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Helmholtz and Maxwell : the significance of the Hertzian synthesis Lund, Erik August 1992

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Helmholtz and Maxwell: The Significance of the Hertzian Synthesis by Erik August Lund. B.Sc. The University of British Columbia, 1989. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOF THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of History)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA July 1991. © Erik August Lund, 1991.  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of  I/ /s ky  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  A u 1,/^97 I  Abstract  The problem of energy is a serious difficulty For modern physics arising out of the Nineteenth Century. In modern times, the concept of energy is linked both to the First Law of Thermodynamics, or the Law of Conservation of Energy, and the velocity of particles. Other usages of energy include the language of electrodynamics which locates it in space, and quantum mechanics. Despite that, its existence is in debate.  The confusion is one of origins. Common perceptions, which locate the idea of energy amonG the by-products of the empirical law of conservation of energy are mistaken. Rather, the law of conservation of energy is First Formulated as a metaphysical statement by a generation of true natural philosophers whose most prominent spokesman was Hermann von Helmholtz. Helmholtz's Kantian Formulation of what he called "the Law of Conservation of Force" does not require energy. That idea is, rather, invented by J.C. Maxwell, in the mistaken impression that he merely employed an entity whose existence was already proven. When the Halmholtzian and Maxwellian traditions meet in the work of Heinrich Hertz, they are reconciled in such a way as to discard important elements of Maxwell's theory and leave Kantian ideas intact.  The Kantian Formulation coupled with interpretations which retained the language oF the Maxwell theory remain Fixed in historical hindsight as the consensus position of classical physics, and this obscures both the true origins of energy and the separate origins and progress of the First Law oF Thermodynamics.  111  Table of Contents Abstract Table of Contents Introduction Chapter I:  ^  The Nature of Force in ^ 18 Historical Perspective  Chapter II:  Momentum and Living Force in Historical Perspective  37  Chapter III:  The Nature of Heat in Historical Perspective  45  Chapter IV:  The Nature of Electricity in Historical Perspective  51  Chapter V:  Historical Perspectives of the Nature of Light  57  Chapter VI:  Herman Helmholtz and the Conservation of Force  65  Chapter VII: James Clerk Maxwell and the^ 95 Rise of Energy Theory Chapter VIII: Hertz and the Exorcism of Energy Conclusion  ^  Bibliography  ^  117 131  ^  134  iv  Introduction  This essay constitutes its author's attempt to match the great feat of Theseus. My Minotaur, which you will meet in these pages all too often, is the rich and ripe Westerm tradition of mathematical physics in all its recondite glories. My Ariadne has been the philosophical system of Immanuel Kant, from which vantage I have entered the thought oF Graf Hermann von Helmholtz and found my way back. Hopefully the reader will not himself need such aid in order to appreciate my results. As this essay attempts to bring to life the Fullness of Nineteenth Century intellectual life, with special emphasis on "natural philosophy," it will often speak in general terms of concepts mathematical and physical: such loose and general language will undoubtedly occasionally offend the specialist, to whom I apologize in advance.  The precise topic to be addressed below is the history of the idea of energy. Here the temptation is overwhelming to begin with the end: that E=MC2. But that end is incomprehensible without an historical approach. This point was made clear to me when a physicist of my acquaintance, when attention was brought to the fact that the equation implied that energy had mass, denied this equivalence. That physicist, was, of course, incorrect in his assertion. I  Nevertheless, his diffidence about the "equation" is -  understandable. Modern physics gives a number of equations that express the quantity of energy. There are equations For the potential energy of springs, equations For massless particles, equations for the energy of massy particles with velocity, and without, and so on. The commodity of energy is changed from one to another form endlessly, being always "conserved." Yet it never has a single identification as a single thing. It is always the energy of, the property of, something else. Occasionally statements of rather peculiar character are made about it: locating it, for instance, in empty space. The problem of energy, as I would designate it, has not been fully grasped because of the larger concerns involved in the paradoxes of quantum physics as practised today. Against them the paradoxes of energy stand in low relief. Yet historically, the problem of energy came first, and it was not resolved, but rather shunted aside by the epochal events of 1905.  This essay has been written from the standpoint of the Final, evanescent consensus of classical physics. This was described by Lord Kelvin as "the nineteenth century school of the plenum," one ether for electricity, heat, and magnetism."2 One might be forgiven for being sceptical  about the school of plenum aE a Nineteenth Century Formulation. It appears to have guided Kelvin's work From 18513 but it only became important to Helmholtz when he began work on his electric theory, published in 1869.4 Germans, by and large, only began to speculate seriously about the aether in the eighteen eighties and nineties.5 Previously, the hypothesis of forces acting at a distance had proven a useful and stylistically superior alternative.S The aether might better be called the "Turn of the Century School." Undoubtedly it was preparing for a victory unprecedented since Newton as the foundations of a true unified theory of nature when Einstein and Bohr began to publish results that brought the aather into disrepute.7  Yet it would be a mistake of the First magnitude to assume that a new school of physicists had "disproven" the existence of the aether. Edmund Whittaker in his History of the Aether and Electricity published in 1910, still called aether the final explanation of electromagnetic phenomena. "The aether is the solitary tenant of the universe, save for that infinitesmal fraction of space which is occupied by ordinary matter."S Russell McCormmach well expresses the continuin! regret of German physicists of Whittaker's generation at the neglect of serious work on the world aether as late as the end of the World War.1° It should be especially noted that Whittaker  4. provides as full an account of special relativity as of any other theme in his text. The perverse accreditation of the theory to Poincará in no way effects the fullness oF that account and recognition of the theory's significance."  Reasons for the abandonment of aether theories are to be found in profusion in the literature of the philosophy of science. Some of these theories, like Thomas Kuhn's concept of paradigm replacement, quite properly question the degree to which strict logical proof can possibly influence such processes, and indeed question simplistic nutions off proof as wel1.12 Others still place the phenomena of theory replacement beyond the realm of human knowledge by asserting that much scientific change takes place in an unconscious way.13 Social changes are important in science as well, in particular the world wars with their disastrous consequences For the vitality of German thought and science. What all these theories have in common is a reduction in the sense off crisis and loss felt by the exact sciences as a result oF the introduciton of relativity and quantum mechanics in the period often seen as the watershed of change from classical science to modern --the last decade off the Nineteenth Century and the beginning of the Twentieth.14 That break, still makes its presence felt in the modern classroom.  5. A clear division is drawn between classical sciences and "modern." That division, therefore, and its period of onset must be seen as of historical significance. In the classroom where today the scientist is trained, the notion oF two standards of proof is carefully implanted. The classical physics oF mechanics, thermodynamics, and gross electrodynamics are held to be susceptible to clear and unambiguous descriptions of real events. The modern physics (still so-called despite being almost a century old) is presented as operationalism: mere description of what appears to happen. The student's thirst for real explanation is deliberately frustrated in the interests of teaching a new and different kind of science.16  The new science makes use of statements that are known to be untrue.18 Potential functions, written ostensibly to describe reality, assign to empty space the quality of energy. Yet energy is taken to be the mass and speed of a particle, conjointly. How can energy exist in empty space? The obvious answer is that it cannot: this formalism exists only as a necessary means to describe situations in which physics is in fact constrained by the limits of quantum mechanics from describing literally. The example of the energy of the electric field is merely one of many examples of those paradoxes which the veil that quantum mechanical considerations draws over the microscopic imposes.  To penetrate that veil and gain useful insights,  6 modern physicists are taught to maintain a sceptical distance From reality. Electrons and photons are said to be at one time particles, and another vibrations. The electron qua particle is also said to change locations without passing through the intervening space.  Whatever one's views of the successes of modern physics, it is impossible not to note the division drawn between the physics of the Nineteenth Century and that of today. It is drawn by physicists, and has everything to do with the death of the aether. Particle-wave duality derives directly from the abandonment in the sense that the duality would be meaningless if the aether did exist. Less directly, the abandonment of the aether meant the victory of quantum physics. For the aether is a continuous medium impossible to divide into quantized units of energy, distance, and momentum as does quantum mechanics. The aether provided a simple explam.tion for the constancy of the speed of light: the alternative is accepting a bent universe oF perversely nonintuitive character.  It is my belief that the death of the aether was not so much the product of the new physics as provocative of their creation. The aether's decline came First. This is  7. a claim not made easily in the light of the testimony of Lord Kelvin. Yet Kelvin's enthusiasm For the work of Heinrich Hertz, which he took as vindicating the 'Nineteenth Century School' in the Introduction to Hertz's book Electric Waves From which I have already quoted must be appreciated along with his comments in 1900 on "Some Clouds on the Horizon."17 These clouds on the horizons of physics proved to be exactly the problems that brought down classical physics. Yet Kelvin's prescience in his warning arises from his recognition that classical physics had persistently Failed to deal with these clouds. They were continuing problems, and no method of analysis such as had been applied over the last three decades had resolved these conundrums. Unlike the "problems" oF Newton's system which were triumphantly resolved by Laplace, these clouds did not lead to wrong conclusions: they lad to no satisfactory conclusions at all!18 The First cloud, that of the structure oF the aether, had yet to find any explanation that made sense.  It is possible, looking at the history of repeated failed attempts to deal with "Cloud no. 1" --the solidity of the aether through which planets move with no Friction measurable on even an astronomical time frame-- to go back before the turn of even the Nineteenth Century: nine decades of failure. In histories like Whittaker's one gains an inescapeable impression of classical physics less in perpetual triumph over nature than of perpetual crisis. ^Yet this is as much an ex post facto generalization as the conventional picture  3. of the rise of science. History cannot be done from the standpoint of hindsight.  The events of 1905 resonate in our consciousness still. The language of modern science has been invoked repeatedly as an explanation off modern trends in philosophy. Quantum mechanics is acclaimed as confirmation of Eastern mysticism. Special relativity is invoked to support deconstructionist literary theory. In fact, the central theme oF modern science is sometimes taken to be, along with that of modern thought, the collision with the impossibility of knowledge. This is not an argument can make at length here: It is sufficient For my purposes to note the dramatic importance of the connections made between science and modern culture.  I can make no attempt at understanding this contemporary phenomena before the history is securely grounded. No trend of this magnitude, no thought of this importance can possibly be divorced From its history. And that history can only be done by bringing the past into the focus of its own light. We must invoke pure history, and understand Helmholtz as he understood himself, and not as modern scientists are too often content to understand him: as a pure predecessor to modernity whose occasional Failure to exhibit modern concerns brands him as a failure for not understanding what ought properly to have been his own concerns. This is not how to understand how science was done in historic time.  S. It is "history" that at best contents itself with discovering method and opportunity and which attempts to reconstruct motivation from the question, "what do these methods and opportunities mean to me in my professional work?" In the court of true history, motive must also be proven, and the only act which can reconstruct motive arises from asking the question, "what do these methods and observations mean to the historic subject in his professional work?"  For me this means that the only proper approach to 1905 is From 1808, or even farther back. Such an approach only can make sense out of Helmholtz's Conservation of Force, as so many others have failed to do.19 Those thoughts which are properly located in their historic milieu can only be discovered through a conscious and sympathetic history, and are consequently often overlooked in their synthetic totalaity by those who should know better. Proper understanding of Helmholtz's work, for one, is crucial though not central to this work, and this is best understood when one understands the true wellsprings of Helmholtz's thought.  And it is to that point that I have finally come. This essay is concerned with uncovering a hidden flaw in the final consensus, the school of plenum. It is no very well-  1 0.  hidden flaw, having been pointed out as such by Wilhelm Ostwald repeatedly .20 It is the concept of energy. Analysis based on the concept of energy stands at the heart of "Cloud no. 2," --the Equipartition of Energy Theorem in molecular dynamics. We shall also see to what degree it had become a factor in aether theory and so contributed to the First Cloud. Previous historians of the concept of energy have by and large neglected its true origins and its actual fragility as a "science-producing doctrine," as modern philosophy of science is wont to characterize such abstractions. My task is entirely concerned with setting it right through examinations of the work of Helmholtz and Maxwell, and their reconciliation in the work of Heinrich Hertz.  Therefore the reader may well think that much ha.‘; been claimed for a work that ultimately is concerned with a sterile debate in the history of science: semantics in the service of technical controversy. Nothing can be further From the case. The enduring use of the concept of energy as a political and poetic tool underlines its continuing significances: even when that significance delines in actual science. That perplexity arises from the dual problems of the central livortance the Doctrine of the Conservation oF Energy and Mass and of the evanescent concept of energy itself. Whereas  11.  Force and mass are easily picturable abstractions which do things, energy is a property measured by as many quantitites as it has fields of importance, and which is nevertheless said to be of universal importance. although it does nothing. This paper will suggest that the historic origins of energy do not lie in the concept of "conservation of energy." The property that is actually conserved is of far less significance than energy as it was first formulated.  It would be well to linger here on the distinction between modern and Nineteenth Century conceptions of energy. Modern physics takes as its point of departure in understanding energy the First Law of Thermodynamics: the Law of Conservation of Energy. That law is construed as a purely empirical statement. It is distilled from experience that something is conserved, and that something is called energy. Experiment tells us that this "energy" is the movement of molecules in the aggregate. For this reason the First Law is taken as inextricable from the concept of energy today.  Nineteenth Century physics approached the problem very differently. To the discoverers of the First Law, it was a metaphysical requirement, given before experience. By metaphysical, I wish to be understood as including the  I E.  theological certainties which were available to British scientists like Kelvin and James Joule. However, of the various articulations of the truth of Conservation of Force a priori to experience, I shall consider only that of Hermann von Helmholtz in detail, as the most important of all the various statements of that law. More, in finding the basis of this metaphysical certainty, I shall make clear that the distinction between force and energy is not merely verbal confusion. Force, as it was then understood, was a perfectly adequate concept to form the basis of a law which would called the law of conservation of force.  For this reason, the origins of the Nineteenth Century concept of e.nergy are located not in thermodynamics, but in Maxwell's Electromagnetic Theory of Light, which first required the autonomous concept of energy. Thus, most of my "history of energy" will in fact be a prehistory of ener g y. I will demonstrate that in Fact there existed no need For the concept of energy until Maxwell's 1872 Treatise. To Nineteenth Century science, paradoxically for us, the Law of Conservation of Energy could stand without the antecedent concept of energy.  13. That formulation of the concept of energy was undertaken to serve the purposes of an electroma6netic theory that is as dead as the luminiferous aether. The collapse oF that theory, Maxwell's, has much to do with the events of 1905 --the end of Classical science. But it is energy, among a whole list of recondite concepts, that has endured the wreck of the Maxwellian world, and energy which, like a djinn released from its bottle, has wrought such mischief on the understanding of the old physics. It scarcely is central to the story of classical science, but an important player in a story that seems more like the homecoming of the Achaeans than that of Theseus with which I introduced this work. This "energy," which is the energy of Maxwell and especially of Foynting's Theorem pre-eminently, may seem too ignoble for such comparisons. But it is fair to call it, even as it exists today, one of the great enigmas of physics. The other energy, which was originally the force of the Law of Conservation of Force, is much easier to understand.  Following the fate of energy allows us to see a yawning gap between two communities of physicists who thought they were commonly engaged in building physics. The failure of British and German scientists to understand each other  14. is another part of the whole story of the decline of classical physics. But as important as the nature of that gap is the source thereof. Here, too, I must suggest far more than I can argue. We shall see below that the central strands of berman physics were intellectual and philosophical21 while British science appears to have abandoned pretenses to system-building and coherent metaphysical specul1tion based on careful philosophy. This account then suci9ests that an important part in the decline in classical physics is played by the rise of British analytical philosophy and its replacement of Kantian idealism. That story too can only be investigated once my ground is securely laid in the essay before you.  Thus my account is that of the history of energy, and only of energy. A monograph: but of no less importance for that. The connections I see will one day be developed to the point where the influence of natural philosophy on philosophy can be discussed properly and at length. For now it is sufficient to lay practical foundations and observe the interactions of philosophy and science within a narrowly defined problem of physics. That done, the ground will prepared for a larger scale study about, not energy, but philosophy: natural, and otherwise.  15  These promises for the future serve to underline what I regard to be possible cignificances of my work. The text below is concerned with that work: the grafting of the concept of energy on the pre-formed and flourishing concept oF "conservation of Force" which I can claim to have rediscovered. That graft has utterly obscured the true origins of the conservation principle and completely wiped out the memory of the greatest success of the application of Kantian principles* to natural philosophy. That fusion in turn inevitably reinforced and made inassailable a valuable concept of romantic science: energy. Energy came to be a romantic intrusion into a severely classical and coherent science: sabotage of non-trivial consequences •22  IN the course of this account, it may seem to the reader as though Heinrich Hertz is the author's paladin. It is Hertz, after all, who slays the Maxwellian demon and who attempts to expel From physics the concept of energy. He, it seems, clearly recognizes the "threat" oF this concept However, it is my desire, despite occasional rhetorical excesses, to point out that Hertz's concern is with the disutility of energy: its presence in mechanics is mystification. His attempt to discard energy (and, it must be added, Force) in favour of purely mechanical causative mechanisms is a pure vindication of an older style of physics. That  If by Kantian I am allowed a long stretch to Helmholtz's interpretation thereof.  IS. vindication, contra Kelvin, is evidence in itself of the and diversity of opinion and lack of mutual understanding that flourished in classical physics and which becomes visible through careful historical study. The themes of alienation of dferman from British science, of a three-fold division in science between Kantian idealism, Scottish empiricism, and Nineteenth Century romanticism are brought together in this account of the supplanting of the force in the "conservation of force" and its subsequent eviction.  *Such divisions are scarcely news, of course, but the depth of this one, coming in an unsuspected area where unanimity was thought to reign is itself significant.  17.  Endnotes, pp.  1. 2. 3. 4.  French, Special Relativity, pg. 1. Hertz, Electric Waves, pg. xv. Smith and Wise, EnerLy and Empire, pg. 376. See the relevant sections of Archibald, or for a less technical though still difficult discussion, Buchwald's "The Background to Heinrich Hertz's Researches in Electrodynamics S.^Ibid. 6. Archibald, Ibid. 7. McCormmach, Night Thoughts oF a Classical Physicist, pp. 99-103. 8. Whittaker, History of Theories of the Aether and Electricity, London: Longman, Greens, and Co, 1910. 9. Ibid. pg. 1. 10^McCormmach, ibid. 11. Whittaker, dg. 444. 12. Thomas S. Kuhn, Structures of Scientific Revolutions, Chicago: University of Chicago tress, 1970. 13. See Bellone, Paper World, and Elkana's "Helmholtz's Kraft: an illustration of Concepts in Flux." 14. Hesse, Forces and Fields, pg. 259. 15. Resnick and Halliday, Basic Concepts in Relativity and Early Quantum Theory, pg. 209. 16. Larmor, Electrodynamics, pg. 79. 17. Bellone, pp. 178-180. 18. See for instance Beichler's Hyperspace Models of the Aether in America" for an example of an effort to put lack of coherence to work. 19. Conclusions very similar to mine were ?resented in Fullenwinder, "Helmholtz: The Problem of Kantian Influence." 20. Jungnickel, Intellectual Mastery of Nature, vol. 2, pp. pp. 219, 223-225. 21. Elkana, Discovery of the Conservation of Energy, Introduction. 22. Stephen Brush, "The Chimerical Cat: Philosophy of Quantum Mechanics in Historical Perspective," although categorizing individuals (particularly Hertz) in a fashion opposite to my conclusions develops the notion of competing realist and romanticist traditions in physics in a way well worth considering. My own usage, "classicist" versus "romanticist" is drawn from literary usage and as applied to physics is rather vague. It seems tome, ho4vr, that vagueness is no discdvantage in this sort of metaphorical borrowing. To the degree that romanticism is an imprecise term in literature, it will retain that imprecision in physics! My other alternative to romanticism, "Kantian idealism," is not intended to set up a general dichotomy, but rather has a very specific meaning peculiar to physics.  1 3.  Chapter 1  The Nature of Force in Historical Perspective  The first part of this work will follow the plan of developing several subjects important in the history of physics to the points which they reached in the crucial year of 1847 the year of the publication of Helmholtz's Cie Erhaltung  der Kraft. In order to clarify the issues at stake, I shall first briefly discuss significant elements of modern understandings of these realms of physics. Upon each of these concepts: force: momentum: energy: heat: electricity; and light; Helmholtz's revelations had a central and concept-transforming significance. Thus these chapters will often contain my comments on the differences between modern and Nineteenth Century conceptualizations. These are the changes I wish to highlight as the necessary consequences of the "Concept of the Conservation of Force." As will be seen, some of those consequences are not those assumed by modern physicists in their explanations of the past. They are the reasons, most simply, that the concept of Conservation of Force is not the Concept of Conservation of Energy.  19. What, then, is force? The simple answer is that it is a necessary concept. Human discourse about the physical world evidently requires the concept, although its meaning is protean. The historical account of force is one of a shrinking role as its function as the cause of mutability in the world of nature is more tightly defined: in the course of this shrinking there occurred a brief period in which the concept of energy could flourish.  Modern physics takes force, along with matter, and the velocity and acceleration of matter, to be the essential ingredients in dynamics, the science of real objects in motion. By real I mean objects possessed of mass, and therefore within the realm of human experience. For good reasons and with valuable results, the science of force has been combined with the mathematics of abstract motion of massless points, lines and volumes (kinematics) to comprise the field of dynamics. The science of dynamics is summarized by the three laws of motion.  I. An object at rest or in constant motion in a straight path tends to remain at rest or in motion unless acted upon by an outside force. Force is equal to the mass of the object upon which the force acts multiplied by the acceleration of the object produced by that force: F=MA. For every force there is an equal and opposite reaction.1  20. These three laws contain within themselves the axioms of modern dynamics which concern the concept of force. First, note that the first law makes the claim that no change occurs in the action of an abject unless a force acts on it. It also abolishes the distinction between being stationary and uniform linear motion. No experiment, it correctly claims, can distinguish between the two states. The linear element of this law is important too: spinning a cord about one's head requires a constant force, since it is nonlinear motion, and therefore accelerated. Motion in this definition is composed both of abstract speed and direction, and a change in one of these is equivalent to a change in the other, in the sense that either requires a force.  The second law may be taken to assert that wherever z.omething is bein accelerated, a force is acting. Thus it is natural to talk about the force of gravity when an object is Falling towards the earth at ever increasing speed. This rule can also be taken as defining mass. Note that in almost every interaction of a weighty object with a gravitational field* the force is a product of the mass and the acceleration due to gravity, g. This product, separate and distinct From mass, is known as weight.  The phrase "gravitational field" is intuitively obvious in modern physics, but its origin is of tremendous importance historically. It does not need to be understood here, even if I will shortly consider its history in some detail.  21. The third law is used to understand situations of forces acting. It is an interesting assertion and one of non-obvious consequences. It is taken to assert in dynamics that no change can occur that is not the measured effect of a set cause. The results of actions are always in proportion to the action. Confined to dynamics, this is the law of cause and effect. When it is universalized through the global application of the mechanical model of nature, it becomes the law of Conservation of Force. For no cause can produce an effect (no Force can produce a result) that is not in strict proportion to that cause. Except For the original application of force that bean the universe, all resultant forces occur in pairs which cancel out.  These laws of motion are the products off a long struggle with an extremely complicated problem: what happens when one moving object collides with another. In order to explain this, these laws require a formality of language about direction. Two billiard balls colliding head on are very different From one billiard ball overtaking another and colliding with it, no matter that their speeds are identical in the two cases.  The third lavv demonstrates that Forces are distinguished  22. by direction. Some Forces are opposite to each other. Indeed, since forces are distinguished by acceleration, and since objects can accelerate in three orthogonal directions in three-dimensional space, it follows that a force must be described by not only its magnitude, but its direction. The same is true of quantities composed of velocity and distance: they are known together as vectorial quantities.  With the modern scientific understanding of force in hand, it is now dossible to explore other, historical meaninbs of force. Force has its origins in Greek philosophy as the source of mutability in a world in which there can be observed a puzzling mixture of mutability and eternal recurrence. As has been observed, modern dynamics describes force as the cause of change in motion. Thus it can properly be understood as the cause of change. The modern conception has moved very little from this Greek conception of force as the "natural power." What has changed, more or less, is the realm in which purely natural philosophy has sought a unitary explanation of change in the form of cause.1 Whereas For Aristotle force had to be the cause and explanation for the movement of stones, the growth of rabbits, and the wars of men, modern physics confines its role to the world of mechanics. Yet where philosophers can be Found who claim  23. that all activity in nature reduces to mechanical efFects, the two positions are not far different.  In another respect modern times has seen curious echoes of Greek thoughts. A rival school to Aristotle's dispute his contention that matter was continuous and infinitely divisable, proclaiming that instead matter was nucleated into atoms surrounded by the absolute emptiness of the void. The mediating power, or force, that acted across that void in order to cause change they either called an influence or else invoked a subtle aether which pervaded the universe and which communicated forces. In Aristotle's system, on the other hand, "impetus," that kind of force which produces violent motion, can be promulgated only by direct contact:. between mover and moved.  In no way does this discussion definitely enumerate all the Creek theories of force. What it does do is underline the amazing precocity with which the Greeks settled on issues and terms that would remain in dispute until Helmholtz's day and beyond.  With Galileo, however, the nature of philosophical consideration of nature bean to change, and the terms of the debate provide  24. a continuity From Greek times to modern that underlines the permanence of some themes of natural philosophy that is overlooked in some histories of the rise of science. Historical understanding requires careful attention to the evolving concept of force as the cause of change.  Galileo's concerns were set for him by his interest in the trajectories of Freely-moving objects as much as by his anti-Aristotelian Frame of mind. No careful writer today would speak of his "method" without attempting a discussion of a theory of scientific method, which is not my purpose here. But it is nevertheless not unfair to speak of Galileo as highly empirical in prejudice. Experiment and demonstration were crucial to his work. A set oF experiments involving a ball rolling on a variably-inclined plane stands at the basis of his dynamics, for instance. He left behind the distinct literary impression of being an atomist, that is, of believing that nothing existed in nature but those small and massy, homogenous corpuscles of breek atomism. Modern scientists admire Galileo for his objective materialism.But this is over-simplifying the case. Galileo was willing to advance hypotheses less than Fully supported by the Facts, and his famous assertion that the Earth moved was one of those: Galileo never published a valid proof of his most famous result. Knowing this prepares us to confront some peculiar and inoomplete concepts in Galileo's vocabulary.  25. Galileo believed that there are two kinds of motion. The first is "natural motion," which he described as the motion of a free object in nature. This was understood as free inertial movement in the horizontal plane. But Galileo noted that the horizontal plane is only apparently a plane: in fact it is the surface of a sphere, to wit, the Earth. Movement on the surface of the Earth is in fact circular motion. Thus inertial moment and the orbits of the planets around the Sun 4re squally natural motions. The second sort of motion, ordinary, occurs when one object strikes another and compel:, it to move.  Natural motion and forced motions are independent, and act upon objects independently. This approach allowed Galileo to describe the ballistics of not only objects in free fall but those falling with a horizontal momentum. He was also able to show certain results for an object moving freely upwards. However, in his system the "gravitas" or heaviness of an object A  had nothing to do with its natural downwards motion."  As noted, Galileo was able to measure the rate of Free fall and produce a remakeable result. In equation form, it goes like this: define the distance a free falling object descends in one unit of time, s. S is related to the distance Fallen in an arbitrary time (t) 0 according to 0=St2. In modified form this equation is the modern one describing  26. the rate of fall of an object due to gravity. For this reason it can look to moderns as though Galileo's contribution was to the science of force, or dynamics. And while this is true, it is not what Galileo thought he had accomplished, since to him the natural motion of an object was not something that had to be c...usdS by a Force.  Of a generation younger than Galileo's, Rene Descartes was also the most significant of his successors. Descartes is best known today as the founder of modern epistemology. Unflinching scepticism revealed to him certain things known prior to experience: that he existed, as did God, that there were two realms of existence, one purely material, the res extensa, and one purely spiritual, the res cogitans. The latter could have no effect on the Former, and the reverse. The world of material is coextensive with space: everywhere that there is space, there is also matter. Descartes' particular brand of materialism required that effects, or forces, not be transmitted through space by influences or attractions, if influences and attractions are understood as non-material. The alternative is that effects that appear to act across space are actually mediated by a material substance. It also denied the division between natural motion and Forced motion insisted upon by Galileo.S For this reason Descartes Felt a need to explain the phenomena of gravity, and the  97.  circular motion of the planets, which Descartes' new system stated must be "forced" by some influence.  Descartes' solution to this dilemma was his assertion of the identity of space and matter. A subtle and indetectible matter pervades "empty" space 7 and conducts pressures that constitute the means of interaction between the source of "force" and affected object. This universal matter is indetectible itself to human senses, although its pressions are manifest as light, heat, and so on. It is in constant agitation: whirled into a vortex, the centre oF the maelstrom is manifest as the Sun. The vortex moves the solar bodies in their orbits and accounts for both light and the apparent action of gravitational force. (Which is actually the push of the vortex, like the light of the Sun.)  Descartes strove to create a universal philosophical system, and one of the problems that interested him was dynamics. The problem of the physics of collision was an important one, inasmuch as Descartes was committed to a mechanical philosophy in which every interaction in res extensa must be understood as the product of material objects  in motion by contact.8 For this reason if no other, Descartes made an attempt to analyze the problem of collision. His  28. system already told him that objects are defined by extensionS and as a result he attempted to define mass in spatial terms, neglecting the distinction between mass and weight. These considerations doomed Descartes' system from the beginning .10  Descartes' dispensing with the distinction between natural motion and his astronomical system, which assigned the planets the characteristics of normal matter (along with Kepler's similar steps) suggested to the mind of Isaac Newton the need to explain the movement of the planets. He did not regard Descartes' explanation as useful, and his own search for an alternative was the first concern in developing the Newtonian Mechanics. That such an explanation might involve attributing to each planet a gravity like that associated with the air was no great leap at the time. After all, even in the Cartesian system all the planets whirled along in the same vortex and were therefore exposed to the "push" oF the vortex's "gravity." Newton's account, the one that shaped the future oF physics* called for a universal extension of these gravities out to the infinite reaches of space and assigned each planet gravity in accordance with its mass. This was new. The Newtonian laws of motion required that gravity be understood as force: Galileo's equation was now understood as a relationship  *Still at this time called natural philosophy. The Nineteenth Century name-change, often taken as mere semantics (or, worse, the separation of mathematical from physical research) constituted actually the separation of the philosophical Faculty From the scientific.  29. describing the action oF the force of gravity, and it extended naturally to explain the motion of the moon by assuming that it was actually an inverse-square force law in disguise.  Newton's laws of motion, to a modern physicist given to idolatry, are the perfect laws of motion as given at the head of this chapter. This is true in an algebraic sense, but the assertion must be slightly modified when due attention i. paid to Newton's own formulations, which have been modified in subtle but important ways. The laws as stated here can be used to produce and to understand Newton's results: they fall short of a historical understanding. The most important example if these modifications is that of the second law. To a modern physicist, PA. A, the acceleration of an object, is also sometimes written as the second derivative of the distance travelled. (i.e. it is the rate of change of the rate of change of the distance travelled.) A=d2X/dT2. Newton, however, wrote the second law F=(mv)'. In Newton's parlance this is identical to the first derivative of momentum, my. His formulation thus takes "the quantity of motion" to be equal to the momentum of an object and builds dynamics on this basis. This Formulation makes the mass in the expression plastic, an implication edited out by Leonhard Euler's reformulation in the Eighteenth Century which gave us the modern form off the equations.  30.  This subtle distinction is, fortunately, not so misleading as to present any great difficulties. In this respect it is distinctly unlike the Law of Conservation oF Force.  For our purposes the most important aspect of Isaac Newton's planetary system is his final law of gravitational force, which stated that massy objects situated at a distance from each other attract each other with a force proportional to the products of their mass and inversely proportional to the distance squared. This law leaves open the cause of gravity itself: how does it reach across space? Newton begged the question. Over time attempts were made to resurrect versions of Descartes' subtle matter and pressions to account For this attraction. The major stream of post-Newtonian physics, however, accepted this law as requiring that forces be propagated across space instantaneously as a result of the properties of either space itself or of hard massy objects.11 Not least among Newton's accomplishments was the definition of masslE, namely as the "volume and density conjointly." Lack of such a definition sank Descartes, and pace the thoughtless criticism of some later writers13 it is noteworthy that Newton's flawed definition was not only an improvement, but the best that those same Nineteenth Century writers could do!14  31. Newton's laws were reformulated and reinterpreted in the middle of the Eighteenth Century, assuming their modern Form. This was done in part because contemporary mathematicians had come to a far fuller commitment to the language of that branch of mathematics known as fluxions or calculus which deals with changes and rates of changes in mathematics. Applied to the equations of physics, calculus suggested new ways of looking at the work oF Newton and his predecessors. Thus, Galileo's equation of the rate of fall whose reinterpretation had already led Newton to his equation of free fall and thence to the inverse-square law11: was reinterpreted again. Now it became a generalized equation applying to any object under the effect of constant acceleration (constant force) which states that the distance travelled d is the product of the time taken to travel it t and the acceleration a so that d=3at2. This example of the generalizing of the specific situation of a Falling object into the abstract language of motion under the influence of constant acceleration is a clear example of what lay ahead For mechanics: the resort to a generalization so complete that it deliberately made no room for geometrical intuition and appeals to physical reality to account for physics. In the words of J.L. Lagrange, "My physics will be without figures, diagrammes, appeals to intuition or geometry."16*  Author's translation.  32. It is sometimes difficult to grasp just what this programme meant to those who employed it. Probably the simplest way of speaking about the method is to say that it discarded the older notion of geometric links between the magnitude and direction of a quantity without substituting for that link the modern conception of the vector. But this implication of the programme of the Analytical Mechanists was buried in their generalized desire For abstraction and generalization. Their methods, therefore, are like the methods of the high wire artist of the "old school." In pursuit oF elegance they abandoned the safety-net without adopting instead the modern safety-belt and instead exposed their works to extravagant danger of the sort that arises from forgetting to mind direction.^Laplace was the least vectorial of natural philosophers, and after him the swing back to vector notation and practicality began.  But why did the Analytical Mechanists dispose of the older Newtonian concern with direction? The answer is to be found in a strand of Humean thought among the French Enlightenment natural philosophers. 18 In the spirit of that writer's concerns, the school of analytical mechanists tried to discard the concept of force from physics in pursuit of an approach of mechanical interractions that was entirely descriptive. This approach, it was hoped, would sufficiently  33. describe the results of any interaction in terms that did not take into account the highly problematic notion oF a force that "causes" change.  Such a priority produced the novel concept of constraints.19 A number of requirements are known to apply to a physical interaction. For example, momentum and "energy" must be conserved. A number oF other constraints also exist and are laid out in great detail by Laplace in his Celestial Mechanics.E0 These constraints together fully govern possible outcomes of dynamic events and allow the Formulation of an equation of motion.21 In the hands of Laplace or Lagrange, this equation contains no explicit reference to Force and is thus free oF the Faulty assumption of causality.  The new method had some conspicuous successes. In particular, the mysterious slowing of the outer planets previously attributed to frictional effects proved in fact to be a normal process in the continuing and stable succession of the planets. Reaching this conclusion using Newton's methods was simply not possible, and Newton himself had attributed the reversal of this effect, which was necessary in order that even the Biblical time scale of the universe be scientifically possible, to the mysterious providence of God. Laplace's results proved the error of this assumption and suggested that even iF Friction slowed the movements of the planets, it did so on a timescale vaster than the days of men. "There is no place For God in my hypothesis," he is Frequently quoted as saying.2"1  34. It also had Failures. One of Laplace's more celebrated proofs of this period was his demonstration that gravity was instantaneously felt across distance by objects. Contiguous action through a medium would seem to call for a time-lag in propagation, and this result more or less dealt a deathblow to "aether" theories of oravitation.23 Aether theories continued to show vitality in dealing with magnetism, light, and electricity (and later even heat) which had been reduced to inverse square laws very similar in form to that of gravity. This fact presented an additional difficulty For the enterprise L,f unification of these disparate strands of the weave of physics, the compelling need for which began to become evident in the years before 1847. In the event, Laplace was mistaken, but the implications of this fact was ultimately only first understood by Einstein.  At the same time as the flourishing of the school of analytical mechanics, German philosophy built up its own reaction to British empiricism. For when Immanuel Kant subjected the pure act of reason itself to critical critique (Der Kritik  ^  der relnen Vernunft) this Prussian philosopher  claimed to discover that there must be grounds and reasons Co make possible the very act of empirical thought. There must be knowledge available to the mind before any experience  was even possible. These categories, the so-called synthetic a prioris, we. are concerned with only to the degree that we understand that the principle of causality was among them. Kant united the law of cause and effect with the Newtonian force law, as did the French analytical mechanists. But his emphasis reversed the priority of the French, making Force the very centre of his thinking on natural philosophy. For it is known before experience, known in a way that no other thing within the realm of natural philosophy could be known. 24 This return of emphasis to force also brings us to the point at which the centrepiece of this paper, the law of conservation of force, is formed, and thus brings to an end the discussion of the history of force. But to simply state the nature of force as a concept in the mind of Hermann Helmholtz in 1847 it will be necessary to understand the various physical concepts which were at that time still intermingled with "force" as an autonomous concept.  36. Endnotes , pp. 18-32E..  1.^This set of laws of motion will be recognized as those referred to by most physicists as a version of "Newton's Laws." I withhold recognition of them as such out of a desire to distinguish Newton's efforts From Euler's reformulation, upon which I shall comment later. The physicist will also note that this version oF Newton's Second Law is farther from the spirit of Newton's Formulation than that accepted by modern physics. I have, therefore, misrepresented the fidelity of modern physics to the Newtonian tradition. My intention in doing so, however, was purely to provide a context in which to discuss Euler's reformulation. To discuss this important subject without the simple distinction here drawn would require a direct entry into the difference between Newton's and Euler's ideas of calculus. (Upon which cf. Westfall's Never at Rest) Such an endeavour would unduly Frustrate the laymen at whom this work is aimed. I do, however, apologize to the physics community For the intentional misrepresentation of the efforts of their broadest majority. In my own defence, I would add that that defence often does not apply to engineering pedagogues. 2.^Collingwood, Idea of Nature, pp. 50-75. 3. See Brush, Abstract, or Bellone, Introduction. Actually the idea of bialileo as pioneer of a Fairly empiricist and antimetaphysical precursor to modern science is a near ubiquitous trope in modern literature relating to science in early modern times. 4. Wastfall, Force in Newton's Physics, pg. 30. 5. Ibid. pg. 8. 6. Ibid. pg. 59. 7. Sloan, "Descartes and the Sceptics," pg. 24. Also see Descartes, System of the World, passim. 8. Ibid. 9. Descartes, Meditations, pg. 110. 10. Westfall, Force, pg. 69. 11. Schofield, pp. 91-191. 12. Newton, Principia, pg. 1. 1.^Thomson and Tait, Natural Philosophy, pg. 220. 14. Ibid. 15. Westfall, Never at Rest, pg. 151. 16. Lagrange, Mecanique Analytique, pg. 1. 17. Laplace, Celestial Mechanics, pg. 40, For example. 18. Hankins, pg. 4. 19. Lagrange, vol. 2, pg. 6. 20. Laplace, Book I, passim. 21. Ibid. pg. 120. 22.^Ro6er Hahn, "Laplace and the Mechanistic Universe," pg. 256. Whittaker, pg. 233. 24.^All quite clearly explained by Kant in Critique oF Pure Reason.  37 Chapter II Momentum and Living Force in Historical Perspective  This chapter is, in essence, the history of conservationi:= (Conservatism?) Modern physics places special emphasis on two quantities which are said to be conserved. First of these is momentum, which is a property inseparably associated with the motion of objects and which is equal quantitiatively to the mass of the object multiplied by its velocity. This quantity is therefore a vectorial one: when two marbles collide, each proceeding in opposite directions with equal masses and equal (but opposite) speeds and they come to a dead stop, momentum is conserved. For the two momenta are equal and opposite to each other, and cancel out. Sy the same token, the two marbles might also strike and be propelled away from the collision in the reverse track, each with the identical momentum that the other had just possessed: momentum is conserved. When two marbles collide travelling at angles oblique or obtuse they act exactly as do marbles colliding head on: the "parts of the momentum" at richt angles to the collision are unaffected. So when two marbles come flying across the ring at converging angles  *Until 1847 these laws were usually known as preservation laws. cf . Laplace, Celestial Mechanics. "Preservation," it seems to me, has a distinctly less global and active ring than conservation, although this may be mere prejudice.  38. and collide inelastically (perhaps they have been covered in glue) then, having Followed a path like the legs of the divider, they then proceed together us though travelling along the stem of the divider. Momentum, as a property of three-dimensional space, has three components, and these components are incommensurable with each other. This is enough to understand how momentum can be conserved in a world of constant starting and stopping.  The other conservation principle to which modern physics has frequent recourse is that of the conservation of energy. Energy is a quantity whose total amount can neither increase nor diminish. Physical events can only change its nature, not its quantity. The energy produced by burning a barrel of oil is exactly sufficient to reconstruct all the combusted molecules of oil out oF carbon dioxide. Modern physics attempts to reduce all energy to the velocity of particles according to the formula Energy=1/2mv2. This term is not a vector quantity. When two marbles moving at high speed collide and stop, momentum is conserved, but kinetic energy is not. Modern physics looks For heat and other forms of energy in such a collision and finds it. But before modern laboratories could measure these other forms oF energy, its conservation was rather mysterious and could be counted upon only when one was dealing ^with a single isolated particle.  39. In dynamics the statement that an object will be thrown up again to the height from which it fell by the expenditure of the energy of its descent represents the whole of the law of conservation of energy.' It is written mathematically that given height h, mass m, acceleration due to gravity, g, and velocity v, mgh=kmv2. At one time, and for very good reason, the sum on the left was written with the distance the object falls in the First time unit of falling substituted For g, a number one-half of g. The introduction of the "%" factor led to bitter controversy. What absurdity leads one to thing that half a quantity is conserved? The new Formulation results in this equation telling us how gravity works on a Falling object. But it does not tell us what speed an object gains with each second, nor what happens when the object strikes something, or even what it does to a support upon which it rests. What it tells us is important: the whole subject matter of the "method of energetics." Energetics allows physicists to make statements about the constraints on physical events that depend not on knowing what happened, but on what must happen in their wake. While this is a power shared to some degree by the related concept oF momentum, it is nowhere clearer than with the powerful notion of "kinetic energy."  'Of course, dynamics also makes use of the fact that in "perfect" collisions no energy is transformed into heat and so, and therefore that the sums of energy before and after must be ecival to that before. In calculations made on two-dimensional surfaces the potential energy expression does not even enter it. thus this statement might be taken as hyperbole. Or not.  40. Here, as elsewhere, Rene Descartes is at the threshold of modernity. Descartes' distinction between the res cogitans and res extensa, his radical materialism, could make no place for the introduction of new motion into the world once the Creation was done and the laws of cause and effect reigned supreme. God had set the clockwork in motion, and his intervention in the wcrld by creating motion was an unnecessary intervention thereafter save for the purpose of miracle. Just what Descartes meant by "motion" is a little vague, but it seems clear that usually he intended for it the term mv.1 Descartes' materialism looks in this context a great deal like the conservation of momentum. That conservation of motion, Descartes claimed, showed that an object could be lifted to its original height after falling a certain distance by the total amount of force impressed on it, just like a clock pendulum.  The mathematical tools Descartes employed were far superior to those of Galileo, and with them he penetrated Further. Nevertheless, in this case he was led into error. The correct Formulation of the "conservation of Force" problem is, in modern terms, the above mentioned conservation off kinetic energy equation. Descartes was oblivious to the value oF the expression 1/2mv2 in modern dynamics: but then, he scarcely needed it for hie purposes. Hiu mathematical error was detectible only by thus who followed confidently where he pioneered.  41. Reformulating the argument and creating the concept of the living force, or vis viva, mvq was a post-Cartesian departure soon enough made. The innovator, G.W.F. Leibniz, dis-covered. in the words of Christiaan Huyghens, that:  Motive forces are in ratio composed, not of bodies and of the speeds as such (an garters's) but of the bodies and off the heights which produce speed, that is, oF oF the bodies and of the square of the speeds.  In effect, Leibniz had returned to Gelileo's equation of free fall. That equation shows that the relation of Force to velocity is not direct, but to the square off the velocity. For this reason Leibniz took the definitive measure of the force inherent in an object to be the total mv2. This quantity was only conserved in ideal situations: Friction dissipated it. Nevertheless, the conservation of vis viva was of great importance in solving problems oF mechanics. Newton's dynamics made no use of it, Finding the conservation of momentum sufficient for its purposes. Newton's metaphysics, which were similar to Descartes' in the role it elicited God also  Emlid  the conservation of momentum as an important testimony  to the original perfection of God's creation, even if his system required continuing Divine intervantion.2 What Newton would have made of the conservation of vis viva erected ass basis off a metaphysical situation is anyone's guess.  The toll of conservation was therefore inherited by the next generation of physicists little used. These Analytical Mechanists are seen today as the originators of a conceptually revolutionary extension of the conservation of vi s viva. The specific problem dealt with was the inclination of objects placed in empty space to change velocity when left to themselves. Newton's physics provides a simple tool for dealing with this "problem:" the law of gravitational attraction. Abjuring this for concern with the causal nature of the force law, the school of the Mechanists arrived at an alternate formulation. An equation was written describing the potential of a location in space. This potential, or power, was realized into acceleration  when an object was placed at that location. Algebraically identical to Newton's Force law, the method had its advantages in complicated situations and avoided talking about force. The method was also independent of directional considerations.  Fifty years later, a trio of British physicists would call this the method of fields of potential energy. Sloppy attributions4 have led many to assume that potential energy and fields were invented by the men who invented the method oF potentials and has therefore obscured the fundamental metaphysical breakthrough that first stated as simple fact that energy exists in space at locations empty of matter. The true and original source of this breakthrough is covered later. Laplace and Lagrange meant this method and equation  43.  equation only to be a superior way of talking about motion supposedly due to gravity without employing the Newtonian equation* which to them implied as prior necessity the "naive' view that all effects are caused.  This account of the history of energy and momentum thus closes at a date at which the concept of energy had yet to appear as a =ingle thing, being still broken up into vis viva and the disparate concepts of heat, light and electricity to be considered below, and before potential energy was even thought of.  That is, Force=-GMm/R2, where , is the universal constant of gravity, and M and m the two masses attracting each other, and R the distance between them. The "-" sign establishes direction, though not as well as more technical notation does.  44.  Endnotes, pp. 37-43.  Westfall, Force, pg. 70. 1. Ibid. pg. 149. 2. Hahn, pg. 239. 3. Hesse, pg. 198. 4. 5.^Schofield, pg. 29.  Chapter III^  45.  The Nature of Heat in Historical Perspective Modern theory describes heat as a subjective experience caused by the reality of a large number of molecules moving more or less freely in random displacement. Molecules of solids vibrate in lattices whose rigid interconnections prevent the solid from breaking apart. Fluid molecules are less rigidly connected, but still have some connection to restrain their vibrations. tiases move more Freely still, and heat in gases is virtually indistinguishable from agitation. The interactions of these molecules in movement involve a complicated system oF collisions which, according to modern physics, cannot (even theoretically) be understood analytically. Only the application of statistics can produce a probabilistic picture of the microscopic world of gaseous or even solid matter.  Because the world of the molecule is statistically indeterminate, it makes sense to speak the language off "heat." Heat may not exist as such, but there is no alternative but to use methods built up to analyze the actions off heat-as-Fluid which have proven useful on the macroscopic level. Among the things modern scientists "know" about heat is that it  46. that it flows in a Fashion analogous to water or electric current; that it represents a Form of energy, and can therefore neither be created nor destroyed; that heat can only be converted into other kinds of energy by "pumping" it From a high temperature to a lower-temperature region; and that heat can only be pumped up to a higher temperature region by the use of energy.  The concept of temperature, too, requires a modern and technical definition. The reader will here note an implicit analaogy between temperature and the height of Fluids -For just as Fluids Flow from a higher to a lower place, doing work along the way, so does heat flow from high to low temperature producing work. The magnitude of temperature is the height of the heat, and is therefore visualized by the atomist as bin' in Fact a region in which the molecules are speeding about at a certain average rate.  Having commented on the present understanding of heat and temperature it remains to put them in historical perspective. This will require separate discussions oF the problems oF physical and animal heat. For unlike the generation of Galileo, which began to move towards the modern understanding of dynamics once the problem oF animal and natural motion were separated, modern thermodynamics arose when animal and physical heat were united through the paradigm oF combustion.  47 The Eighteenth Century had two major and competing ways off thinking about heat. The First was the atomist position, which differs only subtly from the modern.  1  In this heat  is only an abstract way oF talking about the multitudinous movements oF minute corpuscles. The second held heat to be a subtle Fluid,2 whose entry and exit from combusting and growing things led to the eFFects experienced as haat. Rather than trace an at best confused history of these two traditions and argue about their relative signiFicance, I shall confine myselF to comment on the sticking points Setween them. First of all, the corpuscularists oFten objectec to the philosophical dualism inherent in accepting the Fluid oF caloric. Caloric, like atoms, was an hypothesis proposed to save the phenomena.^And why make two hypotheses when one would do?2 This Ockhamite prejudice had no normative Force, but the prohibition against multiplying hypotheses is an important guiding principle oF science all the same.  In contradiction to the corpuscularists, those who used caloric models oF subtle Fluids found that it Far better modelled the actual phenomena, better explaining how heat Flowed. Without the principle of conservation of energy and statistical dynamics, or even the knowledge of their necessity, caloric principles were the only ones to produce  48. even limited results. The caloric research programme found the analogy with fluid flow deeply productive: on the other hand, it was a very strange fluid that had no, or even negative, weight, as experiment indicated For caloric. As a result oF these experiments, caloric came to be regarded as a weiGhtless Fluid, and thus began to move towards an abstraction so complete as to be indistinguishable From obsolescence.  Up to 1814* Chemistry continued to be done on the basis of the assumption oF the reality oF caloric.4 With continuing progress in the Field oF steam-driven engines caloric-based theory entered the realm oF physics through engineering. the correlation between heat and the work done by engines could still be understood in terms off caloric. ^So could the motion of heat from one temperature to another, which was central to the new theory of engines of Carnot the Younger.3 However, one can see in the evolution oF a massless and insubstantial caloric transformable into mechanical effect the dematerialization oF caloric into a state of matter: the kinetic theory oF heat making its return, but now in a way that could still embrace the abstract concept oF heat as an activity oF matter.  '.-The significance of the date is just what one might think. The Bourbon restoration led to the replacement of an Imperialera scientiFic community by a new and royalist generation of scientists like Fourier, Ampere, and the Catholic Cauchy. Here again grand politics became involved in the most basic way in a scientific revolution.  49. It was in acceptance oF the kinetic theory of heat that Helmholtz formulated his principle of conservation of force, but he did so with reference to the problem of animal heat. Animal heat was then an intractable issue. For once chemists became able to measure the temperature of the combustion of foodstuffs and understand the role of temperature in thermodynamic theory, they were unable to account for the absence of high combustion temperature in the human metabolism. For this reason the kinetic theory of heat was less firmly founded in animal biology than elsewhere. However, Helmholtz essentially ignored these issues in his science. Actual understanding of the phenomena of animal heat was only achieved by Liebig later in the century. In the meantime Helmholtz required the linking of animal and mechanical heat in order to speak of the universality of the conservation of force. For his version of that law required that it not be violated, whatsoever the circumstance. It was the unbreakable law that heat must always derive from work done by some agent, From some force, and must be fully convertible to the same. This a priori certainty led to the modern and complicated theory of metabolism which has arisen as from the necessity oF proper explanation.  SO.  Endnotes, pp. 45-49.  1. Schofield, pg. 73. 2. Stillman Drake, Schofield Review. S.^Smith and Wise, pg. 288. 4.^Elkana, Discovery, pg. 56.  Chapter IV  ^  5 1.  The Nature of Electricity in Ristorical ierspective  Modern physics states that electricity is a "force" in kind rather like gravity. It inheres uniquely to subatomic particles called electrons and protons. OF the two, the theory of the electron is more important, since electrons are more mobile. The number of electrons present in an object defines its electric charge. IF there are more electrons than protons, the object is negatively charged. Only a Few electrons need to be displaced for there to be a notable electric charge detected in a small body. By the same token, since electrons are essential to the binding action that turns atoms into molecules, even chemical reactions can produce free electrons. This is the basis of the action of batteries. Protons attract electrons, and repel each other: opposites attract and likes repel.  Matter can be divided into two kinds with respect to their responses to electricity. The first kind are dielectrics, which resist the movement of electricity, the second conductors, which present little resistance. Dielectrics can hold electric charge and induce it in other dielectrics: this is understood  EP. to be an example of induction. The forces produced by electric charges act only on other electric charges, attracting or repelling. Thus when an uncharged insulator is brought up to a charged one, the electrons of the uncharged one will  be  repelled and redistribute themselves, producing  an electric charge on the "uncharge" insulator. This phenomena also occurs with electric currents and magnetic fields, and is called in general induction.  In conductors, electrons can move freely from places of higher potentials to lower. As a result, they redistribute themselves quickly to cancel out the effects of a charge and carry electric currents from high potential to lower potential areas. Currents themselves exert forces on each other and produce magnetic fields. Potential here is exactly analogous to temperature. Every quantity of stored electric charge has a potential associated with it, whether in a battery or a capacitor. More confusingly, every electron contributes to the potential oF every point around it, producing in its vicinity a "potential Field." Thus an electron placed close to a huge mass of electrons will have a very low (that is, high negative) potential due to the nearby electrons' potential Fields. Left to itself it will flow rapidly away. Note that this is another way of saying that electrons repel each other: the language of fields and potentials, hare as elsewhere, can be replaced without violence by Newton's Formulations oF point sources oF attractive and repulsive  Forces.  53.  For the history of the phenomena, a study oF the Eighteenth Century suffices to cover almost all the major points involved. While explaining electric phenomena was an important of Hellenic philosophy, that civilization lacked the ready access to industrial chemicals and wire that would have allowed the construction of batteries and circuits and so led to more complete theories of electricity thi:Th ones that addressed themselves to the attraction and repulsion oF static charges and magnets only.  The Eighteenth Century had this technology'° and soon noted a close link between electricity and chemical reactions. Chemically, it offered explanations in terms of an electric Fluid, or of several electric fluids. Mechanically, the interactions of electric charge were discovered to be identical in form to Newton's law of gravitational attraction. ^This, too, was accounted for with a theory of minute electrical corpuscles, each possessing the capacity to attract and repel other electric corpuscles. No significant effort was made to develop a theory of electricity in which charge was like velocity in the kinetic theory of heat, a causal  quick review of important materials of early electric experiments reveals the following: sulphuric acid, wire, and foil. A wire making industry in Europe was a natural sequel to the need for springs in Flintlock mechanisms. Sulphuric acid follows from the leather-tanning industry while foil in large quantities requires steam-hammers. (cont. next page.)  property of the actual corpuscles said to be charged.  54.  Significantly, by the time that equipment had advanced to the point of allowing the phenomena adduced above to be noted, an earlier generation of Newtonian corpuscularians had died or abandoned the field.1 Corpuscular theories may well have been out of fashion before significant work on electricity began to get done.  The early Nineteenth Century saw a complete elaboration of a theory of electricity based on two fluids made up of particles that repelled and, conversely, attracted each other according to a central force law. Such a law could be extended, if with great difficulty, even to account For the force exerted by an electric current on a magnet, at right angles to the line connecting current on a magnet, at fight angles to the line connecting current and magnet. Such mathematical virtuosities led to a widely held conviction that electricity would turn out to be explicable by currents of electric particles. Such particles had potentials like those of heat, fluids, and gravity and produced heat and light while Flowing in currents through conductors. Because the theory suggested that electricity could be explained by matter in motion, the phenomena of electricity appeared  (cont.) Other than the impact of the "pre-industrial revolution" on the price of these items, and the lack of saltpeter and Flintlocks in ancient Greece, there is also the absence of a Greek tanning industry, consequence of the same lack of field animals of which lack of saltpeter is a result.  55.  to lie well within the realm of the principle of conservation of force's grand unification.  *E6-26^'PTaT40408^•  .dd 'saqoupu2  '  Chapter V  57.  Historical Perspectives of the Nature off Light  Modern science considers light to be the eye's apprehension of the collision of minute particles called photons on the eye. The same photons, falling on the skin, produce the sensation of heat, emphasizing the subjectivity of sense impressions. Light has reality as a phenomena beyond what is perceived by the eye, but it is a reality vary different From the experience of light. Now according to a well-known result of quantum mechanics liuht iz ulso ^wave, and it is as a wave that I will from here on refer to light.  To say that light is composed of waves is, however, to present a Fairly polished analogy as a complete picture of reality. For what is a wave? the answer is that a wave can be one of two things. It could be a series of pulses, volumes of compaction in a medium succeeded by rarefactions thereof. This motion is well modelled by the movement of traffic at a busy light, as one v hicle after another acculerates, opening an interval between it and the car ahead: and so on, so that it appdara^as though instead off cars moving, Forwards, there are pulses moving backwards. Multiply  58. the number of pulses and impose periodicity upon them (i.e. more traffic lights changing in a regular succession) and one has a fair picture of how that pulse of empty space moves through a medium in what is referred to as a long wavetrain. The second form of wave is to be observed when a tensely strung string is plucked. The result is that the string vibrates in certain set patterns oF sinuous curves. In this wave, no particle of string actually moves longitudinally at all.^(At least ideally, In reality a medium always has a longitudinal wave associated with a transverse waves, since there is no such thing as a perfectly elastic yet perfectly rigid anything, and this is the requirement of a purely transverse wave.) Waves of this type exhibit what at First appears to be a highly counter-intuitive behaviour. For the movement of the wave is not accompanied by the movement of the least particle. This peculiar behaviour can be observed in nature by watching a piece of driftwood bobbing on the ocean.  Science has good reason to treat light as a transverse wave, but none to treat it as a longitudinal one, and this has been true since 1805. Modern physicists For this reason assert that light is a transverse wave, and that colours  59. "are" actually different wavelenuths. (In fact, colours are nothing but what is seen, and this assertion constitutes a necessarily ambiguous definition.)  Colours have two significances in modern physics. First of all, there are many possible wavelengths of light. A colour is associated with each possible wavelength of light and there are therefore a near infinity off colours. But since the eye "adds" separate wavelengths off colour falling on it From the same surface, which may reflect a whole spectrum of wavelengths, and perceives that spectrum as a single colour in no way distinguishable From the colour produced by some single and unique wavelength, there is also a human aspect to light. The special light of the sun appears white, and so do a multitude of other possible sums of single-wavelenuth light rays. This simple Fact has universal significance: For it tells us that the eye can in no way distinguish between "pure colour" and the additive sum of several pigments: colour is a property in itself of all light, and also a subjective impression of the senses.  The history of optical theory in the Seventeenth and Eighteenth Century is that of the development of the study of light as a thing in itself. Where previous natural philosophy built on a simple, perhaps even simplistic epistemologyl which equated the study of light with the study of human knowledge and which regarded "lioht" as an aspect of the problem of knowledge of nature, as a vehicle of the perceptions  only, the new physics began to study light as an external  60.  phenomena. Light was now, to the heirs of Descartes, a subtle pression of the medium.  Subsequently, atomist philosophy insisted that light had a corpuscular nature. For how else could light be a ssubstance? On the other hand, the notion of light as a disturbance in the medium became the theory of the wave nature of light. Both sides had experimental results that appeared to confirm their stand. Ultimately, however, the weight of experimental evidence came down on the side of the wave theory. In the hands of French physicists oF the Emlihtenment the theory of wave mution was refined to tha point that a fairly complete description of light as a longitudinal disturbance in the aether was developed: unfortunately, a new generation of royalist French scientists for their own part uncovered evidence that light was a transverse wave.  Transverse waves, it will be recalled, are propagated through a rigid medium. But if the aether were rigid, how could it be permeable to the motion of bodies? Solving this problem occupied immense and futile hours of many great mathematicians and physicists. Their endeavours led to  61. investigations of the physical nature of the aether, and in turn to premonitions of links between light and electricity. For electricity was still thought of as an imponderable fluid whose forces act through the aether by many. So discovery of the mechanical workings of the aether could hardly not have an effect on electrical theory.  As it happens, not one but two links were discovered: one by Helmholtz in 1847 in the Conservation of Force, and one by Maxwell in 1872 in his Electromagnetic Theory of Light. Helmholtz's link integrated light into a theory that accounted for the capacity of electricity to create light and even of light to create electricity under the rubric of a conservation law that asserted that to the degree that light caused phenomena it should be understood as being part of the causal system Helmholtz invoked in his unifying theory. Now that the Conservation of Energy is a virtual cliche of basic science, Helmholtz's success is minimized. Who, aFter all, is surprised that hot filaments glow, and that electricity makes filaments hot?* On the other hand, the fact that one can generate electricity by the wave of a hand and some simple apparatus and that light is integrated into the world of human knowledge through the process of vision seems a far more worthy sat of revelations.  As light has effects, in the form of production oF heat, it must be concluded that light is a force. Helmholtz's simple logic moved heat into the realm of mechanics a Full half-century before the discovery of the momentum of photons.  2  Optical illusions and the phenomena of colour underline the psychological content of physiological optics: Helmholtz, supremely aware of these physiological aspects of vision, was not unmindful of the fact that his theory of conservation of force in the end integrated through the medium of vision every part of physics with the processes of human thought. The method of this integration and its motives will be examined in the next chapter.  I come, then, to the end of a highly abbreviated account of prominent issues in physics as they were understood and were still topics of lively debate in 1847. Below I shall set out my account of the work of unification as it was carried out, and of the significance of each of the issues so Far canvassed in Helmholtz's unification of 1847. By doing so I shall show that a reinterpretation of the history of that unified body called Classical Physics is timely, and that the Helmholtzian unification was more loose and at the same time more rigid than is today perceived: but well-constructed philosophically. The second unification, the law of Conservation of Energy, was more original, and more romantic and anti-philosophical (at least, to the mechanical philosophy)^than it is today given credit For being.  Optical illusions and the phenomena of colour underline the psychological content oF physiological optics: Helmholtz, supremely aware of these physiological aspects of vision, was not unmindful of the fact that his theory of conservation of force in the end integrated through the medium of vision every part of physics with the processes of human thoucht. The method of this integration and its motives will be examined in the next chapter.  I come, then, to the end of a highly abbreviated account of prominent issues in physics as they were understood and were still topics of lively debate in 1847. Below I shall set out my account of the work of uniFication as it was carried out, and of the significance of each of the issues so far canvassed in Helmholtz's unification of 1847. By doing so I shall show that a reinterpretation of the history of that unified body called Classical Physics is timely, and that the Helmholtzian unification was more loose and at the same time more rigid than is today perceived: but well-constructed philosophically. The second unification, the law of Conservation of Energy, was more original, and more romantic and anti-philosophical (at least, to the mechEnical philosophy)^than it is today given credit For being.  64.  Endnotes, pp. 57-63.  1.^See relevant chapters of Meijering. Also, Collingwood, and Descartes.  Chapter VI  65.  Hermann Helmholtz and the Conservation of Force  Hermann von Helmholtz was referred to even in his liftetime as the Chancellor of German Science.1 This title he earned in various ways: by his role as head of research at the University of Berlin: by his assistance of Wiedemann in the editorship of the Annalen der Physik und Chemie: by his series of magisterial popular scientific lectures published from the early eighteen fifties; but first and foremost by the quality, range and importance of his scientific researches. Those researches extended across all the important fields of classical physics and beyond them into the realm of physiology of the senses. Polymathic as these accomplishments at first Jlance seem, they are brought together by a central concern that was fundamentally epistemolojical. Either as a philosopher or as a psychologist, Helmholtz abstracted and generalized his concerns, uniting in a clobal research programme his various interests in a way that made central the nature of the human condition. Natural philosophy for Helmholtz has as one of its most important goals revelation of the nature  66, of man in the light of the discoveries of mathematics and the physical sciences. It is within this programme, so well exemplified by the 1847 paper "Ueber die Erhaltung der Kraft" that Helmholtz must be understood.  Hermann Helmholtz was borne the oldest child of a family of six children in Potsdam in Prussia on the 31st August, 1821. His father was a gymnasium teacher, well educated in the romantic style of his day but constrained in the opportunities he could offer his son. Helmholtz showed an early interest for an talent in mathematics and the physical sciences, but in his youth there was little prospect for a beginning student in the physical sciences lacking private means.* The family's connections were, on the other hand, more than sufficient to obtain for young Hermann an army scholarship. And thus in 1839 he arrived in the city of Berlin to study the arts of medicine and surgery for the relief of the soldiers of the King of Prussia.  Helmholtz's enthusiasm for pure research, however, was transparent. His first scientific effort was published in 1843, the year after he graduated from the FriedrichsWilhelm Institute in 1842, following his Lhasis.2  -°Helmholtz's original biographer, Leo Koenigsberger, made much of Helmholtz's lack of means. Koenigsberger's account has been subjected revisionist scrutiny recently. In fairness to him, however, Helmholtz did have to study medicine rather than physics as he preferred. On the other hand, he mixed with prominent surgeons in Berlin, did not lack for creature comforts, and his father was a personal friend of Fichte.  67. Comments in talks given later in Helmholtz's life make clear that his innovative and investigative approach to the healing arts led his oludr colleagues to question his true vocation while he was still an intern.3 True or not, the inference makes more reasonable the mute evidence oF the effort implcit in the publication of his first paper in the year of internship. Next year, the young man became squadron surgeon and military doctor in the Hussars of the Prussian Guards. Koenigsberger records that the atmosphere of the "remote" garrison town of Potsdam was inhospitable to science: and even more so his merry and well-mounted companions!* But by 1845 the distractions had worn off and preparations were completed for a series of scientific papers that began to flow back to Berlin from Helmholtz's own newly built laboratory in the midst of th brooks and woods of the Berlin countryside!4 The papers went to his old teacher at the K.iser Friedrich Wilhelms Institue and were carefully refereed there before being published by the teacher, J. Mueller, in Mueller's Archiven. Last and most important of these works, published separately in pamphlet form was Ueber die Erhaltung der Kraft. With this paper Helmholtz found his own, adult voice as a scientific investigator and natural philosopher. And incredibly, it was completed in the rural setting of Potsdam.  *Hussars in the early Nineteenth Century armies were assigned the complementary tasks of raiding and reconnaisance. Ancestors to modern rangers and commandoes, the hussar cavalry was supposed to show high spirit, cavalier disregard For  68. Helmholtz's early work was in direct response to a popular conception of the nature of biological organisms in the older generation: the idea of the "vital force." .This.modsrn bate noire, however, must be reconsidered in order to unc:erstand  its role in this period, and just what Helmholtz was actually reacting to. Mueller and his contemporaries belonged to a generation of what Timothy Lenoir called in his recent Strategy of Life5 the "Kantian teleomechanists." These teleomechanists accepted Kant's dictum that organic activity would eventually be explicable in terms purely of mechanisms understandable through the laws of mechanics discovered outside biology. However, they also followed Kant in believing that the process oF biological growth was too oroz,nized to be understood except in a teleological fashion. The final organizational state oF an organism must be understood as in itself having a role in the ordering of its growth. In the final purpose, or telos, of an organism, could be found its first cause for existence. Kant called For a process to be understood as acting in nature which in the purely mechanical world seems non-existent: but this was a long way From claiming, as some did, that this point of view was anti-mechanist. In their work, the later generation of teleomechanists dubbed  (cont.) military Formality, and impeccable taste for clothes and horseflesh. The Guards Hussars helped set the fashion For' wearing a death's-head insicnia. It was intended to represent the devil-may-care attitude of the huLsar. "The only hussar who lives to see thirty is the scoundrel."  69. their First cause the "vital Force," where we might refer to "evolution" today.  In the hands of a later generation of speculative natural philosophers, the question was raised: could the vital force not also be a true force, and like gravity, electricity and so on actually cause change in a direct and mechanical way? Admittedly even an organizing power is indirectly responsible for moving matter in space: inasmuch as the vital Force was the context which made possible the work of the First cause, and the causing of change was the primary defining characteristic of forces in general, the question was reasonably raised.  For Helmholtz the answer was unque.iicalably "nc." The vital Force acted through the intermediary of Forces that were known to mechanics exclusively. Only the direction of their actions was in the hands of the "vital force," which for this reason lay outside the realm of the mechanically comprehensible universe of cause and effect. To demonstrate this, he began a series oF experimental investigations oF the action oF muscles.6 Inspired by Mueller's dominating concerns, Helmholtz sought experimental confrimation that the Lebenskraft could be divested of its special rola as a cause of order --and so demoted From the position oF Kantian Force-- and reduced to a mere director of Forces.  70. His investigations were intended to show that any work done by a biological system could be attributed to known actions of mechanical and chemical forces. To achieve this, Helmholtz investigated the muscle action of a frog's leg. The ability of an electric current to stimulate those muscles to contract and thereby do work was well enough attested. Helmholtz set out to discover whether or not "the mechanical force and heat generated in the organism can be completely deduced from the process of material exchange or not."7 That is, could the theory of combustion account for the action of muscles? In the end, Helmholtz felt confident in having demonstrated two things in his experiments: First that muscle action is the result of a measurable chemical conversion of material substance: and second that the process is localized in the muscle.8 As further confirmation of his theories, it was natural that Helmholtz would undertake to measure the heat produced in the muscle during the contraction of the muscles and correlate this --somehow-- to the work done. Experiments to measure this heat, and to localize it in the muscle tissue where chemical combustion took place was the natural next step. Helmholtz's goal throughout was to demonstrate that no heat was generated in the muscle except through chemical combustion. He identified heat with the "force-like"  71. action theorized by vitalist biologists for the Lebenskraft. Obviously, his programme of research in no way dealt with the larger problems off organic growth, concern for which led Kant to his original proposal of the Lebenskraft's role to begin with. Lenoir contends that Helmholtz was uninterested in this aspect of vitalism, believing that here at least Helmholtz was willing to accept Kant's thesis, although he sternly pursued the goal of abolishing the Lebenskraft as defined by the vitalist s from physiology.S  Sy excluding the less tractable problem of growth, Helmholtz's research programme remained incomplete. Here an argument From consideration of personality might well be made. In his new laboratory, Helmholtz was now well-equipped For a wide range of electrical and mechanical investigations. The necessary apparatus was originally developed for his exacting experiments in measuring muscle heat: but they now called out for other and more physical applications. Helmholtz's primary concern, even as biologist, has been with the nature of force and heat. His next paper would be a paper on the physics of force.  72.  In 1847, Helmholtz published a work on the "correlation oF natural forces," this one drawing not only on the experience of biology, but oF all the realms of classical physics as well. His rapidly expanding laboratory skills had broadened the reach of his investigations and interests to the near universal. His investigations now extended to addressing every physical phenomena under the heading of the "closing of cycles." Thus, for instance, the mechanical effect of a falling millstream can be harnessed to drive two metal plates over each other, producing friction. This friction produces, of course, heat. This much Helmholtz has observed in the factory. 10 But that heat can easily be used to produce steam and run a steam engine, which can in turn be employed to lift water from the bottom of the mill stream to the top. In another succession of cause and effect relationships the physical world had recently been enlightened by Faraday and Oersted. A moving magnet could be used to produce electrical current, and that current to exert attractive and repulsive forces on current carrying wires or magnets, thus producing mechanical effect which could drive a moving magnet and thus generate electrical current.11 In America, the story went, an inventor had discovered a way to reduce water to oxygen and hydrogen by electrolysis, and then burn the two products, producing thereby sufficient heat to run a steam  73.  engine that in turn ran a dynamo. This dynamo then generated dlectrical current which produced oxygen and hydrogen as Feedstock for the steam engine. In this fashion, a surplus of heat could be drawn off as well! Helmholtz quotes this legend approvingly not because he has suddenly been converted to the usefulness of this perpetual-motion machine, but because the closed-cycle process it describes conforms to his picture of nature, with the exception of the excess heat, which is a mere confidence trick.12  Oil the question of the perpetual motion machine Helmholtz comments at greater length. Ostensibly, this veritable Holy Grail of modern cranks occupies a central place in Helmholtz's conclusions on conservation of force. Boiled down, the argument might read, "Inasmuch as it is impossible to construct a perpetual motion machine (something we know purely empirically) it must follow, since forces cannot be destroyed without effect, nor, since they cannot be created as by a perpetuum mobile without cause, that forces are conserved." Literally,  It was no more to be asked, how can I make sure of the known and unknown relations of natural forces so as to construct a perpetual motion? But it was asked, if a perpetual motion machine be impossible, what are the relations which must subsist between natural forces? ...My inquiry was made public in 1847.13  74. If, as all our experiences have taught us, a perpetual motion machine is impossible, what does this tell us about nature? For Helmholtz, the answer is that force must be conserved. Well one might ask how such a weak reed of proof could be accepted. One does not have to go too Far to find a scientist who, despite his undoubted brilliance, did not see so immediate a link between the impossibility of a perpetuum mobile and conservation oF force. William Thomson and his brother James came to the principle of Conservation only reluctantly, demanding of those who claimed its universal application, such as Jamas Joule, proof of such things as the production of heat during liquid Flow due to friction of Fluid molecules one upon the other. These two, beginning their thermodynamic investigations from the point of view of discovering what work is done by lowering heat from one temperature to another in various ways, at first could not believe that there were not, even in theory, some ways of lowering temperature without producing useful work. Their conversion to conservation only came late and with extensive researches that confirmed that there was no way of annhilating Force, just as there was obviously no way of creating it.14Such researches occupied none of Helmholtz's time before his announcement of the principle.  69.  75.  Smith and Wise point out that William Thomson, despite his general agreement that what God created was not destroyed, wopuld nevertheless in individual situations look for signs of destruction off work, and assume conservation only when it was proved. [God] created in the Fundamental sense of making things out of nothing, by the exercise of His absolute power, and thereafter sustained them in being by His ordained power, except in the event of a miracle. William [Thomson] would frequently place energy conservation within this theological perspective.1 For instance, in his analysis of the freezing oF water, Thomson suggested a simple case that appeared to contradict the Conservation principle. Letting a stream of water at 320 Fahrenheit run across the upper part off [a Stirling engine, which is an engine designed to run a closed thermal exchange cycle in which sources of both heat and cold are used to drive the engine] while the lower part was held in a basin of water at the same temperature. When the engine was turned forwards, heat would be taken from below by the plunger and deposited in the space above, this heat being supplied by the water in the basin, all of which would be converted gradually into ice at 32°, without the expenditure of work. [Italics original.]lb  In Thomson's view, then, the Stirling engine could be could be used to illustrate what he had termed here a 'physical drinciple,' that the making of ice, consistent with Carnot's theory, involved no expenditure or production of work, For it involved no temperature difference.17  76. Thomson's thrmodynamic concerns obscured the fundamental and central character of the notions of conservation that even he had formulated. Helmholtz's insight, was, in comparison, crystal clear, although less productive of useful engine theory by a wide margin.  Mechanical effect, or work, could not freely be gained or lost. But was this the lesson of the perpetuum mobile? Obviously not in Thomson's case! And even for Helmholtz, the insight that leads to the simple assertion that the conservation of force comes from the impossibility of the perpetuum mobile is lacking. 18 Thomson's tutor in these matters, Joule, stated his case very simply when he successfully persuaded Thomson. "Believing that the power to destroy belongs to the Creator alone, I entirely coincide with Roget and Faraday in my opinion that any theory which, when carried out, demands the annhilation of force, is necessarily erroneous."19  The important question is whether or not Helmholtz had a similar metaphysical proof of the conservation of force that gave him an a priori belief in that conservation. Seeking evidence of such a proof, attention quickly lights on a well-known story. We know that Helmholtz showed the  77 crucial paper to his friend Emil du Bois-Reymond and that du Bois-Reymond convinced Helmholtz to delete a very philosophical introduction to his paper as being unsuitably metaphysical.2° What was in the introduction? The answer, according to modern authorities21 is that much of the introduction was included in his 1871 republication. He did not include in that later paper what he had come to regard as mistaken. This, I would argue, as would Fullenwinder, " consisted of a proof of conservation of force. Such a proof, given before the experience upon which even today the law of conservation of energy is based, would have been of fundamental importance in shaping Helmholtz's physics.  this proof was metaphysical in nature, and requires a careful attention to the philosophical issues that so concerned Helmholtz. In particular, the account weighs heavily in disentangling Helmholtz's thought from his revisionist commitment to the philosophical system of Immanuel Kant. Fortunately, in that process we can afford to be more concerned with Helmholtz and less with Kant.  For Helmholtz, human understanding of nature begins with epistemology: the "first philosophy" of Rene Oescartes.23  78. For Helmholtz was concerned pre-eminently with the foundation upon which the possibility of human knowledge was built. As far as knowledge about the external world goes, Helmholtz considered this knowledge purely empirical.* Knowledge, Helmholtz argued following Kant, could take several forms. It could be synthetic, adduced from general principles or axioms, or analytical, which is to say built inductively From other knowledge. Knowledge can be had about the subjective world of experience either before (a priori) experience, or as a result of experience^(a posteriori.) Was it possible that all knowledge came a posteriori? Kant answered that it was not. Certain things are known before experience, and cannot, intuitively, be doubted. The two most germane examples here are the Euclidean geometrical axioms, and the ordering of the number sequence, which is the same as knowledge of the single direction of the arrow of time. Knowledge of this kind is a priori, since it is logically prior to any understanding of experience. And we know that it is synthetic knowledge a priori because it is impossible intuitively to doubt it. This knowledge is true, and enters into every possible attempt to perceive the external world.  Helmholtz accepted the synthetic a prioris but was strongly  *However, there is some difficulty with the law of causality, For discussion of which, see Fullenwinder.  79. It must be stressed emphatically that it is an error to regard nativism as a form oF Kantian apriorism, as still sometimes occurs. The purport of Kant's theory is to explain the apodictic validity of the axioms of geometry.. .But nativism is a theory of sense perception, [and] its aim cannot then be to give a Foundation For a rigourous mathematical lawlikeness of space, since all perception as such supplies only approximate data.".= These words of Moritz Schlick, commenting on Helmholtz's own critique of nativism, reflect the continuing concern of Helmholtz's school (if I may go that far) to differentiate Kant's concept of the necessity of a priori knowledge For the purpose of interpretation of sensation (the transformation of sensation to perception according to Helmholtz)26 from nativism. Helmholtz's concerns in contesting the nativist school are so clear that it is scarcely necessary to comment further on them. Naturalism has, of course, its defenders. Were it my intent to be Fair to them, I would quote them here. Instead, however, my concern is with Helmholtz, and I shall allow his criticisms to stand unmodified.  Both Helmholtz's own empiricism and the competing school of nativism represent very modern approaches to the problem of perception. Pre-modern philosophy generally asserted that the sense became informed in some way with the essential form of the thing that was perceived. The mind is authentically and actively involved in perception and is also infallibly  80. concerned to limit their role in accordance with the progress of science since Kant's time. Indeed, he seems to have doubted that the a prioris constituted knowledge at all in the strictest sense, since he progressively stripped them of actual content. Nevertheless, Helmholtz maintained that there was a necessary role for the a prioris. Like Kant he considered certain things known about nature to be necessary prior to any understanding of experience.  What was a priori For Helmholtz? The answer to this is as much scientific as it is philosophical. In his later systematic and substantive investigation of the physiology of the senses of sight and sound Helmholtz confronted the problem of discovering the necessities for interpretation of the input of the senses. He was, he repeatedly tells us, concerned above all to answer the contentions of the school of naturalists. Naturalism, to Helmholtz, is the belief that "at least some part off visual perception [is] an innate mechanism, in the sense that certain impressions of sensation are supposed to release certain ready-made spatial representations."24 He wished to refute the contention that nativism is a version of the Kantian concept of perception.  81. informed with the real nature of that with which the mind was informed. Difficulties in interpretation were attributed to the mind alone. The sensory organs area no more that the windows of the mind through which the Force of perception entered the mind. Moderns, beginning with Descartes, questioned this theory of unmediated sensation, contending that the sensations of the senses stood only For themselves. Newton's pragmatic discovery of the mixture of the colours revealed that the sense of sight was unable to distinguish the "real" nature of light and infallibly detect the colours that intermix in a single optical colour. This discovery set up the context in which Goethe, and through him all German philosophers interested in perception, confronted the modern age.27 Inspired by G oethe,^Helmholtz turned to optics and attempted to discover the true nature of perception. Unlike the great poet, he accepted Newton's results, but he shared Goethe's concern for the "torture" to which Newton subjected nature. What could any single optical phenomena tell human beings about nature? The actions of the eye are fallible, and Helmholtz was fascinated by optical illusions. In fact, the eye left to itself is so completely the prey of optical illusions that it is impossible for the eye alone to provide a complete account of that which the aye experiences as sensation.  82. The problem became one of understanding the mechanism of interpretation oF sensory apperceptions. In order to understand the senses, Helmholtz began to refer to actual snesation in the eye as a sign: signs refer only to themselves. The contents of the sign were, as Johannes Mueller had already said, "no more than the specific energies of the sense."* The burden of interpretation, of creating perception, Falls elsewhere. Helmholtz asserted that perception was the product oF experience: that is, except for the crucial step of knowing the outside world.  Here, and here only, there remained a role for the synthetic a priori. What was it that was known before experience? The one principle that was necessary to learn all else from experience? Nothing less than the principle of causality. For how could even so simple a perception of external reality as the cause and effect link between the enervation of a limb and its consequent movement be made without the a priori of causality? The law of causality actually is an a priori given, a transcendental law. A proof of it from experience is not possible, since the first steps of experience, as we have seen, are not possible without employing inductive inferences, i.e. without the law of causality. But even suppose that complete experience could tell us --though we are still far from being entitled to affirm this-- that everything so far observed had occurred in a lawlike manner. It would still Follow from such experience only by inductive inference, i.e. by presupposing the law** of causality, that the law would then also hold in the future. Here the only valid advice is: have trust and act! 'Oas unzuglaengliche/Oann wird's Ereignis.'29  For notes, see next page.  83.  This passage presents the reader with a clear difficulty in discovering just what Helmholtz thought his a prioris are --knowledge, or physiological necessities, as he at one point concedes^them to be.3° Schlitz and Hertz fastened on these difficulties and argued that Helmholtz was more non-Kantian than he realized; his synthetic a prioris are in Fact not knowledge at all, and have no standing as proper subjects For philosophical investigation. For they contain nothing but principles, which do not refer to anything necessarily true about the world.*** They have no standing as proper subjects for philosophical investigation, and are no more interesting than the structure of the retina. More modern writers31 have partly rescued Helmholtz. Fortunately, it has been possible to discover the role of causality in Helmholtz's system without discussing his alleged errors, and this debate need not be considered in discovering the origins oF the Law oF Conservation of Force, or as I am now prepared to call it, the Law of Conservation of Cause. On the other hand, the question of the status oF the causality law --true knowledge or not-- is an interesting one. If the latter, it suggests a peculiar link between mind and external reality with distinctly Hegelian overtones. Given  The original German for Mueller's "specific energies of of the senses" is unknown to me. Since the drift of this essay is the demonstration of the late date of the invention of the concept of energy, it would be more satisfying to me to track down Mueller's exact usage. For the moment, however, it escapes me. Strictly, Helmholtz means that lawlikeness, or order, is presupposed, and that in his analysis, lawlikeness without  84. the link between conservation of energy and the Hegelian Naturphilosophen, such a thought suggests whole avenues oF investigation.  The system of Kant made room for modes of thought not properly constitutive of consciousness: this is in his system the realm of intuition. In Helmholtz, too, intuition has a special place to be accounted for, outside the apparent realm of consciousness. Having not discussed the origins of consciousness in Helmholtz's system, it will be here necessary to briefly speak of the proper realm of consciousness. My intent here is to close a loophole. Is intuition a way of understanding the world without regard to the a priori of causality, and thus a way of perceiving violations of the law of cause and effect? The answer is no. For Helmholtz intuition is unconscious inference. Of all Helmholtz's quasi-psychological inventions, the unconscious inference has been the most controversial: it states simply that a certain category of logical inferences from experience, the realm proper of consciousness, go on unconsciously in the mind. The reason For this is their essential simplicity and the unexamined basicness of those inferences to life  (cont.) without causality is meaningless. For further discussion, see Schlitz's commentary in Helmholtz, Epistemological Writings, pp. 178-180. The distinction here made is between asserting that the law of causality is true in nature, and asserting that the law of causality is a necessity a priori to understanding nature. The former asserts a Fact about nature, and is  85. in the world. For example, the intuitive certainty we have that there is only one straight line that can link two points is something so apparently necessary to our understanding as to be apparently an a priori necessity to thought. Helmholtz argued that, on the contrary, it was an act of consciousness, of inductive thought that led to this conclusion.32 But it was inductive thought at such a basic level as to be one that the seat of consciousness does not note as a product of itself.* The implications of holding causality as a priori necessity to all perception of reality is simply this: at the minimum, the human consciousness is entirely a product of mediated experience and can for this reason make no sense of external reality in which the law of causality is violated: for the mind would not be conscious of the violation. That all things have causes is the necessary point at which one begins to understand a new experience! Thus, and again at a minimum, since it is always possible that this is not merely a perception of reality but ^requirc.m,ant imposed upon it as a pure subjectivity, all things have causes. Because force is merely a causal agent all things happen through the application of force. And each force has in turn its own cause, in proportion to the effect it  (cont.) knowledge. The second is, rather, a pre-condition to knowledge and is true of the mind and not of nature. Even the reflexes (for example focussing the eye) are so explained.  produces. ^The closed loop of the burning water, or any  86.  other of Helmholtz's examples, thus is a closed loop in causation, in which the certainty that no more Force is manifest at the end than in the beginning (and in total, no less) is simply a statement about the necessary order of the universe.  There is no doubt that in 1847, Helmholtz felt that at this point he could write a simple Q.E.D. Buried in this account are assertions that he later recognized had no place in a work of science and which du Bois-Reymond immediately saw could not be included in a scientific pamphlet. They were, however, for Helmholtz, proof positive and sufficient For a Arinciple of Conservation of Force.  When one moves out into the larger domain of that group of fourteen investigators who, according to T.S. Kuhn34 simultaneously discovered the concept of conservation of Force (or energy, as Kuhn anachronistically chooses to call it) one finds that the convictions that Helmholtz articulates are often close to their minds as well. Joule's remark that work can neither be created nor destroyed because of the nature of iccd's creation has already been noted: but Mayer said the same thing35 and Faraday was unambiguous  87. even years later under pressure From Maxwell to change his tune. By Force Faraday meant the 'source or sources of all possible actions of particles or materials in the universe, these being often called the powers of nature.'36 Kuhn, in referring to the metaphysical certainty of the truth of the conservation principle even refers directly to the use of the "perenially serviceable philosophical tag about equality of cause and effect"37 to make the last few steps to the conservation of force. Only in his estimate of the importance of the concept does Kuhn go wrong. Kuhn's error arises from the difficulty he has in accepting that, were strict causality the only step necessary, that the "law off conservation of energy" was not Formulated in tha Eighteenth Century, or earlier. But the Fact is that the Eighteenth Century, and earlier times, had as much off the law as was needed: the principle of causality itself. Since heat and electricity were not then mechanically understood --partly because they could not be mechanically produced-they were not included in the law of conservation of "vis  viva" or Descartes' conservation of motion. Earlier notions of the imperishability of motion were adequate to the needs of the times. As for the concept of energy: no wonder it was not invented in the Eighteenth Century, for the need  88. for it did not arise until Maxwell's theory of electrodynamics was promulgated, as I propose to arue. And when Maxwell required energy, the law of conservation of force was cannibalized to provide it.  One concern remains to be addressed here, and this is the assumption so often made that Helmholtz's concept of conservation of force was an indefinite and immature notion that could turn easily, and by degrees, into the conservation of energy. This assumption forms the taking off point of Elkana's thought on the subject38. This position may take either Elkana's carefully nuanced position of gradual change or the one of most commentators, of which Elkana supplies the thought of James Clerk Maxwell—Elkana's positiQmi is one that the confusion is not merely verbal. The confusion between 'force' and 'energy' (as we use these terms in the works of Helmholtz and some of his contemporaries) was not only a verbal one, as most of the commentators tend to assume, but rather a necessary prerequisite For the final clarification of the concepts. Only an undefined entity could have been the subject of a general belief in the principle of conservation in nature... Such a belief was one of the major factors in the actual establishment of the conservation of energy principle in its final and mathematical, that is correct and well-defined, form.29 Maxwell's position was simpler, and less disingenuous, since it does not have a theoretical axe to grind. It is, however,  overly uneelf-reflective. ^  89.  There can be no doubt that a very great impulse was communicated to this research in 1847 [by] Helmholtz's essay 'Ueber die Erhaltung der Kraft,' which we must now (and corrod-:li, as a matter of science) translate 'Conservation of Energy,' though in the translation which appeared in Taylor's scientific memoirs, the word 'Kraft' was translated as 'Force' in accordance with the literary usage of the time 40 Maxwell's comments implicate the translator Taylor as a special culprit. However, Helmholtz used the word "Kraft" to refer to force throughout his career. It is found in the posthumous third edition of the Physiological Optics as force in a highly epistemological passage and there translated as force by an American translator of tne Nineteen Twenties. Maxwell's theory of translator error is utterly insupportable. The problems with Elkana's rather patronizing notion of "the necessity of an undefined concept" are exposed not only by Helmholtz's unsparing clarity, but by the contemporary reception of Elkana's work.41 The passage in question from the Physiological Optics deserves to be quoted at length. A work of 1867 in origin, it was twice reviewed and reprinted by Helmholtz and has the shining virtue off simplicity and clarity. For those who have struggled through Helmholtz's "Facts in Perception,"* which is, according to Moritz Schlick the "richest in content amongst Helmholtz's epistemelogical  Not to mention the arcane commentary with which Schlick, Hertz, Yehuda Elkana, and the translators of first and second edition have larded the papers.  studies,"42 it comes as a revelation.  ^  90.  The law of causation bears on its Face the character of a purely logical law, chiefly because the conclusions derived From it do not concern aci:ual experience, but its interpretation. Hence it cannot be refuted by any possible experience. For if we founder anywhere in applying the law of causation, we do not conclude that it is false, but simply that we do not yet completely understand the complex of causes mutually interacting in the given phenomena. And when at length we have succeeded in explaining certain natural processes by the law of causation, the conclusions we derive from it are that certain masses of matter exist, and move in space, and act on each other with certain motive forces. But the conception of both matter and force are entirely abstract in nature, as is shown by their attributes. Matter without force is assumed to exist in space, but could not act or have any properties. Thus it would be of no importance whatever for all other affairs in the world or for our perceptions. It would be practically non-existent. Force without matter is indeed said to act; but it cannot exist independently, for whatever exists is matter.* Thus the two conceptions are inseparable; they are merely abstract modes of regarding the same objects oF nature in various aspects. For that very reason neither matter nor Force can be direct objects of experience, but are always merely the revealed cause of the facts oF experience.43 This passage, unjustly ripped from a longer text of equal richness, constitutes the fullest revelation of Helmholtz's thought. Unfortunately, its audience has been confined For generations to student opthamologists. Here Helmholtz as much as states that he would have found energy conservation (at least to the degree that it allowed for the existence of energy as an autonomous entity) an illegitimate extension of his own conservation of Force.  ,^. n-Thla off-hand and contentious remark clearly reveals Helmholtz's prejucices. Although he undoubtedly had what'he regarded as an adequate proof of the remark, the fact that he does not here rehearse it indicates to what degree he thinks it uncontroversial.  91. There remains the problem oF discovering how Maxwell could have developed his concept of energy and not noted its difference from the German idea, and how the German scientific community could have adopted the British Maxwellian usage of energy while remaining oblivious to the implications of this usage while remaining oblivious to the implications of this usage of the generalization of the state of energy into energy as a real thing. The latter problem requires a look at the German adoption of the word "Energie." True, in 1877 the Philosophical Faculty of bottingenproposed an essay contest to prove that conservation of energy and die Erhaltung der Kraft were one and the same.44 Even Helmholtz in 1881 started to refer to "der Konstanz der Energie" in place of the older conservation of force. Still, too much can easily be made of this. Helmholtz still thought that energy itself was nothing but the vis viva of a particle.45 As mechanics reduced more and more phenomena to models of matter in motion, "Energie" became a more and more useful as the description of the total Kraft impressed on a system. If heat were nothing but moving molecules, then heat was in total only the Energie of all its particles: and so on. Where such an analysis had not yet been victorious, Helmholtz still spoke of kraft, and Spannenkraft, or potential. This usage persisted in articles written throughout the eighteenseventies and eighties.46 Nor was Helmholtz unaware of the fact that the British used the word "energy" more Freely  than he used Energie. In tabular Form in an article he  92.  prepared for the benefit oF English readers in 188147 he describes the universal metric dimensions of energy under the heading oF the symbol "E," clear reference to the English energy. In the accompanying text, however, he makes clear his preference for retaining the careful usage of vis viva, Kraft, and Spannenkraft. Clearly he preferred this sort of technically precise terminology. Helmholtz's lamzuage distinguished him even from the younger generation of German physicists he so much influenced. In an article in which Helmholtz describes Hertz's doctoral project, Helmholtz c.,escribes Hertz as measuring the inertia of an electric current.48 Hertz himself in his discussions of this experiment always referred to the kinetic energy of an electric current.49  The difference between Helmholtz and Hertz probably illustrates, however, a different level oF rigour and caution in the two men. What was truly meant by Maxwell and Poynting by the word energy went unremarked in Germany, and indeed everywhere but Britain and Yale, where J. Willard Gibbs was the only scientist outside the charmed circle of Maxwellians to grasp the essential elements oF Maxwell's theory .60 To Helmholtz, energy is just exactly not a mysterious and zieneralized entity capable of beings conserved, but a manifestation  93. of the rigid applicability of the law of causality. Energie in the sense that Briton and German would agree to use it, the %mv2 expression, is actually the mathematical expression For the total amount of force imparted on an object over a period of time. Thus it represented to Helmholtz, the sum of all forces acting on an object. That it was conserved Followed, as I have said, From the simple law of causality. That in many cases this equation also expressed the total Force in a situation where it was conventionally measured as heat Helmholtz would also have conceded. It was the loose language that suggested that energy itself Flowed, and applied to every possible situation in which the conservation oF Force law applied that Helmholtz thought he was critical of. But underlying that carelessness from the British point of view was an even more radical conception of energy.  Endnotes, pp. - 5-s3.  1. 2. 3. 4. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Z1. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  94.  McCormmach, pg. 12. Koenigsberger, v. 1, pg. vi. Helmholtz, On Thought, pg. 55. Lenoir, Strategy of Life, Chicago: University oF Chicago Press, 1982. Ibid. pp. 197-215. Ibid. pg. 200. Ibid, pg. 202. Ibid. pg. 212. Helmholtz, "On the Transformations," pg. 195. Ibid. pg. 197. Ibid. pg. 197. Ibid. pp.198-199. Ibid. Smith and Wise, pg. 307. Ibid. pg. 297. Ibid. Elkana, Discovery, pg. 10. Smith and Wise, pg. 306. See Fullenwinder. Helmholtz, Epistemelogical Writings, pg. xvii. Fullenwinder. Descartes, Meditations on the First Philosophy Helmholtz, ibid. pg . 135. Helmholtz, ibid. pg . 177. (Commentary by Schlitz.) Helmholtz, On the Sensation of Tone, INtroduction. See Amrine. Helmholtz, Physiological Optics, v. 1, pg. 47. Helmholtz, Epist. pg. 142. Ibid. pg. 75-77. See Fullenwinder. Helmholtz, Epistem. Chapter 2, passim. Fullenwinder. Kuhn, Essential Tension, pg. 67. Elkana, Discovery, pg. 122. Hermann, Energy, pg. 61. Kuhn, Essential Tension, pg. 70. Elkana, "Helmholtz's Kraft," Introduction. Elkana, Discovery, pg. 9. Ibid. pg. 15. See Clark. Schlitz, in Helmholtz, Epistem. pg . 163. Helmholtz, Phys. Op. v. III, pp. 34-35. Elkana, Discovery, pg. 187. Helmholtz, "Systems of Absolute Measurement," pg. 437. See Helmholtz articles in Annalen, as listed. Ibid. "Systems of Absolute Measurement," pg. 437. Hertz, Principles, Helmholtz's Introduction. Hertz, Memoirs, pg. 113, For example. Buchwald, Maxwell to Microphysics, pg. 177, or Knudsen.  Chapter VII ^  95.  James Clerk Maxwell and the Rise of Energy Theory  From 1822 to 1847 Mich.,o1 Faraday, who tagan hi a life as apprentice to Humphrey Davy at the Royal Institute, was Free to engage without close supervision in the activities For which the place was instituted: scientific investigation and demonstration. Faraday's credentials as a natural dhiloscpher were unusual. Hu had little math and less desire to learn it. On the other hand, he met through the Intstitutb thz. philosophical circles in which Davy moved. From Davy he learned an extraordinary mastery of experimental method. From Coleridge he had at second hand the German philosophy, in particular Kant. Directly from Coleridge and Davy he had the spirit of British romanticism. And from his Sandemanian* background he imported another set of conceptions of the world. This set of intellectual antecedents he formed with the guide of experiment into a picture of the world very different from that of Helmholtz.  Sandemanians are a small sect of Scottish Dissenters. They educate their youth well, iF idiosyncratically. This particular lad was directed by circumstance into the extremely unusual "trade" oF science, rather than satisfying his curiosities in College. The result was a truly unique scientist, and one especially unlike the mathematically Formidable but unphilosophical sraduate of Cambridge who brought Britain most oF its scientific successes of the Nineteenth Century. Even the men of Dublin, Glasgow and Bdinburgh were somewhat alien to Faraday's peculiar spirit.  96. Faraday's private investigations in physics and chemistry were united by an interest in electrochemistry. He decomposed compounds with electric currents and built electrochemical cells (batteries), which endeavours led him to electricity and the realm of physics. Faraday's First important physical result he discovered in the action of an electric current. He discovered current induction: the change in the direction or intensity of an electric current induced current in other conductors. This effect weakened the source current, which made sense in terms of conservation of force, and acted across space in like fashion to Newton's attractive and repulsive forces, but raised troubling questions. Faraday also soon discovered a similar effect due to moving magnets, as well as a force acting upon electric currents due to magnets and vice versa. This force raised even more difficult questions. For unlike the central forces of Newton and Helmholtz, which assumed that the only real forces were central forces acting at a distance, the magnetic-electric effect occurred at right angles to the radial vector! Neither an attractive nor a repulsive force, it violated rules formulated to explain the whole phenomena of force acting at a distance which demanded that such forces act in or opposite the direction of the source of force.  Faraday explained his discoveries with a new conceptual  97.  language. His new concept was that of the Field, his new language that of field physics. He proclaimed that the action of electric and magnetic fields explained his discoveres, and these fields became the central element in Faraday's theory oF electricity and magnetism.1 His interest turned nzturally to a new problem: that of magnetism. Faraday's own solution rejected emphatically the old concept of forces acting at a distance. Although heroic attempts ware made in Germany to rescue the concept,2 Faraday thought the whole idea logically absurd.3 He preferred to think of objects naturally moving from one point in space where there was an excess of magnetism or electric Field strength to a place with less. Driven by such thought to conceptualize quantities oF electricity and magnetism manifested in space, Faraday began to speak of his Fields as "lines" of force.4 Mathematical systematization of Faraday's ideas by his Followers made heavy use of the Formalism of Laplace and Lagrange described in Chapter III. No mathematical version of Faraday's theory could really be his theory, however, and Faraday's concerns were very different From those of the Analytical Mechanists. Where they wished to banish the concept of force from the lexicon of science, Faraday adopted the Field while retaining Force, wishing rather to eliminate the idea  action at a distance. Faraday's concept of Force, which  98.  derives from Kantian idealism and a version of religious voluntarism, was the vague and general cause of change already Familiar to the followers of Kant.  Faraday's idea of the field was something new, on the other hand. It implied that matter is nothing but the centre of lines of force radiating out into space. The actual matter was merely an entity to which could be assigned a set of behaviours that actually result from the interactions of lines of force.3 Matter extended indefinitely as source of action, for it filled all space. Matter fills all space, or at least, all space to which gravitation extends.. .For gravity is a property off matter dependent on a certain force, and it is this force which constitutes the matter. This, at first sight, seems to Fall in very harmoniously with.. .the old adage, "matter cannot act where it is not."3 Faraday's matter and Faraday's space are indistinct and intimately linked by their common possession of the property of force. Force itself is significant in itself only as the source of action. The final step to energy theory will come when the same theory treats a quantity both as an abstract description off the states/results of action of matter (Faraday's Force) and as scmething physically present in space (Faraday's lines of force): when this step is made, it is energy, and  99. no longer Force which is so described.  Faraday's general and unmathematical picture was embraced and transfomedto serve the purposes of mathematical physicists whose researches and theories built on his ideas while attempting to mathematize them. In particular, Baron Kelvin* and James Clerk Maxwell attempted to assimilate Faraday into their own programmes. They valued Faraday's vivid language and metaphors for their prescriptive value: for British physics was built upon a tradition rather misleadingly called "practical:" the tradition of models.7  As any student of Nineteenth Century British physics soon realizes, being able to build a coherent mechanical model based on the mathematics oF the theory was a minimum requirement for proving the theory. Understanding and acceptance of a physical theory could flow only from a model. When William Thomson sought measured and judicious words with which to discuss the contributions of Rankine to British physics, he hit on two issues that remained crucial for him all his life. We cannot Find a foundation for a great deal in his mathematical writings, and there is no explanation of his kind of matter. [substance.] I never satisfy myself -until I can m.:ka a mechunical model oF a thin. If I.can  *Baron Kelvin of Largs was born William Thomson of blasgow. In partisan reward for loyal service to the Liberal Unionists at a difficult time and in recognition of his achievements, he received a "scientific peerage" in 1891. His biographers have ever since sought to confuse all and sundry by referring indiscriminately to "Thomson," "Lord Kelvin," and "Baron Kelvin," or even William.  make a mechanical model I can understand it. As long ^ as I cannot make a mechanical model all the way through I cannot understand; and this is why I cannot get the electromagnetic theory [of Maxwell.]S  100.  On the subject of abstract mathematics, Thomson was blisteringly clear. His compatriot P.L. Tait echoes Thomson in attacking the molecular dynamics of Ludwig Boltzmann as "algebraic terrorism," according to Enrico Bellone.1° It is not necessary to pursue Thomson's battle with Boltzmann to understand Thomson's distaste for abstract theory in Thomson's definitive demonstration of his own methods, the Natural Philosophy of Thomson and Tait.11 Of course, it didn't hurt that the collapse of the Botltzmann-Maxwell theory of molecular dynamics would leave Thomson's own vortex theory "without a rival."12 Most important to Thomson however, was that his theory, unlike that of Botlzmann and Maxwell, treated the molecular system as infinitely extended, and therefore it could only be "idealized by treating a finite number of atoms statistically," even though any indeterminacy was "only apparent," and a matter of "man's limitations."13 Thomson's ideal of nature was one in which all was mechanically determined, and this was what he demanded of his models.  Naturally enough, no model could suffice in itself to "prove" a theory, and no modal can be said actually to describe directly phenomena that cannot be observed acting like the  model.  10. This much is recognized today as it was then. However1 ,  the assumption that Nineteenth Century scientists thought like modern ones and employed models for their heuristic values has led to some misinterpretation of their significance.14 The models were not merely means of engaging a physical intuition. Rather they were an approach to the mechanical explanation of nature, a physical theory that was the fundamental reality of life just exactly because nature is mechanical!* To be unable to construct a model for a theory is to prove it unsound^or incomprehensible. Whatever can be said about a theory lacking all possible physical-mechanical explanation, one thing is true: the theory does not describe nature! Therefore the value of playing with models is that the whole scientific enterprise is at stake in these aids to intuition.  This consensus did, of course decline, and it is in the work of Maxwell that the simple and straightforward approach that Thomson followed broke down and became the nearly ineffable "British dynamic programme."16 As the foremost modern Maxwell scholar points out,17 Maxwell's Treatise contains no model of the aether. Yet his theories ascri:De to that aether a wide range of physical activities in the propagation of electromagnetic effects. The reason for this is at one  ,^. Which is not to say that Thomson was a "mechanist." Rather, he thought that nature was comprehensible, which means that it necessarily followed that it could be described in terms transferrable to a mechanical model. If this is "vulgar metaphysical materialism,"18 so be it.  102a level simple: For there is no physical analogy which can explain the actions oF the aether in Maxwell's electromagnetic theory oF the aether. Maxwell's "dynamic" theory requires that there be no longitudinal waves in the aether at all, but that the aether does propagate transverse waves.19 This is the source oF Kelvin's strong disapproval oF the electromagnetic theory oF light. AFter Maxwell's death, in Fact, Thomson was involved in a controversy with Oliver Heaviside on the grounds oF his insistence that telegraphic signals were in Fact longitudinal waves. Heaviside, zealous* in his deFence oF all aspects oF Maxwell's theory as he interpreted it, stood up For the truth oF transverse waves at the British Association Meeting oF 1885 against Thomson.2° Thomson's "practicality" led him to the in the event erroneous belieF that telegraphy waves were longitudinal pulses in the medium, and upon this he based his claims against Heaviside's innovations in telegraphy and against Lodge's lightning rods.21 Thus was Thomson and his simple Faith in a comprehensible universe outmoded.  Maxwell, and even more so the Maxwellians, realized early that the universe probably wasn't comprehensible. Their approach to models was thereFore rather cavalier. Explicit  deFine one Maxwell as set down by Oliver modifications were signiFicant driFted Far indeed From being rather than Heaviside!  who Follows the theories oF Heaviside."22 Heaviside's enough that he .1tventually a Maxwellian like Maxwell  102b  in their theories was a n3w aether ...the electromagnetic aether. This aether was no longer distinguished by mechanical structures at all, but by its conformance with Maxwell's equations. [the Maxwellians] insist[ed] that the only tractable problems were those that could be treated by altering the ether's structure according to circumstance ... [they insisted] that there was simply no point in trying to determine the mechanism by which matter acted upon the ether --even though the essence of the British theory required the most precise specification of the result of that very interaction.23;' Buchwald goes on to make clear what was at stake. By 1878 only Followers of obsolete schools in Germany and Britain still thought "of the aether as a mechanical structure."24 This new electroma g netic theory of light, built Free of the constraints of too-Faithful model-building, was a novel conception indeed, and Full of odd notions to be inferred about nature.  The essence of the theory was a set of equations Maxwell collected From previous attempts to understand electricity. These theories he then linked to a picture of reality which is virtually forgotten today. For to Maxwell electricity was a property of the aether. Charge previously attributed to electric Fluids bound in or to particles was in the  Buchwald's intent in this passage is to indicate the difference between British and Continental physics, and he makes no comment on the very similar generation gap in British physics. Truly "the past as a Foreign country!"  103. new theory bound in something analagous to stress in the all-pervasive aether. The cause of such stress might be compelled to move, which Maxwell considered to be what we observe as the motion of current, or induction, depending on whether it passed down a conductor or across space. Of current Maxwell said that it follows the same rules as a disturbance in an incompressible fluid, so that it Follows that "every electric current forms a complete circuit."25  Maxwell's incompressible fluid analogy indicates that he thought of the medium as like the atmosphere and the sea. Within it, the same pressure is felt everywhere, and when a shock-wave moves, it does so everywhere but without moving a single molecule. This is because in an incompressible Fluid there is no room anywhere for molecules once they have moved from their assigned place, except by the changing of the shape of the fluid mass, something not possible with the universal aether. In comparison, the ostensibly identical modern theory sees electric current as infinitely compressible, and it is possible to store as much electric fluid in a -:apacitor as it is designed to hold: in theory, an infinite amount! Of course, Maxwell's theory does not have an electric Fluid, but rather an electric medium through which waves are propagated. Despite the similarity of language with  104. respect to currents, it must be realized that For Maxwell this stress in the medium has manifestations that are in some circumstances anything but electrical.28 Consider any portion of the dielectric, large or small, to be separated (in imagination) from the rest by a closed surface, that we must suppose that on every elementary portion of this surface there is a charge measured by the total displacement of electricity through that element of the surface reckoned inwards. The charge therefore at the bounding surface of a conductor and the surrounding dielectric which on the old theory was called the charge on the conductor, must be called in the theory of induction the surface charge of the surrounding dielectric.27 In any case where this description is applied to an insulator exposed to empty space, the "surrounding" dielectric is the vacuum of the aether. And by extension, the "charje of the surrounding dielectric" is the charge on the aether. True, this example describes a surface effect and modern physics often asserts strange things about boundaries: why should Nineteenth Century physics be any different? In the theory of capacitors, however, Maxwell extends the same analysis to the whole volume of a capacitor system28 Thus in this case, and indeed everywhere, electric "charge" is distributed through space. Although this formalism is still used today, the example cited above makes it clear that Maxwell meant it literally.  10E .  Naturally enough given his emphasis on the role of the aether, Maxwell placed great importance on his explanation of the propagation of electrical activities across space. Induction and the forces of attraction/repulsion that acte between charged particles he explained by means of electric Fields. These fields he described mathematically by the use of his vector potentials, whose elimination from Maxwell's theory by Helmholtz and Hertz gave us the Maxwell theory as we know it today.29 The vector potentials, which by the way have very little to do with potential energy appear to show that electric effects occur when the vector potentials change. And such is the nature of the vector potential that it extends across space, but contains no time factor, so that when the vector potential produced by one stresssystem changes, it does so simultaneously across all space. Electromagnetic effects are propagated across space instantaneously, just as Laplace "proved" that gravity was.2°  Now Maxwell's theory is not known as the Electromagnetic Theory of Light without reason. Within the scientific community Maxwell is Famous for discovering that light is electromagnetic radiation, as Hertz is famous for discovering radio waves, which is to say electromagnetic radiation with optical characteristics  similar to light, but produced by oscillating electrical currents and therefore clearly a product of electricity. Hertz's results have been taken as proving Maxwell's contention tht light is an electromagnetic phenomena by Finding radio waves, which is a set oF colours, invisible to the eye, that can be produced electrically. Yet as we have seen above, Maxwell does not appear to invoke anything like radio to explain the propagation of electrical phenomena. Today we regard radio as the carrier of Forces of attraction and of electrical induction in the case of changing currents. But for Maxwell these were instantaneous effects of changes in the vector potentials. Indeed, several amateur scientists discovered and demonstrated radio phenomena in the years before Hertz's crucial experiments.31 Sut such phenomena before Hertz were not seen as associated with Maxwell's theories. Observations oF electric effects occurring across space there were in plenty, and Maxwell, having accounted For them in his explanation of induction, saw no need to investigate their "wave nature."32 Electric waves were not predicted by his theory, so far as Maxwell understood his own theory, simply because they were not necessary to explain electric phenomena. Light, which did need to be explained, was well accounted for by the equations. But there was no need to explain electric waves, which did not  107. exist to the best of Maxwell's knowledge.  Maxwell's theory was considered at the time remarkable primarily for its explanation of the phenomena of light. His mathematics produced a constant multiplying a wave-function which had the mathematical form of a velocity. Its units, he determined, were those of speed, and therefore according to Maxwell's understanding of nature, it must be the velocity of a disturbance of the aether. Whatever the disturbance was, it had the form of a regular transverse wave and moved at the speed off light. Clearly the equations described light itself! But Maxwell did not know, and was not interested in, the source of this phenomena, and so did not conclude that light was produced by electrical activity in the invisible wavelengths of radio. He was not adverse to wave theory, and used the same equations to describe telegraph signals, but these waves were invoked where waves were required: the idea that all inductive effects in the medium are waves was not one that entered the picture of telegraphy. "Free standing" telegraph signals were obviously potentially interesting subjects of investigation, and after the Heaviside modification of the Maxwell equations both Heaviside and Fitzgerald contemplated looking For them, but this was For the Future and does not change the fact that waves were not a necessary consequence oF the theory.  After all, Maxwell knew what induction was.  ^  108.  The main experimental evidence that Maxwell presented in support of his theory was his formula for the speed of light, c=^, where; and^are the "specific capacity for electrostatic induction" and the magnetic permeability," respectively, and the Faraday effect ...Maxwell's selection of the evidence confirms the view that his strongest interest in testing the theory lay in the domain of the electromagnetic theory of light. As regards a test off his theory^in the "electromagnetic," [radio] trace can be found of a theory of electric oscillations, and in the first volume condensor charges are treated as aperiodic phenomena. [This is not true, and in fact condensor discharges are the basis of the production of radio waves in Hertz's experimental work.] More important, perhaps, is the absence in Maxwell's writings off any theory connecting a propagating field and an oscillating current as its source fact, all experiments on free propagation proor to the 1880s were extraneous to Maxwell's theory.33 O'Agostino and subsequent writers have pointed alike to vector potentials and not to electric waves as the explanation in Maxwell's theory to the problem of propagation of electric effects.  We have repeatedly encountered "energy" in Maxwell's system. He uses the word loosely to refer not only to the work necessary to assemble charges and which is done by currents, but to refer to the electrical potential energy and to the potential for action stored as charge in batteries and capacitors, and finally to the mysterious cause of stree propagated through space by those vector potentials,  Energy  moves across space whenever the vector potentials change,  and whenever the current flows. This sort of energy, as I have already said, is a property of the aether. Distributed through space i.. the potential energy of an infinite number of charged boundaries, even where there is no charge, there is still energy: the vague and no longer physical stress on the aether.  Yet that same aether appears to have no real existence for Maxwell and the Maxwellians. No physical explanation of it makes sense, and the clear impression is that no such attempt should be made to understand it as a thing in itself. Models like Fitzgerald's elaborate system34 are reduced to purely heuristic functions: very good they might be at reproducing most effects, but in certain respects they were inevitably deficient. (As was any mechanical model of the electromagnetic aether.) Certainly none would satisfy the needs of a mechanical philosopher. For this reason, as I have intimated, I see the Maxwellian world as one of a post-mechanical, even post-philosophical programme. The dawning realization must be that concepts invented to explain mechanics cannot be used in other branches of physics with complete coherence. And since this is true, it must be inferred that these models do not adequately describe nature in total. But if they are mere artifice, what does this imply for the whole human endeavour to understand nature? But that is no struggle to be engaged here.  110. So in the end Larmor and Lorentz's electromagnetic aether35 divested itself completely of the necessity of mechanical explanation. This new aether was chracterized above all by the "Lagrangian function" that describes the field. Energy had become a necessity of this new electromagnetism, a substitute For the mechanical model that had previously explained its very mechanical-medium like activities. Although still visualized as a state of mechanical effect in the aether, the new aether did not allow any such mechanical modification. Rather, it was usually spoken of in abstract tones. Those unable to grasp the British manner of speaking about energy, like Hertz, proposed paradoxes that to their mind illustrated the foolishness of speaking of energy flow. Hertz's paradox, which is too long to be quoted here, involves the superficially simple situation of a dynamo strap, which carries energy in the direction in which a relaxed strap is pulled, and opposite the direct of travel of the tensed strap that moves the dynamo. That is, energy moves opposite the direction of the work done! Where is the physical carrier that moves the energy?36 Hertz was sceptical about the usefulness of the idea as well, not just the British usage. In the present state of our knowledge respecting energy there appears to me to be much doubt as to what signiFicance can be attached to its localization in and the following of it from point to point. Considerations oF this kind have not yet been successfully applied to the simplest of transfers of energy in ordinary mechanisms: and hence it is still an open question whether, and to what extent, the conception off energy admits of being treated in this manner.  Willard Gibbs, who penetrated the Maxwellian system to its darkest core, noted the central novelties in a commentary preserved in his notes. He skewers them succinctly: among them that Maxwell, "assumes (22ff) that momentum and energy lie in the electromagnetic field, in particular in the distribution of the magnetic field effects, as distinguished from supposed linear conductors."37  Now the fact that today physics still uses the formalisms of Maxwell's time and speaks of energy being located in space38 without committing itself to the belief that energy exists as a thing in itself rather than as a state of matter or potential state of matter may suggest caution to some. This is fair, and we are entitled to ask just how real was this "energetic reality." Certain physicists spoke out clearly for the literal truth of a world of energy flows underlying reality. Oliver Lodge and P.G. Tait together, For instance, published a book called The Unseen Universe39 in which they argued that the substratum of the material reality we observe is a universe of energy flows: intangible, yet the source of all motion and action. This energy in particular was the source of a life-force which manifested itself in extoplasmic visitations and the return of spirits. The book was science conscripted in support of the rising  new religion of spiritualism, and any such language was  112.  scrupulously avoided by practicing scientists doing science, at least in theory. Maxwell made no commitment to Lodge and Tait's ideas, although he refrained From rejecting them out of hand.4° Others, especially such continental thinkers as Ouhem 41 were less kind. But such scepticism cannot oe taken for the Final word. It testifies quite .adequately to a lack of adherence to the idea as formal reality by some scientists. But when the idea of energy is physical orthodoxy and a necessary prerequisite to doing science, how can it possibly not spread? Here the attachment of energy to the conservation law via the old notion of "conservation of kinetic energy (which is an early Nineteenth Century Formulation of vis viva in its origins) was doing some mischevious work. Its manifest validity appeared to testify to energy's existence,and as a result metaphysical games played with the notion were perhaps less carefully scrutinized than they ought to have been.  Thus, we begin to have the language of conservation of Force. But whereas before the conservation of force or energy had been a way of speaking about the ultimate and inevitable reduction of all forms of potential to do work,  113. all force waiting to act, to the motion of minute bodies and hence to kinetic energy --"for all that exists is matter" -- the new language was one of vague generality. Conservation of energy had arrived, along with the necessary new concept of energy. Here it was, this new and novel thing, characterized by an entity to be conserved that went far beyond cause to become a thing. More real than the aether whose claims to material (mechanical) structure had been discarded, it appeared to represent a fundamental reality. In the hands of working scientists of the school of energeticists it had become more real than force or matter. the most prominent energeticist advanced these views at a climactic conference in Luebeck at the 1895 general meeting the German Association. It must be recognized that the object of science is not to construct mechanical pictures but to connect measurable quantities with one another. The quantitites of energy, space, and time are all that need enter the equations with which we describe natural phenomena. Energy replaces force and matter, the concepts of mechanics; energy is all we experience directly; energy is the most general invariant known to science. The abstract concept off energy offers a unified world view as clear as the mechanical one and without the latter's difficulties.42 Christa Jungnickel's summarization of Wilhelm Ostwald's famous speech to the Association does justice to the actual subtlety of the man's thought but also reveals the distance this new science had travelled from Kant. but the pendulum was about to swing against this romantic and poetic science.  Endnotes, pp. 95-11.3. ^  1. 2. 3. 4. 5. 6. 7. 8. 9. 10.  114.  Hesse, pg. 203-206. See relevant sections of Archibald. Whittaker, pg. 201. Smith and Wise, pg. 261. Whittaker, pg. 217. Hesse, pg. 200, Ibid. See Hunt, "How My Model was Right." Smith and Wise, pg. 809. Kargon, pg. 200. The language is extravagant and not cited. Given the author, this may mean anything. See Bellone, pg. 160. 11. Thomson and Tait, Treatise on Natural hhilosophy, Cambridge: University Press, 1879. 12. Smith and Wise, pg. 428. 13. Ibid. pg. 430. Ibid. pg. 464. 14. 15. See Buchwald, "Thomson's Mathematization of Faraday's Electrostatics." 16. Buchwald, Maxwell to Microphysics, pg. 20. 17. See any modern text. Bellone, pg. 160. 18. 19. See Simpson for an extensive discussion. 20. Smith and Wise in Kargon, "The Practical Imperative," pg. 340. Ibid. pg. 342. 21. O'Hara, pg. 27. 22. Buchwald, "Optics of Moving Bodies," pg. 58. Ibid. pg. 62. 24. 25. Maxwell, Treatise, vol. 1, pg. 376. 26. Buchwald, Maxwell to Microphysics, pp. 41-54. 27^Maxwell, Treatise, v. 1, pg. 155. Ibid. vol. 1, pg. 100. 28. 29. Further discussion of these issues is promised in Suchwald's upcoming book, 30. Whittaker, pg. 233. 21. O'Agostino, "Hertz's Researches," pg. 272. 32. Hertz, El Waves, pg. 32. 33. O'Agostino, ibid. pp. 270-271. 34. Hunt, "How My Model Was Right..." pg. 298. Buchwald, ibid. pg . 137. 35. Hertz, ibid. pg . 220. 36. 37. Knudsen, pg. 227. 38. Lorraine and Carson, pg. 78. 39. Maxwell, "Paradoxical Mhilosophy." Ibid. 40. 41. See Wilson. 42. Jungnickel, pg. 220.  Chapter VIII  115.  Hertz and the Exorcism of Energy  It was the braf Hermann von Helmholtz's tragedy that after a long life in the service of science, and a service well regarded by his contemporaries, that he was predeceased by those who might have been his successors. Helmholtz's fate would soon be overshadowed by the great struggle between Einstein and the romantics of quantum mechanics like Heisenberg and Schrodinger whose battle is less history than current events. Einstein's "naive realism"1 contested with the real and instrumental Uncertainty Principle in a recapitulation of Helmholtz's struggle with Maxwell's vague formalisms which served to advance pragmatic science without providing for the new formulations a satisfactory philosophical grounding in metaphysics.2 The modern struggle has been more fierce For being waged within a single community rather than between two national sciences, but still recalls the early battle, which has been swept out of sight by the conformity forced upon Classical physics by internalist history. Still, for the sake of his concerns Helmholtz had grounds to complain to fate for the loss of the intellectual heirs to whom he  he looked for the continuation of his works. In particular, there was the loss of the still-young Heinrich Hertz.  Virtually the last task of Helmholtz's life was the melancholy one of preparing the introduction to Hertz's posthumous publication, the Principles of Mechanics, in which he said Amongst all my pupils I have ever regarded Hertz as the one who had penetrated furthest into my own circle of scientific thought, and it was to him that I looked with the greatest confidence for the further development of my work.3  These remarks also show the continuing and deepening relationship between the two men. Hertz came to Helmholtz's laboratory a young man, diffident about his capacity to succeed in the physics to which his heart was drawn. In his First years he was happiest in the laboratory. Ingenious there, he showed little evidence of a desire to penetrate, as Helmholtz did, into the deeper reaches of theory. That penetration which eventually did occur is evidence of the value that Hertz came to place on this relatively uncongenial work, and oF the importance of Helmholtz's example. Hertz's memoirs show clearly that he followed the path laid out by Helmholtz through Kant towards a full understanding of scientific theory. Hertz himself testified in the strongest possible terms to his indebtedness to Helmholtz.  117.  And now, to be more precise, what is it that we call the Faraday-Maxwell theory? Maxwell has left us as the result of his mature thought a great treatise on Electricity and Magnetism; it might therefore be said that Maxwell's theory is the one propounded in that work. But such an answer will scarcely be regarded as satisfactory by all scientific men who have considered the question closely. Many a man has thrown himself with zeal into the study of Maxwell's work, and, even when he has not stumbled upon unwonted mathematical difficulties, has nevertheless been compelled to abandon the hope of forming for himself an altogether consisten conception of Maxwell's ideas. I have fared no better myself. Notwithstanding the greatest admiration For Maxwell's conceptions, I have not always felt quite certain off having grasped the physical meaning of his statements. Hence it was not possible For me to be guided in my experiments directly by Maxwell's book. I have rather been guided by Helmholtz's work, as indeed may plainly be seen... This, and not Maxwell's peculiar conceptions or methods, I would designate as "Maxwell's theory." to the question, "What is Maxwell's theory?" I know of no shorter or more definitive answer than the Following: Maxwell's theory is Maxwell's system of equations.4 Hertz's tribute to Helmholtz, Following Helmholtz's tribute to Hertz, the former written while Hertz was already suffering From his abscesses, the latter after the First off Helmholtz's two strokes_ reveals Further their closely-linked fates. T;hey also indicate the degree to which Hertz drew on Helmholtz's own work in electricity, which I should discuss now. That work, begun in 1869 and continued for twenty years embraced both electrochemistry,and investigations in electrostatics and dynamics. It was apparently heavily influenced by Maxwell as well as the older German theories of Weber, indeed it claimed to be a synthesis of the two theories. Yet despite his  118. apparently synthetic mastery of Maxwell's theory, there is no evidence that Helmholtz grasped the more significant peculiarities of Maxwell's system to which Hertz refers.5 Not surprisingly, considering that no barman physicist, and indeed no non-British scientist except for bibbs had achieved a full understanding of Maxwelle, Helmholtz's theory was un-Maxwellian in the extreme, and is in fact one of the best exhibits of the Fruits oF his own philosophical system.  Helmholtz's epistemology was based on the perception and interpretation of the effects of causes which are inferred from effects, the only things that can be directly known. To put it another way, Helmholtz limits the realm of analytical knowledge to the category of relationships manifested through effects. The human being can speak knowledgeably only about interactions, In this Helmholtz follows the prescriptions of philosophy most forcefully pressed by Kant against presuming knowledge of the objective world of the thing in itself. Helmholtz's thought about the law oF causality illustrates his concern with presumiml. knowledge of the actual origins off those phenomena which are perceived by the mind through interaction with the senses.  119. However, in claiming that the law of causality is in some way really about the outside world, Helmholtz blurs the distinction between subjective and objective, as I have already noted. In a way, Thomas S. Kuhn skirts close to this possibility by noting a connection between the metaphysical language of the Conservation of Force and the language of the Hegelian Naturphilosophen, into whose camp Helmholtz's blurring takes him a very small step.7 I am not fully content with Helmholtz's own argument about how the law of causality makes the actual jump into the objective world. Although the argument of causality-as-psychological-necessity is suggestive, I suspect that it is not all that Helmholtz had in mind. And that he himself was aware of this weakness is suggested by his electrical theory. For in this theory Helmholtz has taken the very difficult step of attempting to describe electrical and magnetic behaviour purely in terms of observed interactions of matter. This serious attempt to categorize all electrical activity purely in terms of the relationships of observed entities with each °there must represent one of the most serious and at the same time most mature oF all Helmholtz's attempts to do physics on the basis of a pre-established metaphysics.  Helmholtz's methods were far closer to the concerns of the pragmatic scientist than were some of those of Faraday  120. and Maxwell, For all their metaphysical soundness and impractibility inasmuch as Helmholtz's concerns had the result of avoiding the invention of hypothetical entities. Unfortunately, Helmholtz's theory was also less than completely successful as science.9 Although he was successful in eliminating Maxwell's vector potentials from the theory. He was unable to fully explain electromagnetic phenomena, and his theory had to be developed and modified by Hertz to reach full maturity. 10 To what degree the modern "Maxwellian" electromagnetic theory of light, which is actually the Hertzian theory, is indebted in turn to Helmholtz and his careful Kantianism, is a aubj,Elct wall worth further *stUdy.  For the English-speaking world, the intimate alliance of Helmholtz and Hertz is all but forgotten with the belittling dismissal of Hertz's work in the field of electromagnetic theory. It was a "confirmation of Maxwell's theory," modern textbooks imply11 that established Hertz's reputation. "I see that Hertz is not a Maxwellian though he is learning to be one,"12 Heavside said in a letter to Fitzgeral. O'Hara argues on the basis of his readings in Heaviside's correspondence that "Hertz's conversion to Maxwellian physics was a gradual process, and he was able to free himself only by degrees from the tradition of German electrodynamics."1: However, Heaviside, in common with Hertz and Gibbs, was at work transforming the mathematical language of Maxwell's theory at the time. The other two recognized the degree  121. which they had moved away from Maxwell's language, something not clear to the Maxwellians of the 1890s, or even their biographers.13 Hertz's editing, however, was one of the most crucial: for he removed the most distinctive Feature of the Maxwell equations, the vector potentials.14  Modern scholars are perfectly correct in aayino that Hertz discovered the electromagnetic radiation oF the radio spectrum. Frequent previous observations of what was actualy radio by the likes of D.E. Hughes and Edison to which D'Agostine refers15 failed to establish that the observed phenomena was a periodic wave, or provide theoretical justification for the existence of such a wave. Thus Hertz's discovery was significant because it was such an identification. However, Hertz was also the first man to design equipment capable of producing periodic waves. His theory made it clear that electrical activities could also be propagated across space as aperiodic imulses: that is, as things other than waves. The electric fluid, which had already reappeared as Lorentz's electron15 was now explicitly revived in Hertz's work as the charge of a dielectric and that which Flowed to produce current. Electric Forces again acted across the medium, which did retain some of the activities which the Maxwell theory assigned it, however. Above all, the  127.  the electron and the distance Forces associated with it allowed the generalized talk of Maxwell about stresses in the medium and the energy in the medium to be discarded again in favour of the language of Forces acting at a distance. The concepts of energy and Field remained useful abstractions, but the Maxwellian usage which assigned them real existence was so completely buried as to be forgotten by history.  It may seem odd to encounter at this late date, 1894, a theory of electric waves that propagate through the aether along with a return to action at a distance exerted on one electron by another. Was this not, after all, exactly what theories of Maxwell's type were supposed to have discarded Forever? The short answer is no. Hertz's modifications to Maxwell's theory was a proof that aether waves could axist. The aether was demonstrated to exist when those waves were found, and the source of those waves was unambiguously located in electrons, which were the carriers of electric charge and thus the causes of all electrical activity.17 The existence of electric waves is for Hertz proof positive of a picture of nature in which charged objects are the sources oF electric action [implicitly, electrons are the sources of charge] and the aether the medium oF their propagation. It is this that makes Hertz's electric waves so pregnant with interest. Why, indeed, was it Hertz and not Maxwell  1E3.  explored the production of waves? Because Maxwell was intereted in the aether as the source of electrical action.  OF course that source is not merely a transverse wave in a medium! There are more subtle modifications of that medium which are the sources of charge, current, magnetic fields, and whatever else counts as electrical phenomena: all traceable to the energy of the aether, or the energy in the aether. Electrons and electric waves belong to a sort of aether which is merely a supernumary to the real world of electricity.  Hertz locates the source of electric action in the charged object, and for this reason has no real need to speak of the energy stored in the aether, while on the other hand he believed it necessary that every sort of electric action be carried across space by the medium in finite time. Electric waves, which are the products of interruptions in electric current flow, produce induction. Attraction and repulsion are more steady-state influences, but equally dependent on the wave-speed of the medium for propagation from effecting to effected object.  124.  Here at last, and not in Maxwell, can one find the real reason why the history of physics places so much emphasis on Maxwell's "discovery of waves." For on the face of it, Maxwell's light waves seem little different from the systems that went before. Did not Stokes and Cauchy, Faraday and Young, all talk of light as a wave? But it was Maxwell, and only Maxwell, that located the centre of electromagnetic action in the aether, and this was the true meaning of his waves. Hertz reversed this placement and put the centre of electric action back in the charged body. His waves represent the removal of the crux of the matter from the active aether to the material source of effect. In doing this, Hertz made the aether less real: and energy, too.  Hertz made his own reservations about energy clear in his last work, the Principles of Mechanics. In introducing the idea of energy we cannot proceed in the usual way, starting with Force, and proceeding from this to a force-functions, to potential energy, and to energy in general... we have to specify by what simple, direct experiences we proposed to define the presence of a store of energy, and the determination of its amount. In what precedes we have only assumed, not shown, that such a determination is possible. At the present time many distinguished physicists tend so much to attribute to energy the properties of a substance that every smallest portion of it is associated with a given place in space, and that through all the changes in place and all the transformations of the energy into new forms it retains its identity. These physicists  125.  must have the conviction that definitions of the the required form can be found... But when we try to thrown them into a concrete form, satisfactory to ourselves and likely to command general acceptance, we become perplexed.^...There arises a special difficulty, From the circumstances that energy, which is alleged to resemble a substance, occurs in two such totally dissimilar forms as kinetic and potential energy... All these difficulties which must be removed or avoided by the desired definition of energy. We do not say that such a definition is impossible, but as yet we cannot say that it has been Framed. 18 So in concise form Hertz states a general dissent From From the idea of energy. In his overriding concern For the disimilarity of the "two forms of energy" one detects a clear echo of Helmholtz's persistent use of not energy, but work, force and tension, that is, of separate terms For the two concepts. However, Hertz's reservations here are drawn from the realm of mechanics. No such censure need necessarily be read into his discussion oF electromagnetism. But Helmholtz did suggest in 1893 his intent to return to theory of electromagnetism and re-derive it from the Principle of Least Action in order to replace the older derivation "From energy."18 The short letter in which he declared his intent, received by Hertz shortly before his death, does not spell out what Helmholtz thinks is the previous derivation "from energy," although he probably means the modified Maxwell theory that he and Hertz had developed. The remark suggests that Helmholtz and Hertz recognized the need for Further clarification of the metaphysical basis of their theories. Perhaps to rid them of overly general use of what had come to be understood as the concept of energy? A tantalizing possibility: but the time  126. time had run out for both men: the new electromagnetism would not be Kantian, but quantum mechanical.  Some comment is probably in order on Hertz's "heroic experiments." O'Agostino has argued that Hertz's researches and discoveries were more problematic than many think. "2° O'Agostino suggests that whereas scientific experimental apparatus had begun the Nineteenth Century carefully linked to the theory being tested, so that the phenomena could be explained purely in terms of that theory, Hertz's equipment's workings were to be understood only through electromagnetic theory. Thus Hertz could be convicted of attempting to confirm his theory using apparatus For whose interpretation Hertz depended on the theory he was testing. (For instance, Hertz's theory showed that the discharge of capacitors was periodic: he used capacitor discharge to produce electric waves, and when he found these to be periodic, he concluded that they were caused by the periodic discharges of his capacitors, and concluded that his theory was confirmed. Or so it might be argued.) As a proof, therefore, Hertz's experiments are a "vicious circle." O'Agostino quotes Hertz as desiring to provide a "convincing Bild." That is, to provide a picture of his theory at work.21 What Hertz did  ,  Author's Translation.  could only be described as an experiment iF his theory was  127  already accepted. It is no wonder, than, that Hertz's experiemnts have come to be accepted as confirmations of an aspect of Maxwell's theory. For in a strictly logical sense, this is what it might be taken for. OF course, Hertz's work also has the more significant role of confirmation of his version of Maxwell's theory, which pace logical problems, it is for all practical purposes. The acceptance of Hertz's work, thus, depended in part on the sort of "pragmatic," in fact, namOiLkagpOhbanil,.approach to .s.ciance that I have set in opposition to Helmholtz's approach of rigorous metaphysical grounding.  On January 1st, ,1894,Hertz died of a chronic oral abscess. Later that year he was Followed by the braf Hermann von Helmholtz. German science remembered both men warmly, and Helmholtz in particular was eulogized throughout the world. Their passings, coincident with the passing of a scientific era that finally ended when Helmholtz's friend and peer, Lord Kelvin, died in 1907, has obscured their opposition to scientific romanticism. That triumphant programme of metaphor and paradigm which has embraced as agenda the Fact, probably always true, that science has no logical3 basis except that which working scientists choose to give it.  128. Endnotes, pp.^115-127.  1.  Bellone, pg. 160.  Brush, pg. 411. 2. Hertz, Principles, pg. viii. 3. Hertz, Electric Waves, Introduction. 4. S. Buchwald, Maxwell, pp. 177-passim. Ibid. 6. See Fullenwinder. 7. 8. Buchwald, "Background," pp. 280-286. S.^Ibid. pg. 286. 10. Ibid. pg. 291. 11. Halliday and Resnick, pg. 566. 12. O'Hara, pg. 39. 13. Buchwald, Maxwell, pg. 263. 14. Hertz, Misc. Papers, pp. 280-288. 15. O'Agostino, "Hertz's Researches," pg. 271. 16. Whittaker, pg. 419. 17. In conversation, Or. Eiuchwald has expressed an insightful and original interpretation of Hertz's own understanding of his apparatus which will undoubtedly modify this account considerably. Not being in a position to comment further, I will simply note that Or. Buchwald's book on the subject is expected in the Fall. 18. Hertz, Principles, pp. 21-22. 19. Hertz, Memoirs, pg. 351. 20. O'Agostino, "Fiourquoi.." pg. 65. 21. Ibid. pg. 76.  Conclusion  ^  129.  By the middle of the Nineteenth Century the field of natural philosophy had become somewhat divorced from philosophy proper in Great Britain, but philosophical concerns still dominated a number of dBrman scientific communities. Building on the Kantian answer to Hume's scepticism about the applicability of causal reasoning, the school of J. Mueller pursued causal explanations of biological activity. These explanations were in turn integrated into a larger reconciliation of Kantian mechanism and teleological paradigms.  The teleological conception in its grosser from was challenged by the young Hermann Helmholtz. He proposed a new interpretation of Kantian apriorism that appeared to discard teleology in biology and offer a universal statement of the necessity of causality prior to experiental knowledge. The universal statement of this truth was Helmholtz's Conservation of Force. This concept of force as the ultimate cause of change in nature escapes modern and simply mathematical and vectorial definitions of force without being incompatible with them. For this reason the Helmholtzian concept of force had a broad enough applicability to be used to describe the causes of all phenomena within the realm of science. It was in  130 a broad sense a unifying concept and also imposed upon physics  a style that held as primary the assumption that explanation of "cause" in physics could be accomplished by relating observed change in nature with correlated observed activity. That correlated activity was taken as the necessary cause of change and was therefore defined as force. Not surprisingly, other, "romanticully inclined" .g.ciontiuts did not complot ly accept Helmholtz's programme.  This concept of conservation of force embraced and included the earlier notion of conservation of vis viva, or, as Thomas * the concept Young called it, "conservation of energy., '. of energy only took on a meaning beyond that of the vis  viva in mechanics when Maxwell applied the Poisson equation to electric fields and began to call Poisson's potential the potential energy of an electric field. From there Maxwell went on to speak of the propagation of energy through the void. Maxwell's disciple, Poynting, described electrical activity entirely in terms of energy flows. Probably as a result of semantic confusion Maxwell thought his concept of energy was the same as Young's and therefore that the German-Joule-Thomson "Conservation of Force" was a statement of the conservation of energy as he formulated the concept.  *See Elkana, Discovery, pg. 25.  131.  In this mistaken assumption Faraday for one tried and failed to disabuse him. Other British physicists, in particular Lord Kelvin, but also his collaborator  .b. Tait enjoined  upon Maxwell a greater caution in the use of mechanical analogy. Understanding Maxwell as like them --in that_his First concern must be to hang his aether based theory of electromagnetism on a credible mechanical model of nature For the sake of consistency and reality^-- they mistook Maxwell's romantic view of nature for the^certainties of the mechanical philosophy. Thus, to the end of his life Kelvin was convinced that Maxwell's theory was simply flawed by the absence of a mechanical model. He did not have the insight into "error" to realize that Maxwell's concerns were different and more pragmatic, and with his priorities set on the fundamental flaws of Maxwell's theory (as he saw them) Kelvin failed to see that taking Maxwell seriously led to a revision of the concept of energy which Kelvin himself had helped introduce to British physics.  The Maxwellians who followed Maxwell thus from the first were not well-disposed to mechanical explanation. they proposed as alternative an electromagnetic aether but did not deeply explore the metaphysical implications of such an artifact. On the contrary, their metaphysical exporations were inclined to lead them into Spiritualist accretions to Victorian Christianity, and thus even farther from mechanical materialism.  132.  The Maxwellians were eventually confronted with a German "proof" of Maxwell's electromagnetic theory of light from a camp that had previously indicated its hostility to true Maxwellianism. This was the camp of Helmholtz, which had been quick to throw out essential elements of Maxwell's theory in the course of reconciling it to the main streams of  darman thought. Although they don't appear to have realized  it, Hertz's work was more of the same.  This reinterpretation eliminated the need for Maxwell's concept of energy. Energy became nothing more than an abstraction to be retained if it could be used to advantage. Hertz indicated a strong desire to rid physics of energy entirely within the realm of mechanics. His ruminations appear to have led him to consider energy an unnecessary concept, a needless multiplication of hypothetical entities. He would have been more sure of this were he fully aware of just what kind of entity energy really was in Maxwell's theory.  Hertz's scepticism about energy and his teacher's Conservation of  Force concept are genuinely irreconcilble with the cGncept  of  energy still used by physicists who honestly believe  they are employing "Maxwell's equations." The problematic  133. synthesis that in fact reigns continues to render the language of physics unnecessarily opaque. Evidence of the incoherence that can result from this opaqueness is to be amply found in the ubiquitous use of the concept of energy as a virtually magical thing in itself by pseudo-science of all kinds down to the present day.  -30-  134. Bibliography I.^Primary Sources Descartes, Rene, Discourse On Method and the Meditations, London: Penguin, 1968. Helmholtz, Graf Hermann, Hermann von Helmholtz: Epistemological Writings, Boston: D. Reidel, 1977. the-Mansfot.mationsof the_Natural_Forces," American Journal of Science, vol. 24, 1851. pp. 189-216. -Don-ItLought_In_Medicine, Baltimore: Johns Hopkins, 1938. On the Sensa:tilz,ns_of Tone, London: Longman, Green, and Co. 1875. "The Origins of the Correct Interpretations of Our Sensory Impressions," in Helmholtz's Writings on Perception, Boston: D. Rzddel, 1978. Popular Scientific Lectures, London: Longman, Green, and Co. 1884. "Professor Helmholtz on systems of Absolute Measurement," Philosophical Magazine,^1882:2. Series 5, 14. pp. 430440. "Ueber die Electricitatsleitung," Annalen der Physik und Chemie, 1878: pp. 201-216. "Ueber eine Electrodynamische Wage," Annalen der Physik und Chemie, 1873: pp. 22-54. Hertz, Heinrich, Electric Waves, New York: MacMillan, 1894. Memoirs, Letters, Diaries. San Francisco,liSan Francisco Press, 1977. Miscellaneous Papers, New York: MacMillan, 1895 Principles of Mechanics, New York: MacMillan, 1910.  13E.  Kahl, Robert. Selected Writings of Hermann von Helmholtz, Middletown, Conn: Wesleyan University Press, 1971. Kant, Immanuel, Critique of Pure Reason, London, MacMillan, 1896. Kargon, Robert, and Peter Achinstein (ed.) Kelvin's Baltimore Lectures and Modern Theoretical Physics, Cambridge, Mass: The MIT Press, 1987. Lagrange, J.L. Mecanique Analytique, Paris, Librairie Scientifique et Technique, 1965. Laplace, Marquis de. Celestial Mechanics, New York: Chelsea Publishing, 1966. Maxwell, James Clerk, Treatise on Electricity and Magnetism, Oxford: Clarendon Press, 1892. Newton, Sir Isaac. Principia Mathematica, Glasgow: MacMillan and Son, 1871. Thomson, Sir William, and P.G. Tait, Treatise on Natural Philosophy, Cambridge; University Press, 1879.  Secondary Sources. Archibald, W.T. Eine Sinnreiche Hypothese, Ph. O. Thesis, University of Toronto, 1982. Barnouw, Jeffrey, "Goethe and Helmholtz: Science and Sensation," in Goethe and the Sciences: A Reappraisal. (F. Amrine, E.J. Zucker, H. Wheeler, eds.) Boston: O. Reidel, 1987. Beichler, J.E. "Hyperspace Mcdels of the Ether in America," in The Michelson Era in American Physics, Stanley Goldberg, Roger H. Stuewer, (eds.) American Institute of Physics: New York, 1988. pp. 206-233. Buchwald, "The Background to Hertz's Researches in Electrodynamics," in Nature, Esperiment, and the Sciences, T. H. Levire, and W. Shea, (eds.) Boston: Kluwer, 1991. "Thomson's Mathamatization of Faraday's Electrostatics," Historical Studies in the Physical Sciences, 8:1978.  126. From-Maxwell to Microphysics, Chicago: University of Chicago Press, 1985.  Chalmers, A.F. "The Limitations of Maxwell's Electroma=netic Theory," Isis: 1973. vol 64. pp. 469-483. Clark, Peter. "Elkana on Helmholtz and the Conservation of Energy," British Journal for the Philosophy of Science, 1976. vol. 27, pp. 165-175. Collingwood, Idea of Nature, Oxford: Clarendon Press, 1945. Drake, Stillman. Schofield Review in Isis 62: 1971, pg. 239. O'Agostino, Salvo. "Hertz's Researches on Electromagnetic Waves," in Historical Studies in the Physical Sciences, v. 6, part 1; 1976. pp. 260-323. "Pourquoi Hertz et non pas Maxwell a-t-il d6couvert les ondes electrique," Centaurus, 22: 1989. pp. 66-75. "Weber and Maxwell on the Oiscovery of the Velocity of Light in Nineteenth Century Electrodynamics," in On Scientific Discovery, Mirka Orazen Iirmek, Robert S. Cohen, and Guido Cimino, eds. Boston: D. Reidel, 1977. Elkana, Yehuda. The Discovery of the Conservation of Energy, London: Hutchinson Educational, 1974. "Helmholtz's Kraft: An Illustration of Concepts in Flux," Historical Studies in the Physical Sciences, 2:1979, pp. 263-293. Fullenwinder, S.P. "Hermann von Helmholtz: the Problem of Kantian Influence," Studies in the History and Philosophy of Science. March, 1990. vol. 21, no. 10. Hahn, Roger. "Laplace and the Mechanistic Universe," in God and Nature, David Lindberg and Ronald L. Numbers, (eds.) Berkeley: University of California Press, 1986. Harman, P.M.- "Mathematics and Reality in Maxwell's Dynamical Physics," in Kargon, pp. 267-299. Energy, Force and Matter, New York: Cambridge University Press, 1982.  127.  Halliday, David, and Robert Resnick, Physics. Toronto: John Wileyand Sons, 1978. Basic concepts in Relativity and Early Quantum Theory, Toronto: John Wiley and Sons, 1983.  Hesse, Mary. Forces and Fields, Toronto: Thomas Nelson and Sons, 1961. Holt, Niles R. "A Note on Wilhelm Ostwald's Energism," Isis, vol 61: 1970. pp. 286-389. Hunt, Bruce J."How My Model Was Right:' G.F. Fitzgerald and the Reform of Maxwell's Theory," in Kargon, pp. 299323. "Practice vs. Theory: the British Electrical Debate," Isis, 74: 1983.^pp. 341-355. Jungnickel, Christina, and Russell McCcrmmach, Intellectual Mastery of Nature, Chicago: University of Chicago press, 1986. Jordan, D.W. "D.E. Hughes, Self-Induction, and the Skin Effect," Centaurus, 26: 1982, pp. 123-153. Kargon, Robert. "Model and analogy in Victorian Science: Maxwell's Critique of the French Physicists," Journal of the History of Ideas, vol 30, jul-Sept. 1969, pp. 423-436. Knudsem, Ole. "An Eclectic Outsider, J. Willard Gibbs, on the Electromagnetic Theory of Light," in Goldberg, Stuewer, pp. 224-235. Koenigsberger, Leo. Hermann von Helmholtz. Braunschweig: Friedrich Vieweg und Sohn, 1903. Lorraine, Paul and Dale Corson. Electromagnetic Fields and Waves. New York: W.H. Freeman, 1970. Lenoir, Timothy. The Strategy of Life. Chicago: University of Chicago Hress, 1989. Maxwell, James Clerk. "Maradoxical Philosophy," in Nature Vol. XIX:1878, no. 477.^pp. 141-143.  Merz, John Theodore. A History of European Thought in the in ti-re Nineteenth Century, Toronto: Dove, 1985.  1=2.  Mason, Stephen F. A History of the Sciences, New York: MacMillan, 1956. Miller, Arthur T. "A précis oF Edmund Whittaker's 'Relativity Theory oF Poincare and Lorentz," in Archives Internationales d'Histoire des Sciences, vol 37: June, 1987, no. 118. pp. 92-103. O'Hara, J.G. and W. Pricha, Hertz and the Maxwellians, London: Peter Peregrinus, 1987. Schofield, Robert. Mechanics and Materialism, Princeton: University of Princeton Press, 1970. Simpson, Thomas K. "Maxwell and the Direct Experimental Test of his Electromagnetic Theory," Isis, vol 57: 1966. pp. 419-432. Sloan, Philip R. "Descartes and the Sceptics," Studies in the History and Philosophy of Science, 8:1977, no. 1. pp. 299-323. Smith, Crosbie, and Norton Wise. Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge: University of Cambridge Press, 1989. "The Practical Imperative: Kelvin Challenges the Maxwellians." in Kargon, pp. 323-349. Stromberg, Wayne H. "Helmholtz and Zoerner," Journal oF of the History of the Behavioural Sciences, vol. 25: 1989. pp. 375-381. Westfall, Robert R. Force in Newton's Mhysics. London: MacDonald, 1971. Never at Rest, Cambridge; Cambridge University ^ess, 1980.  "The Rise of Science and the Decline of Orthodox Christianity; Kepler, Descartes, and Newton, in Lindberg and Numbers. Wilson, David B. "the Thought of Late Victorian Physicists; Oliver Lodge's Ethereal Body," Victorian Studies, vol. XV. Sept. 1971. No. 1, pp. 29-48.  Wise, Norton M. "the Maxwell Literature and the British Dynamical theory," Historical Studies in the Physical Sciences, vol. 13, 1985. part 1, pp. 174-201. . WoodruFF, A.E. "the Contributions oF Hermann von Helmholtz to Electrodynamics," Isis, vol. SS: 1968. pp. 300-211.  


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