Chapter XXV

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)

0

½

0

0

Positron

101

1

0

0

0

Rotational base

100

0

0

0

0

Electron

10(1)

(1)

0

0

0

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 RtI² . 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 mv².
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 x 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 divide 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 x 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 x 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 x 10^{10} e.s.u.
/ 0.1521 x 10^{15} sec) = 3.161 x 10^{6} e.s.u./sec = 1.054 x 10^{3} amp  (107) 
The electrical energy unit, the watthour, is the equivalent of 3.6 x 10^{10} ergs. The natural unit of energy, 5.0 x 10^{4} ergs, can therefore be expressed as 1.8 x 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 I²R.
I²R = I²Rt/t = (5.0 x 10^{4}
ergs / 0.1521 x 10^{15} sec) = 3.289 x 10^{12} ergs/sec = 3.289 x 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 = I²R/I = 3.289 x 10^{5} watts / 1.054 x 10^{3} amperes = 3.119 x 10^{8} volts  (109) 
Another division by unit current brings us to the natural unit of resistance, R.
R = IR/I = 3.119 x 10^{8} volts / 1.054 x 10^{3} amp = 2.958 x 10^{11} ohms  (110) 
(See Appendix B for description of material omitted from this edition.)