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Unipolar Induction: An Unsolved Problem of Physics and Scientific Method By Harry H. Ricker III 1.0 Introduction This paper investigates the fundamentally important problem of unipolar induction that after 180 years of investigation and discussion remains unsolved. Two issues will be examined in the course of this investigation. The first one is the question: Has the problem of unipolar induction actually been resolved by the currently accepted theory that purports to explain it? The second question is: Can the problem of unipolar induction be solved within the current practice of the scientific method? The thesis of this paper is that the answer to both questions is: No! That is that the current physical theory is unable to properly answer the unipolar induction problem and that the current approach to the scientific method has failed to provide an acceptable answer, so that the problem will remain unresolved until there is a change in the institutional approach to scientific problems of this type. 1.1 Background The problem of unipolar induction arises from experiments performed by Michel Faraday in 1832 as part of his investigation of electromagnetic induction. These experiments created some difficulties that Faraday sought to answer in a series of experiments that he performed in 1851. These experiments resulted in the surprising conclusion that the magnetic field lines do not rotate or participate in the rotational motion of the magnetic lines of force, which produces an electromotive force or emf. 1 This conclusion was received as counter-intuitive and has been resisted as the correct explanation ever since. There is an extensive literature detailing experiments both for and against the conclusion advanced by Faraday. Opponents argue that the magnetic field lines do rotate with the magnet and present experiments and arguments that support that position.2 Albert Einstein in his 1905 paper, which is the foundation of the special theory of relativity, contributed a different solution to the controversial subject. Einstein declared that the problem was essentially meaningless by asserting that the fundamental question at the heart of the disagreement was resolved by his theory because: “questions as to the “seat” of the electromotive forces now have no point.” The effect of his claim was that the problem under dispute had been entirely resolved by recourse to the principle of relativity and Einstein's deductions from that principle rendered the dispute obsolete, as his relativity theory gave the proper theoretical framework for solution of the problem of unipolar induction.3 Ironically, Einstein's claim to solve the unipolar induction problem through his electrodynamic theory based upon the principle of relativity has been turned against the theory based upon experiments, which clearly can be understood as falsifications of the relativity principle and hence can be seen as falsifications of the Einstein relativity theories. The claim of falsification of the relativity principle advanced by F.J. Muller will be one focus of this paper.4 In recent years, it has become common to find the unipolar induction problem being called Faraday's Paradox, although there is and never was any paradox. The Faraday Paradox is a misnomer as Faraday never talked about unipolar induction as a paradox, in his mind the problem was completely solved by his experimental investigations. The claim of a paradox seems to be fostered by the erroneous thinking created by Einstein's special relativity theory, which when applied to the problem creates paradoxical difficulties. These difficulties are usually dispensed with by asserting that magnetic lines of force do not exist, and thereby remove the apparent paradox that arises form the application of relativistic ideas. To summarize the situation. There are proponents of three viewpoints. One viewpoint is that the field lines do not rotate, one that they do rotate, and another, which is the one adopted by mainstream physicists, is that this dispute is meaningless, that there is no such thing as lines of force, and that the principle of relativity applies. The dissident scientific community sees the problem differently. They interpret experiments as demonstrating that the special theory of relativity is invalid because there is the fundamental case of unipolar induction where there is no emf produced when a magnet and circuit are in relative motion, and there is another case of unipolar induction where there is an emf produced when there is no relative motion. Both cases contradicting the relativity principle. 1.2 Approach To The problem Because the unipolar induction problem has been discussed and provoked controversy for 180 years without successful resolution of the difficulties, it is clear that the usual approach of the scientific method of solution has failed to be effective. Here this problem will be examined as the basis for the method of analysis. That is, it will not be assumed that the usual methods and techniques of science are adequate to the task of solving this problem. This will be turned around and the investigation will focus on exactly why the usual tools of scientific method have failed in this particular case. The thesis presented is that the failure of scientific method in this case is due to the lack of sufficient rigor in the current scientific practice that allows metaphysical and ideological concepts to be accepted without sufficient empirical test and critical examination of logical structure of the arguments. The analysis will consider the thesis that Micheal Faraday had correctly deduced from the experiments the correct principles that were applicable to the unipolar induction problem in 1852. This involved the concept of lines of magnetic force combined with his flux cutting rule to provide the correct empirical basis for the formulation of the mathematical principles of the solution to the problem. Typically studies of scientific method examine cases in which the scientific method produces successful results, here the approach to the problem will be to examine the methods used to reach conclusions and look for failures in method and scientific approach that contribute to the failure to resolve the unipolar induction debate. In the course of this investigation it will be examined why the experimental evidence is not taken to be the decisive factor in the resolution of the debate and why the special relativity theory is upheld despite the facts of experiment that contradict it. 1.3 Objectives The thesis of this paper will be to argue that the experimental evidence that led to Faraday's conclusions in his Twenty-Eighth Series was sufficient to provide the correct basis of the applicable theory of unipolar induction, but that Faraday's enunciation of the correct interpretation was flawed and resulted in gross misinterpretations. The cause of the gross misinterpretations will be attributed to conflicting theoretical ideas regarding the physical laws used to interpret the experimental evidence. Furthermore, it will be argued that the current scientific paradigm based upon the principle of relativity makes it difficult, if not impossible, to reach the kind of conclusions obtained from the evidence of experiments in unipolar induction. Einstein's claim that the controversy was meaningless has also contributed to the confusion and conflict. Hence this debate is now know as Faraday's Paradox, which emphasizes the need to resolve the paradox by banishing Faraday's lines of magnetic force. This failure in identifying the correct theoretical interpretation currently faces the difficulty that the applicable theory is not subject to objective scientific investigation but must conform to ideological prejudices. In particular the ideology of relativity prevents a correct theoretical interpretation. In the final analysis it is proposed that the failure results from the improper use of scientific method and that blocks efforts to effectively resolve the problem of unipolar induction. In other words, because ideological and theoretical prejudices supersede the weight of the empirical evidence, the problem of interpretation persists. The final, and most important objective, will be to show that a return to the basic principles discovered by Faraday can be made consistent with all of the experimental evidence if we dispense with the ideological prejudices derived from the introduction of the electron theory in combination with Einstein's special theory of relativity. 2.0 Historical Discussion Of Experimental Evidence and Theoretical Disputes The relevant literature regarding the historical aspects of the unipolar induction problem is very extensive. The reader is referred to the paper: Unipolar Induction: a Case Study of the Interaction between Science and Technology by Arthur I. Miller for a good historical review and introduction to the topic from a modern viewpoint 5. Unfortunately Miller's historical study ends with World War II, and does not include experiments performed in the modern era by F.J. Muller and A.G. Kelly, which provide a detailed examination of the phenomenon. He also does not discuss the dissident scientific literature where the experimental evidence produced by unipolar induction experiments is adduced to refute Einstein's special theory of relativity. For a 19th century historical introduction that provides detailed knowledge of the early history of the subject, the reader is referred to a series of articles by G. W. De Tunzelmann that appeared in The Electrician in 1888. 6 The last peer reviewed physics discussion on this topic appeared in 1999, under the title: Unipolar Induction: a neglected topic in the teaching of electromagnetism, by H. Montgomery.7 For a brief introduction of the unipolar induction problem and how it is being treated within the larger context of teaching conceptually oriented physics courses, the reader is referred to the paper by I. Galili and Dov Kaplan.8 For a more recent review of the history of the unipolar induction debate, that is within the dissident scientific camp, the reader is referred to the paper Unipolar experiments, by A.G. Kelly. 9 Kelly does a good job of briefly reviewing the different opinions and then proceeds to describe his own experiments. However, Kelly's work, as well as that of F.J. Muller, is outside of mainstream scientific work and no notice of the work of either Muller or Kelly is given in the mainstream publications of Montgomery and P. Hrasko.10 A review of the physics of 2.1 Historical Summary Although Miller presents his paper as A Case Study, he presents the thesis that the unipolar induction dispute can be fully resolved in the modern physics approach of dismissing the concept of lines of force as a explanatory heuristic, and replacing it with Einstein's principle of relativity. He admits that the special theory is, unfortunately, not capable of being applied to a rotating reference system, but that general relativity is required for the solution. He concludes that: “So in 1979 the problem of unipolar induction still awaits a complete solution.”11 In 1999, H. Montgomery presented a paper which proposed a solution to the unipolar induction problem. The solution was merely a modification of Faraday's solution proposed in 1851, that the lines of force do not rotate with the magnet, so that an emf is generated by the stationary lines being cut by the motion of the magnet across them. In Montgomery's solution this is not so obvious, however, he justifies it by saying: “The fact that one can move or rotate a magnet does not always mean one can move or rotate its magnetic field...the field is constant, regardless of whether the magnet producing the field is moving or not.” The same solution as given by Montgomery appears in the paper, The Unipolar Induction, by P. Hrasko with the publication date of March 2008. Hrasko rejects the special relativity solution and adopts the new solution proposed by Montgomery. He says: “The correct explanation of the phenomenon is based on the observation that all the elements of the magnet rotate in the field of all the other elements. The magnet therefore rotates in its own magnetic field...” Hence we discover that the most recent official word on this subject issuing from mainstream physics is merely a repetition of the solution proposed by Faraday in 1851, which was later deemed unacceptable and led to the long standing dispute. So the final official word from the physics community is simply just a return to the starting point after more than 100 years of unresolved controversy. Meanwhile, in a paper published in 2004, A.G. Kelly gives a completely different opinion regarding the unipolar induction phenomenon. Kelly concludes, after reviewing the different opinions and preforming experiments, that: “The lines of force do rotate with the magnet....The Faraday Generator phenomenon is caused by the cutting of the stationary circuit by the lines of force of the magnet, as the magnet rotates. It has previously been supposed that the magnet is cutting its own lines of force.” The salient fact is that no notice of Kelly's experiments or his conclusions has been taken by the mainstream physics community. Hence the official policy is as advocated by Montgomery and we see this is confirmed by the more recent paper by Hrasko, which takes no notice of Kelly's conclusions despite the fact that he has done the most through work in this area than anyone else has. 2.2 Michael Faraday12 Faraday is credited with the discovery of electromagnetic induction, that is the evolution or production of electricity from magnetism. This is accompanied by the conversion of mechanical work into electrical energy, which although not usually discussed, fulfills the conservation of energy so that electrical energy does not appear to be produced out of nothing. The primary experiments regarding electromagnetic induction appear in the First Series of November 1831. the particular experiment known as unipolar induction appears in the Second Series of January 1832. The experiment is pictured in Plate III, and discussed in sections 225 through 229. Unfortunately, a reader will not find the famous theory of lines of force in these two sections. It is not until the Twenty-Eighth Series that Faraday discusses his famous lines of magnetic force, and it is in this series that he discusses the unipolar induction solution. In the Twenty-Eighth Series Faraday bases his experimental method upon the experimentally verified conclusion: “So a moving wire may be accepted as a correct philosophical indication of the presence of a magnetic force. (Section 3083) ... Lines of magnetic force may be recognized, either by their action on a magnetic needle, or on a conducting body moving across them...I propose to develop and apply the method by a moving conductor on the present occasion. (Section 3076).” Hence Faraday's method is clearly to use the moving conductor to probe a field of magnetic force. His conclusions are stated this way. “When lines of force are spoken of as crossing a conducting circuit (3087), it must be considered as effected by the translation of a magnet. No mere rotation of a bar magnet on its axis, produces any induction effect on circuits exterior to it; for then, the conditions above described (3087) are not fulfilled. The system of power about the magnet must not be considered as necessarily revolving with the magnet, any more than the rays of light which emanate from the sun are supposed to revolve with the sun. The magnet may even, in certain cases (3097), be considered as revolving amongst its own forces and producing a full electric effect, sensible at the galvanometer.” (Section 3090) The reader is urged to read the statements in the previous section with regard to the modern understanding of the problem produced by the contemporary physics establishment to see that the statements of Faraday and the modern viewpoint are equivalent. In a final note to the reader, the statement given above by Faraday is consistent with the most recent experiments performed in the modern era. Hence the experimental evidence remains substantially unchanged, it is the interpretation that has been disputed, and after 160 years of disputation and changing viewpoints the evidence and the interpretation presented by Faraday have not been overthrown. However, this does not resolve the essential problem that the explanation proposed by Faraday doesn't make much sense when converted into the currently accepted theoretical framework. In this framework, the theory requires some kind of motion to provide the mechanical energy that produces the electrical energy, and this requirement produces the difficulty, that the concept that the lines of force are not moving with the rotating magnet, makes no sense. This was exactly the problem that produced the controversy, and so the problem remains unresolved. 2.3 The Special Relativity Dispute The reader should note that in the papers by Miller, Montgomery and Hrasko, the solution proposed by Einstein, that the question of the rotation, or not, of the lines of force was meaningless, was discarded in favor of the solution proposed by Faraday, which was the reason for the dispute in the first place. That is to say that the solution, which seeks to answer the problem by recourse to the principle of relativity, has been discarded. Perhaps this is merely an illusion due to the fact that the problem of unipolar induction is an obscure problem for modern physics. One could ask at this point, do the views of Montgomery and Hrasko actually reflect the majority opinion or perhaps the problem is too obscure to command any reaction at all to the current rejection of the relativity principle as a solution to the problem? This seems to be rather strange given the numerous publications in which the relativity solution was claimed to be the solution. The most prominent among them being Einstein's famous relativity paper of 1905. This question can be answered by saying that there have been strong proponents of the special theory of relativity as applicable to the unipolar induction problem, but that the influence of this group seems to be declining. For example, Wolfgang Panofsky and Melba Phillips in their book, Classical Electricity and Magnetism, make the following very strong relativistic interpretation: “Inasmuch as this equivalent moment is a consequence of the relativistic definition of simultaneity, unipolar induction is fundamentally a relativistic effect.”13 The strong position taken by Panofsky and Phillips, has the difficulty that it renders the special theory of relativity subject to refutation based upon experimental evidence that shows the effect contradicts the claims of the special theory of relativity. This is basically Muller's assertion, in that he shows that the experimental data is incompatible with the principle of relativity, because it is absolute motion that produces the emf. Hence if one accepts that unipolar induction is a relativistic phenomenon, then one also has to deal with the problem that it is absolute motion that produces the observed emf, and this contradicts the principle of relativity. 2.4 Wikipedia's Solution Here the solution proposed by Wikipedia will be examined to see what if any insight it offers to the history of the unipolar induction disputes. Wikipedia's article is found under the title “Faraday Paradox”. The term unipolar induction is never mentioned. They do not refer to either of the papers by H. Montgomery or P. Hrasko. They also ignore any discussion of experiments and specifically do not cite Muller's or A.G. Kelly's experiments. This implies a significant bias, which is characteristic of Wikipedia. More significantly there is an obvious bias in attempting to resolve the Faraday Paradox through theory and not by appeal to empiricism.A The paradox is described this way: “The experiment is described by some as a "paradox" as it seems, at first sight, to violate Faraday's law of electromagnetic induction, because the flux through the disc appears to be the same no matter what is rotating. Hence, the EMF is predicted to be zero in all three cases of rotation. The discussion below shows this viewpoint stems from an incorrect choice of surface over which to calculate the flux.” “The paradox appears a bit different from the lines of flux viewpoint: in Faraday's model of electromagnetic induction, a magnetic field consisted of imaginary lines of magnetic flux, similar to the lines that appear when iron filings are sprinkled on paper and held near a magnet. The EMF is proposed to be proportional to the rate of cutting lines of flux. If the lines of flux are imagined to originate in the magnet, then they would be stationary in the frame of the magnet, and rotating the disc relative to the magnet, whether by rotating the magnet or the disc, should produce an EMF, but rotating both of them together should not. “ “In Faraday's model of electromagnetic induction, a circuit received an induced current when it cut lines of magnetic flux. According to this model, the Faraday disc should have worked when either the disc or the magnet was rotated, but not both. Faraday attempted to explain the disagreement with observation by assuming that the magnet's field, complete with its lines of flux, remained stationary as the magnet rotated (a completely accurate picture, but maybe not intuitive in the lines-of-flux model). In other words, the lines of flux have their own frame of reference. As we shall see in the next section, modern physics (since the discovery of the electron) does not need the lines-of-flux picture and dispels the paradox.” “After the discovery of the electron and the forces that affect it, a microscopic resolution of the paradox became possible. In Figure 1, the metal portions of the apparatus are conducting, and confine a current due to electronic motion to within the metal boundaries. All electrons that move in a magnetic field experience a Lorentz force of F = qv × B, where v is the velocity of the electrons and q is the charge on an electron. This force is perpendicular to both the velocity of the electrons, which is in the plane of the disc, and to the magnetic field, which is normal (surface normal) to the disc. An electron at rest in the frame of the disc moves circularly with the disc relative to the B-field, and so experiences a radial Lorentz force. In Figure 1 this force (on a positive charge, not an electron) is outward toward the rim according to the right-hand rule.“ The strange aspect of the Wikipedia article is that it gives three different solutions to the paradox. It A Reference is made to Kelly's work only within the context of justifying a particular argument . There is no use of experiment as an empirical guide to resolve the paradox as one would expect if science were actually an empirical discipline. presents a solution based upon the Faraday flux cutting rule, the Lorentz force rule, and according to the special theory of relativity. Resolutions of the paradox are suggested for each case, but they don't seem to be correct or very convincing. This will be discussed in more detail later in this paper. The main conclusion that is derived form reading Wikipedia's discussion of the Faraday paradox, is that the paradox is poorly stated and unclear, the correct resolution of it is obscure and ambiguous, and, most importantly, there does not seem to be a clear cut consensus regarding a resolution of the problem. 3.0 The Problem Of Scientific Method In the historical section, we see that, after many years of dispute over the correct interpretation of unipolar induction, the result is that mainstream, or official establishment science, has revived the viewpoint of M. Faraday, the rejection of which was the reason for the dispute. B However, we also find that this conclusion is rejected in the paper of A.J. Kelly. This situation presents no problem for official science, for we find that they have effectively ignored the opinions of dissident scientists, and pay no attention to the factual evidence presented by them, although this evidence consists of the most thorough and extensively performed experiments. Curiously, if we examine the papers by the mainstream scientists, we find no mention of experiments at all.14 It seems from this that what separates mainstream science from the dissident science is that mainstream relies upon theory exclusively for the formation of its conclusions. From this the thesis is presented that both the mainstream and the dissident community have allowed the metaphysical assumptions underlying the unipolar induction debate to influence the interpretation of the evidence. The difference between the two camps is that the dissidents do make recourse to the experimental evidence, while mainstream does not see the necessity of doing that.C 3.1 The Metaphysics of Unipolar Induction Here the basic metaphysical issues involved in the dispute will be discussed. Metaphysics, as used here, refers to ideas about the nature of things in the real world of nature. The particular metaphysical concept that underlies the unipolar induction problem is whether or not there exists magnetic lines of force and how they behave in the case of unipolar induction. The idea of lines of force is due to Faraday and he used it as a primary explanatory concept in his theory of electromagnetic induction. The explanatory concept employed by Faraday in his physical model, was that an emf was produced when the lines of magnetic force cut across the wire of a circuit due to motion of the wire. Refer to sections 3076 and 3083 of his Experimental Researches in Electricity. The other metaphysical difficulty that is involved is the problem of what is motion. This is much more difficult to discuss and involves some deep ideological prejudices stemming from Einstein's principle of relativity. Einstein asserts that all motion is relative and he makes no distinction regarding whether or not his principle applies to all types of motion or not. That is to say, are both rotational motion and B The mainstream has adopted Faraday's conclusion regarding rotation of the magnet but maintains the curious position that there are no lines of force that rotate with the magnet, but that the electrons are effected by a Lorentz Force acting on them as they rotate within the field of the magnet. C Here the word mainstream refers to official science that appears in major peer reviewed journals and in arXiv. Dissident science refers to scientific publications that are not found in the major peer reviewed journals, but may be found on internet science sites, or NPA publications, and often reflects disagreements with the accepted mainstream paradigms. Dissident science is almost never as a rule cited in mainstream papers or journals, and can be identified by doing searches at mainstream science databases , which do not include dissident scientific works or record citations of them. translational motion fundamentally without any absolute character? That is must both motions be relative or is one relative and the other not? This becomes an important question, because when the experimental evidence is examined, it is found that upon the hypothesis that both types of motion are relative motion, then this hypothesis is refuted by the experiments. Faraday had already shown in his experiments discussed in his Twenty-Eighth Series that there was a profound difference between the translation of a magnet and a rotation of a magnet. This was the basis for the dispute as Faraday tried to distinguish between the two types of motion so as to account for the contradictions that arose from the experimental facts. Faraday therefore tried to explain the contradictory experimental results by distinguishing between the motion of lines of force in translation and in rotation. Hence in Faraday's conclusion, while a magnet's translational motion carried lines of force with it, rotational motion of a magnet did not. This resolved the experimental difficulties that arose from his lines of force model in the case of rotational motion and unipolar induction. The modern mainstream approach makes a sight modification of the same solution. In the modern approach there are no lines of force, and so there is no longer any problem that arises between the cases of translational and rotational motion. On the other hand, the dissident scientific community sees this contradiction that arises from the unipolar induction experiments as a refutation of Einstein's special theory of relativity because the unipolar induction experiments clearly show that an emf is produced only for absolute rotation, and not relative rotation as one would expect from Einstein's theory. 15 Hence as a result, Muller proclaims that his unipolar induction experiments are a direct experimental refutation of Einstein's special relativity theory. This particular claim may explain why we find no experimental evidence in the mainstream papers on unipolar induction, because the experiments do not support the currently accepted mainstream paradigm that special relativity is fully verified by all the experimental evidence. This presents a real threat for the currently accepted metaphysics of Einstein's principle of relativity. That is the idea that all motion is relative. 3.2 What Is Scientific Method? Traditionally the scientific method is supposed to be an approach to questions regarding metaphysics that attempts to resolve them through use of experimental evidence. That is disputes, such as the disputes over the metaphysical issues that arise from the phenomenon of unipolar induction, as discussed above, ought to be resolved by recourse to empirical methods. However, as we saw above, this has not been done by the official mainstream scientific establishment. That is to say that no official mainstream scientific paper has been published in the modern era that seeks to resolve the unipolar induction controversy by recourse to an empirical investigation. This is to be contrasted with the dissident claims of F.J. Muller and A.J. Kelly which do seek resolution in the empirical evidence. As part of this investigation, published textbooks were examined. Not one of them addressed the unipolar induction problem through the agency of demonstration experiments, or reference to experimental evidence at all. All were primarily concerned with the presentation of theory and problems, and their mathematical solutions, not one problem solution was shown to be in accord with any experimental result. Wikipedia, which is usually very good reflection of mainstream thought, also takes a primarily theoretical approach and offers almost no experiment facts or evidence in an effort to resolve the disputes. There is one particular case that is of importance to this discussion. This is a paper by L. Mencherini: relativistic interpretation of Kennard's (1912 and 1917) and Mullers (1979) experiments on the unipolar induction.16 Mencherini's purpose is to dispute Muller's conclusions regarding the interpretations of his experiments in favor of Einstein's special theory of relativity. But Mencherini's approach is entirely based upon theory, and not upon the empirical evidence. In other words, Mencherini disputes Mullers' conclusion that special relativity is refuted , by the unipolar induction experiments, by simply asserting that the theory of relativity can explain all of them in theory. So there is no difficulty to be resolved. This presents us with an epistemological tautology. Mencherini asserts that the empirical facts do not refute the relativity theory by an argument that assumes that the theory is correct and hence uses theory to dispute the contrary empirical evidence. Should this type of thing be allowed in science? Since it happens all of the time, the answer must be yes, and if this is the correct answer as to how science is being done, then it is clear that the primary criterion of modern science is not empirical evidence but internal consistency and mathematical beauty of theories.D The answer to the question, what is scientific method, can be seen in the examples that have been cited in this study. The scientific method consists of proposing a given metaphysical ideology or belief system as a solution to a particular scientific problem and then looking for whatever experimental evidence that can be produced to support the proposed solution. The method therefore starts from metaphysical assumptions and proceeds to empirical facts only for confirmation or verification of the metaphysical idea. Hence, the metaphysical ideas come first in pride of place and the investigation of nature occurs only as a means towards the end of verification of the metaphysical ideology. This type of approach is evident in both the dissident and mainstream scientific camps. For example we see that A.J. Kelly's purpose in preforming experiments was to confirm his belief that the metaphysical conception of lines of force is a valid conceptualization of a magnetic field of force, and since it is a realization of a realist physical model of reality, the idea that the lines do not physically rotate was simply a physical absurdity. Muller's motivation was to demonstrate that Einstein;s special theory of relativity was false and found confirmation of this in the experiments. Hence both he and Kelly looked for evidence in the experiments and discovered that the evidence supported their metaphysical conceptions. On the opposite side, L. Mencherini, started from the idealist viewpoint that the principle of relativity was correct, “because it involves both the hypothesis of isotropy and uniformity of space, and the principle of Universality of the speed of light,” and he then proceeded to interpret the experimental evidence so as to confirm this metaphysical conception. Hence the method of science is to proceed from metaphysical principles and then only seek to inquire into the natural world as a means to justify this metaphysical preconception. Thus the method is verification of metaphysical ideology and not to seek any new or different information that nature may provide in the course of objective investigation. 3.3 Two Different Theories Of Electromagnetic Induction From the viewpoint of philosophy of scientific method, one very obvious problem is that mainstream maintains two different theories of electromagnetic induction. A further difficulty is the role that is supposed to be played by Einstein's special theory of relativity with respect to one of these theories. Mainstream physics books claim: The correct physics is always given by the two basic laws F=q(E + v x B) Curl E= -dB/dt 17 D One problem in Mencherini's argument is his use of an obscure method of his own invention. One can see a difficulty in his position where he begins his argument by stating the theory of relativity must be true before considering the empirical evidence in the case. One is not surprised to discover he vindicates relativity at the end of his argument because he started out by assuming that relativity was correct as his basic assumption. Hence no empirical facts could be presented in evidence that could refute that claim. His work is an example of tautological reasoning. However, the theoretical physics underlying these two equations is completely different. The first one stems from Einsteins special relativity and the second one from the traditional Faraday Flux law of 19 th century electromagnetism. A very obvious fault of this statement is the lack of a logical connective. Are both laws true at the same time so that they are equivalent statements of the same physics, in which case we would use the logical AND, or are they mutually exclusive true statements so that we should use the logical OR with implied exclusivity. This particular problem is left deliberately ambiguous, such that no correct inference can be drawn from the statement of the applicability of these laws. This question is a very important one for the following reason. It is possible to derive the first expression on the right starting from the expression on the left as is done by Lorrain and Corson. 18 That is to say, that the Lorentz Force is simply a result of Faraday's Flux rule. In fact the Lorentz Force law is exactly Faraday's lines of force theory regarding “The value of the moving wire or conductor, as an examiner of the magnetic forces.” But the Lorentz Force law is a law that applies to the electron theory of Lorentz, and is supposed to be the force experienced by an electron moving with relative velocity v with respect to a magnetic induction field B. This is quite different from Faraday's conception of the law, where the velocity v is with respect to the rest frame of the circuit in which the galvanometer is located. In Faraday's conception of lines of force, the resulting detected current was a measure of the magnetic forces in the field as expressed by the number of lines of force which were cut by the moving wire probe. The detector could be made to register a larger effect when the velocity of the moving wire was increased. Hence to make his law mathematical we arrive at the Lorentz Force Law. But his velocity of the wire is not relative to the motion of the field of the rotating magnet, which is required by the Lorentz Force Law, as he tells us in the offending paragraph, i.e. 3090, that is the source of the controversy. Hence in Faraday's view, the relevant velocity in the vxB law is not velocity relative to the moving lines, but relative to the circuit containing the galvanometer. Unfortunately, Faraday does not clearly define for us this last fact and we have to infer it from the corpus of the experiments we now have in our possession. The claim being advanced here is the following. That is that the current method of science would appear to rule out the use of two entirely different laws of physics being applied to the same physical phenomenon. But that in the case of electromagnetic induction we have two different theories that are applicable to any particular physical problem. That is we can use a physical model that is based upon the traditional Faraday Flux Cutting Rule or we can use a model based upon the electron theory and Einstein's theory of relativity, which produces the Lorentz Force Law. The difficulty lies in the fact that both of them produce the same equation, and hence the same prediction regarding the emf that is to be measured. Hence they are basically indistinguishable physical theories form the viewpoint of the mathematics of the situation. Since mathematical predictability is the criterion for scientific decision making, it is therefore impossible to distinguish the two different theories on the basis of the usual mathematical methods of science. That is to say the usually accepted criterion of scientific decision making fails in this situation, and this explains to failure to resolve the disagreements over the correct theory to be applied in this case. It turns out that the two different physical models are different with respect to the definition of the velocity v in the Lorentz Force law. In the electron theory, this velocity v is defined relative to the rest frame of the magnetic field. In the Faraday Flux Cutting Law, the velocity v is defined with respect to the rest frame of the circuit containing the galvanometer. Therefore there is a physical difference in the physical model that attempts to explain the source of the measured emf. The difficulty is in discerning where in the corpus of the experimental evidence this difference can be revealed. This was obviously the motivation of Muller's experiments. 3.4 The Problem Of Scientific Falsification and Verification There are two problems in verification of scientific facts. They are false negatives and false positives. How these are dealt with is an important problem. In science, because ideology rules, despite the claims of objectivity, there is a problem that an actual falsification is considered a false negative. That is it is not considered a valid falsification. On the other hand, there are times when a falsification is considered valid when it is an erroneous conclusion. Such an example occurs, when it is claimed that Faraday's Flux Cutting Law is invalid in some special cases. An example of this is discussed in section 17-2 of Feynman's Lectures. There an experimental example is presented which purports to show that the Faraday flux rule is invalid. But we are told that the alternative Lorentz Force Law does provide the correct answer. It appears that this conclusion is entirely false, that is to say there is no falsification of the Faraday Flux Cutting Law, such that the alternative law can be used. That is to say that the claim that there are two laws to be used as valid physical models is false as is shown in the experiments section of this paper. An example of a false positive would be the experimental evidence that asserts that the magnetic lines of force do not rotate with a magnet. This claim has serious difficulties that arise from the actual physical understanding of the physical model involved. It is obviously a physical absurdity to assert that lines of force do not rotate with the physical rotation of a magnet. However, there is also the difficulty in understanding why experiments that are performed in a manner that do cut the physical lines of magnetic force don't produce a positive result. However, suppose we set out to test this claim by developing experiments to test it. This is what has been done and the result is that it is confirmed in experiments.E But this conclusion is rejected by experimenters such as Kelly as a false positive. 3.5 Difficulties With The Relativistic Theory and Its Method The fundamental belief that results from Einstein's theory of relativity, is that all motion is relative. This statement is true not so much as a physical fact but because it is correct as a definition, because one can consider any absolute motion as relative motion, when defined relative to a frame. The difficulties in unipolar induction arise from the metaphysics of relativity where one is supposed to believe that relative motion is reciprocal or symmetrical with respect to different definitions of rest frame. This definition fails when tested experimentally. But, and this is the difficult part of the problem, that failure results from the metaphysical idea regarding what is the source of the induced current and not a result of a denial of relative. It is clear from the definition of motion, that all motion is relative, what makes Einstein's idea significant is that he claims that there can be more than one rest frame in the definition of laws of physics and that this causes no contradictions or inconsistencies. One feature of the relativistic method is that which involves the definition of the velocity v in the Lorentz force Law. Is this velocity relative to the source of the field or to the circuit which detects the resulting emf? Muller's experiments show that the claims of the relativistic theory of the soucre of the detected emf face refutation. That is the spacial teory of relativity is found to have no correct predictve power in cases of rectilinear motion where an emf is to be produced in a wire circuit in motion relative to a magnetic field. Hnece the theory discussed in Panofsky and Phillips section 9-5 is falsified by the experimental evidence. E For example Lecher confirmed the claim experimentally. See A.I. Miller. 3.6 Can Theory Change Occur? The claim advanced in this paper is that despite the claims of the different current theories, none of them can adequately be reconciled with the experimental evidence, without some kind of paradox. However, the claim advanced here, is that it is possible to explain all of the evidence on the basis of the hypothesis that all of the cases are easily explained using the Faraday Flux Cutting Law in either of the forms given by Feynman, where the velocity v used in the Lorentz Force Law is the velocity of the moving part of the circuit relative to the galvanometer part of the circuit defined as at rest. This claim removes the difficulties with the current interpretations but faces the difficulty that ideological preconceptions block scientific paradigm change, despite the fact that the current paradigms are unable to resolve the disputes. Does Faraday's Paradox Really Exist? Currently, Wikipedia in its article on unipolar induction, which is called Faraday's Paradox, 19 fosters a number of fallacies which tend to promote the inability to resolve the difficulties. The main feature of the problem is the following. There is no examination of the empirical or factual experimental evidence involved in the controversy. From the viewpoint of Michael Faraday, there was no paradox, misinterpretation, or confusion of any kind. His purely empirical approach had completely solved the problem, and his method was logically consistent and complete. Wikipedia fails to express this fact, and by calling the problem Faraday's Paradox, creates an entirely false interpretation. From the viewpoint of an experimental basis for scientific interpretation, the theory advanced by Faraday was logically complete and consistent with all empirical facts. It was only later, when theoretical questions arose, that the controversy developed. Significantly at that time, the attempts to resolve the theoretical problems were empirical. That is the scientific community sought to resolve the debates over the theory, by recourse to experiments. This is entirely the reverse of the modern approach. The idea that there is a Faraday's Paradox is entirely a modern invention. F It rises because there exists a problem in reconciling the empirical evidence with the modern electron theory and Einstein's special theory of relativity, which is expressed in terms of the Lorentz Force Law. The idea that there is a paradox proceeds from the thesis that there is something wrong with the Faraday Flux Cutting Law:“The false impression might emerge that the two phenomenon of induced emfs are derivatives of Faraday's law, which appears fundamental and all-encompassing.” 20 The paradox is a direct result of the fact that there are two Faraday Laws, and not just one, and so a paradox was invented, not because there was something wrong with the Flux Cutting Law as discovered by Faraday, but because it could not be integrated into the ideology of modern physics. In the modern viewpoint, there is a failure to understand that the Flux Cutting Law is a fully verified and established empirical physical law. That is because physical laws, in the modern view, have to have a theoretical foundation, drawn from a metaphysical principle, not an empirical one. In the modern viewpoint, the empirically derived magnetic lines of force have no justification because they collide with the metaphysical ideas of Einstein's special theory of relativity. Hence the empirically derived lines of force must give way to more modern metaphysically derived ideas, and so the Faraday Paradox F There is no explicit discussion of a Faraday Paradox that could be found prior to the last decade. There were references to assertions that the unipolar machine was paradoxical, such as in “One-piece Faraday Generator: A Paradoxical Experiment form 1851”, and in endnote 19, but no reference at all to a Faraday Paradox until recently. is invented to justify dispensing with Faraday's magnetic lines of force and the Flux Cutting Law that uses this conception. This is done by creating doubt regarding the empirically derived Flux Cutting Law, by adducing false experimental evidence that this law fails. In the modern approach, the role of experimental evidence is reversed. Instead of being the basis for empirically established physical laws, the role of experiment is changed to be merely a test for theoretically established laws. This leads us into a problem regarding false positive experimental evidence. That is, since there is no thoroughly established empirical investigation, the evidence is drawn from a single experiment, that may be nothing but an erroneous false positive. But this false result is accepted as correct because it confirms the dominant popular theory that is currently fashionable to believe in. Put differently, experiments are designed to support current scientific ideology rather than to rigorously test its validity. Given this mind set, it is not a surprise that the Faraday paradox has no empirical resolution. Therefore, there is no discussion or analysis of the empirical facts, which could easily resolve the controversy. 4.0 Analysis Of The Experimental Evidence The thesis presented here is that in 1851 Faraday had already in hand all of the experimental facts necessary to reach the correct conclusions regarding the physical laws involved in the problem of electromagnetic induction and unipolar induction as a special case. However, his communication of these results must be deemed ineffective as his statements regarding the interpretation caused a continuing controversy and an incorrect development of the applicable laws of physics. The particular offending paragraph is the statement in section 3090 of his Experimental Researches, which was cited in the above section 2.2. This referred to the fact that lines of force do not rotate with the magnet. Here Faraday was making a distinction between translation and rotation effects of induction. This distinction continues today to be the main source of the difficulty in resolving the unipolar induction disputes. Currently there exists a large number of experiments on electromagnetic induction, but they are not gathered together or put into a form that makes them easily accessible for analysis. This is most probably the reason for the difficulty in understanding Faraday's conclusions and the reasons for obtaining them as he did. He does not present the data in a simple matrix format as modern engineers are taught to do. This writer knows of only one case where this is done and that is the work of F.J. Muller. There the results of a comprehensive set of experiments are presented in the form of a tabular matrix. A.I. Miller has presented the data from Faraday's experiments in a matrix format as well, but the experimental results he presents in matrix form were not available until publication of Faraday's Diary in 1932, and they are not as complete and extensive as Muller's data. Unfortunately Muller's experiments are not as complete as one would like in that he does experiments upon special cases and one would desire that these be shown to be applicable as more general cases. This will be discussed later. Finally there are some unusual special cases that require solution and result in confusion and difficulties in understanding. These are discussed in the book by Bewley, 21 and in different places throughout the physics literature.22 4.1 Faradays Experiments- A.I. Miller's Tables23 In his Unipolar Induction case study, Miller presents in Figures 3 and 4 results obtained by Faraday. The two cases involve different aspects of the case of unipolar induction. In the results of Figure 3, he presents the results obtained for a rotating disk in a magnetic field. Here the disk is placed on one pole of a cylindrical magnet. When the disk and the magnet are rotated together, there is a detected current, when the disk is rotated with the magnet at rest there is a detected current, and finally, when the disk is not rotated and the magnet is rotated, there is no detected current. When the experiment consists of only a conductive magnet, the traditional case of unipolar induction, the results obtained were as follows given in Figure 4 of Millers paper: when the magnet is rotated and the external circuit is at rest a current is detected, when the magnet is at rest and the circuit is in motion in the opposite direction a current is detected, and when both the magnet and circuit are rotated in the same direction, no current is detected. The common result in both cases can stated as follows: Only when there is a difference in motion between the part of the circuit moving within a magnetic field, and the part of the circuit where the galvanometer is located, is there a detectable current. Hence we can explain the first experiment with the disk as follows. A current is detected only when the disk is moving with respect to the part of the circuit containing the galvanometer, and it matters not whether the magnet is rotating or not. In the second experiment involving a magnet rotating within its own field, when the magnet rotates and the external galvanometer circuit moves with it, there is no detected current. However when the magnet moves and the external circuit does not, or the converse, there is a detected current. The observant reader may notice that the above statement of the conclusion is not as precise as it should be. This is what contributes to the difficulty. This has to do with the role of the magnetic field in the production of the current. It develops from the experiments that the crucial requirement is that the current is produced only when there is a difference in motion within the circuit irrespective of the motion of the magnetic field source or whether or not the entire circuit is exposed to a magnetic field. The decisive factor is that the part that is moving must be moving in a magnetic field, and if different parts of the circuit are exposed to the field at the same time, they must be moving with respect to each other in order to produce a current. Finally, it should be noticed that the galvanometer part of the circuit establishes an absolute rest frame for the definition of rotational motion. That is to say if the galvanometer is at rest in a laboratory, then this defines the laboratory frame as the absolute rest frame for the experiment. Now given this definition of an absolute frame, it can be seen that it is absolute rotational motion in the presence of a magnetic field that produces a detectable current. This is the same as saying that absolute motion of a part of the circuit exposed to a magnetic field produces a current. Before the relativist reader denies this conclusion, he should notice that here we are discussing rotational motion and that is what makes the motion absolute. Faraday makes this distinction in section 3090 of the Experimental Researches.G 4.2 Lechers' Experiments24 In this section experiments preformed by Ernst Lecher in 1895 for the purpose of refuting a contention by S.Tolver Preston that Faraday's interpretation of the experiments was incorrect. Lecher's purpose was to demonstrate experimentally that Faraday's hypothesis that the magnetic lines of force do not rotate with the magnet is correct. This discussion will lead us to introduce some new terminology which will make the theory and experiments clearer when they are being discussed. Lecher built an apparatus which consisted of two unipolar machines mounted upon the same axis operating back-to-back. That is, to say it differently, there were two unipolar induction machines on the same axle, set up so as to operate in series or separately. That is the first one spinning or not, and the second one spinning or not, where they could be set spinning independently. The key to the experiment G This statement is also true for the case of translational motion usually discussed in textbooks where there is a rectangular circuit in a uniform magnetic field. A detected current is produced when one of the sides is allowed the move with respect to the other three sides. This is a case of absolute motion where the three sides define the rest frame and the sliding part is in motion with respect to the rest frame. was the ability to connect the galvanometer so that the different parts of the machines could be combined in series in different ways. The important aspect of the arrangement was the fact that the magnets were placed end to end so that their fields combined to produce a larger field than either one of them taken alone. The crucial element in Lecher's experimental demonstration was that he demonstrated that the magnitude of the effect produced by the two magnets in series, was that it made no difference whether they were both spinning, or only one was spinning. In other words, the strength of the magnetic effect in producing a current did not depend upon the state of motion of either magnet, as long as one was spinning. This effect was definitely greater than that of a single spinning magnet by itself. So the effect produced had no dependence upon the state of magnetic rotation of the additional magnet placed in series, with the spinning one. One can see clearly that in this experiment the physical theory being used was leading the experiments to be incorrectly interpreted. That is because the experiments were designed to detect a difference in the detected current magnitude based upon the assumption that the state of rotation of the magnetic field was the decisive factor in the physics of the experiment. The experiment has an equivalent interpretation, which is that it is only the effective magnitude of the magnetic filed at the location of the part of the circuit that is in absolute motion that is the determining factor in setting the magnitude of the detected current. The magnet motion has no effect. Lecher's conclusion was that the magnetic field does not rotate with the magnet, which was a refutation of S.Tolver Preston's claim. Here it is timely to introduce some terminology. The case where the rotating magnet and the circuit in motion are the same will be called the homopolar case. This will distinguish it from the case where the Faraday disk and magnet can be in different states of motion. When the disk and the magnet both rotate you have the homopolar case of unipolar induction. Since homo means same. Now the meaning of unipolar induction will be discussed. If we have a spinning magnet, such as in the example of the Lecher experiment, if we measure the current produced between the north pole and the middle of the magnet we will detect a current magnitude. However, if we seek to increase that effect by placing the galvanometer leads at the north pole and south pole thinking this will double the effect, the result is no current can be detected. That is the current magnitude is zero. If we measure from the middle of the magnet or its “equator” and its south pole, we will detect the same magnitude current as between the north pole and the equator, but with reversed polarity. So the meaning of unipolar becomes clear that it is the action of only one, meaning “uni”, of the magnetic poles in producing a current. So in a unipolar generator or motor we use only the action of one of the magnetic poles and not the other. If in the motor or generator the moving circuit and the magnet producing the field have the same state of motion, we call it homopolar. In Lecher's experiment, he measured between the equators of two axial magnets connected in series and found that the current was significantly larger in magnitude than that produced by a single spinning magnet when mounted alone by itself. His demonstration consisted of showing that the current was the same when one or the other of the series magnets was rotated, but was null when both were rotated. From this he concluded that Faraday's statement was correct that the motion or rotation of the magnet was not a determining factor in the production of the detected current. Unfortunately this is not exactly the correct way to state this. The correct way is to say that the determinative factor in the production of detected current is the absolute rotational motion of a portion of the circuit in the presence of a magnetic field. In these experiments the part of the circuit that is in rotational motion is the homopolar magnet through which the galvanometer circuit is completed. When the magnets were mounted backto-back the magnitude of the field was increased, and this accounts for the experimentally detected increase in current. 4.3 Experiments To decide If The Field Rotates Or Not Rather than discuss the many experiments performed after 1852 up to the modern era, the reader is referred to the paper by Kelly, which discusses them in detail. Here we will address the experiments performed by Kelly and try to discover any new insights he offers. In doing so we will compare and contrast his results with those performed by Faraday and reported in his Experimental researches In Electricity. Kelly divides his experiments into three groups. The first set of experiments are similar to those performed by Faraday in his Twenty-Eighth Series, illustrated in Figure 5, and discussed in sections 3093 and 3094. Kelly does the experiments differently. Like Faraday, he places the wires in different orientations relative to the rotating magnet, and spins them in different ways. Faraday performed only two tests. That is he rotated the external circuit and the magnet at the same time, and the magnet with the external circuit at rest. These correspond to Kelly's tests (b) and (c). Kelly performed the additional experiment of revolving the circuit with the magnet at rest, which he labels as (a). In all cases no emf was detected by ether Faraday or Kelly. Kelly's section two experiments were conducted upon a rotating conductive magnet and his experiments (d), (e) and (f) are basically the same as reported in Miller's Figure 4, which were discussed previously. Kelly's experiments (d), (e), and (f) correspond to Figure 4 of Miller, and gave identical results. Kelly's section three experiments involved a rotating disk and correspond to Miller's Figure 3. Kelly labels his experiments (g), (h), and (j). They give exactly the same results as obtained by Faraday. Kelly does four additional experiments that he labels (k), (l), (m) and (n). In (k) the external circuit and the disk are rotated together so that there is no relative motion for these, the result was no emf. In (l), The magnet is rotated along with the previous arrangement. That is magnet, disk, and external were rotated together. The result was no detected emf. In experiment (m), the magnet and the circuit were rotated together with the disk at rest, and this produced a detectable emf. Finally, in experiment (n), the external circuit was rotated with both the disk and magnet at rest. This experiment produced a detected emf. Before proceeding, it should be noted that experiments (g) and (m) are symmetrical with respect to the inversion of the rest frames, and give the same result as expected. Experiments (h) and (n) are symmetrical with respect to inversion of the rest frame, and also give identical results. Finally, experiments (j) and (k) are symmetrical and produce the same result of no detectable emf. This leaves us with the final combination or all thee parts rotating together, as in experiment (l), which is symmetrical to the situation where all the parts are at rest. In this case there was no detected emf. Up to this point we can conclude that all of Kelly's experiments confirm those of Faraday. We notice that in all of them, an emf, or current is detected only when there is a relative motion of the different parts of the same circuit, such that we can say that a detected current is produced when there is a motion of the moving part of the circuit, when it is exposed to a magnetic field. But the motion of the magnetic field relative to the circuit has no effect whatsoever upon whether a current or emf is detected or not. (We get no detected current or emf, when the moving part of the circuit is not in a magnetic field as we will find from Muller's experiments.) Up to this point, the experiments of Kelly and Faraday have agreed on all points We have now reached the point where we find a disagreement that justifies Kelly's conclusion that the lines of force rotate with the magnet, which Faraday asserts is not the case. The crucial disagreement involves Figure 10 section 3099 of Faraday's Twenty-Eighth Series. The effect of the difference is that where Faraday finds no effect, Kelly does find a positive result. That is, according to Kelly the position of the external circuit wires does indicate the action of an emf produced by a rotating magnetic field. Hence kelly is justified in his conclusion that the lines of force do rotate with the magnet when it is in motion. However, this conclusion has no effect upon the theory introduced here. That is because in the theory introduced here. The motion of lines of force has no predictive power to say whether there is a detectable current, or emf, produced by a rotating magnet. 4.4 Muller's Experiments The primary importance of Muller's experiments is that he performs them for cases wherein the fields are not uniform across the entire closed circuit. Kelly asserted that it was the detectable presence of the rotating lines of force in the external circuit that was decisive in his conclusion. Muller's experiments were designed to eliminate such external fields. This allowed a comparison of experiments where there were and were not symmetrical fields. In addition Muller performed experiments for rectilinear and rotational motion of the circuit elements. Muller's results were in complete agreement with the experiments of Faraday and Kelly. Hence we have no experimental contradictions to resolve. The importance of Muller's experiments is that they demonstrate that in order for a detected current or emf to occur, the requirement is that part of the complete circuit be in motion relative to the other parts and the moving part of the circuit must be exposed to a magnetic field for a current or emf to result. Muller also showed that it makes no difference for his conclusions whether the moving part of the circuit is executing a rotational or rectilinear or translational type of motion. As a result of Muller's experiments we see that the hypothesis made earlier was confirmed by the additional experiments which eliminate the problem of the “seat of the emf”. Muller resolved this difficulty in the following way. He used iron plates to guide and confine the magnetic field, so that the only part of the circuit that was exposed to a magnetic field was the moving part. In this case, the part that played the role of the Faraday disk, or the rotating conductive magnet. This showed conclusively that the seat of the emf in the Faraday disk generator was in the moving disk, or conducting magnet, and not in other parts of the circuit. This removed the last possible doubt that perhaps Faraday's experimental conclusions were incorrect, and that his experiments described in section 3099 were false. A second conclusion, which for Muller was a decisive one, was that the relative motion of the source of the magnetic field, had no determinative effect upon whether a current, or emf, was produced in the experiment. This conclusion completely undercut Einstein's special theory of relativity as applicable as a valid physical theory to the phenomenon of unipolar induction. Put differently. Since Einstein's theory leads to the Lorentz Law equation, E=vxB, where v as defined as relative to the magnetic field, and the the value of v has no predictive effect upon the detection of current or emf in the experiments, then the Loerntz Law and the relativity theory must be invalid as a physical model in this problem. In conclusion, the decisiveness of Muller's experiments lies not in the fact that they show anything new, all of the conclusions drawn from them were already available in the experiments of Faraday, but in the fact that they remove uncertainties that could confuse the arguments and obscure the facts as they were already known to Faraday. So it has taken us 180 years to get to the point where disagreements regarding theories can be resolved through experimental evidence. 4.5 Experimental Anomalies Resolved The purpose of this section is to discuss some of the experimental anomalies that arise and produce confusion and incorrect interpretations. The first and most important is the rocking plates experiment that is cited in many physics books. Following Feynman, this experiment is cited as a violation of the Faraday flux cutting rule. This is incorrect, because the rule correctly explains it. There are two rocking plates that have a moving contact point that completes the circuit. As the plates rock back and forth when exposed to a magnetic field, the contact point moves so as to change the flux enclosed by the circuit. However, there is no current or emf detected. The explanation is simple. The plate on the left rotates on a hinge clockwise, while the plate on the right rotates on a hinge counterclockwise. Since the plates rotate in opposite directions, according to the flux cutting rule, they produce opposing emf and so the net emf that results is zero. Hence the flux cutting rule is not invalidated as claimed in physics books. Another paradoxical experimental is Hering's Experiment. A circuit with a sliding contact is placed over a bar magnet. The circuit is then drawn across the magnet transversely and there is no emf detected as a result of this action, although the circuit moves across the magnetic flux inside of the magnet. In this case the experiment seems to invalidate the flux cutting rule. It does not for the following reason. As the circuit is drawn across the magnet, there are two opposite actions that take place according to the flux cutting rule. The first is the flux cutting of the circuit moving across the bar and the second is the decrease of the flux inside the circuit due to the magnet moving in the opposite direction. The two different effects are opposite and result in net zero emf as is confirmed by the galvanometer.25 Here we looked at experiments that are interpreted as refuting Faraday's Flux Cutting Law. In both cases we discovered that the claims were unfounded. Upon careful investigation we found the law was confirmed. 4.6 The Erroneous Spinning Magnet Experiment26 In recent years an experimental proof that there are no magnetic lines of force has been introduced to support the contention of Faraday's Paradox, and its resolution in the claim advanced by Einstein, that there are no magnetic lines of force. This claim, if validated, would demolish the entire empirical foundation of electromagnetic theory and create a crisis in classical electromagnetic theory. This experiment is a classic example of a false positive experiment, and shows that isolated experiments performed to prove a poorly defined claim through a poorly defined experimental procedure should be received with caution. The experiment is ridiculously simple and derives its impact from that apparent simplicity. However, its procedural basis is faulty. It is basically a modern repetition of Lecher's experiment, in that the basis of the experiment lies in a measurable distinction between the states of rotation and rest of the fields of cylindrical magnets. That is, it makes an implied prediction, a prediction that the lines of flux theory never makes or claims to make, and uses this implied false prediction to disprove the lines of force theory. The experiment consists of lining up two magnets with rotational symmetry, and showing that the rotation of one magnet has no effect on the other. In the Don Lancaster experiment, two cylindrical magnets are suspended by strings and their own mutual attraction. When one or the other magnet is rotated, the other remains at rest. That is the introduction of rotary motion into one magnet has no effect upon the other. The implication is that the magnetic lines of force do not rotate with the magnet. The experiment is false because, in that experiment, a magnet with rotational symmetry has no power to predict any observable effect upon the other, because of the symmetry of the lines of force that make up the magnetic field. Because of the rotational symmetry of the field lines in the plane of rotation, there is no discernible difference in the field as the magnet is rotated. Hence there is no change in the disposition of forces, and no observable effect can be predicted. This is exactly what is observed in the experiment. Hence the experiment proves nothing regarding whether the lines of force rotate with the magnet or not. The predicted result is the same, whether it is assumed the lines rotate or do not rotate with the magnet, because of the rotational symmetry of the magnetic field. 5.0 Analysis Of The Theoretical Disputes This section examines the solution of the problem from the viewpoint of the disputes over the theoretical interpretations. The best modern review of the unipolar induction problem from a theoretical viewpoint is given by P. Hammond, A Short Modern Review Of Fundamental Electromagnetic Theory.27 We will proceed based upon the conclusions drawn from the analysis of the empirical evidence in section 4.0. That is to say, we will proceed from the experimental evidence to understand why the problem failed to be solved within the realm of theory. The order will be historical. Wilhelm Weber's Die Unipolar Induction Our story really begins with Faraday and his objections to Ampere's theories of electrodynamics and magnetism. But to simplify, we will start the historical discussion with Weber's paper “Die Unipolar Induction” of 1841. Weber's paper addressed the problem of what he called unipolar induction, “that is, induction by the motion of a single magnetic fluid”. Weber used a force law due to Gauss. “From this rule Weber deduced that the cyclic motion of a magnetic mass produced an electromotive force in a conducting loop if and only if the motion embraced the loop. If Weber went on, the magnetic fluids really existed in a magnet and if they were separated within macroscopic cells a la Coulomb, the rotation of a magnet around its axis had to produce an electromotive force in any stationary path between the north pole and the meridian of the magnet (closed by an external fixed wire, because for any cell cutting the path, only the boreal fluid embraced the path in its motion.” 28 Hence in 1841 Weber had already introduced a theory to explain the famous unipolar induction experiment discussed by Faraday. The main feature of Weber's theory being that an emf was produced due to a rotational motion of a magnet relative to the external circuit. Faraday's Flux Cutting Rule The flux cutting rule has its mathematical embodiment in Faraday's Law of Maxwell's equations. There is however, a problem, which is the source of the difficulty. The difficulty involves some misunderstanding regarding the correct use of the Faraday Law. The essence of the problem boils down to this. The flux cutting law has to be applied with the understanding that there are different cases or ways of producing an electromagnetic induction. Kurrelmeyer and Mais say there are four different ways to induce an emf in a coil. 29 Here we will be concerned with just two of them. They are transformer emf, and an emf due to deformation of circuit. It is the deformation of circuit that is the phenomenon that is involved in the unipolar induction problem. The difficulty arises because there are two different ways of expressing the induction law for electromagnetic induction due to a deformation of a circuit. One is to move a part of the circuit through a magnetic field. Faraday found that the effect was minimal if the deformation, or change of shape of the detection circuit was such that the wire moved parallel to the magnetic lines of force. The effect was maximum when the deformation was such that the wire was moved across, or cut, the lines of magnetic force. The effect of transformer emf was a little different, in that the effect was produced by moving an entire circuit into a region where the magnetic field strength was changed as a result of the motion of the circuit. The emf would also be produced if the source of the field was moved relative to the detector circuit. The difficulties arise form the use of a single Faraday flux cutting rule to explain all cases of electromagnetic induction. A particular difficulty arises when there is an apparent cutting of the field lines, but there is no emf produced. This usually occurs when the motion of the circuit is with respect to a uniform magnetic field. In this case there is a symmetry with respect to the field, such that the motion of the circuit causes no change in the total flux cutting across the circuit boundaries. That is, when the circuit moves through the field, the effect of flux cutting is null due to the fact that as much flux leaves the circuit as enters it. In these cases, one has to interpret the problem in terms of deformation of the circuit. This is that, when the shape of the circuit is changed, what is the effect of flux cutting the circuit such that there is a net change in flux? This is the applicable rule with respect to the Faraday disk or unipolar generator. The decisive fact in the equation of the flux law, is what is the change of flux that is crossing the circuit boundaries? It turns out that this calculation of flux takes no notice of the motion of the source of the flux as long as the flux is uniform or constant in time. That is, put differently, the rotation of the lines of force, do not increase the amount of flux cutting the circuit in a specific period of time. This is an experimental fact. In other words, when calculating the flux change, all that is required is to assume a uniform magnetic field at rest with respect to the rest frame of the detector circuit, and then calculate the velocity of flux cutting with respect to that rest frame. That is the velocity is that relative to the circuit, or put differently, the velocity used in the calculation is a measure of the velocity of change of shape of the circuit. James Clerk Maxwell's Interpretation30 In Chapter III of Volume 2, of his treatise Maxwell gives four cases of electromagnetic induction. But he omits to discuss the case where the circuit is deformed or changing, and this is a significant oversight as he doesn't discuss the unipolar induction problem. In article 532 Maxwell specifically discusses the case of a wire moving on two rails in a uniform magnetic filed and gives the solution based upon his flux change law rule of article 531. This is the problem discussed by many physics books as the problem of the emf induced in a moving wire. But in these books the solution is not the one given according to Maxwell, in these books, it is discussed as the Lorentz force exerted upon an electron within a moving wire. In this case, no particular attention is given to the difficulty involved in the definition of the velocity v of the moving wire. In Maxwell's solution no difficulty is involved in defining the change in position, or velocity, of the wire because the flux cutting rule naturally defines the velocity as relative to the circuit at rest. The Case For Double Interpretation (But Not a Paradox) In a paper published in 1885, Dr S. Tolver Preston points specifically to the problem of unipolar induction as a case of “double interpretation”. That is his thesis was that the experiments were ambiguous and were therefore open to two different ways of interpretation. 31 Before we proceed, it should be noticed that this thesis is false for a very good reason. That reason being that Preston failed to read Faraday's papers very carefully, for if he had done so, he would have noticed that in section 3099 of his Twenty-Eighth Series, the double interpretation was ruled out by experiment. H That is in these experiments Faraday proved to himself that the “seat of the emf”, was not in the external circuit. Preston's argument was that the conclusion that the lines of force do not rotate, contradicted generally accepted theory. This is what has touched off more than 125 years of controversy and its attendant confusion, such that modern popular physics discusses this unresolved problem as Faraday's paradox. H The reader is reminded that modern experiments fully confirm this conclusion. Preston's claim amounted to saying that the empirical method failed in this case because the experiments admitted two different physical interpretations. The first interpretation was Faraday's, that considered the unipolar induction emf was produced when a rotating magnet moved within its own lines of force, thereby crossing them to produce an emf. In this case the seat of emf was said to be in the magnet. The other case supposed that the field lines did rotate with the magnet and that the emf resulted when the lines cut across the wires of the external circuit. Here the seat of emf was said to be in the external circuit, or simply the circuit. In both cases the emf was created by cutting lines of flux, but that the locations where this action occurred were different. This ambiguous situation became a question as to the seat of the emf, that is where exactly in the system was the action of the lines occurring. This is the meaning of the question regarding the seat of the emf. But we should note that this debate, takes no notice that Faraday had explored this question in his section 3099 and decided that the seat of emf was in the magnet. Hence what followed was an attempt to resolve what was essentially an empirical question, that occurred because the experimental evidence produced a result that collided with accepted magnetic theory. In 1891, Preston proposed an experiment to decide between the two different interpretations. 32 The idea was that the revolving magnetic field producing an emf would be different for the two alternative cases. There were a number of experimental attempts to make the required measurements, but they produced inconclusive results.33 It is clear that one could say that the criticism directed by Preston at Faraday's interpretation of the evidence had some obvious validity, because of the contradictory assumption contained in the idea that the field lines do not rotate with the magnet. However, Faraday had deduced his conclusion from a comprehensive series of experiments, and the challenge to Faraday's conclusion implied that either Faraday's conclusions were false, because of a mistake in his program, or that theoretical investigations were philosophically superior to empirical ones. It is clear that the divide between Continental European physics and British physics was an important factor, where the Continental physics placed more credulity in theory than experiment. What Faraday, Weber, Preston, and others misunderstood is that their interpretations were influenced by their ideas about how the current or emf was induced. Faraday failed to see that his theory discussed in sections 3001 through 3104 could be interpreted differently and hence he failed to be convincing regarding his arguments, as he failed to convincingly eliminate the alternative proposition of moving lines. But what Faraday's opponents also failed to notice was that decisive experiment in Section 3099, that supported Faraday's interpretation. What is clear is that Faraday did not produce enough supporting evidence or give this result the emphasis that we see it deserved in hindsight. Hence it is only from the viewpoint of the knowledge of the modern experiments that we can understand that Faraday's program was complete. Hence if one accepted the proposition that the moving lines were the cause of the emf, due to crossing or cutting the circuit, then one would have to accept the conclusion of stationary lines of force. Einstein's Solution For the Problem of Moving Lines Of Magnetic Force Simply put, Albert Einstein's attempted solution to the controversy of the problem of moving lines of magnetic force was to invent his special theory of relativity. 34 Unfortunately, Einstein's solution was not simple, but extremely complex. His summary statement of his solution, that the problem of moving lines had “no point” within his theory, belied a complex theory, which was not readily applicable to the existing question. Hence, except for the physicists interested in relativity, Einstein;s solution was not worth much as a solution to the difficulties. Frankly it produced the opposite result, instead of solving the problem, he made it much more difficult to solve than ever before. From the viewpoint of unipolar induction, the statements that Einstein makes in his first paragraph as introduction are factually incorrect. That is because, “For if the magnet is in motion and the conductor at rest,” as Einstein says it, in the unipolar induction case, there is no measured current, but Einstein incorrectly says there is “an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated..” Then later he says, “But if the magnet is stationary and the conductor is in motion, no electric field arises in the neighborhood of the magnet. In the conductor however, we find an electromotive force...which gives rise...to electric currents...” So Einstein is apparently not addressing the unipolar induction problem, here or the factual basis of his theory is entirely false, as he has no understanding of the experimental facts. A.I. Miller, however assures us he is addressing unipolar induction, and this interpretation is confirmed by referring to the last paragraph of section 6, where Einstein refers back to the introduction and says:”Moreover, questions as to the “seat” of electrodynamic electromotive forces (unipolar machines) now have no point.” This is all very baffling. If indeed he is specifically saying that his theory solves the problem of unipolar machines, then his facts are totally incorrect, and it is likely that his theory is no solution to the unipolar induction problem as he claims.35 Reduced to its essential aspects, Einstein's claim appears to be that he removes the asymmetrical problem, regarding the source of the emf that arises in Maxwell's electrodynamics, through the principle of relativity, that asserts that all motion is relative, based upon Einstein's claim that there is no absolute rest or aether frame that motion can be referenced to. In addition, it seems that his justification for this principle of relativity is the asymmetry of electrodynamics in the case of unipolar induction. (For which his experimental facts are in error.) Unfortunately this claim of the applicability of the relativity principle to unipolar induction collides with the experimental facts presented in Section 4 of this paper. This really is a serious problem, but there is nothing new about it as it has been pointed out by other authors. Charles Proteus Steinmetz On Unipolar Induction Carl Hering's Revision Of Some Of The Electromagnetic Laws In the 1920s Carl Hering published many papers that presented evidence that the currently accepted laws of electromagnetism required revision. Although Hering did not address the unipolar induction problem his experiments cast doubt upon the Faraday flux cutting rule and have been the basis for concluding that this law is faulty.I In his paper titled Revision Of Some Of The Electromagnetic Laws, he was critical of Maxwell;s law of induction given in article 541 of his treatise. Hering proposed a counter example that he claimed was an exception to Maxwell's “true law of magneto-electric induction”. Unfortunately, as is discussed in section 4.5 of this paper, the particular experiment proposed by Hering does not contravene the Faraday-Maxwell law. However, it has been generally accepted that his experiment does constitute an exception to the law and this has promoted the idea that Faraday's flux cutting law is not universally true. This leads to the idea that there are two laws that describe the phenomenon of electromagnetic induction. I The reader is referred to Figures 5 and 6 of P.Hammond's paper and the accompanying text. 6.0 Summary of Observations On Scientific Method, Experimental Results, Theoretical Explanations, and Final Conclusions The current scientific approach to the unipolar induction problem is summarized in the modern label, Faraday Paradox, which is assigned to it. In the first place, the label Faraday Paradox is entirely false since nothing Faraday discovered or wrote concerning this phenomenon implied any paradoxical results or experimental anomalies. So to call Unipolar Induction Faraday's Paradox is simply wrong, dishonest, and a false invention. There is, in fact, nothing in the experiments or the conclusions drawn by Faraday that can be called a paradox, or incorrect, or misleading. What is involved is a misunderstanding regarding conceptual ideas involving the magnetic field that developed over a period of time and gradually evolved to the point where modern misunderstanding is so great that the misunderstanding has become a paradox. The difficulty has been exacerbated by the introduction of the modern electron theory, and worst of all, Einstein's special theory of relativity. Neither of these being capable of developing a fully consistent theoretical interpretation, the problem became unsolvable, and hence was labeled as a paradox. This illustrates the points being made regarding the efficacy of scientific method. The method as actually practiced is so full of opportunities for misunderstanding, erroneous theoretical interpretations, false experimental positives and negatives, and subject to changing scientific fashions that it is incapable of reaching correct and true conclusions. The problem analyzed here is a really good “case study” of failure of scientific method. 6.1 Experimental Results The investigation of the experimental evidence that has been produced over the last 180 years shows no evidence that any of the experiments done by Faraday were in error or produced incorrect or erroneous results. The experiments performed in the modern era confirm Faraday's results. The modern experiments can be interpreted to resolve the dispute regarding the “seat of the emf”. That is the dispute regarding whether the emf was produced within the revolving Faraday disk (or magnet) or in the external circuit. This problem is fully resolved in the experiments of Muller who shielded the external circuit from magnetic fields and obtained the same results as Faraday. Hence the emf is produced within the rotating disk or conducting magnet. The question of moving lines of magnetic force has a simple resolution in the experimental evidence. All the experimental evidence is consistent in demonstrating that the state of motion of the magnetic field makes no difference as to the detection of current or emf. Hence the question of rotation of lines of force has no meaning with respect to the prediction of whether a current or emf is produced, or not. That is because the state of magnet motion is not a determinate variable in the equations used in the prediction. This conclusion is equivalent to Einstein's statement that the question is meaningless. However, the reason's for this conclusion are not equivalent, and this is the source of the modern paradox. The Lorentz Force Law does require that the state of magnet motion be used as a determinate variable in the prediction equation. This is where the paradox and the attendant controversy arises. 6.2 Theoretical Explanations The history reveals that the difficulties arose when theoretical interpretations were applied to Faraday's rule that the lines of magnetic force are not to be understood as rotating with the rotating magnet. A conclusion that was empirically derived, and is consistent with all of the empirical evidence. Today we can fully understand that this conclusion was most likely a false oversimplification. Unfortunately it led to the modern belief that lines of magnetic force do not exist. This is a peculiar belief because the lines of force are visualizations of the magnetic field. Thus to deny lines of force implies the unreality of the field idea as well. Much of the problem of the dis-confirming experimental evidence as applied to the lines of force idea, can be understood as a problem of the symmetry of the magnetic field in the plane of rotation. That is, every angular position of the rotating magnet is is same as every other, so they are indistinguishable. Hence rotational motion causes no change in the field magnitude, although the lines do rotate. This leads to the misunderstanding of what happens when a circuit is rotated around the magnet or the magnet is rotated with the circuit at rest. The field, being symmetrical, induces no change in the field magnitude that is intercepted by the circuit. Hence there is no induced transformer emf. There is no deformational emf, because the circuit is not deformed by the motions. From this Faraday concludes that the magnetic lines of force do not rotate with the magnet. That is because their motion has no sensible effect. This is what he should have said: The state of motion of the magnetic lines of force has no sensible effect, so that no difference is detectable between when the magnet is rotated or is at rest, so the results of the experiments can be most easily understood as what happens when it is imagined that the lines do not rotate with the magnet, so that the rotation of the disk or magnet has the effect of cutting across stationary lines of force when moving. We can not completely absolve Faraday for all responsibility in this problem. In introducing his method of the moving wire, he failed to make the observation that this involved a case of a change of shape, or deformation, of the detection circuit he was using as a probe. This is a case where the physics involved in the method of probing the field was not considered in the analysis of the effects produced. Since the moving wire was mostly outside the magnetic field being probed, his assumption that the moving wire measured the strength of the field was mostly justified. Faraday failed to take into account the fact that when probing the field with the wire only part of the circuit was moving, but when he rotated the entire circuit there was no actual change of the total magnetic effect. The advent of the electron theory of Lorentz and the introduction of Einstein;s special theory of relativity can be identified as the cause of the modern misunderstanding. It seems that modern physics was not satisfied with a macroscopic theory and sought a microscopic understanding in the Lorentz Force Law acting upon the electrons of a circuit experiencing induction. However, it is clear that the experimental evidence regarding the seat of the induced emf indicates rather clearly that the Lorentz Force Law has no predictive power, because the induced emf has no functional relation to the state of motion of the magnetic field. Hence the velocity variable v in the Lorentz Law is indeterminate. This rules out the special relativity theory as applicable to the phenomenon of unipolar induction. 6.3 Final Conclusion The difficulties arise when we attempt to assign a predictive or causal role to the rotational motion of magnetic lines of force within Faraday's flux cutting concept. That is we should not speak of the motion of the lines of force as applicable to predicting the resulting emf. This is because of the rotational symmetry of the field, such that every angular position is identical to every other. Hence any theoretical law which attempts to assign a velocity of motion to the lines of force faces an indistinguishably problem. That is, it is impossible to base a predictive rule upon a motion of the lines of force. This rules out the applicability of the modern electron theory and special relativity through the use of the Lorentz Force Law. The only reason that modern physics assigns the name Faraday Paradox to the unipolar induction problem is that the above conclusion is fashionably unpopular, because both the microscopic electron theory, and the special theory of relativity are considered to be correct and unassailable. Hence the problem becomes paradoxical, since there is no solution with these theories that doesn't involve some contradiction, because they violate the experimental facts. In the final analysis, only the Faraday flux cutting theory has the ability to resolve all the difficulties. This is easily done by noting that the velocity of flux cutting, is the velocity of the moving wire relative to the rest frame of the detecting circuit. 1 M. Faraday, Experimental Researches In Electricity, Great Books Of the Western World, Vol 45. 2 A.J. Kelly, Unipolar Experiments, Annales de la Fondation Louis de Broglie, Vol 29, no 1-2, 2004 Available on Internet by Google search. 3 A. Einstein, On The Electrodynamics of Moving Bodies, 1905. Available on Internet by Google search. 4 F.J. Muller, An Experimental Disproof Of Special Relativity Theory (Unipolar Induction) Available on Internet by Google search. 5 A.I. Miller, Unipolar Induction: a Case Study of the Interaction between Science and Technology, Annals, of Science, 38(1981), pp 155-189. See also the book by Miller, Albert Einstein's Special Theory of Relativity, 1981, chapter 3. 6 G.W. De Tunzelmann, Unipolar Induction, Serial articles in The Electrician, 1888. Pages 139, 171,203,232, 262, 300, and 365. For the controversy, see pages 450, 480, 511, 542, 572, 573,and 611. All available at Google Books. 7 H. Montgomery, Unipolar Induction: a neglected topic in the teaching of electromagnetism, European Journal of physics, 20(1999), pp 271-280. 8 Igal Galili and Dov Kaplan, Changing approach to teaching electromagnetism in a conceptually oriented introductory physics course, Am. J.Phys, 65 (7), July 1997, pages 657-667. 9 See endnote 2. 10 P. Hrasko, The Unipolar Induction. 2008 arXiv:0803.3616v2 Not a peer reviewed journal but the primary mainstream site for electronic publication. 11 See endnote 5, page 183. This section appears to have been the conclusion section of a draft paper which was later added to and amplified by adding more sections. 12 See endnote 1. 13 Wolfgang Panofsky and Melba Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading MA, 1962, page 337. 14 See endnotes 6 and 8. 15 See endnote 4. 16 L. Mencherini, Relativistic interpretation...on the unipolar induction experiments, Speculations in Science and Technology, 1993 Vol 16, No. 2, page 114. 17 Feynman, Leighton, Sands, The Feynman Lectures On Physics, Vol II, section 17-2, page 17-3. 18 Paul Lorrain and Dale Corson, Electromagnetic fields and Waves, W.H. Freeman, 1970, equation 8-36, page 341. 19 http://en.wikipedia.org/wiki/Faraday_paradox 20 See endnote 7, page 663. 21 L.V. Bewley, Flux Linkages and Electromagnetic Induction, Macmillian Co., 1952. 22 Feynman, Leighton, Sands, The Feynman Lectures On Physics, Vol II, section 17-2, Figure 17-3. 23 See endnote 5, pages 158 and 160. 24 See endnote 5, pages 162-164. 25 George Cohn, Electromagnetic Induction, Electrical Engineer, May 1949, page 443. 26 Don Lancaster, Don Lancaster's Tech Musings, February 1998, http://www.tinaja.com/glib/muse121.pdf See also http://www.youtube.com/watch?v=IlUY3snoWI8 27 P. Hammond, A Short Modern Review Of Fundamental Electromagnetic Theory, Proceedings Of IEE, Vol 101, Part I, No. 130, July 1954, page 147. 28 O. Darrigol, Electrodynamic from Ampere to Einstein, Oxford, 2000, page 55. 29 Bernhard Kurrelmeyer and Walter H. Mais, Electricity and Magnetism, D. Van Nostrand, Princeton, 1967, page 210. 30 J.C. Maxwell, A Treatise On Electricity and Magnetism, 3rd Edition, Dover, 1953. 31 S. Tolver Preston, On some Electromagnetic Experiments of Faraday and Plucker, Philosophical Magazine, February, 1885, page, 131. Available at Google Books. 32 S. Tolver Preston, The Problem of the behavior of the Magnetic Field about a Revolving Magnet, Philosophical Magazine, 1891, page 100. Available at Google Books. 33 E. G. Cullwick, The Fundamentals Of Electro-Magnetism, Cambridge, 1939, Appendix III. 34 A.I. Miller, Albert Einstein's Special Theory of Relativity, Emergence (1905) and Early Interpretation (1905-1911), Addison-Wesley, 1981. 35 See endnotes 3, 4, 34, and the discussion of the experiments in section 4 of this paper.