# Magnetism

Corresponding to the electric charge, which is a one-dimensional rotational vibration in opposition to the one-dimensional electric rotation, is a two-dimensional equivalent, the magnetic charge, which is a two-dimensional rotational vibration in opposition to the two-dimensional magnetic rotation.

In undertaking a general examination of the magnetic phenomena originating from such charges, the first requirement is a clarification of the dimensional characteristics of the various magnitudes involved. While a certain amount of confusion has been introduced into currently accepted theoretical concepts by a lack of recognition of the fact that the gravitational equation F = mm’/s2 and its electromagnetic analogues are merely special expressions of the general force equation F = ma and the corresponding dimensional variations, this situation has not been particularly serious in the phenomena heretofore examined. When we turn to magnetic effects, however, still further complications of the same kind are introduced by another hitherto unrecognized fact: the two-dimensional nature of the magnetic motion. It will therefore be advisable to establish the dimensions and units of the various magnetic quantities before discussing the characteristics of the magnetic forces, even though this may to some extent reverse the logical order of presentation.

We may begin with the charge itself, which is a two-dimensional rotational motion (vibratory) and is therefore the two-dimensional equivalent of mass, just as the electric charge is the one-dimensional equivalent. From a space-time standpoint, therefore, magnetic charge is t2/s2. The corresponding magnetic force equation is t2/s2 x 1/t = t/s2, which we may state as

 F = M/t (126)

As in the case of the analogous one-dimensional and three-dimensional forces, the magnetic force between two charges can be expressed by a modification of equation 126 in which t is omitted because it has unit value, and the dimensionless ratios I and s2 are inserted.

 F = MM’/s2 (127)

If unit charge is defined in terms of this equation without the introduction of any coefficient, the unit is related to the electrostatic unit derived from equation 124 by the factor s/t; that is, t2/s2 x s/t = t/s. The physical expression of the natural unit of magnetic charge is not clearly indicated by the information currently available either from experiment or from those theoretical deductions that can be made at this rather early stage of the development of magnetic theory from the Fundamental Postulates of this work, and we will not attempt a direct evaluation of this unit at the present time. It is not used in the derivation of the units applicable to other magnetic quantities.

Magnetic potential, like electric potential, is charge divided by distance and it therefore has the dimensions t2/s3. The potential gradient, potential divided by distance, is the magnetic field intensity,

t2/s3 × 1/s = t2/s4.

Another concept is that of magnetic flux, which is defined as the product of area and field intensity. Multiplying the space-time components of these quantities, t2/s4 × s2, we find that we are back to t2/s2, the expression for magnetic charge. The flux is therefore dimensionally equivalent to the charge and unit flux is customarily used instead of unit charge in establishing the related units. It is expressed in volt-seconds or in maxwells, the latter unit being equivalent to 10-8 volt-sec. The natural unit of magnetic flux is the product of the natural unit of electric potential, 3.1190×108 volts, and the natural unit of time, 0.1521×10-15 sec, and amounts to 0.4743×10-7 volt-sec or 4.743 maxwells. The justification for deriving the basic magnetic units from an electric quantity, the volt, can be seen by expressing this derivation in space-time terms: t/s2 × t = t2/s2.

We may now divide the natural unit of magnetic flux by the natural unit of space, 0.4559×10-5 cm, obtaining the natural unit of magnetic potential, 1.040×106 maxwells/cm or gilberts. Another division by unit space gives us the natural unit of magnetic field intensity,

2.282×1011 gilberts/cm or oersteds.

The natural unit of magnetic flux density or magnetic induction is the natural unit of magnetic flux divided by the natural unit of area, which arrives at exactly the same numerical result, 2.282×1011, but in this case the unit is called the gauss. Here again as in the electrostatic system, we find that the field intensity and the flux density are merely two different aspects of the same thing, and the proportionality constant connecting the two is dimensionless. A considerable amount of simplification and clarification of theoretical relationships could be accomplished in both the electric and magnetic systems by eliminating one set of units in each case.

Another basic magnetic quantity is inductance, L, which is the term applied to the production of an electromotive force in a conductor by variations in an electric current. The mathematical expression is:

 F = -L dI/dt (128)

The inductance in space-time terms is then:

 L = t/s2 × t × t/s = t3/s3 (129)

These are the dimensions of mass, hence inductance is equivalent to inertia. Because of the dimensional confusion in the magnetic system the inductance is commonly regarded as being dimensionally equivalent to length and the centimeter is actually used as a unit. The true nature of the quantity is illustrated by a comparison of the inductive force equation with the general force equation F = ma.

```F = ma = m dv/dt = m d2s/dt2
F =      L dI/dt = L d2Q/dt2```

The equations are identical. As we have previously found, I is a velocity and Q is space. It follows that m and L are equivalent. The qualitative effects likewise lead to the same conclusion. Just as inertia resists any change in velocity, inductance resists any change in the electric current. It has been possible to express the inductance in centimeters without getting into any difficulties only because the values of the other quantities involved are constant when we are dealing with electrons only. This is the same situation as in the illustration previously used, where we set up a hypothetical system that expressed the mass of water in cubic centimeters without introducing any serious numerical inconsistencies as long as it is used only in application to water under normal pressure and temperature conditions.

Recognition of the equivalence of self-induction and inertia also clarifies the energy picture. An equivalent mass L moving with a velocity I must have a kinetic energy ½LI2 and we find experimentally that when a current I flowing in an inductance L is destroyed an amount of energy ½LI2 does make its appearance. The explanation on the basis of existing theory is that this energy is “stored in the electromagnetic field,” but the dimensional clarification shows that it is actually the kinetic energy of the moving electrons.

The vibrational motion which constitutes a magnetic charge can have either a space displacement or a time displacement, but since all magnetic rotation in the material universe is in time and the charges which we recognize as magnetic are oppositely directed, all of the magnetic charges as herein defined have displacement in space. In spite of this uniformity in the inherent rotational direction, however, magnetic charges display directional effects because of the geometry of the two-dimensional motion.

To illustrate this point let us consider the positions of the axes of rotation. The axis of a one-dimensional rotation can be represented as a stationary line. This axis therefore occupies a fixed position irrespective of the location of the reference point and no question concerning motion of the axis arises. If the rotation is three-dimensional the position of axis A is no longer fixed, but the locus of all positions of this axis is a sphere and although the position relative to any specific reference point is continually changing, the time average of the changes is the same for all reference points and the motion of the axis therefore has the same aspect from all directions. Where the rotation is two-dimensional, however, the locus of the positions of axis A is a circle and the relative direction of the motion of this axis depends on the reference point. From one direction the motion is clockwise, whereas from the other direction it is counterclockwise. One of these directions is that of the space-time progression, consequently the other must be the opposite. This motion of the axis modifies the direction of the magnetic motion itself relative to the reference point. In the direction in which the resultant motion opposes that due to the space-time progression the magnetic charge has the normal properties of a positive (space displacement) charge; in the opposite direction it acts as a negative charge. Between the two extremes the magnitude and direction of the charge is determined by the geometry of the charged body. The effect is zero at the midpoint, anywhere in the plane of the circle of rotation.

Since the positive and negative magnetic charges are merely directional effects of the same motion they cannot be separated and there is no magnetic equivalent of the isolated electric charge. If any magnetically charged aggregate is broken up into smaller units, each individual fragment regardless of size still has positive and negative poles, or centers of the respective directional effects. For the same reasons given in the discussion of electric charges, like magnetic poles repel each other whereas there is a force of attraction between unlike poles.

Magnetic charges, like their electrical counterparts, are normally unstable in the local environment and are consequently short-lived. There are, however, some materials which have the ability to retain the charges on a more stable basis and magnetized materials of this kind constitute permanent magnets.

While the magnetic charge is a vibrational motion, the essential feature of magnetic motion in general is not the vibrational character but the two effective dimensions. Any basic motion effective in two dimensions only is magnetic and exerts magnetic forces on other objects with magnetic motion. It is therefore possible to develop a magnetic force by means other than a magnetic charge. We may, for instance, cause motion in two dimensions by giving a translational motion to a one-dimensional rotating unit of time or space. This unit, a positron or electron, whether charged or uncharged, then has an effective velocity component in each of two dimensions but not in the third dimension, and it consequently exerts a magnetic force. The magnitude of the translational motion of an electron is represented by the velocity, v, and that of the rotational motion by the rotational velocity s/t which reduces to s, or Q in the electric system of notation, because of the unit value of t. The two-dimensional motion is then Qv, and we may multiply this expression by the magnetic field intensity, H, to obtain the magnetic force.

 F = HQv (130)

In space-time terms this is

 F = t/s2 = t2/s4 × s × s/t (131)

Equation 130 is normally written F = Hev, on the assumption that it is the electronic charge that participates in the production of the magnetic force. As has been explained, it is actually the rotational velocity of the charged electron that enters into this relation, not the charge, and the uncharged electron produces exactly the same result. We cannot observe the uncharged electron individually but we observe such units collectively as an electric current. Here again the magnitude of the two-dimensional motion is represented by the product of the translational velocity and the rotational velocity. The translational velocity is the current I. As in equation 130 the rotational velocity reduces to the quantity, Q, but in this case the quantity is not a fixed magnitude as it depends on the number of electrons involved and it is therefore proportional to the length, l, of the conductor. The two-dimensional velocity is then Il and we may again multiply by the magnetic field intensity, H, to obtain the force.

 F = HIl = t2/s4 × s/t × s = t/s2 (132)

The relative ease with which magnetic effects can be produced and controlled by means of electric currents has made electromagnetism the most familiar type of magnetic phenomenon in present day engineering practice. The general principles and relationships which are involved are well-established and since the revisions of the basic concepts of electricity and magnetism which have resulted from the development of the consequences of the Fundamental Postulates of this work do not alter those subsidiary relations to any significant degree, it will not be necessary to cover these items in detail in this presentation. In view of the drastic changes that have been made in the assignment of electrical and magnetic dimensions, however, it may be advisable to demonstrate the dimensional consistency of the major relations as they are derived from the principles deduced in the foregoing pages by reducing the other two principal force relationships to space-time terms.

EMF of Current (Rate of change of flux)

 F = V = dø/dt = t2/s2 × 1/t = t/s2 (133)

Magnetic Force of Current (Ampere’s Law)

 F = I ds M/r2 = s/t × s × t2/s2 × 1/s2 = t/s2 (134)

The direction of the electromagnetic force obviously depends on the direction of the current that produces it. The basic rotational motion of the electrons is in the gravitational direction; that is, it opposes the space-time progression and tends to move the rotating units together. When two currents also have the same translatory direction the magnetic forces are coincident and there is a force of attraction between the two. Parallel wires carrying currents in the same direction therefore attract each other. If the currents are moving in opposite directions this relation is reversed and a force of repulsion exists.

An alternate method of imparting another dimension of motion to the electrons is to move the entire mass in which they are present. Observation of the magnetic effect is inconvenient if this motion is translational, but by rotating the mass the required velocities can be attained under conditions permitting accurate observation. The magnetic effect thus produced is gyromagnetism. It is quite probable that the magnetism of the earth is primarily a gyromagnetic effect.

When an intermittent force such as that of an electric or magnetic charge is applied to a unit that is free to move, the latter unit, under favorable conditions will be set into motion of the same nature, giving it an induced charge. This process is similar to the production of mechanical vibrations by sound waves. A water glass, for instance, that starts to vibrate when a low note is played on the piano might be said to have acquired an induced oscillation. The charge likewise exerts an intermittent force and therefore tends to cause vibrational motion.

At this point it should be emphasized that according to the Principle of Inversion the negative charge of the electron and the positive charge of the material atom are equivalent and interchangeable. Any motion of an atom is equivalent to a similar but oppositely directed motion of the space unit in which it is located or to an equal motion of any other space unit. The same force that causes a positive vibration of the atom will therefore cause a negative vibration of the electron. Conversely it is immaterial whether the inducing charge is a positive atomic charge or a negative electronic charge. The result in either case is the induction of charges of both kinds, negative charges in electrons and positive charges in material atoms. Theoretically a negative charge on an atom (a negative ion) should only be able to induce similar negative atomic charges, since there are no free positrons in the local environment, but experimental verification of this point is not available at present.

In a conductor the charged electrons are free to move to accommodate themselves to the existing electric potential. The charged atoms cannot move if the conductor is solid, but they can accomplish essentially the same result by transferring the charge in the same manner in which they received it; that is, by induction. The charges therefore distribute themselves in accordance with the potential, and they can be drawn off through conductors, separated, or otherwise manipulated.

Magnetic charges can likewise be induced in any substance that is free to move in the magnetic dimensions, but the availability of such substances is limited. There is no common sub-material particle comparable to the electron which can take a magnetic charge (as defined herein) and, as we will find in a later section, most elements have an oppositely directed vibrational motion which prevents them from acquiring such a magnetic charge. In a suitable material, however, a charge may be induced by bringing a magnetically charged body (a magnet) into close proximity.

Similar results can also be produced by electromagnetic means. In an electromagnet the electron motion itself does not have the intermittent characteristics needed for inducing charges, but the magnetic effect of any individual electron on any individual atom is dependent on the direction of their relative velocity, and since that direction changes as the electron goes past the atom, the resulting force has an oscillating character.

The magnetic induction process can also be applied in the inverse manner by moving a conductor in the field of a magnetic charge or electromagnet, in which case an emf is induced in the conductor. The motion of the conductor itself has no magnetic effect since the material atoms already have three-dimensional motion, but there are free electrons within the conductor which are given a second dimension of motion in the process, and this produces a magnetic effect in the manner which has been described.

The lowering of the superconductive transition point by application of a magnetic field as mentioned in the discussion of superconductivity is another inverse magnetic effect. Since the flow of current creates a magnetic force, it follows that magnetic forces modify the flow of current and hence alter the relation between the thermal and electric temperature scales.

One of the noteworthy differences between the gravitational force and the forces due to electric or magnetic charges is that the gravitational force cannot be screened off or reduced by the contents of the intervening space, whereas the electric and magnetic forces are subject to very substantial modification by matter intervening between the point of origin of the force and its point of application. While this is outwardly a very striking difference, so outstanding, in fact, that it is often cited as strong evidence to indicate that gravitation must have an entirely different origin than electric or magnetic forces, it is in reality only a result of the three-dimensional character of the gravitational forces. In all cases the presence of matter between the point of origin of one of these forces and any location in space alters the net resultant force acting at that location. The gravitational forces, always attractive, are additive, and the intervening substance merely increases the total by the amount of its own gravitational force. Electric and magnetic forces, on the other hand, are anisotropic and the directional effect of the intervening forces of the same kind may operate to reduce the original force rather than add to it. Induced charges, particularly, are capable of distorting the original force pattern out of all recognition, even to the extent of complete neutralization.

Since each material substance affects the electric and magnetic forces in a manner determined by its rotational characteristics and its ability to respond to induction, it is possible in each case to derive a numerical value which represents the magnitude of the effect produced by the particular substance. This value, a dimensionless ratio, is the dielectric constant, εr, in the electric system and the permeability, µ, in the magnetic system. For free space the value of each of these quantities is unity.

We may now generalize the electrical force expression, equation 123, so that it is applicable to the situation in which the charges e and e’ are separated by a medium of dielectric constant εr.

 F = ee’/εr s2 (135)

Equation 127, the corresponding magnetic expression, may be similarly modified to cover the general situation in which the intervening medium has a permeability µ.

 F = MM’/µ s2 (136)

The study of the numerical values of the dielectric constant and the permeability is one of the more recent phases of this investigation and it is not far enough advanced to enable including the results in this current presentation, except in one particular area. Some of the preliminary findings may, however, be of interest even though they are necessarily tentative. It is indicated that there are two separate effects to be considered. Inasmuch as the three-dimensional gravitational rotation has a component parallel to any one-dimensional or two-dimensional motion, there is an interaction between mass and charge similar to that between charge and charge, but of a much smaller order of magnitude. Each substance has an inherent dielectric constant and permeability due to this interaction. In addition to possessing these inherent characteristics some, but not all, substances are susceptible to induction and add an inductive component, which is normally much larger than the gravitational component.

The gravitational component is independent of the temperature, and where temperature effects are observed they are due to secondary causes such as the change in density. The inductive component, on the other hand, is dependent on the existence of free rotational displacements which can be given charges, or opposing vibratory space displacements. The thermal motion, which is a space displacement, has the effect of reducing the net time displacement available as a base for the charge and hence it reduces the inductive capacity. The general trend of the inductive components of the dielectric constant and the permeability is therefore downward with increasing temperature.

The hydrocarbons are typical of substances with no inductive component in the dielectric constant. In these compounds the observed value of Ê decreases slightly as the temperature rises, but this is merely a density effect as the quantity (Ê - 1)/d remains practically constant through the range of temperatures where the experimental results are the most accurate. Octane, for instance, goes from 1.357 at -50° to 1.362 at +50° C. There is some decrease in the experimental values at still higher temperatures but it is questionable whether this decrease is real.

Some of the substances with inductive components have relatively high dielectric constants even at room temperature. For example, the observed value for ethyl alcohol at 20° C is 25.07. In many other substances the dielectric constant at room temperature is quite low, somewhere in the neighborhood of twice the constant gravitational component, but it rises to much higher values at lower temperatures.

The direction of the dielectric and permeability effects is determined by the direction of the atomic rotation in the free dimensions: those which do not participate in the electric or magnetic vibrational motion. In the electric system the free dimensions are magnetic, and since the magnetic rotation is entirely in time in the material universe the dielectric effect is always positive; that is, the dielectric constant of a material medium is always greater than unity. In the magnetic system the free dimension is electric and the permeability effect may be either positive or negative, depending on the direction of the electric rotation. In the electropositive elements (Divisions I and II) the electric rotation is positive, like the magnetic rotation, and the permeability is therefore greater than unity. The electronegative elements (Divisions III and IV) have negative electric rotation and the permeability effect is in the opposite direction, resulting in permeability values less than unity. As in the case of valence, it is possible for some atoms to reorient themselves in such a way as to reverse the normal force directions, but these reorientations are relatively rare in the magnetic system and the great majority of the elements and their compounds follow the normal pattern as outlined.

In dealing with the magnetic system it will be convenient to use the magnetic susceptibility, which is defined as (µ - 1)/4¶, rather than the permeability itself. The susceptibility of free space is zero and the positive and negative permeability effects are represented by positive and negative values of the susceptibility.

The electronegative elements are not normally subject to magnetic induction since they have no positive electric rotation to give the necessary positive direction to a charge, except in those few instances where reorientation has taken place. The susceptibility of these elements and the compounds of similar characteristics is therefore limited to the gravitational component, and since the latter is negative because of the negative direction of the electric rotation, these substances have relatively small negative susceptibilities which are independent of the temperature. The term diamagnetic is used to designate such properties.

The electropositive elements and the compounds of similar magnetic behavior are generally classified as paramagnetic, if the positive susceptibility is small, or as ferromagnetic, if it is large. The theoretical development in this work leads to somewhat different conclusions but in view of the incomplete status of the magnetic investigation these conclusions should be regarded as tentative for the present. From this new theoretical viewpoint it would appear that there should be a class of paramagnetic substances corresponding to the diamagnetic group with relatively small positive susceptibilities independent of temperature. When we examine the experimental susceptibilities of the electropositive elements this is just what we find. The majority of these elements have susceptibilities of approximately the same magnitude as the diamagnetic values, ranging from near zero to slightly over 1.00. Furthermore, these small positive susceptibilities show little or no temperature variation. The value reported for magnesium at 700° C, for example, is identical with that reported at 20° C. Where any temperature variation does exist it is usually an increase in the susceptibility at the higher temperatures, which is directly opposite to the behavior of inductive paramagnetism and suggests that secondary causes may be responsible.

The remaining electropositive elements have much higher susceptibilities which are strongly temperature-dependent, and while there is a very large difference between the susceptibilities of the ferromagnetic elements and the other elements of this group, it would seem that they all belong in the class of inductive paramagnetics. The existence of an inductive effect depends on the availability of free rotations which can act as a base for the charge. As mentioned earlier, no such free rotation exists in most elements because there is an oppositely directed rotational vibration, to be discussed later, which inhibits the magnetic vibration. This opposing motion, however, is a single entity and consequently it is dimensionally symmetrical; that is, it has the same displacement in both magnetic dimensions and is limited to the first space-time unit in the electric dimension whenever the magnetic rotation is confined to this one unit. Since each element of the atomic rotation is independent, any unsymmetrical portion of the atomic rotation can take a magnetic vibration even though the associated symmetrical rotational units are vibrating in a different manner. An unsymmetrical rotation in one dimension is inadequate for a magnetic motion but if such rotations are available in two dimensions induction of a magnetic charge is possible.

The effect of this requirement of two free dimensions is to limit magnetic induction to those elements which (1) have two vibrational units rotating in the electric dimension, and (2) have unequal primary and secondary magnetic displacement. The normal electric rotation does not enter the second space-time unit below Group 3A and the elements of the lower groups are therefore unable to respond to magnetic induction as long as they are in their normal states. Groups 3B and 4B are also excluded in their entirety because their magnetic displacements are 3-3 and 4-4 respectively and there is no unsymmetrical magnetic rotation. This leaves only those elements of Groups 3A and 4A which have electric rotation in the second space-time unit: the iron-cobalt-nickel group and the rare earths. It is not immediately apparent why the inductive capacity of the 3A elements should be so much greater than that of the 4A group but this question will have to be left for later treatment, along with the question of magnetic induction in chemical compounds.

The diamagnetic susceptibility has been studied in considerable detail and it has been found that this property is merely the reciprocal of the effective magnetic rotational displacement. There are, of course, two possible values of this displacement for most elements but the applicable value is generally indicated by the environment; that is, association with elements of low displacement generally means that the lower value will prevail and vice versa. Carbon, for instance, takes its secondary displacement, one, in association with hydrogen, but changes to the primary displacement, two, in association with elements of the higher groups.

This same quantity, the reciprocal of the magnetic displacement, plays an important part in the refraction of light. In the discussion of the refraction phenomenon in a subsequent section of this work the effective displacement, the total value plus or minus the initial level, will be evaluated for a large number of substances and tabulated as the refraction constant, kr The diamagnetic susceptibility is identical with the refraction constant except for certain differences in the initial levels and since the available refraction data are much more complete and far more accurate than the available magnetic susceptibility measurements, it will be advisable to calculate the susceptibilities from the corresponding refraction constants rather than to attempt direct calculation.

In Table CVI the column headed kr lists the refraction constants as computed in connection with the refractive index calculations. The next two columns show the derivation of the initial level adjustment. Normally the magnetic initial level is the same as the refractive initial level in the interior groups of the molecule but is 1/9 unit higher in the end groups. Under normal conditions, therefore, the sum of the individual differences in initial level, dI, is m’/9, where m’ is the number of rotational mass units in the end groups of the molecule, and the average difference for the molecule as a whole is m’/9m. In the normal paraffins, for example, there are 18 rotational mass units in the two CH3 groups at the ends of the chain. The value of dI for these compounds is therefore 18/9 = 2.0. Branching adds more ends to the molecule and consequently increases dI. The 2-methyl paraffins add one CH3 end group, raising dI to 3.0, the 2, 3-dimethyl compounds add one more, bringing this value up to 4.0, and so on. Some modifications of this general pattern are encountered where there is a very close association between the CH3 groups and the remainder of the molecule. In 2-methyl propane, for instance, the CHCH3 combination acts as an interior group and the value of dI for this compound is the same as that of the corresponding normal paraffin: butane. The C(CH3)2 combination likewise acts as an interior group in 2, 2-dimethyl propane, and as a unit with only one end group in the higher 2, 2-dimethyl paraffins.

## Table CVI Diamagnetic Susceptibility

PARAFFINS
kr dI dI/m Calc. Observed
Propane .834 2.000 .077 .911 .898
Pentane .818 2.000 .048 .866 .874
Hexane .816 2.000 .040 .856 .858 .865 .877 .898
Heptane .814 2.000 .034 .848 .850 .852
Octane .813 2.000 .030 .843 .845 .846 .872
Nonane .812 2.000 .027 .839 .843
Decane .812 2.000 .024 .836 .839 .876
Hexadecane .807 2.000 .015 .822 .828
2-Me propane .827 2.000 .059 .896 .898
2-Me butane .823 3.000 .071 .894 .892
2-Me pentane .816 3.000 .060 .876 .873
2-Me hexane .814 3.000 .052 .866 .860 .862
2-Me heptane .813 3.000 .045 .858 .857
3-Me pentane .816 3.000 .060 .876 .877
3-Me heptane .808 3.000 .045 .853 .858
2, 2-di Me propane .823 2.000 .048 .871 .874
2, 2-di Me butane .816 3.000 .060 .876 .873 .883 .885
2, 2-di Me pentane .814 3.000 .052 .866 .866 .869
2, 3-di Me butane .809 4.000 .080 .889 .883 .885
2, 3-di Me pentane .809 4.000 .069 .878 .873 .875
2, 3-di Me hexane .808 4.000 .061 .869 .865
2, 2, 3-tri Me butane .809 4.000 .069 .878 .878 .894
2, 2, 3-tri Me pentane .808 4.000 .061 .869 .872 .874
2, 2, 4-tri Me pentane .813 3.000 .045 .858 .859
ACIDS
kr dI dI/m Calc. Observed
Acetic acid .511 0.333 .010 .521 .520 .524 .528 .535
Propionic .564 1.000 .025 .589 .578 .587 .589
Butyric .600 1.000 .024 .624 .627 .632 .636
Caproic .644 2.000 .031 .675 .676
Enanthic .659 2.000 .027 .686 .680
ALCOHOLS
kr dI dI/m Calc. Observed
Methyl alcohol .599 1.000 .056 .655 .650 .660 .667 .669 .674
Ethyl .658 2.000 .077 .735 .717 .728 .732 .744
Propyl .686 2.000 .059 .745 .740 .752 .766
Butyl .708 2.000 .048 .756 .743 .754 .758
Amyl .722 2.000 .040 .762 .766
Hexyl .730 2.889 .050 .782 .775 .780 .805
Octyl .744 2.889 .039 .784 .788
Dodecyl .761 2.889 .027 .791 .792
Isopropyl .686 3.000 .088 .774 .759
Isobutyl .708 3.000 .071 .779 .772 .798
Isoamyl .722 3,000 .060 .782 .782 .799
sec-Butyl .708 3.000 .071 .779 .773 .782
sec-Amyl .722 3.889 .078 .800 .794
tert-Butyl .704 3.000 .071 .775 .775
tert-Amyl .722 3.889 .078 .800 .804
MONOBASIC ESTERS
kr dI dI/m Calc. Observed
Methyl formate .511 0.333 .010 .521 .518 .533
Ethyl .564 1.000 .025 .589 .580 .588
Propyl .600 1.000 .021 .621 .625
Butyl .625 1.000 .018 .643 .645
Metiiyl acetate .556 1.000 .025 .581 .570 .572 .574 .586 .590
Ethyl .593 1.000 .021 .614 .607 .613 .621 .627
Propyl .625 1.000 .018 .643 .645 .651
Butyl .644 1.000 .016 .66D .663 .667
Methyl propionate .593 1.000 .021 .614 .614 .624 .628
Ethyl .619 1.000 .018 .637 .644 .651
Propyl .644 1.000 .016 .660 .666
Methyl butyrate .619 1.000 .018 .637 .645 .650
Ethyl .644 1.000 .016 .660 .667 .669
Propyl .659 2.000 .028 .687 .687
Ethyl isobutyrate .644 2.000 .031 .675 .674
Isobutyl formate .625 2.000 .035 .660 .654
Isoamyl .644 2.000 .031 .675 .675
Isopropyl acetate .625 2.000 .035 .660 .656
Isobutyl .644 2.000 .031 .675 .676
Isoamyl .659 2.000 .027 .686 .687 .690
Isoamyl propionate .671 3.000 .038 .709 .705
Isoamyl butyrate .685 3.000 .034 .719 .717
DIBASIC ESTERS
kr dI dI/m Calc. Observed
Methyl oxalate .486 -1.000 -.016 .470 .472
Ethyl .546 1.000 .013 .559 .552 .554
Propyl .585 1.000 .011 .596 .600
Methyl malonate .514 1.000 .014 .528 .520
Ethyl .564 1.000 .012 .576 .573 .578
Mthyl succinate .537 1.000 .013 .550 .555
Ethyl .578 2.000 .021 .599 .600
AMINES
kr dI dI/m Calc. Observed
Butylamine .774 1.000 .024 .798 .806
Amylamine .779 1.000 .020 .799 .795
Heptylamine .786 1.000 .015 .801 .808
Isobutylamine .774 2.000 .047 .821 .843
Diethylamine .774 1.000 .024 .798 .776 .835
Dibutylamine .788 1.000 .014 .802 .802
CYCLANES
kr dI dI/m Calc. Observed
Cyclopentane .784 1.778 .044 .828 .843
Me cyclopentane .785 1.889 .039 .824 .833
1, 2-di Me cyclopentane .786 1.889 .034 .820 .828
Cyclohexane .787 0.889 .022 .809 .785 .804 .810
Me cyclohexane .790 1.000 .018 .808 .792 .804
Et cyclohexane .788 1.000 .016 .804 .812
BENZENES
kr dI dI/m Calc. Observed
Benzene .778 -3.111 -.074 .704 .698 .702 .709 .712 .732
Toluene .782 -3.333 -.067 .715 .712 .714 .717 .729 .734
o-Xylene .786 -3.111 -.054 .732 .733
m-Xylene .786 -3.333 -.057 .729 .720 .743
p-Xylene .786 -3.555 -.061 .725 .722
Ethylbenzene .782 -2.778 -.048 .734 .738
Heptylbenzene .783 -2.111 -.022 .761 .762

The behavior of the substituted chain compounds is similar, but there is a greater range of variability because of the presence of components other than carbon and hydrogen. The alcohols, a typical family of this kind, have a CH3 group at one end of the molecule and a CH2OH group at the other. The value of dI for the longer chains is therefore 26/9 = 2.889. In the lower alcohols, however, the CH2 portion of the CH2OH unit reverts to the status of an interior group and dI drops to 2.0. The methyl alcohol molecule goes a step farther and acts as if it had only one end. A similar pattern can be seen in the lower acids and acid esters. Since we have found that the effective units of these compounds in some of the phenomena previously studied are double formula molecules, it appears probable that the magnetic behavior of methyl alcohol and other compounds with similar characteristics can also be attributed to the size of the effective molecule.

The organic rings act as double chains and the susceptibility pattern of the cyclic compounds is identical with that of the straight chains. The initial levels of the aromatic rings are one step lower; that is, the end groups of the double chain have the same initial levels as in refraction, and the levels of the interior groups are 1/9 unit below the refraction values. Methyl substitutions enter the ring and follow the ring pattern. Longer branches act as attached chains and the initial levels of the highly branched compounds therefore rise toward the levels prevailing in the straight chain structures.