physics Lib. 
 
 Q.C 
 
 Zl 
 
 <S92n 
 
 THE NEW SGIENC 

 
 THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 LOS ANGELES 
 
 APR 2 2 1863
 
 THE NEW SCIENCE 
 
 THE 
 
 FUNDAMENTAL PHYSICS 
 
 BY 
 
 W. W. STRONG, PH. D.
 
 THE NEW SCIENCE 
 
 OF 
 
 THE FUNDAMENTAL PHYSICS 
 
 BY 
 W. W. STRONG, B. S., PH. D. 
 
 S. I. E. M. CO. 
 
 MECHANICSBURG, PA., U. S. A. 
 1918
 
 COPYRIGHTED, 1918, BY W. W. STRONG 
 
 (All rights reserved)
 
 Library 
 
 c 
 2.1 
 
 Q 
 
 This work is dedicated to two whose love has been as true as nature, the 
 inspiration of my life, the fondest treasure of my memories, and the founda- 
 tion of the hope that these loves are the earnest of the great transformation 
 to a love unbound by fate and a truth unfettered by ignorance. 
 
 The blessings of such unselfish love inspires this, my credo of life: 
 
 I believe in the intelligible ordering of all phenomena by a Good and 
 Supreme Being in whose image we are privileged to understand and direct 
 His creations. 
 
 I believe in the most perfect philosophy of the world and of life that we 
 can devise as the guide for ourselves and our organizations so that the 
 heritage of the Past and the works of the present will bring most directly 
 the Great Democracy of Truth and Love to all men. 
 
 And I dedicate the full striving of my heart and mind to the gaining and 
 giving of the Truth and Love of my Heavenly Father to men with the full 
 Faith that we here prepare for that most glorious transformation to the per- 
 fect ordering of our perpetual Homeland with our Father and our brethren. 
 
 118830G
 
 The author wishes to record that the formation of the Research Corpora- 
 tion by Dr. F. G. Cottrell appears as an important step toward the time 
 when the ambitions and dreams of our youth will be for knowledge and 
 truth and the employment of wealth will be for the realization of all those 
 visions that experience intimates will be for the uplift of all. 
 
 vii
 
 PREFACE 
 
 There has been in the writer's and there is probably among all 
 of us an intense longing for the fundamentals in life. Busy as 
 we may be with the common details and tragedies of existence, 
 there are times when we contemplate a much more enduring 
 scheme of living and thinking than that which now guides or 
 rules us. The college student sometimes elects his subjects 
 with reference to what he is lead to believe is of fundamental 
 value in so far as he can judge. A very few people direct the 
 energy and the enthusiasm of their lives along carefully planned 
 channels in which they believe the most fundamental and valu- 
 able results will be obtained. For the great unthinking majority 
 it is as in politics, every man always votes for the best candidate 
 and so as regards the fundamentals of our philosophy of ex- 
 perience and of living most of us vote right. 
 
 The unsophisticated might be awed into believing that surely 
 the pages of our select journals and books of science written by 
 the inspired disciples direct from the research fields of nature, 
 would contain in them part of the real philosopher's stone; and 
 this I sincerely believe is true. Those of us that have been in 
 those fields of research also know that they are indeed stony 
 stony even unto becoming a wilderness of doubt; and that while 
 sojourning there we must subsist upon the manna of our opti- 
 mism, else the promised fundamentals beyond the Jordan become 
 clouded by the fleshpots of our Egypt of selfish, " what's the use" 
 philosophy, and that we may still be in pursuit of the funda- 
 mentals when every citizen possesses a heart enriched by the 
 experiences of Gethsemane, and whose mind has been trained 
 by years of fruitful research in the fields of knowledge. 
 
 But were all goals to be achieved only Nirvana would remain, 
 and our optimism is to be measured by the progress that is 
 being made, rather than pessimism as regards the reaching 
 of the absolute. Surely the recent discoveries and the visions 
 given us by the new Science inspire a most unbounded optimism, 
 that yet greater progress is to come.
 
 x PREFACE 
 
 There is arising among the sciences and in technology many 
 new developments that foretell a new natural philosophy or 
 outlook upon knowledge that promises to greatly clarify and 
 simplify knowledge. We appear to be in the midst of a period 
 of a revival of knowledge as well as of the humanities, steps of 
 which have been marked by the new geometries and the principle 
 of relativity. 
 
 Events appear to hold the promise that the concentrated efforts 
 of peoples to win in a war will be replaced by a more unified 
 aim to know life and nature and to apply this knowledge more 
 fully to the service of man. The following essay is the writer's 
 bit in a movement which he hopes will eventually provide every 
 man and every organization with the most advanced and well- 
 ordered program for the direction of their efforts. 
 
 W. W. S. 
 
 500 S. YORK ST., MECHANICSBURG, PA. 
 March 8-June 7, 1918.
 
 CONTENTS 
 
 PAGE 
 
 Dedication v 
 
 Preface ix 
 
 Contents " xi 
 
 4. The Goal of the New Science 1 
 
 5. The Disappearance and Conservation of Energy, Electric Charge 
 
 and Mass 6 
 
 6. lonization Phenomena 13 
 
 7. The Gateways of Knowledge and the Growth of Science 23 
 
 8. Some Problems in Physics 31 
 
 9. The Directed Elements 34 
 
 10. The Entity Systems of the Universe 38 
 
 11. The Atomic Structure of Matter and the Equipartition of Energy 
 
 in the Newtonian World 43 
 
 12. The Disintegration of Atoms by Radioactivity and the Nature of 
 
 Our System of Matter Elements 49 
 
 13. Some Models of Atoms and Atomic Nuclei 54 
 
 14. The Ritzian Atom, the Magneton and the Neutron 62 
 
 15. The Corpuscular Theory of Light 68 
 
 16. Huyghens' Secondary Wavelet Centers 69 
 
 17. Electric Lines of Force 70 
 
 18. The Electromagnetic Theory of Radiation, the Theory of Gravi- 
 
 tation and the Equipartition of Energy 72 
 
 19. The Electric Nature of the Ether, the Hypothesis of Electroethons 
 
 and Radions 78 
 
 20. Some of the Universal Constants of Nature 81 
 
 21. The Fundamental Definitions and Units and the Ceer Theory. . 84 
 
 22. The Etementarquanta Theory. 93 
 
 23. The Relativity Theory -, 100
 
 4. THE GOAL OF THE NEW SCIENCE 
 
 The outline of the older natural philosophy is quite well 
 exemplified by the contents of the ordinary textbooks of physics. 
 In quite separate divisions there are treated mechanics and the 
 properties of matter, kinematics, dynamics, gases, liquids and 
 solids; heat, wave motion and sound, light, magnetism and elec~ 
 tricity. In a similar fashion the different sciences and branches 
 of engineering are separated from each other on account of the 
 way that they have developed historically and it has only been 
 quite recently that a new science has arisen from a critical ex- 
 amination of the groundwork of the sciences. 
 
 This new science is essentially a more complete application of 
 laboratory methods to the basic units, measurements and laws 
 of science. It aims to apply the empirical method and eventu- 
 ally the same method, units and apparatus to all phenomena. 
 The new science is essentially a philosophy of the laboratory and 
 aims for the universal extension of the experimental method. It 
 states that no term or theory of the natural world possesses any 
 meaning unless it is usable in the laboratory. Such terms as 
 time, length, direction and mass must be definable in terms of 
 experiences of the natural world and unless they can be so defined 
 in a given region of experience they possess no meaning there, 
 fundamental though these terms may appear to be. 
 
 Philosophically the view that the world consisted of the four 
 elements, water, fire, earth and air would be quite convenient 
 and comprehensive for the Greeks. In Plato's time some could 
 consistently believe that everything is explained by motion or 
 that all is rest. For a large group of phenomena the phlogiston 
 theory is ample and probably no theory appeared so complete to 
 some minds as the vortex ether theory of the atoms. The past 
 philosophies of phenomena have been quite fruitful and if we 
 change their phraseology they bear a remarkable likeness to the 
 theories of today. Call the four Greek elements solids, liquids, 
 gases and energy: speak of the motion theory as the kinetic theory 
 of gases and liquids: adopt the theory of a stagnant ether; change 
 
 1
 
 2 FUNDAMENTAL PHYSICS 
 
 phlogiston to energy : and view the atoms as consisting of rings of 
 electrons rotating about the nucleus of the atom and we perceive 
 a remarkable similarity of ideas. 
 
 The workers of the new science aim to develop as simple and 
 as comprehensive a philosophy of phenomena as did the workers 
 in the past. But they are devising a system and a laboratory 
 method best suited for the study of phenomena as the first step 
 in the problem and as the investigations continue the very fun- 
 damental]elements of the experimental system employed are to be 
 modified so as to further these investigations. As a concrete 
 problem let us consider the motion of an alpha particle (which 
 consists of a helium atom carrying a double positive unit of elec- 
 trical charge) with a velocity of 120,000 miles a second. The 
 collisions of this particle with other particles of matter is entirely 
 different from those we are familiar with when lower velocities 
 are concerned. This alpha particle will pass through all of an 
 atom except a very minute portion called the nucleus and it will 
 leave a path strewn with the wreckage of atoms, all broken to 
 pieces, many of the broken parts being charged, while the medium 
 is filled with the disturbances that we speak of as radiations. 
 In order to describe these phenomena we may consider these 
 changes from afar and under conditions of comparative rest and 
 quiet or we may bravely try to establish our experimental outfit 
 on the rapidly moving alpha particle itself. And the results 
 of the two methods of observation will of course appear very 
 different and perhaps for a long time we will be unable to corre- 
 late the two sets of observations. 
 
 The charge of the alpha particle will cause it to be surrounded 
 by an electric field which will be comparatively weak if the field 
 is uniform. If however our place of observation had been a beta 
 particle moving with the same velocity the potential of the par- 
 ticle would be a million volts and we would have been forced to 
 develop a laboratory and a system of science that would apply 
 to these conditions of intense electric fields. 
 
 Let us now try to measure time on the alpha particle. In the 
 first place we have never devised a clock except for conditions of 
 comparative rest. Would any of our chronometers run regularly 
 when possessing a speed of 120,000 miles per second? If the 
 observer was 6 ft. from the clock and made observations by sight 
 the clock would move a distance of 4 ft. while the light was pass- 
 ing from the clock to the observer, assuming that the velocity of
 
 THE GOAL OF THE NEW SCIENCE 3 
 
 light is unaffected by the velocity of the observing system. 
 Would not the measurement of time greatly depend as to whether 
 the clock and the observer was in the line of motion of the alpha 
 particle or not? How can the mass of a body be determined under 
 these conditions? What kind of observers will be able to direct 
 the measurements? Can we devise an automatic set of appara- 
 tus that could record the measurements that we wish to have 
 made and place the apparatus on the alpha particle? These 
 are some of the problems that confront the new science and con- 
 siderable advances are being made outlining and answering some 
 of the easier of these problems. 
 
 The science that is developed on the rapidly moving alpha 
 particle may then be called the alpha particle science. As the 
 beta particle is very much smaller and is surrounded by a very 
 intense electric field we will have a beta particle at rest physics 
 and a rapidly moving beta particle physics. Such phenomena 
 as the propagation of light may then be very different according 
 as we view them from our own standpoint, in regions like our 
 own but with very intense electric fields, or from rapidly moving 
 alpha and beta particles. The new science aims to unify all 
 these sciences of the systems, no matter how differently they 
 may appear, into one harmonious whole. It purposes to correlate 
 the laboratory in the mind with the laboratory of the ishop. 
 Length, time, and the other "fundamental units" and the laws 
 of science are defined and measured if possible under every 
 condition that is known. There is to be one common science 
 based on the same laboratory plan for the inside of the atoms, 
 for molecular spaces, for conditions as they may exist in the center 
 of the sun or for free space. 
 
 The origin of the new science is to be found in the new geome- 
 tries developed from axioms differing from those assumed by 
 Euclid. The discovery of the electron, radioactivity, and 
 studies in radiation and the propagation of light with reference 
 to the earth's motion have furnished the beginnings and the 
 outlook of the new fields to be covered. On account of the 
 prominent role played by electrical phenomena it is necessary 
 to restrict this treatment largely to a decription of an ensemble 
 of electrical charge, mass and energy, for so far as we know 
 electrical charge always appears with a certain quantity of 
 mass and energy, the latter being usually of the potential type. 
 As all knowledge comes to us through the senses, it seems well
 
 4 FUNDAMENTAL PHYSICS 
 
 to consider very briefly the transformations in phenomena 
 imposed upon us by the gateways of the senses and to indicate 
 how it may be possible to introduce laboratory methods into 
 mental phenomena. The various entity systems are viewed 
 in regard to the problems introduced for the new science and an 
 outline is given of a possible system of laboratory method that 
 would be applicable to all of these entity systems. 
 
 All of our scientific advances by the laboratory method have 
 shown that the magnitudes of quantities defined by the expres- 
 sions "greater than" or "less than" are constituted of parts. 
 These parts have been sorted into classes, the parts in each class 
 being found to be alike in some or all of their properties. The 
 smallest parts of a magnitude will be called the elements or 
 atoms of that magnitude. The citizens of a nation constitute 
 its elements or the atoms of ordinary masses of matter, its 
 elements. The term element as thus used depends upon the 
 point of view and is a relative term. The term ultimate element 
 could be defined as the smallest magnitude that any quantity 
 can be partitioned into. Thus as far as we -know the electron 
 is the ultimate element of electrical charge and it may be one 
 of the ultimate elements of the universe in the absolute sense 
 if the electron does not possess parts or as we may say a 
 "structure." In the vortex ether theory of matter there was 
 only one ultimate element of the universe as regards ordinary 
 matter and free space. 
 
 A natural system such as a star, an animal, a magnet or an 
 electron will be spoken of as an entity or an entity system. A 
 laboratory or an assumed grouping of elements, such as a cavity 
 of radiations used in the definition of a black body will be called 
 an ensemble. An aim of science is to discover the ultimate 
 elements and to explore and derive laws for the simplest en- 
 sembles. As an example of this kind of problem we might 
 consider space or the free ether as we will name it. In many 
 theories the free ether is assumed to be isotropic and to be without 
 structure. How can it be possible to apply the term extension 
 to such an ether for there is no way of defining direction? How 
 is there to be any relation tp time for in any such ether it would 
 be impossible to measure time. Terms such as time and direc- 
 tion are therefore meaningless for such an ether because there 
 is no way to define them. There is then no time or direction 
 qualities to an isotropic ether possessing no structure.
 
 THE GOAL OF THE NEW SCIENCE 5 
 
 Consider an ensemble of the above ether and radiation ele- 
 ments. If this ensemble is without a structure how can we define 
 a length because we must possess some marking elements for 
 a unit of length or how can we speak of time in such an ensemble 
 because we are unable to measure length? For the above en- 
 semble the velocity of the radiation cannot be employed to meas- 
 ure time because there is no way of defining length. For this 
 ensemble of ether and radiation the terms length, direction 
 and local time can possess no local meaning but must be received 
 from some other ensemble. For a medium as the ether to be 
 intelligible, to possess directed qualities and to be described 
 by equations, employing terms such as length and time, it is 
 necessary that it possess a structure and certain other 
 " fundamental " qualities. 
 
 The new science develops a consistent and a local philosophy 
 for each ensemble and determines as fundamental a system of 
 local definitions, units and laws as possible. The laws of the 
 transformations of the local philosophies of the different 
 ensembles is then determined. The philosophy that possesses 
 the most universal application a,mong the natural entities and 
 whose convenience is greatest may then be adopted for general 
 use.
 
 5. THE DISAPPEARANCE AND CONSERVATION OF 
 ENERGY, ELECTRICAL CHARGE AND MASS 
 
 It has long been assumed that energy disappears or changes 
 its form and one can consider phenomena as largely if not 
 altogether marked by energy changes. To us the conception 
 of energy is most satisfying when we consider kinetic energy 
 or one-half mv 2 . Potential energy is in an intangible condition 
 or form for how can we conceive of this energy as existing except 
 in the medium or the ether. Since we apparently know so little 
 of the ether we can almost speak of the energy as being lost. 
 The classical illustration of the transformations of kinetic and 
 potential energy is that of the vibrating pendulum. In the 
 middle of its swing the energy is all kinetic while at the ends of 
 the swing the energy is all potential. Our laboratory work con- 
 sists of experiments with the energy in the kinetic form. To be 
 studied energy must first be converted into the kinetic form 
 adapted to the problem at hand. A piece of uranium or a piece 
 of coal can be used as regards their radioactive or chemical energy 
 content only when radioactive energy or when heat is developed. 
 
 The law of the conservation of energy is found to hold when 
 we consider the existence of the two forms of energy and we feel 
 entirely justified in treating potential energy as "existing" 
 in the same way as kinetic energy because it can be converted 
 into the kinetic form. 
 
 Our ordinary world as we see it every day is one in which 
 kinetic energy is usually being converted back and forth into 
 potential or "heat" energy. And it requires much of our engi- 
 neering effort to maintain our kinetic condition. Friction is ever 
 working against the moving elements. Most of us are kept 
 busy to keep things going. Even in the astronomical world 
 the philosophy of many is that the suns are becoming cold and 
 dead and that the revolving planets and moons are slowing down 
 in their motion. Yet this death of kinetic energy that is every- 
 where about us and which we will designate as a condition of 
 our type of physical world is counteracted by more or less 
 unknown elements so that conservation may always apply.
 
 THE DISAPPEARANCE OF ENERGY 7 
 
 The energy world is then ruled by these conditions: energy is 
 conserved: the energy changes of our every day life is marked 
 by the natural tendency of kinetic energy to disappear: and the 
 second law of thermodynamics which may be stated in a number 
 of forms such as the ever increasing value of the entropy content 
 of any isolated system, the impossibility of perpetual motion 
 apparatus or the ever tendency of the universe to run down 
 as regards many energy changes (in the same way as a clock, the 
 potential energy of the spring being converted into the kinetic 
 energy of the pendulum and this kinetic energy changed gradually 
 into the kinetic energy of heat motions). 
 
 The continual flow of energy through so many transforma- 
 tions leads one to suppose that when it ultimately is found to 
 consist of units, particles, quanta, entities, atoms or whatever 
 term we may call them, these ultimate elements may be all alike 
 because all quantities of energy, like electrical charges, depend 
 upon the total amount of energy present and are independent 
 of the nature of the elements of energy combined to form the 
 whole. 
 
 The appearance of electrical charges bears some analogies 
 to the appearance of energy. The commercial problems relating 
 to electricity have to do with the generation, the transmission 
 and the absorption of charges of electricity, the phenomena of 
 magnetism being assumed as being due to the motion of electrical 
 charges. The constitution of electrical charges is very simple 
 in that all electrical charges appear to be built of elementary 
 parts all having the magnitude of 4.7 (10)~ 10 e.s. units, all these 
 units being identical except as they may be positive or negative 
 in character. 
 
 Like kinetic energy electrical charges never appear except in 
 connection with masses of matter thus making the trio of kinetic 
 energy, mass and electrical charge an inseparable ensemble as 
 far as experimental knowledge extends. As kinetic energy is 
 characterized by its tendency to disappear so free electrical 
 charges always disappear unless special precautions are taken to 
 prevent this change. The electrical elements possess the unique 
 property however of neutralizing themselves in that the approach 
 of equal charges of positive and negative electrical discharges 
 causes the more or less complete disappearance of the charges. 
 
 The smallest element of negative electricity, the electron, 
 is associated with a mass of matter about the one-eighteen
 
 8 FUNDAMENTAL PHYSICS 
 
 hundredth part of that of the smallest element of matter, the 
 hydrogen atom. Since the ratio of mass to charge is found to 
 vary with the velocity of the electron it has been assumed that 
 this mass is variable rather than the electrical charge. Experi- 
 mentally the magnitude that is measured is the ratio of the 
 charge to the mass so that for the rapidly moving electron we 
 have a condition arising where electrical charge, mass and of 
 course the kinetic energy appears as a variable ensemble for 
 which no experiment has been devised that will permit of the 
 determination of the varying elements. 
 
 As the philosophy that assumes that natural phenomena 
 are extremely simple has led to many of the greatest discoveries, 
 so the assumption that the magnitude of the electrical charge 
 is constant rather than the mass of the electron, makes the treat- 
 ment of the ensemble of energy, charge and mass more simple 
 and apparently just as accurate as would any other assumption. 
 The law of the conservation of electrical charge can thus be 
 considered to be absolute. The second law and the general 
 condition that applies to electrical charges is that all the natural 
 changes in a closed electrical system are such as to make the 
 magnitude of the free charge a minimum. 
 
 No positive electrical charge has been found except as being 
 associated with atoms of matter and the view commonly held is 
 that the positive charges are an essential part of the nuclei of the 
 atoms. The generation of free charges of electricity always 
 results in the disappearance of energy. The disappearance of free 
 electrical charges always takes place in matter and the picture of 
 the process assumes that the positive and negative charges 
 neutralize each other inside the molecules and atoms. The energy 
 that is lost in the generation of free charges is considered as the 
 energy of the electrical field between the positive and negative 
 charges and that on the localization of the electrical field inside 
 of atoms or molecules some of its potential energy is changed into 
 kinetic energy. 
 
 As in energy changes the disappearance of kinetic energy was 
 considered as accompanied by the appearance of an equal amount 
 of potential energy in the ether so the disappearance of negative 
 charges into molecules and atoms could be associated with the 
 appearance of certain characteristics of matter which we ordi- 
 narily associate with the neutral state. In other words the char- 
 acteristic properties of matter may be those associated with what
 
 THE DISAPPEARANCE OF ENERGY 9 
 
 we consider as matter after it has lost all of its electrons. Such 
 matter we will speak of as "natural" or "free" matter. "Ordi- 
 nary" matter will be called "neutral" matter. All electrical 
 charges then become aggregates of electrons and all masses 
 become aggregates of electrons and the "atoms' 7 of "natural" 
 matter. 
 
 The constitution of matter is found to be atomic, all matter 
 being built out of some 92~elementary atoms with accumulating 
 evidence that these atoms may themselves be composed of much 
 simpler systems such as hydrogen or helium. The fundamental 
 property of matter is usually believed to be its mass and the 
 science of chemistry is based on the assumption that mass is 
 conserved. We have seen that the mass of the electron is con- 
 sidered as a variable. Whether this kind of mass is acted upon 
 by gravitational forces remains for future experiments to deter- 
 mine and whether the mass of the various atoms varies as does 
 that of the electron at high speeds also remains for future investi- 
 gations to tell. There may be an electrical and a material mass, 
 or a kinetic and a potential mass corresponding to the energy 
 terms. The law of .conservation might be considered as apply- 
 ing to the two types of mass. "Natural" matter would always 
 naturally disappear into ordinary or neutral matter and the law 
 corresponding to the second law of thermodynamics would be that 
 the complex atomic systems are running down or in other words 
 the radioactivity of the elementary atoms always results in simpler 
 atomic systems through the disintegration of the more complex 
 atoms. 
 
 The law of conservation and the disappearance of kinetic 
 energy, electric charge and natural matter appear to be the same. 
 These elements naturally partition themselves between the ether 
 and neutral matter. Neutral matter is then the vehicle of ki- 
 netic energy, electrical charge and natural matter. The disappear-, 
 ance of kinetic energy, of free electric charges or of natural matter 
 is accompanied by potential energy changes for which the ether is 
 the vehicle. The ether about an ensemble of energy, charge and 
 natural matter may be considered to be in a state or to be 
 approaching a state of equilibrium with the ensemble. Thus the 
 ether about ordinary' matter could be considered as "ordinary" 
 ether and might be the same or different from the ether at a very 
 great distance from any of these elements or from ensembles of 
 one or more of these elements. Experimental work of the most
 
 10 FUNDAMENTAL PHYSICS 
 
 fundamental character remains to be done as to the relations 
 between the free ether, energy, electric charge, and natural matter 
 and the partitioning of these elements between ordinary ether 
 and matter. The law of conservation applies by definition to 
 electrical charges absolutely and to energy and mass only as ele- 
 ments in a closed ensemble of ether, energy, matter and charge. 
 
 The writer proposes the ether to be an analogue of matter 
 possessing a much more fine grained structure. The elements of 
 electrons and natural atoms of matter become the electroethons 
 of the ether. The potential or hidden energy becomes the kinetic 
 energy of the electroethons. The vibrations and sound waves of 
 neutral matter are paralleled by the electromagnetic waves of the 
 ether. As sound waves are pictured as the ordered collisions of 
 particles of matter so the electromagnetic waves are the ordered 
 collisions of electroethon particles. For purposes of illustra- 
 tion rather than as an exact analogue there can be pictured an 
 atmosphere of mobile electroethons in a lattice work of immobile 
 electroethons somewhat similar to the existence of an atmosphere 
 of electrons in a framework of the natural atoms of matter in a 
 metal. An electric field is a region of the ether where the neutral 
 condition has been disturbed in much the same way that an 
 electromotive force disturbs the condition of equilibrium of 
 the electron atmosphere of a metal. 
 
 In treating the second law of thermodynamics Maxwell con- 
 sidered that there could be "demons" that could reverse the 
 changes whose direction was given by the law. Our credo as 
 optimists leads us to believe that there are "angels" that can 
 direct the transformation of any natural phenomena. For 
 example the direction of the radioactivity of matter is that of the 
 disintegration of -the more complex elements. We believe that 
 experimental discoveries will be made that will indicate how 
 "angels" (and perhaps ourselves) can build the more complex 
 atoms from the simpler conserved elements. These "angels" 
 might possibly work in the center of the sun, in very intense elec- 
 tric fields or by "breaking down" the ether under electrical 
 stresses so that even electrical charges or natural atoms would 
 result. And the Director of these "angels" we might define as 
 the "Creator" or "Ruler" of the Universe,' and this form of phi- 
 losophy as "monotheism." 
 
 As regards kinetic energy we know that its magnitude is 
 relative depending on how %mv 2 is defined and measured.
 
 THE DISAPPEARANCE OF ENERGY 11 
 
 Presumably potential energy and possibly mass and electrical 
 charge may be viewed in the same way for the latter two quan- 
 tities are measured by "forces" and accordingly if the system 
 upon which measurements were being made was subjected to 
 acceleration the measurements would be subject to modification. 
 The condition of relativity thus appears amongst the conserved 
 elements. An example of such relativity is that of electrical 
 charge and mass. No electrical charge has ever been separated 
 entirely from a mass, the electron possessing a certain charge 
 and a certain mass defined with reference to the system with 
 reference to which its motion is measured. 
 
 These problems as to the way the ether is modified by its 
 energy content are very important and can be studied by the 
 effect produced upon the velocity of the electromagnetic ra- 
 diations (the writer is now engaged in experiments of this kind) . 
 Indeed apparently no more fundamental and isolated experiments 
 can be performed because these are the simplest ensembles at 
 present open to the new science. 
 
 The marked effects of electric charges and natural matter 
 upon the ether (the electric and magnetic fields), the apparent 
 absolute conservation of these elements and their disappearance 
 by their "mutual neutralization" have few analogues in the 
 coarser grained entity systems unless we consider phenomena like 
 the formation of salts from acids and bases, the phenomena of 
 permanent magnetism and some life phenomena. 
 
 Experiments have already indicated that the structure of 
 electrical charge is more "fine grained" than that of ordinary 
 neutral matter though the atoms of natural matter, the positive 
 nuclei of the ordinary atoms, possess about the same size as the 
 electron. The "fineness" of structure of natural matter is thus 
 made to depend upon the magnitude of the nuclei of the atoms. 
 The ultimate and individual elementary units of energy and of 
 the ether have not been discovered experimentally and it is 
 reasonable to assume that these elements are much finer grained 
 than mass or electrical charge. 
 
 From the Zeeman, Stark and similar effects and the modifi- 
 cation of the velocity of electromagnetic radiations by matter it 
 seems certain that electrical charges remain as such in the neutral 
 atomic and molecular systems. The disappearance of energy 
 and mass in the ether without changing its properties to any great 
 extent would lead us to believe that the ether may be such a
 
 12 FUNDAMENTAL PHYSICS 
 
 "dense" energy and mas medium that the increment due to 
 these disappeared elements affects the "density" but little. The 
 older elastic ether theory developed from these disappearance 
 phenomena. 
 
 The possible conditions of relativity in any ensemble are so 
 numerous that it is always highly important to reduce the num- 
 ber of elementary units in the ensemble to the minimum. The 
 new science aims to obtain the ultimate units or atoms of all the 
 entity systems of the universe and then consider if any of the 
 properties of these elementary atoms can be defined as "ab- 
 solute" in the sense of "nondisappearing." Other elements 
 will then be described relative to the "absolute" elements. If 
 the elements that appear to be definable in an "absolute" man- 
 ner do not determine a physics uniquely then the new science 
 will develop all the consistent systems of physics that appear to 
 equally simulate phenomena and employ the system that is 
 simplest and most convenient.
 
 6. IONIZATION PHENOMENA 
 
 According to the freedom of neutral atoms of matter we clas- 
 sify bodies into solids, liquids and gases. In solids the atoms may 
 possess an orderly arrangement in planes (as is the case in crys- 
 tals) or a more or less disordered arrangement (as in substances 
 such as glass). The atoms are not free to move about. In 
 liquids the molecules possess some freedom of movement but are 
 not "free." In gases the molecules are comparatively "free" 
 except during collisions. The kinetic energy content increases as 
 one passes from solid to liquid to gas. 
 
 Electrical charges are "bound" in neutral matter. The 
 "binding" is greatest in the insulators or nonconductors. It 
 becomes very much less in electrolytes when a difference of po- 
 tential of a few volts will "free" the charges. It is least in metals 
 where an "electron atmosphere" or electron gas is quite "free" 
 to be acted upon by very small electromotive forces. 
 
 Temperature can be employed as a measure of the kinetic 
 energy of molecules when in the gaseous state. The absolute 
 zero of temperature being a condition where the kinetic energy 
 vanishes. Conductivity varies as the freedom of the electrical 
 charges in matter and .becomes practically perfect for metals for 
 the absolute zero of temperature. Electrical currents will flow 
 in metals at very low temperatures for hours after the applied 
 e.m.f. has been discontinued. 
 
 High temperatures of all substances results in their intense 
 ionization and increased conductivity. The upper limit of 
 temperature results from the generation of free electrical charges 
 or ions and the flow of kinetic energy into "potential energy" 
 then restricts the attainment of any highei^temperatures. The 
 density of the potential energy may be assumed to measure the 
 "temperature" of the electroethons. 
 
 The motion of atoms or molecules in solids and of ions in non- 
 conductors is ordered and consists largely of oscillations about 
 positions of equilibrium. The motion of molecules and ions in 
 liquids is more disordered. The motion of molecules in gases, of 
 electrons in metals and of ions in substances at high temperatures 
 
 13
 
 14 FUNDAMENTAL PHYSICS 
 
 is largely disordered, the values of the "free paths" and velocities 
 of the particles following Maxwell's law and being that of the 
 variation in the distance of the bullet marks on a bull's eye pat- 
 tern used as a target in rifle practice. 
 
 Ordered motions are added to the natural motions when a 
 direct electric current flows through a metal, a vacuum tube or 
 any conducting substance, when heat flows, or when a mechan- 
 ical pressure is transmitted. Alternating motions are added to 
 the natural motions when alternating currents of electricity, heat, 
 or mechanical pressure or sound waves are transmitted through a 
 substance. 
 
 Thanks to the existence of electron atmospheres we are able to 
 cover the earth with a network of cables, telegraph, telephone and 
 electric power transmission lines. We can picture these as 
 "electric lines of force" making a loose lattice work everywhere. 
 The electric cars would be the "ions" following the "electric 
 lines of force of the polarized electric field" the cables overhead 
 or beneath the electric car. The atoms and molecules could be 
 represented by the trains on the railroads and the automobile 
 trucks on the national highways. The locomotives are the 
 "energized" atoms giving kinetic energy to the train molecules. 
 The chunks of coal and the tanks of gasoline are the quanta, 
 radions or elements of radiation that are being partitioned to the 
 molecular elements. Coal and gasoline represent "potential," 
 stored or lost kinetic energy. The motion of the automobile 
 trucks is disordered and is represented by gas motions while the 
 motive electric cars in a city are more like the motions taking 
 place in the lattice work of solids and liquids. 
 
 The analogy between our system of electrical current trans- 
 mission by threads of electron atmospheres and the lattice line 
 structure of an atmosphere of electroethons indicates that the 
 supposed difficulty of the ether problems may not be as great as 
 at first surmised. In the first place we at first feel that a system 
 of matter could with difficulty pass through an ether lattice work. 
 The diameter of an atom is about 10~ 8 cm. while the diameters 
 of the atom nucleus and the electron are about 10~ 13 cm. The 
 emptiness of the atom is then equivalent to the emptiness of the 
 United States when filled with about 1000 buildings 30 ft. square. 
 Even though a large part of our population enjoy the telephone 
 and the electric current the "porosity" of these electron atmos- 
 pheric threads through the country is "extremely tenuous."
 
 IONIZATION PHENOMENA 15 
 
 Each atom could be cut by an ether thread and yet the ether lat- 
 tice structure could be much more tenuous than our lattice sys- 
 tem of telephone threads. The nature of the ions and the 
 ionic radiations will permit an outline the electron and "natural 
 matter" world. 
 
 An ion consists of a certain amount of electrical charge with a 
 certain quantity of matter. Experimental evidence indicates 
 that every atom of matter contains one or more atoms of negative 
 electricity or electrons. These electrons may be ejected from 
 the atoms or molecules of matter under certain conditions, leav- 
 ing the atoms or molecules positively charged. The atoms or 
 molecules may gain or lose negative electrons and by this means 
 an innumerable number of different kinds of negative and posi- 
 tive ions can be formed. All kinds of ions are combinations of 
 atoms and molecules that have either lost or gained electrons. 
 
 Ions composed of a comparatively small number of atoms or 
 molecules are called simple ions. Thus the ions produced in 
 chemically pure gases at low pressures are simple ions. When 
 the gases are not pure; when fog, dust and similar particles are 
 present, the ions may be very complex. The ions resulting from 
 many kinds of chemical reactions such as those to be found in 
 the neighborhood of flames are complex. There is probably 
 no sharp dividing line in the above classification, the division 
 being one of convenience. 
 
 An ion is a charged particle that may be considered to be 
 practically at rest or at least it does not possess any greater kine- 
 tic energy than does a gaseous molecule at the same temperature. 
 It may be given kinetic energy of motion by the action of an elec- 
 tric field. The "particles" that constitute radiations such as 
 a, /3 or cathode ray particles are moving rapidly and are not 
 usually spoken of as ions. 
 
 Under no condition is the number of free ions in a given space 
 of the same order of magnitude as the number of atoms. Ionizing 
 agents in general produce equal numbers of positive and negative 
 ions or at least this is usually assumed to be the case. It is 
 possible that the ions formed may possess charges of different 
 magnitude so that the number of positive ions need not neces- 
 sarily be equal to the number of negative ions. It requires 
 some time for an ionizing agent to act before the number of 
 ions being formed is equal to the number of positive and negative 
 ions recombining. It is in phenomena of this kind that the
 
 16 FUNDAMENTAL PHYSICS 
 
 term coefficient of recombination is used. This coefficient is 
 probably not a constant but depends upon the process under 
 which ionization takes place. In most cases the production 
 of ions is approximately uniform throughout any given body 
 and under these conditions the coefficient is practically a con- 
 stant. The term coefficient of diffusion is defined in the same 
 way as in the theory of gases. Its constancy also depends upon 
 the uniformity of the ionization. 
 
 Any gas that is ionized when placed between electrodes 
 maintained at a certain difference of electrical potential will 
 permit an electrical or ionization current to flow. This current 
 increases to a maximum value called the saturation current 
 for an increase in the potential difference up to a certain value 
 called the saturation potential difference. These current poten- 
 tial curves depend upon the nature, the pressure, the tem- 
 perature, etc., of the ionized medium. They also depend upon 
 the nature of the ionizing agent. 
 
 In ionization literature the terms ray and radiation are often 
 used indiscriminately. x-"rays" and x "radiations" are both 
 used. The term "ray" applies to the emission from "z-ray" 
 tubes and from the radioactive bodies. Thus we have a, /3, 
 7, 5 and x-rays, recoil rays, cathode and the various vacuum 
 tube rays. When the nature of the emitted particle or wave 
 is characteristic and possesses properties that can be accurately 
 measured, the term radiation is used. Thus we have black 
 body radiations, the radiations from definite radioactive prod- 
 ucts, characteristic x radiations, etc. The term secondary 
 radiation is generally used because these radiations are often 
 characteristic of the kind of matter emitting them. The terms 
 "ray," "beam of rays," "pencil" of rays, etc., are used in much 
 the same way as they are used in optics. 
 
 It may be considered convenient to classify radiations into 
 the "bullet" or atomistic and the "medium" types. 7 and 
 x-rays are of the wave or pulse type. Experimental evidence 
 indicates that the ionization produced by the x and 7 rays is 
 due to the secondary radiations excited by these rays. Indeed 
 it may be possible that all ionizing rays consist of moving 
 particles, these particles being invariably charged. According 
 to this view the process of ionization would be a collision phe- 
 nomena, the resultant ions being due to the action of an electric 
 field upon molecules or atoms.
 
 IONIZATION PHENOMENA 
 
 17 
 
 Primary Radiations 
 I. Electromagnetic radiations: 
 
 1. Hertzian waves. 
 
 2. Reststrahlen and radiant heat. 
 
 3. Light... 
 
 4. Ultraviolet light. 
 
 5. X-rays. 
 
 II. Cathode rays 
 
 III. Ionic radiations due to the action 
 of the electric force: 
 
 1. Anode or positive rays 
 
 2. Canal rays. 
 
 3. Negative rays. 
 
 4. Entladungstrahlen. 
 
 5. Magnetic rays. 
 
 6. Neutral rays. "Retrograde" 
 rays are probably neutral 
 during a large portion of their 
 path. 
 
 IV. Thermionic radiations: 
 
 1. Electron radiations. 
 
 2. Rays of positive and negative 
 ions and neutral matter. 
 
 2 
 
 Secondary Radiations 
 
 (a) Normal photo-electron radia- 
 tions. 
 
 (6) Selective photo-electron radia- 
 tions. 
 
 (a) Normal photo-electron radia- 
 tions. 
 
 (6) Selective photo-electron radi- 
 tions. 
 
 (c) Secondary cathode rays. 
 
 (a) Secondary cathode rays. 
 
 (6) 5 rays. 
 
 (c) Secondary scattered x-rays. 
 
 (d) Homogenous x radiations. 
 (a) Secondary cathode rays. 
 (6) Secondary x-rays. 
 
 (i) Homogenous x radiations 
 characteristic of the anti- 
 cathode. 
 
 (ii) Independent x-rays char- 
 acteristic of the velocity of 
 the primary rays. 
 
 (a) Secondary rays produced by 
 neutral rays. These may con- 
 sist of positive or negative ions 
 or of neutral particles. 
 
 (6) 5 rays or slowly moving 
 electrons. 
 
 (c) Soft x-rays and possibly char- 
 acteristic x radiations of Sn 
 and Pb.
 
 18 FUNDAMENTAL PHYSICS 
 
 V. Radioactive radiations : 
 
 1. a rays. 
 
 Atoms of helium with a 
 double positive charge. 
 
 2. ft rays. 
 Electrons. 
 
 3. y rays. 
 
 4- Recoil rays. 
 
 Atoms of radioactive 
 products. 
 
 (a) 5 rays. 
 
 (6) Secondary y rays, 
 (.c) Secondary recoil rays, 
 (a) 5 rays. 
 
 (6) Secondary y rays, 
 (c) Secondary recoil rays, 
 (a) Secondary /3 rays. 
 (6) Secondary scattered y rays, 
 (c) Homogenous y radiations, 
 (a) 5 rays. 
 
 (6) Secondary recoil rays consist- 
 ing of particles struck by the 
 
 primary recoil ray particles. 
 5. Penetrating radiation. 
 
 Of the above radiations, photo-electron radiations, primary 
 and secondary cathode rays, primary and secondary ft rays, 
 high temperature negative thermionic radiations and 5 rays 
 consist of streams of rapidly moving electrons. The only essen- 
 tial difference between these various types of electron radiation 
 lies in the fact that the electrons possess different velocities. 
 5 rays consist of very slowly moving electrons. ft rays derive 
 their energy from atoms undergoing radioactive change and usu- 
 ally consist of very rapidly moving electrons. Cathode rays 
 are due to electrons that have fallen through electric fields of a 
 certain potential difference (7) and have acquired a kinetic 
 energy %mv z = Ve. 
 
 The other radiations either consist of "waves," "pulses," 
 "entities" or moving particles composed of one or more atoms of 
 matter, a rays are rapidly moving helium ions carrying a 
 double positive charge. ft and 7 rays derive their energy from 
 atoms undergoing radioactive change. There are then three 
 types of high speed radiations, the ether, electron and atomistic 
 radiations. All these radiations are ionizing agents except the 
 long wave length ether radiations. 
 
 Ionizing radiations are either spontaneous or subject to ex- 
 perimental control. The a, ft and 7 rays are spontaneous in 
 origin and their initial properties on emission cannot be al- 
 tered in any way by changes in the surrounding physical and 
 chemical environment. While many of the other radiations 
 are emitted by atomic or molecular systems, these systems can 
 be controlled in certain ways by the action of outside forces. 
 Thermionic radiations depend upon the temperature, the nature
 
 IONIZATION PHENOMENA 19 
 
 of the incandescent surface, etc. The nature of x-rays depends 
 upon the velocity of the exciting cathode ray particles. 
 
 With the possible exception of the spontaneous radiation, all 
 the "material" or electron radiations are due either to the exist- 
 ence of high temperatures or to electric fields. 
 
 Experimental evidence supports the view that only material 
 or electron radiations produce ionization directly. X and 7 
 rays and ultraviolet light seem to ionize bodies indirectly through 
 the action of secondary electron radiations. It therefore fol- 
 lows that the ionization of neutral particles takes place during 
 the moments of collision between these particles and the rapidly 
 moving radiation particles. According to this view ionization 
 is a collision phenomenon. 
 
 Though intimately related in the phenomena as they ac- 
 tually take place, the various ionizing radiations can be discussed 
 and classified according to the changes which take place in the 
 radiations when they pass through matter, the changes pro- 
 duced in the atoms from which they originate and the changes 
 produced in the molecules and atoms of the absorbing matter.' 
 
 (A) Effects on the ray particles and beams of radiation pro- 
 duced by the atoms and molecules of absorbing matter. 
 
 (a) The ray particles lose their velocity. This decrease of 
 velocity obeys certain laws and depends upon the nature of the 
 particles, the nature of the atoms with which they come into 
 mutual action or collision and the dynamic conditions of each 
 collision. (6) The rays or radiation beams lose energy due to 
 decrease in velocity though not necessarily according to the or- 
 dinary mechanical relation, (c) The ray particles or entities 
 may disappear, (d) The ray particles or entities may be trans- 
 formed so that a different type of radiation results, (e) The 
 direction of the rays may be changed. This changed part may 
 be either of a reflected or a scattered type. 
 
 (B) The effects that take place during the formation of the 
 radiation particles or entities. 
 
 (a) The velocity of a and particles appears to be related to 
 the period of disintegration of the parent atom. (6) /? and 7 
 rays are usually emitted by the same product probably simul- 
 taneously, (c) a particles may be emitted in pairs, (d) The 
 emission of a particles often precedes the existence of short period 
 disintegration products, (e) The parent atom may become 
 a recoil ray particle. (/) The emission of primary rays by an
 
 20 FUNDAMENTAL PHYSICS 
 
 atom may be accompanied by the emission of secondary radia- 
 tion due to the passage of the primary ray particle through the 
 atom, (g) Various vibrations and changes in structure of 
 the parent atom may accompany the ejection of any radiation 
 particle or entity, (ti) The energy changes due to the forma- 
 tion of the primary and secondary radiation particles may take 
 place according to the elementarquanta theory. 
 
 (C) Some effects produced in the molecules and atoms of 
 the matter absorbing the given radiation. These effects may be 
 temporary or they may possess any degree of permanency. 
 
 (a) The atoms or molecules may be dissociated into neutral 
 parts. (6) The atoms or molecules may be ionized. The ions 
 may be formed within the molecule or they may separate from 
 each other and exist as independent particles. Secondary 
 electrons radiations are of this latter type, (c) The atoms, 
 molecules or their ions may be caused to become recoil ray par- 
 ticles, (d) Atoms may be permanently broken down. This 
 constitutes a transmutation of the element and has not been 
 positively proven to take place, (e) The atom or molecule may 
 be caused to emit some of its intrinsic energy. This constitutes 
 a "trigger" effect and has not been proven to take place. (/) 
 The atom or molecule may absorb energy and store it in a ki- 
 netic or a potential form, (g) Parts of the atom or molecule may 
 be put into vibration. This may result in a transformation and 
 radiation of the energy absorbed. Phosphorescence and fluores- 
 cence are examples of this kind, (h) The ionizing particles 
 may combine with an atom, molecule or ion and form a new sys- 
 tem. The resultant particle need not necessarily be a radiation 
 particle. The production of particles by dissociation, ioniza- 
 tion and possibly by transmutation is opening a new field in dy- 
 namical chemistry, and promises much from both the theoretical 
 and practical points of view. 
 
 From the point of view of generating the ionizing agents many 
 problems arise. Even in the visible part of the spectrum it is 
 very difficult to obtain monochromatic light. The ordinary 
 incandescent lamp does not possess an electric current to light 
 energy emission efficiency of more than a few (a) per cent, and 
 the efficiency of converting the original energy of the coal into 
 electric current is only some twenty (6) per cent, at best. 
 
 If then we wish to generate ultraviolet light of X 2500 to X 2550, 
 we might use a very hot incandescent filament and screen out by
 
 IONIZATION PHENOMENA 21 
 
 absorption all of the spectrum except those wavelengths thus 
 obtaining a certain "very small (c) percentage of ultraviolet light 
 out of the total radiation energy of the incandescent filament. 
 We then employ this ultraviolet light to generate ozone and again 
 obtain a certain percentage (d) of energy transformation which in 
 no case would be large. The total efficiency of the various proc- 
 esses is almost infinitesimally small, abed, and this condition is 
 typical of the generation of all ionizing agents. 
 
 Not only is the efficiency of the process small but only a few of 
 all the possible short wavelengths of the electromagnetic radia- 
 tions and only a few of the thousands of possible atomistic radia- 
 tions at comparatively low velocities are obtainable. We ought 
 to be able to get beams of gold radiations (charged Au atoms) 
 possessing any velocity we wished up to our assumed limit of 
 3(10) 10 cm. per sec. We might wish to know whether the 
 benzene rings would remain stable for all possible velocities. 
 Would these radiations resemble the beams of helium ions known 
 as a rays? 
 
 With the electron radiations we are more successful. In 
 x-ray tubes we can generate these electrons with velocities 
 approaching that of light. By using windows these electron 
 radiations can be utilized outside the x-ray tube. But even here 
 the efficiency of generation and the intensity of the electron 
 beams are small. 
 
 The generation of the atomistic radiations has only been 
 applicable to the lighter atoms in gases at low pressures. In 
 vacuum tubes weak radiations of the gaseous atoms such as oxy- 
 gen and nitrogen can be generated with varying velocities 
 approaching say a tenth that of light. But these radiations are 
 easily absorbed by any material that can be used as a window for 
 a vacuum tube and hence only very weak atomistic radiations 
 can be transmitted outside the tube. 
 
 Atomistic radiations homogenous in constitution, magnitude and 
 direction of velocity are not generated in gases at ordinary pres- 
 sures because the gases do not support an electric field of sufficient 
 intensity. As soon as these radiations are generated they begin 
 to transmit their energy to the gas molecules during collision and 
 this prevents the acquirement of any considerable velocity at all. 
 
 The problem of generating atomistic radiations will be greatly 
 aided by the use of very high voltages, very large vacuum tubes 
 and rapid vacuum pumps. In this way it may be possible to
 
 22 FUNDAMENTAL PHYSICS 
 
 produce a great many new kinds of atomistic aggregates and ions 
 and possibly to disintegrate matter, i.e., produce artificial radio- 
 activity and even to build up new atoms. Only one kind of 
 atomistic radiation possessing a high velocity, the a rays, is 
 known and on account of its being ejected by a number of radio- 
 active products it is assumed to be a component part possibly of 
 all atoms. The question of the philosopher's stone, of learning 
 the structure of the atoms, of analyzing and synthesizing them is 
 to be answered when and only when the subject of atomistic 
 radiations has been fully investigated.
 
 7. THE GATEWAYS OF KNOWLEDGE AND OUR 
 * SCIENTIFIC DEVELOPMENT 
 
 Every one of us receive our knowledge through the sense 
 organs and the nervous system so that all phenomena of the 
 outside world are received by the mind after the intricate and 
 not well understood transformations made by these mechanisms. 
 One of the big problems of science consists in accurately de- 
 scribing these transformations. 
 
 It follows as a corollary that we do not now know of any 
 "agent" in the outside world except in terms of the perceptions of 
 the mind. Revolutionary as scientific discovery has been we 
 have found no new "agent" in nature. At one time x-rays 
 were thought to be such but now it is quite certain that they are 
 electromagnetic radiations. If x-rays had been a new "agent" 
 its nature would have remained unknown because only the 
 properties "felt" by our senses could have been understood. 
 It is for this reason that the terms electric, magnetic and gravi- 
 tational fields of force mean so little to us beyoncl the mechanical 
 effects which they produce. An illustration of this kind is 
 given " by Bragg's theory of x-rays before they were shown to 
 possess the same diffractive properties as light. The x-ray 
 according to Bragg was an "entity" that received energy from 
 an electron striking the anticathode. It was propagated "with 
 the velocity of light" just as a "particle of matter." In this 
 "entity" stage absolutely nothing was known of the x-ray 
 except as a carrier of energy. When x-rays were absorbed by 
 ionizing a gas Bragg assumed that the "entity" again became 
 an electron and the ionization was produced by the electron. 
 In other words the "entity" stage was the x or "unknown ray 
 state acting as the vehicle of the electron's energy. 
 
 It seems probable then that if we did not have eyes and a 
 temperature sense we would know nothing of the electromagnetic 
 
 23
 
 24 FUNDAMENTAL PHYSICS 
 
 radiations in the way we do. It would indeed be very interesting 
 to develop a philosophy of nature ignoring one or more of the 
 "fundamental" sense elements such for instance as inertia or 
 temperature. , 
 
 Our evolution as a race and as individuals has contained 
 determinative factors as to what our natural philosophy shall be. 
 The flow of consciousness in ourselves is without beginning or 
 end (for if it ends we of course cannot know it). It is a flow of 
 "entity" elements carried into the main channel by the branch 
 sources of the sense organs. It originates in its womb of darkness 
 and hence the muscular sensations or the mechanistic phi- 
 losophy is the earliest to appear and remains more or less dominant 
 through life. It therefore results that to us the universe 
 appears as a mechanical structure a world of forces. The 
 Newtonian mechanics need not give us the laws of this force 
 world necessarily but some system of mechanical forces seems 
 directed by our origin and environment as the guide to our 
 natural philosophy. 
 
 It is reasonable to assume that by opening new gateways of 
 knowledge our philosophy would be entirely changed. We 
 might imagine some "field of force" or radiation that could 
 directly affect the molecular processes of the brain. Molecules 
 of a certain type could be introduced into the brain. Experi- 
 ments for example have been made where a person was placed 
 in an intense magnetic field. The only effect seemed to be a 
 light sensation on the retina. Some day there may however be 
 opened to us a world of melody by some now unknown agent of 
 the external world and many of us believe that a future life 
 transforms us to a new universe of phenomena by opening 
 many new gateways of knowledge and by freeing us from 'the 
 incessant molecular changes of our present world. 
 
 It is very easy then for us to picture the elements of the mental 
 world freed from the temporary gateways of the present molecular 
 systems (nerves, etc.) and opening (through systems obeying 
 the law of conservation of properties) into the ensembles of the 
 "fundamental" elements. The "disappearance" of the mental 
 elements does not indicate that they are not conserved for by 
 analogy this 'is a frequent phenomenon in the outside world. 
 As the ether appears as the reservoir of "lost" but conserved 
 elements of the outside world so it may also serve for the mental 
 elements.
 
 THE GATEWAYS OF KNOWLEDGE 25 
 
 To continue, the course of our training and the development 
 of our civilization have controlled and determined the course of 
 our philosophy just as environment and the past guides the 
 evolution of the animals. Our words carry a meaning to us 
 long before we know of forces in physics. Our arithmetic and 
 grammar are accepted processes in any theory of electricity 
 which we may develop and try as we may we cannot rebuild any 
 parts of our natural philosophy without at least using some of 
 the stones of the previous structures which had been erected. 
 An illustration of the effect of grammar upon theoretical physics 
 is sometimes given by the history of our views of the ether. We 
 had discovered the wave properties of light and we could 
 conceive of the phenomena only as the undulating motion of 
 some medium. As a verb requires a noun so "to undulate" 
 required a subject and influenced in part at least by our train- 
 ing in grammar we felt and many feel today that "the ether 
 undulates." 
 
 As a result one finds that the tactual and muscular sensations 
 predominate. We imagine a world of things separated by dis- 
 tances; these things may be portions of matter that we can 
 actually touch or they may be atoms or molecules. Whatever 
 they are, most of us conceive them as belonging essentially to the 
 realm of the tactual and muscular. Our world is largely one of 
 matter in motion, a c.g.s. world. But why should the concepts of 
 one sense seem more "fundamental" to us than those of another? 
 Does not each sense organ possess its own peculiar sensation 
 concepts and are not each of these concepts of the same theo- 
 retical value? Are not other quantities as important as those 
 indicated by the senses? Indeed an almost infinitude of worlds 
 are possible assuming some other trinity of units than the centi- 
 meter, gram and second as being the predominate ones. 
 
 It is thus possible to attribute the domination of some sense 
 concepts by others as being due to the fact that some of these 
 concepts have been much more important to us in our develop- 
 ment, both as individuals and as a race. But this does not prove 
 that they are the most valuable for the description of the external 
 world and that they should therefore possess the greater scientific 
 value. 
 
 One thus comes to recognize the narrowness of many of our 
 views of the external world and the relation between the world 
 outside the senses and the world inside. The meaning of space,
 
 26 FUNDAMENTAL PHYSICS 
 
 time, matter, energy, etc., are dependent upon the limited ave- 
 nues connecting the inner and outer worlds. We can easily con- 
 ceive of a means of communicating between these worlds directly 
 without the aid of the senses. We might be endowed with an 
 entropy sense; a sense corresponding to any thing or function of 
 things and changes in the outside world. Then, too, could not 
 systems in the mental world be "tuned" to the physical world? 
 And may not this "tuning" be accomplished some time experi- 
 mentally by the introduction of certain atomic or molecular sys- 
 tems into the brain as is done with the digestive tract previous to 
 taking x-ray photographs. 
 
 The alphabet of the language we select to describe the outside 
 world is the one most convenient to our type of mind. Another 
 type of mind might use an entirely different alphabet and it 
 sometimes seems reasonable to think the number of alphabets 
 innumerable. Our ideas as to the convenience of any given 
 system of symbols is only determined by the present state of our 
 knowledge. But somehow we believe we are ultimately to reach 
 what we picture is "reality." 
 
 We continually try to make our units absolute and to place the 
 "center of our coordinate axes" at a place suitable to natural 
 phenomena yet somewhere, someway and somehow our system is 
 largely limited by our past experience from our birth, both as 
 individuals and as races. Nietzche may bring us a strange sys- 
 tem but he has simply and but slightly changed either the origin 
 or the bearings of philosophy. So we in our efforts to make a 
 world picture of phenomena are constantly making use of our 
 past experiences, for all terms must be interpreted in the language 
 of experience. Some day when people become truly scientific 
 the state will purposely train persons to obtain as varied an inter- 
 pretation of nature and life as possible. Imagine a person whose 
 only sense was hearing. What would he write as the encyclo- 
 paedia of knowledge ? Compare with that person one who saw the 
 universe by means of any electromagnetic vibration, who pos- 
 sessed a sense attune to the electric field and the magnetic field, 
 who could "feel " the various phases of each molecular impact and 
 we get some appreciation of what a "broad view" of our world 
 and the universe should be. Our advancement in science will 
 become very rapid when a large number of the people will throw 
 off the shackles of heredity and environment and develop new 
 "philosophies" of Truth. Up to the present only some of the
 
 THE GATEWAYS OF KNOWLEDGE 27 
 
 powers of a very few individuals directing an infinitesimal portion 
 of the wealth of society have endeavored to effectually map out 
 the Republic of Truth. 
 
 By sufficiently correlating our sensation stimuli we are able 
 to find a source for all the stimuli that our sense organs 
 receive. 
 
 The source of sensation stimuli may be defined as matter. The 
 means by which these stimuli reach our sense organs are "direct" 
 (touch, taste, and muscular sensations) and "indirect" (sight, 
 sound) . The terms direct and indirect are sufficiently evident to 
 all of us. But how are stimuli transmitted by the indirect 
 method? Only two means are conceivable. Either the indirect 
 method consists of particles, entities or what not, passing from 
 the source of the stimulus (i.e., matteV) to our sense organs, par- 
 ticles that we do not or cannot notice, or there is an intervening 
 medium that carries the means that affects our sense organs. 
 The former method may be designated as the "bullet" type of 
 radiation and the latter as the "wave" or "pulse" type of radia- 
 tion. All our experience is unanimously in support of the view 
 that it is impossible for us to receive either separate or direct 
 sensation stimuli -from a single or any natural group of "bullets " 
 or direct sensations from the "medium" itself so that it follows 
 that matter must be the source of all radiations. Neither 
 the "bullets" nor the "medium" can therefore consist of 
 matter as above defined. All our concepts of the physical 
 world except some of those that can be derived by the 
 "direct" method of sensation must be correlated by the use 
 of space, the element necessitated by the term motion. Our 
 concepts of time, space, the "ether," the "electric," "mag- 
 netic" and "gravitational" forces, etc., are plans of the 
 physical world for "explaining" or rather correlating and 
 classifying our sensations. 
 
 ' Our present work is largely restricted to the application of the 
 "atomic" theory to our view of the external world. Whenever 
 we obtain sufficient knowledge concerning any concept of the 
 external world so as to be able to apply the atomic theory to 
 the phenomena representing that concept then that concept 
 ceases to be merely a plan and becomes something finite and 
 discontinuous. Terms that simply represent plans of the exter- 
 nal world usually possess continuous and infinite values. Any 
 quantitative application of such terms to the external world or
 
 28 FUNDAMENTAL PHYSICS 
 
 of anything is arbitrary. There can be no natural unit of time, 
 of space, of the electrical field or of the ether until these quantities 
 are shown to be atomic. Concepts that are merely plans of the 
 world are used for convenience. When these terms cease to be 
 useful they are discarded. Any term representing something 
 in the world that possesses an atomic composition may be said 
 to be "real," the atoms being natural units. It is one of the aims 
 of the physicist to prove an "atomic" composition for as many 
 physical concepts as he can. 
 
 At present some of our more important physical concepts are 
 those of space, time, matter, the electric, magnetic and gravi- 
 tational fields and possibly a chemical field of force. Energy 
 is found to be related to matter or vice versa. The means by 
 which energy is transmitted from one portion of matter to another 
 portion is by three methods, the "bullet," the "medium" and the 
 "direct contact" methods. All types of radiation that cannot 
 be shown to consist of moving particles of matter must naturally 
 be included in the "bullets" or the "medium" types of trans- 
 mission. In the bullet type of transmission "entities" or ele- 
 mentarquanta " of unknown properties must carry the energy 
 from the emitter to the absorber. In the medium type the inter- 
 vening medium is made to carry the energy and this process 
 necessitates the particles of the medium transferring 'the energy 
 from one to the other. 
 
 Crudely drawing a rough analogy between the humanistics 
 and the natural world we might correlate the terms money and 
 energy and people and matter. The elements of money are 
 cents, of energy, radions, of people, men and women, and of 
 matter, electrons and the natural atoms. Money in the pocket 
 is kinetic energy that makes "the mare go." Relations with 
 other people result in the interchange of the circulating medium. 
 Money in a bank is a field of force that draws men to or away from 
 it according as their bank account is positive or negative. The 
 marriage of a positive and a negative ion destroys a tremendous 
 amount of kinetic energy of pocket change as those old neutral 
 atoms of married men can verify. And most of the collision 
 phenomena of individuals can be or at least is attributed by 
 their enemies as being one of money relations or forced by 
 future hopes of this variety. So it is that terms are used 
 in "exact" and "fundamental" science and in the other affairs 
 of men.
 
 THE GATEWAYS OF KNOWLEDGE 
 
 29 
 
 TRANSFORMATION PROCESSES OP PHENOMENA 
 
 Mental 
 World 
 
 Continuous currents 
 of entities in the 
 stream of time. 
 By analogy many 
 believe that cer- 
 tain elements in 
 this world are con- 
 served as in the 
 physical world. 
 
 Gateways of 
 Communication 
 
 A flow of entities back 
 and forth between 
 - the two worlds is 
 brought about by 
 energy transforma- 
 tions. "Angels" are 
 convenient "ele- 
 ments" hypothe- 
 cated to simplify, 
 control and make the 
 transformations 
 more direct. 
 
 The Physical 
 World 
 
 Continuous currents of 
 > entities in the stream 
 - of time and space. 
 All "laws" indicate 
 a conservation and 
 n o n d isappearance 
 of certain elements 
 in this world which 
 can therefore be de- 
 fined as the "funda- 
 mental ' ' elements . 
 Eventually our con- 
 venient elements 
 (c.g.s. elements) will 
 be made the "funda- 
 mental" elements. 
 
 Because the elements of one world can be transformed into 
 elements of the other world and because there are "fundamental" 
 elements in the physical world we believe that these remain 
 conserved during their transformation and hence must exist 
 as such in the mental world. A law similar to the second law of 
 thermodynamics could intervene by making the flow of these 
 fundamental elements such that they would eventually reach the 
 reservoir of the physical world. But by analogy we can imagine 
 "angels" that could control the transformation processes and 
 even reverse their flow. 
 
 The above assumption that all the phenomena of the physical 
 world are intelligible, i.e., can be transformed into elements of 
 the mental world and vice versa and that all these elements can 
 be derived and are constructed from a few fundamental elements 
 that are conserved (i.e., are indestructible) may be assumed as 
 a system of philosophy, the "source," "base" and "ending" 
 of the system being the fundamental elements. 
 
 As the "elements" of the mental world are obtained from the 
 transformation of "elements" of the conserved ensemble we 
 will assume that the laws of this ensemble apply to both realms. 
 
 Law 1. There is a conserved nondisappearing ensemble of 
 mental elements in which an electrical element is "absolutely" 
 conserved. 
 
 Law 2. The equations of transformation between the "ele- 
 ments" possess a natural direction of flow.
 
 30 FUNDAMENTAL PHYSICS 
 
 Law 3. The "medium" provides the only means for this 
 flow of transformations. 
 
 To summarize we have transformations in the Newtonian 
 world brought about during "collisions" or the "contact" of 
 magnitudes of ordinary matter. Apparently the ether does not 
 function in these transformations, at any rate the "contact" 
 of two portions of matter is the necessary and sufficient condition 
 and "free space" is a perfect screen in preventing the inter- 
 changes. The senses of touch, taste, smell, hearing and the 
 muscular sense apparently operate by the contact process. Our 
 individual and racial growth has founded our knowledge very 
 largely upon a Newtonian philosophy. 
 
 The transformations which take place through the ether and 
 whose emission and absorption are largely if not entirely "elec- 
 trical" (such as light and heat) are observed through the eyes 
 and the temperature sense. How the nerves transform these 
 sensations before they reach the brain we do not know though 
 they appear to be at least partly electrical. This condition 
 affords the hope that the mind can be reached directly or in- 
 directly by other electrical methods and that new channels of 
 information to the mind may be discovered. This view is 
 especially inviting if the mental processes themselves are electrical 
 rather than Newtonian, the chemical changes being regarded as 
 largely electrical. 
 
 The mental world then, is pictured as an ensemble of the 
 fundamental elements of the natural world directed by angel 
 elements of which we, as individuals, are entity systems. We 
 may assume that angels may possess as fine grained a structure 
 as the natural entities, and that the angel elements are as 
 certainly conserved and nondisappearing, though as subject 
 to transformation, as are the elements of the natural world. 
 Should we care to do so the electrical attributes of the positive 
 and negative could be assigned to the mental elements as they 
 have been to ordinary matter and the ether thus making a 
 complete parallelism in this triune ensemble.
 
 8. SOME PROBLEMS IN PHYSICS 
 
 The new science started in geometry. It appeared as an 
 analysis of the axioms assumed by Euclid. We may consider the 
 three geometries to be based on the view that the angles of a 
 triangle are equal to, greater than or less than two right angles 
 and develop the three consistent systems of geometry for 
 Euclidean, hyperbolic and elliptic space. The new science 
 movement consists of a thorough criticism of the axioms or 
 "fundamental" "elements" of any branch of knowledge, the 
 development of as many consistent treatments or "systems" 
 of knowledge as the fundamental elements permit and then 
 comparing these systems to reality by the most exacting and 
 comprehensive empirical methods available. 
 
 Applied to natural phenomena the new science applies the 
 keenest analysis possible of the methods, apparatus and the 
 units of measurement. From the "laws" of nature it de- 
 velops as many consistent systems of science as are possible. 
 That system (applied perhaps in many ways directly and in- 
 directly) which agrees "at every angle" with "reality" when 
 tested experimentally, is then accepted. In natural philosophy 
 the branch of relativity exemplifies the nature of the new science, 
 the problems which it faces and the methods which it employs to 
 answer them. 
 
 That the development of the new science is extremely difficult, 
 will be recognized as soon as we enter the laboratory. Let 
 us assume that our physicist is to demonstrate the measurement 
 of the unit of electric charge before a Pharaoh, who has set out 
 to develop the new science of electricity. No metrical instru- 
 ments are available so that convenient units must be selected. 
 (1) A convenient length is chosen and used as a standard; (2) 
 the Newtonian or some similar type of mechanics is carried 
 sufficiently far to define and measure forces; (3) electric charges 
 are generated and disposed so that they simulate point charges; 
 (4) a method of measuring electrical charges is devised and a 
 "definition" and a method of obtaining two "equal" electrical 
 
 31
 
 32 FUNDAMENTAL PHYSICS 
 
 charges is agreed upon; (5) Coulomb's law that the force (F) 
 of repulsion of two charges (d, e^) when placed at a distance r 
 
 from each other is F = -r-f is obtained experimentally. 
 
 K/T 
 
 (6) The law F = -j-\ must be verified as being consistent with 
 
 all phenomena as they may be known in the realm of Pharaoh. 
 The law is then assumed to be " universal." (7) The magnitude 
 of the charges is independent of the kind of matter with which 
 they may be associated; (8) the temperature; (9) the kind of 
 matter along r; (10) the presence of a magnetic field; (11) the 
 earth's gravity field; (12) the rotation of the earth or its motion 
 in space; (13) k is assumed to be a constant; (14) the force F 
 is assumed to be independent of the streams of energy flowing 
 about the charges. 
 
 (15) After having subjected Coulomb's law to a thorough 
 investigation of which the above is but a very superficial analy- 
 sis and having found it to be consistent with the ideas of 
 Pharaoh, we employ it to define the unit of electric charge. 
 Two " equal" " point" charges of electricity, each possesses unit 
 magnitude when they repel each other with a force of one dyne 
 when separated a distance of one centimeter in a medium whose 
 dielectric constant is unity. 
 
 The difficulties of the new science can be the better appreciated 
 when Pharaoh asks if these conditions apply to two electrons 
 carried along by the front of a light wave; by two electrons 
 existing in the center of the sun; by two electrons rotating in 
 a uranium atom; or by two electrons in the brain of a person 
 swept by the thought storms of "new" science. 
 
 Yet the difficulties of applying the philosophy of the new sci- 
 ence to natural phenomena are not as appalling as we might at 
 first expect, and this condition is due to the most marvelous 
 simplicity of natural phenomena. If there is any reason for 
 optimism and for faith it lies in our being able to successfully 
 apply the new science to phenomena unreachable to our sense 
 organs and to find that the fundamental elements of these 
 phenomena are extremely simple and apparently form a single 
 consistent system. 
 
 We have only to point to the complex phenomena of elec- 
 tricity. So far as our knowledge extends all electrical phe- 
 nomena can be consistently explained by means of the electron
 
 SOME PROBLEMS IN PHYSICS 33 
 
 and natural atoms. The hidden shadow of this is the positive 
 charge denoted as the positive electron. Like " potential " energy 
 the positive electron is assumed to explain the disappearance 
 of the negative electron. 
 
 The "single consistent system" is denoted as the natural 
 philosophy of the new science. The new science asserts that 
 there is an ensemble of fundamental elements in the universe and 
 that all natural phenomena consist in the transformations of 
 the fundamental elements according to laws which it is the prob- 
 lem of science to ascertain. With a knowledge of the fundamen- 
 tal elements, the laws of the system and a certain "locus" of 
 conditions, the whole universe system can be mapped. It is the 
 aim of the new science to so map all natural phenomena and then 
 to test these results experimentally. 
 
 The modus operandi of this tremendous task is that of divid- 
 ing the universe into entity assemblages. In any entity as- 
 semblage phenomena may be considered as forming a system 
 where a common "atmosphere" prevails. As an example we 
 may consider the ordinary earth phenomena to form an entity 
 assemblage where Newton's laws of motion consistently apply. 
 There is the atmosphere of Newtonian mechanics everywhere 
 pervading the assemblage. It of course follows that the entity 
 assemblage will be determined largely by the point of view. 
 We shall view phenomena in terms of the apparatus, convenient 
 units, methods of observing and laws of physics required to map 
 them as the factors determining the entities. 
 
 The procedure will be that of developing a consistent and con- 
 venient system of physics for each entity assemblage. The 
 ensemble of entity assemblages will then be considered with a 
 view of adopting a single universal system of physics. When 
 this work has been successfully completed the new science of 
 physics will be the result.
 
 9. THE DIRECTED ELEMENTS 
 
 Amongst the elements that are necessary in the development 
 of a science employing geometrical processes are those that 
 possess the quality of direction. In the Newtonian mechanics 
 rigid bodies are well suited for defining directions as the parts 
 can be marked and a set of coordinate axes established with com- 
 parative ease. But when the simpler ensembles of natural ele- 
 ments such as rapidly moving electrical charges and the ether are 
 to be given a geometrical interpretation the problem of defining 
 direction and of measuring elements that possess a directive 
 quality is very different. 
 
 The natural direction most used in the past has been that of 
 the axis of rotation of the earth. Knowing that this axis is 
 subject to a certain amount of wobbling, the North Pole star 
 has been used to define direction. But it is fully understood 
 that this "north" direction is not constant or absolute when so 
 defined. It is then natural to hunt through the entity systems 
 of nature to see if in any sense direction can be absolutely defined 
 or if it will always be necessary to speak of direction in a local 
 sense and employ that local direction (such as that of the earth's 
 axis) that is most convenient for our purpose. 
 
 Of the "directed" quantities it appears that the ether states 
 such as the electrical, magnetic and gravitational fields possess 
 somewhat- similar "directive" properties. The gravitational 
 "direction" is unidirectional in that a mass always experiences 
 the same directive effect whereas the electric and magnetic 
 fields exert reversed directive effects according as a plus or nega- 
 tive and a north or south magnetic pole is placed in the field. 
 Ordinarily the "direction" quality of the electric field is assumed 
 fixed the same as it is for the gravitational field. We may go 
 so far as to consider the physical world as possessing a certain 
 number of direction "elements" and that these elements may 
 possess an "atomic" structure. 
 
 The elements that appear with directive properties include 
 electric charge, natural matter, time and length if defined by 
 means of a rigid lattice structure such as possessed by crystals 
 
 34
 
 THE DIRECTED ELEMENTS 35 
 
 and assumed for a "latticed" ether. If our lattice structure is 
 not isotropic, this property serves to define direction also. Some 
 of these directed qualities resemble the series of positive and 
 negative numbers in that the sum of a "negative" and a "posi- 
 tive" unit results in a disappearance of both units. Directed 
 qualities of this type may aid in defining an origin for an ensem- 
 ble. Other magnitudes such as temperature, mass and entropy 
 do not possess "negative" values. 
 
 There are certain systems that appear to possess "absolutely" 
 directed quantities. We can imagine a system of science de- 
 veloped in the interior of a crystal (placed in a liquid) for which 
 an "absolute" origin of space coordinates could be defined that 
 would introduce a symmetry into phenomena that would other- 
 wise not be possible. The lattice work of the crystal would pro- 
 vide a means of defining "direction" in an "absolute" manner 
 especially if the crystal lattice work is not isotropic. The most 
 symmetrical form of physics that could be developed would 
 apparently be that in which the center of the crystal would be 
 the origin of the coordinate axes. The "direction" of any 
 atom from the origin in the lattice work could be defined as so 
 many "lattice" spaces along each one of the crystalline axes. 
 If the minimum length of measurement was the distance be- 
 tween two neighboring lattice elements, then the "atomic" 
 angle of "direction" would be that subtended by a lattice ele- 
 ment at the boundary of the crystal. 
 
 The number of independently "directed" elements of the phys- 
 ical universe may aid in indicating the number and nature of 
 the "fundamental units" of science. The number of "direc- 
 tions" may give the degree of the manifold of phenomena. 
 Thus we may agree that the ether fields of force give us the three 
 "directions" of extension, the succession of events gives us the 
 "direction" of time and the entropy and radioactive changes 
 give us the "direction" or the "running" down of the universe. 
 If these could be considered as fundamental and independent 
 "direction" elements just as length, mass and electric charge 
 have been considered as fundamental physical elements then 
 the universe "space" would consist of five dimensions and phys- 
 ical transformations would take place in a 5-manifold. The 
 degree of the manifold will determine the nature of the geometry 
 to be adopted. 
 
 Let us assume that the physical space is to be defined by ul-
 
 36 FUNDAMENTAL PHYSICS 
 
 timate and directed elements that are conserved and never dis- 
 appear. Let us assume a lattice type of an absolutely stagnant 
 ether and that the magnitudes of the axial quantities are to pos- 
 sess positive and negative characteristics. An arbitrary origin 
 and]direction is marked on the lattice work. A stream of radia- 
 tion is directed so that its energy flow is along that of the arbi- 
 trary axis. The electric and magnetic vectors of this radiation 
 stream could be assumed to define two more axes; an electric 
 charge and a time axis could be added thus constituting a 5- 
 manifold space. On account of the universal existence of the 
 ether in all entity systems it seems most promising to expect 
 any absolute definition of directed elements to be made with ref- 
 erence to the structure of the ether. Up to the present all 
 definitions of this sort have been local and except for the ether 
 there appears no other base for a universal science. It is for 
 this reason that the transformation of the direction properties 
 of any magnitude from one ensemble to another is very difficult. 
 We can picture the energy changes and atomize the direction 
 qualities that enter into these changes by assuming radion 
 elements for the elementarquanta. These radions contain the 
 elements of directed energy. To give extension there is assumed 
 six types of radions, a type for each quadrant, there being positive 
 and negative radions whose oppositely directed energy neutral- 
 izes with the result that any element containing these two 
 elements would be at rest. The radions could be considered as 
 as rx, ry and rz. The motion of any body could be 
 described as being due to its containing a given number of these 
 radion elements in the way that we describe motions and forces 
 by considering the projected components on the axes. Colli- 
 sions would be described by the interchange of radions. Fields 
 of force would be regions where a certain type of radion pre- 
 dominated and matter, charge and the ether would be the 
 vehicles of radions. We could assume the radions to be con- 
 served and to be the ultimate energy elements. The assumed 
 positive and negative characteristics of charge, natural matter 
 and the electroethons could be attributed to the radions. A 
 reason for not attributing these energy properties to the ether 
 is that the, ether is frequently assigned a stagnant quality when 
 we wish to define direction absolutely. This objection is removed 
 however, when we consider the energy direction of the radions 
 to be conserved.
 
 THE DIRECTED ELEMENTS 37 
 
 If, then, energy can all be considered to be kinetic and the 
 trend of modern discovery supports this view, it is possible 
 to believe that all directed quantities may consist of three 
 elements. A quantity such as time may be the measure of 
 energy changes and therefore a function of other quantities. 
 , The theory of relativity indicates that we can only determine 
 relative motion and that in the case of rotation, we can say, 
 that if our universe was set rotating, the physical laws would 
 be changed.
 
 10. THE GENERAL ENTITY VIEW OF THE UNIVERSE 
 
 In taking a survey of phenomena we find that there are systems 
 that are more or less complete in themselves and to a great degree i 
 isolated from each other. These systems are invariably com- 
 posed of similar parts, individuals, groups, atoms or entities as 
 we may wish to name them. This universal condition is de- 
 scribed as the entity view of the universe. To be seen in a clear 
 light the entity structure of any system must be observed from 
 a finer grained system than the system under observation. 
 From our every day world water may be considered as a continu- 
 ous fluid and its behavior can be accurately described by hydro- 
 dynamical equations assuming that water is a perfect fluid. 
 Viewed from the electron world however, water consists mostly 
 of space filled at rare intervals with whirling electrons and the 
 positive nuclei of hydrogen and oxygen atoms. 
 
 The entity or atomic theory of phenomena has been found to 
 be universal and applicable everywhere if a finer grained system 
 could be employed in the laboratory than the one under observa- 
 tion. Experience would therefore lead us to consider all systems 
 as constituted of entities. The second experimental law of the 
 entity structure of systems is that the number of different 
 entity elements becomes less as the system becomes finer grained. 
 The complete entity view would then lead us to consider the 
 finest grained system as consisting of a single entity element. 
 
 (a) The large star and nebulae systems that drift in groups 
 through space probably give us our coarsest grained system with 
 the stars as entity elements. The adaptation of the laboratory 
 and the units to suit the system is very well illustrated by the 
 use of the light year as the unit of length for this system. 
 
 A few relations appear among the stars and the nebulae. The 
 redder and apparently "older" stars and a class of nebulae possess 
 greater velocities than the hotter stars. An effect, such as a 
 differential light pressure on a moving star, might result in a 
 star system increasing its velocity as it grew older. The universal 
 appearance of substances, such as hydrogen, sodium, calcium 
 and iron in the star systems, indicates a common atomic constitu- 
 tion of the universe, and the view is that the universal existence 
 of this form of matter is due to similar boundary conditions 
 
 38
 
 GENERAL ENTITY VIEW OF THE UNIVERSE 39 
 
 with the ether, rather than to any intercommunication of this 
 matter between the stars. These forms of matter have been 
 genetically formed in situ in the particular entity system from 
 the ether and the elements that the ether can transmit, such as 
 the electromagnetic vibrations. The origin of a star center 
 may even be cyclonic, starting from a peculiarly unstable condi- 
 tion of the medium. 
 
 The sorting that takes place in an entity system, is illustrated 
 by the appearance of spectra in the nebulae and nebulous stars 
 that are unknown on the earth. Were it not for "low 
 temperature" compounds, such as water and the radioactive 
 elements, hydrogen and probably helium, would be unknown 
 to us. Assuming the width of spectrum lines to vary as the 
 square root of absolute temperature, Buisson and Fabry have 
 found the " temperature " of the Orion, nebula to be about 15,000. 
 
 (6) Our solar system with entity .elements of the planets, 
 satellites, and comets is probably the best ordered entity system 
 known and the most accurately described at the present time. 
 Undoubtedly this system as a whole is one of the atoms in a 
 star system. The almost perfect ordering of the system is 
 due to its being in a steady gravitational state. Only collisions 
 with minute particles in space occur. We have only to imagine 
 collisions with similar systems to obtain a very disordered condi- 
 tion. The atomic elements of matter can be compared with 
 'much profit to our solar system, the " emptiness" of space inside 
 of the atoms being even more pronounced than is the case of our 
 solar system. 
 
 (c) The phenomena that take place on the planets and the 
 sun such as sun spots, storms or the formation of water streams or 
 islands are extremely disordered though there may appear similar 
 entity elements. These elements are short lived. It may be 
 stated that in general the ordering and simplicity of any entity 
 system is proportional to the life period of the entity elements. 
 In the planetary systems many of the phenomena are of the cy- 
 clone variety in that their origin is more or less sporadic and due 
 to a play of forces that are infinitesimal compared to those de- 
 veloped at a later stage. Once started the cyclone type of phe- 
 nomena possesses a track or life that is at least partly amenable 
 to mathematical treatment and prediction but their birth can- 
 not be very accurately predicted. 
 
 Cyclone phenomena differ from the trigger type in that the
 
 40 FUNDAMENTAL PHYSICS 
 
 latter possess a greater degree of uniformity and owe their 
 origin to a source usually outside of the system. 
 
 (d) Animal and plant life illustrate atomic structure very well 
 in that the individual plants and animals may be considered as 
 the natural units with the cell to be the universal elemental 
 unit in this whole kingdom of life. Like the atoms of matter 
 the cell possesses a structure. 
 
 The world of life presents its individual units with certain 
 polar characteristics of sex which may be pictured as the fading 
 out of the very pronounced polar characteristics of electrical 
 and magnetic entities and of the natural atoms of matter. Many 
 chemists speak of valency as possessing polar characteristics 
 and it is only natural to expect that if the life entities are the con- 
 tinuation of the series of the molecular systems then the polar 
 characteristics not only of the physical life of the individuals but 
 also of the mental and the moral atmospheres of these entities 
 may be the glimmering traces flowing from those extremely fine 
 grained entity systems where these properties are so pronounced. 
 
 The operation of illy defined forces to produce entity systems 
 is illustrated in the university. A man must be either a chemist 
 or a psychologist or some other type of entitist or else he finds 
 himself alone, ostracized and running little chance of securing a 
 stable position in the satellite electrons that are drawn to the nu- 
 cleus president and board of trustees by the financial forces. 
 The brilliancy of illuminating knowledge to the surrounding 
 spaces of ignorance and the reception of all the hard blows of 
 collisions is the function of the satellite electron teachers while all 
 the force of the system is held by the central nucleus. And if 
 the system is subjected to outside criticism the divine rights of 
 the central powers complacently permits of the ejection of one 
 or more of the outer electrons. So we perceive the faint echoes of 
 the elementary material systems resounding in the clash* and din 
 of the far removed entities in the realms of life, even in the sacred 
 institutions of learning. 
 
 (e) The molecular systems form the natural units of our or- 
 dinary world. The molecules are the units of neutral or or- 
 dinary matter and they constitute the natural frontiers of the 
 realm of Newtonian mechanics. The treatment and laws of 
 solids, liquids and gases is essentially the science of molecules and 
 comparatively small molecular systems. An exact and complete 
 molecular science, a full understanding of life phenomena,
 
 GENERAL ENTITY VIEW OF THE UNIVERSE 41 
 
 the discovery of the missing links between the life elements and 
 the molecules and the practical acquirement of the powers of 
 the angels to control molecular and life transformations remain 
 as some of the fundamental problems for state and other social 
 organizations to grapple with their full energies. 
 
 (/) The chemical world lies between the boundaries of the mo- 
 lecular and atomic worlds. Many claim that the transformations 
 that take place here are essentially electrical while others-postu- 
 late chemical "fields" of force of an elementary nature. The 
 very nature of these claims emphasizes the tremendous field 
 here inviting research work. The backward state of our knowl- 
 edge of chemistry is due to our not being able to experiment 
 with individual chemical reactions and for the reason that these 
 reactions are extremely variable and are short "collision" phe- 
 nomena rather than conditions of long steady states such as is 
 exemplified by our solar system. 
 
 (g) The atomic world is described in a separate chapter and the 
 ionization world has been briefly treated. The Newtonian 
 philosophy no longer applies and another science arises. The 
 world of the electrons and the natural atoms is essentially an 
 electrical world. The world of ordinary "contacts" ends. The 
 muscular senses are dumb. There is no tactual touch to these 
 phenomena. -This is the world of the eye and of radiations. 
 This is the world of the " radions, " electricity, magnetism, natural 
 atoms and the ether. A new philosophy reigns. We may call 
 this the electrical philosophy and it has to do with electrons and 
 the "natural" atoms. 
 
 Almost a science has developed concerning the family groups 
 of the periodic system of the natural atoms. The radioactivity 
 of the heavier atoms has shed much light upon these family 
 relations in a genetic sense and future experiments promise to 
 show that the 92 natural atoms may possess as simple a consti- 
 tution as electrical charges. The life history of the stars is 
 closely associated with the birth and death of the natural" atoms. 
 
 (h) The subatomic world is sketched under the structure of 
 the atoms. This region remains almost entirely for future ex- 
 ploitation as does the (i) radiation entity systems and (j) the 
 ether. We presume that the relative "grain" or fineness of 
 structure of these entity systems is roughly as given: (a) Star 
 clusters; (6) suns; (c) "cyclones" (temporary); (d) living beings 
 (temporary?); (e) molecules; (/) neutral atoms; (g) electrons and 
 natural atoms; (A) ^helium nuclei; (i) ether electroethons and
 
 42 FUNDAMENTAL PHYSICS 
 
 (j) radions. The i and j groups can be given their mathemat- 
 ical significance of imaginary quantities. 
 
 So much for the existence of entities in the natural world. 
 As you read this page your eye crosses it in jerks; each jerk in 
 a way being transformed into a thought entity. A thought 
 entity, a phrase or a word may be considered as a molecule or 
 an aggregate, this latter being constructed of words, the simple 
 molecules and ultimately of letters, the atoms of our thought 
 structures. Our number system is even simpler, all numbers 
 ("molecules") being formed from nine elementary atoms. Our 
 music is also based on a few notes covering only several octaves. 
 
 In a way each thought of the outside world is an entity corre- 
 sponding to an assumed entity in the natural world. Our sci- 
 ence has shown that the elementary entities (electrons and atoms) 
 of the outside world are almost as simple as our atom letters. 
 In addition as the entities become infinitesimal and of a lower 
 order the units are found to become simpler. The means of com- 
 munication of energy between the larger order of units (suns) 
 seems to be the same as that between the smallest units (atoms, 
 electrons, atom nuclei), thus leading us to believe that all inter- 
 communication between entity systems must be by means of the 
 ether electromagnetic processes. 
 
 The entity philosophy is indeed of a very wide and subtle 
 application on account of our mental process. Any thought 
 entity based upon knowledge of the outside world can be ap- 
 plied to that knowledge so that innumerable entities may be as- 
 sumed. Any physical magnitude may thus be assumed to possess 
 an atomic structure and the assumption made a natural hypo- 
 thesis to be tested by experiment. And if the ultimate elements 
 of the physical world are atomic in nature, presumably all phys- 
 ical magnitudes will at least ultimately be found to possess 
 an atomic structure. Our fundamental units will however be 
 those of nature. For example the ultimate unit of time would be 
 the shortest periodic occurrence in nature that can be observed, 
 the unit of length, the shortest physical entity that can be used as 
 a measuring bar and the -unit of mass, the smallest mass entity 
 that can be separated from other masses. 
 
 The general entity theory of nature also asserts that every 
 measurement of natural phenomena must yield a rational in- 
 tegral number when the natural entity elements are employed 
 as units. All natural phenomena are granular and ratios of all 
 natural quantities may be commensurable.
 
 11. THE ATOMIC STRUCTURE OF MATTER AND EQUI- 
 PARTITION OF ENERGY IN THE NEWTONIAN WORLD 
 
 It was established by Dal ton and his contemporaries that mat- 
 ter is constituted of an aggregate of discrete entities which are 
 all alike for any homogeneous substance. The smallest portion 
 of matter that can be manipulated by the chemist consists of a 
 vast assemblage of molecules, and his knowledge always relates 
 to the average behavior and relations of a crowd of molecules. 
 Among the smallest quantities of unelectrified matter ever 
 detected was that of neon, one of the inert gases of the atmos- 
 phere (there is about one part of neon to 100,000 parts of air). 
 Prof. Strutt has shown that the neon in one-twentieth of a cubic 
 centimeter of air at ordinary pressure could be detected. In this 
 quantity of air there are about ten million million molecules of 
 neon, or seven million times as many neon molecules as there 
 are people in the world. 
 
 Dealing thus with such immense numbers of molecules, it is 
 not surprising that nothing concerning any possible individu- 
 ality of atoms and molecules has ever been detected. Indeed, 
 little is known of the nature of neutral atoms and molecules, or of 
 the forces that operate in interatomic spaces. All our laws are 
 for masses of matter that are extremely large compared with 
 atoms, and cannot be applied to 'them, without exterpolation. 
 However, chemists have shown that all matter is made up of a 
 number of elementary substances which they cannot decompose. 
 The relative weight of the atoms of these elements are known, and 
 it is becoming more and more probable that chemical combina- 
 tion consists of an arrangement of atoms alongside of each other 
 under steady cohesive forces, the properties of each atom being 
 somewhat, though not essentially, modified by the near presence 
 of the others. It is not wonderful then, that although we are 
 certain that molecules have a very definite structure, when we* 
 inquire into the details of their constitution we do not have much 
 more than the distant analogy of familiar dynamical systems to 
 aid us. 
 
 43
 
 44 FUNDAMENTAL PHYSICS 
 
 The last century gave us a good example of how assumptions 
 and hypotheses that are not disproved by experiment seem to us 
 like the truth itself. The analytical methods of chemistry suc- 
 ceeded in showing that all matter was composed of some ninety- 
 two elements. As no division of matter smaller than the atom 
 was known, and as no case was known of the loss or gain of 
 weight, one of the most fundamental properties of matter, scien- 
 tists in general began to consider the elementary atoms as the 
 foundation stones of the material universe, which, amid all the 
 changes of molecular structure, remained forever the same. 
 
 On the physical side, the mathematical development of the 
 kinetic theory of gases has extended the utility of the atomic 
 theory very greatly. In the kinetic theory the properties of 
 gases are explained by assuming every gas to be composed of 
 minute particles or molecules in continuous motion, colliding 
 with each other at intervals that are short compared with the 
 times between collisions. No definite conception of the mole- 
 cules or of the forces acting between them is assumed. The 
 molecules could either be considered to be elastic spheres or 
 Boscovitch centers of force, and the gas would show the 'same 
 general statistical properties. 
 
 The kinetic theory of gases affirms that matter is composed of 
 definite units of mass or molecules, and that heat energy con- 
 sists of the kinetic energy of the motion of these molecules. 
 This kinetic energy may consist of energy of rotation as well as 
 of translation. 
 
 In 1859 Maxwell announced the theorem of the partition of 
 kinetic energy. In more recent years the mathematical demon- 
 stration has been perfected by Maxwell, Boltzmann, Jeans, and 
 others, so that the evidence has become quite strong in favor of 
 the hypothesis that energy is distributed equally among different 
 types of molecules and also among the various degrees of freedom 
 of each type of molecule considered independently. The mole- 
 cules seem to be surrounded by fields of force, and it is probably 
 these fields that we measure. Apparently, collisions take place 
 when molecules approach each other sufficiently close for their 
 fields of force to slightly overlap. The nature of these forces is 
 such that molecules, on collision, behave like elastic spheres, 
 practically none of the kinetic energy of heat being frittered 
 away into energy having a comparatively high frequency. 
 
 The nature of molecular forces is a problem concerning which
 
 ATOMIC STRUCTURE OF MATTER 45 
 
 a great number of assumptions have been made. As an example 
 we may take a few hypotheses as applied to liquids. Mills 
 was able to explain some latent heat phenomena by assuming a 
 molecular attraction obeying the inverse square law. Klee- 
 man has deduced the following law, 
 
 (I. !\ 
 \X.TJ 
 
 where Z is the distance between the molecules, S \/mi is the sum of 
 the square roots of the atomic weights of the atoms of the mole- 
 cule, X c is the distance between the molecules at the critical 
 temperature, T c , and the function <p is unknown though it is 
 constant at corresponding temperatures. In the equation of 
 state of Van der Waals, it is assumed that the attraction between 
 molecules varies as the inverse fourth power of the distance be- 
 
 K 2 
 
 tween them. Tyrer gives the law -^ where K 2 is a constant 
 
 for a given pair of molecules, and n is not less than 5 and may be 
 greater than 7. 
 
 Fortunately many of the properties of gases can be treated 
 without any assumptions being made as to the nature of the mole- 
 cular forces, the molecules being considered as perfectly elastic 
 bodies occupying a certain volume of space, and possessing a 
 certain amount of heat energy. 
 
 The general theorem of equipartition of energy states that the 
 energy of the body is distributed among the different degrees of 
 freedom by which the state of the body as a dynamical system is 
 described, and that an equal share is allotted to each degree of 
 freedom. The mathematical development contains assumptions 
 that can hardly be justified, yet experimental evidence corrobo- 
 rates the view in general. 
 
 It should be kept in mind, however, that the theorem of equi- 
 partition must be applied in a somewhat restricted form. The 
 energy which corresponds to certain degrees of freedom often 
 does pass away rapidly as energy of radiation, whereas the en- 
 ergy of other degrees of freedom passes away with extreme slow- 
 ness and by indirect means. It is the latter energy that is indi- 
 cated by the thermometer and is distributed equally among the 
 degrees of freedom of this type. Jeans assumes that the de- 
 grees of freedom that permit their energy to be lost by radiation 
 also possess a temperature which he calls subsidiary. The 
 two types of degrees of freedom are called principal and vibra-
 
 46 FUNDAMENTAL PHYSICS 
 
 tory. When a gas is heated, practically all the energy is dis- 
 tributed among the principal degrees of freedom. 
 
 The distribution of energy in different degrees of freedom of the 
 molecules of various gases has been treated in popular manner by 
 Magie and others, and serves to indicate the nature of molecular 
 structure. Let C v be the specific heat of a gas at constant vol- 
 ume; C p the specific heat at constant pressure; E the increase 
 in the energy of translation of the molecules of a gas when the 
 temperature is raised from to 1C. at constant volume; K 
 the energy corresponding to one degree of freedom which a gram 
 molecule of the gas receives when its temperature is raised 1C.; 
 m is the molecular weight; and 7 = C P /C V . From the laws of 
 thermodj^namics it follows that 
 
 2E 
 
 7 ~ l = 3 C v 
 
 Assume that each one of the n degrees of freedom acquire the 
 same amount of kinetic energy, say K, The energy of transla- 
 tion is then increased by 3K, so that 
 
 Where P is an unknown quantity of potential energy. 
 
 Assuming that P = o, and that the molecules are points having 
 nothing but translational energy, n = 3: 7 = 1.66. This value 
 of 7 is obtained experimentally for the monatomic gases. Fol- 
 lowing is given a table of valus of 7 and n calculated from the 
 2 
 
 formula. 7 = 1 -\ j 5 - 
 
 n -\- o 
 
 Gas 7 n 
 
 Mercury 1.666 3.00 
 
 Krypton 1.666 3.00 
 
 Helium 1.652 3.07 
 
 Neon 1.642 3.12 
 
 Argon 1.63 3.20 
 
 Ethylene 1.248 8.06 
 
 Hydrogen 1 . 402 4 . 98 
 
 Nitrogen 1.405 4.94 
 
 CO 1.409 4.89 
 
 Air 1.405 4.95 
 
 Nitric oxide 1.394 5.08 
 
 Oxygen : 1.402 4.98 
 
 CO 2 1.300 6.67 
 
 Nitrous oxide ... 1 . 304 6 . 58
 
 ATOMIC STRUCTURE OF MATTER 47 
 
 Assume that P is due to the displacement of the atoms in 
 the molecule. Assume that the motions of these atoms are 
 simple harmonic; then the mean value of P corresponding to 
 each internal degree of freedom is equal to the mean kinetic 
 energy. Let a be the number of degrees of freedom of the atom 
 taken as a whole, and i the number of internal degrees of freedom. 
 Then 
 
 . . __ 
 
 Each internal degree of freedom contains equal amounts of 
 kinetic and potential energy, each amount of energy being equal 
 to that in an external degree of freedom. 
 
 In the case of the monatomic gases, i = o, n = 3, = 3 
 mCp = 4.943. The theoretical value of 7 is 1%, and it is found 
 experimentally that the value of 7 ranges between 1.64 and 1.66 
 for mercury vapor, krypton, helium, and argon and the vapors 
 of many metals. The value of 7 therefore indicates that the 
 whole energy of these gases is translational, and that the mole- 
 cules of these gases are spherically symmetrical so far as their 
 internal structure is concerned. If the structure of the molecules 
 was not spherical, some translational energy would be changed 
 into rotational energy at each collision, but the value of 7 indi- 
 cates that there is no such equipartition, and the dissipation of 
 this rotational energy must be very small, since the gas loses 
 energy very slowly. It therefore follows that little if any energy 
 goes into producing rotation. 
 
 In the case of diatomic molecules, the value of n = 5 gives a 
 value of 7 that agrees very well with the experimental value as 
 found for hydrogen, nitrogen, oxygen, nitrous oxide and hydro- 
 bromic acid. This value of n corresponds to the number of 
 external degrees of freedom if the distance between the atoms of 
 these molecules remains constant. The values of 7 for chlorine, 
 bromine and iodine, indicate that each of these gases has an in- 
 ternal degree of freedom to which energy is distributed. 
 
 The possibility of the variability of the distance between the 
 atoms of some of the diatomic molecules, may be correlated 
 with the fact that bromine, iodine and chlorine have such char- 
 acteristic absorption spectra, and dissociate at comparatively 
 low temperatures.
 
 48 FUNDAMENTAL PHYSICS 
 
 The elucidation of the conditions underlying the partition of 
 energy among the degrees of freedom of bodies is a very inter- 
 esting and important study and the few data here given serve 
 more as an illustration of the subject than as an outline of our 
 knowledge.
 
 12. THE DISINTEGRATION OF ATOMS BY RADIO- 
 ACTIVITY AND THE NATURE OF OUR SYSTEM 
 OF MATTER ELEMENTS 
 
 Some very remarkable relationships have been discovered in 
 recent years as regards the nature of the system of matter atoms. 
 Atoms have been compared as regards their atomic weights, 
 their chemical properties, their electrical properties, their spectra 
 and lastly and probably most fundamentally by means of their 
 characteristic x radiations, as discovered by Moseley, and which 
 states that the square root of an atom's x radiation frequency 
 is proportional to the atomic number which represents the 
 number of excess electrons outside the nuclei. This law gives 
 92 elements all but six of which have been discovered. 
 
 The disintegration of the atoms of uranium and thorium into 
 a large number of resultant atoms in a genetic series has thrown 
 much light upon the nature and the relationships of the high- 
 number atoms and that these atoms all contain helium. The 
 discovery that an atom of lead may have a variable atomic 
 weight and yet manifest the same chemical properties and emit 
 the same spectral lines has lead to the theory of isotropes, atoms 
 that we ordinarily consider alike as regards their properties 
 except as regards the exact nature of their nucleus and which 
 have different disintegration histories. 
 
 The law governing the rate of disintegration of any simple 
 radioactive element or product is an exponential one. If there 
 are N atoms of this product at a time t = and N atoms at the 
 time t then, 
 
 N = Ntf-" 
 
 e is the base of the natural system of logarithms and X is a con- 
 stant characteristic of the given radioactive substance. One 
 
 has, 
 
 (IN - xt 
 
 ^i = - 7V Xe = - \N 
 at 
 
 The number of atoms disintegrating per second is a fraction 
 equal to the product of X and the number of atoms existing at 
 4 49
 
 50 FUNDAMENTAL PHYSICS 
 
 the time. The same law applies to an irreversible monomolecular 
 chemical reaction. The time (7 1 ) required for half the active 
 material to disintegrate is 
 
 #_ = 1 = ~ xr T = log 2 
 No 2 Xloge' 
 
 The average life of any atom is given as follows: 
 
 ^ < X N dt = I \ N t dt = I Note~=~ = 
 
 The disintegration of a mixture of radioactive substance can 
 be obtained in the same way as given above, the computations 
 becoming quite difficult however, for a large number of radio- 
 active substances. 
 
 The above law for the disintegration of a simple radioactive 
 substance is that given by chance. Let \dt be the probability 
 that an atom is destroyed in the time dt. If this probability 
 is independent of the instant considered and of the number of 
 atoms, then X is a constant. If N is the number of atoms and 
 dN the number that disintegrate in the time dt, one has, 
 
 -~=\dtaudN = JV oe " X< . 
 
 This law only applies when N is very large. When N is small 
 the value of -dN will show fluctuations with the time. 
 
 There appears to be a relation between the velocity of the 
 emitted a particle and the constant of disintegration X. A 
 form of this relation sometimes given is log X = a + bV n , a and 
 6 being constants, V the initial velocity of the a particle and n 
 a number such as 1 or 2. The complexity of ft rays and the 
 possible diffraction effects produced by 7 rays promises to give 
 us many valuable glimpses into disintegration phenomena. 
 
 In the radioactive changes that take place with the emission 
 of ft rays, the ft particles may be ejected from the atom through 
 different "avenues." The emission of 7 rays may therefore, 
 depen^l upon the "avenue" through which the ft particle escaped. 
 According to Rutherford it seems that 7 rays are the 
 "characteristic" x radiation of the given element. Rutherford 
 has also shown that the energy of the ft particles emitted by a 
 product such as radium C can be represented by a value pEi + 
 qE z where E\ and E 2 are constants and p and q are positive
 
 THE DISINTEGRATION OF ATOMS 51 
 
 integers (or zero) having a different value for each group of /3 
 rays. A detailed energy study of the radiations will throw 
 much light on radiation theory. 
 
 The nature of molecular collision phenomena indicates that 
 the outer regions of the molecules and atoms are the seats of 
 repulsive forces. Whether the atoms possess a structure or 
 "shell" from which certain "avenues" of egress or absorption 
 of electrons is possible is of course an open question. If as we 
 believe there are reasons for assuming a structure for the ether 
 in the nature of a lattice work it is natural to expect the atonis 
 to possess a peculiar ether framework. In the ether vortex 
 theory the atom contained closed vortex rings. We may pic- 
 ture the atoms as containing closed ether "threads" or "lines" 
 of force such that an electron would rotate about one of these 
 closed "lines" of force in the same way that it follows a "line" 
 in the ether. The repulsion experienced during coPisions would 
 be due to the mutual reactions between these lines. While 
 following a "line" the electron would be in a steady state but 
 in passing to another line radiation might take place. Isotropes 
 such as radium lead, thorium lead and ordinary lead might pos-. 
 sess the same "line" structure and would be alike as regards 
 radiation properties while the nuclei differ. 
 
 Experimental evidence has been obtained for the formation 
 of a branch series in the study of radium C. Recoil methods 
 indicate that radium C is complex consisting of radium Ci and 
 radium (7 2 . A very small amount of radium Cz is obtained by 
 recoil from the active deposit and it appears that radium C\ may 
 disintegrate into either radium D or radium C 2 . Similarly in the 
 breaking down of uranium it seems that two products, uranium 
 X and uranium Y may be formed simultaneously, the relative 
 amount of uranium Y being very small. In the case of thorium 
 some experimenters have concluded that thorium C\, and the 
 parent of thorium Cz are simultaneous products of thorium B. 
 
 K. Fajans considers that the scheme of disintegration of RaB 
 may be as follows: 
 
 RaC 2 -*- 
 
 ft 
 RaB - RaC 
 
 RaC ' 7T^ RaD -* RaE - RaF
 
 52 
 
 FUNDAMENTAL PHYSICS 
 
 The period of RaCi, is 19.5 min. and of RaCz, 1.4 min. The ra- 
 tio of the numbr of atoms disintegrating in the branches RaC 2 
 and RaD are as 3 to 10,000 about. 
 
 Atomic Element Uranium series Actinium Series Thorium Series 
 
 Number 
 
 92 Uranium 
 
 91 Uranium Xi 
 
 90 Thorium loniui 
 
 89 Actinium 
 
 1 
 
 88 Radium ^ Radium 
 
 uz 
 ^ 
 
 UY 
 
 UXi RaAc 
 
 Thorium Radiothorium 
 
 Niton 
 
 i 
 Nitor 
 
 V i. 
 Actinium 
 
 Mesothorium 
 
 Act niumX Mesothorium Thorium X 
 
 I | 
 
 Actinium emanation Thorium emanation 
 
 1 I 
 
 84 Polonium Radium A RaC' RaF Act. A 
 
 AcC' 
 
 83 Bismuth 
 
 82 Lead 
 
 81 Thallium 
 
 RaC 
 
 RaB 
 
 RaE 
 
 I' 
 RaD 
 
 AcC 
 
 Act B 
 
 lead 
 
 lead 
 RaC 2 
 
 ThC' 
 
 k 
 
 I 
 lead 
 
 lead 
 
 lead 
 lead 
 
 I 
 ThA 
 
 1 
 ThB 
 
 ThD 
 
 The short heavy arrows indicate a disintegration where a /3 
 particle has been emitted from the central nucleus. The atomic 
 number is increased by one. A long arrow indicates the loss of 
 an a particle and a decrease of the atomic number by two. Ele- 
 ments with the same atomic number are isotropes and possess the 
 same chemical and physical properties. Element 92 has 6 
 valency and 86 other "outer" electrons; 90 has 4 and 86; 88 
 has 2 and 86; 86 has and 86; 84 has 6 and 78; 82 has 4 
 and 78.
 
 THE DISINTEGRATION OF ATOMS 53 
 
 The radioactive changes of the atoms are of tremendously great 
 value in analyzing the system of elements. A careful comparison 
 of the radiation, atomic weight, chemical and other properties 
 of the atoms leads to many important relationships and it is 
 not being too optimistic to say that in the immediate future we 
 may discover the ultimate elements that go to make the nuclei 
 of the atoms and to construct the family tree of the whole sys- 
 tem of elements and to learn the laws involved in these changes. 
 Perchance we may even be able to direct some of these changes.
 
 13. ATOM MODELS AND ATOM NUCLEI 
 
 Hypotheses concerning the structure of atoms are compara- 
 tively new since it has only been a few years that any clues have 
 been obtained relating to inner atomic phenomena. Lord Kel- 
 vin and Helmholtz were inclined to view atoms as a type of vor- 
 tex ring in the ether and by assuming that the ether was a fric- 
 tionless fluid they could show that these rings would continue to 
 rotate forever once they had been set into motion. The inde- 
 structibility of the ether atom agreed with the chemist's views at 
 that time. Atomic models of this type were not found to be 
 helpful in "explaining" the properties of atoms and hence they 
 gradually ceased to interest investigators. 
 
 The discovery of the electron, the prediction of the effect of a 
 magnetic field upon the vibrations of light centers by Lorentz 
 and its experimental verification by Zeeman, the many electron 
 phenomena of spectroscopy and radioactivity, the Stark effect 
 of an electrostatic field upon the vibrations of light centers, the 
 absorption of a and /3 rays, Barkla's and Moseley's work on x 
 radiations, these and many other phenomena have recently 
 contributed important data that aid greatly in an interpretation 
 of the intra-atomic world and have actually made the subject 
 of atomic structure a branch of experimental science. Inves- 
 tigators have therefore frequently endeavored to picture the 
 atomic structure from their point of view as being spectroscopic, 
 chemical and radioactive. It is for this reason that the same 
 problem has been elaborated in such a way as to lead one to 
 suppose that several atom models are equally capable of explain- 
 ing known phenomenon. In the present chapters we will de- 
 scribe several types of models. 
 
 In attempting to explain atomic structure and the phenomena 
 that take place within atoms or even in their near vicinity we 
 must remember that we have truly entered into a mystic "coun- 
 try." Gravitation, the existence of point forces, our laws of 
 mechanics, of magnetism and electrostatics, our methods of 
 measurement, the use of Euclidean geometry, the nature of 
 light and electromagnetic waves may be meaningless expressions 
 
 54
 
 ATOM MODELS AND ATOM NUCLEI 55 
 
 for these phenomena. How can we define a unit of length to an 
 intra-atomic being? How can we define a unit of time? What 
 is the nature of radiation under these conditions? Can it be 
 expressed by equations in the same way that it is expressed for 
 free space or are its properties all different? What happens when 
 a beam of x-rays pass an atom? How does an atom absorb 
 or radiate energy? What effect does a violent collision have 
 upon an atom? What takes place when one radioactive atom 
 changes over into an entirely different kind of atom? 
 
 Amongst the earliest types of the electron model of the atom 
 is that elaborated by J. J. Thomson. This atom consisted 
 of a uniformly distributed volume charge of positive electricity 
 in a sphere of atomic size. In the outer region of this sphere 
 were large numbers of negative electrons, the charge of the elec- 
 trons being equal to that of the positive sphere, these charges 
 practically neutralizing each other. The electrons were usually 
 assumed to be rotating about the atom in much the same way 
 as the particles in the rings of Saturn. For this reason Thom- 
 son's atom model is often called the Saturnian atom. At one 
 time it was thought that a large part of the mass of this atom was 
 due to the electrons in it. This large number of electrons thus 
 required was a view welcomed by the spectroscopists who aim 
 to explain the complex spectra of the elements. 
 
 The Rutherford atom differs from the Thomson atom in 
 that the positive charge is concentrated into a small volume at 
 the center of the atom. Both types of atom assume much the 
 same distribution of negative electrons. The Ritz atom model 
 assumes the existence of magnetic poles and makes little if any 
 use of positive and negative charges though of course magnetic 
 poles could be obtained by the proper motion of one or more 
 electrons. A free magnetic pole (magneton) has also been as- 
 sumed, the magneton playing the same role in magnetic phe- 
 nomena that the electron does in electricity. Various "dipoles" 
 "neutrons," positive electrons, etc., have been hypotheticated. 
 
 The English physicists have been very active in developing 
 an atom model for the interpretation of physical phenomena 
 and probably the two best known models are those of Thomson, 
 and Rutherford and Bohr. The early work of Thomson and 
 others of the Cambridge school proved the existence of elec- 
 trons in the numerous types of vacuum tube discharge, in the 
 emission of electricity by hot bodies, in the photoelectric effect
 
 56 FUNDAMENTAL PHYSICS 
 
 and directly or indirectly in nearly all phenomena of ionization 
 and radioactivity. The Zeeman effect, dispersion and many 
 other optical phenomena, metallic conduction and the various 
 electrical and thermal properties of the metals indicated that the 
 negative electron existed as a component part of practically 
 every kind of atom. On the other hand no corresponding free 
 "positive electron" has ever been isolated and although in- 
 direct (spectroscopic) evidence of its existence has been obtained 
 yet this evidence is far from conclusive. Positive charges are 
 always found to accompany masses of atomic size so that it 
 is natural to assume that positive charges are due in every in- 
 stance to the removal of negative electrons from the "atom." 
 Positive atom ions therefore differ amongst themselves in the 
 way that atoms differ. On the other hand negative electrons 
 appear to be identical no matter from what kind of atom they are 
 removed. 
 
 Thomson naturally assumed his atom model to consist of 
 electrons and a positive charge sufficiently large to' neutralize 
 the charge of the electrons. The positive charge was consid- 
 ered to be uniformly distributed throughout the atom, the elec- 
 trons moving about freely through this positive charge and being 
 attracted toward the center by a force whose intensity is indi- 
 rectly proportional to the square of the distance of the electron 
 from the center. Some electrons may describe closed orbits 
 within the atom or within the atom's neighborhood or they may 
 vibrate about certain positions of equilibrium. Rings of electrons 
 rotating about the center of the atom may exist. These rings 
 may all be in one plane (Saturnian atom) or they may be located 
 in different planes. ' 
 
 One of the most successful simulations of the Thomson atom 
 to phenomena is its "explanation" of the various families of 
 elements. The Mendelejeff classification of the elements is 
 based largely on the "valency" properties of different atoms and 
 Thomson showed how a model containing one or more rings of 
 electrons could represent the different families and the different 
 valencies. The analogy is indeed very striking but it remains a 
 mere analogy. It is pretty generally conceded that valency 
 in chemistry is an electron phenomena and many have gone so 
 far as to consider the valency of an atom to be the number of 
 electrons it is capable of gaining or losing. This view of valency 
 gives this quantity a vector quality. This interpretation of
 
 ATOM MODELS AND ATOM NUCLEI 57 
 
 valency also offers a picture as to how atoms can combine with 
 each other to form molecules of greater or less stability. Un- 
 fortunately we have few ways of verifying any conclusions of this 
 kind and it may be said that our knowledge of interatomic struc- 
 ture is more certain than our knowledge of intramolecular struc- 
 ture. On the whole it seems quite certain that chemical phe- 
 nomena and most of the physical properties of substances depend 
 upon "some outer" or "valency" electron atmosphere of the 
 atoms and that the remainder of the atom plays a very small 
 part in these phenomena. The absorption of the bullet type of 
 radiation (a, /3 and the ion radiations) is in marked contrast to 
 the absorption of light and heat and is more or less entirely in- 
 dependent of the physical and chemical nature of the absorbing 
 substance, depending only upon its density. According to this 
 view the stability of atoms is to be attributed to the part other 
 than the "electron" atmosphere while the wonderful variety of 
 physical and chemical changes are due largely to the changes 
 taking place among the various interlocking electrons. The 
 universal distribution of electrons results in these changes being 
 infinitely more simple than they would be were there as many 
 types of electrons as there are atoms of matter. The im- 
 penetrability of solids under ordinary conditions, their small 
 diminution of volume when cooled to very low temperatures 
 and their small compressibility seem to indicate that the 
 "electron atmosphere" of an atom or molecule possesses quite 
 a definite volume which is not greatly affected by the heat mo- 
 tions of molecules. 
 
 Some interesting models of the Thomson atom have been made 
 by floating magnets upon mercury or by suspending small charged 
 spheres so as to be acted upon by a central force. Under these 
 conditions the magnets and spheres arrange themselves in con- 
 centric circles depending upon their number and the intensity 
 and direction of the forces. Probably the most elaborate work 
 of this kind has been done by Crehore. By assuming definite 
 models it is possible to calculate when two atoms can combine 
 with one another or in other words occupy places where the 
 interacting forces are in equilibrium. These positions of equilib- 
 rium depend upon the velocity as well as the number of electrons 
 in the model. In the case of two atoms having two electrons each 
 it is shown that there are two places where the forces of attraction 
 and repulsion neutralize. In this way it may be possible to
 
 58 FUNDAMENTAL PHYSICS 
 
 explain the size of molecules, the spheres of action of molecules, 
 the formation of aggregates, etc. 
 
 In order to account for the reflection and scattering of a rays, 
 Rutherford's theory assumes that the atom must be the seat of 
 sufficiently intense electrical forces to reflect an a particle in 
 certain encounters. He assumes that an atom possesses a central 
 nucleus of charge Ne sufficient to neutralize the surrounding 
 charges. This charge is considered as a point charge and an a 
 particle passing near this nucleus will be caused to move in a 
 hyperbolic orbit giving a deviation <f> to'the a particle, where Ne 
 is the central charge; p the perpendicular distance from the nu- 
 cleus to the original path of the a particle, E the charge of the a 
 particle of mass m and velocity v, 
 
 2p 
 
 - 
 
 Let a beam of Q a particles pass through a thin screen of thick- 
 ness t containing n atoms per unit volume. The number of a 
 particles per unit area (to be counted by the scintillation method) 
 on a screen at a distance r from the radiator is 
 
 ntb 2 cosec 4 ~ 
 y = ~lQr r ~ 
 Geiger has found that y varies as t ; and as cosec 4 ~ over quite a 
 
 wide range of angle. The value of Ne is about lOOe for gold, 
 N varies as the atomic weight. 
 
 Darwin assumes a type of atom similar to that assumed by 
 Rutherford. The penetration of atoms by a and /3 particles is 
 then reduced largely to the action of the outer electrons in re- 
 ceiving energy. Bohr assumes that the rate of decrease of 
 velocity of the a or /3 particle depends on the frequency of vibra- 
 tion of the electrons in the absorbing material. Bohr concludes 
 that the hydrogen atom only contains one electron outside the 
 nucleus while the helium atom contains two such electrons. 
 
 Nicholson has assumed that the whole mass of the atom is of 
 electrodynamic form due to the presence of equivalent amounts 
 of positive and negative electricity. The negative charge con- 
 sists of electrons and is now generally admitted to constitute but 
 a small part of the total mass of any atom. The unknown posi- 
 tive charges may therefore be regarded as consisting of units that
 
 ATOM MODELS AND ATOM NUCLEI 59 
 
 are very small compared with that of the electron and since the 
 
 g2 
 
 inertia is proportional to * e being the charge and a the radius, 
 
 the mass contributed by the positive charge may be made to 
 represent nearly the whole atomic mass. These positive charges 
 may be assumed to be distributed uniformly throughout the 
 atom. 
 
 The single positive electron is not supposed to exist in a free 
 state. Permanence may be assumed, according to Nicholson, 
 to systems of two, three, four, five, etc., negative electrons in 
 rings at equidistant intervals around a single concentrated 
 positive charge. Four so-called protyles or primary atoms are 
 constructed according to the first four models given above and 
 the atoms of the various elements are supposed to consist of 
 these protyles uniformly distributed throughout their volumes. 
 These protyles are coronuim, hydrogen, nebulium and proto- 
 fluorine respectively. These protyles may consist of multiples 
 of the above electron construction. Their relative atomic 
 weights are Cu 0.5131; H 1.008; Nu 1.6277 and Pf 2.3604. 
 The extraordinary agreement between the calculated and the 
 observed atomic weight is remarkable. 
 
 Element Constitution Calculated International 
 
 atomic weight atomic weight 
 
 Helium NuPf 3.988 3.99 
 
 Lithium H 2 Nu 3 6.900 6.94 
 
 Glucinum H 2 Pf 3 9.097 9.10 
 
 Boron H 3 He 2 11.000 11.00 
 
 Carbon H 4 He 2 12.008 12.00 
 
 Nitrogen H 6 He 2 14.020 14.01 
 
 Oxygen H 4 He 3 15.996 16.00 
 
 Fluorine H 7 He 3 19.020 19.00 
 
 Neon H 6 Pf 6 20.210 20.20 
 
 Sodium H 7 He 4 23.008 23.00 
 
 Gold 8(He 2 Pf 3 H 3 )2(He 2 Nu 2 Pf 3 H 3 )Nu 2 Pf 2 H 2 
 
 Radium 8(He 2 Nu 2 Pf 3 H 3 )2(He 2 Pf 3 H 3 )He 3 . 
 
 If there is any protyle basis of the theory of elements, the 
 disintegration products of uranium and thorium will serve as a 
 test for the theory. 
 
 A few characteristics of atomic weights as considered by 
 Harkins are : 
 
 (a) The atomic weights on the hydrogen basis approximate 
 whole numbers and are usually lighter, rather than heavier
 
 60 FUNDAMENTAL PHYSICS 
 
 than the nearest whole number. Harkins puts forward the 
 theory that the "packing" of hydrogen atoms in the nuclei reduces 
 their mass. 
 
 (6) Since the alpha particle is emitted by the even number 
 elements and the even numbered elements of low values show 
 differences in their atomic weights by 4, there is evidence that 
 these elements are helium compounds, nHe', according to 
 Harkins. 
 
 (c) Most of the odd numbered elements of low atomic weight 
 can be represented by nHe' + H's, the primes indicating that 
 the mass of He and H has been decreased by being packed 
 into the nucleus. 
 
 (d) Some 98 per cent, of the meteorites consist of the even 
 numbered elements. As far as abundance of the elements is 
 concerned the system plays out at about 30. The conclusion is 
 reached that helium forms the substructure of practically all 
 matter. 
 
 The Bohr type of atom is quite successful in explaining the 
 spectra of hydrogen and the K and L x radiations of the 
 elements. The following items briefly indicate the nature of 
 the model. It is designed for radiation purposes and is con- 
 sidered to obey the classic laws of electrodynamics during the 
 steady state. It is during this steady state that the ordinary 
 inverse square forces are assumed to hold. 
 
 (a) Assuming that the inverse square law holds for the forces 
 (F) exerted by the atomic nucleus (E) upon negative electrons, 
 then Moseley's law leads to the distance (a) of the innermost 
 electron (e) orbit from the nucleus being inversely proportional 
 to the atomic number. 
 
 F = ^ = (27m) 2 ma or for two different atoms, -\ = -^rA 
 
 (1 HZ 
 
 with Moseley's law yr = 7= one has -^r = . Millikan 
 
 ** Vw 2 * 2 
 
 considers that these conditions can be assumed because only 
 circular orbits are to be considered stable and are indicated by 
 the Zeeman and magnetic effects. 
 
 (6) The L x radiations obey Moseley's law in the same way 
 as the K lines, the frequency being about one-eighth as great. 
 The L lines indicate the second electronic orbit to be about five 
 times as great as the first.
 
 ATOM MODELS AND ATOM NUCLEI 61 
 
 The data indicate that for hydrogen the K lines appear in the 
 ultraviolet at about 90/zM as has been obtained by Lyman. 
 The L series appears to be the ordinary Balmer series in the 
 visible spectrum. The M series is Paschen's infra-red spectrum. 
 
 (c) The frequencies of the Balmer series of hydrogen is given 
 
 by v = N (^-j j-J where n\ = 2 in the visible region and 
 
 n 2 takes values 3, 4, 5, etc., for the different lines. Paschen's 
 infra-red lines have n\ = 3 and Lyman's bands n\ = 1. Bohr 
 assumed that hydrogen consisted of one electron rotating about 
 the nucleus in a series of nonradiating orbits governed by 
 conditions described in (a). 
 
 (d) Radiation takes place when an electron moves from one 
 orbit (Ai) to another (A 2 ) in such a way that hv = A\ A 2 
 where h is Planck's constant and AI is the energy of orbit 1. 
 
 (e) The possible orbits of hydrogen are determined by the 
 kinetic energy of rotation (T) being equal to % rhn where r 
 is a whole number and n is the orbital frequency. From (c), 
 
 (d) and (e) N = T^ The value of N observed spectro- 
 
 scopically agrees with that calculated for this Bohr atom, 
 
 .V = 3.294(10) 15 . 
 
 / jT 2 /i 2 \ 
 
 The radii (a = T ^ J for hydrogen are in the ratios 1, 4, 9, 
 
 16, 25. The diameter of the normal hydrogen atom comes to 
 1.1 (10)~ 8 cm. The Bohr atom explains why hydrogen does not 
 absorb the spectra which it emits. 
 
 (/) Condition (e) implies the atomic nature of angular 
 momentum. 
 
 (g) The smaller the number of electrons in the outer part 
 of the atom the less should be their mutual actions and hence 
 the less deviation from the Moseley law. This is found to be 
 the case. 
 
 (h) The Bohr view of the atom in an unmodified form applies to 
 hydrogen, to helium that has lost a charge and to the inner 
 electron of the heavier atoms. The fact that it assumes the 
 electron orbits to be in a single plane does not necessarily mean 
 that in the complex atoms a disc structure is necessary.
 
 14. THE RITZIAN ATOM, THE MAGNETON AND THE 
 NEUTRON 
 
 Important work on the series of spectrum lines has been done 
 by -Kayser and Runge, Rydberg and Ritz. Ritz has developed 
 a theory of the constitution of the atom that explains the series 
 distribution of spectrum lines based on a magneton (Bauer). 
 
 The different formulas of spectral series may be said to be an 
 extension of Balmer's equation for the principle lines of hydrogen. 
 This series is the secondary spectrum which is obtained in vacuum 
 tube discharges. The formula is: 
 
 w 2 1 rl I 
 
 N is a constant and m is the number of the line under considera- 
 tion of wave length \ m . Pickering has observed a series of 
 supposedly hydrogen lines in f Puppis that follows the law : 
 
 The constant N is the same as in Balmer's formula; m has 
 the values 1, 2 . . . . The series has not been obtained in 
 the laboratory. Kayser and Runge have represented series by 
 equations of the form 
 J. 
 X, 
 
 The series are primary or secondary according to the values 
 of the constants A, B, C. Rydberg's -formula can be stated as 
 follows: 
 
 ^- = A + Bm~ 2 + Cm~ 3 - 
 
 The formula of Ritz is, N being a constant for all elements 
 while a, b, a' and b r differ for the various elements. 
 
 J_ 1 1 
 
 N\ ~ I b\ 2 ' 
 
 62
 
 THE RITZIAN ATOM 63 
 
 Most physicists have applied the same kind of differential 
 equations to the source of light vibrations as would apply to 
 elastic vibrations. These equations contain the frequencies 
 as squares while the simple laws of series lines contain the 
 frequencies as a first power. Ritz assumes that the frequency of 
 the oscillations is proportional to the force that produces the 
 oscillations, the force being due to a magnetic field. The inten- 
 sity of magnetic field required is about (10) 8 gauss. This is in 
 agreement with the theories of magnetism of Langevin and 
 Weiss and of the pressure shift of Humphreys and Mohler, 
 these theories assuming a field of about (10) 7 gauss. 
 
 The intense magnetic fields, to which is due the vibrations 
 which give rise to series lines, consists of magnetic poles dis- 
 tributed within the atom according to simple geometrical laws. 
 From the poles come fields H and H'.. The fields H n and H' n 
 normal to the plane of vibration of each particle determine the 
 frequency of its circular motion. Increasing the intensity of 
 the field causes a proportionate increase in the frequency. 
 Every solid of revolution rotating around its axis may, by a 
 suitable distribution of electric charge, become equivalent to 
 a linear magnet. When the magnetic poles approach the surface, 
 the electric density increases indefinitely in their vicinity and 
 the surfaces carrying the electricity become practically equivalent 
 to point charges. These solids are alternately positive and 
 negative, having rotations in opposite senses. Electrostatic 
 attraction fixes them together as a linear chain. 
 
 Ritz supposes that the magnetic fields within atoms is due to 
 elementary magnets of length a and having poles of intensity m. 
 According to this view, where A depends on the charge and 
 mass of the corpuscle, 
 
 ^/J_ J_\. 
 
 a 2 \w 2 m 2 / 
 
 which is the same equation as Balmer's. To explain other series 
 it is assumed that the orientation of the magnets with respect 
 to the corpuscle, or the number of magnets is changed. If n, 
 is the distance of the electron P to one pole N and n 2 the distance 
 to the other pole, the frequency n of the resulting circular vibra- 
 
 tion is : n = HK = K/JL ( ^ -- ^ } By letting the first magnet 
 have a length ~, one obtains Balmer's formula. Other formulae
 
 64 FUNDAMENTAL PHYSICS 
 
 can be obtained by giving different values to n, and to the lengths 
 of the magnet. 
 
 The theories of Ritz also explain many complicated cases of 
 the Zeeman effect and Cotton has discussed the positive Zeeman 
 effect in terms of Ritz's views of the atom. 
 
 According to Ritz a vibration of frequency v = N (-r J is 
 
 \TC 7YI I 
 
 produced by the magnetic field of (m 2) elementary magnets 
 turned toward each other, which are all identical: in addition to 
 this magnet series the electron is subject to rigid combinations. 
 Higher numbers of the order correspond to higher magnet 
 polymerizations, which constantly become less stable, so that 
 the lines become broader with an increasing number of the order, 
 and also become constantly weaker. The magnetic field in an 
 atom Ritz considers as being produced by two poles of opposite 
 sign, which separately may occupy different positions in the 
 atom. In the case of hydrogen, these points lie at equal dis- 
 tances on a straight line. In any combination formula each of 
 the terms represents the influence of one pole, and the possible 
 positions of the separate poles permit the most varied combina- 
 tions of the poles in pairs. As to a certain minimum prescribed 
 in the number of the order m which occurs in the case of no 
 known processes of vibration this mode of representation only 
 affirms that the magnet poles are held by the structure of the 
 atom at a certain minimum distance from the electron vibrating 
 within an atom. 
 
 The theories of Ritz have been applied with greatest success 
 to series spectra. Band spectra may be considered as due to 
 closed rings or polygons of elementary magnets, these structures 
 forming an important part of the atom. A series spectrum 
 may result when these structures have been excited in some way 
 by electrical or chemical processes. 
 
 The researches of P. Curie and others showed that the dia- 
 magnetic susceptibility of a substance is independent of the 
 temperature whereas the paramagnetic susceptibility is in- 
 versely proportional to the absolute temperature. Accordingly 
 there must be a fundamental difference between the two kinds 
 of magnetism. Langevin's theory makes diamagnetism a char- 
 acteristic property of each molecule, the resultant magnetic 
 moment of the revolving electrons in each atom being zero. 
 An external magnetic field only affects the orbits When the
 
 K X (10) 6 
 
 
 K X (10) 6 
 
 Pb - 1.37 
 
 Cd. 
 
 -1.16 
 
 Au.., - 3.07 
 
 Tl., 
 
 -4.6 
 
 C, diamond 0.49 
 
 Cu. 
 
 -0.82 
 
 C, amorphous .... 2 . 02 
 
 Al. 
 
 1.8 
 
 Hg - 2.6 
 
 Be 
 
 0.29 
 
 Ac... . . - 1.4 
 
 R 
 
 . 4.32 
 
 THE RITZIAN ATOM 65 
 
 revolving electrons possess a magnetic moment the substance is 
 paramagnetic. For a diamagnetic substance the susceptibility 
 
 K = 2~ Ne z r z , m being the mass, e the charge and r the radius 
 
 of the electron orbits, N being the number of electrons per 
 unit volume. 
 
 K x (10) 
 
 Na 2.2 
 
 Pd 5.15 
 
 Pt 29.0 
 
 Si 0.2 
 
 N 0.0537 
 
 Mo 2.2 
 
 Bi -13.7 Mg 0.57 Os 0.62 
 
 The phenomena of magnetism are extremely complex and 
 seem to be very closely related to the processes that take place 
 during chemical reactions, in optical phenomena and in mechan- 
 ical changes. These properties of matter appear to be due to 
 electrons revolving in orbits in the outer parts of atoms. 
 
 According to Langevin molecules contain a large number of 
 electrons moving in closed orbits, each of which has a certain 
 magnetic moment. In an increasingly intense magnetic field, 
 according to Lenz's law, the motion of the electrons would be 
 modified so as to oppose the increase of the intensity of the field 
 and would thus show the phenomena of diamagnetism, as well 
 as the Zeeman effect. Paramagnetism is then only the property 
 of such molecules or aggregates whose resultant magnetic 
 moment is not zero. The theory of Langevin fails to explain 
 many of the magnetic properties of solids although it explains 
 the magnetic properties of oxygen. 
 
 In order to explain the magnetic properties of solids, Weiss 
 imagines a molecular magnetic field that is to be measured by the 
 magnetic action of an aggregate of molecules upon any one of 
 them. Such a field is considered as uniform and its intensity 
 and direction are given by its effect on the hypothetical isolated 
 molecule. If H m is the strength of the molecular field, d the 
 density of the magnetic material, m its molecular weight, A a 
 constant and O m the magnetic moment per gram-molecule of 
 material,
 
 66 FUNDAMENTAL PHYSICS 
 
 o- m0 is the limiting value of <r m when H becomes very large or 
 T (the absolute temperature) very small ; a = p 
 
 According to the theory of Weiss, the magnetic moments of 
 molecules are integral multiples of a common magnetic moment 
 which he calls the magneton. This unit magnetic moment 
 would be expected to be independent of the temperature, the 
 latter affecting the size and arrangement of the molecular 
 aggregates. 
 
 Weiss and Onnes have studied the magnetic properties of 
 various ferromagnetic substances at low temperatures and the 
 following gives the experimental value of the magnetic moment 
 of a gram atom or of a ^ gram-molecule. 
 
 Nickel ................................. 3,381 
 
 Cobalt ................................. 9,650 
 
 Iron ................................... 12,410 
 
 Magnetite ............................. 7,417 
 
 The values for iron and nickel are quite exact and are in the ratio 
 of 11:3. After making certain temperature corrections Weiss 
 
 calls ^ = = 1123.5, the gram magneton. Dividing 
 
 by the number of atoms in a gram-atom Weiss gets a number 
 16.4 (10)~ 22 which he considers to be the magnetic moment 
 of the magneton or elementary magnet. A magnetic molecule 
 is a quantity of matter whose magnetic axis possesses 2 degrees 
 of rotational freedom. 
 
 Substance Z m (10) <r m0 
 
 FerrocyanideofKandNH 4 1.73 11.70 10.41 
 
 Pyrophosphate of Fe and NH 4 7 . 99 24 . 60 21 . 89 
 
 Ferric and ammonium citrate 8 . 04 24 . 68 21 . 96 
 
 Sodium ferripyrophosphate 9 . 66 27 . 10 24 . 04 
 
 Sodium ferrimetaphosphate 13 . 00 31 . 50 28 . 03 
 
 Ferric chloride 13.10 31.39 27.93 
 
 Ferric sulphate 15.20 33.80 30.09 
 
 Potassium f errometaphosphate 1 1 . 30 29 . 20 25 . 99 
 
 Sodium ferro-oxalate 12.30 30.48 27.11 
 
 Sodium ferropyrophosphate 13 . 00 31 . 37 27 . 91 
 
 Ferrous sulphate 12.90 31.12 27.69 
 
 Uranium sulphate 3.24 15.76 14.03
 
 THE RITZIAN ATOM 67 
 
 The Parson "electron" or "magneton" (Smith, "Misc. Col- 
 lections," Vol. 65, No. 11, ' 1915) is a thin ring of negative 
 electricity (about 1.5 (10)~ 9 cm. in radius) revolving with a 
 velocity approaching that of light and possesses electrostatic 
 and magnetic properties. 
 
 The change of wave length of spectrum lines due to increase of 
 pressure discovered by Humphreys and Mohler has been attri- 
 buted by Humphreys as being due to the magnetic properties 
 of surrounding atoms. This theory was advanced owing to a 
 supposed connection with the Zeeman effect. Livens attributes 
 the effect to an increase in the density of the vapor emitting or 
 absorbing the given light. 
 
 Duane has proposed a magnetic moment (M) for the holding 
 of positive nuclei (E) together against their electrostatic repulsion. 
 He proposes to account for the ejection of an a particle by assum- 
 ing that it is disturbed sufficiently for it to get beyond the critical 
 
 E 2 QM 2 
 magnetic field. The critical distance 70 is 5 = T- and if the 
 
 7*0 TO 
 
 disturbed displacement exceeds r the a particle will escape. 
 
 Oxley finds that the change of magnetic susceptibility on the 
 crystallization of some 40 diamagnetic substances indicates 
 fields of 10 7 gauss. Merritt has intimated that the fluorescence 
 of uranium compounds gives evidence of the presence of magnetic 
 fields. 
 
 Some experimenters have resorted to the view that a gas may 
 contain certain molecules, or neutrons, which are in a condition 
 allowing of easy ionization. Neutrons may themselves be formed 
 by the action of ionizing agents. One can easily imagine a di- 
 atomic molecule being split into the monatomic condition, and 
 these atoms may be comparatively easy to ionize. According 
 to Wellisch and Bronson a rays may produce neutrons, 
 relatively more neutrons being formed in the early part of the 
 range of the a particle. In this way an effort is made to explain 
 the fact that the "saturated" portion of the ionization, current 
 curve is not parallel to the current axis. The radioactive rest- 
 atoms are considered to be in the neutron condition.
 
 15. THE CORPUSCULAR THEORY OF LIGHT 
 
 The nature of light and of radiant energy in general has been 
 a subject of discussion ever since the introduction of the experi- 
 mental method in science. Among the classic controversies on 
 this subject was that between Newton, Hooke and others of 
 the time. Hooke supported the wave theory while Newton 
 upheld the view that light consisted of the propagation of some 
 sort of corpuscular radiation. Hooke believed that space was 
 permeated by an elastic medium, the ether, which was capable 
 of propagating vibrations. This ether pervaded matter in which 
 it possessed less density than in free space, and it did not neces- 
 sarily consist of a single substance. 
 
 Newton considered that ether and the light "emanation" 
 were capable of mutual interaction and that when light passes 
 through strata of ether of different densities, it was deflected 
 from its rectilinear course. The heat resulting from the ab- 
 sorption of light Newton thought might be due to vibrations 
 set up in the ether. Color was associated with some property 
 of the corpuscles acting in a way somewhat like Helmholtz 
 resonators in setting up waves in the surrounding medium of 
 different frequencies. 
 
 It may be of interest to note that it was customary for chemists 
 to include light corpuscles among the chemical elements for a 
 long time after Newton had died. When Lavoisier announced 
 however, that the weight of substances was the same before 
 chemical reactions as after they had taken place, the classifica- 
 tion of the elements became much the same as that used today. 
 
 About this time radiant heat was also considered to consist 
 of rays-of light-corpuscles. When it was found that light and 
 heat could be separated by selective absorption, it was necessary 
 to accept the "heat corpuscle" as a separate element called 
 caloric. Caloric was considered as filling the interstices be- 
 tween the particles of ponderable matter. This view gave a 
 reasonable explanation of the expansion of bodies on being 
 heated. Whether caloric possessed weight or not was left an 
 open question.
 
 16. HUYGHENS' SECONDARY WAVELET CENTERS 
 
 To explain the phenomena of color Newton assumed that 
 "every ray of light, in its passage through any refracting surface, 
 is put into a certain transient constitution of state, which, in 
 the progress of the ray, returns at equal intervals, and disposes 
 the ray, at every return, to be easily transmitted through the 
 next refracting surface, and, between the returns, to be easily 
 reflected by it." The "length of fit" was supposed to be pro- 
 portional to what we now consider as the wavelength. 
 
 At about the same time, Huygens wrote his defense of the 
 wave theory of light, and developed the principle that each 
 surface element of a wave front or locus of disturbance, may be 
 considered as the source of a secondary wave which will be 
 propagated in the form of a spherical wave if the medium is 
 isotropic. The wave front at any subsequent time is simply the 
 envelope of the secondary waves from these various surface 
 elements. By this means refraction and reflection were easily 
 explained. Huyghens assumed that the solid particles of 
 transparent bodies affected the elasticity of the ether, and thus 
 altered the velocity of light in them. Metals were opaque 
 because they contained the particles that damped the luminous 
 motion.
 
 17. THE FINITE STRUCTURE OF THE ELECTRIC FIELD 
 
 The conceptions of Faraday lead naturally to the view that 
 the electric and magnetic fields may possess a structure. 
 The electric lines of force may occupy only a small portion of the 
 space which they traverse and a finite number of electric lines 
 of force may radiate outward from a charge of given value. 
 Indeed it has been suggested that one line of electric force might 
 proceed from a unit charge of electricity or an electroethon. 
 The cross section of this elementary line of force might remain 
 constant or it might vary as one proceeded away from the electric 
 charge at the end of the line. In other words the electric field 
 might be considered as possessing an atomic structure. 
 
 The conception of lines of magnetic and electric force is very 
 useful in discussing a large number of physical and engineering 
 problems. For these purposes any arbitrary unit such as a 
 Faraday tube of electric force or a gauss may be used. 
 
 Light may be pictured as a transverse motion along the fibers 
 of the ether. The energy of a wave front would not be distrib- 
 uted uniformly over the surface but would be concentrated at 
 the points of the surface cut by the lines of force. 
 
 A theory of this kind permits considerable latitude of varia- 
 tion in case the electric charge or magnetic pole is moving. 
 Do the lines of force move with the charge or the pole? Do 
 the lines of force consist of ether threads surrounded by vacuous 
 space or do they consist of some peculiar state of the ether? 
 If the latter is the case, then does all the ether move with the 
 tubes, or part of the ether or only the disturbance? 
 
 When lines of electric force cross the boundary of two contigu- 
 ous media possessing different dielectric constants, the necessary 
 conditions imposed upon the differential equations representing 
 the electromagnetic wave motion are that the tangential com- 
 ponent of E on either side of the boundary is continuous and the 
 normal component of the electric displacement is continuous. 
 
 70
 
 FINITE STRUCTURE OF THE ELECTRIC FIELD 71 
 
 This involves a refraction of the line of force in crossing the 
 boundary. If the dielectric constants (Ki and KZ), the angles 
 which the lines of force makes with the normal (0i and 2 ), the 
 refractive indices for light (MI and /x 2 ) in the two media (1 and 2) 
 are given, then : 
 
 Ki cot 61 = Kz cot 2 and MI sin 0i = ^2 sin 2 . 
 
 In any theory of the transmission or reflection of electromag- 
 netic waves by two or more different media it is always necessary 
 to make certain assumptions concerning the boundary conditions.
 
 18. THE ELECTROMAGNETIC THEORY OF RADIA- 
 TION, THE THEORY OF GRAVITATION 
 AND THE EQUIPARTITION OF 
 ENERGY 
 
 Between the time of Newton and of Faraday, various views 
 were taken as to the nature of electricity and the medium in which 
 electromagnetic and optical phenomena take place. During 
 this time the one and two fluid theories of electricity were in 
 vogue. After the establishment of the wave theory of light by 
 Young and Fresnel, the luminiferous medium was treated for a 
 long time as an elastic solid. No connection was known to hold 
 between optical and electromagnetic phenomena. 
 
 It is to the genius of Faraday that we owe our present hypo- 
 thetical working models as to the structure of electrical and 
 magnetic fields and the correlation of electrical and magnetic 
 phenomena. The curves produced by sprinkling iron filings on 
 a paper placed over a magnet led him to the idea of magnetic 
 lines of force, curves whose direction at any point corresponds 
 to the direction of the magnetic intensity at the point. Faraday 
 considered all space to be filled with these magnetic lines of force, 
 every line being a closed curve. The density of the lines of force 
 through a unit area is taken to be proportional to the magnetic 
 intensity at a central point in the area, and its magnitude is 
 arbitrarily defined. The fundamental principle of the induction 
 of currents was discovered by Faraday and, stated in his own 
 words, is: "Whether the wire moves directly or obliquely across 
 the lines of force, in one direction or another, it sums up the 
 amount of the forces represented by the lines it has crossed," 
 so that "the quantity of electricity thrown into a current is 
 directly as the number of curves intersected." 
 
 Faraday also suggested that the particles of an insulating 
 dielectric under the action of an electric field become polarized, 
 the particles acting like electrical -doublets. Lorentz added to 
 the theory by assuming ions to exist in the dielectric, these ions 
 being subjected to certain elastic and viscous forces. 
 
 72
 
 ELECTROMAGNETIC THEORY OF RADIATION 73 
 
 We may consider that the electromagnetic theory of light is 
 due to Faraday, for it was he who suggested that if the existence 
 of a luminiferous ether is to be admitted, it may also be taken as 
 the seat of magnetic phenomena as well. 
 
 Maxwell succeeded in translating Faraday's conceptions into 
 mathematical equations. The lines of magnetic or electric force 
 
 represent the direction of a vector (B = \i.R for the magnetic 
 
 field or D = KE for the electric field), and the magnitude of this 
 vector is inversely proportional to the cross section of the tubes of 
 force formed by the lines. This relation between magnitude and 
 direction is a property of any circuital vector such as a vector 
 that represents the velocity of an incompressible fluid at any 
 point. Hydrodynamical sources and sinks correspond to elec- 
 trical charges or magnetic poles. 
 
 The energy of electrification resides in the medium, provided 
 it is capable of transmitting electrical action. 
 
 The energy in any part of the medium is considered by Max- 
 well to exist as a state of constraint or strain called the electric 
 
 polarization (D = ^ ) In general the direction of the force 
 
 (E} and the displacement are the same. 
 The energy per unit volume of the dielectric arising from the 
 
 polarization is ^ED cos 6, where is the angle between E and D. 
 
 In "fluid" dielectrics the electric polarization is accompanied 
 by a tension in the direction of the lines of force equal to the pres- 
 sure in all directions normal to the lines of force, the amount of 
 the tension or pressure per unit area being numerically equal to 
 the energy per unit volume at the same place. 
 
 From this view Maxwell derived his equations of the electro- 
 magnetic field. 
 
 = kE 
 B = nH 
 
 4wD = kE = curl H . 
 - B = - nH = curl E.
 
 74 FUNDAMENTAL PHYSICS 
 
 The entire magnetic intensity round the boundary of any surface 
 measures the quantity of electric current which passes through 
 that surface. 
 
 The view introduced by the electromagnetic theory of light is 
 that the energy of radiation is essentially of the same nature as 
 the energy that is localized about a charged body either at rest 
 or in motion. The ether is the medium of the energy of radiation 
 and of electromagnetic energy, and its properties are so chosen as 
 to satisfy the requirements of the equations of Maxwell. As far 
 as optical phenomena are concerned the ether medium is con- 
 sidered homogenous as regards its power of containing energy. 
 The velocity of radiation is rectilinear and is the same in every 
 direction. 
 
 In his "Thoughts of Ray Vibrations" Faraday suggested that 
 an atom may only be a field of force surrounding a point center 
 a view similar to that of Boscovich and Michell. Such an atom 
 would have no definite size. It could be considered as completely 
 penetrable and extending throughout all space. It was also 
 suggested that light and radiant heat might consist of transverse 
 vibrations propagated along the lines of force radiating from the 
 atomic centers. In this way Faraday proposed to "dismiss the 
 ether." 
 
 H. A. Lorentz, in 1892, began a series of memoirs upon an 
 electron theory all electrodynamical phenomena being attri- 
 buted to moving electric charges. In contrast to the older 
 electron theories of Weber, Riemann and Clausius, the electrons 
 were considered as acting upon the medium rather than between 
 each other. Electrons do not (Clausius' theory) act instan- 
 taneously at a distance but through a space subjected to Max- 
 well's equations, the actions being propagated with the velocity 
 of light. 
 
 One form of the equations of Lorentz is: 
 
 div D = 47rc 2 p, 
 
 div H = 0, 
 curl D = - H 
 curl H = ^f> + 47rpF 
 
 The "ponderomotive" force on an electron of charge e and 
 velocity V being eD + e[V-H].
 
 ELECTROMAGNETIC THEORY OF RADIATION 75 
 
 The equations of Lorentz, based on the electron theory, 
 assume an absolutely motionless ether to which neither density, 
 elasticity nor any mechanical property is ascribed. To such an 
 ether Thomson's lines of force, Lodges' idea of density and. 
 Bjerknes' and Korn's mechanical analogies would have to give 
 additional properties. 
 
 The fact that radiant energy would exert a definite amount 
 of pressure on material surfaces was first predicted by Maxwell 
 on the view of dielectric stresses; by Bartoli from thermody- 
 namic principles and by Planck from electrodynamical prin- 
 ciples by assuming a perfect reflector to be a perfect electrical 
 conductor. The electric vector of a light beam induces a finite 
 charge on the surface of the reflector and a finite current within. 
 The current in the field of the magnetic vector of the beam 
 results in a mechanical force. The resultant of the two me- 
 chanical forces gives the radiation pressure. 
 
 If R represents the time rate per unit of area at which elec- 
 tromagnetic energy is transferred at a point then Poynting's 
 theorem gives R = VEH sin 6 where 6 is the angle between E 
 and H. V = Edr along a line of electric intensity. By using 
 Poynting's theorem the energy of the electric and magnetic fields 
 is ~E 2 and ~# 2 . 
 
 O7T O7T 
 
 The electromagnetic theory of Maxwell based on a polarizable 
 ether and the mechanics upon which it rests may be spoken of as 
 the classical theory. It has had many brilliant successes and 
 from it many of our laws of today such as the Rayleigh law for 
 long wave length radiation and the Wien displacement law for 
 radiation have been derived. The Rayleigh law assumes the 
 equipartition of energy and Wien assumed that the length of a 
 wave sent out by a molecule depends only upon the velocity of 
 the molecule [V = /(X)] and the intensity of the radiation be- 
 tween X and X + d\ is proportional to the number of molecules 
 (as given by Maxwell's law) which send out waves between X 
 and X + d\. From these assumptions the intensity of radiation 
 v(X, 9)d\ of a black body at the temperature 6 produced by the 
 waves X to X + d\ is 
 
 6) = -& where C and c are constants.
 
 76 FUNDAMENTAL PHYSICS 
 
 The principle of the conservation of energy asserts that 
 R + r = a constant, where R is ordinary mechanical kinetic 
 energy and r is the "hidden " or potential energy. If the system 
 can be expressed in generalized coordinates (xi, x 2 , . . .) then 
 r is a function of x, xf . . . while R is a function of the co- 
 ordinates and their first derivatives (x, i, x 2 , . . .) with 
 respect to the time. Now (R + r) in a time dt follows a cer- 
 tain path or sequence of changes in an interval of time dl. 
 There are many possible paths and Hamilton's principle asserts 
 
 a path of "least action" and is: 51 (R r)dt = 0, where R r 
 
 Jto 
 
 is the Lagrangian function (L). Consider a field of force of 
 components FI, F z , F 3 due to a density distribution of r' de- 
 rivable from a Lagrangian function and K* = (v\F\ + v^F z + 
 v 3 F 3 ) so that 2 (a) v a K a = 0. 
 
 Instead of subjecting the system to the possible motions 
 determined by Hamilton's principle they are subjected to the 
 motion defined by the equation 
 
 df(R - r)dt + J^" K 8x " dt = - 
 
 ds 
 Now Einstein shows that if R r = m -j-> then the point 
 
 of mass m moves as it would in a gravitational field. (Einstein 
 has R r = m\/^ ab g ah v a v b . 
 
 A large number of such material points free from each other 
 passes into continuously distributed matter without internal 
 forces and the laws of motion of such a system follow from those 
 of a single point. Let dS be an element of volume in the exten- 
 sion, then (xi = dx, Xz = dy, x 3 = dz, x = dl, K is the external 
 force per unit volume). 
 
 f(R - 
 
 K 8x - dS = 0. 
 
 This would" represent the general principle for such a gravitation 
 force field. 
 
 The theorem of equipartition of energy refers to the distribu- 
 tion of energy among the coordinates of a system. Consider a 
 system to be described by a large number n of coordinates (ari, 
 x 2 , . . . ) and n momenta and that the energy is a homogenous 
 quadratic function of the x' s and the momenta. Separate from 
 the energy all the squared terms involving coordinates and 
 momenta (the R'), and take two sets of a large number of these
 
 ELECTROMAGNETIC THEORY OF RADIATION 77 
 
 terms xR and yR, then the law of equipartition states that the 
 average of the xR' t is the same as the average of the yR',. 
 This law has been applied to a large number of different systems 
 as for instance the condition of an electron atmosphere in a 
 metal, the surrounding gas and the radiation wavelengths of 
 radiation without. It is questionable if this application is 
 justifiable because the selection of the xR' 3 and yR' a should not 
 be exclusive so that the xR' s are chosen from among the electrons 
 in the metal and the yR' s from among the gas molecules. 
 However it is remarkable that the law does give us accurate 
 results such as the Rayleigh law for long wavelength radiations. 
 The general elementarquanta theory is of somewhat this type 
 (Wilson). If Xi, x 2 , . . . xj are the positional coordinates of a 
 material system and Zi, 2 2 , . . . zj are the impulse coordinates, 
 then the steady periodic motion of the system (or of an ensemble 
 of elementary systems of this kind) is such that each plane is 
 divided into regions of equal probability, the mean value of 
 
 which for any state of the system is - z^dxi = h (a uni- 
 
 versal constant). Each system is conservative except at very 
 short intervals when it absorbs or emits energy. During the 
 conserved periods the system follows the Hamiltonian dynamics. 
 
 During the critical epochs J z\dx\ = ph, J z 2 dx z = oh, i z 3 dx 3 = 
 
 rh, p t ff and r are positive integers and the integrations cover 
 the Xi, Zi, corresponding to the period 1/v,-. 
 
 From classic electromagnetic theory Schott and Crehore de- 
 velop an atom model consisting of electrons in a ring rotating 
 about the nucleus. The electrons are then subjected to radial 
 and tangential forces. For two electrons at the end of a diam- 
 
 eter (2a) the radial force is e 2 l v 2 + sj-jj -\ ' The ra- 
 
 dial force vanishes at 01 = 2(10)- 10 and a 2 = 1.8(10)~ 8 cms. 
 All regions for a greater than a 2 or less than ai gives a repul- 
 sion and between these values an attraction. The velocity of 
 the electron is independent of the value of a. By slightly 
 changing classic theory Crehore derives the constant of gravi- 
 tation. He considers the weight of an atom to be proportional 
 to the kinetic energy of the electrons relative to the nucleus.
 
 19. THE ELECTRICAL NATURE OF THE ETHER AND THE 
 HYPOTHESIS OF ELECTROETHONS AND RADIONS 
 
 Some of the characteristics of the atomic structure of entity 
 systems are: the definite character of the atom elements: the 
 frequent simplicity of the first order laws such as those of gravita- 
 tion and of gases: the universal occurrence of the finer grained 
 elements everywhere and the wealth of lower ordered structure 
 and phenomena that accompany what constitutes the individu- 
 ality of each of the atom elements. One has only to view the 
 earth's surface and consider that from the point of view of an 
 atom element in the solar system the earth itself consists only 
 of a point possessing a given mass. 
 
 As regards first order effects the ether will be found no doubt 
 to possess a very simple structure and the equations of elec- 
 tromagnetic theory indicate that some of the properties of the 
 ether are of the polarization type so characteristic of electrical 
 and magnetic phenomena. But at the same time it may not be 
 wise to require too elementary a structure to be the medium of 
 all that complex of radiation and force fields that the ether is 
 considered to be. 
 
 We will assume that the ether in an ensemble of electroethons 
 ee, possessing relatively mobile and immobile, negative and posi- 
 tive characteristics similar to the elements of neutral matter, 
 the electrons e and the atomic nuclei h. Energy transfer takes 
 place through the interchange of energy elements r. 
 
 These energy elements or radions may be the mobile electro- 
 ethons or they may be independent of these. We may picture 
 them as constituting a gas whose particles possess the light ve- 
 locity and which constitutes the only reservoir of energy at the ab- 
 solute zero of thermal temperature. The ether, matter and elec- 
 trical charge constitute the vehicles for carrying radions. Either 
 the radions or the electroethons constitute that portion of the 
 ether carried by matter according to the experiments of Fizeau. 
 
 78
 
 ELECTROETHONS AND RADIONS 79 
 
 The ether will be viewed as a porous lattice work that can be 
 defined as stagnant and when free of force fields always propa- 
 gates radiation with the velocity c. The electroethons can be 
 pictured as resembling the electron gas as it exists in the lattices 
 of the conducting metals. The porosity of the ether is such as 
 to offer no friction to the passage of matter through it. It can 
 be imagined that even the e and h elements may be aggregates 
 or ordered structures of the ee elements. The force fields are 
 due to peculiar distributions of polarization of the ether lattice 
 whereby the flow of the r elements between the ee, e and h ele- 
 ments is modified. The tangible model of the vehicles of the r 
 elements is to consider the " interior" of the ee, e and h elements 
 to contain the r elements as a gas. 
 
 The interchange of r elements among the masses of matter is 
 considered as a flow of these elements between e and e elements; 
 e and h elements, e and ee elements and h and ee elements. The 
 outer "atmosphere" of the neutral atoms being electrons it 
 follows that the surfaces of solids and liquids consist of an elec- 
 tron " film." Ordinary mechanics, gas, temperature and sound 
 phenomena may represent the interflow of r elements between 
 the e elements, as long as potential energy changes are not in- 
 cluded. Potential energy is to be viewed as a relation between 
 r and ee elements of the ether radiations and force fields. loni- 
 zation phenomena relate primarily to the interchange of r 
 elements between the e and h elements. 
 
 The Great Unknown 
 ->f 
 
 1. Life and Mind< ^Gateways of the Senses< > Physical World. 
 
 Worlds/ 
 
 Neutral Matter (M) 
 
 2. Natural Matter*-^ >Ether Medium, Radi- <-- >Electrical World 
 
 (E+) 92 Atomic ation and Force Fields (E-) Electrons and 
 Nuclei composed composed of ee and r Magnetons, e elements, 
 of h elements. elements. 
 
 "Free Space" (S), with a c Velocity Characteristic 
 
 3. Immobile Ether< ^Energy Elementar-< >Mobile Ether. 
 
 Force fields due quanta. Radiation ag- ee elements. 
 
 to a flux of mobile gregates of e = h'v 
 
 ether and r ele- groups. Composed of 
 
 ments. ee + ele- r elements. 
 
 ments.
 
 80 
 
 FUNDAMENTAL PHYSICS 
 
 Potential Energy (P) World 
 
 Ionization Phenomena. 
 
 Motion of e, and h, E 
 + and E elements. 
 Electrical currents and 
 magnetism. Interme- 
 diate velocity world. 
 Interpenetrating e 
 "film" elements, 
 lonization World. 
 
 < > Electromagnetic Ra- 
 diations in matter and 
 in the ether. Largely 
 e and ee motions. Ve- 
 lo cities approaching 
 but never considered 
 to exceed c. Waves 
 due to the interpene- 
 tration of e "films." 
 Radiation World. 
 
 4. Mechanical Mo-< 
 
 tions. Heat and 
 sound. Radiations 
 of M particles. 
 "Contact" Trans- 
 formations be- 
 tween e elements. 
 Low velocity 
 world. Waves due 
 to the contact of 
 e "films." World 
 of Newtonian 
 Mechanics. 
 
 Radiation "Molecules" by Planck's law are e = hv = jhvr 
 where v is the frequency of the radiation and j is an integer. 
 Experiments remain to tell whether there is a "continuous" 
 series of these molecules or a discontinuous series as is the case 
 of matter molecules. The general atomic theory would answer 
 that the latter condition holds. 
 
 The theory of radions would lead to the result that at the 
 absolute zero of temperature there is a condition of equilibrium 
 of radions between the atoms of neutral matter and the electrons 
 such that the radions in each molecule and possibly in each atom 
 neutralize each other.'
 
 20. SOME OF THE UNIVERSAL CONSTANTS OF NATURE 
 
 The chapter of the new science that has to deal with the 
 determination of a more fundamental set of definitions and units 
 has been greatly advanced by the discovery of the method of 
 studying atoms of electrical charge and of the atoms of natural 
 matter. These discoveries permit for the first time of the use 
 of individual atoms of electricity and matter for the definition 
 of the natural fundamental units of electric charge, and possibly 
 of mass. 
 
 One of the previous methods of defining units was that of 
 selecting a set of laws that appeared to be of universal applica- 
 tion, carefully determining the constants of this law, and then 
 defining the constants in terms of units of the Newtonian system 
 of mechanics. It has been in this way that the conceptions of 
 the Newtonian system has penetrated into our whole philosophy 
 of nature though we may make an effort to view phenomena 
 independently. An example of this was cited in the discussion 
 of Coulomb's law .and the definition of the unit of electric charge 
 in the electrostatic system of units. In this definition which is 
 used in all theory the charges are of unit magnitude when they 
 are equal and act as point charges repelling each other with a 
 force of one dyne while the dyne is defined in the phenomena of 
 the acceleration of mass by Newtonian forces. An electric charge 
 is thus defined by means of a mass and in later experiments when 
 the ratio of electric charge to mass is found not to be constant it is 
 assumed that the electric charge is constant while the mass 
 varies. To be consistent a set of units should be defined through- 
 out the whole range of conditions for which it is to be employed. 
 Ultimately the units of the Newtonian mechanics must be de- 
 fined for what we have designated as the electrical or energy 
 worlds. 
 
 On account of Newton's universal application of gravitation 
 and the wonderful success of the law in mathematical astronomy 
 it has frequently been assumed to be one of the most fundamental 
 laws of the universe. 
 
 F = a "-=-' 
 
 6 81
 
 82 FUNDAMENTAL PHYSICS 
 
 F is the force of attraction between masses m and mf a distance 
 r apart and G is a "universal constant." Unfortunately this 
 law is not a convenient one for laboratory study though it appears 
 applicable with great precision to coarse grained (astronomical) 
 systems. It has been suggested that this law represents the 
 "left over effects" of the electrical laws of attraction and repul- 
 sion. At present we do not know whether the mass of the elec- 
 tron is subject to this law or whether the mass of the natural 
 atoms of matter are of the gravitational type. 
 
 The corresponding inverse square laws for magnetic, electrical 
 and gravitational attraction furnish a basis for the c.g.s. units 
 and indicate a marvelous simplicity and a common origin. 
 The relation between the pressure (p) volume (v) and absolute 
 temperature (T] of a gas pv = RT is of significance because of 
 its interpretation by the kinetic theory in terms of the motions 
 of the gas molecules and the electron atmospheres of metals in 
 temperature equilibrium with the surrounding gas and the ether 
 radiations of the black body type. T is a unit in the c.g.s., 
 thermodynamics. There are many empirical laws worked out 
 under limited conditions that should be extended as widely as 
 possible. For instance the time of electrical contact of impact- 
 ing steel spheres in microseconds T = 74.7 v^r, where d is the 
 
 diameter and V is the velocity of the spheres in c.g.s. units 
 is suggestive of a large field of research work. The laws of 
 collision are very important as these give epoch points of the 
 laws of transformation of the variable elements of ensembles. 
 The principle of least action, Hamilton's principle, certain 
 hydrodynamical differential equations, Maxwell's and the later 
 electromagnetic equations, the laws of thermodynamics, the 
 phase rule, Kirchoff's radiation propositions, Huyghen's wavelet 
 centers, Poynting's law, Provost's theory of exchanges, the radia- 
 tion laws of Stefan, Boltzmann, Wien and Planck (asVe = hv) 
 are a few of the laws of nature, the groundwork of which has 
 not been at all correlated. The "laboratory" black bodies and 
 "cavities" for measuring fields of force should be carefully 
 considered from an experimental point of view. The oppor- 
 tunity of employing a and j8 particles opens a new region of 
 "cavities" for experimental study. The following are the 
 values of a few constants, the invariants of the transformations 
 amongst the atomic assemblages of matter and ether. These
 
 UNIVERSAL CONSTANTS OF NATURE 83 
 
 invariants may be pure numbers, magnitudes with dimensions 
 and directed magnitudes with dimensions. 
 
 Electron e = 4.774 (10)~ 10 
 
 Avagadro's constant N = 6.062 (10) 2 
 
 Gas molecules per cm. 3 at 0C. and 76 cm n = 2.705 (10) 1 
 
 Kinetic energy of translation of a molecule at 0C. E = 5.621 (10)~ 4 
 Change of translational molecular energy per 
 
 1C = 2.058 (10)- 
 
 Mass of hydrogen atom m = 1 . 66 (10)~ 4 
 
 Planck's element of action h = 6.55 (10)~" 
 
 Wien's constant of spectral radiation Ca = 1 .43 
 
 Stefan-Boltzmann constant of total radiation ... a = 5.72 o (10)~ 12 
 
 Grating space in calcite d = 3.030 A 
 
 The fundamental units may be chosen so that the gravita- 
 tional constant (G), the velocity of light (c) in free space, the 
 gas constant (K), Planck's (h) constant, or the constant of 
 electrical (&) and magnetic (/*) attraction shall possess assigned 
 values. If G = c = R = h = l we have Planck's "absolute" 
 system of units. 
 
 G = [G]m- l l 3 t-* 
 c = MB-' 
 R = [R]mlH-*6- 1 
 h = [hlmlH- 1 
 K = [K]l-*ml*t-* 
 
 where e refers to electric charge and 6 to temperature. All the 
 dimensional constants can then be expressed in terms of r, 
 R, h and K of the above constants. 
 
 The laboratory has discovered a large number of "effects" 
 for many of which a comprehensive theory has not been de- 
 veloped. The more complicated types of the Zeeman effect 
 belong to this class while the electrostatic Stark effect on sec- 
 trum lines is barely touched by theory, so complex are the com- 
 ponents of effected lines. Indeed the whole subject of line and 
 band spectra furnishes many worlds for many Alexanders to 
 conquer, much more worthy and requiring higher talent than 
 disorganized Persias. The conditions in spectroscopy are 
 indicated because every physicist has the instinctive feeling that 
 here lies the answer to the questions involving the structure of 
 the atoms. All provinces of scien'ce contain undeveloped fields 
 and one of the pressing problems of the laboratory is that of the 
 development of apparatus and methods of attack that will 
 permit of quicker and more effective offensive movements into 
 the regions that are unexplained and unexplored. -
 
 21. FUNDAMENTAL DEFINITIONS AND UNITS AND THE 
 CEER THEORY 
 
 The treatment of natural quantities is made possible by means 
 of assigning certain magnitudes and in some instances a sense or 
 direction property. The atomic elements are the magnitudes 
 that are smallest. We have seen that throughout nature entity 
 magnitudes are composed of practically identical elements. 
 The aim of the laboratory is to obtain the smallest number of 
 elements for the description of phenomena and to select these 
 elements so that they can be the most universally and con- 
 veniently used. 
 
 In the past, definitions and units of a local character have 
 usually been selected for given natural systems. The foot 
 length is convenient in the making of shoes. The meter is 
 adapted to geodetic work. The definition of unit density in 
 terms of water or the unit electric charge in terms of the repul- 
 sion of spheres are all examples of convenient local units. The 
 great disadvantage of these local units is that they have been 
 defined for different local systems and none of them have been 
 based upon the natural atomic elements. Units defined in 
 terms of the natural elements would have their magnitudes and 
 perhaps their sense qualities frequently expressed in a one to 
 one correspondence to the elements themselves. Suppose that 
 the unit of electric charge is defined in terms of the charge of 
 the electron. Every number representing an electric charge 
 would then be a positive or negative integer. 
 
 A natural system of units would then always employ integers 
 in the expression of the elements used for the definitions. If 
 the finest grained elements are employed in the determination 
 of the units then all magnitudes and senses or directions would 
 be expressed in terms of integers. This is the general atomic 
 theory of natural philosophy and this philosophy is being 
 continually supported by experiment. In so far as it is sup- 
 ported by experiment it is a part of the new science. 
 
 The smallest number of natural elements required to explain 
 phenomena constitute the ensemble of defining elements. 
 
 84
 
 FUNDAMENTAL DEFINITIONS 85 
 
 Whether there is a unique ensemble of this kind or whether a 
 number of equally simple ensembles will be available remains 
 for experiment to determine. At any rate we may aim to select 
 our laboratory definitions and units from the most universally 
 distributed and fine grained of the entity elements. 
 
 The transformations between the entity systems have been 
 found to be of two types, contact transformations taking place 
 during the collisions of matter (apparently described by the 
 Newtonian mechanics when the velocities concerned are com- 
 paratively small and new electromagnetic laws when the 
 velocities are high) and the ether transformations which take 
 place between portions of matter that may be at great distances 
 from each other. If we are to view the outer parts of atoms as 
 being constituted of rotating electrons and an ether more 
 or less modified by the presence of the atom (and this condition 
 is supported by experiments as far as they go), then contact 
 transformations possess an electrical and ether quality. Then 
 if experiments indicate that the ether is electrical in character 
 it may follow that all natural transformations possess an elec- 
 trical quality. Assuming that both contact and ether trans- 
 formations are electrical and that these transformations are 
 universal for all the entity systems of the universe it follows 
 that our definitions and units should be selected to make our 
 scientific laws simulate these contact and ether transformations 
 as closely as possible. 
 
 The conditions of energy interchange also suggests that if 
 possible our definitions and units should describe these inter- 
 changes as simply as possible. 
 
 The elements appearing in all natural changes then appear 
 to be the vehicles of electrons and the atoms of natural matter, 
 the carrier or the ether and the elements that appear and 
 disappear among the ensemble of ether, electrons and the 
 natural atoms. Whether any of these elements are absolutely 
 conserved will remain for experience to decide. Our present 
 theories usually accept the view that the electron as regards its 
 electrical charge, the natural atoms as regards their simple 
 elements such as possibly the hydrogen and helium nuclei and 
 the ether of free space are absolutely conserved, the unchanging 
 elements of an eternal universe. 
 
 The elements that are variable and that appear and disappear 
 such as kinetic energy, potential energy and the radiation quanta
 
 86 
 
 FUNDAMENTAL PHYSICS 
 
 are certain changes among the absolutely conserved elements 
 that are to be measured by magnitudes such as mass, time, 
 velocity, acceleration and temperature. 
 
 The following table defines certain physical magnitudes in 
 terms of certain elementary units, e, the electrical charge of the 
 electron (or perhaps eventually ee of the ether); c, the velocity 
 of light and r the element of energy, e possesses a + and 
 sense while c and r are directed elements and may be employed 
 to define the three elements of extension. 
 
 DIMENSIONS OP LABORATORY UNITS 
 
 Laboratory assumed to be at rest 
 
 (Laboratory with velocity /3 
 
 
 C ff 8 k 
 
 
 
 
 
 
 . 
 
 
 
 CK se 
 c.g.s.e. 
 
 
 .e.r. 
 
 ' 
 
 ransverse 
 
 ongi u ina 
 
 Geometrical: 
 Length 
 Area 
 
 I 
 J" 
 
 I 
 
 I* 
 
 d 
 
 d* 
 
 eV-i 
 eV-2 
 
 6 2 r -l 
 
 e<r- J 
 
 z<vr^=z 
 
 b 
 
 Volume 
 Kinematical: 
 Time 
 
 I* 
 t 
 
 l> 
 t 
 
 d' 
 c'M 
 
 e e r -4 
 
 c -l e 2,.-l 
 
 er- 
 eV-i 
 
 (tf tt) 
 
 \/l 02 = ( 
 
 Velocity 
 Acceleration . . . 
 Mechanical: 
 Mass 
 
 Momentum. . . . 
 Force 
 
 ft- 
 U-i 
 
 m 
 
 mU~ l 
 mlt~* 
 
 -i 
 
 ft-* 
 
 TO 
 TO- 
 
 ndr* 
 
 c 
 c*d-i 
 
 c-d->e 
 
 c-id-'ez 
 d-W 
 
 c 
 
 &e-iT 
 
 c-V 
 
 c~ l r 
 e~V 2 
 
 I 
 
 e-*r 
 
 r 
 
 r 
 e~V l 
 
 m< = 
 Vl-^ 2 m 
 
 w/d-Wi 
 
 Energy 
 Pressure 
 Electrical: 
 Charge 
 Potential 
 Capacity 
 
 mlH-* 
 ml-H-* 
 
 tliimlr 
 t-Wmiri 
 
 kl 
 k 
 
 min-* 
 
 ml-H-* 
 
 e 
 J'mr*e- 
 en-*m-H* 
 en-'m'H 1 
 
 d-"e' 
 d-z 
 
 e 
 d-'e 
 d 
 
 r 
 
 e-tft 
 
 e 
 e~'r 
 eV" 1 
 
 r 
 e-r 
 
 e 
 e-ir 
 e*r-' 
 
 
 
 Current 
 Resistance 
 Electric field... 
 Magnetic field.. 
 Magnetic pole. . 
 Permeability . . 
 
 k\tim\t-* 
 k-U 
 
 *-lHmlr> 
 
 t'rimir* 
 
 k-\ttm\ 
 I 
 
 ell-* 
 e-*lmt-i 
 6-imZT* 
 eJ-U-i 
 e-'2*mri 
 e-/m 
 
 cd-^e 
 c' 1 
 d~*e 
 d-*e 
 e 
 
 ce~ l r 
 c' 1 
 e-*r* 
 e~*r* 
 e 
 
 e->r 
 
 z 
 
 e-r 
 
 e-r2 
 
 
 
 
 The first column of dimensions gives the values as obtained in 
 the electrostatic system by using Coulomb's law and the funda- 
 mental units are taken as inductivity, length, mass and time. In 
 the second column the fundamental units are electric charge, 
 length, mass and time. For the medium where the inductivity 
 remains constant this quantity can be omitted from considera- 
 tion as is done in the last five columns.
 
 FUNDAMENTAL DEFINITIONS 87 
 
 There is in common use two systems of units, the electrostatic 
 and the electromagnetic according as the inductivity or the per- 
 meability are used as dimensions. If m, I and t are given integral 
 exponents then the inductivity appears as an elasticity and the 
 permeability as a density or vice versa. There is no alternative. 
 Corresponding to this condition is that relating to the directions 
 of the ether vibrations and the problem as to whether electrical 
 energy is potential and the magnetic energy kinetic or vice versa, 
 using the vibrations of a mechanical system as the pendulum as 
 an analogue. Either the electric or the magnetic fields can be 
 represented by a mechanical analogue but the relations of the two 
 fields cannot be so represented. 
 
 In the third column the fundamental units c, the velocity of 
 light in free space, rf, the diameter of the electron and, e, the charge 
 of the electron are considered as the natural units. In the 
 fourth column the fundamental units are taken as c, e and r the 
 energy of the radion. lie is ever found to be a multiple of a unit 
 such as ee then ee would become the natural unit of charge. This 
 system will be called the absolute system of natural units because 
 it lays at the bottom of our laboratory experience that these 
 natural elements are absolutely conserved and are constituted of 
 identical atoms. 
 
 The laws upon which the above system of units are based are 
 the laws of our own laboratories which we consider invariably at 
 rest when making experiments. Our mechanics indicate that 
 motion is relative and that by mechanical means we cannot ob- 
 serve the velocity of any laboratory by experiments made in 
 that laboratory. Electrical experiments indicate that the 
 assumption that electrical charge remains constant gives a con- 
 sistent explanation of phenomena and if there is discovered an 
 element of mass that is found to be conserved then that element 
 can be employed as an absolute unit. Experiments also indicate 
 that we cannot measure the motion of our system by measuring 
 the velocity of light in different directions. 
 
 When we consider that the kinetic energy of a system is meas- 
 ured in terms of we 2 and that the value of this energy is relative 
 to the way the velocity of a system is measured it follows at once 
 that I, m and t must necessarily be relative to each other and the 
 velocity given to the laboratory if our assumed laws of r and c are 
 to hold. A relative theory based on these conditions will be 
 outlined shortly.
 
 88 FUNDAMENTAL PHYSICS 
 
 The application of such a relative theory for electromagnetic 
 theory is complicated by our not knowing the dimensions of the 
 permeability and the inductivity hence the relative theory as 
 applying to the electrostatic system is developed. 
 
 An interesting application to ancient cosmosgony may be 
 noticed to relate to the definition of time in the cer units, there 
 being the beginning of time when it was said, "Let there be light." 
 
 Consider two laboratories LI and L 2 moving with a relative 
 velocity of v cm. per sec. or with /3 units velocity according to the 
 r dimensions in terms of c = 1, the observing angels A\ and A 2 
 in LI and L 2 , respectively, considering themselves to be at rest. 
 The relative velocity /3 must indicate that if this velocity is 
 apportioned to the two laboratories, the laboratories must move 
 along parallel paths (parallel paths being defined as the paths of 
 two light beams from two stars whose distance from the labora- 
 tory telescope is too great to be measured by any means such as 
 the parallex method and the stars are so close together that they 
 can just be resolved. This may be taken as a definition of parallel 
 lines). Only when three or more laboratories are concerned does 
 relative motion other than along two parallel lines require to be 
 considered. The relative method could then define the units of 
 one laboratory as being absolute. 
 
 The parallel paths of Li and L 2 define a direction and mechanics 
 such that A i and A 2 agree in their measurement of the distance 
 between these lines. 
 
 Let Ai and A z define a unit of time as the time required to 
 traverse a distance equal to the diameter of an electron d. 
 
 Li 
 
 A i assumes he is at rest and that the light track is di perpendicular 
 to the direction of their relative motion. A 2 considers his light 
 track d 2 , AI considers however that while the light traversed d? 
 the laboratory moved to b where bd represents the velocity of the 
 
 laboratory. The unit of his own time A i considers to be -^ = t\. 
 A 2 "considers" his unit to be = t 2 because he thinks he is at
 
 FUNDAMENTAL DEFINITIONS 89 
 
 rest but A i says that his unit is really = 1 2 and is therefore too 
 
 c 
 
 large, di = d 2 . 
 
 Hence (1) t z Vl - /3 2 = ti (to terms in /3 4 ) 
 
 In any laboratory it is assumed that the time intervals are 
 independent of the "direction" in which they are measured so 
 that relation (1) can be applied to " longitudinal" time if we wish 
 to think of such a unit. 
 
 As j = ci and j = c 2 , from (1) if Ci = c 2 we have 1 2 \/l ft* 
 = h (2). 
 Let A i send a radion of momentum MIC to A 2 who determines 
 
 its momentum in his laboratory to be M 2 c, MI ^ = M 2 T whence 
 
 t\ it 
 
 MI = M 2 \/l /3 2 (transverse masses) (3) 
 
 Consider A\ and A 2 each having a radion with the velocity 
 of c 2 in the same direction as ft. A\ considers the energy of 
 his to be Afi(c 2 = 1) and A 2 his to be M 2 (c 2 = 1). But AI 
 claims that A 2 's radion must have M$ z more energy than what 
 his radion possesses and hence is too large. So M\ varies as 
 (1 (3 2 )M 2 where the values of M\ and M 2 are to be viewed as 
 in (3), 'A i not only considering that A z has not correctly indicated 
 the energy of his system but that his masses are to be considered 
 by (3) so that MI = (1 - p*) y *M z (longitudinal mass) (4) 
 
 The definition of time by means of the velocity of a light 
 wav~e immediately indicates the difficulty of defining the simul- 
 taneity of events that occur in two different systems. Consider 
 
 / C ^\ 
 
 that (A. B > ) A 2 arranges in his laboratory 
 
 vibrating atoms or other suitable time measuring apparatus. He 
 regulates these from C where AC = CB = d. A 2 defines the 
 "atoms" at A and B as vibrating synchronously. A-i considers 
 AC = CB = d\/l |8 2 . A i also considers that in "setting" 
 the atoms the velocity of the signal in going from C to A was 
 1 /3 and from C to B, 1 + 0. AI considers that the clock 
 (or atom) at B is too slow and A is too fast, the difference in 
 
 time being d V^f? (^ - j) = ^= (5) 
 
 Let AI establish coordinates on his system of x\, y\, Zi, t\ 
 and Az, 2, 2/2, 22, 2 where x is in the direction of ft. As it has
 
 90 FUNDAMENTAL PHYSICS 
 
 been assumed that the distance between the laboratories is 
 found to be the same by A\ and A z , y^ = y\ and 2 2 = z\> A.\ 
 considers a point appearing to be at x\ from the y z z 2 plane 
 at time ti = 0. When t = ti the point will appear to be at 
 x\ pti from the y 2 z 2 plane. A 2 considers this distance to 
 be x-t because he considers himself to be at rest and from (2) 
 2 \/l /3 2 = Xi /3<i. To AI considering the point x\ from 
 the ytfi plane at t = t\ the clock on L 2 at the same distance Xi 
 
 from y\z\ appears by (5) to be slow by the amount - and in 
 the units of L\ this clock would register \i\ -- - j time. From 
 
 (1) tz \/l ft* = t\ -- - From these relations are obtained 
 
 the equations of transformation of coordinates of two systems 
 in relative motion. 
 
 , 
 
 " 
 
 These are sometimes written in the form where a = - 
 
 , .-0 2 
 tz = <*(*!- ^) x, = aCsi-jS*!) 2/2 = yi and z 2 = z, 
 
 In electrodynamics the fundamental laws are left unaltered 
 When the coordinates of AI are changed to those of A 2 and vice 
 versa. For dynamical phenomena the equations are x 2 = Xi 
 utij 2/2 = 2/1 v h> z 2 = z\ ut\ and t% = ti (where u, v, 
 u are the components of the relative velocity) and transforma- 
 tions of these coordinates leave the equations defining the units 
 unaltered. 
 
 It has been suggested that the fundamental units might be 
 such that a miniature reality could be constructed that would 
 faithfully simulate what we consider such to be. But this view 
 is dispelled immediately when we select a natural set of units such 
 as e, c and r. The ultimate e entity is so gross that individuals of 
 them can be studied for minutes at a time. Any hypothetical 
 reality in miniature must therefore be constructed above the 
 threshold of 'appearance of the natural units and this is of
 
 FUNDAMENTAL DEFINITIONS 91 
 
 course only possible for very small sections of reality such for 
 instance as the picturing of the atom as a miniature solar system. 
 Transformations of this kind are most successful when comparing 
 very gross with fine grained entities. 
 
 The definitions and units of science can be selected in a number 
 of ways and until the experimental fields have been carried into 
 the finest grained structures the framework of science cannot be 
 said to be complete. The following treatment is to be considered 
 as suggestive of the way the axioms of science will be laid when 
 we know the structure of the ether and of radiation. 
 
 The smallest known element in the laboratory is the electron, 
 e. Evidence is accumulating that the atomic nuclei may be com- 
 posed of hydrogen and helium. For simplicity consider the 
 atoms to consist of elements, h, and to be endowed with the 
 properties that we ascribe to positive electricity. The h element 
 is much less mobile than the e element. Experiments indicate 
 that ordinary matter atoms, M, possess the structure M = xe- 
 + [yh + e (x y}], the part within the nucleus being represented 
 by the term in the brackets. This equation will be called con- 
 dition or law II. 
 
 Law 1. M = x(e-} + [y(e +) + (x - y) (e-)} 
 
 The ether (S) will be considered as analogous and a more fine 
 grained structure than neutral matter and its elements will be the 
 electroethons, ee + and ee similar to e and h. 
 
 Law 2. S = 2x (ee +) -f 2x (ee -) 
 
 The radiation or energy elements (r) will be considered as the 
 finest grained of all the structures and they are assumed to pos- 
 sess conserved extension properties and will be denoted by 
 eee + x, eee + y, eee + z, eee x, eee y, and eee z as 
 previously described. 
 
 Law 3. r = S eee's 
 
 For the ether we have the condition law of the neutralization 
 of ee + and ee . For radiation the law 3 of the neutralization 
 of elements. 
 
 A point is defined as the " location " of an r element in the ether 
 lattice framework or in space, A point at rest in the location of a 
 neutralized set of r elements preferably as simple as possible. 
 The points are to be considered as without size or shape or struc-
 
 92 FUNDAMENTAL PHYSICS 
 
 ture because there is no means for indicating such qualities as 
 the points are not the source or sink of any radiation. 
 
 The function of the ee ensemble is that of the electromagnetic 
 medium, it being here assumed that phenomena such as gravita- 
 tion are of this type. These phenomena are considered as due to 
 electroethon collisions and that the history of these collisions is 
 given by the interchanges of the r contents of the electroethons 
 during collision. 
 
 The path of any moving point of an r carrier that does not re- 
 ceive or lose any r elements is defined as a straight line. Pos- 
 sibly the lattice structure of the ee ensemble could also serve to 
 define straight lines and directions. These properties have 
 however been assigned to the r elements. The path of a light 
 ray in the ee ensemble could be used to define a straight line and 
 this is constantly done in surveying. A line of force in the 
 ether field such as the plumb line is adapted for this service. The 
 opportunity of using different methods makes it possible to check 
 the definitions whenever the laboratory facilities are developed 
 sufficiently. 
 
 Rotations require the flow of radions due to their varying den- 
 sity in the force fields. Thus the radion maintains its own energy 
 as regards direction and magnitude unchanged. The magnitude 
 of its energy is assumed to be ic 2 and its direction is employed 
 to define the extension directions, these directions to harmonize 
 with directions as given by the ether lattice.
 
 22. THE THEORY OF ELEMENT ARQUANT A 
 
 In the time of Newton, one of the most serious objections 
 offered to the wave theory of light was its apparent failure to 
 explain the formation of shadows. Sound and water waves were 
 known to show diffraction, whereas at that time all evidence 
 favored the view that the propagation of light was rectilinear. 
 This objection was removed by Huyghens and Fresnel. 
 
 Huyghens regarded every vibrating point on the wave front 
 as the center of a new disturbance. These secondary disturb- 
 ances travel with the same velocity and are enveloped by a sur- 
 face which is identical with the surface from which the secondary 
 disturbances started. The enveloping surface forms the new 
 wave front. This view of wave propagation is Huyghen's prin- 
 ciple. Using the principle of interference discovered by Young, 
 by which is meant the fact that two luminous vibrations may 
 destroy each other, Fresnel explained the phenomena of shadows 
 on the theory that there was destructive interference between 
 the secondary wavelets in the region of the shadow. 
 
 The secondary wave apparently lies wholly in front'of the plane 
 tangent to the wave front at the center of the wavelet and the 
 effect is supposed to be greatest on the normal to the wave surface 
 drawn to the center of the wavelet. This applies to a medium 
 that is transparent. 
 
 The presence of charges in a medium either as ions or electrons, 
 that can be set into vibration by the light wave, results in ab- 
 sorption. This absorption may be considered as the frittering 
 away of the light energy which is necessary to overcome the 
 friction that accompanies the motion of the ions. In the equa- 
 tions from which the dispersion formulae are derived, all that is 
 necessary to assume is that the motion of the ions is accompanied 
 by damping. As to the nature of this transformation of energy 
 nothing is assumed, although it can be shown that the vibrations 
 of electrons may be damped during molecular impacts. 
 
 The radiation from the ions set into vibration by the light 
 wave is emitted in all direction, and thus differs essentially from 
 the secondary waves of Huyghens. Planck has treated this
 
 94 FUNDAMENTAL PHYSICS 
 
 subject and shows how the energy of the advancing wave is 
 reduced by the back radiation of the electrons. This absorption 
 would not be a transformation of the energy into kinetic energy 
 of molecular motion. In the treatment of Planck the phase of 
 the vibrating ion is considered as lagging a quarter of a period 
 behind that of the exciting waves besides the lagging of the 
 radiation of the electron itself by a quarter of a period behind its 
 own vibration. Planck applies his theory in general to resona- 
 tors, so that we may use the term resonator in place of that of 
 the electron or ion. The wave emitted by a system of resonators 
 will thus be a half wavelength behind that of the exciting waves, 
 and will be in a condition to produce interference. Planck's 
 treatment differs from that of Drude in that the damping is 
 referred to radiation entirely. 
 
 Since the work of Huyghens, the wave theory of light, based on 
 an elastic or electromagnetic ether, has been found to be in such 
 good accord with experiment that the old emission theory of 
 Newton was abandoned. The work of Maxwell and Hertz has 
 given the wave theory an electromagnetic interpretation. The 
 theory as thus modified explains reflection, refraction, inter- 
 ference, polarization, etc. The theory has recently been modified 
 again by the addition of the relativity hypothesis in order to 
 explain aberration, the experiments of Airy, Fizeau, and Michel- 
 son and Morley. This hypothesis states that the equations 
 representing the laws of nature remain the same, whether the 
 system of coordinates remains at rest or in motion. These theo- 
 ries view electromagnetic radiation as continuous. 
 
 On the other hand, there are reasons for assuming the radiation 
 of energy .to be in elements of an electromagnetic nature some- 
 what resembling material particles. Planck assumes that a 
 radiating body contains a large number of resonators and that 
 these may lose or gain energy in finite amounts, the portions of 
 energy e depending on the frequency of the resonators v and a 
 universal constant h, 
 
 e = hv. 
 
 The ionization produced by z-rays and ultraviolet light 
 would be expected to be distributed uniformly over the wave 
 surface, all the atoms exposed to the radiation suffering the same 
 change. As this is not the case it has been suggested by Thom- 
 son and others, that the energy is not uniformly distributed on 
 the wave front but that it is concentrated into various points
 
 THE THEORY OF ELEMENTARQUANTA 95 
 
 on the wave surface. This kind of distribution of energy in the 
 wave front would result in the same effect as would be expected 
 from the hypothesis that energy is radiated in finite magnitudes. 
 One of the difficulties confronting the theory of finite elements 
 of energy is its apparent irreconcilability with the Maxwellian 
 equations of electrodynamics. In the earlier forms of the theory 
 of elementarquanta the emission of the elements of energy is 
 assumed to be excited by the continuous absorption of energy 
 from the incident radiation upon one of the assumed oscillators. 
 Planck has also assumed that absorption and emission are en- 
 tirely independent. Emission is assumed to take place sponta- 
 neously in amounts e hv. The calculus of probabilities can 
 then be applied and the probability of the emission of an element 
 e by an oscillator of frequency v in a time dt (which is small com- 
 pared with the interval between two successive emissions), is 
 yndt, rj being a constant of the oscillator and n the number (a 
 positive integer) of elements of energy originally contained in the 
 oscillator. If u is the vibrational energy of the oscillator, n will be 
 
 such that ( -- n\ is a positive real proper fraction. 
 
 The energy absorbed in a time dt cannot be equated to the 
 energy emitted in the same time if the former varies continuously 
 and the latter by increments. Let <p be the entropy of the oscil- 
 lator, and w the probability of the oscillator having an amount of 
 energy u, then <p = k log w where k = 1346(10)~ 16 erg/degree. 
 The new hypothesis gives the mean value of u,. u, at the absolute 
 temperature T as being 
 
 hv 
 
 hv e m + 1 
 
 This value of u, differs from that of the old theory by the 
 
 hv 
 appearance of the additive constant -^' 
 
 The theory involves the emission of energy in quanta in case 
 of electronic motions as well as radiation and the apparently 
 constant energy of the a and particles confirm this hypothesis. 
 
 The problem of the equipartition of energy between the vari- 
 ous degrees of freedom is one that remains unsolved. One way 
 of avoiding the problem is to consider that the degrees of free- 
 dom that are connected with radiational phenomena are in-
 
 96 FUNDAMENTAL PHYSICS 
 
 operative under ordinary thermal conditions. The "steady" 
 supply of energy of one form and the steady loss in another form 
 under experimental conditions is given by Planck's law for the 
 distribution of energy among the various wavelengths of radia- 
 tion. Planck attributes the failure in the application of the law 
 of equipartition to the nature of energy itself, some degrees of 
 freedom absorbing no units of energy and other freedoms ab- 
 sorbing an unequal number of units in some cases. Planck's 
 theory leads to the law for the distribution of energy among the 
 various wavelengths in black body radiation. It may also 
 mean that molecular and atomic motions must be discontinuous. 
 
 Planck's theory represents the radiation coming from a solid 
 as due to a very great number of Hertzian resonators. Each 
 resonator has its own characteristic period, and emits a rigor- 
 ously monochromatic radiation. In consequence of the changes 
 of energy between the resonators, there is established a parti- 
 tion of energy following a certain law, and there also results a 
 certain distribution of radiant energy throughout the spectrum, 
 although the resonators neither absorb nor emit any radiation 
 except that which is characteristic to them. The exchange of 
 energy takes place by the Doppler principle, either the resonators 
 being in motion, or the radiation is reflected, refracted, diffracted 
 or diffused by bodies in motion; and by mechanical phenomena 
 such as collisions. It is not supposed that the resonators have 
 any direct influence on each other, but that the exchanges of 
 .energy will be made through the interaction of matter. 
 
 The relation between the radiation formulae of Wien and Ray- 
 leigh were indicated by Planck who imagines an enclosure filled 
 with black body radiation and bounded by perfectly reflecting 
 walls. Within the enclosure the linear electromagnetic oscillators 
 of frequency v are in equilibrium with the black body radiations. 
 The energy of any radiator Ev and the energy per unit of volume 
 ev of radiation of frequency v is 
 
 Now assume that Ev is composed of an integral number of elemen- 
 tary units of energy c. From a consideration of the number of 
 oscillators and the number of elementary units of energy it fol- 
 lows that the value of the entropy of the system is:
 
 THE THEORY OF ELEMENTARQUANTA 97 
 
 From the second law of thermodynamics as applied by Wien 
 
 Hence it follows that the elementary unit of energy is propor- 
 tional to the natural frequency of the oscillator, e = hv, h being 
 a universal constant. 
 
 Planck then derives his formula, 
 
 For small values of X this becomes Wien's equation 
 
 fj TTTFl 
 
 and for large values of XT 7 Rayleigh's equation, E x = ^ . 
 
 From the theory a correct energy distribution curve is obtained 
 and the value of the unit charge of electricity can be calculated 
 from the radiation constants. 
 
 The theory of elementarquanta haw been developed as essen- 
 tially related to the problems of radiation and the picture of the 
 resonators has not been correlated with the nature of the atom 
 structures as we know them. The theory is susceptible to a much 
 wider interpretation than that of explaining the variation of 
 radiation with temperature. 
 
 Assume that the atomic structure of energy is ultimately 
 kinetic, conserved and constituted of directed radions. Then 
 Planck's e's are the "molecules" of energy and the law is e = 
 hv = nr where n is a positive integer. Then the partition of 
 energy would take place only during the collisions of portions of 
 matter either in the neutral or electrical states or in the so-called 
 unstable or radiating states of matter due to collisions or to ether 
 transmission. Assuming electroethons we can make partition of 
 radions a collision phenomena. Fields of force become regions 
 where there is not an equilibrium state of the radions and a flow 
 of radions takes place to matter or electrical charges in these 
 regions. The process is so fine grained that we must consider
 
 98 FUNDAMENTAL PHYSICS 
 
 this picture as saying the same thing as is done in speaking of 
 forces and force fields. The advantage of either view is at pres- 
 ent a matter of convenience. 
 
 The wide applicability of many of the laws of classical me- 
 chanics in the electrical and radiation world also seems to indicate 
 that these, laws apply to the whole realm of energy changes of 
 radions just as the electrical laws apparently apply to the whole 
 electron realm. 
 
 According to one form of elementarquanta theory it follows 
 that no atomic vibrator can absorb energy except in units of size 
 hv. A diatomic gas cannot absorb energy from molecular im- 
 pacts unless the energy of these impacts exceed hv. It begins 
 to absorb when the energy exceeds this value and this absorption 
 increases rapidly with rise of temperature. The atomic vibrators 
 of C1 2 and Br 2 begin to do this at low temperatures because the 
 intraatomic bonds are weak and their frequency values are small. 
 The fact that H 2 acts like a monatomic gas below 60 absolute is 
 explained on the same basis. Dulong and Petit's law of the 
 equality of atomic heats and Kopp's law of the additive proper- 
 ties of atomic heats in compounds have been interpreted by 
 Boltzmann as being due to the fact that atoms of solids may have 
 natural periods of vibration and that these atoms are in thermal 
 equilibrium with a gas when their mean vibratory kinetic energy 
 is the same as the mean translatory energy of the gas molecules. 
 The energy content of an atom of a solid would therefore be 
 twice that of a monatomic gas molecule. The fact that elements 
 of low atomic weight such as C, Bo, Si at ordinary temperatures 
 and many other elements at low temperatures behave abnormally 
 is explained by some on the elementarquanta theory. Linde- 
 mann has obtained the relation between v and the melting point 
 T of any substance, its atomic weight m and its atomic volume 
 
 ]T 
 
 2 
 
 mv^ 
 
 The approximate validity of this formula is favorable to the 
 quanta theory. 
 
 The limit of visibility to the eye is about a sixth magnitude 
 star or about 0.003 microlux while a surface becomes invisible 
 when its luminosity is less than 4(10)~ 10 candles per square cen-
 
 THE THEORY OF ELEMENTARQUANTA 99 
 
 timeter. The minimum flux of light perceptible to the eye is about 
 8.5(10)- 14 lumen or 1360(10)- 12 ergs per second. The potassium 
 photo-electric cell approaches an efficiency equal to that of the eye. 
 Planck's energy quantum is 3.8(10)~ 12 erg for the frequency 
 0.58(10)~ 15 of maximum visibility. The number of quanta re- 
 ceived by the eye when receiving the minimum visible light is 
 about 360 per second. Any instrument a thousand times as 
 sensitive as the eye should indicate discontinuities in the light 
 emission. It seems that the selenium cell would be sufficiently 
 sensitive to indicate variations of this kind. 
 
 The explanation of the atomic heats of solids has been ex- 
 plained on the theory of agglomerates. Benedicks derives 
 Planck's law on the assumption that the energy (W) of a mole- 
 cule of crystallized solid is equal to 3RT (the energy if the atoms 
 were free) Wo (the energy of agglomeration when T = 0) -f- 
 F(T) (where the disintegration of the aggregate due to the rise 
 of temperature is taken care of). The factors influencing F(T) 
 are cohesion (a vectorial quantity for crystals) and thermal 
 motion. Assuming a formula obtained by Langevin for the 
 action of a magnetic field on a paramagnetic gas, Planck's law 
 can be derived without recourse to any quanta theory.
 
 23. THE RELATIVITY THEORY 
 
 The general concensus of opinion at present is that the funda- 
 mental facts of electromagnetism, the aberration of light, and 
 many optic phenomena require the assumption that the ether 
 does not partake of the motion of material bodies which pass 
 through it. For example, the experiment of Fizeau, in which 
 the velocities of light were compared when going with, and when 
 going against, a stream of water, was interpreted by Fresnel 
 as indicating that the the ether was in part dragged along with 
 the water. This view was based upon his theory of refraction, 
 which assumed that the ethereal density was increased in material 
 media, and only the excess of ether was carried by the matter. 
 On any resonance theory of dispersion and refraction there is 
 no excess density of the ether in matter, and so Fizeau's experi- 
 ment requires a stationary ether. The theory of the stagnant 
 ether requires, however, a positive result in the experiments of 
 Michelson and Morley, Trouton and Noble, etc. The only 
 satisfactory hypothesis to account for the negative results ob- 
 tained by these observers is to assume that the dimensions of a 
 body parallel to the direction that it is moving in the ether is 
 contracted by an amount \/l /3 2 . This shortening is very 
 small, in the case of the earth moving in its orbit it would be 
 about 6.5 cm. 
 
 The theory of the foreshortening of a body in the direction of 
 its motion through the ether is justified by other reasons than 
 that of explaining the negative results of Michelson and Morley, 
 Trouton and Noble, etc. The electrical forces between charged 
 bodies for instance are modified by the motion of these charges 
 through the ether. Now it is a fundamental theorem in elec- 
 trostatics that a charged system can be in equilibrium only when 
 the electrical forces are balanced by other forces. If the inter- 
 electronic forces are ethereal in origin and subject to the same 
 laws as the electromagnetic forces, then the Michelson and 
 Morley experiments afford evidence for believing that the inter- 
 atomic and intermolecular forces are ethereal in their nature. 
 Lorentz has shown that the electrons must themselves undergo a 
 
 100
 
 THE RELATIVITY THEORY 101 
 
 foreshortening. Rayleigh and Brace have shown that there is 
 no double refraction due to action depending upon the earth's 
 motion. This implies that the periods of vibration of the elec- 
 trons in the line of motion must be equal and in order that this 
 be so, the longitudinal and transverse masses of the electron 
 must be altered by the motion in the same manner as the forces 
 in these directions. Neither the rigid spherical electron of 
 Abraham nor the constant-volume electron of Bucherer satisfy 
 these requirements. The electron of Lorentz satisfies the re- 
 quirements if when at rest it is a sphere of radius a, and when 
 moving with a velocity v it becomes an ellipsoid of revolution 
 with its shorter axis in the direction of motion. If ra is the 
 mass at rest, mi the longitudinal and m^ the transverse mass, 
 then mi = m (l 2 )~** and ra 2 = w (l 2 )~ w as we have 
 seen. 
 
 At present there are two theories which attempt to explain 
 the optical and electrical properties of systems in relative motion. 
 These theories are the Lorentzian theory of a stagnant ether, 
 and the Principle of Relativity. The deductions from the two 
 theories are very similar and agree with many if not all of the 
 experiments that have been performed. The necessity that 
 gave rise to these theories was the accumulation of the unsuc- 
 cessful experiments to detect the earth's motion through space 
 by its effect on terrestrial phenomena. 
 
 In the theory of relativity there are two postulates. The first 
 postulate states that the uniform translatory motion of any 
 system cannot be detected by an observer in the system, 
 making his observations on it alone. In other words, any law 
 or any theory deduced from any set of laws is the same for all 
 systems between which there is no relative acceleration. Ordi- 
 nary experimental laws hold until the relative velocity of any 
 parts in a system reach (10) 8 cm. per second. Such a system 
 may be considered as quiet and for it the Newtonian mechanics 
 will apply approximately. 
 
 The first proposition assumes that the velocity of light is a 
 magnitude that is "physically infinite" so that the addition or 
 subtraction of finite velocities does not change its magnitude. 
 This condition is a sort of definition similar to the absolute zero 
 of temperature and the use of the velocity of light as an infinite 
 quantity may be interpreted physically as being equivalent 
 to stating that it is impossible to give any material particle a
 
 102 FUNDAMENTAL PHYSICS 
 
 velocity equal to that of light just as it is impossible to cool any 
 body to the temperature of absolute zero. 
 
 The main object of the Principle of Relativity is to establish 
 a relation between the laws of a quiet system and those of a 
 system which is moving relatively to it. This Einstein was 
 able to do by introducing certain propositions that do not con- 
 cern the laws of any quiet system. In the theory, space is 
 considered homogenous and three-dimensional. Time is homo- 
 genous and unidimentional. This means that the transforma- 
 tion of space and time coordinates between systems that are in 
 relative motion are linear transformations. It is also assumed 
 that it does not matter upon which system an observer may be 
 situated, the measured relative velocity between two systems 
 will be the same. The word "stationary" is only a relative 
 term and anything that can be said about a moving system with 
 reference to a " stationary" system (by definition) can also be 
 said about the "stationary" system with reference to the moving 
 system. 
 
 The second postulate becomes necessary when it is required to 
 determine when two events occur simultaneously in two different 
 systems, a quiet and a disturbed system. A method of making 
 comparisons of this kind is to send light signals between the two 
 systems. It is then necessary to make assumptions as to the 
 space velocity of light and the second postulate of relativity 
 assumes that the velocity of light is independent of the relative 
 velocity of the source of light and the observer and is always 
 constant in a homogenous medium. / 
 
 The further development of the Principle of Relativity is 
 mainly a mathematical one. The results are somewhat as 
 follows. Suppose LI and L 2 are two quiet systems whose 
 relative velocity is v. An observer is situated in LI and has 
 instruments for measuring x, y, z 2 , t , P, Q, R where P, Q, R . . . 
 are certain physical quantities that may be functions of the 
 coordinates and the time. A similar observer in L 2 measures 
 corresponding quantities, x r , y', z, t' , P', Q', R' . . . . The 
 known laws of each quiet system give relations of the following : 
 
 f(x,y,z,t,P,Q,R, . . .) = 0. f(x',y',z',t r ,P',Q',R f ,) = 0. 
 From the Principle of Relativity it follows that the relations
 
 THE RELATIVITY THEORY 103 
 
 between the coordinates are as follows, /3 being the ratio -, c 
 
 c 
 
 being the velocity of light in space. 
 
 Or - vt) 
 
 VT^J>' v ' *' 
 
 ('-?) 
 
 The laws or equations of electromagnetism are simply rela- 
 tions between the coordinates of certain so-called rigid bodies 
 referred to standard frames of reference, time as defined by clocks 
 and certain electromagnetic processes. One of our first problems 
 is that of defining time. Our judgments of time depend on 
 determining the simultaneity of occurrence of two events. "A 
 friend leaves the house at four in the afternoon," simply means 
 that the leaving of the house by this friend happened at the same 
 time that the hour-hand of the clock pointed to four. The 
 question of simultaneity is not a difficult one when the events 
 happen in the same place. When the events happen at a distance 
 from one another it is no longer an easy matter to say when two 
 events are simultaneous. The relations between the time recorded 
 in two systems is given under the section describing units. 
 
 In order to define when two events are simultaneous (for it 
 has been shown that the coincidence of two events depends upon 
 whether the observer is moving along with the system or not), 
 it being possible for two events to be simultaneous when regarded 
 in one coordinate system and not being simultaneous from a 
 coordinate system moving with respect to the first, Einstein has 
 defined two widely separated clocks A and B, as being together 
 when the time required for light to pass from A to B (T B -T A ) 
 is the same as the time for the light to pass from B to A(T f A -T' B ). 
 Under these conditions the unit of time of a "moving" 
 system appears longer to an observer who considers himself to be 
 "stationary" and the leading clock is behind time. The unit 
 of length in the "moving" system appears shorter. 
 
 Local time according to Lorentz is the time measured by a set 
 of observers who are moving uniformly in a straight line relative 
 to a standard set of observers. The relation of local and standard 
 time is a reciprocal one, the local time of one set of observers 
 being the standard time of the other set of observers, and vice 
 versa. 
 
 Proper time (Eigenzeit of Kowski) is defined for each particle,
 
 104 FUNDAMENTAL PHYSICS 
 
 and may be considered as the age of the particle. When a par- 
 ticle is in motion, its increase of age depends on the increase of the 
 standard time and its velocity. If the particle is moving uni- 
 formly, the increase of age is equal to the increase in local time. 
 The age of a particle will thus depend on the nature of its path 
 and upon its velocity while traversing this path. 
 
 In the case of linear translation we have seen that this can be 
 transformed away so that no trace remains. The transformation 
 that does away with rotation alters the equations of relative 
 motion in a definite manner indicating that its magnitude is a 
 physical constant. 
 
 As regards gravitation let us consider the acceleration a of a 
 gravitation field in the direction of a coordinate Xi such that 
 
 d z xi ' 
 
 -jTf = a. Introduce new variables x z , tz such that a = and 
 
 then -j-rj = and we would describe the appearance by saying 
 
 there was no gravitation at the point. The Einstein view of 
 gravitation is somewhat like this: in a space free of gravitation 
 and other forces a 'material point describes a straight line and in 
 xyzt space its "world line" is also straight defined by gij. Intro- 
 duce gravitation and the definition (gij) of the world line (still 
 straight) becomes more complex and involves functions of 
 (x, y, z, t). No arbitrary constants are involved and gravitation 
 is made a property of space. As the xyzt space is the vehicle 
 of all physical phenomena so these must all be affected by gravi- 
 tation. There are ten gij coefficients and only six equations to 
 determine them. Four conditions can therefore be arbitrarily 
 chosen. Were there ten equations there would be an absolute 
 space and time. 
 
 The relativity theory appeared after a long period during which 
 scientists had agreed to consider length, mass and time as abso- 
 lutely invariant magnitudes. As long as atoms were the eternal 
 rigidly material bodies that chemists believed they were, it was 
 natural to believe that the mechanics of rigid bodies was a suffi- 
 cient explanation for all phenomena. The relativity theory gives 
 us a more proper view of length, mass and time as magnitudes 
 used by the laboratory rather than fundamental magnitudes of 
 nature. In the discussion of the fundamental units (in so far as 
 our experimental knowledge extends) of electrical charge, velocity 
 of light and energy the "relative" theory developed from the use
 
 THE RELATIVITY THEORY 105 
 
 of these units was found to follow naturally. There is therefore 
 nothing mysterious about the theory so far as experiments cover 
 the field. When we try to exterpolate beyond the region of 
 experiment we may obtain curious results. To see the experi- 
 mental application of relativity let us consider a few applications. 
 
 To describe the relativity effects introduced by laboratory 
 conditions let us consider several systems in relative and un- 
 accelerated motion. System 1 consists of submarines in water; 
 system 2 of aeroplanes in the air; system 3 of molecules of air; 
 system 4 of planets in the ether; system 5 of electrons in the 
 metals; system 6 of alpha particles in the ether; system 7 of elec- 
 troethons in the ether; system 8 of bullets in the air; system 9 of 
 elementarquanta in the ether, and system 10 of waves in the ether. 
 
 The laboratory observers in these different systems wish to 
 communicate with each other and to compare their standards 
 and the laws which they have measured. Evidently the condi- 
 tions of the medium must be such that they know the laws of 
 the medium as regards energy or other transmission. The 
 bullet type of communication for example, is found to be an 
 accelerated motion for material media. 
 
 The condition of relativity imposes approximations in that 
 the means of communication between the laboratories, the signals, 
 must first be studied by the laboratories before their units are 
 compared and under conditions that may be local. Consider 
 aeroplanes in air with the experimenter exposed and using 
 sound as the signalling means. He may conclude that the sound 
 transmission depends upon the direction of the sound and of the 
 aeroplane flight. If he encloses his laboratory and experiments 
 with sound transmission in this space without measuring the 
 air pressure he will find the velocity of sound to depend upon the 
 direction the sound is measured (provided the velocity. of the 
 aeroplane and his altitude above the earth) is sufficiently great. 
 
 Let us assume that systems 1, 2 and 3 can only signal by using 
 sound waves that have been found to possess a constant velocity 
 S. This condition we can imagine to be comparatively easy for 
 submarines because they are observing in an almost incompres- 
 sible medium. Systems 4, 5, 6, 7, 8 and 9 employ light waves 
 whose velocity we will also call c. Because the observers are 
 assuming the velocity of the free medium to be constant its 
 velocity could be used as a definition. Interesting questions 
 can be asked whether any system can move with a greater velocity
 
 106 FUNDAMENTAL PHYSICS 
 
 t'han c through a medium without experiencing acceleration. 
 What phenomena takes place when the velocity c is approached? 
 
 When referring to any system S will be used when to any 
 particular system as a submarine in water, *Si and when to 
 different laboratories (A, B, C, . . .) in any system S a , Sb, S c , 
 etc., or to any particular system as the experiments of Michelson 
 and Morley with reference to the relative motion of the earth 
 and the ether, S^ a , S&. 
 
 As regards the equipment of the laboratories it can only be 
 suggested that the science of laboratories has not been advanced 
 sufficiently for to indicate a general set of apparatus and units. 
 Experiments indicate that neutral atoms become ionized when 
 their velocity is increased sufficiently and corresponds to the 
 motion of ions through about 500 volts. It follows that appa- 
 ratus such as clocks are only adapted to conditions where the 
 relative velocities are small. 
 
 Now it is evident that the laboratories of those systems 
 employing sound for signalling purposes will meet very peculiar 
 problems when they compare their experimental data if the 
 relative velocity of the systems approach that of sound. Indeed 
 if the relative velocity of two submarines in the water was greater 
 than that of sound it would be impossible for them to communi- 
 cate with each other. The problem of different laboratories 
 established on different air molecules would present very unique 
 problems too. Here we would find sudden changes in the 
 velocity of the laboratory such as would apparently introduce a 
 "very intricate physics " for molecular laboratories. An electron 
 laboratory introduces us to a new world on account of the intense 
 electric field about the electron. Bullets in air are mentioned 
 because these may possess a velocity greater than sound and 
 suggest that particles may move through the ether with a velocity 
 greater than that of light. 
 
 The kernel of the new science is to be found in the require- 
 ment of a laboratory meaning for all definitions, terms, units 
 and laws. You speak of the longitudinal diameter of the 
 electron with a velocity approaching that of light. The attitude 
 of the new science is to require a definition of the above terms. 
 And the difficulty of doing this is certainly apparent after our 
 brief discussion of the c e r units and the ten systems considered. 
 And unless length, time and mass can be given "laboratory" 
 definitions they are meaningless. Many of the " peculiar"
 
 THE RELATIVITY THEORY 107 
 
 results of the relativity theory are thus meaningless because 
 terms, definitions, units and laws were discussed for conditions 
 where laboratory experiments have never been made. 
 
 These are some of the laboratory fields remaining to be ex- 
 plored. We should feel cheered that the discoveries of the 
 past have been so rich in permitting us a vista of the whole 
 history of phenomena as a single whole; the elements themselves 
 apart from our minds for which the consciousness of space and 
 time may not exist; the laws like Hamilton's principle that con- 
 sists in a relation between the whole system of configurations 
 which their past contains; and for which as far as we can deter- 
 mine the future and the past are interchangeable. True it is 
 that when we reenter the laboratory the stern sphynx of nature 
 holds her secrets hidden but the vision that she has given us of a 
 possibility of comprehending at one glance the world line of all 
 phenomena in a generalized "space" of the fundamental ele- 
 ments of the universe is indeed manna from heaven. It brings 
 us into a deep harmony w T ith the Great Intelligence and we see 
 in the way our efforts has rewarded us the measure of our image 
 of Him and that it is the duty of man and of all his organizations 
 to be blessed by the fullest communion and harmony with the 
 Divine Plan.
 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 
 Los Angeles 
 This book is DUE on the last date stamped below. 
 
 Form L9-116w-8,'62(Dl237s8)444
 
 UC SOUTHERN REGIONAL LIBRARY FACILITY 
 
 AA 000526270 4 
 
 UCLA-Physics Library 
 
 QC21S92n 
 
 L 006 590 814 7