In our original consideration of the rotational characteristics of the elements we noted that the rotational datum, the condition of zero net displacement, has rotational displacements 100, whereas hydrogen, the first of the rotational combinations which is recognized as an element, has displacements 21(1). Obviously there are a number of other possible combinations intermediate between these two, but hydrogen is the lowest combination with an effective displacement in both magnetic dimensions and hence those below hydrogen differ from the rotational combinations which we identify as the chemical elements in this important respect, a difference which affects their properties to such an extent as to exclude them from the classification matter which we apply to the elements and to their mixtures and compounds. These submaterial combinations were passed over in the earlier discussion to enable taking up the more familiar chemical elements first, but we are now ready to identify them and to examine the properties by which they make their presence known.
As in our previous study of the elements, it will be convenient to begin with those combinations which have no electric displacement. Helium, the lowest element of this type, has rotational displacement 210. If we eliminate one unit of magnetic displacement we arrive at a combination with displacement 110. This submaterial relative of the inert gases we will identify as the neutrons.
In this connection it will be noted that there is a significant difference in nomenclature between the elements and the submaterial combinations. We know the elements primarily as aggregates and hence the names which have been applied to them refer specifically to the aggregates. The name helium, for instance, normally applies to a helium aggregate. If we wish to talk about an individual particle we use the term “helium atom.” The submaterial combinations, on the other hand, are known only as individual particles and not as aggregates. The name neutron is therefore applied to the single particle and there is no need to use the term “atom” or its equivalent.
By eliminating one more unit of magnetic displacement we obtain the combination 100, which we have already recognized as the rotational datum, the rotational equivalent of nothing at all, the combination with a net total displacement of zero which forms the starting point for all rotational activity.
As in the various series of material elements we may now add electric displacement to each of these submaterial magnetic combinations. An addition of one unit of electric time displacement to the neutron produces the combination 111. Here we have two units of displacement, one magnetic and one electric. The question of the identity of this particle then arises.
One of the principal means of identifying the submaterial particles is by their masses. In the elements each unit of net electric time displacement above an initial level of two (one unit per magnetic dimension) constitutes one natural unit of rotational mass, or two units on the atomic weight scale. The limitation of the effective magnetic displacement to one dimension in the neutron group results in a decrease to onehalf unit of mass (one unit of atomic weight) per displacement unit and also reduces the initial level to onehalf unit. In this group, therefore, each unit of net electric time displacement above an initial level of one constitutes onehalf natural unit of rotational mass, or one unit of atomic weight.
On this basis the atomic weight of the neutron is one unit and that of the 111 combination is two units. With net displacement two and rotational atomic weight two, this 111 particle is difficult to distinguish from hydrogen and is easily converted to that element by a process which will be discussed later. Because of these properties this particle has not yet been discovered experimentally and is as yet unnamed.
In the other direction, a unit of electric rotational space displacement added to the neutron results in the combination 11(1), which we identify as the neutrino. This particle has a net displacement of zero and therefore has no rotational mass.
Similarly we may add a unit of electric time displacement to the rotational base 100, obtaining the combination 101. Since this is a single unit on a zero base it is essentially nothing but a rotating unit of time. As a particle it is known as the positron or positive electron. In like manner we may add one unit of electric space displacement to the rotational base and obtain the combination 10(1), which is merely a rotating unit of space. This we identify as the electron, the negative analogue of the positron. Neither the positron nor the electron has any effective displacement in the magnetic dimensions and the primary rotational mass of both particles is therefore zero.
The electron and the positron are symmetrical with respect to spacetime and the probability principles consequently indicate that in the universe as a whole they should originate in approximately equal numbers. In the material sector of the universe, however, the positrons are readily absorbed into the structure of the elements, whereas there is only a limited field for the utilization of space displacement (electrons) in these combinations. As a result free positrons are rare and shortlived, while there is a large excess of free electrons present at all times.
The same situation prevails with respect to the neutron group. The neutron itself and the positive member of the group, the unnamed 111 combination, are quickly absorbed or converted to hydrogen, but the 11(1) structure, the neutrino, is subject to the same limitations as the electron. We may therefore deduce that there is also a substantial excess of free neutrinos present at all times. A definite experimental verification of this point is still lacking but we will see later in the discussion that some of the effects of this concentration of neutrinos can be identified.
The following tabulation shows the relationship between the lowest group of elements and the various submaterial particles:
Rotational Displacements 
Net Displacement 
Mass Factor 
Primary Rotational Mass 
Rotational Atomic Weight 


Lithium  211  3  1  3  6 
Helium  210  2  1  2  4 
Hydrogen  21(1)  1  1  1  2 
Unnamed particle  111  2  ½  1  2 
Neutron  110  1  ½  ½  1 
Neutrino  11(1)  ½  
Positron  101  1  
Rotational base  100  
Electron  10(1)  (1) 
The most familiar of the submaterial particles is the electron. Since there is an excess of electrons present in our material universe at all times, because of the inability of the atoms of matter to utilize more than a fraction of those available, the electrons play an important part in many physical phenomena and our next objective will be an examination of the various relationships involved in these phenomena.
Due to their net time displacement the atoms of matter are able to move freely in space. Since motion is a relation between space and time, the relation of space to the time displacement of the atoms constitutes motion. The electron, on the other hand, is essentially a unit of space and its relationship to space in general is the relation of space to space, which is not motion. As long as it remains in its normal state, therefore, the electron cannot move through open space but under the proper conditions it can move through matter, which is a time structure.
Motion of the electron through matter requires two free dimensions (that is, dimensions with displacement in time) since the electron rotation takes place in one dimension and the translatory movement in another. In the electropositive elements all three dimensions are free, as the rotational displacements of these elements are entirely in time. The electronegative elements of Division III also provide the necessary crosssection in time because they confine their rotational displacement in space to one dimension, but the elements of Division IV have space displacement in two dimensions in some of their modifications and this prevents motion of the electrons. These substances which lack the required twodimensional crosssection for electron motion will be identified as insulators or dielectrics, whereas the substances which permit the movement will be identified as conductors. The electron motion itself will be identified as an electric current.
Inasmuch as each electron is essentially a unit of space, the movement of these electrons in conductors constitutes motion of space through matter. The magnitude of the motion is measured by the number of electrons per unit of time; that is, units of space per unit of time. But this is the definition of velocity; hence the electric current is a velocity. From a mathematical standpoint it is immaterial whether a mass is moving through space or space is moving through the mass.
In view of this identification of the electric current with velocity it follows that the passage of current through matter modifies the velocities previously existing; the resultant net velocity in each case being the algebraic sum of the original velocity and the velocity due to the current. As brought out in the preceding pages, the atoms of matter have both translational and rotational velocities and the electric current modifies both; hence it has two separate effects. Consideration of the rotational effect will be deferred until later, and we will now examine the effect on the translational or thermal velocity.
Since the thermal motion in a solid or liquid conductor is vibratory it has no directional limitations and the current increases the velocity in all cases. This means that the passage of current imparts heat to the conductor. Heat energy is the kinetic energy of the moving atoms: the product of the mass and the square of the velocity. The heat energy produced by the current flow is therefore the resultant of two factors: the magnitude of the velocity (current) and the amount of mass involved. This amount of mass, however, is not fixed as it is in the movement of mass through space which constitutes the thermal motion of the atoms. In the latter phenomenon the mass is constant while the space depends on the duration of the movement. In the current flow the space (number of electrons) is fixed whereas the mass depends on a the duration of the movement. If the flow is only momentary each electron may move through only a small fraction of the total amount of mass in the circuit, whereas if it continues for a longer period the entire circuit may be traversed repeatedly. The total mass affected by the flow of current is therefore the product of the mass per unit time by the time of flow. In the movement of mass through space we have the analogous situation of the total space being the product of the space per unit time (velocity) by the time of movement.
It is apparent from the foregoing that the mass per unit time is an important factor in the flow of electric current. If the current is constant the amount of mass traversed per unit time depends on the characteristics of the conductor through which the current is moving. We will identify the value of this quantity at unit current flow as the resistance of the conductor. The product of resistance and time, Rt, gives us the mass and multiplying the mass by the square of the velocity (current) we obtain energy RtI^{2} . Except for the difference in terminology this expression for the thermal energy of an electric current (the heat developed by the current flow) is identical with the expression for the kinetic energy of moving matter, ½ mv^{2}.
With this understanding as to the nature of the quantities involved we may now evaluate the natural units of the electrical system in terms of conventional units as a basis for further mathematical treatment. For this purpose we must again select some measured quantity which we can identify in terms of the natural unit, so that we can derive a conversion ratio from the relation of the numerical values of this quantity as they appear in the two systems. The most convenient value of this kind is that of the natural unit of quantity, Q, the electrical equivalent of space, the currently accepted figure being
4.8022×10^{10} e.s.u.
Here, however, we encounter a numerical discrepancy which is rather small but still greater than we like to see in a basic figure from which all of the other values in the electric and magnetic systems will be derived. Another possible method of evaluating the natural unit of quantity is to multiply the Faraday constant, the nature of which will be examined later, by the mass equivalent of unit atomic weight. Using the previously calculated value of the latter quantity we arrive at 4.8069×10^{10} e.s.u. as the natural unit.
Some such discrepancies are to be expected in view of the uncertainty as to the actual degree of precision in the physical measurements, and in setting up the system of conversion constants to relate the natural and conventional units it is necessary to pass judgment on the relative accuracy of the different determinations and to select the values which appear to be the most firmly established. It would seem that we are quite safe in accepting the values of the natural units of time, space, and mass as calculated in the earlier pages; first, because the measurements from which they have been derived are direct determinations that have been carried out with a high degree of precision, and second, because calculations based on these values of the natural units lead to values for the mass of the hydrogen atom and the molar gas volume which agree exactly with the experimental determinations.
In calculating the mass equivalent of unit atomic weight, however, we arrive at a figure which differs somewhat from the accepted value, and when this in turn is applied to the Faraday constant the same discrepancy is carried forward into the value of Q. The explanation of this conflict apparently lies in the fact that the accepted value of Q is not a direct determination but has been calculated from spectroscopic data. As we will find in the more detailed study of radiation in the subsequent pages, the spectral pattern is affected by a great variety of conditions in the atom and its environment and the spectroscopic value could easily include some unrecognized “fine structure” effect. When we turn to the direct determinations of the electronic charge we find that the result obtained in the most accurate work of this nature, Millikan’s oil drop experiments, was 4.807×10^{10} e.s.u., which agrees exactly with the value calculated from the Faraday constant and the natural units as previously established. We will therefore accept this value as correct. From it we may now compute the natural unit of current, I, which is equal to the natural unit of velocity, or one unit of quantity (space) per unit of time.
I = Q/t = (4.807×10^{10} e.s.u. / 0.1521×10^{15} sec) = 3.161×10^{6} e.s.u./sec = 1.054×10^{3} amp 
(107) 
The electrical energy unit, the watthour, is the equivalent of 3.6×10^{10} ergs. The natural unit of energy, 5.0×10^{4} ergs, can therefore be expressed as 1.8×10^{13} watthours. Dividing this natural unit of energy by the natural unit of time we obtain the natural unit of power, a quantity which is expressed electrically as I^{2}R.
I^{2}R = I^{2}Rt/t = (5.0×10^{4} ergs / 0.1521×10^{15} sec) = 3.289×10^{12} ergs/sec = 3.289×10^{5} watts 
(108) 
The natural unit of power divided by the natural unit of current gives us the natural unit of electromotive force, designated as IR or E.
IR = I^{2}R/I = 3.289×10^{5} watts / 1.054×10^{3} amperes = 3.119×10^{8} volts 
(109) 
Another division by unit current brings us to the natural unit of resistance, R.
R = IR/I = 3.119×10^{8} volts / 1.054×10^{3} amp = 2.958×10^{11} ohms 
(110) 
(See Appendix B for description of material omitted from this edition.)