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KRONOS Vol III, No. 3

ON THE CONVECTION OF ELECTRIC CHARGE BY THE ROTATING EARTH
Copyright © 1977 by R. E. Juergens

In Worlds in Collision Velikovsky claims that the Earth's rate of rotation was altered repeatedly during close encounters with Venus and Mars, and that electromagnetism had much more to do with these effects than did gravitational or other mechanical forces. In Cosmos without Gravitation, besides arguing that gravitation itself must be an electromagnetic phenomenon, he urges consideration of the likelihood that the Earth and the other planets, as electrically charged bodies, create their proper magnetic fields by their rotation. Such proposals have brought him little but mockery from scientists too busy to study his work,(1) but they were made in all sincerity, and when examined objectively in the frame of reference appropriate to that work they hold up well under close scrutiny.

It is to be regretted that in the span of a full quarter-century no accredited geophysicist ever came forward to take up Velikovsky's cause. One would think that the sheer weight of space-age discoveries -- most of them pointing to an electric universe in the Velikovskian mode -- might have rallied at least a few professionals. But, strangely enough, this has not happened. And it is left to us who might rather be bystanders to take up the study.

Let us assume, with Velikovsky, that the Earth carries significant electric charge. Let us further assume, as suggested elsewhere, (2) that this charge is actively imposed on our planet by the demands of an electrified cosmic environment. As we shall see, these premises suggest mutually consistent solutions to several problems in geophysics in addition to those pointed out by Velikovsky. As complementary assumptions, therefore, they show promise as the basis for a wide ranging geophysical working hypothesis.

Electric Convection and the Earth's Polar Moment of Inertia

Several years ago, Sagan stated that the most serious objection to Velikovsky's conclusion that the Earth's rotation was slowed on several occasions during the catastrophes of the second and first millennia has to do with correcting the effect: "How does the Earth get started up again, rotating at approximately the same rate of spin? The Earth cannot do it by itself, because of the law of conservation of angular momentum."(3)

At that time, I suggested this: If the deceleration were due to a transitory increase in the electric charge of the Earth, then the resumption of a "normal" rate of spin might well be laid to a subsequent loss, or drain off, of the excess charge. The phenomenon would be entirely in keeping with, and indeed attributable to, constraints imposed by the law of conservation of angular momentum.(4)

One of Velikovsky's earliest and most strident critics, raising this same issue, emphasized the close analogy between the rotating Earth and a massive flywheel. (5) It is interesting, therefore, to note that Booker, in a straightforward work on the fundamentals of electrical science, stresses the fact that electric charge placed on a rotating flywheel increases its polar moment of inertia.(6) The presumption, of course, is that the charge is convected as the flywheel rotates and thus constitutes an electric current. It follows that electric charge added to the Earth and convected by its rotation must increase the planet's polar moment of inertia.

Now, should this happen -- should appreciable, unaccustomed charge be emplaced on the Earth, other conditions aside -- the law of conservation of angular momentum must come into play. The increase in polar moment of inertia must be accompanied by a decrease in angular velocity of rotation, such that the product of the two remains constant; this is what the law says. Increase the Earth's electric charge, and the length of its day must also increase.

If the increase in electric charge is great enough, the resultant decrease in the rate of spin will undoubtedly become apparent to most inhabitants of the planet, assuming that their attention is not completely distracted by coincident events. At any rate, such occurrences seem to be recalled with varying degrees of precision by many ancient records, as pointed out in Worlds in Collision.

The second of our premised assumptions helps to explain the restoration of spin following a hypothetical charging episode. If the Earth's customary burden of charge reflects the requirements of its customary environment, any excess charge acquired during an extraordinary event will presumably be dissipated into the environment rather quickly in the aftermath of that event. The Earth, effectively "grounded" to the interplanetary medium, must almost immediately begin to shed its excess charge, and its spin rate must increase accordingly.

When the process is completed, assuming that the environment itself has not been significantly altered by the passing event, we may expect to find that the length of the day is just about what it was before.

It is instructive to attempt a quantification of this mechanism. When this is done (see Appendix 1), albeit with heavy reliance on simplifying assumptions, we arrive at a rough estimate that a rapid emplacement on the Earth of some 1018 coulombs of excess charge might just as rapidly cut its rate of spin in half. This is to say, if we may imagine Venus, in the middle of the second millennium, transferring this amount of electric charge to the Earth, we may confidently expect one effect to be an approximate doubling of the length of the day.

Our estimate assumes the Earth to be a rigid globe and is thus a conservative one. Were the crust of the planet able to overcome the bonds of viscosity presumed to couple it to the deeper interior -- a phenomenon discussed more than once by Velikovsky -- a lesser charge might have the same effect on surface rotation. In this case the restoration of spin would be a more complicated process: We might expect internal friction to tend to set the crust to spinning again, but at the expense of internal angular momentum; then, as the crust lost its excess charge, it would seek to rotate faster than the interior and be forced to return angular momentum to the interior. The establishment of relatively uniform angular velocity throughout the body of the Earth might take years -- "years of noise."(7)

It must be emphasized that nothing has been assumed about the magnitude of the Earth's "normal" electric charge. The planet is clearly a material body of great mass, such that by far the greater part of its present-day moment of inertia is surely attributable to that mass and its distribution within the Earth. Still, whatever electric charge is normally convected as the Earth rotates must contribute to the total.

Electric Convection and the Earth's Rotational Glitches

In 1960 Danjon reported a sudden deceleration of the Earth's rotation following a solar flare of record intensity.(8) According to his observations, the length of the day increased by 0.85 millisecond and thereafter began to decrease at a rate of 3.7 microseconds per day. Eventually the rate of spin stabilized near its pre-flare value.

This announcement raised quite a few eyebrows. Quite impossible, said the experts. One skeptic pointed out that the phenomenon implied an increase in the Earth's polar moment of inertia of such magnitude as might only be produced, for example, by instantly lifting the entire Himalayan massif to a considerable height. Danjon, anticipating such objections, argued that "it is very likely electromagnetism alone that will furnish the explanation for these variations . . ." But his claim was generally disregarded.

Then in 1972 it happened again, even more impressively. Danjon was gone (deceased 1967), but Plagemann and Gribbin were on the watch. They found that on August 7-8, following a week of frenzied solar activity, the length of the day suddenly increased by more than 10 milliseconds. And again there was a gradual return to normal.(9)

Borrowing a term from pulsar astrophysicists, Plagemann and Gribbin called the sudden deceleration of the Earth a "glitch."

Again, disbelief on the part of the establishment led to excesses. Neglecting the important facts that, following Danjon, Plagemann and Gribbin had predicted the phenomenon, had been on the alert for unusual flare activity, and had been rewarded for their vigilance, O'Hora and Penny of the Royal Greenwich Observatory pooh-poohed the whole idea: "Indeed, if a solar storm of such exceptional magnitude... exerted such little influence on the rate of rotation of the earth, then there are good grounds for believing that changes in the length of the day are induced by some other mechanism."(10)

It does not seem unfair to suggest that challenges to the notion of electromagnetic glitches in the Earth's rate of spin are motivated primarily by the difficulty of imagining a cause-and-effect relationship between solar flares and planetary rotation. If this is so, then perhaps the complementary assumptions we have adopted may help to dispel such difficulties.

The increase in the length of the day reported by Danjon is very nearly 10-8 day. Now, barring the application of an external torque to reduce the Earth's angular momentum -- and this seems ruled out by the apparently "automatic" restoration of normal spin observed by Danjon and by Plagemann and Gribbin -- such an effect must involve a temporary increase in the Earth's polar moment of inertia of approximately the same proportion. Since the "normal" value is about 1038 kg-m2, we may say that Danjon observed an increase in polar moment of inertia amounting to 1030 kg-m2.

Adapting the electrical braking calculation of Appendix I to this phenomenon, we find that the glitch of 1959, if attributable to the electric convection of suddenly emplaced excess charge, could have involved a short-term gain of 1014 coulombs of negative charge by the Earth.

It is interesting to note that a mere 10,000-fold multiplication of the suggested cause of the Danjon effect -- a glitch of such relative inconsequence as to be of questioned reality - might produce the Velikovsky effect -- a glitch whose magnitude makes it apparent to nearly every inhabitant of the Earth.

Qualitatively, a flare-induced gain of charge by the Earth may be understood in terms of probe theory. The Earth, as a material body immersed in the interplanetary plasma, is fully analogous to an experimental probe immersed in a laboratory plasma. And if solar flares are essentially electric discharges, as numerous investigators have suggested,(11) it is only to be expected that they will affect the electrical balance between Probe Earth and its environment.

Loeb points out that localized disturbances (discharges) in a plasma medium send out "waves of potential gradient," as he calls them.(12) These ripples are transitory fluctuations in plasma potential, and they propagate outward from their sources "at speeds approaching that of light." It follows that electrical disturbances on the Sun must send waves of potential gradient throughout the region pervaded by the interplanetary plasma.

Probe theory (see Appendix 11) suggests that the Earth, when electrically at peace with its environment, should have an electric potential somewhat lower than that of the interplanetary plasma. With reference to the figure in Appendix 11, we would say that the Earth should reside most of the time at or near Point C. Here, as the figure indicates, the net electric current across the Earth's sheath (magnetosphere) would be zero.

Let us assume, however, that a moderate solar flare sends out a wave of moderately reduced electric potential. The effect on the Earth might be quite imperceptible. The passing of the wave might merely reduce the negative bias of the planet with respect to the plasma, or it might even reverse the roles, making the Earth slightly positive with respect to the plasma. In any case, so long as the Earth remained between Points C and F on the probe-characteristic curve, there would be only a relatively slight flow of negative charge from the plasma to the planet. Probably the most evident effects would be changes in the sheath - a gradual collapse of the positive-space-charge sheath until Point E is reached, and then a gradual buildup of a negative-space-charge sheath between Points E and F.(13)

But what if unusually intense flare activity were to generate a wave (or series of waves) of decreased potential sufficient to shove the Earth past Point F? There would be a sudden, torrential influx of negative charge from the outside, conceivably a flow great enough to have a perceptible effect on the Earth's rotation. As long as it took for the wave of depressed potential to pass, or until negative charge accumulating on the Earth could again shift the planet leftward of Point F, the outpouring of negative charge from the heavens would be sustained.

This picture, it seems to me, has merit in that it not only suggests a cause-and-effect relationship between intense solar flares and rotational glitches on Earth but also offers an explanation for the apparent fact that lesser glitches are not associated with lesser flares. (We have not considered the effects of waves of increased potential, but it is evident from the probe characteristic that no significant change in the electric charge of the Earth should result.)

The details of this hypothetical charging process necessarily remain obscure. We might suppose that incoming electrons would be largely funneled into polar regions by the geomagnetic field; evidence for this could be drawn from the known relationship between ordinary solar flares and auroral displays(14). But perhaps we should also consider the possibility that a reversal of the atmospheric electric field to be expected when (and if) the Earth moves to the right of Point E on the probe characteristic - would produce a downward flow of ionospheric and magnetospheric electrons from all directions. Whatever might happen, the atmosphere and the geomagnetic field must complicate matters.

Electric Convection, Geomagnetism, and Magnetic Reversals

A century ago the phenomenon of magnetism produced by electric convection had been foreseen by Maxwell but never proved in theory and never observed. In 1878, however, Rowland reported an experimental demonstration of the effect.(15) He showed that an electrically charged, rotating body generates a magnetic field indistinguishable from that which would be generated were the same body fixed in place and a conduction current of electricity made to flow around it.

Inspired by his finding, Rowland asked whether the Earth's magnetism might not be due to electric convection. He set about calculating how much charge the planet would have to carry to explain the general character and strength of the geomagnetic field. But his result dismayed him. He judged that such a great charge -- something like 1013 coulombs -- could not possibly reside on the Earth; the planet would be tom to pieces by the mutual repulsions among the charges.(16)

Since Rowland's time, other investigators have turned to electric convection as the cause of the Earth's magnetism, only to abandon the quest in the face of further objections. (17)

All these problems seem amenable to solution, however, if electric charges may be located not only on the Earth, but inside it as well, and if a mechanism can be conceived that will keep them in place and prevent them from blowing the planet to bits. As it happens, our second assumption fulfills all these requirements.

At least one attempt was made to deduce the Earth's normal charge from the strength of its atmospheric electric field. In this instance, the investigator concluded that the Earth's charge was too small by a factor of 108 to explain geomagnetism in terms of electric convection. (18)

This kind of calculation assumes that interplanetary space is a nonconducting void, such that planetary charge will be manifested in an electric field whose strength varies as the inverse square of the distance from the center of the planet. But, as I suggested several years ago,(19) the atmospheric electric field and its continuation outward through the magnetosphere are in all likelihood features of the Earth's spacecharge sheath -- a region in which a relatively small difference in potential between the Earth and the solar-wind plasma is bridged. If this be so, then there is no reason to suppose that potential gradients (field strengths) anywhere in the sheath are indicative of the Earth's total electric charge.

An example illustrates the potential fallacy in the kind of calculation just mentioned. Taking purely arbitrary figures, let us say that the Earth's surface potential is 1.0000 x 1016 volts, the potential of the distant plasma is 0.9999 x 1016 volts, and the thickness of the sheath is I earth-radius, or 6.4 x 106 meters. In this case, we find that the average potential gradient in the sheath is 0.0001 x 1016 /6.4 x 106 = 1.5 x 105 volts per meter. Now, on the other hand, were this same 1016 -volt Earth isolated in empty space, void of plasma, we could expect to find that the electric potential 1 earth-radius above the surface was one-fourth that of the surface, or 2.5 x- 1015 volts. The average potential gradient across this part of the void would be 7.5 x 1015 /6.4 x 106 = 1.2 x 109 volts per meter.

[Note: The values in the last two sentences have been corrected by Juergens. See:
Corrigenda]

It is apparent that if we take the measurable field strength - in this example, about 105 volts per meter - and seek to deduce the total charge on the Earth with total disregard for the existence of the plasma, we come up with an answer roughly four orders of magnitude too small. Similarly, the calculation suggesting that the Earth's electric charge is 108 times too small to explain geomagnetism carries little conviction, since it was performed at a time when space was believed empty.

If, then, electric convection remains a viable explanation for the Earth's magnetism, what can we say of geomagnetic reversals?

We have already spoken to the question of rotational glitches an sought to explain them in terms of adding negative charge to the Earth. Intuition suggests that the ingredients of such events, or episodes, might have effects tending to cancel one another so far as magnetics is concerned: Added negative charge would tend to increase convection currents due to rotation; but the coincident electrical braking of rotational velocity would tend to reduce those currents. Thus the Danjon effect, of itself, might be expected to have little influence upon the magnetic moment of the planet.

The Velikovsky effect, on the other hand, would seem capable of reversing the geomagnetic field under certain circumstances. Presumably the interplanetary discharge responsible would have to drain negative charge from the Earth, and indeed drain so much negative charge as to leave the planet with a net positive charge. Then, with continuing direct rotation, both the convection current and the magnetic field of the planet would be reversed.

Electrical braking says nothing about the sign of the charge, or the increase in charge, involved in the process. The Earth's normal polarity is apparently negative; increase the negative charge and the spin rate must slow. On the other hand, should the polarity be reversed and the new (positive) charge increase past the numerical value of the normal negative charge, slowing of rotation would again be expected. So we may suppose that an interplanetary bolt leaching away more than twice the Earth's usual negative charge would not only reverse the geomagnetic field, but would also decelerate the planet's spin. And since (as we suppose also) the Earth's normal charge is a tiny fraction of 1018 coulombs, it seems reasonable to suggest that an electric discharge either delivering or withdrawing 1018 coulombs of negative charge would approximately double the length of the day.

But reversing the electric polarity of the Earth should have other effects, too. First, the withdrawal of the normal negative charge should have an accelerating effect on rotation. Then a further withdrawal of negative charge, producing a net positive charge on the planet, should have a decelerating effect. Therefore, on the basis of the electric-convection hypothesis, one would expect the onset of a period of geomagnetic reversal to be marked by a shortening and then a relengthening, of some magnitude, of the Earth's period of rotation.

For the stretch of history covered by Velikovsky's published works there is known evidence for only one geomagnetic reversal - some time in the eighth or early seventh centuries.(20) Interestingly, a shortened day is also recorded in that same time frame - the day when Ahaz was buried.(21)

The Talmudic tradition cited by Velikovsky has it that this particular day -- not the next day, or any that followed thereafter -- was shortened. Suppose, then, that toward mid-afternoon in Judea a bolt from Mars withdrew perhaps twice the normal negative charge of the Earth. As far as rotation is concerned, the first effect would be a speedup in the spin rate; the Sun would hasten to an early setting. Then, after sunset -- and quite conceivably unnoticed in the turmoil attending the "commotion" -- the motion of the celestial sphere would be slowed again to near normal. (In effect, of course, the night would be shortened about as much as the day preceding it.)

By the next morning the Earth's rotation would seem more or less as usual," but the residual positive charge on the planet would be generating a reversed geomagnetic field.

The Talmudic tradition credits another disturbance, in the time of Hezekiah, with correcting the day-shortening that occurred when Ahaz was buried. On the later occasion a day was prolonged, and sunset was delayed. But we need not conclude that a physical regime instituted on the first occasion lasted for many years. Normal electrical conditions and normal geomagnetic polarity were probably restored rather quickly after the first event. The Hezekiah event was in all likelihood a temporary slowdown due to an increase in negative charge.

The date of the Ahaz event, late in the eighth century, fits well with the evidence of reversed magnetism in certain Attic and Etruscan vases. But could the Earth maintain reversed electrical polarity long enough - weeks? months? - for potters to turn out wares in such quantity that some could be expected to show up in archaeological digs?

Were the commotion on the day when Ahaz was buried indeed due to a reversal of the Earth's electrical polarity, we might say that it shifted the Earth well to the right of Point F on the probe characteristic. Would not plasma electrons then rain down in torrents until normal conditions were re-established? And would this process not be completed long before potters anywhere could complete even one clay vessel?

Negative answers to these questions may draw some support from the observed lengths of time it takes the Earth to recover from mere Danjon events - matters of some weeks. Then, too, electrical polarity reversals might shift the Earth so far to the right on the probe characteristic as to "disable" the plasma, so to speak. The probe characteristic is derived from experiments in which free charges from a plasma are both available and "willing" to contribute to the intense charging currents indicated by the steep rise in the curve beyond Point F. The plasma we are dealing with, on the other hand, is the so called solar wind. If, as suggested elsewhere,(22) this plasma is actually the "negative-glow" plasma of an electric discharge that powers the Sun, then its electrons may be too "busy" at other tasks to be instantly distracted by anomalous electric charge on the Earth.

In physical terms, this means that plasma electrons will be totally "unaware" of the Earth's improper electric charge until or unless they are contacted by the electric field in the Earth's sheath. Only those electrons whose proper motions in the plasma bring them to the sheath boundary can be influenced by this field. And even then, only those whose proper motions are suitable to begin with can be collected by the Earth; many electrons, entering the sheath at unsuitable angles and with excessive velocities, will simply orbit partly (23) around the Earth and make exits from the sheath at other points.

In time, of course, the Earth's improper polarity will be corrected. Its "alien" positive charge will cause the sheath to expand "in search of" negative charges, and it will keep on expanding until enough are collected. Still, considering the scale of distances in the Solar System, the tenuity of the interplanetary plasma, and the suggested preoccupation of that plasma with the fulfillment of the Sun's needs, we may reasonably speculate that restoration of normal geomagnetic conditions following a complete reversal might take at least a full terrestrial season. And the available evidence would not seem to ask for more.

Electric Convection and Secular Deceleration of the Earth's Spin

That the Earth's rate of rotation is slowing perceptibly with the passage of time appears to be an established fact.(24) This secular retardation is generally laid to tidal drag by both the Sun and the Moon. But Munk and MacDonald pointed out years ago that such a mechanism presents problems; in particular, it offers no satisfactory explanation for the dissipation of rotational energy.(25) And more recently Rochester has pointed out that "the 'modern' rate of secular deceleration due to tidal friction is probably close to twice the value used by Munk and MacDonald . . . [and] in turn nearly doubles the problem of accounting for the accompanying energy dissipation . . ."(26) Thus the phenomenon is imperfectly accounted for by tidal friction.

Could it be that the Earth's electric charge increases with time?

This is precisely what one would expect if, as suggested, the Sun derives its energy from the outside by way of an electric discharge. We may suppose that the current sustaining such a discharge could flow only so long as the Sun could be induced to accept ever more charge and an ever-increasing electric potential. But as long as the potential of the Sun increased, that of the interplanetary plasma (negative glow) would also increase, and so would those of the individual planets that are immersed in and grounded to the plasma.

In keeping with matters already discussed, a secular increase in the Earth's electric charge must to some extent secularly increase its polar moment of inertia and gradually slow its rotation.

So it seems probable that a full accounting for the phenomenon of secular retardation must apportion effects between at least two causes: Tidal drag; and electrical braking. Careful extraction of tidal drag effects from the total might even give us a measure of how much charge the Earth is induced to accept in a given period of time. This, in turn, might tell us how much of the Earth's polar moment of inertia is attributable to sheer mass and how much to electric charge.

Adding an electrical component to secular retardation raises a problem concerning the Earth's magnetism. If geomagnetism be laid to the rotation of the negatively charged Earth, then increasing the charge might be expected to intensify the magnetic field. On the other hand, rotational retardation resulting from increasing charge could be expected to decrease the strength of the magnetic field. Actually, the geomagnetic field seems to be decaying,(27) so it may be that the latter effect is more pronounced than the former. In any event, the problem bears careful study.

At the beginning of this essay I suggested that geophysicists of every persuasion might profit from the adoption, as a working hypothesis, of the complementary assumptions premised here. But in support of this suggestion our discussion has been confined entirely to issues bound up in the phenomenon of electric convection. Obviously there is much more to be said, that must be said, before the idea can be sustained once and for all.

Velikovsky long ago brought some of these matters to the attention of science; unfortunately, science elected not to attend at that time. Then, as fate would have it, technology, with and without the blessings of scientists, sent man and his devices deep into space, and similar matters forced themselves upon the attention of science. Strangely enough, however, even this failed to prompt a return by professionals to the fundamentals of electrical science. They chose, rather, to concentrate their thoughts and their writings at the leading edges of theoretical notions based on assumptions too old, too dull, and too well-accepted to inspire re-examination.

No one would argue that geophysics is an easy science. Its complications are probably more puzzling than those of any other branch of physics. Yet it could be that many of these complications arise because geophysicists -- alone among all physicists -- inhabit their field of study and cannot see the forest for the trees.

* * *

APPENDIX I

Electrical Deceleration to Double the Length of the Day

Booker (Reference 6) shows that "for acceleration or deceleration of [a charged] flywheel, the wheel would function as though it were uncharged and had a mass M' given by M' = M + LQ2. . ." Here M is the mass of the flywheel rim, L is the inductance of the rim, and Q is the electric charge per unit length of rim. It is assumed that the spokes and axle have negligible moments of inertia and negligible influence on the electromagnetic behavior of the flywheel. SI units are used throughout the analysis.

The inertial effect of the quantity LQ2 -- an apparent increase in mass for the flywheel rim -- is due to electromagnetic induction as the charge rotates with the rim, creating an electric current.

Suppose we adapt this to the problem of terrestrial rotation by assuming that any suddenly emplaced (excess) electric charge becomes distributed over the entire globe in a time that is negligibly short.

To facilitate calculations (and increase the similarity between the Earth and a flywheel, let us deform the planet a bit and think of it as a rather squat cylinder spinning about its cylindrical axis. Figure I indicates this transformation.

[*!* Image]
Figure 1 -- (A) Axial cross-section through the Earth and its core (solid circles), with outlines of equivalent solenoids (cylindrical model) shown dashed. (b) Inclined view of model solenoid only, showing quantities referred to in text.

To approximate the mean intensity of an electric current that varies, on the real Earth, from zero at the poles to a maximum at the equator, we take the length of our cylinder, S, to be rather less than the polar diameter of the Earth, which is actually about 1.27 x 107 meters. Since this adjustment, however, concentrates the charge on too small an area (the "rim" of the cylinder) and thus tends to increase both the charge density and the current produced by the rotation of the cylinder, we make another correction by reducing the radius of the cylinder to something less than the equatorial radius of the Earth, which in reality is 6.4 x 106 meters.

Consider, then, a cylindrical model of the following dimensions: radius, r = 5 x 106 m; length, s = 1 x 107 m. It follows that the cross section area of the cylinder, s = 2.5p x 1013 m2.

From Booker's equation, given above, and from the fact that the moment of inertia, C, of a flywheel rim is the product of the mass of the rim and the square of its radius, it follows that adding charge to a flywheel rim increases C by an amount C' given by

C'=(LQ2)r2      (i),

which can be solved for Q:

Q = (C'L-1 )1/2 r-1       (ii),

Since Q is charge per unit length of flywheel (cylinder) rim, whereas we wish to find the total charge, q, that results in a given increase in moment of inertia, we multiply Q by 2pr and find that

q = 2p(C'L-1)1/2       (iii).

We must next evaluate the inductance, L, of the model, taking into account the (presumably) high magnetic permeability of the real Earth's core. As is apparent from Figure 1, the core occupies an important fraction of both the volume of the Earth and that of the model. We cannot go too far wrong, therefore, in assigning the entire interior of the model a permeability of, say, 103, typical of ferromagnetic materials.

The inductivity of vacuum is 4p x 10-7 henry-m-1 (Booker, p. 408). Multiplying this by the assumed permeability, we arrive at an inductivity, p, of 4p x 10-4 henry-m-1 for the model.

Booker also provides (p.409) an expression for the inductance of a cylindrical solid carrying an electric current on its "rim" (in effect, a solenoid): L=p, S/s. Since we have adopted his notation, we may write directly:

L = 4p x 10-4 x 2.5p x 1013 x 10-7 ~ 104 henrys       (iv).

With this numerical result we reduce Eq. (iii) to a more convenient form:

q ~ 6.3 x 10-2 C'1/2       (v)

which rounds off a bit further to

q ~ C'1/2 /10       (vi).

When C' is in units of kg-m2, q is in coulombs.

Applying this very rough approximation to the Venus-Earth encounter that Velikovsky dates near - 1500, and assuming that on that occasion the Earth's spin rate was rather suddenly reduced to half its usual value by a rapid transfer of charge from Venus to the Earth, what may we say of the total charge involved?

To satisfy the law of conservation of angular momentum, which demands that the product of angular velocity and moment of inertia remain constant, the excess charge in this case must double the moment of inertia. That is, C + C' = 2C; and C' = C. Normally (in our time), C for the Earth is about 1038 kg-m2. We are saying, therefore, that C'=1038 kg-m2 is the increase in moment of inertia effected by the encounter with Venus (given our present assumptions). Inserting this value in Eq. (vi), we find that some 1018 coulombs added to the Earth's normal charge would produce the effect of a 48-hour day.

APPENDIX II

Plasma Probes

Before the turn of the present century investigators were inserting metallic wires, disks, and spheres into the plasma regions of laboratory electric discharges in attempts to learn what was going on electrically in this strange, fourth state of matter. But until Irving Langmuir and his colleagues of 50 or so years ago took up this field of inquiry, no one was able to make valid deductions from probe results.

An innovation of Langmuir's was a probe whose electric potential could be adjusted with respect to one of the discharge electrodes. With this Langmuir probe, as it came to be called, he was able to show that the "floating potential" acquired by an isolated (insulated) probe of the kind used by all earlier researchers was not really the potential of the plasma itself, as everyone had always supposed. Instead, floating potential was always substantially lower than plasma potential.

Langmuir was able to explain this phenomenon on the basis of the different mean "temperatures" of the positive ions and the electrons making up the plasma. The electrons, moving with much higher random velocities than the positive ions, are able to overcome adverse electric fields of some considerable strength and reach the probe even though it has a negative bias. The faster electrons continue to be collected by the probe until its potential is lowered enough to stop the process. At this point, the probe has reached its floating potential.

[*!* Image]
Figure 2 -- Volt-Ampere Characteristic of Plasma Probe.

By varying his probe potentials up and down with respect to plasma potential, Langmuir developed the raw data for a volt-ampere characteristic curve. The general features of this characteristic are the same for any probe and any plasma. Langmuir's theory of probe behavior has been improved on since his time, but the behavior he observed remains the behavior of probes today.

When a probe is sufficiently negative with respect to the plasma (placing it to the left of Point B), the only current it corrects is the random current of positive ions whose proper motions bring them into contact with the electric field in the sheath surrounding the probe. (To a first approximation, the plasma itself is field-free.) Plasma electrons contacting the sheath boundary are repelled back into the plasma. A further decrease in probe potential has little effect on the positive-ion current, except insofar as it increases the thickness of the sheath and thus also its ion-collecting area in contact with the plasma. (Cosmic rays constitute such a positive-ion current.)

Increasing the potential of the probe - shifting it to the right of Point B - permits some electrons - the fastest ones - to reach it. At Point C enough electrons are collected to cancel the current effect of the positive ions, and the net current to the probe is zero.

At Point E the probe is at plasma potential, receiving the full random currents due to both electrons and positive ions; the plasma is in contact with the probe, and the space-charge sheath has disappeared.

Region EF is one in which electrons are accelerated from the plasma to the probe, while positive ions are repelled by the (rebuilding) sheath field. (The Earth, accordingly, experiences a "Forbush Decrease" in cosmic rays.) The probe receives the entire random current of plasma electrons, so that a further increase in the positive potential of the probe might not be expected to result in an increase in current, except -- as before -- that due to sheath expansion.

But when Point F is reached the electric field in the sheath is so strong that electrons acquire energies sufficient to ionize neutral particles. This releases many more electrons, and there is a sudden increase in current to the probe. The steep rise in the curve to the right of Point F therefore presupposes the presence of neutral particles in the medium constituting the sheath.

(This last point raises a question in the context of the present discussion, since the interplanetary plasma is essentially devoid of neutral particles. But in the Earth's sheath (magnetosphere and atmosphere) neutrals are relatively abundant, so it would appear that our hypothesis that the planet has on occasion been to the right of Point F is basically tenable.)

NOTES AND REFERENCES

1. It is, of course, only with tongue in cheek that one may suggest that the rejection of Velikovsky's work and the deliberate mobilization of professional forces in a campaign to vilify him had anything to do with the individual or collective industry of scientists.

2. R. Juergens, Pensee, vol.. 2, No. 3, Fall 1972, p. 6.

3. From the text of a paper presented at the symposium on "Velikovsky's Challenge to Science," held during the 140th annual meeting of the American Association for the Advancement of Science, San Francisco, February 1974. Text as released to the press at the time.

4. R. Juergens, Pensee, Vol.. 4, No. 2, Spring 1974, p. 38.

5. C. Payne-Gaposchkin, The Reporter, March 14, 1950.

6. H. Booker, An Approach to Electrical Science, (New York; McGraw-Hill, 1959), p. 621.

7. Cf. 1. Velikovsky, Worlds in Collision, (New York; Doubleday, 1950), Chapter 4.

8. A. Danjon, Comptes rendus des Seances de l'Academie des Sciences 250 (1960), 1399. A similar effect was reported by Danjon (Comptes rendus247 (1958), 2061) in connection with a 1956 eruption on the Sun.

9. Reports concerning this event are summarized by Gribbin in New Scientist for 10 May 1975, p.339.

10. Quoted in Science News 104, 136 (September 1, 1973).

11. E.g.: C.E.R. Bruce, A New Approach in Astrophysics and Cosmogony (London; Bruce, 1944); J. W. Dungey, Philosophical Magazine 44 (1953), 725; R. G. Giovanelli, Monthly Notices, Royal Astronomical Society 107 (1947), 338; F. Hoyle, Recent Researches in Solar Physics (Cambridge; Cambridge University Press, 1949),. A. B. Severny, Izv. Krym. Astrofiz. Observ. 1 (1958), 102.

12. L. Loeb, Science 148 (11 June 1965), 1417. According to Loeb, a high-potential (positive or negative) source with a rapid rise in the voltage at one discharge terminus is required to produce such waves. The space waves thus initiated can propagate away from the source even after the triggering effects have expired. Thus, if solar flares are indeed electric discharges, the so-called "particle events" associated with them may not consist of particles ejected from the Sun by the flares, but rather of pre-existing solarwind particles accelerated by the advancing space waves.

13. The expansion and contraction of sheaths is discussed, e.g., by 1. Langmuir and H. Mott-Smith, General Electric Review No. 27 (1924).

14. P. McIntosh discusses the geophysical effects of the solar activity of early August, 1972, in Sky & Telescope for October 1972. Auroral activity and a moderate magnetic storm followed the August 7 flare. Radio communications were strongly affected. In one case, taxi drivers found that they were receiving instructions from distant cities. Greater auroral displays followed the lesser eruptions prior to August 7.

15. American Journal of Science, Ser. 3, Vol. 15, p. 30 (1878).

16. Philosophical Magazine, Ser. 5, Vol.. 8, p. 102 (1879).

17. A. McNish in Terrestrial Magnetism and Electricity, J. Fleming, ed. (1939) covers this subject in half a page (323) and gives no source for the following argument: "Furthermore, as viewed by an observer partaking of the Earth's rotary motion the tangential component of the field would be reversed so that the rotation of surface-charge will in no way account for the effects, the observed magnetic field being in the same direction, relative to cosmic space, at the equator and at the poles-" However, according to A. O'Rahilly, statements of this kind are based entirely on speculation; cf. Electromagnetic Theory (New York; Dover, 1965, Vol.. 2, p. 608), a republication of Electromagnetics (193 8).

18. This case is also cited by McNish (Ref. 17) without attribution.

19. R. Juergens, Pensee , Vol.. 2, No. 3, Fall 1972, p. 6.

20. I. Velikovsky, Earth in Upheaval (New York; Doubleday, 1955), "Magnetic Poles Reversed."

21. Cf., Worlds in Collision, "Isaiah," and "Ignis e Coelo."

22. R. Juergens, op. cit.

23. Cf., I. Langmuir and H. Mott-Smith, op. cit. (Note 13).

24. A recent estimate of the present rate of deceleration is that the day is lengthening by 2 milliseconds per century (Scientific American, October 1974, p. 56).

25. W. Munk and G. MacDondald, The Rotation of the Earth (London; Cambridge University Press, 1960).

26. M. Rochester, "The Earth's Rotation," EOS, Trans. A.G.U. 54, 769 (1973).

27. McNish (Ref. 17) also discusses this, pp. 325-327.

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