently breaks up into helium and " niton," both of which are gases. The emanation [165] RADIO-ACTIVITY [Sec. 46 (niton) decomposes, in turn, forming a solid substance, radium A, which is soon converted by a similar change into radium B, and so on. It is supposed that the final product of this series of changes is chemically identical with lead. Similar " disintegration series" of substances are de- rived from uranium, thorium, and actinium, as shown in the table (II, Section 5). A series may " branch" at certain points. It is now believed that both radium and actinium are ultimately derived from uranium, by such a process. Besides these special radio-active bodies others have now been shown to possess slight radio-active powers. Many investigators believe that all substances are some- what radio-active, but it is not yet entirely certain whether the faint activity which exists, is an intrinsic property of the substances or whether it is to be ascribed to the presence within them of small traces of the radio-active bodies proper. The Law of Decay of Radio-Adice Substances. As stated in Part I, the rate of decay of a radio-element, so far as yet found, is independent of all external condi- tions. The law of this decay is that, for a given element, the same fraction of any specific volume will always break up in the same period of time. Thus, if we should start with an ounce of radium A, it would be hah* gone at the end of three minutes. In three minutes more one-half of the remainder or one-quarter of the original amount, in addition would have broken up, and so on. It is clear that a law of change of this sort would theoretically never lead to the total disintegration of any given quantity of the substance, however small. This is why the "life " of a radio-element is stated in terms of the time required for one-half of a given amount of it to decay. [166] Sec. 46] LAWS OF RADIO-ACTIVITY These " half-times" vary from about twenty-six bil- lion years in the case of thorium to only one ten-billionth of a second in the case of radium C'. The intensity of the radiation from any radio-active substance is naturally inversely proportional to the time required for a quantity of it to decompose. It has been shown by Geiger and Nuttall that the shorter the period of lif e of a radio-element the faster its alpha particles move. There is a similar relationship for the beta particles. The Position of the Radio-Elements in the Periodic Table. The position of the principal radio-active elements in the periodic table is especially worthy of notice. It will be seen (Section 6) that not only are they among the heaviest of the elements, but that all of the heaviest ele- ments are radio-active. Apparently the relative insta- bility of the radio-elements is a corollary of complexity of internal structure, and is analogous to the unstable char- acter of the higher chemical complexes, such as the organic compounds of which living bodies are made up. However, mere weight is not the only factor involved, since uranium, the heaviest element known, and the parent of the majority of the radio-active substances, is one of the least active of them all. It is estimated that the time of decay of uranium is long compared with the age of many of the minerals hi which it is found. If it were not for this fact, and the similarly low activity of thorium, all signs of radio-activity would have disap- peared from the earth long ago. It is probable that other series of radio-elements, perhaps of even greater atomic weight, have existed in the past, but have left no recog- nizable traces behind them. REFERENCES E. Rutherford: " Radio- Active Substances and their Radiations" (1913), (Standard treatise). [167] METHODS IN RADIO-ACTIVITY [Sec. 47 F. Soddy: "The Interpretation of Radium" (1912) (popular lectures), and "The Chemistry of the Radio-Elements" (1915). R. K. Duncan: "The New Knowledge" (1905), Parts 4 and 5, pp. 87-193 (popular). C. W. Raffety: "An Introduction to the Science of Radio- Activity" (1909). A. T. Cameron: "Radio-Chemistry," (1910). Section 47 HOW THE RAYS FROM RADIUM ARE STUDIED We have seen in Part I and in Section 25 that moving electrically charged bodies can be turned from their straight-line paths, or deflected, by the action of a mag- net. Hence it is possible to get a first indication as to which, if any, of the rays from radium are electrical particles, and which are electrical waves, by placing a magnet across their paths. The first type of rays will be deflected while the second will not. The extent to which they are deflected, when combined with certain other measurements which have been mentioned hi Section 25, shows the speed at which they are travelling, as well as the sign of their charge and the ratio of this charge to their mass. When an experiment of this sort is tried upon a bundle of rays from radium, certain of the rays are found to be uninfluenced and to move on in a straight line as before. Another set is deflected slightly, while a third suffers very marked change in path. The last two are diverted in opposite directions, which proves then- charges to be positive and negative respectively. The first type of rays are the " gamma rays," the second the " alpha rays," and the third the "beta rays." The methods which are used in measuring the speeds, charges and [168] Sec. 48] NATURE OF ALPHA RAYS masses of the alpha and beta particles are similar to those described in Section 25 for the " cathode rays." The fact that the beta particles can penetrate even thick pieces of solid matter is proven by simply directing a pencil of beta rays towards a plate composed of the solid substance in question, and noticing that the rays appear in a somewhat diffused and attenuated state on the other side of the plate. As already mentioned, C. T. R. Wilson has devised a method by means of which it is possible to photograph the paths of single alpha particles in their motion through a gas. REFERENCES The methods employed in the study of radio-activity are popu- larly discussed by R. K. Duncan in his "New Knowledge" (1908), Part IV. Section 48 HOW RUTHERFORD PROVED THE ALPHA RAYS TO BE HELIUM ATOMS The fact that the alpha rays are atoms of helium was proved in a very striking and simple experiment by Ernest Rutherford. Helium is a gas, and it is a well-known fact that every gas when subjected to the action of an electri- cal discharge gives off light of a peculiar color, which can be split up by a glass prism into the so-called " spectrum" of the gaseous substance (see Section 39). Rutherford very carefully removed all traces of helium from a large glass tube and then placed within this tube a smaller one of very thin walls containing gaseous helium. After per- mitting the apparatus to stand for several days he passed an electrical discharge through the larger tube, and ex- amined the light to see if the spectrum of helium was present. He found it to be absent, showing that ordinary [169] NATURE OF GAMMA RAYS [Sec. 49 helium could not pass through the walls of the smaller tube. He now replaced this latter tube by an identical one containing not helium but radium emanation, which is constantly throwing off alpha rays. Since the walls of the tube were thin the great speed and energy of the particles in the rays enabled them to penetrate the walls and enter the atmosphere of the larger vessel. After the apparatus had stood under these conditions for a period of time Rutherford again passed an electrical discharge through it, and found that it distinctly showed the spectrum of helium. This seems to be conclusive proof that the alpha ray particles are actually atoms of helium. The mass or weight of the alpha particles has also been measured and has been shown to be of a magnitude in harmony with this conclusion. REFERENCES See Rutherford's " Radio-Active Substances and their Radia- tion" (1913), pp. 137-140 and Chapter XVII. Section 49 THE NATURE OF THE GAMMA RAYS We have seen in Section 37 that electrical waves can be regarded as kinks hi lines of electrical force which are produced whenever the velocity of motion of an electri- cally charged particle is altered. Now we know that the beta particles bear electrical charges, and that they are suddenly emitted from the atoms of radio-active sub- stances at a tremendous speed. In accordance with the theory, then, they ought to give rise to electrical waves of very high frequency, that is, the kinks which are pro- [170] Sec. 49] SECONDARY RAYS duced in their lines of force should be exceedingly sharp. This conclusion seems to harmonize with what we know about the gamma rays, which are apparently made up of the electrical waves in question. When the beta particles are stopped in their headlong flight by striking the atoms of some other substance we should expect further gamma (or X) rays to be produced, because any change hi the velocity of one of these par- ticles should give rise to an electrical wave, whether the change be of the nature of an acceleration or a retarda- tion. It has been found by experiment that such rays are actually produced under the circumstances specified. They belong to the class of " secondary rays" hi which, also, must be included the further beta radiation which is set up by the gamma rays themselves when they are absorbed by material bodies. Another type of secondary rays produced under en- tirely analogous conditions and probably of the same gen- eral nature are the well-known "X rays." Certain very recent experiments which prove beyond a doubt that the latter, and probably also the gamma rays, are not moving material or electrical particles, in the usual sense, will be discussed in Section 55. In that place, also, will be considered the explanation of the great power of gamma and X rays to penetrate bodies opaque to ordi- nary light. REFERENCES Concerning the gamma rays, see R. K. Duncan's "The New Knowledge" (1908), pp. 109-112. Also Norman Campbell's "Mod- ern Electrical Theory," second edition (1913), pp. 273 /. [171] INTRA-ATOMIC ENERGY [Sec. 50 Section 50 THE ENERGY OF THE ATOM The enormous energy of the inner constitution of the atom is probably very closely connected with the great stability of atoms in general. Even the atoms of radium are only relatively unstable, since if we consider any single radium atom it has what we might call an "ex- pectation of lif e " of several thousand years. The great stability of the atom is due to the fact that the forces which hold the parts of the atom together are very great, and the magnitude of these forces is closely associated with that of the intra-atomic energy. We have several times spoken of the forces of chemical affinity and cohesion as residual in character, as repre- senting the attractions which are, so to speak, "left over" after the parts of the atom have been cemented together. If chemical energy (for example) is a residue of the intra- atomic energies we should expect it to be relatively much smaller than these energies, just as the stability of the molecule is relatively much less than that of the atom. We have become accustomed to the quantities of energy liberated in chemical changes and have taken them as standards, so that when we come to consider the primary energies of the atoms these seem unbelievably great. REFERENCES Concerning intra-atomic energies read R. K. Duncan "The New Knowledge," Part 5, Chapter HI. The energy liberated in radio-activity is discussed by J. J. Thomson in his "Electricity and Matter" (1904), pp. 152 /. [172] Sec. 61-52] RADIO-ACTIVITY OF POTASSIUM Section 51 THE RADIO-ACTIVITY OF POTASSIUM As nearly everyone knows, the element potassium is a constituent of ordinary caustic potash. Yet this common element has been shown by Norman Campbell to be definitely radio-active. The rays which it emits appear to be principally of the "beta" type, the intensity of the rays from potassium being about one one-thousandth that of the beta rays from uranium. All of the potassium salts are radio-active, and thus far no evidence has been adduced to show that this activity is due to impurities. Other of the so-called alkali metals, for example rubid- ium, have been shown to possess slight radio-activity. REFERENCES See Norman Campbell: "The Radio-Activity of Potassium" in the Proceedings of the Cambridge (Eng.) Philosophical Society for 1908, Vol. 14, pp. 657-567. Also Campbell's " Modern Elec- trical Theory," second edition (1913), pp. 187-188. Section 52 INORGANIC EVOLUTION We have seen in Section 39 that all of the elements possess characteristic " spectra" which consist of series of lines. For most elements these series are quite complex and the positions of the separate lines in the spectrum, that is, the wave-lengths of the lights which compose them, do not change. However, the exact number of lines which are present depends to a certain extent upon the conditions under which the element is made luminous. The spectrum from a flame has fewer lines than that from an electric arc. Now astronomic observations have shown that in the [173] INORGANIC EVOLUTION [Sec. 52-53 light from many stars the spectra of certain elements are curiously incomplete. In general, the hotter a star is the more incomplete the spectra of its elements appear. If we suppose that the different sets of lines hi the spec- trum of the element are produced by the vibrations of different electrons, or systems of electrons, within the atom, it is natural to infer that the simplification of the spectra in the hottest stars stands for an actual breaking up of the atoms in these stars. But in addition to this it has been shown, by Sir Nor- man Lockyer on the basis of spectroscopic evidence, that hi the very hottest stars are to be found only the simplest elements, such as hydrogen, helium, etc., along with partly formed elements of higher atomic weight. The cooler a star is the more elements it contains, and the higher are the atomic weights of these elements. These facts suggest that the elements are undergoing an actual evolution in certain of the heavenly bodies, an evolution which depends primarily upon the fact that these bodies are passing through a process of cooling. The lightest and simplest elements are formed first, and after them the heavier and more complex ones. Among the latter are the radio-active substances. REFERENCES Sir Norman Lockyer's own account will be found in his "Inor- ganic Evolution, as Studied by Spectrum Analysis." A simpler presentation of the facts is given by R. K. Duncan in Part VI of "The New Knowledge" (1908). Section 53 THEORIES OF THE STRUCTURE OF THE ATOM Thomsons Theory. Up to very recent times the most promising conception of atomic structure was that elabo- rated by Sir J. J. Thomson in a highly mathematical [174] Sec. 63] THOMSONIAN ATOM paper published in the English Philosophical Magazine, in 1904. Although it is practically certain that the theory, as originally stated, is not accurately true, it must never- theless be admitted that no other view has appeared which gives us an equal feeling of insight into the mystery of the chemical elements. On the basis of the known laws of electrical attraction, Thomson calculated the constitution of the series of hy- pothetical atoms which would be generated by the suc- cessive addition of electrons to a large sphere of positive electricity always of sufficient charge to just neutralize the electrons. For simplicity, he assumed the electrons to be concentrated in a single plane. He was able to show that the electrons would arrange themselves into rings and that with an increase in the total number there would be a periodically recurring tendency for fresh rings to be formed, in addition to those already present. How- ever, the latter, also, would be obliged, from time to time, to increase their electronic contents in order to maintain the stability of the system. With the formation and development of each new ring the properties of the atoms might be expected to repeat to a limited extent, those which were passed through in the development of the previously formed ring. The presence of the latter owing to the general modifica- tion of the forces of the system which it would involve -would preclude a*n exact repetition of properties. It is clear that a very close analogy exists between this theoretical series of atoms of Thomson's and the actual system of the elements, as revealed in the periodic table. The first member in each " period" in the table (see Sec- tion 6) may be supposed to coincide with the formation of a new ring, which would contain, in the given element, only one electron. [175] STRUCTURE OF ATOM [Sec. 63 As stated in Part I, the recent "nucleus theory" of the structure of the atom supposes that the positive elec- tricity, instead of forming a large sphere, coextensive with the general volume of the atom, is concentrated in a very minute central region. However, we still hear of concentric rings, or shells, of electrons surrounding this nucleus, and it is probable that, in a general way, the arrangement of the electrons resembles that in the Thomsonian atom. The Nucleus Theory. The " nucleus theory" was proposed by Rutherford to explain the manner in which the alpha rays from radio-active substances are scat- tered as a result of their passage through material bodies. This scattering may be supposed to be caused by the ac- tion of the intrinsic forces of the atoms of the body upon the charged particles which make up the rays. The degree of scattering is measured by the angle made by the path of the ray as it leaves the thin sheet of substance, through which it has passed, and its original line of travel. Now experiment shows that even when the average degree of scattering is relatively low, a small fraction of the rays are turned through a very large angle, often so that their motion is actually reversed in direction. Since the original speed of the alpha particles and their charge are known, it is possible to calculate what con- ditions would be necessary to cause a deflection of this magnitude. In the case of the element gold, such calcu- lations show that the positive electricity of the atom must be concentrated on a sphere about one trillionth of an inch in diameter, which is only one ten-thousandth part of the diameter of the atom itself. It is estimated that in passing through hydrogen gas, some of the alpha ray particles come within one twenty- five-trillionth of an inch of the centers of the positive [176] Sec. 53] NUCLEUS THEORY OF ATOM nuclei. Since this is less than the diameter of an electron it seems probable that the bare positive nucleus is smaller than are the negative particles hi the atom. In Section 25 we have seen that on the assumption that the electron is made of pure negative electricity, it is possible from a knowledge of its mass and charge to calculate its size. Now, the facts indicate that the mass (or weight) of the positive component of the atom is enormously greater than that of the electron, so much so that it is practically equivalent to the total weight of the atom. On this basis, calculation shows that the nucleus of the hydrogen atom if its mass is wholly electrical must have a diameter of about one ten-quadrillionth of an inch, or one eighteen- hundredth that of the electron. This result appears to be in harmony with that reached by the study of the alpha- ray scattering. The supposition that the positive components of the nucleus of most atoms have electrons closely bound up with them is necessitated by the facts of radio-activity. The tremendous speed with which the electrons of the beta rays are sent off, demands original intra-atomic forces which could only result from an exceedingly close packing together of the atomic parts which are involved. Moreover, there seems little room for doubt that there are at least two classes of electrons in the atom, (1) those which directly determine its physical or chemical proper- ties, and a fraction of which can be separated from the atom and replaced again without great difficulty, and (2) those which leave the atom only during a radio-active change, and the loss of which means an apparently irrevocable alteration in the fundamental nature of the element. It seems probable, however, that electron groups of varying degrees of superficiality, so to speak, exist within [177] STRUCTURE OF ATOM [Sec. 53 complex atoms. These may be thought of as correspond- ing with the successive rings of the Thomsonian atom. The most superficial system of all is that of the so-called valency electrons, which are probably responsible for the more obvious chemical properties of the substance and, as Stark believes, for its band spectra. Still deeper electron layers give rise to the recently discovered X ray spectra (see Section 55). The Number of Electrons in the Atom. Numerous attempts have been made to calculate the number of electrons in the atoms of the various elements. This can be done on the basis of the degree hi which rays of several sorts are scattered in passing through sheets of the elements in question. The more electrons there are- that is, obstacles for the rays to encounter the more scattering will occur. Results obtained by a number of different methods indicated that the number of electrons is approximately equal to one-half the atomic weight. But it is clear that if, as in the case of hydrogen, one unit of positive charge is always associated with one unit of weight, the number of electrons in the atom would have to be accurately equal to the atomic weight in order to balance the charge of the nucleus. We are led, there- fore, to suppose that there are as many electrons bound up in the nucleus as there are in the body of the atom. The number of these latter, " external" electrons is con- trolled by the magnitude of the unbalanced charge of the nucleus, which is represented by the "atomic number" (vide infra). As a matter of fact, as an examination of Table I, Section 5, will show, the nuclei of the heavier elements must contain more electrons than the body of the atom. Isotopism. Radio-activity, as we have stated, is indubitably an affair of the nucleus, and it appears to [178] Sec. 53] ISOTOPES AND ATOMIC NUMBERS depend upon the ejection either of a doubly, positively, charged helium atom alpha particle or a singly, negatively, charged electron beta particle. It is ob- vious that if the nucleus loses one alpha particle and then two electrons its resultant charge will be the same as before these three radio-active changes had occurred. Consequently, the number and arrangement of its exter- nal electrons will be the same as before the change, and the two elements, although differing in atomic weight by four units, will have identical chemical and physical properties. As shown in Table II, Section 5, many such so- called isotopes have been demonstrated among the radio- active elements. A mixture of isotopes acts like and indeed is a chemically pure substance, and there is no chemical reaction which can be used to separate its components. However, these components can easily be distinguished from each other by radio-active tests. Chemical tests distinguish between only ten kmds of radio-elements, whereas radio-active tests show thirty- four or more. Atomic Numbers. The expulsion of an alpha particle from an atom causes the corresponding element to move two places from right to left in the periodic table (see Section 6); the loss of a beta particle reverses this move- ment one place. It appears, then, that the position of an element in the table depends not upon its atomic weight, directly, but upon the resultant positive charge of its nucleus, which is called its atomic number, and the successive places in the table correspond with unit dif- ferences in this charge. Consequently, in so far as the table is regarded as a chemical schema, its principle should be restated as follows: "All of the chemical properties of the elements are periodic functions of their atomic numbers (instead of weights)." Chemical analysis, it \[179] STRUCTURE OF ATOM [Sec. 63 would appear, is really an analysis of matter only into different types, not into different elements. The recent discovery of a means of measuring the wave- lengths of X rays has shown that all of the elements, under the right conditions, give off X rays, the lengths of which are characteristic of the element in question. It has been found possible to calculate these wave-lengths by means of a very simple formula involving the atomic number or, vice versa, to deduce the atomic number from the wave-length. Measurements of this sort by Moseley indicate that the atomic number of gold is 79, and that from aluminium to gold, in the periodic table, only three possible elements are missing. The atomic number of the heaviest element, uranium, appears to be 92, although there is some disagreement concerning this point. If this is correct and if uranium is the heaviest element which can exist, then it means that only 92 different chemical elements are possible. The Hydrogen Atom. In some respects hydrogen occupies a unique position hi the system of the elements. The alpha ray particle, which is a helium atom with a double positive charge, may be thought of as consisting of the helium nucleus stripped of its external electrons. The ordinary hydrogen ion, bearing one positive charge, is probably the bare nucleus of the hydrogen atom. How- ever, the alpha particle contains four units of weight to two of charge, while the hydrogen ion has one unit of weight to one of charge. On the basis of the argument previously presented it would appear that while the helium nucleus has bound up with it two electrons, the hydrogen nucleus, or ion, consists of pure positive electricity, and is, hi fact, a positive electron. On the supposition that the uncharged hydrogen atom is thus made up of two electrical particles, one positive [180] Sec. 53] THE HYDROGEN ATOM and the other negative, the Dutch physicist, Bohr, has shown that by use of the known electro-magnetic laws and the new "quantum" theory of light (see Section 54), some very remarkable conclusions can be reached. For a long time it has been known that the position of the " lines" in the hydrogen spectrum can be calculated with amazing exactness by means of a certain mathematical formula (named after its discoverer, Balmer) which had been arrived at empirically by a method of trial and error. Up to the recent work of Bohr, however, it seemed im- possible to derive this formula by means of the laws of simple mechanics and electricity from any conceivable hypothesis about the structure of an atom, especially from a simple one. But by introducing the assumptions of the new theory of light, Bohr has shown that the for- mula in question follows very simply from the conception of the hydrogen atom above described. This result can hardly be considered other than epoch-making in the history of atomic and optical theory. Bohr's theory disposes of a difficulty which has bothered physicists for some time, u/z., the problem as to why the electrons within the atom continue to rotate about the center of attraction, instead of rapidly falling into it. Centrifugal force would keep them out as long as they maintained their speeds, but the ordinary laws of radia- tion demand that these speeds should constantly dimin- ish, owing to the continuous emission of energy in the form of electrical waves. However, the quantum theory necessitates that such emission should occur only in discontinuous units of fixed magnitude. Consequently, it would be impossible for the electron to drop gradually into the atom; it would be obliged to fall in steps or jerks. Each jerk would generate a characteristic wave, corre- sponding with a definite line in the spectrum of the ele- [181] THE QUANTUM THEORY [Sec. 64 ment it being consistent with the facts to suppose that line spectra are formed only when electrons are separated from or returned to a definite place in the atom. When the electron has completed any drop and radiated the corresponding energy it remains in equilibrium, probably rotating about the nucleus, but no longer radiating. It is difficult to handle mathematically the problems connected with the exact structure of atoms more com- plex than that of hydrogen, but it seems probable that these atoms are made up of larger numbers of positive particles, and electrons, rotating in more complex ways. It is apparent that there is a close analogy between the structure and internal processes of atoms, as conceived in modern theory, and those of astronomic systems. This is why the type of atom above considered is some- times characterized as the "Saturnian atom." REFERENCES J. J. Thomson's theory of atomic structure is well summarized in popular form by R. K. Duncan in "The New Knowledge " (1908), Part 5, Chapter II. Thomson's own account appears in popular form in his "Electricity and Matter" (1904), Chapter V. See also Norman Campbell's "Modern Electrical Theory," Second edition (1913), Chapter XIII. Bohr's articles are in the Philosophical Magazine for July, September, and November, 1913, Vol. 26, pp. 1, 476 and 857. J. J. Thomson's latest theory will be found in the same journal for October, 1913, p. 792. On isotopes see Frederick Soddy's "The Chemistry of the Radio-Elements" (1915), Part II. On atomic numbers and the Bohr atom: W. H. and W. L. Bragg's " X Rays and Crystal Struc- ture" (1915), pp. 77 to 87. Section 54 THE QUANTUM THEORY OF RADIANT ENERGY The Nature of the Theory. When light travels from one part of space to another there is a motion of a certain [182] Sec. 54] LIGHT ATOMS amount of "radiant energy" through the intervening dis- tance, and at any time during the motion this energy must be localized in a definite region of space. The ques- tion as to whether radiant energy is or is not atomic may consequently be asked in the following way. Is light energy travelling in free space spread out uniformly and continuously in that space, or is it concentrated hi a limited number of relatively small and clearly defined regions, the amount and intensity of the energy in each of these regions being invariable for a given kind of light? The first alternative is the one which had been accepted up to quite recent times. It assumed that radiant energy can be emitted from bodies continuously, in any amount and at any intensity, that it spreads out uniformly from its source like a perfect non-molecular fluid, becoming steadily weaker the further it goes from the source, ac- cording to the well-known " law of inverse squares." The second alternative, which corresponds to the modern doctrine of light " quanta," denies all of these assump- tions. It states that light is not radiated from bodies continuously, but instead in sudden outbursts, each of which is of definite magnitude and intensity determined only by its wave-length or frequency. It would be im- possible for a body to radiate a fraction of one of these units, so that quantities of radiation which are not inte- gral multiples of the units in question cannot exist. Moreover, the intensity of one of these light atoms, or quanta, does not decrease with its distance from the source, and consequently it does not spread out as it travels. The reason that light seems to fall off in intensity with distance lies in the fact that the number of light atoms to be encountered in a given region of space natu- rally becomes less the farther that region is from the emit- [183] THE QUANTUM THEORY [Sec. 54 ting body. This conception of the structure of a beam of light means that all optical images are really built up on the same principle as the ordinary " half -tone" engrav- ing, that is, they are made of minute dottings or stipplings far too small to be detected by the eye. (However, the sensitiveness of the retina is so great that a visual sensa- tion can be produced by relatively few quanta of the right kind of light.) Such a striking alteration as this in the theory of light cannot be without strong grounds. In discussing these, no attempt will be made to follow the order of their his- torical appearance in connection with the problem. The Photo-Electric Effect. We have seen in Chapter V, that many solid bodies, especially metals, under the influence of high temperatures, give off electrons. It has been found that they also can be made to emit elec- trons at ordinary temperatures if their surfaces are exposed to the action of ultra-violet light or X rays. If we are not to assume that the metal becomes radio-active under the action of the light, we must suppose that the energy of motion of these emitted electrons comes from the light itself. The very curious fact now appears that this energy that is, the highest speed with which any of the electrons travel is independent of the intensity of the light which shines upon the surface. If the light is weak, relatively only a few electrons are given off, but those which do appear have the same velocity which is characteristic of the effect with lights of higher intensity. These results seem to be compatible only with some such notion of the atomic structure of light as we have just outlined. Measurements upon the speeds of the electrons in the photo-electric effect as the phenomenon is called prove that their energy of motion, although independent [184] Sec. 54] THE PHOTO-ELECTRIC EFFECT of the intensity, is closely proportional to the "frequency" of the rays employed, that is, the shorter the "wave- length " of the radiation the faster the emitted electrons move. This connection between "frequency" and energy is one of the fundamental principles of the quantum theory; it resolves itself ultimately into the statement that the energy of any light quantum is directly propor- tional to its frequency. The higher the frequency the higher the energy, but for a given frequency the energy is fixed and invariable. If this principle is valid, it is clear that it should be im- possible to generate quanta of high frequency from those of low frequency, since this would contradict the law of the conservation of energy. In accordance with this, it has been shown experimentally that when one kind of radiation is changed into another as, for example, " fluoresence " and "phosphorescence" the alteration in wave-lengths is, in most cases, from high to low frequency. This empirical principle is known as Stores' law. It holds for the transformation of X rays, as well as for those of ordinary light. Such transformations as these must always be accom- plished by permitting the light to fall upon some material body, and there is practically no doubt that the active factors in the change are the electrons which are bound up in the atoms of the body. Experiment makes it prob- able that all such electrons have natural rates of vibration, which depend upon the constitution of the atoms or mole- cules of which they form parts. The photo-electric effect and its analogues in all probability depend upon the ejection of electrons from atoms under the influence of the electrical forces in the light ray. The quantum theory, however, makes it seem probable that (1) the energy of the light cannot be transferred to the electron unless the [185] THE QUANTUM THEORY [Sec. 64 frequency of the light is at least approximately the same as that natural for the electron itself, and (2) if the elec- tron takes up any of the energy of the light quantum it must take it all. In harmony with this view it is found that so far as present measurements permit us to judge, the energy of the electrons emitted under the action of light and X rays is the same as that of the respective light quanta. Other Fads Underlying the Theory. There are fur- ther important results of the idea that an electron, atom, or molecule can take on or part with only whole light quanta, and only such quanta as have approximately their own natural frequencies. For example, it can be shown theoretically, upon certain reasonable assumptions with regard to the molecular conditions underlying the facts of specific heat, that if the quantum theory is true the specific heats of all substances at or near absolute zero, should themselves be very close to zero. At low tem- peratures the average energy of vibration of the atoms is so small that only a few of them are able to retain whole quanta of energy, and if they are unable to retain whole quanta they cannot have any energy at all. Consequently, at low temperatures the atoms of a body lose their power to absorb heat, and hence the body suffers a radical de- cline in its specific heat. (See Section 24.) The recent experimental work of Nernst and his co-workers has shown that such changes in the specific heats of bodies actually do occur, and that their manner of occur- rence satisfies expectations based upon the quantum theory. However, probably the most important consideration of all which is presented at some length in Chapter X, and which, unfortunately, is too involved to be developed much more completely here is that which first led the [186] Sec. 54] HIGH AND LOW TEMPERATURES German physicist, Max Planck, to propound the quantum theory. It concerns the manner in which the amounts of light of different wave-lengths emitted by glowing solid bodies at various temperatures are related with the wave- lengths and temperatures in question. This relation is represented in the " curve of distribution" of energy in the spectrum, which has been discussed hi Section 39. For any given temperature there is a certain wave-length which has a higher intensity than any other. Wave- lengths greater or less than this have increasingly lower intensities. Various only partially successful attempts had been made by several physicists to explain the exact relations between temperature, wave-length, and inten- sity in terms of the electron theory of radiation. Planck found that such an explanation could be given if it be assumed that the radiation takes place discontinuously, and that each quantum of light radiated has an energy proportional to its frequency, i.e., inversely proportional to its wave-length. The demonstration of the possibility of such an explanation proved to be of epoch-making importance in theoretical physics. Significance of the Quantum Theory. The possible far- reaching significance of these developments in the theory of radiation may perhaps be suggested by a few state- ments, the whole meaning of which, however, can only be appreciated by one closely acquainted with physical science and its history. In the first place, it has been shown conclusively by the English physicist, Jeans, that although the facts just mentioned as Planck's first basis for the quantum theory demand an atomic view of the nature of radiation, the interpretation given to them makes them wholly inconsistent with the most funda- mental principles of the science of mechanics. In other words, it would appear that, to a certain extent at least, [187] THE QUANTUM THEORY [Sec. 54 events in the world of atoms and electrons do not follow the laws of ordinary mechanics. Secondly, it appears that these events do involve in a very definite way certain considerations based upon the theory of probabilities or chance. For some time it has been known that the so-called second law of thermody- namics, which states that the amount of available energy in the universe tends constantly to decrease, could be derived from a study of the relative probabilities of given configurations of the molecules composing any group of bodies. Certain arrangements of the molecules are more probable as the outcome of a disturbance than are others. There would always be a tendency for the less probable configurations to be replaced by the more probable ones. This tendency corresponds with the statement that the " entropy" of a given group of bodies tends always to increase; the greater the entropy of the group the less available energy there is in it, the nearer all of energy in the system is to being uiiiformly distributed heat. This latter state of affairs is the most " probable" of all states of the molecular system, and the " entropy" of the system as a whole is merely another expression for the probability of the particular configuration of molecules or molecular conditions existing within it. In order that considerations of this sort, involving the doctrine of chance, should be applicable to a subject matter, it is absolutely necessary that this subject matter consist of discrete individuals or particles, in short that it be atomic. Now, it has been shown very decisively that the conception of entropy and the principles of thermo- dynamics at large are definitely applicable to the be- havior of radiant energy, and hence we must almost inevitably conclude that such energy is atomic hi nature. It is of course quite possible that radiant energy is [188] Sec. 66] NATURE OF X RAYS atomic while other forms of energy are not, that there will be a limit to the application of the principles of atomism to the physical universe. Indeed, certain well- known physicists still hold that even the facts which support the quantum theory of light can be explained without any radical change in our present doctrines. The exact outcome of this contention still rests in the balance. REFERENCES A remarkably complete, although somewhat mathematical dis- cussion of the Quantum Theory and its grounds is given by Norman Campbell in his "Modern Electrical Theory," second edition (1913), Chapter X. A somewhat simpler, but also very clear ac- count is that by R. A. Millikan, "Atomic Theories of Radiation," in the journal Science for January 24, 1913 (Vol. 37, pp. 119-133). For a popular discussion of the growth of atomic theories in phys- ics see Sir Oliver Lodge's "Continuity" (1914). Section 55 X RAYS AND THEIR MEASUREMENT The Origin and Nature of X Rays. X rays are formed when the cathode rays, of which we have spoken in Section 25, are stopped hi their course by striking a solid plate, commonly called the " anti-cathode." Since the electrons of the cathode rays are moving much more slowly than are those of the beta rays (see Section 49), the " kinks" (see Section 37) of which they are made up are not so sharp, but they are nevertheless very much sharper than those of ordinary light. As mentioned incidentally hi Section 53, it has been shown that a fraction of the X rays given off by the anti- cathode have a wave-length and penetrative power which is characteristic of the element of which the anti-cathode is composed. These " characteristic X rays" are of [189] X RAYS [Sec. 55 shorter wave-length the higher the atomic weight of the element, and are wholly independent of its state of chemical combination. Most of the elements give out characteristic X rays of two different wave-lengths, and when these are analyzed by an X ray spectrometer, they form the "X ray spectrum" of the element in question. Why X Rays Penetrate "Opaque" Bodies. It is the extreme "sharpness," or very high frequency, of the gamma and X rays which chiefly distinguishes them from ordinary light, and which gives them their special power to penetrate solid bodies which are opaque to light. Bodies absorb light only because their atoms are able to respond, or " resonate," to the vibrations in the light wave (see Section 41). But when these vibrations are very rapid or, what means the same thing, when the "kinks" are very short the atoms of the substance can- not respond with sufficient quickness, and hence the light is not absorbed. There is some question as to whether this explanation holds exactly on the quantum theory of radiation. However, there is doubtless also a specific relation between frequency, as such, and degree of ab- sorption, since certain bodies strongly absorb X rays of one frequency and not of others. The Corpuscular Properties of X Rays. Certain phys- icists, among them W. H. Bragg, formerly supported the view that the gamma and the X rays are not waves but are moving particles. The reason for -this advocacy lay hi the fact that these rays, in passing through matter, behave as if their energy were concentrated in very mi- nute, moving regions, instead of being spread out over a continuous " wave-front," as light energy is supposed to be in the classical theory. However, as we have seen in Section 54, latter-day developments have proved that ordinary light has the same sort of distribution, so that [190] Sec. 55] PROPERTIES OF X RAYS the evidence in question counts no more against the wave- theory of X rays than it does against that of light in gen- eral. Recent developments, briefly discussed in Part I, have completely converted Bragg and his school to the wave theory or at least to the general theory of radiation. The Reflection and "Diffraction" of X Rays by Crystals. The reflection of X rays from a crystal surface is somewhat different from that of ordinary light. The reason for this is to be found in the fact that although the atoms of the crystal are regularly arranged, they are still so far apart compared with the wave-length of the rays that the discontinuities produce a sensible effect. In Chapter VI of Part I the reflection of ordinary light has been explained as due to the generation of a return wave by the electrons of the atoms hi the surface of a body which is struck by light. This is what occurs also in the case of X rays, but owing to their penetrative power and relatively short wave-length the return waves from dif- ferent planes of atoms in the crystal do not fuse with each other harmoniously, except hi certain favorable directions. In other directions there is interference, that is, the waves from one layer of atoms oppose those from another layer and wipe them out. In fact, the X rays are so short that the atoms of the crystal form for them a "diffrac- tion grating," similar in action to the mechanically ruled gratings used to bring about the interference of ordinary light waves. Now, the direction in which interference does not take place in the case of X ray reflection depends upon the wave-length of the rays. Consequently, if we measure the angle at which the reflection of a given set of rays occurs most readily, and if we know the structure of the crystal, we can calculate the wave-length. Conversely, [191] X RAYS [Sec. 55 using rays of known wave-length, we can deduce the structure of a crystal with the constitution of which we are not familiar. (See Figure 27.) Q ------- Fig. 27 STRUCTURAL PLAN OF A SIMPLE CRYSTAL This drawing represents the structure of a crystal of potassium chloride, a substance similar to ordinary salt, as deduced from its action upon X rays. The dark spheres represent chlorine atoms, the light ones atoms of po- tassium. It will be seen that the unit of structure of the crystal is the individual atom, since all of the atoms are equidistant from their imme- diate neighbors. For the sake of clearness, the spaces between the atoms have been exaggerated, as compared with their diameters. There are always a number of different ways in which geometrical plane surfaces can be drawn through the atoms in a crystal, and each of these theoretical surfaces is capable of reflecting or diffracting X rays. The result is that if a beam of rays is sent into a crystal, it is partly [ 192 ] Sec. 66] LIFE AND CATALYSIS split up into secondary beams which take different direc- tions, characteristic of the inherent planes of the crystal atoms. When these latter beams are caught upon a photographic plate a pattern is produced from which the constitution of the crystal can be inferred. REFERENCES Concerning the X rays see: C. W. C. Kaye's "X Rays" (1914); and W. H. and W. L. Bragg's "X Rays and Crystal Structure," (1915). Also: S. P. Thompson's "Radiation" (1898), Chapter III. Bragg's arguments with reference to the corpuscular properties of the rays are given in Norman Campbell's "Modern Electrical Theory," second edition (1913), pp. 292-304. Section 56 LIFE AND CATALYSIS Living bodies are complex mixtures of active chemical substances. These substances are constantly reacting with each other and as a consequence the bodies in question would soon be destroyed if it were not for the fact that the chemical changes are so organized and con- trolled as to ultimately bring compensation for the de- struction which they cause. This control and regulation which is so characteristic of the activities of living beings probably depends in the last analysis upon a purely chemical principle called catalysis. This principle implies that the mere presence, in chemical mixtures, of very minute quantities of cer- tain substances, can determine the nature of the changes which take place in these mixtures. Controlling sub- stances of this sort are called catalyzers. The effects which they produce can be explained in terms of atoms, molecules and electrons. [193] LIFE AND CATALYSIS [Sec. 66 The catalyzers which control the life processes in dif- ferent organisms are characteristic of these organisms, and are undoubtedly transmitted to them from their progenitors through the germ-cells from which they originally developed. The reason why certain catalyzers and not others have been constantly transmitted from parent to offspring through many generations is to be found in their special power to regulate the chemical changes in organisms so as to permit the survival of the species. In other words, the present physical and chemical structure of organism must be explained not only in terms of atoms and molecules but also in terms of the history of living matter upon the earth. The most important elements hi the constitution of living organisms are carbon, hydrogen, oxygen, and nitrogen, although many others are essential. These elements are combined, usually, to form "colloidal" systems of particles (see Section 3), and many of the fundamental peculiarities of living things depend upon those of colloids. Organic catalyzers are called enzymes, and on the above theory, enzyme action explains the mystery of heredity. REFERENCES See L. T. Troland's "The Chemical Origin and Regulation of Life," in the Monist for January, 1914. END OF PART TWO [194] INDEX NOTE: Page numbers in italics refer to the more extensive discussions of a given subject. Absolute zero, 20, 107 , no chemical action at, 29 , state of atoms at, 55 Absorption of light, 30 jEther, present status of, 146 Alcohol, formula of, 80 Allotropism, 84, 88 Alpha rays, 34, 35, 168 , counting particles in, 56 , origin of, 45 , proved by Rutherford to be helium atoms, 169-170 , scattering of, 67, 176 Argon, 138 Aston, F. W., on meta-neon, 75 Atom, energy of, 772 , internal forces of, 10 , nucleus, size of, 176-177 , nucleus theory of, 44-45, 71, 74, 776-778 , openwork structure of, 42 , permanence of, 10 , Saturnian, 61, 182 , radiation from, 181-182 , single, effect due to, 35 , solar system theory of, 42 , structure of, 41-43, 43-46, 174- 782. (See Atomic structure) , Thomson's theory of structure, 174 , unit of crystal structure, 113 Atomic heats, 118 magnitudes, 58 - numbers, 46, 179-180 structure, recent discoveries con- cerning, 43-46 and spectra, 155 Atomic volumes, 3-4 and atomic weights, 67 weights and atomic numbers, 46 , irregularity of, 75 , methods of determining, 65 , table of, 62-3 Atoms, 2 and electrons, relations between, 126-128 and life, 50-51 and molecules, relative sizes of, (Fig. 1), 3 and positive electricity, 23 , arrangement in molecule, 76-86 , attraction of identical, 138 - neutral, (Fig. 22), 138 , charges carried by, 24 , density of, 4 , individuality of, 5 , kinds of, 2-3 , number in unit volume, 54, 56 of a liquid, (Fig. 5), opposite page 6 of a solid, (Fig. 7), opposite page 10 of light, 183 , shape of, 2, 60-61 , sizes of, 2 , methods of finding, 53-58 , species of, 62 , spontaneous disruption of, 10 , structures of, and periodic table, 70 , tendency to form groups, 5 , visibility of, 58-59 Attraction, forces of, within bodies, 97 Avogadro, principle of, 66, 107 [196] INDEX B Balmer's formula, 181 Battery, electric, action of, 25 Becquerel, Henri, 52, 165 Benzene, derivatives of, (Fig. 13), 81-82 , ring formula of, 80-83 Beta rays, 34, 168 - and X rays, 189 , from potassium, 173 , origin of, 45, 177 , penetrating power of, 35, 42, 169 , relation to gamma rays, 38, 171 , scattering of, 67 Black body, radiation from, 152 Bohr's theory of atomic structure, 181 Boiling points, 105 , effect of ionization on, 140- 141 Boyle, law of, 106 Bragg, W. H., on corpuscular prop- erties of X rays, 190-191 Brownian movement, 16-17, 110- 111 , path of particle in, (Fig. 16), 100 Campbell, Norman, on radio-activ- ity of potassium, 173 Carbon, allotropic forms of, 85 , compounds of, 77 Catalysis, 145 - and life, 793-794 Cathode rays, 120 , action of, (Fig. 18), 121 , action of magnet on, (Fig. 19), 122, 163 and X rays, 189 Cell, electric, 145 Cells, 149 and atoms, 50-51 Chances, molecular, and averages, 93 Charles, law of, 16, 106 Chemical affinity, 91, 736-739 action, 7 and electrons, 27-28 Chemical affinity and ionization, 126 , molecular basis of, 142-144 change, effects and conditions of, 144-146 , mystery of, 88 energy, 146 , in relation to radio-activity, 172 formulae, 77 properties of atom, determina- tion of, 45, 89 reactions, reversibility of, 143 , velocity of, 143 valency, 141-142 Chlorine, atomic weight of, 65 Coagulation, 59 Cohesion, forces of, 11, 92, 172 Cold, nature of, 20 Colloids, 59, 112 - and life, 194 Color, due to reflection, 158 mixture, and white light, 158 , physical basis of, 87, 757-759 , sensations of, 158 Compounds, 6 , properties of, 86 Conduction, electrical. (See Elec- trical conduction) of heat. (See Heat conduc- tion) Conductivity, electrical, basis of, 130 , of gases, 98 Cooling, due to evaporation, 19 Copper, color of compounds of, 88 Critical points of liquids, 105 Crystal, as a unit of structure, 112 , fixity of molecules in, 103 , planes of, 192-193 , structural plan of simple, (Fig. 27), 192 structure and molecular form, 85 and X rays, 49, 53, 773, 114, 797-793 Crystalline state, 112 Crystals, liquid, 19, 112, 114 Curie, M. and Mme., 165 Current, electrical. (See Electrical current) [196] INDEX Dalton, John, 52 Diamond, 88 Dielectric capacity and electrolytic dissociation, 139-140 and index of refraction, 160- 161 Diffraction, 191-192 of X rays, 113, 191 Diffusion, 98, 99-101 and atomic size, 57 paths, (Fig. 16), 100 Dispersion, of colloids, 59 of light, laws governing, 160 Distribution curve of temperature radiation, (Fig. 25), 153, 757- 752 Du Long and Petit, on atomic heats, 118 Dynamo, action of, 25, 33 Elasticity, 87 Electrical conduction, in gases, 737- 732 , in liquids, 131-132 current, direction of, 131 , effects connected with, 729- 737 , nature of, 24 , produced by chemical change, 145 force lines, kinks in, 147 , nature of, 146-147 forces, importance in nature, 724 lamp, principle of, 25 motor, principle of, 32 power transmission, 26, 733 resistance, nature of, 129, 130 waves, absorption of, 30 , generation of, 30 , reflection of, 31 Electricity, conduction in gases, 93 , conduction through liquids, 140 , in all bodies, 23 , laws of attraction and repulsion, 22 , positive and negative, 22 , positive, form in Thomsonian atom, 175 Electricity, relation to magnetism, 32 , " speed " of, 24, 25 Electrolysis, 737-732, 139-141 , deposition by, 55 Electrolytic dissociation, 739-747 Electron, and its behavior, 27-27 , charge of, 23, 120, 122, 123 , contains only negative elec- tricity, 124 , density of, 22 , discovery of, 52, 720 , flattening at high speed, 124 , mass of, 120, 123 , measurement of, 120-124 , natural unit of electricity, 55 , radiation from, 46 , shape of, 22, 124 , size of, 21, 123 , structure of, 22, 724 , weight of, 22 , Zeeman effect, 29, 149 Electrons, 2 , action of magnetic field on, 129 , affinity of atoms for, 736-739 , affinity of elements for, 26 and chemical action, 27, 28, 29 and ions, reactions between, 125-128 and light waves, 29, 147 and line spectra, 155 and magnetism, 32-34, 164 and selective absorption of light, 158 and temperature radiation, 150- 151 and valency, 142 , arrangement in atom, 175 , as beta rays, 34-35 , emitted by metals under action of light, 184 , evaporation of, 27, 134 , " free," 26, 130 , and heat conduction, 110 , in atom, 42-46, 175, 178 , two groups of, 177 , in the electric current, 24 , moving, deflection by magnet- ism, 32, 762-763 , number in atom, 178 , position in atom, 44, 45. [197] INDEX Electrons, rings of, in atom, 175 , valency, 89, 177 Elements, 5, 6 , affinity for electrons, 26 , chemical, as atomic mixtures, 74 , number possible, 180 , electro-positive and negative, 26, 136-138 , evolution of, 41 , inert, explanation of, 138-139 , life of, 41 , molecules of, 83 , periodic table of, 68-76 , primitive, in hottest stars, 174 , properties of, and periodic table, 69 , radio-active series of, (Fig. 11), 36-37 , radio-activity, alleged of all, 40 , specific nature of, 62-63 , systematic relations of, 68 , table of, 62-63 , undiscovered, 70 Emulsions, 59 Energy, 2 , atomic nature of, 48 , chemical, 146 , equipartition of, 95-96, 111, 118 , intra-atomic, 39, 172 , kinetic, 95 , given off by radium, 40 Entropy, 188 Enzymes, 194 Equations, chemical, 90 Equilibrium, chemical, 143-144 Equipartition of energy, 95-96, 111, 118 Ether, 29 , methyl, 78 Evaporation, 13 , cooling effect of, 19 Evolution, inorganic, Lockyer's theories, 173-174 , organic, 194 Expansion, due to heat, 18 Fluids, motion of particles through, 56 Fluorescence, 185 Fog, condensation around ions, 122, 123, 126 Forces, inter-atomic, 91 , intra-atomic, 91 , magnetic, direction of, around moving electric charge, (Fig. 26), 162 Formulae, chemical, 77-75 , graphical, meaning of, 78 , structural, 77 Free electrons, 26 and electrical conductivity, 130 and heat conduction, 110 Frequency, and energy of light quantum, 185 Freezing points, 87 , effect of ionization on, 140- 141 Friction, causes heat, 19 , molecular explanation of, 12 Fusion, latent heat of, 103 Gamma rays, 34, 35, 36, 168 , nature of, / 70-1 71 , origin of, 45 , relation to beta rays, 38 , wave-length of, 156 Gas law, 108 , model of a, 14-16 pressure, cause of, 15, 16 Gases, atomic heats of, 119 , conduction of electricity through, 131-132 , emission of light by, 152, 153 , simple laws of, 106-108 Gay-Lussac, principle of, 107 Geiger and Nuttall, on life of radio- elements, 167 Gold-leaf, molecular thickness of, 54 Gravitation, 91 F Families, in periodic table, 69 Faraday, Michael, 52 Films, thin, 54 Hall effect, 129 Hardness, 87 [198] INDEX Heat and allied phenomena, II- 21 and chemical action, 28, 145 conduction, 16, 57, 109-110 and electrical conduction, 130 , due to electric current, 25 , due to friction, 19 energy, 118 in bodies, amount of, 20-21 motion, visibility of, 16 , radiant, 13, 29-30, 102 , produced by chemical change, 144 wave, 156 Heats, latent, 102-105 Helium, 138 , in alpha rays, 35 , Rutherford's experi- ment, 170 , in atom structure, 71 , in stars, 174 Heredity, 194 Hertz, H. R., 52 Hertzian waves, 29, 48, 156 Hydrocarbons, five isomeric, (Fig. 12), 79 Hydrogen, 96 f atom, structure of, 71, 74, 180- 181 ion, nature of, 180 Hysteresis, 165 Index of refraction, 160 Interference, of X rays, 113, 191 Intra-atomic and inter-atomic forces, 91 Inverse squares, law of, for radia- tion, 183 lonization, 126 , energy of, 126 of substances dissolved in water, 139 Ions, atoms and electrons, forces between, (Fig. 20), 127 , conduction of electricity by, 131-132 , how produced, 125-126 , motion through solutions, 140 Isomerism, stereo-, 84-86 Isomers, and structural formulae, 77-80 Isotopes, 45, 53, 71-75, 89 , table of, 64 Isotopism, 178-179 Jeans, J. H., on quantum theory, 187 Kinetic energy, 95 Kinetic molecular theory, 92-9^, 115 Kleeman, R. D., on atomic shapes, 61 Latent heats, 102-105 Laue, M., experiments on X rays, 49 Lenard, P. A., 52 Lenses and prisms, action of, 160 Life and atoms, 50 and catalysis, 59 and colloids, 59 Light, absorption of, 30, 157-158 and chemical action, 28 and electronic vibration, 29 and magnetic field, 34, 149 , conditions of production, 150- 155 emission by gases, 152, 1 54 frequency of, 157 ionization due to, 126 polarized, 86 produced by chemical change, 145 reflection of, 31, 157 refraction of, 159-161 selective absorption of, 157 ultra-violet, 156 velocity of, 156 , in different media, 31 , wave-length of, 156 waves and electrical force-lines, 146-148 Lines of force, electrical, 146-147 Line spectra, 154 and structure of the atom, 42,43 [199] INDEX Liquid, model of a, 17-18 state, 13 Liquids, conduction of electricity in, 131-132 Lockyer, Sir Norman, on inorganic evolution, 173-174 Loreutz, H. A., 52 M Magnetic field, due to motion of electricity, 161-162 Magnetism, 163-165 , dia- and para-, 163 , permanent, 33, 164 , relation to electricity, 32, 767- 762 Magnetization, mechanism of, 164 Malleability, and temperature, 103 Mass action, law of, in chemistry, 142-143 Matter, history of modern theory of, 52-53 Maxwell, J. C., 52 Mean free path (of molecules), 97-99 and electrical conduc- tivity, 130-131 , properties dependent on, 98 Mechanics, fundamental laws of, 92, 93 , laws of, and atomic events, 787- 758 , statistical, 93, 94, 97 Melting, 13, 14 points, 87 Membrane, semi-permeable, 109 Mendelejeff, and periodic table, 70 Mercury vapor, 83-84 Metals, heat conduction in, 110 , thermo-electric series of, 135 Meta-neon, 75 Mica, 112-113 Millikan, R. A., experiments of quantum theory, 48 Molecular action, and probability, 93, 94 activities, individuality of, 94 chaos, 142-143 forces, internal, 86-87 Molecular motion, speeds of, 94-97 speeds, distribution curve of, (Fig. 17), 116 , distribution law of, 775-777, 151 theory, kinetic. (See Kinetic molecular theory) volumes, and gas law, 108 weights, 66 Molecule, arrangement of atoms in, 76-86 , motion between impacts, 97-99 Molecules, 5, 6 and visible particles, relative sizes of, (Fig. 2), 4 , electrical constitution of, (Fig. 10), 28 , frictionless, 12, 13 , gas, motion of, 14 , mean free path of, 97-99 , motion of, 77-27 of a gas, (Fig. 8), opposite page 12 of steam, (Fig. 4), opposite page 6 of water, (Fig. 3), opposite page 4 , structure of, and crystals, 85 Moseley, H. G. J., on atomic num- bers, 180 Motion, laws of, 92, 93 Motor, electric, principle of, 32 Neon, and meta-neon (Isotopes), 75 Nernst, W., on specific heats, 186 Newton, laws of, 93 Niton, 166 Non-conductors, electrical, 130 Oil films, 54 Organic compounds, 76 , formulae, (Fig. 6), 8-9 Osmotic pressure, 108-109, 144 Oxygen, atomic weight of, 66 Periodic table of the elements, 68- 76 [200] INDEX Periodic table and atomic numbers, 46 , blanks in, 70 , defects in, 70 , significance of, 70 , Thomson's explanation of, 175 Periods, in periodic table, 69 , and electron rings, 175 Perrin, J., on the Brownian move- ment, 110 Phosphorescence, 185 Photo-electric effect, 184 Physical properties, basis of, 87 Planck, Max, on quantum theory, 46, 187 Positive electricity, form in Thom- sonian atom, 175 Potassium chloride, crystal struc- ture of, 113 , radio-activity of, 40, 41, 773 Power, electrical transmission of, 26, 133 Pressure, of a gas, 16, 106-107 , osmotic, 108-109 Prism, action of, on light, 155 Probability and entropy, 188 and molecular action, 93, 94 Protyle, 71 Prout's hypothesis, 71 Pyrometer, optical, 151 Quantum theory of radiant energy, 46-49, 53, 147-148, 182-189 and specific heats, 119-120, 186 and hydrogen atom, 181 and temperature radiation, 152, 187 , difficulties with, 48-49 , significance of, 187 Radiant energy, similarity of all forms, 49 Radiation, due to acceleration of an electron, (Fig. 23), 148 , due to temperature, 150-152 Radiation, quality dependent on temperature, 47 , recent discoveries concerning, 46-50 Radio-active substances, 165-168 Radio-activity, 34-41 and atom structure, 44 , cause of, 38 , energy of, 39-40 , general property of matter, 40, 166 , laws of, 166, 167 , not chemical, 39 , penetrating power of rays, 124 Radio-elements, 40 , chemical diversity of, 179 , discovery of, 165 , isotopes among, 74 , life of, 166 , position of, in periodic table, 167 , successive disruptions of, 38 , table of, 64 Radium, 34 , atomic weight of, 40 atom, stability of, 172 , discovery of, 165 , rays from, study of, 168-169 Rayleigh, Lord, radiation law, 47 Rays, alpha. (See Alpha rays) , beta. (See Beta rays) , cathode. (See Cathode rays) , gamma. (See Gamma rays) , X. (See X rays) Reactions, chemical, kinds of, 90 Reflecting power, basis of, 158 Reflection, diffuse, 31 of light, 31 of X rays, 49 Refraction, index of, 160 of light, 31 , relation to absorption of light, 161 Resistance, electrical, 98 , nature of, 129-130 Retina, the, 158 Roentgen, W. C., 53 Rowland's experiment, 161 Rutherford, Ernest, 53 , on helium in alpha rays, 769- 770 [201] INDEX Rutherford, Ernest, on scattering of alpha rays, 176 Schmidt, G. K., 165 Secondary rays, 171 Series, disintegration, of elements, 165 , thermo-electric, 135 Soap-bubble films, 54 Solid and crystalline states, 112- 115 and liquid, stages between, 114 , liquid, and gaseous states, 13 , model of a, 18 Solution, and electrical decomposi- tion, 139-141 , simple laws of, 106-108 Sound, 13, 101-102 Specific heats, 118-120 , at low temperatures, 119, 186 Spectra, line, 755 , varying complexity of, 173 Spectral lines, 42, 43 Spectrum, normal, 156 Stark effect, 150 Stark, J., 150 Statistical mechanics, 93, 94 Stokes' law, 185 Stoney, G. J., 52 Sugar, constitution of molecule, 6,7 Sugars, formulae and crystals of, 85, 86 Sulphur, allotropic forms of, 84 Surface tension, 104, 117 Tartaric acid, crystals of, (Fig. 15), 85 , molecular structure of, (Fig. 14), 84 Temperature, and molecular energy, 94-95 and radiation, 47 radiation, 150-152 , and quantum theory, 187 Temperatures, low, and specific heats, 119, 120 Thomson, Sir J. J., 52 , and meta-neon, 75 , discovery of the electron, 120-124 , theory of atom structure, 774-775 Thermodynamics, second law of, 188 Thermo-electric circuit, (Fig. 21), 134 Thermo-electricity, 133-136 Thermo-electric series of metals, 135 Thermopile, principle of, 133-134 Transparency, theory of, 30 Traube, J., on atomic volumes, 67 Triads, of elements, 68 Ultra-microscope, 58 Ultra-violet light, 156 Uranium, life of, 167 Vacuum tubes, 98 Valency, chemical, 141-142 , in periodic table, 69 electrons, 89, 177 Van der Waals, gas formula of, 57, 108 Vapor, above liquid, temperature of, 117 , molecules of, at liquid surface, (Fig. 9), 15 pressure, 775-777 , laws of, 116 Vaporization, latent heat of, 104 Viscosity, of gases, 57 Voltage, 26, 30 W Water, decomposition of, 7, 66, 90 Waves, electro-magnetic, gamut of, 50, 755-757 , Hertzian, 29, 48, 156 Weights, atomic. (See Atomic weights) Wien's law, 47 Wilson, C. T. R., photography of ionization paths, 126, 169 [202] INDEX X rays, 184, 185, 186 and atomic numbers, 180 and crystal structure, 113 , characteristic, 189-190 , corpuscular properties of, 190-191 , diffraction of, 191-193 , discovery of, 53 , measurement of, 189-193 , nature of 49, 189-190 , penetrating power of, 190 , reflection of, 49, 19 1-193 X rays, similarity of gamma rays, 171 , spectra, source of, in atom. 178 spectrometer, 190 , wave-length of, 156 Zeeman effect, 29, 34, 149-150, 155, (Fig. 24), 150 , Paul, 149 Zero, absolute, 20, 107 [203] LIST OF WORKS ON ELECTRICAL SCIENCE PUBLISHED AND FOR SALE BY D. VAN NOSTRAND COMPANY, 25 Park Place, New York. ABBOTT, A. V. The Electrical Transmission of Energy. A Manual for the Design of Electrical Circuits. Fifth Edition, enlarged and rewritten. With many Diagrams, Engravings and Folding Plates. 8vo., cloth, 675 pp Net, $5.00 ARNOLD, E. Armature Windings of Direct-Current Dynamos. Exten- sion and Application of a general Winding Rule. 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