Distributed Scalar Motion
Consideration of probabilities for deviation from the bias position of unit value in any direction shows that in a generalized three dimensional system, effective deviation cannot exceed unit value. A unit of displacement does one of two things: it offsets the natural progression in both directions in one dimension as previously discussed or in any one direction of one dimension of a more complex Notational Reference Point phenomena. Since the natural progression cannot be observed because it has no effect by itself, offsetting one direction of one dimension of primary motion had absolutely no effect. Therefore, the first effective unit of displacement offset the natural progression completely in one dimension by having a one Dimensional two directional linearly represented displacement in that dimension. That, then, is the mode by which representation is accomplished for the first unit of displacement at each and every representable reference point.
As a direct result of the ambiguity of direction between primary and displacement motion, two identical units of 1D1d_{L} displacement in the same dimension is equivalent to primary motion in the opposite direction. Thereby, the equivalent of two units of 1D1d_{L} displacement in each of the three dimensions of an individual reference point coordinate system is the absolute limit for effective displacement at each reference point. Therefore, additional units of displacement beyond the first unit must be only partially effective toward continued effectiveness for displacement in all other directions due to distribution effects. The use of photon type displacements is the first in a series of steps in obtaining the distribution of displacement representation. The series achieves a set of minimum values of effective deviation from the scalar background of unity in all representable directions. The complex motion structures having net deviation values of motion between offset and effective one unit inward in space at individual reference points constitute atoms or subatoms of matter.
Primary motion is representable in a generalized three dimensional reference system only as one directional outward from a reference point. So long as simple outward progression is the only aspect of scalar motion under consideration, the representation in three dimensional space as a linear progression in any direction is the most probable representation. By representing the displacement motion as one Dimensional two directional in one of three dimensions, the progression of primary motion must be represented in a different geometric dimension from that of the displacement motion. The addition of a second unit of displacement must be represented either as being of the same mode in a dimension perpendicular to both the dimension of the first displacement and the primary motion, or as rotational around one dimension or both dimensions perpendicular to the two directional linearly represented displacement motion.
If the second unit of displacement is linearly represented, it must be represented perpendicular to the first displacement and its magnitude must be harmonically related to the first and be in the same displacement direction, either positively or negatively. Probability considerations indicate that this kind of double photon structural unit has high probability for having associated with it two additional units of displacement having rotational representation in the opposite displacement direction. If it does not spontaneously separate, any subsequent interaction causes separation; therefore, one can say that such structures have a transient existence at best.
Since motion is continuous, a continuity for change must be represented in each individual three dimensional system. In a dimensional system representation of change can be accomplished by either a change of magnitude or a change of direction. A simple continuous change of geometric direction by the mathematical expedient of rotational representation satisfies the requirement of continuity just as well as does a continuous change of magnitude from a given reference point. Continuous change of direction provides continuity of magnitude for any displacement in all directions relative to a specific reference point, but could not have anything other than a scalar effect relative to any other reference point. Thereby, the second step of distribution for a net deviation would most probably be rotationally represented deviation around one or more of the dimensions of the individual three dimensional reference system.
The Laws of Probability demand distribution of all units of displacement motion among the various possible representations in such a manner that for a given total number of units of displacement, minimum effective displacement from unity is represented as a result. A displacement represented as rotational around dimensions of space, or of time, perpendicular to the first displacement is not fully effective in a single linear direction of either aspect. The second displacement unit rotationally represented in the other dimensional aspect from that of the first displacement provides maximum distribution of displacement effect of the net displacement while continuing to represent primary motion in one direction of one of the dimensions of both aspects. Minimum effective magnitude of displacement from unity for all subsequent combinations of motions at each reference point is insured by requiring alternation of scalar direction of displacement for all required changes of mode of representation and occasionally for other reasons.
The various possible combinations of linear and rotational displacement around one set of coordinate axes gets quite complex, but taking them one step at a time simplifies the many possibilities. See Chart 6 page 113 in the Appendix for a quick overview of the sequence for the representation of the modes initially diagrammed on page 28 and discussed in this and subsequent chapters.
Positive rotational progression without an associated negative rotational unit is not observed because chance selection of the directional mode for representing primary motion is strongly biased for one directional linear. A rotational representation requires absolute specification of a particular orientation of a particular reference system having a specific number of available dimensions; too many limitations to make it possible to establish any kind of representation of general curvature for primary motion in either three dimensional aspect. Since primary motion must be represented in both of the three dimensional aspects, rotational directionality of primary motion cannot exist and, therefore, cannot be observed in a generalized three dimensional system devised for multiple reference points. The most direct result of this is that generalized space is geometrically straight. It cannot be curved in any manner and, therefore, effects ascribed to that kind of condition by the previously accepted theoretical systems of the late 20^{th} century are explained in a different manner.
Simplification of description for obtaining a three dimensional distribution of units of displacement motion is accomplished by referring to the presence of rotationally represented displacement motion even though a rotational representation relative to an individual reference point seems like only a direction. Rotational directionality must exist in connection with the representation of displacement motion in an individual reference point system and although actual rotation of the reference point coordinate system is not only not required, its result would be unnecessarily ambiguous. Rotational representation is required as a possibility in an individual reference point system. With ambiguity only for the direction of axial representation, rotational stability in a generalized system of coordinates has high probability for existence; i.e., the limited ambiguity causes the representation possibility in the generalized system for stable unidirectional rotation; i.e., gyroscopic stability.
Probability distributions indicate that 2D1d_{R} displacement achieves greater distribution effect than one 1D1d_{R} representation. Thereby, selection of 2D1d_{R} representation is favored as the means of representation for the second unit of displacement. One unit of oppositely displaced (from that of the photon) 2D1d_{R} displacement motion in an individual three dimensional reference system offsets the effective magnitude of the photon displacement, and more than offsets directionality of effect. This is the first compound motion describable as rotationally distributed motion to have a fully representable effect in either three dimensional aspect. This structure has the effect representable as remaining stationary in one of the three dimensional aspects. It is called a rotational base. Rotational bases do not have effective displacement magnitudinally; all they have is direction in either space or time. All displacements added to a rotational base must have effective displacement in at least one dimension of an individual Notational Reference Point coordinate system in order to have measurable effects in a generalized three dimensional coordinate system.
Thus, a photon having a unit of negative speed displacement compounded by the addition of a unit of 2D1d_{R} positive displacement has no net displacement value, but does have representable directional effect in space. This structural arrangement can have other displacements added to it since it has now been stabilized in three dimensional space. This structure is referred to as the single photon material rotational base, or as the material subatomic base.
Because primary motion must always be present, it must be represented relative to each and every individual reference point regardless of the complexity of the compound motion being represented at that point. Even though representation of primary motion at atomic reference points is not a direct representation its effect must be present, and even that may eventually become offset by additional displacements to be discussed later. Primary motion provides an outward progression from all apparently stationary reference points in generalized dimensional space. This representation of primary motion is responsible for the general outward progression of the generalized dimensional aspect; the separation of atoms one from another, the spatial progression observed for distant galaxies, as well as the normal progression of time.
SubAtomic Particles of the Material Sector
There are several theoretically possible ways to sequentially add units of speed displacement as rotational representations; one most probable, others possible in specific situations, some completely unstable and therefore, impossible. Adding a unit of 2D1d_{R} negative displacement to the rotational base is not possible as a stable representation because such displacement would exactly cancel the positive rotational displacement that formed the rotational base. Adding units of 1D1d_{R} positive displacement or negative displacement are both possible because both results have a spatially inward effect. Net positive displacement magnitude and direction is necessary to maintain stability of compound motions in generalized space.
The displacement rotations may be perpendicular to or around the photon itself as an axis. The one around the photon having positive displacement is called the positron; the one having a similarly oriented but negative displacement is called the electron. Since formation of the rotational base has already distributed the effects of the compound motion in all directions in space, the dimension of oscillation of the photon merely defines the dimensional position of one of the axes relative to the other two in the individual Notational Reference Point system.
The addition of a unit of 1D1d_{R} positive displacement to the rotational base and limited to one of the perpendicular dimensions has equal probability of being relative to either of those dimensions. It is the equal probabilities of positional representation that causes the indicated notations of ½ unit in each of the possible notational positions (as in the massless neutron). Less than whole units of motion cannot actually be present in any representation because motion is unitary.
After the addition of a unit of positive displacement perpendicular to the photon, a unit of 1D1d_{R} negative displacement around the photon axis will reduce the net effective displacement of the compound motion to zero. The combination is not destroyed as may initially be thought because the displacements whose magnitudes are offset are in separate geometric dimensions. The resulting structure progresses with the natural reference system at the speed of light in three dimensional space. Notice that no net effective displacement is present in one of the dimensions perpendicular to the photon displacement, thereby permitting the required, where possible, linear representation of primary motion to be effective. The neutrino remains in that unit of primary motion indefinitely; i.e., until interaction with some other compound motion structure.
Several other compound motion structures are possible. Each specific structure has the effect of its displacements distributed in all directions in three dimensional space. Each new representation of compound displacement motion causes the appearance of some new property or characteristic not observed with each of the other combinations.
In order to decrease the verbiage required to describe the units of speed displacement which are added together to make up the represented compound motions, a shorthand symbology has been developed. For particles constructed on the single photon rotational base, the notation consists of a sign or symbol representing the presence of charge, a letter to designate the kind of rotational base and three numerals to indicate the effective rotationally represented displacements around each axis.
A negative sign () indicates a negative electric charge, as it is presently described for the observed isolated electron. A positive sign (+) indicates a positive electric charge as presently described. An asterisk (*) placed first in the notation indicates that which is called a magnetic charge. The letter M in the notation designates the material sector rotational base which consists of a photon having negative 1D2d_{L} displacement in combination with positive 2D1d_{R} displacement for the particular subatomic Notational Reference Point. The first digit is for one of the perpendicular axes; the second digit, the other perpendicular axis; the third digit, the third axis, which is the reciprocal of the geometric direction of the dimension of the 1D2d_{L} displacement motion.
The letter C designates a photon having 1D2d_{L} positive displacement with 2D1d_{R} negative displacement distributed in the dimensions of the time aspect of the NRP dimensional system. The C indicates that that rotational base is the base for particles of the cosmic sector of the physical universe.
Particles constructed on the M 000 rotational base fall into three categories:

Massless subatomic particles;

Similar particles which have acquired mass; and

Particles which are combinations; i.e., compound particles. These have mass but are not sufficiently complex to exhibit full atomic characteristics in ALL possible interactional situations.
The numerical value in each position of the Notational Reference Point subatomic notation represents that quantity of effective rotationally represented displacement in the appropriate dimension. The numerals may also be thought of as representing effectively excess units of positively oriented time or space due to positive or negative displacements, respectively. Each such positive unit of time or space is not negating the effect of a corresponding unit of that aspect of the normal progression of primary motion in that dimension because it is perpendicularly oriented and rotationally directed. Parentheses around the numerals indicate units of negative displacement while lack of parentheses indicates units of positive displacement.
Table 1: The SubAtomic Particles
The SubAtomic Particles^{9} 

M 000 
Rotational Base 

M 001 
Positron 

M 00(1) 
Electron 

M ½½0 
Massless neutron (muon neutrino) 

M ½½(1) 
Electron neutrino 

*M ½½0 
Charged electron neutrino 

Particles with Acquired Mass 

M 00(1) 
Charged electron 

+M 001 
Charged positron 

M 11(1) 
Proton 

+M 11(1) 
Charged proton 

Compound Particles 

M 11(1) 
M ½½0 
Compound neutron 
M 11(1) 
M 1½1½(2) 
Mass 1 Hydrogen 
Table 2: Identification of Axes with SubAtomic Notations
The photon dimension is represented as the Z axis, the 3^{rd} digit of Subatomic reference point notations.
By changing M to C (or vice versa) and placing parentheses (or removing them), the exact reciprocal chart for the particles of the cosmic sector is obtained.
As an exercise of and for more complete understanding, the student should construct a model for the single photon rotational base and observe the effect on the model of the various displacement representations for all subatomic particle notations.
For the model use the full uncut circle of matteboard supplied with this book. Draw two perpendicular diameters on each face of the circle in such a manner that the opposite faces match each other; the ends of the diameter lines meet at the edge. Insert straight pins or map pins in the edge of the circle at opposite ends of one diameter.
For the different representations given in the chart, one of the diameter lines represents the photon while the other diameter represents one of the perpendicular axes. A wire or long pin through the hole in the center represents the other axis perpendicular to the photon. Rotation of the photon line around this axis alone would generate a disk like representation; this is the disk of your model. Rotation of the disk around the diameterend set of pins produces the sphere like appearance of the rotational base and is representational of the other part of the twodimensional rotation that forms the rotational base of all subatomic species representations.
Since the dimensions of time are analogous to the dimensions of space, a rotation of your model in some dimension of space can be thought of as though it were in time without introducing any error other than that which may occur in your keeping things straight in your own mind.
Even though rotation of your model causes the directions of the perpendicular axes to be continually changing, rotational representation as a mathematical tool does not necessarily cause axial rotation. For some interactional processes such rotation may be appropriate, but for most analytical situations, rotation of the entire system in generalized space is not appropriate. The dimensional motions inside the radius of the individual Notational Reference Point coordinate system cause only scalar effects outside of that radius in that which becomes generalized space; the outside region.
In each case in which there is effective displacement the normal outward progression of motion is continually providing the next natural locations for the displaced motions of the compound motion structures. Since the outward scalar progression is randomly oriented in generalized dimensional space, the compound motion moving inward in opposition to randomly oriented primary motion moves in randomly selected directions. The continual inward movement in randomly oriented directions in dimensional space allows all compound Notational Reference Point structures to have reasonable probability for interaction with other similar structural representations, as well as any which progress with the natural reference system; i.e., light speed particles.
In order to extend the magnitude of the rotational displacements beyond one, a second vibrational unit is required. The second vibrational unit may be directly added to the base photon to become part of the photon rotationally represented as the rotational base for the subsequent structure or, as is more probable, the additional vibrational unit may be added as part of a perpendicularly oriented rotational base. This latter case is illustrated by the required units of vibration and rotation being provided by the material neutrino structural notation, which has the appropriate 1D and 2D displacements associated in the neutrino subatomic unit. This is the situation encountered in combining the neutrino notation with the proton notation to form the mass one hydrogen isotope notation, as noted in the preceding chart of compound particles. The summation of the two simple particles shows that the mass one Hydrogen notation does not have a full unit of 2D1d_{R} positive displacement in both perpendicular dimensions of its Notational Reference Point configuration. If certain other requirements are met during the combining process, the notational description identified as the mass one isotope of hydrogen becomes stable.
Writing in another half unit of displacement to convert the unit of 1D1d_{R} positive displacement in the Hydrogen mass one notation to a unit of 2D1d_{R} would have the notation M 22(2) which has low probability for stability; obviously a problem in notational representation. An alternate method of description is used for the notational representation for all subsequently represented atoms of matter for which probability calculations indicate high probabilities of stable existence.
A Model for Atoms in the Material Sector
The rotational base for all ground state notational descriptions for atoms of matter start with one unit of negative 1D2d_{L} motion in each of two perpendicular dimensions to which two units of 2D1d_{R} motion, one for each photon, have been added to form the rotational base combination; 110. Once this compound structure is obtained, additional units of displacement motion cause the appearance of properties or characteristics which allow identification of physical and chemical properties that are different from each of the previous structural notations.
One of the most significant results of the concept of subatomic particles and atoms composed of compound motions is that it is no longer necessary to invoke mysterious hypothetical forces to explain how the parts of atoms and particles are held together. There are no parts other than the several distinct representations of the motions of which each is composed. Each kind of particle and each kind of atom has special and distinctive characteristics due to the specific combination of representable displacement motions incorporated in each compound motion. Extended discussions of the various phenomena associated with the interactional characteristics of the compound motions and further combinations of dimensionally representable motion are treated as separate topics; e.g., chemistry, mechanics, thermal properties of matter, light phenomena, electric and magnetic phenomena.
In attempting to describe the representations of displacement motions comprising subatoms and atoms of matter, several of the limitations to actually representing those motions in the region of normal experience require the student to exercise thought and imagination in the construction and interpretation of both mathematical and physical models. The probability principles have a preset bias toward the natural progression of unity because of the nature of the basic postulate and the limiting definitions and assumptions about the concept of motion and its mathematically representable behavior. The distributions listed by their NRP symbolic notations give some indication of the relative stability of the ground state configurations. Probability considerations dictate that the distribution of rotational displacement units be limited, usually, to only one stable combination among the various possible ways of distributing a given total number of rotational displacements. Of all of the possible arrangements, the ones with the greatest probability for stability have smaller numbers representing speed displacements rather than larger values and symmetrical distributions rather than asymmetrical distributions.^{10}
Consideration of the limited number of ways in which two photons can be combined with additional displacements indicates that the two 1D2d_{L} displacement motions must not only be perpendicular, but that the added rotationally represented displacements must also be interacting dimensionally, as well as, magnitudinally.
Construction of another model will assist in identifying the interactions and the necessary resulting appearances. Supplied with this book are two other disks, each of which has a radius cut approximately the width of the thickness of the disk. Draw diameters on these disks in a manner similar to that used in making your single photon rotational base, except that this time one of the diameters must be coincident with the radius cut. Label each of the disks. The diameter coincident with the radius cut is to be marked with a C at each end; i.e., near the circumference. On disk “a” the other diameter is labeled with an A at the ends near the circumference. On disk “b” the other diameter is labeled with a B at the ends near the circumference.
Intersection of the disks “a” & “b” shows the common axis for rotation to be CC. Disk “a” is formed by rotation of line AA around line BB and disk “b” is formed by rotation of line BB around line AA. For visualization purposes, two dimensionally represented rotations around AA and BB can be accomplished if, and only if, the second part of each 2D rotation is synchronous with the first part of the other 2D rotation around the other axis, AA or BB.
Each subsequently added unit of 2D1d_{R} displacement adds synchronously, thus increasing the rotationally represented displacement in that dimension by one 2D1d_{R }unit for the entire structure. This combination of rotations constitutes the basis for describing a physical model of the 2D1d_{R} displacement motions necessary for the theoretical structures of atoms of matter.
Rotational representation is a mathematical device used to show a difference in a directional property required for representation of scalar motion in a dimensional system of reference. The physical model is an even more limited representation of the mathematical model, and therefore, cannot be considered as anything other than a tool for understanding. The physical model is absolutely NOT a picture of reality. Rationalization of the visualizable physical model and a nonvisualizable mathematical description for the required motions in a three dimensional coordinate system leave considerable room for confusion. Thinking about the consequences of various actions and discussions with other students of the Reciprocal System of theory will eventually reduce the confusions to a minimum.
For all atomic structures in the Material Sector, the double photon rotationally represented structure is an interacting system based on negatively displaced photons; thus, the NRP configuration does not require specification of a type of base. Adequate notation requires only a set of numbers which represent the absolute magnitudes of rotationally represented displacement from unity in each of the dimensions of the compound motion structures and a way of depicting those numbers to indicate the direction of displacement, positively or negatively. The first and second digits represent the 2D1d_{R }displacements while the third digit refers to the 1D1d_{R} displacements.
It has been found through numerous correlated calculations that in order for the representation to have characteristics which correspond to, and therefore qualify the notations to be representative of, atoms of matter, the double photon rotationally represented system must have at least one effective positively displaced 2D1dR displacement. One positive 2D1d_{R} displacement is required to offset or neutralize the magnitude of displacement effect of both of the first two 1D2d_{L} negative displacement units of the NRP base photons. Thus, the first structural representation, which has no displacement around the third dimension that can qualify as being representative of an atom, has the notation 210 rather than 110.
A unit of 1D1d_{R} displacement around the third or common axis of the two interacting rotationally represented systems applies to both 2D rotating systems. Each 1D1d_{R} displacement for the entire 2D interacting system is two natural displacement units, one for each part of the interacting rotationally represented structure. For the physical model, a 1D1d_{R} displacement is represented as a rotation around the CC axis; the two parts being represented by the two disks. An atom is NOT two intersecting disks, but is a combination of motions which must be represented in dimensionality by appropriate mathematical expedients.
Simplifying the Language of Representation
In the initial development of the consequences of the postulates for a universe of motion, there were no guideposts for the identification of the effects of various combinations in which the possible representational modes for displacement motion could be taken, although mathematical probabilities dictated the order in which complexation could occur. After long periods of development, in excess of fifty years, such identifications have been made. Along with these developments, explanations for most observed phenomena and many unobserved phenomena, as well as completely unobservable phenomena, have been obtained. Since correlations for various properties and characteristics of matter have been made for the representational modes and magnitudes of displacement motion, an approach similar to that usually taken in the descriptions for the results of the previous theories of atomic structure is being taken here. The basic concepts are described and explained giving the notation and the meanings attached to the symbology with the expectation that understanding and comprehension will gradually be gained through familiarity.
All atoms having the same NRP structural notation are referred to as atoms of the same element. Elements which have no 1D1d_{R} displacement, and therefore, no deviation from unity in this dimension do not have the ability to orient with a primary valence for a chemical relation to other elements. Thus, these kinds of atoms are referred to as inert elements or the rare gases. Discussion of the mathematics of electric and magnetic phenomena (Chapter 8), and interatomic “force” relations (Chapter 6), as well as, the concepts of valence and chemical orientation (Chapter 5) as used in the Reciprocal System of theory will provide a clearer understanding of 1D2d_{R} and 2D2d_{R} displacements.
The phenomena of static electric effects and electric charges have been found to be associated with 1D2d_{R} displacements in the atomic and subatomic NRP structural representations. Therefore, in describing the properties of subatoms and atoms of the universe of motion, the one Dimensional axis for rotational representation of the atomic and subatomic NRP configurations is called the electric axis. Displacements described as IDld_{R} represented around the electric axis are referred to as electric displacements.
Similarly, magnetic effects are found to be associated with displacements described as 2D2d_{R} displacement motion. Therefore, the two Dimensional axes are the magnetic axes and 2D1d_{R} displacements around these axes are referred to as magnetic displacements. Use of the terms electric displacement and magnetic displacement do NOT imply actual appearance of electric or magnetic effects. Static electric or static magnetic effects are not present until the appropriate 2d_{R} motion is possible and required as a representational mode by the energetics of the process in question.
Extending Displacements Beyond Two
At the first or unit level of 1D2d_{L} displacements, 1D1d_{R} and 2D1d_{R} dimensional differences have no numerical effect since 1^{3} = 1^{2} = 1. But where the rotational representation must extend to greater displacement values, the numerical effect of a 2D1d_{R} displacement “n” being equivalent to (n × n) or n^{2} 1D1d_{R} displacement units is noticed due to the interactional character of the 2D rotating systems, “n” 2D effects is not just 2n 1D effects, although that relationship must also be considered. Each unit of 1d_{R} displacement around the 2D axes is a unit of natural displacement, but the 1D natural displacement equivalent of “n” 2D displacements is (2n)^{2} = 4n^{2}. Because one unit of 1D1d_{R} displacement of the entire structure is two natural 1D1d_{R} displacement units, the number of electric displacement units equivalent to various magnetic displacements “n” becomes
Equation 5: Electric Displacement Units
$\frac{4n^2}{2} = 2n^2$ (electric displacement units)
In the notation 210 only one of the magnetic displacement units is effective, magnitudinally. However, the total positive magnetic displacement represented makes it possible to add one unit of negative electric displacement and still have net positive displacement for the entire structure; the notation for such a structure is 21(1). It can be seen that two negative electric displacements exactly offset the effective magnetic displacement, thus destroying the 21(2) as a valid structural representation. Atomic notation 21(2) is essentially the same as 110, the atomic rotational base.
The notation 21(1) represents the first in the series of notations for increasingly complex rotationally representable compound motions; atoms of matter. The second member of the series is the 210 notation followed by additions of positive electric displacement for the third, fourth, fifth, etc. members of the series. It is observed that the members of the series each show an increase in displacement equivalent of one net positive electric displacement unit from that of the previous member.
The effective number of equivalent positive electric displacement units is the same as the atomic number of the elements found in this physical universe. The atomic number is absolutely nothing other than a sequence number from the first kind of structure that has atomic characteristics incrementing some special characteristic of its actual structure so as to cause increments of change measurable by several different resulting properties. Any correlation with a theoretical structure is a characteristic of that theory, not an intrinsic definition of an observed characteristic named by men.
It can be shown mathematically that the inward scalar effect of positive rotational displacement, being opposed to the outward direction of primary motion in all directions of three dimensional space, gives the same response in the theoretical universe of motion that mass gives in the observed physical universe. Applying the relationship between natural units of 1D1d_{R} positive displacement and units of mass indicates that the notation 21(1) should exhibit a mass effect of two natural mass units, which is obviously deuterium. The 210 notation has the equivalent of two positive electric displacement units and a mass effect equivalent to four natural units. Subsequent addition of the equivalent of one positive electric displacement unit adds two natural mass units. Resolution of the apparent discrepancy between observed atomic masses on this planet and the theoretical natural mass of each kind of element can be accomplished only after further development of several other aspects of the theory which are somewhat beyond an Introduction.
A Periodic Classification of the Elements
In the first half of each magnetic rotational group, electric displacement is at a minimum for each element if the increase in equivalent positive electric displacement is accomplished by direct addition of positive electric displacement units. In the latter half of each magnetic group the increase in atomic number is normally attained for the ground state configuration by adding the next unit of magnetic displacement and then reducing to the required net equivalent positive electric displacement value by incorporating the appropriate number of negative electric displacement units. Thus the elements halfway between inert gases have, in the absence of atomic environmental influences, equal probabilities of having either Notational Reference Point configuration indicated in the periodic charts.
In the second and third rows of the charts, the required effective magnetic displacements for these groups of elements is 2. The number of elements between inert gases in these rows of the charts is 2n^{2} = 2(2)^{2} = 8. If x is the required number of positive electric displacement units, then 8x is the required number of negative electric displacement units to reduce the net equivalent positive electric displacement total to the required value. Other far reaching implications for the value of 8 are determined in connection with a somewhat different relationship in Chapter Five.
The pattern for calculating the net equivalent positive electric displacement results from the fact that numerical succession for low speed motions proceeds from 1/1 to 1/2 to 1/3, etc. where each sequential value is the next value, not the total of the individual increments up to that point. Thus, to obtain the net equivalent electric displacement, all previous displacements must be retained and counted along with the equivalence of the current level of electric displacements. For the first level which has only one effective magnetic displacement, there are two elements, 2(1)^{2} = 2; for the second and third levels n = 2, 2n^{2} = 2(2)^{2} = 8; for the fourth and fifth levels n = 3, 2n^{2} = 2(3)^{2} = 18; in the sixth and seventh levels n = 4, 2n^{2} = 2(4)^{2} = 32. Thus, the sequence numbers, or atomic numbers, of the inert gases are 2, 10, 18, 36, 54, and 86. Number 118, which should be the next inert gas atomic number, is intrinsically unstable due to zero point equivalence of the required 1D2d_{L}, 2D1d_{R}, and 1D1d_{R} displacements.
The arrangement of the elements in a periodic table reflects relationships of structural representation, as well as the way in which the various elements enter into chemical combination. It has been found that there are four basic types of orientations possible for interaction among the elements; negative electric, positive electric, positive magnetic, and neutral. The type of associational orientation exhibited by the various elements is confined to the elements having certain structural representations in common and are thus found in the periodic chart in specific common regions. It is convenient to divide the periodic chart into four divisions representing the types of orientational possibilities for atomic interactions involved in the formation of chemical compounds. Other very close interactions, such as those in the elemental forms, in solvate crystals and in solutions, also follow the same pattern.
Grouping of the elements according to magnetic displacements and electric displacements represented in common yields a chart which appears on first glance to be identical to the familiar long form chart. Closer examination shows numerous differences, some of which will be discussed in the sections dealing with chemical orientations and reactions.
In previous forms of the periodic chart, correlated with an early form of quantum mechanics to arrive at numbers referred to as Quantum Numbers, the horizontal rows and vertical columns grouped chemically similar elements together, as well as provided a mathematical basis for further analyzing the characteristic behaviors of many elements. Even though the previous forms and mathematical analysis provided a seemingly adequate explanation for many characteristics of atoms, those forms and those analyses are built on the premise of a matter based universe, not a Universe of Motion, and therefore, cannot be adopted as adequate; let alone correct, relative to the development of consequences of the postulates for the Reciprocal System of theory. It is fairly safe to expect that much of the mathematics of quantum and wave mechanics will be found to have use in some phase of the development of this theory.
In this theoretical development there are two distinctly different types of rotational displacements, the magnetic or 2D1d_{R} displacements and electric or 1D1d_{R} displacements. The long rows, whether horizontally or vertically placed on the chart, contain those elements which could theoretically have the same magnetic displacements. The shorter rows composed of notations having the same electric displacement, when placed vertically, and thus called columns, results in the elements in each column having similar chemical properties.
The Periodic Chart
Emphasis is on the magnetic displacement in vertical columns, with equal electric displacements in horizontal rows.
These charts are based on the requirements of this theoretical development and are for the ground state isolated condition, which may be thought of as the initial structure prior to initial condensation of stellar material.
Table 4 displays electric displacements in a manner similar to the previously accepted longform format. Various other pictorial charts of the elements have been proposed. It has been found that no one chart form can adequately display all property relations among the elements of matter. Compare the required relative positions for the elements of all Divisions with their positions on the previously proposed forms of the Periodic Charts.
Table 4: Periodic Table of the Elements