THE HISTORICAL DEVELOPMENT OF ENERGETICS BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE

Editor

ROBERT S. COHEN, Boston University JURGEN RENN, Max-Planck-Institute for the History of Science KOSTAS GAVROGLU, University of Athens

Editorial Advisory Board

THOMAS F. GLICK, Boston University ADOLF GRUNBAUM, University of Pittsburgh SYLVAN S. SCHWEBER, Brandeis University JOHN 1. STACHEL, Boston University MARX W. WARTOFSKyt (Editor 1960-1997)

VOLUME 209 Georg Helm (1851-1923) THE HISTORICAL DEVELOPMENT OF ENERGETICS

By

GEORGHELM

Translated, and with an Introductory Essay by

ROBERT 1. DELTETE Seattle University, USA

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication Data is available.

ISBN 978-94-010-5915-2 ISBN 978-94-011-4471-1 (eBook) DOI 10.1007/978-94-011-4471-1

Printed on acid-free paper

AII Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originaily published by Kluwer Academic Publishers in 2000 Softcover reprint ofthe hardcover Ist edition 2000 No part of this publication may be reproduced or utilized in any form or by any means, electronic, mechanical, inc1uding photocopying, recording or by any information storage and retrievai system, without written permission from the copyright owner. TABLE OF CONTENTS

Translator's Note 1

Helm's History of Energetics: A Reading Guide 4

Primary Sources 46

Glossary of Terms 50

GEORG HELM: THE HISTORICAL DEVELOPMENT OF ENERGETICS

Preface 55

Contents 57

Part One: The Establishment of the First L aw 65

Part Two: Preparation for the Second Law 107

Part Three: Classical 125

Part Four: New Initiatives, Disputes and Misplaced Efforts 161

Part Five: The Energetic Treatment of Chemistry 181

Part Six: The Energetic Foundation of 253

Part Seven: Factors 299

Part Eight: The Mechanical Approach to Energetics and Mechanical Pictures 363

Index 405

Vll TRANSLATOR'S NOTE

As anyone who has tried it knows, translating an essay or a book for publication is much different from translating passages for scholarly use. I have done much of the latter; I have also done some of the former ~ but nothing on this scale. I came to this project with liabilities. I am neither German nor am I fluent in the language; I am not a physicist or a physical chemist. I do, however, know something about energetics, having written a doctoral dissertation and several essays on the subject. This is one explanation for what otherwise might seem to be ~ and often seemed to me as I was doing it ~ incredible hubris. Other explanations are given in the acknowledgements below. I have read that to be a good translator, one must be a good lover. The suggestion here is that to translate well, one must be intimately acquainted with the text. With this, I agree. At the same , one cannot be a good lover without allowing the other to stand on her own. Friends who have done translation have also told me ~ rightly, I think ~ that there is no such thing as a translation in which the translator does not impose his own style. And this, evidently, is at odds with allowing the text to stand on its own. What, then, to do? I do not think that any reader of Helm's book would proclaim him a great stylist. Certain passages excepted, his writing tends to be stiff and ponderous, such as we might expect from a nineteenth-century German academic. I had therefore to make a decision: to render his in English pretty much the way he wrote it in German, or to rewrite it so that it would be more comfortable to contemporary English readers. For the most part, I decided on the former course, although I was sorely tempted by the latter one. I did so for two reasons. As much as possible, I wanted to avoid the temptation to interpret Helm in translating him: to revise a person's style is to run the risk of altering his intent. Moreover, I think that writing style tells us something about a writer, and to transform his style is to make him into something other than what he was. There are hermeneutical snags here, of course, and I do not pretend to have avoided them all; but I did think long and hard about how best to translate Helm's book, rather than simply writing one of my own. A few comments on the translation I have produced may therefore be helpful to readers of it. To begin with, Helm writes much of his history in the present 2 THE HISTORICAL DEVELOPMENT OF ENERGETICS tense. 1 have followed him here, not just out of fidelity, but because 1 think it gives his subject more immediacy. My central concern throughout has been to convey accurately the content of what Helm wrote. However, 1 often separate long, convoluted sentences into shorter, more easily digestible ones. When there seemed to be natural breaks, moreover, I have divided extended, straggly paragraphs into more wieldy ones. That is, I move, whenever possible, in the direction of simplicity and clarity, without (I hope) distorting Helm's style too much in the process. For the same reason, 1 add pronouns, or replace pronouns with proper nouns, when this seemed to facilitate the reading. 1 also occasionally add words that are not in the text to make connections with what has gone before more readily apparent. My hope in these maneuvers is to make Helm's work more easily accessible. At the same time, owing to Helm's frequent parenthetical remarks and his fondness for examples and elabora• tions, 1 often could not avoid ample use of commas and dashes as a way of rendering his intent clearly, if not always very gracefully. There is also the annoyance that Helm makes use of a number of troublesome words the translation of which is difficult. 1 therefore include a glossary of some of the more problematic terms and phrases and my translations of them. The list is not intended to be exhaustive and 1 do not explain many of my choices; but 1 hope that interested readers will find the glossary both manageable and useful. Two additional comments are perhaps in order. Helm quotes from works written in French and English, as well as from ones in German. 1 translate his German translations of these quotations. When he quotes from German translations of works, moreover, 1 translate the version he employs. It would have been better, no doubt, to use, or translate from, the originals; but I have resisted that temptation for two reasons. First, the originals are frequently obscure or not readily available; second, I wanted to finish this translation in a reasonable amount of time. General readers, I think, will not be led astray here. And scholars interested in the issues Helm addresses will, in any case, want to examine the originals - including the original of Helm's text - and not rely on my translations of them. A related matter concerns the references. Helm often mentions figures or works without providing citations. 1 do not try to track down the sources he refers to in the text but does not cite in his notes. Helm's notes, moreover, are casual, abbreviated and inconsistent. 1 also do not flesh out his notes, to make of them the sort of proper citations we now customarily expect, nor do 1 try to resolve his inconsistencies. 1 translate his citations as given, but do not go beyond that. Where 1 have noticed them, however, 1 have corrected typogra• phical errors in the text and equations, and - when it is obvious - have occasionally added symbols to the equations that were inadvertently omitted. I have also added some terms to his index to make access to particular authors or subjects easier. Anyone who undertakes a project of this sort incurs large debts. 1 cannot properly thank all those who have helped me with it, but 1 do want to acknowledge some of them. Since 1 had already prepared a rough translation of Helm's Energetik in the process of writing my dissertation, a kind invitation TRANSLATOR'S NOTES 3 from Robert S. Cohen to publish the translation as a in this series seemed possible and feasible. In addition, a sabbatical leave gave me the time to rethink the text and rework the rough original. I thank Bob for his encourage• ment and Seattle University for the release time it provided me to complete the project. For help with the German and the historical period in which Helm's book was written, I am indebted to Russ McCormmach, who took time off from a manuscript of his own to assist me with mine. For help with the physics, I relied - as I always do - on the secure knowledge and uncommon good sense of Reed Guy, my colleague at Seattle University in the Department of Physics and a frequent collaborator with me in projects that must seem bizarre to both our departments. Reed is not responsible for my final choices in translation, or for mistakes in translation that still inhabit the text; but he provided welcome support and prevented me from making countless mistakes I otherwise would have made. As always, my most extended and least tangible debt is to my wife, Pat. She has born patiently and usually cheerfully the compulsion, inattention and moodiness which are, it seems, the usual concommitants of my research. She has also read each draft of the work, subjecting it to her careful scrutiny, and has made many suggestions for improvement - most of which have been incorporated into the final version. Even more so than with my dissertation, which I wrote almost twenty years ago, Pat must have wondered whether this project was worth the effort; but she has remained my tower of strength throughout. For her understanding and support, for her faith in me and her constant, loving presence - for that, and much else besides, I thank her. HELM'S HISTORY OF ENERGETICS: A READING GUIDE

1) The introduction to the book you now hold is lengthy and, I hope, useful; but I once had larger plans for it. Originally, I had thought of developing Georg Helm's own version of energetic theory up to 1898, when the book was first published, showing in relief the changes it had undergone. My idea was to do this in a rather technical manner, which befits Helm's own development. Along the way, I was also going to compare Helm's position with the version contemporaneously developed by his uneasy ally, Wilhelm Ostwald; describe the Liibeck debate on energetics, which helps to explain some of the content and tone of the book; and summarize the post-Liibeck critiques of energetics and Helm's consequent history of the subject. For me that plan was defeated by the sheer number of works to be considered and the complexity of the issues they address. 1 In its place, I instead offer a sort of "Reading Guide" to Helm's Energetik. The guide is rather informal and discursive: It is not intended to be comprehensive, will not be overly technical, and will not deal with every twist and turn in the text. Though the book is pitched to physicists and mathemati• cians, my essay is intended for a more general reader - if such there be for this sort of work. As with the translation, my overall objective is to provide easier entry into what is often a very difficult book to understand from a contempor• ary standpoint. My remarks should therefore be read as orienting guidelines to the global contours of Helm's history and its context, coupled with some recommendations on what to look out for, rather than with the expectation of finding detailed analyses or evaluations of Helm's arguments. Notes to primary sources (cited internally by means of superscripts) refer to the list of references at the end of the essay. (An exception is Helm's 1898: In the text I refer to pages from the translation, enclosed in brackets [ ]; but in the notes I refer only to pages from the original. Internal cross-references in the original have been amended, in the translation, to refer to pages of the translation, and are also enclosed in brackets.) Substantive comments and a few citations to more recent works are included as endnotes - for the benefit of scholars, but so as not to interrupt the flow of the narrative. Although I was not able to carry out my original project, its issues do infuse this essay - as will be evident to readers.

2) Before discussing Helm's book, I should like to say something about the man who wrote it. This is not easy, for the available sources are meager.2 Georg Ferdinand Helm was born in 1851 in Dresden, where he spent almost his entire life. The son of a cabinet-maker, he was educated in mathematics and physics at the city's Poly technical Institute; there he was a student of Gustav Zeuner, who exerted an important formative influence. He then studied for three years at the

4 HELM'S HISTORY OF ENERGETICS: A READING GUIDE 5

Universities of Leipzig and Berlin, where he attended the lectures of Wilhelm Henkel, Carl Neumann and probably those of . He received his doctorate from Leipzig in 1881 for a dissertation, written under Neumann, on differential equations in mechanics. For nearly fourteen years, beginning in 1874, Helm taught mathematics and physics at the Annenschule in Dresden, where he was instrumental in the reform of education in physics and mathematics. He left in 1888 to become extraordinary professor of analytical geometry, analytical mechanics and mathematical physics at the Polytechnicum, and remained in that position until 1892 when he was appointed ordinary professor of the same subjects at the newly founded Technische Hochschule.3 Helm then filled this position for fifteen years, until 1906, when he was named professor of applied mathematics. He held that position until he was forced by illness to retire in 1920. Helm was accorded the title "Geheimer Hofrat" in 1903 and was elected rector of the Technische Hochschule for the academic year 1910-1911. He died in Dresden in 1923, after an academic career spanning almost haIfa century. Helm's research, reflecting the influence of Zeuner, Neumann and the mathematic an, Gustav Schl6milch, was largely at the interface between mathematics and physics.4 It also reflected the wide range of his interests and teaching responsibilities. 5 Early on, he investigated problems in analytical mechanics and mathematical physics, including gravitational theory and the aether, as well as in the theory of probability (1877a, 1877b, 1878, 1879, 1880, 1881). A textbook, The Elements ofMechanics and Mathematical PhYSics, based on lectures at the Polytechnicum, appeared in 1884 (1884). Later publications include more studies in mechanics, probability theory, and the possibility of reconciling the principle of relativity with the hypothesis of an aether; investigations into insurance statistics and statistical phenomena in biology; essays on scientific epistemology; and longer treatises on electrodynamics and the basic principles of higher mathematics (1892b, 1895c, 1902, 1912a, 1912b, 1912a, 1917; 1887b, 1899; 1907b, 1916; 1904, 1910).6 He is probably best known today, however, for his systematic development and vigorous defense of energetics.7

3) Helm's interest in developing a theory of energy is first announced in a monograph, The Theory of Energy (1887a), which is developed "historically and critically" in the manner of Ernst Mach's history of mechanics, published four years earlier (Mach 1883), and which proposes (as its subtitle suggests) the formulation of a "general energetics".8 There is no evidence of any such interest in earlier writings, and later ones seldom refer to it explicitly (1904, 144-45; 1907a, 372; 1907c, 29). Helm's active promotion of energetics is, therefore, relatively confined. An essay in 1890 sought to reduce mechanics to energetics (1890b), and another in 1892 was likely intended to bring and magnetism within the compass of the new theory of energy (1892a). An exploratory note (1893) anticipated a book on the energetic development of physical chemistry (1894). These publications, plus more wide-spread interest in energetics, led to an invitation to address the 1895 Lubeck meeting of the 6 THE HISTORICAL DEVELOPMENT OF ENERGETICS

German Association of Scientists and Physicians "on the current state of energetics" (1895a). The heated debate at the Lubeck meeting proved to be a disaster for energetics and an unhappy occasion for Helm personally. It and he were apparently attacked from all sides. Helm was offended and deeply hurt.9 The situation worsened when the physicists Ludwig Boltzmann and Max Planck quickly recorded their negative appraisals of energetics in the Annalen der Physik (Boltzmann 1896b; Planck 1896), with Planck's short essay being probably the most blunt, unkind thing he ever wrote. Given what he thought had happened to him in Lubeck - that he had been set up, lured into a traplO - Helm was outraged. He responded with a vigorous reply, as did his only Lubeck ally, the physical chemist Wilhelm Ostwald (Helm 1896; Ostwald 1896a). But the traumatic effect on Helm of the meeting was deep and lasting, as is obvious from the Preface to his history. That work - or, rather, a book devoted to the "history of the energy principle" - had been commissioned before the Lubeck controversy; but the shape and sometimes the tone it eventually assumed were profoundly affected by the outcome. II (To be sure, Helm's work usually illustrates the detached, "objective" features of a sober German academic treatise; but it is also a very personal statement. The reader who ignores Helm's occasional passion, and the reasons for it, therefore misses a good deal of what the work meant to him.) At the same time, the history of energetics that Helm produced seems to have been a cathartic experience: It allowed him to vent pent-up anger and frustration and gave him new peace of mind. He published on energetic subjects afterwards (e.g. 1907a, 1907b; 1913a, 1913b); but, as indicated above, he did not again exercise himself in aggres• sively defending the new theory of energy. 12

4) In line with the overall intent of this introductory essay, a brief overview seems in order. In his history of energetics, Helm sought to achieve several distinct, although often closely related, objectives. First, he tried to revise, amplify and defend his own development of energetic theory, especially in mechanics and thermodynamics. Accordingly, a fair amount of Helm's book discusses his earlier contributions to the subject - from his first work in 1887, through his studies on the energetic foundations of mechanics, thermo• dynamics and electromagnetism of the early 1890s, to his Lubeck reports and his reply to the published criticism they provokedY Here, Helm's objective is often personal: He wanted to secure his place in the history of the "mathema• tical development of energetics,,14 by defending his own work against the charges of simple-minded error or vacuity made by his principal critics. More importantly, for my purposes, Helm also sought to defend and promote a certain conception of what energetics was really about - a view of the history, nature and goal of physical theory - that would both respond to critics and also separate his vision of a science of energy from that of others, notably Ostwald, who had contributed along similar lines. Here he in part restated ideas he had expressed in earlier works, but more forcefully and systematically, and in part recast them (Parts VI and VII, especially). Finally, Helm sought to describe the HELM'S HISTORY OF ENERGETICS: A READING GUIDE 7 overall evolution of the "energetic tendency in natural science,,,15 and to show that while that evolution had sometimes followed fitful and inauspicious paths, it nevertheless amounted to nothing less than a "great reorientation in the human understanding of natural events" [55]. For the last project there was already a model - although one of which Helm was probably unaware until his own work was well underway. This was Ostwald's Electrochemistry: Its History and Theory, published in 1896 (1896b).16 Helm's history of energetics was intended to show that natural science had progressed fitfully, though not inexplicably, in the direction of a comprehensive and unified science of energy. But his treatise differed from its energetic predecessor in at least two respects. First, it explicitly defended the larger thesis that natural science as a whole - and not simply electrochemistry - had evolved in the direction of a mature energetics; and second, it argued that that evolution had realized, or was in the process of actualizing, a certain conception of energetics, namely, the one to which Helm himself subscribed.

5) Consonant with the generalist approach of this essay, my remarks will focus on Helm's last two objectives, rather than on his first one. Let me begin, therefore, by saying a bit more about his understanding of the historical evolution of science before I discuss his conception of energetics. In a quasi• Hegelian manner, Helm saw this evolution moving in the direction of a completed energetics - a science of energy, rightly conceived. The idea of history with a lelos (goal) is not accepted by most historians today and will probably be difficult for many readers to comprehend; but it is essential to understanding Helm's history of energetics. This idea need not be taken as a claim that history is the working out of the purposes of some Creator who has set the whole process in motion, or, more mysteriously, as a suggestion that the universe itself can somehow have purposes. There is no evidence I am aware of that Helm accepted either of these views. He is best read as thinking that reflection on our scientific past enables us to discern the direction the history of science is taking and the destination it will ultimately reach. The opening quotation from the French physicist, Pierre Duhem [65], with its metaphor of the rising tide, is therefore crucial and should be read carefully, since it provides a graphic illustration of how Helm thinks history works. At the same time, Helm's comments on this passage may be misleading. He tells readers that to understand the emergence of energetics, initial attention should be paid, not to the "efforts of original thinkers, to the ideas of prescient minds, which were not understood by their contemporaries ... [since] these are [only] waves that lick upward, but [which] quickly sink back into the general level.. .. To follow the gradual rising of the intellectual level," Helm says, we must "first focus on the broad knowledge of the age, the generally recognized academic wisdom - however unpleasant to contemplate this may be" [65]. The "academic wisdom" Helm rehearses [65-68] is outdated and his objections to later (and, in his view, also outdated) wisdom are clear. But the main focus of Helm's history is on the "prescient minds" who originated and developed energetics and only incidentally - if sometimes pointedly - on the 8 THE HISTORICAL DEVELOPMENT OF ENERGETICS backward ones who opposed it. In keeping with Helm's metaphor, let me call the former thinkers "advanced waves," and suggest that his real objective is to follow the advanced waves, with only side comments on the obstacles that inhibited them. I suggest that readers interested in following the overall argument of Helm's narrative do likewise. 17 This way of proceeding also helps to make sense of another prevalent feature of Helm's history. In general, Helm tended to view his own work - more modestly than Hegel - as only the most recent stage in energetics - he never suggests that his contribution has completed the task - in a historical process to which many scientists and subjects had contributed (e.g. [401]). Accordingly, his history asserted or implied that investigations in diverse fields had either explicitly encouraged or implicitly supported the formulation of a general theory of energy, and he interpreted the ideas of well-known predecessors and contemporaries as anticipations of, or contributions to, such a formulation. To a large extent, that is, Helm seems to have viewed himself as merely collecting together and consolidating the work of other scientists, who, his narrative intimates, did not always understand the larger, energetic implications of their work. I8 He therefore sought to relate his own contributions to earlier ones in a way that they did not appear to be radical departures from much established theory, but rather as clarifications and extensions of what others had - in part, at least - already done (e.g. [194-200,266-78]; also 1895a, XVI-XVIII). This is not always the case, however. Helm did seek to defend his own originality - as is evident, especially, in Parts VI and VII. But, in keeping with his global interpretation of the history of science, he usually tried to fit as much as possible of previous science within the confines of a properly conceived energetics. To use the tidal metaphor, he saw himself as helping to bring the "advanced waves" to a unified focus (e.g. [279-83, 310-11]).

6) One problem with Helm's generously inclusive approach is that his gaze is often very selective: In following the waves leading to an energetics of the sort he welcomed, he usually looked only at certain aspects of work he admired. As a result, he often misinterpreted his favorite authors - Robert Mayer, William Thomson, Willard Gibbs, and Hermann von Helmholtz - or was inconsistent in describing them. Knowledgeable readers will see this problem immediately; less knowledgeable ones should beware of accepting Helm's historical reconstuctions at face value. Another, more general, problem is that Helm appears uncertain of the story he wants to tell. More precisely, he seems unsure whether, in recounting the history of energetics, he is describing an accomplished, or all but accom• plished, fact, or whether he is still urging - as he had in 1887 (1887a, 3, 45- 47,57-58, 71) - the need for a new beginning. Are the "advanced waves" still being beaten back, or have they finally asserted themselves? For the most part, Helm's attitude in 1898 seems to have been that the evolutionary development of science had already led to the emergence, growth and maturation of energetic ideas, that traditional mechanism and atomism (their opponents) were dying, and that outdated views had only to be resisted HELM'S HISTORY OF ENERGETICS: A READING GUIDE 9 when efforts to save them betrayed a misplaced sense of priority or when they obscured the important differences between molecular-mechanical theories and energetics. Thus, for example, he comments as follows on the idea that is a kind of molecular motion:

It seems to me unnecessary today to take the field against the mechanical hypothesis with the clatter of weapons. It has done its duty. The wave in the sea of scientific theories, of which we spoke in the introduction to this book, has risen and now falls, after having prepared the path for energetic ways of viewing things. One must combat only the attempt to maintain this mechanical hypothesis through all sorts of artificialities, as if the existence of moving atoms was more important than the simple description of experience. Above all, however, the conflation of energetics with the molecular hypothesis - which still has by no means been stamped out - must be resisted [193].

This is an example of Helm reasonably calm and collected, more or less dispassionately surveying the history of scientific ideas. Sometimes, however - especially when, in the heat of argument, he is trying to defend his own ideas - he is less sanguine and more revolutionary. Here is a passage in which he defends one of those ideas against what he regarded as outdated but deeply entrenched prejudice:

In view of the antipathy which [at Lubeck] met the intensity law,19 and the modern energetics attached to it, I am unable to suppress a suspicion. Steps have been taken here, steps regarded by the energeticists as progressive, which now appear so extraordinarily simple and self-evident. [Energetics does see the salvation of physics] in a revision offundamental concepts, [but this] no doubt strikes some as too trivial. I suspect that opponents are ill• disposed towards energetics because it pays less attention to the most sublime things than it does to the most elementary ones .... Certainly, energetics wishes to try a new start on fundamentally new paths; the old tracks are worn out enough! Back to nature, to the nature of all theorizing, to our most basic ideas about natural events!20

There is, then, a tension in Helm's narrative between the serene view that energetics has already triumphed - or all but triumphed - in the evolutionary course of the history of science and the defiant view that the struggle for its supremacy has only just begun. The former view dominates most of Helm's text; but, rhetorically, at least, the latter one seems to prevail - in, especially, the emotional call-to-arms in the last, triumphal pages of his history [403-4].

7) Another tension, again related to Helm's overall view of the history of science, also makes his history of energetics difficult to follow. While insisting throughout his study that energetics must be seen as "a unified intellectual 10 THE HISTORICAL DEVELOPMENT OF ENERGETICS movement" and "a great reorientation in the human understanding of natural events" [55,404], Helm nevertheless recognized, as he had in his Lubeck reports (l895a, III-V; 1895b, 28-30), two distinct, coherent and more or less indepen• dent lines to its development - one from the side of mechanics and another from the side of thermodynamics.21 The main line of development, he now declared explicitly, was from the side of thermodynamics [154,192-94,256-60,380-81]; but he continued to interpret what he called the "principle of analogy" in a way that mechanically-oriented physicists such as Helmholtz and Boltzmann, and Maxwell and Hertz, could be regarded - in much of their work, at least - as having contributed to the formation of a science of energy (see Part VIII and 1895a, IV-V). The natural question to ask, of course, is: "Why did Helm think that energetics constituted a unified intellectual movement when he conceded the existence of two different, independent lines of energetic development (Rich tun• gen), one of which he clearly preferred to the other?" The brief answer - to which I shall return - is that, for him, a mechanical theory counted as a contribution to energetics only if it satisfied certain requirements. Here the important point to stress is that, in his history, Helm's sympathies were evidently with the thermodynamic approach to energetics, which "sees in energy equations nothing more than the purest expression of quantitative relations", and that he sought to interpret the dominant line of energetic evolution in those terms.22 Helm's own conception of a science of energy helps to explain why he would have found that approach most appealing.

8) The conception of energetics that Helm sought to defend and promote in 1898 was one he attributed, in nascent form, to the physician Robert Mayer. That conception is perhaps best approached by contrasting his interpretation of Mayer with Ostwald's, since this approach has the added advantage of highlighting some fundamental differences between Ostwald's vision of a science of energy and Helm's own. Helm and Ostwald included all of the pioneers of among the founders of energetics, but they both accorded a special place of honor to Robert Mayer. Sometimes, their reasons for doing so coincided. Each admired the boldness and independence of Mayer's thought, his skeptical attitude toward prevalent molecular and mechanical hypotheses, and the way he steadfastly opposed any attempt to reduce heat to a form of . Above all, each praised Mayer's insight that all natural phenomena are really energy transformations and his vision of a unifying science of energy.23 But, at the same time, they disagreed fundamentally about the content of Mayer's insight and the meaning of his vision.

9) When Helm praised Mayer in 1898 for the clarity of his insight into fundamental principle, it was for adumbrating the possibility of a science of energy that was a "pure system of relations," exemplifying a phenomenalism of the sort championed by Ernst Mach [80]. Mayer had founded "a new world view," Helm claimed [261], that was both energetic and phenomenalist in HELM'S HISTORY OF ENERGETICS: A READING GUIDE 11 orientation. Like Mach, that is, Mayer was interested only in quantitatively describing and relating the data of experience - the phenomena. Eschewing any metaphysical references to underlying substances or causes, he was satisfied to show that "a relationship exists in consequence of which one phenomenon decreases in favor of another, or increases at its expense" [84]. But Mayer went beyond Mach in suggesting that all our experience, and so all phenomena, are the outcomes of energy relations. That was his "fundamental energetic idea" [76]. This interpretation is fanciful, and, in any case, it conflicts with Helm's earlier reading of Mayer's objective. But that is not my concern here. 24 Instead, I want only to clarify the view Helm attributed to Mayer in 1898, because then Helm did think that a "pure system of relations can be achieved by means of energetics," and this was the "fundamental energetic idea" that he sought to develop, defend and promote in his history of the subject (e.g. [253, 263, 400- 404]). For reasons to be discussed shortly, I will call this Helm's "official position" on the goal of energetics and will collect its main features under one heading, which I shall call the "Relations Thesis". There are epistemological, methodological and (anti)-metaphysical dimen• sions to the Relations Thesis. First, it claims that we can only know phenomena and changes in phenomena, all of which are energetic in character [332, 400]. Second, it claims, in consequence, that the goal of natural science is to describe and relate energy phenomena in the simplest and most unified manner possible. Accordingly, a general theory of energy, or energetics, will relate the phenomena in terms of simple, unifying principles, such as the Law of Intensity and the Factorization Principle, properly construed?5 Third, it rejects all inferences to anything "behind" or "beneath" the phenomena, whether it be atoms or forms of energy. Specifically, it rejects all efforts to substantialize energy or to reify energetic changes in terms of "migrations," "transitions," "transformations," or what have yoU. 26 According to the Relations Thesis, the concept of energy - like any other genuinely physical concept - is empirical and relational, as is the law of its conservation. The energy law was essential to Helm's energetics, of course, even if it was not its basic principle; but for him that law only expressed empirically verified, quantitative correlations between different energetic phenomena. Unverifiable inferences to the existence of an indestructible substance underlying the phenomena were ruled out - dismissed as metaphy• sical speculation - as were any inferences beyond what had been empirically confirmed. "With the pronouncement 'The energy of the world is constant,'" Helm remarked of Clausius' dictum, "the firm footing of the energy law is abandoned, according to which this law is nothing more than an empirical relation between measurable quantities that we find present in any natural process. And for this sacrifice, absolutely nothing is gained in return but an empty saying." He then extended this conclusion to include Clausius' other well-known statement concerning the of the world - that it "tends to a maximum" - commenting that while both had no doubt encouraged a livlier study of energy and entropy than "sober claims that try to express the true 12 THE HISTORICAL DEVELOPMENT OF ENERGETICS importance of these concepts," they were, in fact, "nothing more than metaphysical aberrations" [176].27 The Relations Thesis thus expressed all there is to energetics; but to Helm, writing in 1898, that is all that is needed and warranted. (To follow the overall argument of Helm's history, one must try to keep this in mind - even if Helm does not always adhere to his own policy.) And he portrayed Mayer as its first significant advocate:

Mach has repeatedly and justifiably warned of the mysticism associated with the word 'transform' that has sometimes tried to make its way into energetics. But it emerges clearly from the above words [of Mayer's] that, judged by his manner of thinking, the founder of energetics does not need this warning, although the way he expressed himself in his writings has given some of his followers occasion for misunderstanding. In the sense of its founder, energetics is a pure system of relations [ein reines Beziehungstum] and is not out to place a new absolute in the world. When changes occur, this definite mathematical relationship still exists between them - That is the guiding formula of energetics, and certainly it is also the only formula of all true knowledge of nature. What goes beyond it is fiction [79-80].

10) Ostwald disagreed. In his view, Mayer's most important contribution to energetics was to have ascribed reality and substantiality to energy as well as matter. That was the "essential insight" that Ostwald sought to promote and develop in his first writings on energetics;28 but obstacles had made this difficult. Sometimes, Ostwald claimed that Mayer's insight had been obscured by subsequent developments of the energy concept, especially in thermody• namics, where, he thought, energy often tended to be regarded more as an interesting mathematical function, comparable to the potential function in mechanics, than as a physical reality. Usually, however, he put the blame elsewhere: "One may undoubtedly explain this as a consequence of the rapidly spreading mechanistic conception of nature," a way of thinking he found harder to overcome. 29 Whatever the reason, Ostwald initially only wanted to recover and underline the importance of Mayer's "basic idea", that energy is as real and fundamental as matter. Within a few years, though, he was converted to the way of "pure energetics" and began to defend in his writings the idea that only energy is substantial and real. "The more I reflected on the nature of energy," Ostwald wrote in 1891, "the clearer it became to me that matter is nothing but a complex of energy factors." Given that realization, he concluded that a genuine energetics had to do more than treat energy as "a real substance and not just as a mathematical abstraction" (1891, 566); it had to acknowledge energy as the ultimate substance and the only reality.30 Helm's Relations Thesis was likely on Ostwald's mind, therefore, when he later reflected on the historical evolution of energetics. After proclaiming that his own development of the subject had not only opposed the "sterility of unbridled mechanism," but had also sought to remove energy from "the realm HELM'S HISTORY OF ENERGETICS: A READING GUIDE 13 of mathematical abstraction and to view it as the real substance of the world," Ostwald then proceeded to criticize Helm's initiatives as "a retreat to a position even less progressive than Mayer's" (1926, vol. 2, 157-58).31 For his own part, Helm clearly had large reservations about Ostwald's vision for energetics, but he confined them to correspondence.32 He discussed Ostwald's energetic theory in his history, of course [254, 274, 290, 292-93, 312-13, 340-45,402]. But while he acknowledged the formal shortcomings of Ostwald's proposals, he generally ignored them, preferring instead to focus, more positively, on Ostwald's "search for immediately clear principles" [290] in terms of which to express the basic relations of energetics. His efforts "to arrive at a convincing formulation of these relations - so difficult to grasp in their generality - are worthy of the most prominent notice," Helm wrote. And he added: "In this area, if anywhere, it is easy to find fault, but difficult to do better" [341]?3 Still, there are many critical passages in Helm's history that point in Ostwald's direction, even if Ostwald is not mentioned by name. Here is one example:

I thus consider it ... to be the best thing about energetics that it is capable to a much greater degree than the old [mechanical] theories of adapting itself directly to our experiences; and I see in the attempts to attribute substantial existence to energy a dubious departure from the original clarity of Robert Mayer's views. There exists no absolute; only relations are accessible to our knowledge. Whenever the spirit of research has contentedly reclined on the sluggard's bed of any kind of absolute, it has immediately expired there. It may be a comfortable dream that our questioning can find rest in atoms, but it remains a dream! And it would be no less a dream if we wished to see in energy an absolute, instead of only the most striking expression up to now of the quantitative relations among the phenomena ofnature [401].34 11) Helm's position on the status of energy was never as definite and consistent as Ostwald's late recollection might suggest. In his writings on energetics, Helm vacillates between the ascetic phenomenalism of the Relations Thesis and some form of energetic realism, so that his intent in a given passage is not always clear. Two conclusions, however, are reasonably secure. First, despite his advocacy of the Relations Thesis in 1898, he always spoke of the internal (or intrinsic) energy of a system as if it were a substance. More precisely, he always attributed to a system, as a real possession, a definite , which was a function of its physical and chemical state?5 Early on, Helm also seems committed to another idea which I shall call the thesis of "real presence".36 The real-presence thesis claims that the internal energy of a system can be divided into distinct components (mechanical , heat, chemical energies, and so on), each of which is physically present in the system. Later, however, he rejected as unfounded the idea of real presence, and, in fact, argued vigorously against it, insisting that a physical system no more possesses a definite amount of than it does of heat or volume energy (1898, [337]). 14 THE HISTORICAL DEVELOPMENT OF ENERGETICS

So we may perhaps best summarize the praxis of Helm's history, in contrast to his official position, by saying that while he took for granted a substance view of internal energy, he opposed the thesis of real presence. That is, he treated the internal energy of a system as an undifferentiated "something", but rejected the idea that it can be split up into physically distinct forms. Hence, for example, his approval of P.G. Tait's criticism of Clausius: "We are quite ignorant of the condition of energy in bodies generally. We know how much goes in, and how much comes out, and we know whether at entrance or exit it is in the form of heat or work. But that is all" [172]. Helm did not object in principle to Helmholtz's distinction between "free" and "bound" energy as a heuristic device, or to Rankine's between "actual" and "potential", or even to Clausius' between heat and internal work; but in 1898 he rejected any realistic interpretation of energy components. The appearance of different forms of energy is a sign of internal energy in transition; however, such forms are not themselves really present in different amounts in the energy content of a body.37 12) Ostwald evidently disagreed, but his own considered position is also difficult to reconstruct. From the early l890s, when he first began to write in earnest on energetic theory, he officially subscribed to a view of matter's relation to energy that might be called the "Composition Thesis". On this view, "material objects" (or "bodies" or "physical-chemical systems") are nothing more than energy complexes - spatially co-present and coupled clusters of energy. The Composition Thesis was undoubtedly central to Ostwald's concep• tion of energetics; in fact, acceptance of it in some form or other constitutes much of what he later meant when he spoke of his conversion to "pure energetics" (1926, vol. 2, 168-70).38 In his more detailed discussions of energetic science, however, Ostwald employed a quite different view of matter's relation to energy. Then he casually spoke of an object or system "containing" (or "possessing" or "having") energy of certain kinds in certain amounts - as if a system were not the same as, but something in addition to, its energy content. In short, he assumed that objects or systems were "energy containers". When he did so, moreover, he also usually just assumed, without comment, that every system contains definite amounts of distinct forms of energy (real presence) and that in each case the total energy content is given by the sum of the amounts of each form (really) present.39 This view, into which Ostwald slipped whenever he attempted a mathematical development of energetic theory, might therefore be called the "Containment Thesis".40

13) Gathering together these brief remarks, I may quickly summarize the results of my comparison: In his history of energetics, Helm defends and promotes the Relations Thesis. This is his "official position" and the one he thinks has evolved, or is evolving, in the history of science. The scientific Weltgeist is moving in the direction of energetic phenomenalism. He ignores the fact that his own thought on energetics has changed and that he continues to regard internal energy as both real and substantial. This looks like a version of what I have called the Containment Thesis; and it is, except that Helm, after HELM'S HISTORY OF ENERGETICS: A READING GUIDE 15

1895, vigorously opposes the idea of real presence. By contrast, Ostwald embraces real presence, even when he denies that he is being metaphysical (e.g. 1896a). His "official position" is what I have referred to as the Composi• tion Thesis. For him, the scientific Weltgeist is moving in the direction of energetic realism, that is, toward the recognition that energy is the only ultimate substance. He ignores the fact that his own development of energetic theory is instead based on the Containment Thesis, in accordance with which material systems are at least as real as the energy or energies they contain. 14) In short, Helm and Ostwald were uneasy allies, who disagreed about the fundamentals of energetic theory. But they did have a common enemy: Both thought that the originality and importance of Mayer's achievement had not been appreciated by his contemporaries because scientists were wedded to the mechanical world-view and were reluctant to give it up. Nowhere was this more evident, Helm argued, than in the subsequent development of thermodynamics and the effort to understand its laws. Here, he lamented, most physicists insisted that "the real scientific foundation of thermodynamics had to be sought in the mechanics of atoms." It was as if the were taken to be only "rough estimates," useful for certain purposes, but ultimately unsatisfactory because they did not "open up a view into the mechanics of the interior of bodies." Helm agreed that "to someone for whom the highest goal of theoretical natural science is the analysis of everything that happens into the motion of atoms," thermodynamics probably seemed to be little more than a "bargain basement" theory, since its results were the consequences of more basic causes [193-94]. But he resisted that attitude as contrary to the real spirit of energetics. One can be more precise about the nature of Helm's resistance, and in a way that sheds further light on his view of history and his conception of energetics. Throughout his study, Helm applauded authors whose work contributed to a phenomenological theory of energy; and he criticized those who promoted molecular and mechanical theories, who conflated such micro-mechanical theories with phenomenological ones, or who valued the former sort of theory more than the latter. Mechanical realism was a stage through which history had passed (e.g. [193, 325]); but history also revealed the gradual unfolding - as his study sought to show - of an energetic phenomenalism. Of Clausius' seminal memoir (Clausius 1850) which defined the science of thermodynamics, for example, Helm wrote that it marked "a decisive turning point" in the history of energetics: We have before us here for the first time the foundations of a system of theory which, without hypothetically going back to mechanics or even using mechanical analogies, can nonetheless make the same claim to uncondi• tional and comprehensive validity as does mechanics itself. What [Sadi] Carnot and Mayer aspired to is here fulfilled. The energetic originality of Clausius' work is revealed in a particularly striking way when we compare it with [W.J.M.] Rankine's, also published in 1850. This work arrives at similar results ... but it is based throughout on a mechanical hypothesis: Molecular 16 THE HISTORICAL DEVELOPMENT OF ENERGETICS

vortices are conceived and certain mechanical relations among these vortices are hypothetically interpreted as heat, others as temperature, in order to forge ahead to the results. 41

15) This passage is revealing, but also misleading. It gives an extreme example of the sort of endeavor Helm opposed. But his appraisal of Clausius' memoir is selective and overstated - he did not really think that Clausius had "fulfilled the aspiration of Mayer" (see [193]). Still, the distinction that Clausius began to make in his memoir between what we would now call the "general" and "special" theories of heat does help to locate what is essential to Helm's point of view. Helm praised Clausius' phenomenological general theory, regarding it as fully energetic in spirit; but he regretted Clausius' attempts to construct a special theory - his attempts to "penetrate the interior of nature" and his efforts to provide his general theory with a molecular-mechanical basis - regarding them as "deviations" or "departures" (Abwege) from energetics.42 Clausius himself was always very careful to separate his work on thermo• dynamics from his mechanical interpretations, realizing that the latter were less likely to command general assent;43 but others, such as Rankine, were perfectly willing to incorporate molecules and mechanisms into the very heart of thermodynamics. And Clausius believed, in any case, that an explanation of the laws of thermodynamics based on molecular mechanics was possible, fundamental and needed (e.g. Clausius 1871). Helm did not share that point of view,44 and neither did Ostwald. But whereas Ostwald generally believed that the "interior of nature" sought by mechanical theorists was actually unveiled by a properly conceived energetics, Helm's basic view was that the search for such subtleties was not the proper task of science. Given his advocacy of the Relations Thesis, it is therefore not surprising that Helm admired phenomenological thermodynamics or that he preferred a theory of energy modelled on it. Throughout his history of energetics, in fact, he often simply identified the two. While not denying that "the mechanical hypothesis" or the "molecular hypothesis" - two ideas he also frequently ran together - had sometimes yielded important results,45 he vigorously protested the tendency to interpret such hypotheses as more than conceptual or heuristic devices. Like Ostwald, moreover, Helm opposed attempts to defend realistically construed micro-mechanical conjectures by means of "all sorts of artificialities," and sought to expose the confusion - still all too prevalent, in his view - of atomism and mechanism with what was really essential to energetics, namely, a pure system of relations.46 Helm found such confusions even in what he apparently regarded as legitimate attempts to construct energetics on a mechanical basis (see Part VIII). I shall return to these efforts, and his complaints about them, shortly. Now, I want to pursue a bit more the thermodynamic approach Helm evidently preferred, since adherents of this approach are clearly the "advanced waves" whose fitful progress his study mainly seeks to recount. Doing so will shed further light on the version of energetics Helm defended and also show how he often misinterpreted authors he thought had advanced it. HELM'S HISTORY OF ENERGETICS: A READING GUIDE 17

16) After Mayer, according to Helm, several continental scientists followed the path of a properly conceived energetics;47 but the main impetus, in his view, came from the American physicist, . Nowhere, he thought, had the Relations Thesis found so clear and ardent a proponent: Completely free of [any] bias in favor of the mechanics of atoms, determin• ing with complete impartiality the strict consequences of the two laws of thermodynamics, without any longing glances at and yearning for me• chanics - thus, following the historical development, the work of Gibbs suddenly stands before our gaze. Here the great old idea of Robert Mayer has come to life in mathematical formulae, free from all the molecular• hypothetical adornment.

Helm can scarcely contain himself. Of Gibbs's great memoir on hetero- geneous equilibrium (Gibbs 1876-1878), he exclaimed: What a book, in which chemical processes are treated without the traditional chemical apparatus of atoms, in which theories of elasticity, of capillarity and crystallization, and of electromotive force, are set forth without all the usual devices of atomistic origin! Naked and pure, the true object of theoretical natural science - which is to ascertain the quantitative relations among the parameters determing the state of a material system during the changes subject to investigation - stands before us! (1898, [194])

Then, after remarking that Gibbs "renders the true content of the founda• tions of energetics" in the opening lines of his memoir, Helm proceeded to describe in some detail how Gibbs carried out "his main task of investigating the equilibrium conditions of heterogeneous substances using the tools of energetics," pausing now and then to salute certain of Gibbs's solutions as "very remarkable from the standpoint of energetic methodology".48 Again, though, Helm has selectively misread the history of science, attempt• ing to bolster his own conception of energetics by claiming the authority of Gibbs for that point of view. In fact, Gibbs's attitude toward molecular hypotheses was actually quite similar to Clausius,.49 Like Clausius, he tried to separate the general principles of his thermodynamics, and the consequences that could be drawn entirely from them, from special assumptions about the molecular constitution of bodies and molecular motions. But, also like Clausius, Gibbs never seems to have had doubted that matter was real and particulate in structure, and that an adequate physical theory would have to take account of this fact. 50

17) Also misleading is Helm's reading of Helmholtz's later works on energy. For nearly a decade after they appeared, Helm complained, Gibbs's works were virtually ignored. "Nor," he went on, "was the entropy concept energeti• cally developed or applied at this time in the manner so auspiciously marked out by [August] Horstmann. Instead, people still struggled to accomodate the alien-appearing concept of entropy under the old hat of the mechanics of 18 THE HISTORICAL DEVELOPMENT OF ENERGETICS atoms".51 That situation began to change only in the early 1880s, when the "standstill of energetics" was followed by a succession of important develop• ments. The most significant of these were due to Helmholtz who, late in his career, again turned to research on energy processes, this time to those involved in chemical reactions. That research in physical chemistry resulted in a three-part memoir, The Thermodynamics of Chemical Processes (1882-1883), which, Helm claimed, "treats the difficulties lying in the concept of entropy in a purely energetic manner," without trying "to reduce it to mechanics or even to make it comprehensible through mechanical analogies, as he later did" (1898, [222]). To understand how Helm has misconstrued matters, we must look briefly at what Helmholtz had done. In spite of ingenious ad hoc arguments, it had become increasingly clear by the late 1870s that of reaction did not always allow one to predict the direction and extent of chemical reactions, even though they did so much of the time. That difficulty led Helmholtz, among others, to ask whether the second law of thermodynamics could be adapted to provide a more reliable measure of chemical affinity in terms of the maximum work that a reaction can perform. His own answer appeared in the first installment of the memoir mentioned above, which began by distinguishing between the "free" and "bound" energies in chemical reactions. Helmholtz did this to differentiate between freely transformable kinds of energy, such as mechanical energy, and heat, the transformation of which is subject to limitations.52 From the two laws of thermodynamics, he then derived an equation - one of the so-called Gibbs• Helmholtz equations - which gave the maximum work for a reversible, isothermal process as a function of the free energy, rather than of the heat of reaction; expressed the free and bound energies as functions of internal energy, absolute temperature and entropy; and showed that it is the free energy which determines the direction and extent of a occurring at constant temperature and volume. 53 Helmholtz's work immediately drew the attention of physicists and chemists interested in the application of thermodynamic principles to chemistry - of, for example, Duhem and Henri Le Chatelier in France and Walther Nernst in Germany - who refined and extended the theory of free energy and applied it to a wider range of situations than Helmholtz himself had. Helm approved of these efforts, as he thought they advanced a relation-theoretical conception of energetics, but he did not given them his unqualified support (1898, [228-35]). One thing that bothered him was the tendency of free-energy theorists to interpret free and bound energy as physically on a par with the internal energy of a system, rather than as only mathematical functions whose "value lie solely in the analytical advantage they provide" [231]. This is the mistake of attributing real presence to forms of energy, a mistake Gibbs had not made [234], and which explains Helm's terse dismissal of some remarks Nernst made at the Lubeck meeting [232]; also (1895b), 31. But something deeper also troubled Helm. "Like Helmholtz's youthful work on the conservation of force," he wrote, "the great investigations with which he enriched the ideas of energy in old age are also, in the final analysis, written HELM'S HISTORY OF ENERGETICS: A READING GUIDE 19 with a view to conquering an additional domain ofapplicationfor the principles of mechanics. Thus, as in his work of 1847, [Helmholtz] again follows two paths." One path, Helm explained, was to make thermodynamics as secure and useful as mechanics; the other attempted to reduce thermodynamics to mechanics, "whether through an appropriate mechanical hypothesis for the phenomena of heat or through mere mechanical analogy." But whereas the beginnings of these two approaches were "intermingled" in his 1847 work, Helm thought that Helmholtz had separated them in the last decades of his life and devoted separate essays to each. And he claimed that Helmholtz's memoirs on the thermodynamics of chemical processes were developed in a "purely energetic manner".54 At first glance, this passage appears to reflect nothing more than a recognition in Helmholtz's writings of the distinction, described above in connection with Clausius and Gibbs, between general and special develop• ments of thermodynamics, with Helm welcoming the former as "purely energetic" and rejecting the latter. And, in fact, there is evidence in his history that this is the way Helm wanted his discussion to be read [228]. The problem with that reading, though, is the same one that infects his interpretations of Clausius and of Gibbs: Helm has overlooked - or, rather, simply ignored - the broader context in which Helmholtz sought to place the results of his memoir. One can be more precise here, and in a way that provides another illustration of Helm's selective reading of the history of science. In the first installment of his memoir, Helmholtz tried to account for the difference between free and bound energy by distinguishing between the kinetic energy of ordered and unordered molecular motions - the former allowing for the free transform• ability of most energy and the latter explaining the limitations associated with heat - and he repeated that account in each of the other installments.55 Helm knows this, since he quotes in full the passage in which the explicitly molecular and mechanical distinction is made! His response is that Helmholtz "concludes his derivation of free energy by relapsing into the mechanical hypothesis, which elsewhere in his works on the thermodynamics of chemical processes, as has already been stressed, he avoids completely" [234]. Helm has his reasons - by now familiar ones - for objecting to this "relapse" [235]; but his discussion of it concedes that it was internal to the fabric of Helmholtz's memoirs, that his essays were not "purely energetic" in character and were not intended to be. A plausible explanation for this incongruity, in line with my earlier suggestion, is that while Helm approved of the greater part of what Helmholtz had written, which developed and applied a phenomenological thermo• dynamics consonant with the Relations Thesis, he opposed and so ignored the part which presupposed a micro-mechanical explanation of that development. In his history, Helm evidently preferred a phenomenological approach to energetics, and so emphasized the importance of this approach wherever he found it - even if involved distorting the real intentions of his "advanced waves" in the process. Be aware of this as you read his work. 20 THE HISTORICAL DEVELOPMENT OF ENERGETICS

18) At the same time, though, Helm did not equally praise everyone who, in his view, had contributed to the advance of energetics. I have in mind here especially Max Planck. Although Planck generally shared Helm's phenomen• ological and thermodynamic orientation and his mistrust of molecular• mechanical theories, he was nevertheless a special target for criticism in Helm's history - partly for his terse dismissal of energetics as worthless and partly because Helm and Ostwald both regarded him, quite literally, as a traitor. Helm's attitude appears in the following passage from his history. After describing Planck's development and defense of the second law of thermo• dynamics as the principle of entropy increase, he remarked: I have recounted here in some detail Planck's manner of treating the concept of entropy, even though to date it has not provided any stimulus to further work in this direction. But the difficulties with the entropy concept are so formidable that any attempt to master them deserves special notice. At a time when it was believed that these difficulties could be eliminated through a mechanical interpretation of the concept of entropy, Planck had the independence to overcome them in a purely energetic manner. For what manner of treatment is more deserving of this name than the plan to derive entropy directly from our most universal experiences of the processes of nature? Or the attempt to place a new principle alongside - or even in place of - the Carnot-Clausius principle of classical thermodynamics, and thereby to give expression to the analogy that exists among the forms of energy? To be sure, a peculiar irony of historical development has ordained that the man who once entered the lists with such a purely energetic program sixteen years later denied energetics, with quite unnecessary pathos, in its hour of peril. Perhaps energetics remains more faithful to him than he to it.56 Planck's position was more complex and nuanced than Helm made it out to be. 57 As he saw it, Planck had begun his support of energetics in his dissertation of 1879, which sought to derive the concept of entropy "more directly from experience" than Clausius and tried to generalize the second law of thermo• dynamics, understood as a relation between heat and mechanical work, to energy changes of any sort.58 Papers published in the next half dozen years applied this fundamental theory to a variety of physical situations, including equilibrium, saturation, and changes of phase. The important insight Planck developed in these works was one that had already been exploited by Gibbs, namely, the idea that stable equilibrium in a system corresponds to its state of maximum entropy (e.g. 1882, [209-10]). He then turned his attention, in the mid- 1880s, to the emerging field of physical chemistry, where he found additional applications for his theory and further confirmation of it. In a series of papers collected under the heading, On the Principle of the Increase of Entropy, Planck employed his entropy principle to solve problems of chemical affinity, spontane• ity and equilibrium and, in the final installment of the series, to various electrochemical phenomena.59 Throughout his investigations, moreover, he avoided recourse to detailed hypotheses about molecular motions and was critical of contemporary developments of the kinetic theory of gases. 60 HELM'S HISTORY OF ENERGETICS: A READING GUIDE 21

Helm welcomed these writings of Planck's as energetic in motivation and character, as he also did a book-length essay on the principle of the conserva• tion of energy in which Planck explored the energetic foundations of mechanics. 61 Not wholeheartedly, to be sure. Helm was critical of Planck's derivation of the entropy principle and of some of his applications of it, preferring Gibbs's approach instead (1898, [236-9, 243]). And he regretted Planck's appeal, in his essay on the energy law, to a principle that divided energy into distinct components, each of which was physically present in a system [269]. But given the large areas of apparent agreement, Helm evidently regarded him as an advocate of energetics, or at least as sympathetic to it. 62 He must have been genuinely surprised, therefore, by Planck's written response to the Lubeck meeting. 63

19) Planck did not take part in the Lubeck debate and had not previously commented publicly on energetics. But from the early 1890s, he had shown a lively interest in the development of Ostwald's energetic theory, especially in connection with the second law of thermodynamics, which Ostwald did not regard as a fundamental law of nature. 64 Planck, who did, corresponded at length with Ostwald on the subject, but with little success. 65 He also wrote an essay on the "essence" of the second law (1893; also 1892), motivated at least in part by a desire to have Ostwald understand and appreciate his point ofview. 66 The essential point, Planck explained, was the irreversibility of natural processes, which was embodied in the second law as the principle of increasing entropy. Ostwald did not see matters that way: He confined the meaning of the second law of thermodynamics to reversible thermal processes, had little regard for entropy, and sought to make allegedly more general principles the fundamental principles of natural science. 67 Against mechanical theories of any sort, moreover, he repeatedly affirmed the greater clarity and consistency, hypothesis-free simplicity, and comprehensive unity of energetics. Planck did not agree. Shortly after the contentious Lubeck meeting, he told Ostwald that he thought it was "high time" to make his objections public. 68 Planck opened his harshly worded essay (1896) by saying that he did not intend to "stand up for the mechanical world-view," since that would require "a deep and difficult study." Instead, he said he would focus on the much simpler task of revealing the basic inadequacies of the "new energetics". To begin with, there were large conceptual and mathematical problems - with the notion of volume energy, for example, which Planck thought had no physical meaning.69 He also thought the value of energetics for mechanics had been exaggerated. The energeticists believed that they could treat mechanics in a more general manner by reducing it to a comprehensive science of energy. In Planck's view, however, traditional mechanical presentations of reversible processes were more successful - and certainly much clearer. But his main criticism of the energeticists was that they had ignored the fundamental distinction between reversible and irreversible processes, and the fact that natural processes are all irreversible. So, while energetics pretended to offer a comprehensive world• view, Planck thought it left the real world out. He faulted energetics for lacking 22 THE HISTORICAL DEVELOPMENT OF ENERGETICS sound foundations and secure methods, for pawning off disguised definitions as proofs, and for avoiding the real problems of science by hiding in untestable metaphysics. Planck vigorously protested any further development of ener• getics in the direction it had recently taken, since, he thought, it had produced nothing of value. Its only success had been to encourage young scientists to engage in "dilettantish speculations, instead of a thorough absorption in the study of established masterworks, thereby laying fallow for years a broad and fruitful area of theoretical physics".70

20) Planck's essay was blunt and unforgiving. I have had to abbreviate its accusations, but the last quotation gives the overall tone. Helm was angry and deeply offended, as is evident at many places in his history (e.g. [334-40]). He replied (1896) that he, at least, was not guilty of the conceptual and mathematical errors with which Planck had charged energetics in his sweeping condemnation. He said that he did not need to be lectured on the difference between exact and inexact differentials, or on the difference between quantities that are functions of the state of a system and those that are not; he was a better mathematician and physicist than that! He also insisted that he had always distinguished sharply between the intrinsic energy of a system and its division, for analytical purposes, into different forms. In his view, the expression, pdV, did not represent the change in an amount of volume energy really present in a system - that would be an unwarranted metaphysical assumption - but only one term in the differential of its intrinsic energy, as does dQ, the differential change in heat.71 Helm then turned to Planck's claim that energetics had yielded nothing of value, that it had "no positive accomplishments" to its credit. Here he argued that Planck had viewed the matter too narrowly. Drawing on a distinction similar to one Ostwald had made between "conscious" and "unconscious" energetics (1896a, 154-58), Helm insisted that, broadly conceived, energetics had in fact brought many successes to "theorists, experimenters, and applied scientists," even if they were often obscured by unnecessary hypotheses. Had not Maxwell, Gibbs and Helmholtz successfully employed some of the main ideas of energetics, including the Factorization Principle? And "does not a method which is so generally widespread deserve to be developed, free from alien garb, to be established as an independent method?" In fact, is it not the essential task of the "contemporary theorist" to make clear and precise those ideas of "general validity" that have been used in unclear and imprecise ways? That, Helm wrote, was just what he had tried to accomplish in his own writings on energetics (1896, 162, 166). He conceded that the results had not been entirely satisfactory from a mathematical point of view (1896, 165), and so he appreciated Boltzmann's criticisms, even ifhe did not agree with many of them. But Planck's "protest" was another matter. In Helm's view, it provided neither useful criticism nor assistance in addressing the main problems of theoretical natural science (1896, 167). The "alien garb" from which Helm sought to distance energetics was realistically-construed molecular-mechanical hypotheses, whose lure, he HELM'S HISTORY OF ENERGETICS: A READING GUIDE 23 claimed, even scientists who had advanced the "mechanical direction" in energetics found hard to resist. The ideas whose "general validity" he sought to clarify and present in a rigorous manner are the ones he develops, as partly his own contributions to the evolution of energetics, in Parts VI-VII of his history. These have to with the "universal significance" of the energetic intensities, a factorization principle that would reveal this properly, and a fundamental principle that could include both and also describe the course of any energetic change. I shall not attempt to describe those contributions here in any detail, for their mathematical development is often complex. In line with the intent of this introduction, I instead offer a brief sketch of Helm's reformulation of mechanics, indicate some of Boltzmann's criticisms of it, and then turn to Helm's discussion - in the last part of his history - of the mechanical approach to energetics. This will allow me to round out my general account of his view of the history of science and of the place of energetics in it. 72

21) The basic principle of energetics, in Helm's view, was what he called the "energy principle." This is not the usual integral law of the , which applies only to conservative systems (as its name implies), but an allegedly more powerful differential law, which is applicable to any system whatever, and of which the usual "energy law" is a consequence (Helm 1890b, 309). Helm presented a version of his energy principle for conservative mechanical processes in his (1890b), a work that sought to reduce mechanics to energetics. It was essential to the formal, mathematical development of energetics, he thought, to be able to derive from the energy principle the differential equations of mechanics, which would include the equations of motion for a material point moving freely or under constraints and the Lagrangian form of the equations of motion. 73 In this he thought he had succeeded. 74 Helm intimated in his essay on the energetic foundation of mechanics that the energy principle could be extended beyond purely mechan• ical phenomena to "all physical phenomena" [354]; but he struggled for some time to give that extension what he thought was a suitable analytical expres• sion. 75 In the report he prepared for the Lubeck meeting, Helm stated his general energy principle in the form

1) dE ~ L.JdM, which claims that the total change in energy, E, in an infinitesimal process is equal to, or less than, the sum of the products of the intensities, J, and the changes in the corresponding capacity factors, M, and where the inequality is supposed to describe irreversible processes (1895a, XII; also VII-XI). He defended this version of the energy principle at the meeting as the "most fundamental formula in energetics," arguing that it promised to unify natural science (1895b, 29). In his report, and again at the meeting, Helm also defended the Relations Thesis. He allowed that the energy principle could be reached in two different 24 THE HISTORICAL DEVELOPMENT OF ENERGETICS ways. The first, or mechanical "way" (Richtung) of energetics "represents all natural processes as phenomena of motion" and seeks to reduce the phenom• ena to an appropriate energetic mechanical principle, such as the energy principle for mechanical processes or an equivalent. According to this approach, all energy is conceived of as mechanical and all natural processes are represented by means of mechanical "pictures" or "models" (Bilder). By contrast, the second, or thermodynamic, path to energetics accepts as a given the phenomenal diversity of the various forms of energy appearing in the energy principle; it affirms, in line with Mayer and Mach, that what matters are the quantitative relations among the forms of energy, not the claim that they must all be "pictured" as ultimately mechanical. Once the relevant energy factors, J and M, have been determined and precisely defined for all the various forms of energy, the demand for a unified presentation, or theory, has been met. Nothing further is needed (1895a, III-IV; 1895b, 29-30). Helm clearly favored the thermodynamic approach to energetics, as we have seen; but the official summary of the Lubeck discussion has him less sympa• thetic to a mechanical approach than he was in his written report?6 According to the summary, Helm defended the following position in his remarks: While not categorically ruling out the attempt to construct "mechanical pictures" of natural processes, he regarded such constructions as supererogatory and generally misleading, since he thought that the need for them expressed by many theorists reflected the deeply entrenched view that mechanical phenom• ena were somehow more basic or more intelligible. But, like Mach, he also regarded this as a prejudice and nothing more:

We owe the not to the conception of all thermal processes as phenomena of motion, but to the formula that expresses certain relations between heat and work. Do we, in fact, obtain a deeper knowledge if we then conceive of heat as motion? Isn't velocity an expression for certain experiences just as much as temperature? To leave the empirical content of each form of energy as it is, instead of importing a mechanical picture - that is the realism of modern energetics. The possibility of comprehending the different forms of energy in a single picture [Bild] is not thereby excluded, but it is not the first and most necessary thing. A quantitative description - a theory of natural phenomena - can be accomplished without it (Helm 1895b, 29; my italics).

The summary does have Helm conceding that efforts to construct mechan• ical pictures had sometimes been heuristically beneficial in stimulating re• search; but he then claimed that the detailed development of such pictures had always led, sooner or later, to complications which "render their value illusory". Reliance on such constructions was therefore to be discouraged, especially since mechanical theorists were inclined to forget the distinction between their pictures (Bilder) and realist hypotheses. By contrast, the thermodynamic approach to energetics was both more rewarding (in its results) and less seductive (in its methodology). From that point of view, what needed HELM'S HISTORY OF ENERGETICS: A READING GUIDE 25 fuller investigation were the striking analogies between the various forms of energy - especially their common properties of intensity and capacity - and the quantitative relations that linked them together (1895b, 29-30; also 1895a, XI• XII). Whether this was, in fact, Helm's attitude at Lubeck is uncertain; it is, however, the view - entirely in keeping with the Relations Thesis - that he argued in his history.

22) Boltzmann's general strategy, in his remarks at Lubeck and in writings descending from the confrontation there,77 was to argue - less stridently than Planck, but as forcefully - that the energeticists had greatly exaggerated the actual achievements and future promise of their new science: The claims they had made for energetics as an accurate, simple, and comprehensive theory of nature were, he thought, extravagant and unfounded. There were, of course, areas of agreement. Boltzmann readily acknowledged that the energy concept held a position of "the highest importance" in natural science and that all natural processes were governed by the two laws of thermodynamics. He also welcomed exploration of the analogies among the various forms of energy, although he did not think them as deep and consequential as the energeticists thought them to be. Moreover, he stressed the importance of maintaining a clear distinction between empirically established laws and the hypothetical "pictures" - whether mechanical or otherwise - devised to "represent" them. And he also believed that representations of general laws should be kept "as free as possible from hypothetical elements" if they were to serve as secure "touchstones" for testing the adequacy of theories. But here agreement ceased. To begin with, Boltzmann thought that the energeticists had often violated, in their own writings, the methodological positions they professed. In particular, they had imported obscure special hypotheses and unwarranted assumptions into their discussions of the various forms of energy, the result being a conceptual structure much less satisfactory than the precise and clearly stated propositions of classical mechanics and thermodynamics.78 Boltzmann conceded that the energeticists had managed to "derive" important and well-known results in mechanics and thermodynamics; but he generally found those derivations unsatisfactory. Sometimes, in their quest for novelty, he thought that the energeticists had simply juggled mathematical formulae to obtain, from energetic first principles, results they knew in advance; at other , however, they were guilty of serious confusions and mathematical errors?9 Like Planck, moreover, Boltzmann did not think that energetic endeavors had given rise to any new discoveries. And, again like Planck, he regretted the energetic promise of easy victories for the education of younger scientists (1896b, 64). In short, he thought that the methods and manner of presentation of energetics had not been able to match the accuracy, simplicity, and fertility of more traditional, non-energetic devel• opments of the different parts of physics. A more general objection challenged the sufficiency of the narrow descriptive goal for natural science that Helm defended and promoted in the Relations Thesis. If successful, Boltzmann thought, Helm's efforts might produce a 26 THE HISTORICAL DEVELOPMENT OF ENERGETICS

"natural history" of energy, but it would not yield the unified physical theory that was the real goal of theoretical natural science. The phenomenal laws of energy are "many and varied," he observed in one place, adding that "a mere natural history of all the forms of energy (heat, electricity, magnetism, ) requires new laws for each kind" (Helm 1895b, 31). Such laws certainly had their place, and Boltzmann did not wish to minimize the importance of them for a quantitatively precise natural science. But he saw no reason to rest content with such isolated descriptive propositions, or with a mere catalogue of them. There was, he insisted, no reason to give up the hope that many of these laws - perhaps all of them - could eventually be given "a clearly arranged representation" by means of a "unifying theoretical picture (Bild)." Indeed, he believed that efforts to unify the laws of mechanics and thermodynamics had already achieved notable, albeit incomplete, success, so that "The cultivation of these pictures (that heat is motion in invisible dimensions, and of atomistics generally) is highly important, along with the general theory of heat." To abandon the search for a unified theory, and rest content with a catalogue of energy forms, would be tantamount, Boltzmann thought, to abandoning the essential goal of theoretical physics.8o In seeking such a theory, a close study of the various forms of energy was not to be discouraged. On the contrary, Boltzmann found the analogies between the behaviors of different energies developed by Mach, Zeuner, Helm, and others to be "very interesting," and he urged that this line of investigation be continued. But he did not think that these analogies were as deep and consequential as the energeticists claimed, or that development of them militated against the mechanics-based program of research he preferred.81 Finally, Boltzmann was adamant in insisting that even if one were to concede - as he himself had - that "the mechanical view of nature is not yet perfect," being neither complete not fully adequate in any area except mechanics, that would still not imply that this view should be abandoned and energetics adopted in its place, since energetics was much less satisfactory and "much farther from a complete development." He did not mean to suggest that additional effort should not be devoted to improving energetic theory; on the contrary, Boltzmann said that he welcomed such effort. In the meantime, however, energetics had been given sufficient time to mature that its present inadequacies should not go unchallenged. They needed to be candidly dis• closed; and that is what he had sought to do at Lubeck and in his published remarks.82

23) No precise record remains of what was said at Lubeck, but much of the discussion apparently centered on Helm's attempt to reconstruct mechanics from an energetic point of view (Helm 1895b, 30). Arnold Sommerfeld misunderstood the project, thinking that Helm had tried to do the impossible, namely, derive the equations of motion of any mechanical system from the law of energy conservation alone. 83 Helm rightly rejected that accusation; but he was at least partially responsible for the confusion. Helm expressed his energy principle verbally as "Energy remains constant for any possible change," HELM'S HISTORY OF ENERGETICS: A READING GUIDE 27 suggesting a variational principle, which is what he intended; but he rendered it analytically in mechanics as 2) dT = dA, which seemed to assert no more than the equivalence of an actual differental change in kinetic energy (1) and an actual differential work (,4) (l890b, 307--08; 1895a, VII). Others at Lubeck, including Boltzmann, likely agreed with Sommerfeld. In his written reply, however, Boltzmann instead argued that Helm had managed to derive the equations of motion for mechanical systems from his energy principle only because he had ignored, or conflated, the essential difference between actual differentials, d, and variations, {j (1896b, 40-41; also 1896c, 39 and 1896d, 595). Either that or he had to assume that mechanical energies could be separated into physically distinct, independent components, and claim that energy is conserved for any possible division.84 But what justification could there be for making such an assumption, since the co-ordinates used to describe mechanical systems may be selected at random? Would changing the co-ordinate system also change the energies present? (l896b, 45; 1896d, 595) In any case, Boltzmann thought that Helm was only able to derive Lagrange's equations from his energy principle because he knew the correct results in advance. Beginning from what appeared to be Helm's assumptions, Boltzmann developed them mathematically in a very reasonable manner and obtained different, clearly incorrect equations (1896b, 41-42; cf. 1898, 65-67). In his reply, Helm again insisted that he had not tried to derive the equations of motion from the "energy law," but from the "energy principle"; and he again explained how that principle was to be understood (1896, 646-47). He conceded that he had not been sufficiently careful in developing his ideas mathematically, but thought they could easily be reformulated to eliminate any errors and lingering confusion.85 The key to Helm's revised formulation was the introduction of a new set of infinitesimal variables, all labelled with the subscript 0", to distinguish possible displacements, velocities, forces and en• ergies (and their components) from actual ones. With this new notation in hand, Helm restated the energy principle in mechanics (equation 2) using sigma subscripts, and then reworked his earlier derivations, once again obtaining all the results he had in his 1890 essay on the energetic foundations of mechanics (1896, 649-52). Boltzmann was not satisfied. He did not think that Helm's new notation had clarified the meaning of the energy principle, interpreted as the proposition that "energy remains constant for any possible change." Sometimes his sigma• subscripted quantities were treated like ordinary differentials, sometimes like variations. Helm apparently wanted it both ways, and would slide, Boltzmann thought, from one interpretation to another as the need arose. Knowing the correct results, he was able to manipulate equations to yield them; but that was hardly an advance. Consistently interpreted, Helm's sigma quantities were either the differentials of actual displacements, velocities, etc., in which case he could not derive the equations he wanted, or they were virtual quantities of 28 THE HISTORICAL DEVELOPMENT OF ENERGETICS the sort normally employed when d'Alembert's principle is used to derive the equations of motion or to determine the generalized forces in Lagrange's equations. In that case, however, Boltzmann saw no reason for preferring Helm's obscure and contrived "energetic" development of mechanics to more standard presentations of the subject.86 Boltzmann also had another, more general objection, the gist of which is this: Not only had Helm failed to provide a simpler, clearer and more comprehensive formulation of the laws of mechanics, but he had not managed to avoid "pictorial representations" of mechanical systems and processes. To develop his equations, Boltzmann claimed, Helm often had to rely on the "theoretical picture" of bodies as consisting of "material points between which act forces of attraction and repulsion" - a view he explicitly rejected as one of the unwarranted dogmas of mechanistic physics. Boltzmann did think that the derivation of many important results in mechanics - Euler's equations of motion for rigid bodies, e.g. - demanded recourse to some form of "atomistic picture"; and he also thought that Helm's "lapse" conflicted with his professed phenomenalist methodology.87

24) Helm replied in detail to Boltzmann's criticisms in his history.88 Indeed, much of Parts VI-VIII can probably be understood only with them as a backdrop. Helm began Part VI, which sought to show the gradual evolution of an "energetic way of comprehending mechanics" [256], by insisting, once again, that the usual energy law was not a sufficient basis on which to construct the science of mechanics. 89 He then explained the task confronting energetics: Robert Mayer founded a new world view. Or, if this expression is thought to be too pretentious, he founded a new view of the course of nature .... For him, and for energetics, the conservation of energy is not [an accidental property of natural processes], but rather the concept starting from which natural phenomena, including motion, can be described in a unified manner and understood in their fundamental nature. Energetics must therefore go beyond the well-established theorem of mechanics that kinetic energy always increases by the amount of the work performed - or it must give up being a view that encompasses the whole of nature .... Thus the task arises for energetics of forming its concepts in such a way that they lead beyond the law of the conservation of energy - encompassing the concept of force, as well- and thereby permit the equations of motion [of a mechanical system] to be derived [261].

This extension had been attempted by several authors, Helm thought, including Planck who now spurned energetics.90 It was also attempted in early works of his own, which he thought had been misunderstood and unappre• ciated.91 What he had tried to do in his essay on the energetic foundations of mechanics, Helm explained, was to formulate an energy principle, which, in its mechanical applications, allowed one to derive the basic equations of mechanics, but which did not demand recourse to any ideas other than "the HE L M ' S HIS TOR Y 0 FEN ERG E TI C S: ARE A DIN G G U IDE 29 fundamental ideas also required elsewhere in energetics" [265]. This was the key point, he stressed. Helm again conceded that his 1890 attempt to accomplish this was unsatisfactory from a mathematical point of view, but he thought that his post-Lubeck reply to Boltzmann had clarified the matter and removed the (merely formal) imperfections [271-72]. To make certain that this point was understood, he reproduced all his derivations using the sigma• subscripted notation of that reply and then sketched an energetic reformulation of mechanics by Neumann - another of Helm's "advanced waves" - that he claimed was quite similar to his own.92 There was nothing odd or problematic about his own development, in short, since the "scientific spirit" had already turned in that direction. Helm also thought that Boltzmann's other criticisms were products of error, confusion or misunderstanding. Properly understood, he wrote, energetics did not require any "detour over the atomic hypothesis," even in mechanics [262]. Nor did it reify forces or co-ordinate systems, any more than it did material points or kinds of energy. Appeal to them "does not violate the pure relatedness achievable by means of energetics" or "represent a relapse into the phantasm of the absolute" [262, 269]. All that is required, Helm insisted, is that one analyze the energy equation for a mechanical process "in the only form in which it is physically comprehensible, that is, as requiring the conservation of energy in every possible direction" [270]. Moreover, energetics should not be criticized for providing only a catalogue of energy forms instead of a unified picture, as Boltzmann had done, since the "picture" is secondary and is usually mislead• ing. The important thing was equations that accurately describe the present phenomena and allow one to accurately predict new ones. And, Helm claimed, his energy principle did just that [291-94]. The analytical formulation of the principle required some reworking, as did its verbal expression. The original version, that "Energy remains constant in any possible change" (l890b, 308) probably left the impression that it could not distinguish actual changes from merely possible ones. So Helm now expressed the energy principle for mechanics as follows: "Mechanical energy, taken with respect to any possible direction of motion, is invariable," and asserted that this form of his principle was "likely the most appropriate form for putting mechanics on an energetic foundation" [292, 297].

25) Boltzmann's response (1898) to Helm's more detailed and systematic presentation was basically the one he had already given. By comparison with the mathematical precision of the standard calculus of variations, he found Helm's claim that "In any mechanical system the sum of the potential and kinetic energy must remain constant for any possible change" woefully imprecise. What, exactly, did Helm mean by this? And why did he think that verbal formulation an advance over his earlier one? Certainly, Boltzmann thought, Helm's sigma-subscripted quantities did not illuminate the statement mathematically, since it was not clear to him that those quantities could be consistently interpreted in a way that would allow Helm to derive the equations of motion even for a single material point. 30 THE HISTORICAL DEVELOPMENT OF ENERGETICS

Boltzmann's criticism may be unjustified, but it is difficult to say, since Helm's sigma notation is itself so difficult to interpret. Most of the time Helm was careful to insist that his sigma-subscripted quantities are not actual components of displacement, velocity, force or energy.93 Occasionally, how• ever, he implied that at least some of them were. 94 At the same time, he usually sought to distinguish them from ordinary variations. 95 Occasionally, however, he suggested that the two were identica1. 96 If Helm thought that his sigma• subscripted displacements were the same as actual differential displacements, then, as Sommerfeld, Boltzmann, and others had pointed out, he is unable to derive the correct results, and he knows that. Still, he wants his subscripted quantities to be relevant to the actual displacements, so that the energy principle yields the actual change in any given situation.97 Boltzmann did not understand what Helm could mean; his verbal and analytical statements of the energy principle did not clarify matters. If Helm's quantities were simply Lagrangian variations, then what has been gained? To put the essential point somewhat differently: If, as was known - and as Helm certainly knew - one could derive the equations of motion of a mechanical system from d'Alembert's principle, what advantage did Helm's puzzling notation provide? The answer, of course, is that Helm hoped to base not just mechanics, but all of natural science, on the "energy principle," the mathematical articulation of which gave quantitative expression to the Relations Thesis; and the new notation allegedly permitted him to do that in a precise manner.98 But Boltzmann saw no reason to adopt Helm's reformulation of mechanics in place of more traditional presentations of the subject, since it was neither clearer, simpler, nor more comprehensive. "All I see in this representation," he wrote, "is an abandonment of the conceptual precision of classical mechanics for the purpose of artificial novelty" (1898, 640).

26) In his history, Helm defended his contributions to the reformulation of mechanics and thermodynamics.99 He also defended the more general features of his energetic theory. In one place, for example, he tried to rebut the charge that the Factorization Principle was useless because it did not prescribe a unique analysis for a given form of energy, insisting that he sought analyses that were "physically most advantageous," those which "reproduce the [en• ergetic] relationships evident in natural phenomena."lOO In another, he re• sponded to the accusation that energetics could not be used to promote research, since "one can prove with it only what one already knows," arguing that this reproach was "as much and as little justified as it is with respect to any theory" and that "this situation only manifests more honestly in the case of energetics, with its splendid simplicity, than it does in mechanical theories, which are decked out in 'the bright cloaks' of many hypotheses" [103]. And he defended in many places the heuristic value and unifying intent of the Intensity Law as the "cornerstone of modern energetics."lOl After providing a table of energy forms and their factors, Helm remarked: HELM'S HISTORY OF ENERGETICS: A READING GUIDE 31

Now, however simple these relations appear, and however illuminating [our] survey of the diverse analytical uniformities manifested in the various departments of theoretical physics proves itself to be from the standpoint [I am recommending] - nonetheless, the displeasure with energetics that gained currency in 1895 also led to a kind of charge of vacuity against the intensity law, a charge which does not question its correctness, of course, but only its value and utility [334].

So what is its value? Helm answers as follows:

[The] intensity law liberates us from the compulsion to interpret everything that happens mechanically. Why, then, do we do this, why do we represent a phenomenon hypothetically as a process of motion? With no other intention than to declare that we describe it accurately in accordance with our experience when we regard certain of its parameters as velocities, others as forces, and still others as line segments, , and so on. But since nothing is experienced of the system under consideration other than the entry or exit of forms of energy, it thus becomes a matter in every case of forcing the intensities and extensities of these forms of energy to conform to the point of view that they are mechanical intensities and extensities. At best one thereby obtains a graphic, intuitive mechanical picture [Bild]; but what is essentially beneficial in the process of thought is only the recognition that certain parameters of the system possess those of intensity and others those of capacity [335].

This passage defends the Intensity Law and reaffirms the Relations Thesis, but it also emphasizes something else: For Helm, as for Mach, there is nothing special about mechanical energy. Indeed, mechanics itself has no privileged status, and mechanical representation is not the ultimate objective of physical theory.102

From the standpoint of the intensity law, the picture of all happening in the domain of mechanical processes is [merely] a special case, and it is only habituation [that gives primacy of place to mechanical energy] .... I [there• fore] cannot assign to mechanics any other position in physics than belongs, for instance, to analytical geometry in geometry in general [335-36]; also [256].

27) Still, Helm did think, as I noted earlier, that there were developments from the side of mechanics that had promoted the goal of energetics; but, as I also noted, his attitude toward this "direction" or "path" (Richtung) was hesitant and suspicious.103 He introduced it in his history with the following remark:

Energetics would like to represent our experiences of natural processes as immediately as possible, without the aid of invented mechanical devices. The 32 THE HISTORICAL DEVELOPMENT OF ENERGETICS

temporal changes in the parameters by means of which the states of a system are described are to be stated without hypothetically contriving a mechan• ical system whose components move as though the parameters of the actual system were their co-ordinates. Nevertheless, mechanics can achieve this goal of energetics in a certain way with its own resources and can thereby contest the domain of energetics that was developed out of thermodynamics. I was therefore able to organize simply the survey of the state of the subject I prepared for the Lubeck Convention of German Scientists and Physicians by distinguishing two approaches [Richtungen] to energetics, the mechanical and the thermody• namic .... It is the mechanical direction in energetics to which we must now devote our attention ([363]; my emphasis).

The goal to which Helm referred was, of course, the descriptive one embodied in the Relations Thesis, and he found evidence to support that thesis in the writings of many "mechanical theorists" - in Maxwell and William Thomson, in Clausius, Helmholtz and Hertz, to name only some of the most prominent advanced waves.104 The key to their success, he thought, was the Principle of Analogy discussed in his Lubeck report, which allowed them to apply the equations of mechanics to non-mechanical systems. 105 Helm commended the Principle of Analogy,106 but was wary of it, an attitude which is evident in his discussion of Boltzmann's use.

I quote these splendid remarks of Boltzmann [from his 1892] in order to show that efforts originating in mechanics have the same goal in mind as those that grew out of thermodynamics, if only they keep themselves free of the inherited delusion that, since all experience is appearance, there is a mechanism standing behind sensuous appearance representing the truth, the detailed knowledge of which must be the aim of science. Of course, if someone honestly takes the view that he cares only about a mechanical analogy, and does not silently yearn for the realization of this analogy, he will be easily persuaded that the thermodynamic approach to energetics is the more perfect and consistent one .... Working through [the complications of the mechanical approach] naturally appears entirely justifiable and necessary when the mechanism is the highest goal to which research aspires; but when it is only a matter of a picture [Bild], an analogy, which, in any case, remains valid only to a certain degree - what is the point of all the trappings? It just seems everywhere to be the fate of mechanical hypotheses that they require too many accessories, that they ascribe to the systems in question superfluously many properties. It is not surprising that some of these properties become the starting points for new formulations of questions; but the rest remains as ballast. The thermodynamic approach to energetics [entirely avoids these problems] ... [382]. HELM'S HISTORY OF ENERGETICS: A READING GUIDE 33

Helm has several points to make here, all of which are important to an understanding of his position: First, mechanical theorists, despite their talk of "pictures" and "analogies", were often still secretly committed to the real existence of a noumenal mechanical world, running its course behind the phenomenal world of experience and productive of it; second, even in terms of pictures and analogies, mechanical theorists were hard-pressed to accurately represent the real phenomenal realm - without recourse, that is, to a variety of complicating assumptions; and, finally, the thermodynamic approach, which he preferred, was better able to describe the phenomena in a manner free from dubious hypotheses. The first claim is never far from the surface of Helm's discussion, given his deep aversion to the mechanical world-view and his concern that advanced waves from the mechanical side of energetics continued to be drawn by the siren song of mechanistic realism. To justify the second claim, Helm began by quickly surveying the problems associated with mechanical representations of the second law of thermodynamics. It was one thing to construct mechanical analogies (or invent motions) for which functions could be formulated whose behavior imitated that of temperature or entropy for reversible processes, but the real challenge was to extend such analogies to irreversible ones [394-95]. One might attribute irreversibility to the presence of concealed and uncontrol• lable parameters (or motions), as Helmholtz, among others, had done; but that, by itself, left unexplained the predominant unidirectionality of natural pro• cesses. Why, to put the matter differently, the overwhelming tendency of energy to be transformed into unmanageable and unrecoverable forms? [395-96] Here one might assume that "in nature there exist far more concealed motions than motions which are accessible to our influence," as Hertz had done, and then claim that "a very great probability speaks against the concentration of energy precisely in the special and distinct direction leading from the great number of concealed motions towards the small number of motions over which we have control" [397]. Or one might appeal to statistics in another way, as Boltzmann had, by explaining irreversibility in terms of the overwhelming probability of mechanical systems to evolve from highly improbable states into more and more probable ones, in conjunction with a further assumption about the initial state of the world, that it was highly improbable [398-99]. Helm did not ridicule these efforts; on the contrary, he described them fairly, ifnot enthusiastically. Of Ernst Zermelo's Recurrence Paradox, for example, he remarked that it would be "foolish and unjust" to think that with this "absurdity" the mechanical world-view had been shown to be a "simple failure." One need only say that the recurrence of a given state, while not theoretically impossible, is nonetheless extremely improbable. This is what Boltzmann had argued in his reply to Zermelo, and Helm thought that reply adequate, given what it sought to accomplish [398].107 Still, it will come as no surprise that Helm did not approve of the approach Boltzmann (and Helm• holtz and Hertz) had taken. "[C]onsidered in the most advantageous light, what emerges from these results is only that the mechanical world-view is not simply invalid, but can hold its own even before the fact of irreversibility. It is another 34 THE HISTORICAL DEVELOPMENT OF ENERGETICS question [however] whether such results are appropriately pursued and whether, consistently carried through, atomism provides an appropriate picture of the world."I08 Helm thought not, arguing that the mechanical world-view had become less appropriate as it had tried to become more comprehensive, because it had, at the same time, become overloaded with ad hoc assumptions:

In fact, it seems everywhere to be the inexorable fate of the mechanical hypothesis that in order to describe experience it must burden itself with a crushing excess load of notions having nothing to do with experience. The means so admirably verified for producing a mechanical picture of a small area of experience become more and more inappropriate the greater is the area of experience that they are to reproduce; and, finally, they fail completely.... The mechanical world-view is a universal method of picturing, but it does not furnish a universal world picture; its force disappears with its extension [400].

28) In the last pages of his history, Helm forcefully restated the global conception of energetics he wished to promote [400-4]. He began with some Mach-inspired remarks on what it means to say that something exists. Briefly, Helm's idea was that we ascribe existence to "things" in our environment in order to "secure for ourselves resting points in the flight of phenomena." In itself our experience yields only relationships: one phenomenon follows or is preceded by another. But we regularly employ convenient "catchwords" to fix certain of these relationships or to stand for collections of observations. The danger lurking in this practice, in Helm's view, is that scientists are often incautious in their use of such catchwords, thinking that because they habitually speak of, for example, "atoms" and "forces," these words signify more than just shorthand ways of referring to certain experiences. Atoms have no existence in their own right. The word "atom" is a good catchword for describing certain phenomena - those of stoichiometry, for example; but for many areas of experience, it is awkward and inappropriate. The main point to be kept in mind, in any case, is that "For natural science nothing exists but scientific observations" [401]. From which Helm affirmed roundly:

I also consider it to be the best thing about energetics that it is capable to a much greater degree than the old theories of adapting itself directly to our experiences; and I see in the attempts to attribute substantial existence to energy a dubious departure from the original clarity of Robert Mayer's views. There exists no absolute; only relations are accessible to our knowledge. And whenever the spirit of research has contentedly reclined on the sluggard's bed of any kind of absolute, it has immediately expired there. It may be a comfortable dream that our questioning can find rest in atoms, but it remains a dream! And it would be no less a dream if we wished to see in energy an absolute, instead of only the most striking expression up to now of the quantitative relations among the phenomena of nature [401]. HELM'S HISTORY OF ENERGETICS: A READING GUIDE 35

Here is the Relations Thesis boldly stated, this time explicitly joined with a form of agnostic phenomenalism. ID9 In adopting that stance, moreover, Helm thought of himself as following directly in the footsteps of Mach and Richard Avenarius and of his thermodynamics-based conception of energetics as an appropriate scientific articulation of their epistemological views. These views had still not achieved the recognition they deserved, he complained. "Other• wise, the more profound aspects of energetics would not have been so little understood at Lubeck" [402]. Too many scientists still clung to favorite mechanical hypotheses and rejected, in consequence, the energetics that looked beyond them. This was not the first time, of course, that scientists had "stubbornly persisted" in traditional modes of thought long after they had been shown to be of limited use. That attitude Helm called "scholasticism," after what he regarded as its most influential historical instance, and he insisted that "only new ways [of thinking], more directly linked to experience" could take one beyond its limits. Energetics, he declared, was such a way.IID That was not to say, Helm cautioned, that energetics itself could not be abused, or perverted, in much the way that the methods of mechanics often were. "Each of these approaches can be enhanced to luxuriant mysticism and exuberant imagery; and each can modestly content itself with desiring to be, and to be active in, nothing more than the reproduction of experience" [402]. Everything depended on adherence to the Relations Thesis: "What was opposed and defended [at Lubeck] about energetics is the method of being able to talk about natural processes in a language free of pictures. And for this purpose, the method of energetics is unsurpassed; it is not even approximately equalled by any of the other approaches" [402]. III Still, one need not go so far as to repudiate altogether the value of such pictures. The worth of "theoretical pictures," whether of mechanical origin or otherwise, should be determined by their ability to represent clearly, simply, accurately and completely the relations among phenomena. "But," Helm insisted,

when the imagined notion is taken to be the essence of the matter, when it is taken to be more valuable than the experiences from which it is invented - this is where scholasticism begins. And whoever rejects a completely adequate description of the phenomena such as energetics offers, a descrip• tion not needing the aid of fictions - he has taken his stand with scholasticism. It is therefore not the old methods for describing the phenomena that I regard as dubious, but rather their excess, that blind faith in their general validity and infallibility which encourages all kinds of rescue efforts, invents the most peculiar notions, which are of no use for any purpose other than such a rescue, and then presents these fictions as the truth [403]. 36 THE HISTORICAL DEVELOPMENT OF ENERGETICS

With some of this, at least, the critics of energetics would certainly have agreed: They, too, would have rejected the sort of ad hoc rescue efforts that Helm condemned. But from his reasonable objection, Helm immediately moved to the startling declaration with which he ended his history:

And so, in the controversy kindled in 1895 at Lubeck, [it is not] really a question of atomism or of matter continuously filling space, not a matter of the inequality sign in thermodynamics, or of the energetic foundations of mechanics. All of these are only details. In the final analysis, what is at stake are the principles of our knowledge of nature. Against the omnipotence in theoretically reproducing our experiences claimed by the mechanical method, a youthful method comes forward, permitting us a much more direct description of experience, and yet achieving the generality that is indispensible to every appropriate theoretical reproduction of nature. If the field of energetics is comprehended in this breadth, in which alone justice can be done to its efforts, then the decision is very simple: Here scholasticism - here energetics - that is the choice! [404].

29) This conclusion is a non-sequitur, of course, as Helm must have realized. What it suggests is that passion and residual anger has him trying to extract more from his overall argument than he knew it contained. To be precise: The last sentence erects a false dichotomy between energetics and mechanical theorizing that is not justified by what precedes it. Still more precisely: Helm conceded, however reluctantly, that energetics and scholasticism were not the only options - that mechanical theories could be (and had been) developed in ways that were both genuinely energetic in character and not guilty of "scholastic" excesses. What he should claim, in line with his overall argument, is that a thermodynamic energetics is better able than a mechanical one "to speak about natural processes in a language free of pictures," since it is capable "to a much greater extent than older [mechanical] theories of adapting itself directly to our experience." That, in any case, is the view he defends in the study you are holding and the one he thought that the history of science, however hesitantly, was moving toward.

NOTES

1 The best brief summary of the story in print is Christa Jungnickel and Russell McCormmach, Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, 2 vols. (Chicago: University of Chicago Press, 1986), vol. 2, 217-27, which is also a superb study of the period Helm's history describes. 2 There is no entry for Helm in the Dictionary of Scientific Biography or its mathematical complement; and the Deutsches Biographisches fahrbuch (Berlin and Leipzig), vol. 5, 430, does little more than note his passing in its "Totenliste" for 1923. A useful brief sketch is provided by H.• G. Korber in the Neue Deutsche Biographie (Berlin: Duncker & Humblot, 1968), Vol. 8, 490-91. I have relied mainly on the commemorative address written by Friedrich Wilhelm Emil Naetsch, published in the Sitzungsberichte der naturwissenschaftlichen Gesellschaft Isis zu Dresden (19221 1923), XIV-XVII. Naetsch was a mathematician, a colleague, and evidently a close friend (see Helm's generous acknowledgment of Naetsch's assistance in the preparation of Helm (1910), VI). HELM'S HISTORY OF ENERGETICS: A READING GUIDE 37

Helm seems to have been a plain, simple man whose widely acknowledged competence, dedication, and basic goodness inspired confidence in his students and his colleagues and won for him an intimate circle of friends. Naetsch, who movingly describes him in this way, also speaks of his "harmonious personality," happy family life, and passion for science (XVII). 3 The Dresden Technische Hochschule was the result of a reorganization and enlargement of the Polytechnicum in 1890. Helm was one of the first (and few) full professors of mathematical physics in a German institute of technology. See Paul Forman, John Heilbron and Spencer Weart, "Physics circa 1900," Historical Studies in the Physical Sciences 5 (1975), 5-185; 21. Throughout his career, Helm distinguished "theoretical" (or "analytical") mechanics from "mathematical" physics. For him, as for most continential physicists, the former was essentially a part of mathematics, while the latter was a branch of natural science. See Helm (1884) ii-iv; also i1887a) 4-12. See Naetsch (note 2), XV; Helm (1898) 164-165,254-259 and (1908) (on Zeuner); Naetsch, XV and Helm (1901) (on SchlomiJch); Helm (1898) 101-103, 133-134,229-231,248-249 and (1904) IV, 59-60, 86-87 (on Neumann). 5 Naetsch emphasizes Helm's interest in many fields, his "cultivated versatility," and his "intimate familiarity with all the particulars" of any field on which he chose to write. He was always widening his horizon, Naetsch says, in search of a secure stance from which to view the "great connections in the domain of exact science" (note 2, XVII). Helm taught a variety of courses in mechanics, mathematical physics, and pure and applied mathematics. He soon developed a reputation as a dedicated teacher. His lectures were noteworthy for their clarity and careful preparation and showed a fondness for the historical development of concepts and principles. See Naetsch, XV-XVI; also Helm (1898) 237-239 and (1904) III-IV. Helm was encouraged early to work on problems with technical applications. His major professors were both concerned with the relations between mathematics and other disciplines - mathematical physics in Neumann's case, and applied (technische) physics in Zeuner's. The applied emphasis of Helm's history is evident in many places (e.g. 50-56 [on Carnot], 116-120 [on Rankine], 164-165 [on Zeuner], 205-209). Helm thought that many physical principles - in mechanics, thermodynamics and electricity, for example - had arisen from problems related to technology (see (I 890a); also (I887a) 7-12,16-22; (1904) III-IV), and was very critical of theorists who, in his view, ignored the applications of theory - the biting criticism of Planck (1898, 117) is one example. 6 To my knowledge, there is no definitive list of Helm's publications; but a reasonably accurate one may be obtained from Poggendorffs Biographisch-literarisches Handworterbuch zu den exakten Wissenschaften (Leipzig: 1863-1940), vol. 3, 609; vol. 4,611; and vol. 5-1,516. 7 Korber, writing in 1968, stresses the contemporary relevance of Helm's energetic writings (note 2,491). Naetsch (the mathematician), writing in 1923, mentions Helm's work on energetics only in passing, saying that it was not well-known, and instead applauds Helm's (1910), which showed his commitment to the importance of applied mathematics (note 2, XVII). In this essay, I do not try to estimate the influence of Helm's writings on energetics or of the energeticists in general. It is perhaps worth noting, though, that Helm looks quite like the sort of "classical" physicist Russell McCormmach describes in his brilliantly revealing pseudo-biography, Night Thoughts of a Classical Physicist (Cambridge, MA: Harvard University Press, 1982). Helm wrote on the special theory of relativity (1912a), but tried to interpret Einstein's ideas in terms of the classically accepted aether. He also discussed Planck's quantum hypothesis, but did not think that one had to regard "energy as an atomistically constituted substance in order to describe the actual relations" (19 i3a, 513-14). 8 Mach's influence pervades Helm's writings. A course-grained division would have three over• lapping areas: First, there is the historical and critical orientation of Mach's studies. Helm's (1887a) is evidently modelled on Mach's (1883a), and his (1898) takes much the same approach as Mach's (unfortunately incomplete) (1896a). Second, Helm was attracted to Mach's methodological and epistemological orientation. Here the deep admiration that Helm had for Mach comes out most clearly in his elegant and moving (1916); but Helm's commitment to Mach's methodology and epistemology is clear in much of what he wrote (e.g. 1887a, 1,76; 1894,3-4; 1898,20,100,125, 272). In an emotional defense of the position on energetics he defended in his history, Helm wrote that he hoped knowledgeable readers would recognize the extent to which Mach's ideas permeated the whole structure of his work (363). The ideas he had in mind - having to do with an economical, relational, and phenomenalist conception of scientific theory - are developed in Mach (1872, 1882, 1883a, 1886 1894a, 1894b and I 896a). Third, Helm embraced a number of Mach's favorite ideas - e.g. the idea that all energy is essentially mechanical energy as nothing more than historical prejudice (1887a, 60, 63, 101; 1898,22, 188; cf. Mach 1883a, 1892, 1894a), and Mach's seductive 38 THE HISTORICAL DEVELOPMENT OF ENERGETICS but erroneous comparison of the "fall" of heat through a difference in temperature to the fall of a weight through a given height (1898, 259-60; cf; Mach (1871, 1872,54; 1892; 1896,218,328-46). Helm's indebtedness to Mach deserves more detailed attention, but I will not attempt it here. For my purposes, Mach (I 883a, 472-82) "The Relations of Mechanics to Physics" is especially relevant. 9 See Helm (1895b) 30-32. Also Helm to his wife, 17 and 19 September 1895, in Ostwald (1961) 118-120; Ostwald (1926), II, 180-181, 183; Ostwald (1969) 138-139 n2; and Arnold Sommerfeld, "Das Werk Boltzmanns," Wiener Chemiker Zeitung 47 (1944) 25-28; 25. There seems little doubt that Liibeck was a big occasion for Helm, the reserved and competent but provincial scholar, and its outcome (despite some glosses) a bitter disappointment. See my forthcoming essay "Energetics at the Liibeck Naturforscher versammlung" (in Synthese). 10 Helm (l895b) 32; Helm to his wife, 19 September 1895, in Ostwald (1961) 119-120. Also Ostwald (1926), II, 183. II To give it some context, a bit of the history of Helm's history is worth noting. A half year or so before the meeting, Ostwald had been invited by the publisher Veit & Comp to write a historical study of the energy principle. He declined the offer, but apparently recommended Helm. Helm to Ostwald, 27 April 1895, in Ostwald (1961) 79-80. A few months after the meeting, Helm - still upset and concerned that his written reply to Boltzmann and Planck might be too strident for publication in the Annalen - wrote to Ostwald to ask whether, in the event that it was, it might be published in Ostwald's Zeitschriftfiir physikalische Chemie. He also wanted to know how Ostwald himself planned to proceed. Helm to Ostwald, 18 January 1896, in Ostwald (1961) 81-82. Ostwald counseled Helm to be as calm and dispassionate as he was trying to be. "In general," he wrote, "polemic does not succeed much in such matters; only positive accomplishments are decisive." In this spirit, Ostwald said, he was exploring the possibility of preparing a multi-volume work in which "all of physics was presented energetically, chapter by chapter," and he wondered whether Helm would like to collaborate in that (or some other) joint effort. Ostwald to Helm, 19 January 1896, in Ostwald (1969) 352. Helm declined. He replied that he was already at work on his own "historical presentation of energetics," adding that this was due to Ostwald's initiative (presumably a reference to the Veit & Compo offer), and that all of his available time would be taken up by that project. Helm to Ostwald, 3 February 1896, in Ostwald (1961) 82-83. Owing to the Liibeck meeting, what might otherwise have been little more than a sober explication of energy ideas in physics and chemistry became a passionate defense of energetics. Helm's project - the history to which this essay serves as an introduction - was completed almost exactly two years later; and we may conjecture that it was for Helm, throughout that period, something of a consuming passion. He writes at the beginning of his Preface that the wounds he suffered at Liibeck had healed, but there are numerous indications in the text that they did not heal ~uickly or easily. 1 At first glance, Helm's (1913a) might seem an exception, but it is not. It is essentially a descriptive entry on the "theory of energy" to a scientific dictionary of the sort that was popular in nineteenth- and early twentieth-century Germany. To be sure, the essay does defend energetics in places for the security and generality of its methodology (esp. 508, 527); but it does not contain any of the bursts of passion and urgency that punctuate Helm's history. 13 E.g., 149-152,202-203,225-228. 14 Helm to Ostwald, 16 May 1893, in Ostwald (1961) 75. Also Helm to Ostwald, 20 January 1891, in Ostwald (1961) 73; and Helm (1894) 4. IS The phrase is Ostwald's (1891, 566), but Helm says much the same thing (see 1887a, 2, 71; 1894,3). 16 Many years after the Liibeck meeting, in one of his many reflections on how he had been affected by it, Ostwald wrote: "For me the experience was an invitation to demonstrate the correctness and heuristic usefulness of energetics through practical application of the insights achieved by it to the greatest possible number of particular cases. This happened especially in the cultivation of electrochemistry, which was thereby given the scientific form and order it has retained ever since" (1924, 135). His (l896b) is supposed to detail that discovery. Ostwald's massive history is helpful in understanding a major goal of Helm's. Ostwald's stated objective in this, his first major post-Liibeck work, was to trace the historical evolution of electrochemistry as a branch of contemporary physical chemistry. But he also sought to argue that, rightly viewed, his study showed the "gradual unfolding" - at first halting and imprecise, but later clearer, more self-conscious and confident - of the conception of electrochemistry as a science which investigates the relations between and . He intended his work to serve, therefore, as "a detailed case study" of the emergence and development of "an HELM'S HISTORY OF ENERGETICS: A READING GUIDE 39 important chapter in the science of energetics" (v-vi). There is also the implication, hinted at in several places in Ostwald's lengthy treatise, that historical studies of other branches of energetics ~ of thermodynamics and thermochemistry, for example ~ would reveal essentially the same sort of development. They would show, that is, that the "scientific spirit" had evolved from primitive beginnings, through various setbacks, obstacles and diversions, "to general fruition in the modern theory of energy" (4~6, 756, 806, 811, 1146-47; 6). 17Mixing his metaphors, Helm also refers to the "infertile ground" onto which energetic "seeds" were sown or, later, to the "hostile environment" in which the newly generated seeds had to struggle (1898, 36, 54). I'll stick with the tidal metaphor. 18 For example, Helm (1898) 20, 52, 99, 124, 151~52, 178, 226~27, 311, 328. The same attitude also guides Helm's (I 887a) and (1894). 19 This is the claim that "Every form of energy has the tendency to pass from higher to lower intensity" (1898, 276). More precisely, the intensity law, which is modelled on the behavior of heat (253~54), says that "energy ofa specific form passes from one body to another only when the two bodies have different intensities. and it then passes from the higher to the lower intensity (272). It is central to Helm's energetic theory (see 1887a, 51, 58~9, 61~2; 1898,261, 268, 293~94, 302). 20 Helm (1898), 294~95. The last paragraph of this passage bears a striking resemblance to the "Back to Kant" declarations of the 1860s and 1870s, when philosophers and scientists in Germany were urging a return to Kant and not merely reporting that it had already occurred. See Frederick Gregory, Scientific Materialism in Nineteenth-Century Germany (Dordrecht: Reidel, 1977). 21 Helm (1898) 101, 145, 210, 322. In one place, in fact, he criticized Planck for failing to recognize that there were two approaches to "the unified development of energetic ideas" (292). 22 Helm (1898) 99~101, 322~324. The quotation is from Helm (1895a) IV. 23 See Helm (1887a) 15, 23~26; (1898) 18~28; Ostwald (l892a) 363; (1893a) 40-41; (1895a) 162~ 164 [(1904), 231~233); (1910) 79, 84, 91. 24 In 1898 Helm praised Mayer for "the far-seeing boldness and clarity of [his) reasoning," for his "clarity and logical rigor" (25, 30). In 1887, when he first wrote on energetics, Helm's evaluation of Mayer was less enthusiastic. Then he criticized Mayer's "philosophical excesses" and his "predelic• tion for a priori deductive arguments," accusing him of basing the proof of the conservation of energy on "metaphysicsl monism" ~ by which Helm presumably meant that Mayer had sought to make energy the ultimate substance and the only reality (14-15; also 23~27). If that was Helm's view, then he was mistaken; and he was also mistaken when he later described Mayer as ifhe were a proponent of Machian phenomenalism (cf. Mach 1896a, 245~252). I do not attempt here to work out these contradictions. In general, Ostwald was more inclined to exaggerated interpretations than Helm; but when it came to Mayer, he was both more consistent and more accurate (1887) 13~14 [(1904), 192~193); 1891 566; 189341-43). A balanced account can be found in Kenneth Caneva, Robert Mayer and the Conservation of Energy (Princeton: Princeton University Press, 1993). 25 Helm (1898) 266 76, esp. 276; 291~308, esp. 300~02; also Helm (1887a) 62~65. The Factorization Principle claims (1) that every form of energy can be divided into two components, so that (2) the analytical separation of any form of energy can be made in terms of two (physically significant) factors ~ an intensity factor and a capacity (or extensity) factor (Helm 1898,261,268, 273,314). Ostwald (the realist) factored forms of energy (and not just their representation) as E = ic, where E is a form of energy, i is its intensity component and c its capacity (1892a, 368; 1893, 44, 46--47). Helm (the phenomenalist) insisted that it was only the mathematical differential represent• ing a change in energy that could be factored, and not the energy itself. His version of the Factorization Principle is thus dE = JdM, where J is an intensity and M a capacity (extensity) (1887a, 61~62; 1898, 266~69, 272). Helm's opposition to Ostwald's approach is evident in his history (297~98) ~ although he never mentions Ostwald by name ~ and in his correspondence, e.g. Helm to Ostwald, 16 May 1893, in Ostwald (1961), 75~76. Planck opposed Ostwald (in part) for the same reason; see Planck to Ostwald, 20 March 1892 and 27 April 1892, in Ostwald (1961) 41~44. 26 Helm (1898) 296~99, 313~21, 338-53, esp. 341, 347~50. There are, I think, deep connections linking Helm's Relations Thesis to Mach's anti-metaphysical methodology and epistemology; but, as I said earlier, I will not try to develop them here. 27 Helm quoted Clausius' statements in his history (122). Intended as summaries of the two laws of thermodynamics, they originally appeared as the last lines of a memoir Clausius wrote in 1865 (1865,400). Helm approved of Mach's evaluation: "Propositions about the 'energy of the world,' 'the entropy of the world,' and so on, have no meaning. For such propositions contain applications of metrical concepts to an object [the world] which cannot be measured" (Mach 1896, 338). Quoted bl Helm (125). 2 See Ostwald (1887), 13~14, 20 [(1904), 192~193, 200); (1891), 566; (1893), 41-43; (1895), 162~ 164, 164~165 [(1904), 231~233, 234-235); (1926) vol. 2, 154. 40 THE HISTORICAL DEVELOPMENT OF ENERGETICS

29 Ostwald (1887) 13-14 [(1904), 192-193]; (1891) 566; (1893) 10,40--44; (1895) 161-162 [(1904), 229-231]; (1926), vol. 2,156. 30 See Ostwald (1892a) 375-376, 385; (1893) 4-6; (1895) 155, 158-159, 161, 164-165 [(1904) 220- 221,226-227,229,233-235]; (1902) 163-167; (1926) vol. 2, 153-162. 31 It is worth noting that this is Ostwald's only public criticism of Helm of which I am aware, and that it comes in his autobiography. Otherwise, Ostwald's assessments were typically effusive. For example, Ostwald to Helm, 2 October 1894, in Ostwald (1969) 351; and Ostwald's review of Helm's P894), in Zeitschriftfiir physikalische Chemie 16 (1896) 190. 2 For example, Helm to Ostwald, 13 May 1893; Helm to Ostwald, 19 May 1895, in Ostwald P961), 75-76, 80-81. 3 Given the substantive disagreements between Helm and Ostwald, this is a noteworthy feature of Helm's history. I conjecture that it is due to the fact that Ostwald had recommended Helm for the project and to the suspicion that internecine fights would not promote the cause of energetics. If I am correct in the interpretation I offer, it also reflects Helm's belief that science was moving (or had already moved) in the direction that he preferred. 34 Other passages implicitly critical of Ostwald include most of, e.g., 296-298. The passage quoted in the text indicates - rather by accident - what Helm had in mind when he spoke of energetics as a "relativism" (362). "Relationism" would have been better. 35 Helm (1887a) 50-51, 54, 56-57, 61-62; (1894) I, 58, 68-70, 113; (1898) 226, 296-299. Helm never resolves this tension (or contradiction) in his energetic writings. In 1887 he even makes energy an absolute, calling it "the true element of the world" (56-57)! 36 See Helm (1887a) 34-36, 42-44; (1894) 16,24-28,42-43,58,60,70-73. 37 Helm (1898) 111-112, 121-122, 187-188,222-225,296-299. Helm makes the same point in his Liibeck report: "A form of energy... has reality only at the moment in which it passes from one body to another. Forms of energy as possessions of a body have only a mathematical meaning" (1895a, XII). 38 This section of Ostwald's autobiography is entitled "The Essence of Energetics". 39 For example, Ostwald (1892a) 367-368, 371-378, 380; (1893) 16, 30-35, 41-42, 47, 485-90. 40 This tension, which I also do not attempt to resolve, is especially noticeable and acute when Ostwald discusses the "substances" involved in chemical reactions (e.g. 1893, 500-17). On the composition view, these should just be clusters of energy, but Ostwald treats them as "stoffmengen" which possess energy - including chemical energy! 41 Helm (1898) 81; also 108, 111-112. 42 See Helm (1898) 120-126, 342-343. The quotations are from 121, 120. Also (1887a) 53-56. 43 Clausius (1850), (1854) and (1862); in (1867) 16, 19,21, 108,206. 44 Helm was aware of Clausius' deeper intent, but mentions it in his history only in a regretful aside (145). 45 For example, the law of action and the concept of entropy (138,120). 46 The authoritative source of this conflation, according to Helm, was Helmholtz's (1847) memoir on the conservation of energy (1898, 145). Helmholtz sought to derive the energy law from two beginnings: (I) the impossibility of perpetual motion and (2) the idea that "all actions in nature can be reduced to attractive and repulsive forces, whose intensity depends only on the distance between the points acting upon one another," so that "everything that happens is reducible to acceleration• dependent forces," i.e., from one version of the mechanical world-view (Helm 1898, 35-42; 35,41). 47 Helm (1898) 145-46 (on Zeuner); 131-137, esp. 131, 137 (on Robert Kirchhofl); 141-44, esp. 143-44 (on August Horstmann; cf. 146). 48 Helm (1898) 146-175; the quotations are from 149, 146, 171. 49 See Gibbs (1902) xii, 165-67; also Lynn P. Wheeler, Josiah Willard Gibbs. The History o/a Great Mind, 2nd ed. (New Haven: Yale University Press, 1952), 121, 157. 50 For more details on Helm's (and Ostwald's) misappropriation of Gibbs, see my "Gibbs and the Energeticists," in No Truth Except in the Details; Essays in Honor 0/ Martin J Klein, A.J. Kox and Daniel M. Siegel, eds. (Dordrecht/Boston/London: Kluwer Academic Publishers, 1995), 135-69. Helm does not even mention Gibbs's references to molecules when it would be appropriate to do so, e.g. in connection with the "Gibbs paradox" (162-63). He may be forgiven for not knowing that Gibbs was then working on statistical mechanics, and had been for some time. One would very much like to know what Helm thought of Gibbs's 1902; but, to my knowledge, he never mentioned it. 51 Helm (1898) 175; also 179. Maxwell praised Gibbs and immediately developed some of his ideas. "However, Maxwell's contemporaries did not give to Gibbs's works the more profound attention they deserved. The spirit of the age was not to be overcome so quickly" (1898, 166). This passage shows Helm's tidal view of history at work, as do others on 168 and 174-75. HELM'S HISTORY OF ENERGETICS: A READING GUIDE 41

52 Helmholtz (1882-1883) 959-60, 971. 53 Helmholtz (1882-1883), 2, 971-72; also 983-84 and 3, 94--95. (For Helm's discussion, see his (1898) 179-81.) The last two installments of Helmholtz's memoir showed how the results of his basic research could be applied to several problems in thermo- and electrochemistry. 54 Helm (1898), 178-79. The "paths" of Helmholtz's (1847) have already been mentioned (see note 46). Helmholtz's later works along the second path - which Helm preferred, but did not think were ultimately satisfactory - probably include Helmholtz (I 884a), (I 884b), and (1887), as I have already indicated. 55 Helmholtz (1882-1883) 971-72; 981; 94-5. 56 Helm (1898) 193; also 223. For evidence that Ostwald, too, regarded Planck as an ally, see Ostwald to Planck, 26 June 1893, and 2 July 1893; in Ostwald (1961) 48,52; and Ostwald (1926) 1, 187-88. On the "betrayal," see (1926) 2,30-31. 57 See J.L. Heilbron, The Dilemmas of an Upright Man: Max Planck as Spokesman for German Science (University of California Press: Berkeley, 1986) 9-17; and Thomas S. Kuhn, Black-Body Radiation and the Quantum Discontinuity (Oxford University Press: New York, 1978) 22-28. 58 Helm (1898) 98, 189-91; cf. Planck (1879) 1-6,42. 59 Planck (1887b), (1891a). Helm describes aspects of Planck's thermochemistry in his history P95-204). Also (1894) 41-42. o See, e.g., (1882) 140, 161; (1887b), 197,202; and (1892b), 372-73. Planck had not given up on the mechanical world-view, though. See (1894), (1897) iii-vii. 61 Planck (1887a). Discussed in Helm (1898) 222-24. 62 Helm does not comment in his history on Planck's evident mechanistic leanings in his (1887a), e.g., 137-38. 63 Others (besides Ostwald) were as well. See Arrhenius to Ostwald, 16 February 1896; in Ostwald (1969) 145. 64 Ostwald regarded thermodynamics as essentially the study of the reciprocal transformations of heat and mechanical energy, and the laws of thermodynamics as governing such transformations (e.g. (1889) 244--252; (1893), 12, 484--86). Entropy has a role in his energetic theory only as the capacity factor of heat for isothermal changes «1892a) 370, 382; (1893) 49-50, 485, 490, 494--94. In 1892 and 1893, Ostwald explained irreversibility and energy as the fault of . Because of its peculiar nature, he thought, radiant energy cannot be coupled to energy of other forms, and so cannot take part in reciprocal transformations. Its formation is therefore unidirectional and always results in a loss of "moveable energy." See (1892a) 370-71, 384--86; P893) 1006-22. 5 The correspondence extended over more than two years: Ostwald (1961) 34-59; Ostwald (1969) 345-50. I know of no correspondence between Planck and Helm. 66 Planck to Ostwald, 25 June 1893; in Ostwald (1961) 45-46. 67 See Deltete, "Gibbs and the Energeticists" (note 50), 151-55, 164n68, for a sketch of Ostwald's energetic theory and further references. Also the correspondence between Planck and Ostwald, mentioned above (note 65), for Planck's growing impatience. 68 Planck to Ostwald, 27 December 1895; in Ostwald (1961) 61. 69 Volume energy was one of the forms of "spatial" energy in Ostwald's inventory of energy forms, and for many purposes the most important one (e.g. 1893, 30). He factored it as E = pV, where p is pressure and V is volume «1891) 566; (1892a) 369; (1893) 12-14, 17-18,24--27,30-35, 37-38). Planck argued (rightly) that "volume energy" is not a state function, but rather a path• dependent quantity. He also argued that any quantity of energy, which in Ostwald's energetics "represents substance par excellence," must be a function of the physical and chemical state of a system; otherwise the principle of energy conservation would be undermined «(1896) 73-75; also Planck to Ostwald, 20 March 1892, 22 April 1892, 25 June 1893; in Ostwald (1961) 41-45; and ~1958) vol. 3, 384--85). o (1896) 73, 78. The "broad and fruitful" area Planck clearly had in mind was thermodynamics, to which he had made important contributions, and its second law, which he thought he had set on a proper foundation with his entropy principle. 71 Helm did not like being lumped, indiscriminately, in Planck's critique with people - such as Ostwald - who treated volume energy and heat as state functions. But he seems guilty of the charge in works prior to Liibeck, at least, which sometimes use volume energy as the basis for a discussion of other forms of energy (e.g. (1894),13,14--18,20-28,42-43,58,60,70-73). Helm's response thus involves some backpedaling, and so do other angry references to Planck in his history (e.g., 292- 99). 72 Like Planck, Boltzmann also objected to Helm's attempt to reformulate thermodynamics from an energetic point of view, and for many of the same reasons; the energeticists' treatment of 42 THE HISTORICAL DEVELOPMENT OF ENERGETICS irreversibility, for example, looms large for both. Some relevant texts are the following: Helm (l895a) XII-XIV, (I 895b), 30-33; Boltzmann (l896b) 56-62; Helm (1896) 652-56; Boltzmann (l896c) 39-40, (l896d) 596-97; Helm (1898) 122-23, 149-54; Boltzmann (1898) 640-41. Since Helm's own preference was for a thermodynamic approach (Richtung) to energetics, it may seem incongruent not to sketch Boltzmann's criticisms of that way of proceeding. Put more globally, since Helm evidently thought that the history of science was evolving toward (even if it had not already reached) a complete, thermodynamics-based science of energy, why talk about mechanics? There are good reasons, I think, for discussing Helm's mechanics: First, Boltzmann's criticisms of Helm's thermodynamics (while cogent) are often quite technical; second, Boltzmann did think that mechanics should be regarded as the foundation of natural science - in the absence, that is, of a coherent, consistent, more comprehensive alternative, which he did not think that energetics yet provided; and, finally, a look at Helm's view of mechanics offers a natural entry into the last Part of his history. 73 Helm (I 890b) 308. Also Helm to Ostwald, 20 January 1891; in Ostwald (1961) 73: "[A] unified construction of natural science on the basis of energy concepts must above all understand how to bring the most secure knowledge, namely mechanics, under that point of view." 74 The derivation for a freely moving point is developed on 307-309, those for time-dependent and time-independent constraints on 309-313; Lagrange's equations are derived on 313-314. 75 See Helm (I 887a) 64-65; (1 890b) 307-09; 315; (1894) 42-43,58-60,70. 76 See Helm (l895a) V-VII. I have no satisfactory explanation for the disparity. Perhaps Helm tried to be as impartial as possible in his written report and expressed his own preference more explicitly only in his oral presentation and the subsequent discussion. But it also seems likely that the official summary of the discussion was written by Boltzmann, who expressed the issues in terms of his own (but not Helm's) "picture theory" of scientific theories (see below). Still, given the way that Helm characterized what he called the "mechanical direction" in energetics in his report, one would have expected him to oppose it. Proponents of mechanical energetics, he wrote, seek to construct "a concealed, invented world, which runs its course behind the real [phenomenal] world; a picture of the world which seems to be more or less capable of sensuous representation, but which has evaporated to a system of equations." These equations are able to represent something "palpable," namely motions; but the "thermodynamic approach" (Rich tung) to energetics did not need to fabricate a world of concealed masses behind the motions. Instead, its goal was "to conform as directly as possible to experience; and, since it permits not only the forms of energy themselves but also certain of their distinguishing factors to enter as fully equal elements of our experience, it sees nothing in [energy] equations than the purest expression of quantitative relations" (l895a, III• IV). The last statement is a nice reminder of the phenomenalism expressed by the Relations Thesis; but it remains unclear why Helm would have endorsed - even while finding it unsatisfactory - what he called the mechanical approach (Richtung) to energetics. The key to the puzzle, I conjecture, is the "picture theory" of scientific theories that was proposed and developed by Boltzmann and Hertz, but which I cannot begin to do justice to here. (See Andrew Wilson, "Mental Representation and Scientific Knowledge: Boltzmann's BUd Theory of Knowledge in Historical Context," Physis 28 (1991) 769-795.) Inspired by his close reading of Maxwell, whom he took to be "as much a pioneer in epistemology as in theoretical physics" (1895, 99-100), Boltzmann began as early as 1890 to speak of scientific theories as "purely inner mental pictures (Bilder)" of phenomena (1890, 76). This view, which he argued throughout the 1890s and early 1900s (1892, 1896a, 1896b, 1897a, 1899a, 1899b, 1900, 1902, e.g.), was based on the following core idea: Scientific theories should be regarded as conceptual pictures (Bilder), or representations, of the world, rather than as phenomenal descriptions or realist hypotheses. According to the "picture theory," scientific theories are neither true nor false. Instead, they are to be judged more or less acceptable, according to their empirical adequacy (the extent to which they accurately represent a domain of phenomena), their completeness (their ability to represent those phenomena in a comprehensive and unified manner), and their simplicity (their relative absence of arbitrary or extraneous features). The aim of science, on the picture view, was not to produce theories that are true, but "the most perfect picture representing all phenomena in the simplest and most appropriate manner" (1 899a, 259; also, 1896b, 49-50 and 1899b, 215-16). At some level, difficult to make precise, Helm was attracted to this way of thinking about theories - in spite of his advocacy of the more austere, and Machian, Relations Thesis. But he also had reservations, some of which are included in the text. The BUd conception of scientific theories - both for its promise and its problems - is a rich area for research, which Wilson and others have begun to explore, but which I cannot develop in this essay." HELM'S HISTORY OF ENERGETICS: A READING GUIDE 43

77 Helm (I 895b) 30- 32; Boltzmann (I 896a,c,d), (I 897a) I, 1-3, 193-94, 211-12; II, 1-6, 111-12; ~1899b) 205,216-19. 8 One assumption, already noted above, resolved the internal energy of a gas into components of heat and volume energy. Another postulated the conservation of energy in every possible direction of change of a mechanical system. Boltzmann regarded the former as simply wrong and the latter as an ad hoc maneuver, for which there was no empirical justification. To note: While Boltzmann was usually more careful in distinguishing the views of differerent energeticists, he, like Planck, sometimes lumped them together. 79 Volume energy, mentioned above, was one example. In another, Boltzmann argued cogently that the inequality in Helm's energy principle was either redundant or made no sense for irreversible processes; indeed, if the infinitesimal changes take place between non-equilibrium states, then the energies in the sum cannot even be analyzed into his canonical JdM form (Helm 1895b, 30; Boltzmann 1896b, 59-61; 189867). Helm's error was to conflate external and internal intensities in thermodynamic applications of his principle (1894, 24, 28; I S96, 653, 654--55). He corrected the mistake in his history (149-54, esp. 150-51), but in so doing undermined the novelty of the energy principle (Boltzmann 1898, 67-68). Another example was Ostwald's efforts to quantitatively describe mechanics and thermodynamics, which Boltzmann showed to be usually inadequate, often amounting to no more than bald assertions or disguised definitions (l896b, 43- 45,48-56; 1898, 66-67). 80 Boltzmann (I 896b) 40-41; (I 896c) 39; (I 896d) 597; (l897b) 150-51; (1898) 68. 81 Boltzmann even declared himself a "passionate energeticist" when it came to exploring the analogies among the the forms of energy (1896c, 38). For his reservations, see 1896b, 41-42, 1896c, 38-39; 1896d, 598; 1897b, 148-51; 1899b, 101-02. 82 Helm (1895b) 32; Boltzmann (l896b) 42, (l896c) 39, (I 896d) 597-98, (1897a) I, 3-4, (1897b) 151-52, (l899b) 205, 216--19. Also H.A. Lorentz: "With regard to energetics, which he opposed quite adamantly, [Boltzmann] did not criticize its efforts to create a new world picture in which the transformations of energy are primary; he only thought that the confidence with which its advocates proceeded could not - for the time being, at least - be justified by the successes achieved" ("Ludwig Boltzmann," Verhandlungen der deutsche physikalische Gesellschaft 5 (1907): 206--38; 209). 83 Arnold Sommerfeld, "Das Werk Boltzmanns," Wiener Chemiker Zeitung 47 (1944) 25-28; 25. 84 Cf. Helm (1890b) 308 and (1898) 224. 85 Helm's concessions are grudging; he seems to think that Boltzmann is nitpicking (1896,647; also 649, 650-51). At the Lubeck meeting Helm complained that criticisms of the "energetic foundations of mechanics" he had proposed did not address the "physical side of the matter," but only the analytical form, which he said "needed some improvement" (1895b, 31; 1896, 352). He lodged the same complaint in his history, after he thought the needed improvements had been made (1898, 228). However, Helm's resistance to formal criticism does not square well with his statement to Ostwald that his main concern was the "mathematical treatment of general energetics" (Helm to Ostwald, 16 May 1893; in Ostwald (1961), 75). Helm thought he was being accused of incompetence, and it shows in Part VI of his history (e.g. 226-28). 86 Boltzmann also used this "lack-of-significant-originality" approach in criticizing Ostwald's (very) fragmentary remarks on mechanics (cf. Ostwald (1893),25-27 and Boltzmann (1896b), 42- 45), which were far less sophisticated than Helm's. Boltzmann's judgment was harsh: energetic formulations "do not in the least advance our insight into the principles of mechanics." Even when correctly stated, "they conform entirely to older formulations," but are "infelicitously clothe[d] in the language of energetics" (1896b, 45). Boltzmann correctly surmised that Helm's energy principle in mechanics was only d'Alembert's principle - which Helm implicitly conceded (e.g. (l890b), 307, 310; (1895a), VII). He therefore did not think that Helm - much less Ostwald - had done anything that was both novel and significant. 87 Boltzmann (I 896b) 45-46; also (I 896d) 595-96 and (1898) 65-6. 88 Helm (1898) 15-16,222,226,235,248,268-69,281,282-93,338-40,357-66. 89 "[E]nergetics is not identical to the proposition in mechanics of the conservation of energy" 214; also 211,218,245-46,282-83. 90 Planck might now reject his earlier work, but Helm thought it energetic in character. For example, Planck did not affirm the Superposition Principle only as a special property of mechanical energy, but "accounts for it energetically - however painful that may be for him to admit today - as a property characteristic of the behavior of energy in general." Of course, Helm also thought that the mathematical analysis of energy differentials was the essential point, "not the distinction of individual kinds of energy, which can be changed independently of one another, as self-sufficient components of the intrinsic energy." Planck might now oppose the latter view and abandon 44 THE HISTORICAL DEVELOPMENT OF ENERGETICS

energetics. But aside from the fact that "real presence" is not essential to energetics (indeed, is "without foundation"), Hehn could not resist pointing out that Planck had subscribed to it himself in his own work on the energy law. In any case, the "advance" in that work was not the conception of energies as real, physically isolable and independently variable "stuffs," but Planck's "mathema• tical derivation of d'Alembert's principle from an essentially energetic point of view" (223-25). 91 See (1898) 226, 228 (on Helm's 1887a); 227-28 (on Helm's 1890b). 92 Helm (1898) 212-14, 228-31. For more on Neumann as an advanced wave, see 101-03, 133- 34,216,248-49. 93 (1898) 212-13, 217-18, 227, 228, 229, 237. 94 (1898) 236, 246, 247-48. 95 (1898) 236, 237. 96 (1898)218,220,237. 97 (1898) 236, 247-48. 98 (1898) 220, 246. 99 Boltzmann's critique of Helm's energetic reconstruction of thermodynamics has much the same contours as his criticisms of Helm's energetic mechanics. Boltzmann began by thinking that Helm was either obviously wrong or obscure in his formulations. When Helm sought to clarify what he had done, Boltzmann's reply was that it was still obscure or that it represented no advance over what was already known (see Helm (1895a) XII-XIV, (1895b), 30-33; Boltzmann (1896b) 56-62; Helm (1896) 652-56; Boltzmann (1896c) 39-40, (1896d) 596-97; Helm (1898) 122-23, 149-54; Boltzmann (1898) 640-41). One can imagine the frustration on both sides: Helm claiming that his formulation was both correct and original, even if not expressed in quite the right way; Boltzmann ar§uing that it was either wrong, obscure, or unoriginal. 10 (1898) 269; also 189,232. Helm is responding to Boltzmann's objection (1896b, 56-57) that the energeticists had provided no definitions of the intensity and capacity (extensity) factors of energy apart from the bare mathematical requirement that their products have the dimensions of energy. Boltzmann expressed the view that they were able to make physically useful divisions not because the Factorization Principle told them which ones to make, but only because they knew, in advance, the right ones to make. 101 (1898) 112-13, 188-89,272-76; 272. The Intensity Law says that all forms of energy have the natural tendency (when not prevented from doing so) of moving from regions (or states) of higher intensity to regions (states) of lower intensity (see note 19). A more phenomenalist way of putting the matter, in accordance with the Relations Thesis, is to say that energetic intensities (when not inhibited) are found to come to equilibrium with those of their surroundings. The model for this "law" is the behavior of heat; but the energeticists thought that the model applied to all forms of energy. Cf. my essay Gibbs and the Energeticists (note 50) for further discussion and additional references. 102 This is the place, I think, where Mach's influence on Helm needs to be pursued further; but I will not attempt that here. 103 Helm never seems to have been quite sure what he meant by the "mechanische Richtung" in energetics, how that path was related to the thermodynamic one which he preferred, or how it differed from other mechanical approaches which he opposed. In his Liibeck report, he said that proponents of mechanical energetics seek to construct "a concealed, an invented world, which runs its course behind the real world; a picture of the world which seems to be more or less capable of sensuous representation, but which has evaporated to a system of equations. These equations are capable of representing something palpable, however, namely motions" (1895a, III-IV). Helm did not explain what he meant here, but almost certainly he was thinking of Lagrangian or Hamiltonian descriptions of natural phenomena. Both deal essentially, and not merely incidentally, with energy quantities, and so might be regarded as genuinely energetic in character; both posit a "concealed [mechanical] world" that runs its course behind the "real [phenomenal] world" given to us in observation, but which effectively "evaporates into a system of equations," since virtually nothing is said about the detailed structure of the hidden world; and both are able to represent "palpable" motions. Still, belief in a concealed world running its course behind the phenomena is evidently contrary to the Relations Thesis, as I've already indicated (see note 76). On the other hand, Helm rejected, in his report, certain developments of mechanical ideas as not properly energetic: "No attention will be paid here to the oldest means of transferring the laws of mechanics to all natural phenomena, namely, the mechanical world-view, which conceives of everything that happens as motion. For, although numerous recent attempts to explain gravitation and electrical and magnetic processes by means of atomic or aether hypotheses have of course taken the energy law into consideration, their explanations have their roots, not in this law, but in kinematic ideas. These efforts are therefore not to be included in energetics" (IV). It is not clear what efforts Helm is HELM'S HISTORY OF ENERGETICS: A READING GUIDE 45

rejecting here, since he does not identify their authors. But, whoever they were, they had presumably failed to regard the concept of energy and an energy principle as fundamental, since Helm immediately contrasted their way of extending mechanics with "other means that have emerged to date for applying the equations of motion of dynamics to all the phenomena of nature" - means that had "the development of energy concepts as their essential pre-requisite" (IV-V). 104 Helm (1898) 224-25 (on Maxwell), 342-43 (on Thomson), 342-43 (on Clausius), 326-34 (on Helmholtz), 325-26 (on Hertz). 105 Helm (1898) 334. Helm never explicitly stated the Principle of Analogy, but he intended roughly the following: Just as the kinetic and potential energies of a purely mechanical system can be given as a function of spatial co-ordinates and velocity, so one should be able to formulate corresponding functions for other forms of energy (which are equivalent to the mechanical ones) by using such parameters as temperature, electric charge, chemical potential, and so on (189 5a, IV-V). 106 See e.g. Helm (1898) 333, where Helmholtz is praised for showing "an altogether energetic spirit" in his memoirs on cyclic systems. But, as I have already indicated, Helm is able to interpret Helmholtz as an energetic phenomenalist, such as he wanted, and as he thought the history of science showed, only by glossing over or ignoring what Helmholtz actually intended. See M.J. Klein, "Mechanical Explanation at the End of the Nineteenth Century," Centaurus 17 (1972): 58- 82. 107 Making use of a mathematical theorem proved by Henri Poincare in 1890, Zermelo argued in an 1895 paper that no mechanical proof of the second law is possible, since any mechanical system left to itself would ultimately return to a configuration arbitrarily close to the one from which it began. Sources and a brief discussion of Planck's reply may be found in Kuhn, Black Body Theory, 26-29 and Jungnickel and McCormmach, Intellectual Mastery 2: 214-15. A more extended discussion of Zermelo's paper and Boltzmann's reply to it is contained in M.l Klein's masterful essay, "The Development of Boltzmann's Statistical Ideas," in The Boltzmann Equation: Theory and Applications, E.G.D Cohen and W. Thirring eds., Acta Physica Austraica, Suppl, X (Vienna and New York: Springer, 1973),53-106. 108 (1898) 360. Here, as elsewhere, Helm joins atomism and mechanism as parts of a single doctrine (also 362-63). He also seems to forget that he is describing the legitimate, if suspect, mechanical approach to energetics - the one that makes use of mechanical analogies and "pictures" (Bilder) - and slips into describing it and the mechanical world-view as if they were the same thing. 109 On a less charitable reading, Helm illicitly tries here to draw a metaphysical conclusion (that there is no absolute) from an epistemological premise (that all we know are relations among ~henomena). 10 (1898) 363-64. This paragraph illustrates the tension, noted earlier, between Helm's serene view of history and the view that still required a call to arms. I am reminded of passages from Marx's writings, but won't press the comparison. 111 Helm does not mention, in his conclusion, Planck's charge that the energeticists had ignored irreversibility, likely because he thought that - in his own case, at least - it was mistaken. Nor does he refer to Boltzmann's criticisms of his attempts to describe irreversible processes with the energy principle, perhaps because he thought he had already rebutted them. This is a large issue, which I cannot adequately address here. PRIMARY SOURCES]

Boltzmann, Ludwig (1890). "Uber die Bedeutung von Theorien"; rpt. in (1905), 76-80; trans. in (1974). (1892). "Uber die Methoden der theoretischen Physik"; rpt. in (1905), 1-10; trans. in (1974). _ (1895). Ueber Faradays Kraftlinien, ed. L. Boltzmann (Leipzig: W. Englemann). _ (1896a). Vorlesungen fiber Gastheorie. I Theil. II Theil (1898) (Leipzig: lA. Barth). Translated as Lectures on Gas Theory by S.G. Brush (Berkeley, CA: U. California Press, 1964). _ (I 896b). "Ein Wort der Mathematik an die Energetik," Annalen der Physik 57,39-71. _ (I 896c). "Ein Vortrag iiber die Energetik," Vierteljahresberichte der Wiener Verhandlung zur Forderung des physikalische und chemische Unterrichts 2, 38-44. _ (I 896d). "Zur Energetik," Annalen der Physik 58, 595-598; rpt. in (1905), 137-140; trans. in (1974). _ (l897a). Vorlesungen fiber die Principien der Mechanik, [ Theil (Leipzig: lA. Barth). II Theil (1904). Partial trans. in (1974). _ (I 897b). "Uber die Unentbehrlichkeit der Atomistik in der Naturwissenschaft," Annalen der Physik 60, 231-46; rpt. in (1905),141-157; trans. in (1974). _ (l897c). "Ober einige meiner weniger bekannten Abhandlungen iiber Gastheorie ...'" Verhan• dlungen der Gesellschaft deutscher Naturforscher und Arzte: II, I, 19-26; rpt. in (1909). _ (1898). "Zur Energetik," Verhandlungen der Gesellschaft deutscher Naturforscher und A.rzte II, 1, 65-68; rpt. in (1909), vol. 3, 638-641. _ (1 899a). "Uber die Grundprinzipien und Grundgleichungen der Mechanik"; rpt. in (1905), 253-307; trans. in (1974). _ (l899b). "Uber die Entwicklung der Methoden der theoretischen Physik in neuerer Zeit," Verhandlungen der Gesellschaft deutscher Naturforscher und A.rzte I, 99-112; rpt. in 1905, 198- 227; trans. in (1974). (1900). "Uber die Prinzipien der Mechanik"; rpt. in (1905), 308-330; trans. in (1974). (1902). "Uber die Prinzipien der Mechanik"; rpt. in (1905), 330-337; trans. in (1974). (1905). Populare Schriften (Leipzip: lA. Barth). (1909). Wissenschaftliche Abhandlungen, ed. by F. Haseniihrl. 3 vols. (Leipzig: lA. Barth). (1974). Theoretical Physics and Philosophical Problems: Selected Writings of Ludwig Boltz- mann, ed. by B. McGuinness and (largely) translated by P. Foulkes (Dordrecht: D. Reidel). Clausius, Rudolph (1850). "Uber die bewegende Kraft der Wiirme welche sich daraus fUr die Wiirmelehre selbst ableiten lassen"; rpt. in (1867). _ (1854). "Uber eine veriinderte Form des zweiten Hauptsatzes der mechanischen Wiirmethe• orie"; rpt. in (1867).

This list of primary sources is not intended to be very detailed, much less complete. Citations in the text are all to the German - sometimes to the original organ of publication, but often to a convenient reprint. I have tried to provide enough information so that interested readers may check my sources, if they so desire; but I sometimes do not give all the information one might like in tracking down the originals. When an English translation is to be had, however, I have included an available source; but, again, I have not tried to indicate all the places where translations may be found.

46 PRIMARY SOURCES 47

(1862). "Uber die Anwendung des Satzes von der Aequivalenz der Verwandlungen auf die innere Arbeit"; rpt. in (1867). _ (1865). "Uber die verschiedenen fur die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wiirmetheorie"; rpt. in (1867). _ (1867). Die mechanische Wiirmetheorie (Braunschweig: F. Vieweg). Translated as The Mechan• ical Theory of Heat by T.A. Hirst (London, 1867). _ (1871). "Uber die Ziiruckfuhrung des zweiten Hauptsatzes der mechanischen Wiirmetheorie auf allgemeine Principien," Annalen der Physik 142,433--461. Gibbs, Josiah Willard (1876-1878). "On the Equilibrium of Heterogeneous Substances"; rpt. in The Scientific Papers of J. Willard Gibbs, ed. by H.A. Bumstead and R.G. Van Name. 2 vols. (New York: Longmans, Green, and Co., 1906). _ (1902). Elementary Principles ofStatistical Mechanics. Developed with Especial Reference to the Rational Foundations of Thermodynamics (New Haven: Yale U. Press). Helm, Georg (1877a). "Bemerkungen zu einer Untersuchung des Hrn. Edlung," [Experimenteller Beweis, dass der galvanische Leitungswiderstand von der Bewegung des Leiters abhiingig ist," Annlen der Physik 157 (1876), 645-647], ibid. 319-320. _ (1877b). "Uber die partielle Summation," Zeitschriftfur Mathematik und Physik 22,400--402. _ (1878). "Zu Reimann's Gravitationstheorie," Zeitschriftfur Mathematik und Physik 23,261- 263. _ (1879). "Elementare Ableitung des Newton'schen Gravitationsgesetzes aus den drei Ke• pler'schen Gesetzen," Archiv fur Mathematik und Physik 63, 326-328. _ (1880). "Beitriige zur geometrischen Behandlung der Mechanik," Zeitschriftfor Mathematik und Physik 25,217-233. _ (1881). "Ueber die Vermittelung der Fernwirkungen durch den Aether," Annalen der Physik 14, 149-176. _ (1884). Die Elemente der Mechanik und mathematische Physik. Ein Lehr- und Uebungsbuchfor hohere Schulen (Leipzig: B.G. Teubner). _ (1887a). Die Lehre von der Energie, historisch-kritisch entwickelt. Nebst Beitriigen zu einer allgemeinen Energetik (Leipzig: A. Felix). _ (1887b). "Die bishere Versuche, Mathematisch aufvolkswirthschaftliche Frage anzuwenden," Sitzungsberichre der naturwissenschaftlichen Gesellschaft zu Dresden, 71-80. _ (1890a). "Ueber des Einfluss der Technik auf die Ausbildung der mechanischen Prinzipien," Civilingenieur 36, 159-161. _ (1890b). "Uber die analytische Verwendung des Energieprinzips in der Mechanik," Zeitschrift fur Mathematik und Physik 35, 307-320. _ (1892a). "Die Fortpflanzung der Energie durch den Aether," Annalen der Physik 47,742-751. _ (1892b). "Schwankungen der Erdachse," Sitzungsberichte der naturwissenschaftlichen Ge• sellschaft Isis zu Dresden, 12-15. _ (1893). "Die Ansiitze zu einer mathematischer Chemie," Sitzungsberichte der naturwis• senschaftlichen Gesellschaft ISIS zu Dresden, 13-14. _ (1894). Grundzuge der mathematischen Chemie. Energetik der chemischen Erscheinungen (Leipzig: W. Engelmann). Trans. as The Principles of Mathematical Chemistry by lL.R. Morgan (New York: John Wiley & Sons, 1897). _ (1895a). "Uberblick tiber der derzeitigen Zustand der Energetik," Beilage zu den Annalen der Physik 55, III-XVIII. _ (1895b). "Uber der derzeitigen Zustand der Energetik," Verhandlungen der Gesellschaft deutscher Naturforscher und Arzte, II, 1,28-33. (1895c). "Die Hertz'sche Mechanik," Zeitschrift for wissenschatliche Philosophie 11, 101-107. (1896). "Zur Energetik," Annalen der Physik 57,646-659. (1898). Die Energetik nach ihrer geschichtlichen Entwicklung (Leipzig: Veit & Comp.). (1899). "Statistische Beobachtungen biologischer Erscheinungen," Sitzungsberichte der nat• urwissenschaftlichen Gesellschaft ISIS zu Dresden, 66-67. _ (1901). "Oskar SchI6milch," Zeitschriftfur Mathematik 46, 131-136. _ (1902). "Die Wahrscheinlichkeitlehre als Theorie der Kollektivbegriffe," Annalen der Natur• philosophie 1, 364-381. 48 THE HISTORICAL DEVELOPMENT OF ENERGETICS

_ (1904). Die Theorien der Elektrodynamik nach ihrer geschichtlichen Entwicklung (Leipzig: Veit &Comp.). _ (l907a). "Die kollektiven Formen der Energie," Annalen der Naturphilosophie 6, 366~372. _ (l907b). "Neuere Ansichten iiber den Wesen der Naturerkenntnis," Sitsizungsberichte der naturwissenschaftlichen Gesellschaft ISIS zu Dresden, 56. _ (l907c). "Die kollektiven Formen der Energie," Verhandlungen der Gesellschaft deutscher Naturforscher und Arzte, II, I, 27~29. _ (1908). "Gustav Anton Zeuner," Naturwissenschaftliche Rundschau 23, 61~63. _ (1910). Die Grundlehren der hoherer Mathematik, zum gebrauch bei Anwendungen und Wider• holungen zusammengestellt (Leipzig: Akademische Verlagsgesellschaft). _ (l912a). "Das Relativitiitsprinzip in der A.therhypothese," Physikalische Zeitschrift 13, 171~ 173. _ (l912b). "Der Sammelbegriff als Grundlage der Wahrscheinlichkeitslehre," Sitzungsberichte der wissenschaften Gesellschaft ISIS zu Dresden, 89-90. _ (l913a). "Die Energielehre," in Handworterbuch der Naturwissenschajien (Jena: G. Fischer), vol. III, pp. 508~527. _ (l913b). "Die Energetik auberhalb der Naturwissenschaft," Die Geisteswissenschaften I, 66~ 67. _ (1916). "Ernst Mach, dem naturwissenschaftlicher Denker, zum Gediichtniss," Sitzungsber• ichte der naturwissenschaftlichen Gesellschaft ISIS zu Dresden: 45~54. _ (1917). "Die A.therhypothese," Physikalische Zeitschrift 18, 121~127. Helmholtz, Hermann (von). (1847). Ueber die Erhaltung der Kraft: Eine physikalische Abhandlung (Berlin: G. Reimer); rpt. in (1882-1895); trans. in (1971). _ (l882~1883). "Die Thermodynamik chemischer Vorgiinge"; rpt. in (l882~1895), 2, 958-78, 979~92; 3, 92~ 114. (I 884a). "Studien zur Statik monocyklischer Systeme"; rpt. in (1882~1895), vol. 3. _ (I 884b). "Principien der Statik monocyklischer Systeme"; rpt. in (l882~1895), vol. 3. _ (1887). "Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung"; rpt. in (l882~1895), vol. 3. _ (1882-1895). Wissenschaftliche Abhandlungen von Hermann Helmholtz, 3 vols. (Leipzig: J.A. Barth). _ (1871). Selected Writings of Hermann von Helmholtz, ed. by R. Kahl (Middletown, CT: Wesleyan U. Press). Mach, Ernst (1871). "Eine Bemerkung iiber den zweiten Hauptsatz der mechanischen Wiirmethe• orie"; Rpt. in (1872). _ (1872). Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (Prague: Calve). Translated as History and Root of the Principle of the Conservation of Energy by P.E.B Jourdain (La Salle, IL: Open Court, 1911). _ (1882). "Die okonomisch Natur der physikalischen Forschung"; rpt. in (I 896b), 186~213. _ (l883a). Die Mechanik in ihrer Entwicklung. Historisch-kritisch dargestellt (Leipzig: F.A. Brockhaus). 2nd. rev. ed. (Leipzig, 1889). Translated as The Science of Mechanics. A Critical and Historical Exposition of lIs Principles by T.l McCormack (La Salle, IL: Open Court, 1893) _ (I 883b). "Uber Umbildung und Anpassung im naturwissenschaftlichen Denken"; rpt. in (l896b), 214~235. _ (1886). Beitriige zur Analyze der Empfindungen (lena: G. Fischer). Translated as Contributions to the Analysis of Sensations (La Salle, IL: Open Court, 1897). _ (1892). "Zur Geschichte und Kritik des Carnot'schen Wiirmegesetzes," Wiener Berichte 101, 1589~1613. (I 894a). "On the Principle of the Conservation of Energy"; rpt. in (1896b), 137~185. _ (I 894b). "Uber das Princip der Vergleichung in der Physik"; rpt. in (I 896b), 236~258. _ (I 896a). Die Prinzipien der Wiirmelehre. Historisch-kritisch entwickelt (Leipzig: lA. Barth). Translated as Principles of the Theory of Heat. Historically and Critically Elucidated (Dordrecht: D. Reidel, 1986). _ (I 896b). Populiir-wissenschaftiche Vorlesungen (Leipzig: lA. Barth). Translated as Popular Scientific Lectures by T.l McCormack (La Salle, IL: Open Court, 1895). PRIMARY SOURCES 49

_ (1902). "Die Ahnlichkeit und die Analogie als Leitmotiv der Forschung," Annalen der Naturphilosophie I, 5-14. Ostwald, Friedrich Wilhelm (1887). Die Energie und ihre Wandlungen; rpt. in (1904). _ (1889). Grundriss der allgemeinen Chemie (Leipzig: W. Engelmann). _ (l89Ia). "Studien zur Energetik," Berichte fiber die Verhandlungen der Siichsischen Akademie der Wissenschaften zu Leipzig 43,271-288. Reprinted in Zeitschriftffir physikalische Chemie 9 (1892),563-578. _ (1892a). "Studien zur Energetik II: Grundlinien in der allgemeinen Energetik," Berichte fiber die Verhandlungen der Sachsischen Akakemie der Wissenschaften zu Leipzig 44, 211-237. Reprinted in Zeitschriftffir physikalische Chemie 10 (1892),363-386. _ (I 892b). Thermodynamische Studien von J Willard Gibbs, trans. W. Ostwald (Leipzig: W. Engelmann). _ (1893). Lehrbuch der allgemeinen Chemie. Zweite ungearbeite Auflage. II. Band, I. Teil: Chemische Energie (Leipzig: W. Engelmann). _ (1895). "Die Uberwindung des wissenschaftlichen Materalismus," Verhandlungen der Ge• sellschaft deutscher Naturforscher und Arzte I, I: 155-168; rpt. in (1904). (l896a). "Zur Energetik," Annalen der Physik 58,154-167. _ (l896b). Elektrochemie: Ihre Geschichte und ihre Lehre (Leipzig: Veit & Comp.). _ (1902). Vorlesungen fiber Naturphilophie, gehalten im Sommer 1901 an der Universitiit Leipzig (Leipzig: Veit & Comp.). _ (1904). Abhandlungen und Vortriige allgemeinen Inhaltes (1887-1903) (Leipzig: Veit & Comp.). _ (1910). Grosse Manner (Leipzig: Akademische Verlagsgesellschaft). _ (1924). "Wilhelm Ostwald," in Philosophieder Gegenwart in Selbstdarstellungen (Leipzig: B.G. Teubner), vol. IV, pp. 127-161. _ (1926). Lebenslinien: Eine Selbstbiographie, 3 vols. (Berlin: Klasing & Co., 1926-1927). _ (1961). Aus dem wissenschaftlichen Briefwechsel Wilhelm Ostwalds, I. Teil: Briefwechsel mit Ludwig Boltzmann, Max Planck, Georg Helm und Josiah Willard Gibbs, H.-G. Korber, ed. (Berlin: Akademie-Verlag). _ (1969). Aus dem wissenschaftlichen Briefwechsel Wilhelm Ostwalds, II. Teil: Briefwechsel mit Svante Arrhenius und Jacobus Hendricus van 't HojJ, H.-G. Korber, ed. (Berlin: Akademie• Verlag). Planck, Max (1879). Uber den zweiten Hauptsatz der mechanischen Wiirmetheorie (Munich: Acker• man); rpt. in (1958), I, 1-61. _ (1882). Verdamfen, Schmelzen und Sublimiren," Annalen der Physik 15. 446-475; rpt. in (1958), I, 134-63. _ (1887a). Das Princip der Erhaltung der Energie (Leipzig: Teubner). _ (I 887b). "Uber das Princip der Vermehrung der Entropie"; rpt. in (1958) I, 196-216,217-31, 232-73. (189Ia). "Uber das Princip der Vermerung der Entropie," Annalen der Physik 44,385-428. _ (1891 b). "Allgemeines zur neueren Entwicklung der Wiirmetheorie"; rpt. in (1958) 1,372-81. _ (1892). "Bemerkungen tiber das Carnot-Clausiussche Princip," Annalen der Physik 46, 162- 166. _ (1893). "Der Kern des Zweiten Hauptsatzes der Wiirmetheorie," Zeitschriftffir physicalische und chemische Unterricht 6, 217-221. _ (1894). "Antrittsrede zur Aufname in die Akademie der Wissenschaften zu Berlin von 28. Juni 1894," Sitsungsberichte der preusiche Akademie der Naturwissenschaften zu Berlin (1894), 641- 644. _ (1896). "Gegen die neuere Energetik," Annalen der Physik 57, 72-78. _ (1897). Vorlesungen fiber Thermodynamik (Leipzig: Metzger & Wittig). Translated as Treatise on Thermodynamics by A. Ogg (London, New York and Bombay: Longmans, Green, 1903). _ (1958). Physikalische Abhandlungen und Vortriige, 3 vols. (Braunschweig: F. Vieweg). GLOSSARY OF TERMS

"Abweg" - usually as "detour" or "byway"; sometimes as "deviation", "departure" or "wrong way". "Begriindung" - usually as "foundation"; sometimes as "founding", "ground• ing" or "establishment". "beliebig" - usually has the sense of "willkiirlich", and so is translated as "arbitrary"; but sometimes "randomly chosen" is more appropriate. "Bewegungsgrosse" - usually as "", but occasionally as "quantity of motion". "Beziehungstum" - usually as "pure system of relations", but sometimes as "pure relatedness". "Bild" - usually as "picture", as in "die mechanischen Bilder" ("mechanical pictures"), or "beurteiltes Bild" ("appropriate picture"), or "in einer bilder• freien Sprache" ("in a language free of pictures"); but sometimes as "model". Usually, however, "model" is reserved for "Modell", as in "ein mechanisches Modell" ("a mechanical model"). Helm often seems to equate a "Bild" with an analogy, as in "aber wenn es sich nur urn ein Bild, ein Analogie handelt" ("but when it is only a matter of a picture, an analogy ... "); or when the movement of energy is spoken of as "ein mechanisches Bild, als ein Analogie" ("[as] a mechanical picture, as an analogy"). But I translate "Analogie" as "analogy", rather than as "picture", as in "mechanischer Analogien" ("mechanical analogies"). There are a lot of issues here that I don't try to resolve (see note 76 to my "Reading Guide"). "Dampf" - usually as "vapor"; but sometimes as "steam" when it is clear from the context that "Wasserdampf" is being discussed or in phrases such as "Dampfmachine" ("steam engine"). "dynamische Differentialgleichungen" - sometimes as "differential equations of dynamics"; often as "equations of motion" when it is clear from the context that the phrase is equivalent to "Bewegungsgleichungen". "Eigenenergie" - as "intrinsic energy" instead of as "internal energy". Helm follows William Thomson rather than Clausius, whose "innere Energie" would more appropriately be translated as "internal energy".

50 GLOSSARY OF TERMS 51

"Erhaltung der Kraft" - as "conservation of force", not as "conservation of energy". "Forschern" - depending on the context, as "researchers", "scientists" or "investigators". "galvanische Kette" - as "battery" rather than as "galvanic chain". "gegenseitig" - sometimes as "reciprocal", but usually as "mutual". "alles Geschehens" - as "all that happens" or "everything that happens". Ostwald's "Das Gesetz des Geschehens" is rendered as "The Law of Happen• ing", and "Naturgeschehens" as "natural occurrence" or "natural events", depending on the context. "lebendige Kraft" - as "living force", not as "kinetic energy". Occasionally, I translate "lebendige Kraft" as "" when Helm is quoting - or when it is clear that he is referring to - texts in which that phrase would have been used. "mechanische Wiirmetheorie" - as "mechanical theory of heat" rather than as "thermodynamics". "nicht-umkehrbar" - as "irreversible" rather than as "non-reversible". "Satz" - depending on the context, as "proposition", "principle", "theorem", "law" or "thesis". "Satz" and its variants - such as "Grundsatz", "Fundamentalsatz" and "Hauptsatz" - are problematic in Helm, since he appears to use them casually and inconsistently. "Grundsatz" is usually translated as "basic principle" and "Fundamentalsatz" as "fundamental principle". "Hauptsatz" is generally reserved in the text for the laws of thermodynamics, and so usually gets translated as "law". But not always. Thomson's "Hauptsatze" in Part III, Section 2, is translated as "basic principles" or "propositions". "spannung" - usually as "tension", as in "Spannkraft" ("tensional force") or "Oberfliichenspannung" ("surface tension"); but sometimes as "pressure", as in "Dampfspannung" ("vapor pressure"). "Stoff" - as "substance" or "material", as in "Wiirmestoff" ("heat substance"). Exceptions to this occur in Part 2, Sections 1 and 4, where Helm quotes from Carnot's writings or refers to works of other early nineteenth-century French scientists; there I translate "Wiirmestoff" as "caloric". "Technik" - as "technology" rather than as "technics". But "Techniker" is translated as "applied scientist". "technische" - sometimes as "technical", as in "technische Ausdriicke" ("technical terms" or "expressions"), but often as "applied", as in "technische Mechanik" ("applied mechanics"). "unendlich klein" - as "infinitely small" or "infinitesimal"; "verschwindend klein" - usually as "infinitesimal", but sometimes as "negligibly small" or "vanishingly small". "Veriinderung" - usually as "change", but sometimes as "variation" when it is 52 THE HISTORICAL DEVELOPMENT OF ENERGETICS clear from the context that it is equivalent to the standard variation ("6') in physics. "von selbst" - sometimes as "spontaneously"; sometimes as "by itseIr' ("by themselves") or "in itself' ("in themselves"). "Wechselwirkung" - sometimes as "reciprocal action"; usually as "interac• tion", as in "Wechselwirkungsenergie" ("interaction energy"). "Wirkungsgrad" - sometimes as "efficiency", sometimes as "efficacy". "Wirkungsfunktion" gets translated as "efficacy function" and "Wirkungs• fahigkeit" as "effective capacity". "zerfallen" - as used by Helm with reference to energy, forms of energy, energy equations, forces/influences, actions and motions, this important and recurrent word usually has the sense of "to split up" or "to divide/separate into parts, components or factors". I generally use "resolve" or "resolution" (for "Zerfall" and "Zerfallung") when Helm is discussing forces or motions and occasionally when he is discussing energy. But, usually, I have energy and energy equations being "split up", or "divided into parts", or "separated into contributions", or (sometimes) "analyzed into components", and the like. For example, "die kinetische Energie .. .in drei Energiearten zerfalle" is translated as "the kinetic energy... separates into three kinds of energy". Forms of energy are "analyzed" into factors, although I otherwise try to avoid using "analyze" or "analysis" too often, since people tend to think of these in the popular sense of "study", rather in the chemical sense of "separating (or separation) into constituents". For similar reasons, I do not translate "zerfallen" as "decompose" (much less as "disintegrate", "break down" or "decay") or "Zerfallung" as "decomposition"; these all sound too organic - as if Helm were referring to a compost bed, instead of to energy or an energy equation. Analagous remarks apply throughout to "zerlegen" and "Zerlegung". DIE ENERG ETIK

NACH IHRER GESCHICHTLICHEN ENTWICKELUNG.

VON

DR. GEORG HELM, O. PROFESSOR .1.11 DER 11:. TEOHII. BOOBSOHULB ZU DIIB8DBII.

MIT FIGUREN 1M TEXT.

LEIPZIG, VERLAG VON VEIT & COMPo 1898. PREFACE

Although produced in controversy, this book is not a controversial work. The calming effects of the years that have passed since the tumultuous days in Lubeck are enough to guarantee that these pages will accurately trace the coming and going of opinions, the battle for the truth and the recognition of error. In only a few passages, especially in Part Six, will one be able to tell from the tone of the book that it comes out of this struggle. For these I ask the indulgence of my reader, since they contain explanations the extent of which probably does not correspond either to the difficulty of the questions treated or to their influence. But in such passages the extent of treatment could not - as was otherwise the case - be made to depend solely on a judgment as to the value and significance of the investigations presented. There considerations of defense, more than concern for symmetry, had to determine the structure. Throughout the book, however, there is one dominant idea that permeates its pages: Energetics is a unified development of thought, a unique manner of seeking a comprehensive knowledge of nature, which unfolds from Robert Mayer to the present day. It has exhibited errors and excrescences at all stages of its growth; and much that is generally acknowledged today first appeared in impure form and needed to be refined. But the eye that follows the historical development of energetics will recognize that here, as with all living things, it is the same motive forces which give rise both to the valuable addition and to that which is rejected. The book will therefore vigorously protest the attempt to brand energetics as something useful only in special fields - as its opponents have tried to do - and that discounts its status as a unified intellectual movement. This production of thought must instead be understood as a whole, as a great reorientation in the human understanding of natural events.

Dresden, February 1898 Georg Helm

55 CONTENTS

PART ONE: THE ESTABLISHMENT OF THE FIRST LAW Section One: The Conception of Force before Robert Mayer 65 An Historical Standpoint regarding the Development of Scientific Theories. The Concept of Force according to Gehler's Dictionary. Point of View of German textbooks.

Section Two: Isolated Beginnings of an Energetic Conception 68 Religion and Speculative Philosophy. Heraclitus, Anaxagoras, Empedocles, Democritus, Epicurus, Plato, Lucretius. Euler, Hobbes, Locke, Johann Bernoulli.

Section Three: Heat as a Kind of Motion 70 Heat Substance, Atoms of Heat. Daniel Bernoulli, Rumford, Davy, Fresnel. Mohr. Placidus Heinrich, Liebig.

Section Four: The Founding of Energetics in Mechanics 72 Principle of Living Force according to Lagrange. Change of Living Force in Collisions. The Idea of Transformation in Applied Mechanics. Carnot, Coriolis, Navier, Poncelet. German textbooks. Weisback, Redtenbacher.

Section Five: Robert Mayer's Fundamental Energetic Idea 76 The essay of 1841. First Publication of 1842. A new Concept of Force. Imponderables. "To Transform". Energetics as Relativism. Mayer's Intuition.

Section Six: The Equivalence of Energies 81 Heat is not the Same as Motion, but only Equivalent to it. The Equivalent of Heat. Energetics of the Electrophorus. On Cosmology. The Forms of Energy. Personality and Life of Robert Mayer.

Section Seven: Grove and 86 Grove 1842. Equality of the Forms of Energy, but still the Priority of Motion. A Religious Point of View. Joule versus Clapeyron. Measurements of the Heat Equivalent. Hess 1840. Table of older Determinations of the Heat Equivalent.

57 58 THE HISTORICAL DEVELOPMENT OF ENERGETICS

Section Eight: Helmholtz's Point of View 91 The Perpetuum Mobile Principle. Planck's Commentary on this Principle. Formulations of the Starting Point. Derivation of the Conservation Law from Mechanics. Lipschitz's Objection and Helmholtz's Response. When is the Increment of Work a Total Differential? Central Forces. Conflation of two Ways of Viewing Things. Conservation of Force.

Section Nine: Helmholtz's Applications of Energetics 99 Interference. Friction and Impact. The Two-Fold Point of View on the Relation between Heat and Motion. Electrostatic States. Batteries. Induction. Planck's Critique. Vindication of Energetics from a Reproach. Reception of Helmholtz's Work. Energetic Requirements of new Hypotheses. Popularization of Science.

PART TWO: PREPARATION FOR THE SECOND LAW Section One: Sadi Carnot 107 Energetic Starting Point. Passage of Heat from higher to lower Temperature. Cyclic Process with Vapors. Reversibility. Perpetuum Mobile Principle. Cyclic Process with Gases. A Carnot Process. Heat Equivalent. Life.

Section Two: Clapeyron 113 Graphical Representations. Analytical Treatment. The Temperature Function C. Clapeyron's Formula.

Section Three: Holtzmann 117 Rober Mayer's Standpoint. Clapeyron's Error. Determination of the Temperature Function C. The Heat Equivalent. von Kauffmann.

Section Four: Thomson's Pre-energetic Works 119 The Absolute Zero Point. Clement and Desormes. Determination of the Temperature Function C. Dependence of the Melting Point on Pressure; James Thomson's Cyclic Processes.

PART THREE: CLASSICAL THERMODYNAMICS Section One: The Founding of Thermodynamics by Clausius 125 The Unification of Mayer's and Carnot's Points of View. The Analytical Treatment of the Infinitesimal Cyclic Carnot Process for Gases. The Function U. The Differential dQ. Vapors. Analytical Application of Carnot's Principle. Auxiliary Assumptions and the Function C. The Specific Heat of Vapors. The Heat Equivalent. Energetic Character of Clausius' Work. CONTENTS 59

Section Two: The Founding of Thermodynamics by William Thomson 136 Thomson's Conversion from Carnot's Standpoint to Energetics. The Principles of Thermodynamics according to Thomson. Analytical Treatment. Intrinsic Energy. Deviation of Recent Energetic Theories based on Carnot's Point of View from Older Ones. The Function C. Efflux of Gas. Thermal Currents. Other Applications of Thermodynamics.

Section Three: Preparation for the Concept of Entropy 145 Thomson's Knowledge of Dissipation. The Relation between Heat and Temperature according to Thomson. The Equivalence Value of Transformations according to Clausius. Planck's Critique of this Concept. The Total Differential dQI ().

Section Four: The System of Classical Thermodynamics 153 Intrinsic Energy and the First Law. Carl Neumann's Explication of the Second Law. States of Equilibrium and Reversibility. The Entropy Function. Energy and Entropy of the Parts and the Whole.

PART FOUR: NEW INITIATIVES, DISPUTES AND MISPLACED EFFORTS Section One: Doubts about Thermodynamics 161 Mathematical Difficulties. Reech, Hirn, Tait, Tolver, Preston. Carnot's Principle in the Case of Radiation.

Section Two: Rankine 163 A Molecular-Hypothetical Point of View. The Names "Actual" and "Potential". The Splitting Up of Intrinsic Energy. First Appearance of the Entropy Function. Helmholtz's Judgment. Analysis of Energy into Factors. Rankine as Applied Scientist. Applied Mechanics and Thermodynamics. Second Law of Thermodynamics.

Section Three: Introduction of Entropy by Clausius 171 Departures from Thermodynamics occasioned by the Mechanical Hypothesis. Disgregation. Energy and Entropy of the World. Critique of the Universal Laws.

Section Four: The English Priority Dispute 176 Tyndall emphasizes Robert Mayer. Joule's Claims. Good Words. Colding. 60 THE HISTORICAL DEVELOPMENT OF ENERGETICS

PART FIVE: THE ENERGETIC TREATMENT OF CHEMISTRY Section One: Kirchhoff 181 Introduction of a new Variable. Application of Intrinsic Energy. Kirchhoff's Fundamental Formulae. Kirchhoff's Cyclic Processes. Vapor Pressure over Ice and over Water. Helmholtz's Application of Concentration Chains. Dependence of Heat of Reaction on Reaction Temperature.

Section Two: Beginnings of Thermochemistry 187 Hess, Julius Thomson. Influence of the Molecular Hypothesis. Schroder van der Kolk. Berthelot. Horstmann. Application of Clapeyron's Formula. Dissociation. Obstruction of Progress by Atomistic Views.

Section Three: Main Features of Gibbsian Thermochemistry 192 Liberation from the Molecular Hypothesis. Earlier Conflation of the Molecular Hypothesis and Thermodynamics. Mathematical Method. Gibbs's first Conception of the Laws of Thermodynamics. Connection with the Formulae of Clausius. Isolated Systems. Nature of Reversible Change. The Second Conception of the Laws. Example of .

Section Four: The Gibbs Functions 202 Phases. Intrinsic Potentials. Example for Homogeneous Bodies. Intensity Property of the Intrinsic Potential. Example of Osmosis. Massieu's Function F and Gibbs's Characteristic Functions. The Fundamental Equation. Energy and Entropy of the Whole and the Parts.

Section Five: The Phase Rule and Geometrical Methods 211 The Phase Rule. Two-Dimensional Diagrams. The Gibbsian V-S-E Surface. The Two-fold Corresponding () - P - II Surface.

Section Six: The Measurement of Chemical Intensity 215 Chemical Intensity and Gravity. The Splitting Up of the Fundamental Formula. Second Solution to the Problem. Third Treatment. Chemical Intensity and Electrical Potential Difference.

Section Seven: Helmholtz's Thermochemical Works 222 Helmholtz's Influence. Gibbs's Study of the Galvanic Cell. Helmholtz's Theory of the Galvanic Cell. Helmholtz's Endeavor to extend the Methods of Mechanics. Free Energy. CONTENTS 61

Section Eight: Further Development of the Theory of Free Energy 228 Duhem. Robert von Helmholtz's Summary. Nernst's Standpoint. Le Chatelier's Energetics. The Analytical Use of Free Energy: Gibbs's Point of View. Unjustified Influence of the Molecular Hypothesis.

Section Nine: Planck's Treatment of the Concept of Entropy 235 Connection with Horstmann's Works. The Preference of Nature. Entropy as the Measure of the Preference. Entropy of a Gas; of an Arbitrary Substance. Evaluation of Planck's Point of View.

Section Ten: Planck's Thermochemistry 241 The Principle of Entropy Increase in the Case of Chemical Processes. Gibbs's more rigorous Treatment of the Problem. Planck's Derivation of the Generalized Clapeyron Formula. Chemical Reactions in Gas Mixtures. Concentration. Dilute Solutions. Number of Components. Properties of the Concentration Products. Changes in Aggregation of Dilute Solutions.

PART SIX: THE ENERGETIC FOUNDATION OF MECHANICS Section One: The Development of Energetics in its Different Fields of Application 253 Electricity. Physiology. Philosophy and Political-Economic Theory. Ostwald's System of Measurement. Thermo-technology. Efficiency of a Machine. Value of Energetics for Evaluating Motors.

Section Two: Energy Law and Energy Principle 256 The Energetic Principles of Mechanics. The Differential Equations of Mechanics in Relation to the Energy Law and Variational Principles. The Energy Law with one Degree of Freedom and the Reduction of Problems of Equilibrium to this Case. Energetics is not Identical to the Law of the Conservation of Energy. Boltzmann's Objection regarding Material Points. Internal Forces. The Absolute System of Coordinates in the Relativism of Energetics. Prominence of the Principle of Virtual Displacements. Energy Law and Energy Principle.

Section Three: The Energetic Foundations of Mechanics in Poncelet, Maxwell, Planck, Helm 266 Poncelet's Founding by Means of Impulse. Maxwell. Planck's Superposition and the Resolution of the Conservation Law with Respect to Three Directions. Mathematical Equivalence of this Treatment with the Contemporaneous One of Helm. Critique and Justification of Helm's Work of 1890. Gruner 1897. Carl Neumann's Presentation of the New Principle. General Coordinates. 62 THE HISTORICAL DEVELOPMENT OF ENERGETICS

Section Four: Energetic Treatment of the Concept of Force 278 Geometrical and Mechanical Dependencies: The Nature of Force. Work and the Resolution of Force. The Parallelogram of Forces. The Equivalence of Action and Reaction. Restrictions on Motion Explicitly Containing Time.

Section Five: The Energetic Treatment of Mechanics 283 Union of the Energy Principle with Galilean-Newtonian Mechanics. Treatment of Fluid and Elastic Bodies.

Section Six: Ostwald's Energetic Principles 290 The Principle of the Exceptional Case. Maximum and Singularity. The Energy Principle Distinguishes the Actual Motion from Merely Possible Ones. Ostwald's Maximum Principle. Carl Neumann's Formulation and Proof of this Principle. An older Form of the Principle following Thomson and Tait.

PART SEVEN: ENERGY FACTORS Section One: Zeuner's Analogy between Heat and the Work of Gravity 299 The Forms of Energy. Peculiarity of Heat. Zeuner's Analogy. Analogy for Irreversible Processes. Degree of Efficacy.

Section Two: Other Analogies Among the Forms of Energy 305 Mach. Lippmann. Maxwell and von Oettingen. Popper's Ball Machine. Popper's Product Representation.

Section Three: Intensity and Extensity 311 The Development of the Differential of Intrinsic Energy into Energetic Normal Form. Mathematical Reasons for Other Possible Developments. Duhem's Development. Properties of the Intensities and Extensities. Gibbs's Proof of the Mutual Dependence of these Properties.

Section Four: The Mechanical Forms of Energy 321 Forces Derivable from a Potential. What is Electricity? Kinetic Energy. Galileo's Conception of Velocity as Intensity. Cyclic Carnot Processes with Arbitrary Forms of Energy. Forms of Mechanical Energy. Interaction Energy. Resolution with respect to Three Perpendicular Directions. Popper's and Ostwald's Representation of Kinetic Energy. Monocycles. The Integrating Denominator.

Section Five: Conclusion of the Survey of the Forms of Energy 330 . Different Representations of the same Form of Energy. Radiative and Electromagnetic Energy. Ebert's Formulation of the Intensity and Capacity Factors. Review of the Forms of Energy. CONTENTS 63

Aversions to the Energy Factors. Mechanical Rendering of the Energy Factors. Approach of Energetics to Elementary Questions. Splitting Up of the Energy Equation. Intrinsic Energy and the Forms of Energy.

Section Six: Ostwald's Treatment of the Energy Factors. 340 The Generalized Law of Intensity. The Compensation of Intensities. Law of Happening. Doubts. The Universal Character of the Intensities. The Perpetuum Mobile of the Second Kind.

Section Seven: Special Studies of the Energy Factors of Heat 345 A Theorem concerning Differential Expressions. The Integrating Denominator of the Heat Differential according to Zeuner, Helmholtz, Budde. von Oettingen's Adiabats. Pfaundler's Image for Dissipation. Wald's Point of View. Section Eight: Relations between Intensity and Extensity 354 Wronsky, Dressel. Wiedeburg's new Conception. The Inequality of Clausius. Resistance. The New Entropy Function. Relations between the Two Concepts of Entropy. Delay of Energy Transfer.

PART EIGHT: THE MECHANICAL ApPROACH TO ENERGETICS AND MECHANICAL PICTURES Section One: The Differential Equations of Lagrange 363 The Kinetic Potential. Maxwell. Cyclic Coordinates. Examples from Helmholtz: Electrodynamics, Thermodynamics, Theory of the Gyroscope. Concealed Motion. Relations between Forces and Parameters. The Principle of Analogy. J.J. Thomson. The Dispersion Function.

Section Two: Mechanical Pictures 380 Boltzmann. Comparison of the Thermodynamic and Mechanical Approaches to Energetics. Hypotheses of Clausius and William Thomson. Duhem's Energetic Treatment of Viscosity Phenomena.

Section Three: The Migration of Energy 388 Hertz, Poynting. Objections. Lodge and Foeppl. Wilhelm Wien.

Section Four: The Limits of Description by means of Mechanical Pictures 394 Difficulty of Picturing Irreversibility by means of Conservative Systems. Further Difficulty of Picturing Dissipation. Loschmidt, Boltzmann. Poincare, Zermelo. Limits of the Pictorial Method. Do Atoms Exist? Standpoint of Relativism. Atoms and Differential Equations. Approaches to the Description of Nature. Energetics as the Guiding Idea for All Scientific Approaches.