A Historical Approach to Entropy 2Nd Edition

A Historical Approach to Entropy 2nd Edition

Collected papers of Eri Yagi and her coworkers

Eri Yagi Institute for History of Science A Historical Approach to Entropy, 2nd Edition by Eri Yagi and her coworkers

Published by Eri Yagi Institute for History of Science First printing summer 2018

Chapter I―Introduction 1. Preface to the Second Edition

2. Eri Yagi’s Autobiography in German

3. A list of papers in the First Edition

Chapter II―Clausius at Koszalin, Poland 1. Ref-1) E.Yagi, “R.Clausius’ contribution to the 1st and 2nd laws of Thermodynamics,” Book of Abstracts, 4th Symposium on Vacuum- based Science & Technology, September, Kozsalin, Poland (2009).C1, p.11 (total 1page )

2. Ref-2) E.Yagi, “R.Clausius’ contribution to the 1st and 2nd laws of Thermodynamics,” Power Point named Yagi at Koszalin 1 (total 15 pages)

3. Ref-3) E.Yagi, “Visiting Poland for the Clausius Tower Project (September 2009) Part 1(total 6 pages )

Chapter III―Clausius through various study methods 1. Ref.-4) E.Yagi and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods,” (delivered on 29 July) Abstract, XXIII International Congress of History of Science (2009), Budapest, Hungary. (total 1 page )

2. Ref-5) E.Yagi, and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods: Specially Focused on Technical term Analysis,” Historia Scientiarum, Tokyo, Vol.20-1 (2010) pp.47-56 (total 10 pages) 3. Ref-6) E.Yagi, “The Important Role of Particles through the Mechanical Theory of Heat,” International Conference for the 3rd Centenary of R.G. Boscovich, Pavia, Italy September, 2011 (to be published in the near future) (total 3 pages)

4. Ref-8) Haruo Hayashi, “Clausius’ 5th paper and the theory of the Steam Engine” (2013). (total 1page)

5. Ref-9) E.Yagi and Haruo Hayashi, “Clausius’ theory of heat and the steam-engine,” [Abstract: BSHS Annual Conference 2010]. (total 1page )

6. Ref-10) E.Yagi, “Clausius on Nagaoka’s development of his atomic model (1903),” the 24th ICHSTM, Manchester, Program T160, July 25 (2013) p.343. (total 1 page)

7. Clausius on Nagaoka’s Development of his Atomic Model

Chapter IV―Bibliography 1. Total list of Clausius’ Papers by Kiyoshi Yoda (total 11 pages from K.Yoda’s list in our Japanese translation of 7 of Clausius’ German papers on the mechanical theory of heat, Entoropie no Kigen (The origin and backgrounds of Entropy) (Tokai University Press, Japan, pp.336-351)

2. A list of Eri Yagi ‘s papers from 2002 to 2018 (total 2 pages) CHAPTER I Introduction 1. Preface to the Second Edition

fter we published our first edition of “A Historical approach to AEntropy” (2002, by the International Publication Institution, Tokyo), a number of interesting things happened. For example, the journals Isis 96 (2005):294, and Centaurus 46 (2004):231 introduced the contents with their comments. In addition to these the most surprised reaction was the fact that I was invited by the Clausius Tower Society, Koszalin University of Technology, Poland, for their first memorial conference as the first speaker in 2009. The Koszalin University of Technology is located in the memorial city where Clausius was born in 1822 and stayed before his moving to Szczecin high school (presently in Poland). The University had been planning to build the Clausius Tower since 2009 when the first Clausius Session at the Symposium on Vacuum-based Science and Technology was held. The main part of this second edition will be the Abstract1) of my talk at the conference and the power-point2) of my actual talk, and my experience through the conference3). In addition to these, our Clausius studies have been progressing through various methods which were reported at international congresses. Our papers with Yagi and (Tadokoro) Okamoto are compiled in this second edition4,5). The Boscovich Conference (organized by Pavia university, Italy) was interested in the relation between Boscovich and Clausius and asked me to talk about the possibility of any direct influence. To answer this request my paper (2011) was delivered at Pavia6). In 2013 our group published the Japanese translation of 7 Clausius important papers from German through the Tokai University publisher7) Among those Clausius papers the one (1856) with his theoretical analysis of the steam engine with experimental data (carried out by others) is well

6 A Historical Approach to Entropy discussed by Haruo Hayashi (in Japanese) which is introduced in English here8). In addition to these, I have noticed H. Nagaoka's interest during his atomic model studies on Clausius gas theory. My talk about this Clausius influence on Nagaoka was reported at the international conference at Manchester in 20139).

1. E.Yagi, “R.Clausius’s contribution to the 1st and 2nd laws of thermodynamics,” Book of Abstracts, 4th Symposium on Vacuum based Science & Technology, September, Kozsalin, Poland (2009) p.C1. 2. E.Yagi, “R.Clausius’s contribution to the 1st and 2nd laws of thermodynamics,” Power-Point, 4th Symposium on Vacuum based Science & Technology, September, Kozsalin, Poland (2009). 3. E.Yagi, “Visiting Poland for the Clausius Tower Project (September 2009) Part 1” Prof. Emerita Eri Yagi’s Blog. 4. E.Yagi and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods,” (delivered on 29 July) Abstract, XXIII International Congress of History of Science (2009), Budapest, Hungary. 5. E.Yagi and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods: Specially Focused on Technical term Analysis,” Historia Sientiarum, Tokyo, Vol.20-1 (2010) pp.47-56. 6. E.Yagi, “The Important Role of Particles through the 19th Mechanical Theory of Heat,”, International Conference for the 3rd Centenary of R.G.Boscovich, Pavia, Italy September, 2011 (to be published in the Proceedings in the near future). 7. E.Yagi, Haruo Hayashi, Kiyoshi Yoda and Rika (Tadokoro) Okamoto, “Clausius Entropy no Kigen,” Tokai University Publisher, 2013. 8. Haruo Hayashi, “Clausius approach to the Steam engine” (2013). 9 “Clausius on Nagaoka’s development of his atomic model (1903),” the 24th ICHSTM, Manchester, Program T160, July 25 (2013) p.343.

CHAPTER I : Introduction 7 2. Eri Yagi’s Autobiography in German

arum ich meine Autobiografie in Deutsch schlreibe? Der Grund ist Wdass unser Studium benuetzte Clausius original paprere im Deutsch (1847-1887). Ich bin geboren am, Oktober 1931 in Tokyo. Mein Vater war ein Insekten Forscher. Meine Mutter war ein Medizin Doktor. Ich bin als Fruehgeburt geboren, und meine Mutter hatte viel Arbeit gehabt. In meiner Kinderheit wuenschet ich auch ein Medizin Doktor (eine Aerztin) zu werden, das war mein Traum. Fuer Physik hatte Ich shon seit 15-Lebensjahr Interesse. 1950 bin ich in die Ochanomizu Universitaet (Physik Abteilung ) eingetreten und graduierte 1954. Ich hatte fuer die (institutionall) Geschichte der Physik Interese, weil die Atombombe in Bikini Schaden anrichtete (Atombombe Experiment, 1954). 1955 bin ich in die Tokyo Universitaet mit Magister- und Doktorkursusen eingetreten wo ich die Geschchte der Physik lernte, unter Prof. Hidehiko Tamaki. Zwischen 1960 und 1963, studierte ich mit Magister-und Doktorkursusen an der Yale University in NewHaven USA, wo ich“scientometrix“ unter Prof.Derek Price lernte, sowie die Geschchte der Mathematik, Chemie, Biologie, Medizin, und Amerikanische Naturwissenschaften. Zwischen 1955 und 1959, 1964 und 1965, studierte ich an der Tokyo Universitaet mit Magister-und Doktorkursusen und erlangte den Ph.D.(Physik). Vom November 1963 begann ich die Lehrtaetigkeit in Physik fuer Techniker an der Toyo Universitaet. Zwischen 1963 und 2002, unter- richtete ich Physik und Geschichite der Naturewisshenschaften an der Toyo Universitaet. Dabie erforschte Ich die Geschichte der Physik: zum Beispiel Atomik und Thermodynamik der Physik (Clausius Entropie) und

8 A Historical Approach to Entropy auch Statistische Forschung fuer Japanische Physik und lehrte junge Leute (Assistant) in der Geschichte der Physik. Nach 2002 hoerte ich an der Toyo Universtaet auf und begann mit NPO GKN & JWDSF zu arbeiten. 2009 besuchte ich Koszalin (Kosalin University of Technology, Poland) und hielt dort einen Vortrag ueber Rudolf Clausius Entropie. Ab 2015 habe ich fuer die JWDSF (Japah Wheelchair Dance Sport Federtion) als freiwillige Hilfe gearbeitet, Zwischen 2015 und Juli,2018, als die Praesidentin. Seit 2016 plane ich fuer den zweite Edition von unserer Kollectiv Papiere von Entropie: Die erste Edition, “A Historical Approach to Entropy,” veroeffenlichte ich 2002. Ich habe angefangen, das Zweite Vorwort fuer die Edition zu schreiben. Ich interessierte mich fuer altgriechisch Einfluesse im 19 Jahrhundert in Deutschland, warum Clausius das griechische Wort “Entropie” adoptierte. Warum haben zwei Maenner, Rudolf Clausius und Heinrich Schliemann, das gleich Geburtsche-Jahr (1822) und den gleich Monat(Januar) sowie etwas Einflusse aus “Ilias” von Homeros und die griechischen Veroeffentlichungen ? (August 4, 2018)

CHAPTER I : Introduction 9 3. A list of papers in the First Edition

1. Eri Yagi, Rika Tadokoro, and Haruo Hayashi, (Explanatory paper), “Studies on R.Clausius through various methods” (14pp. & 9figs.) 2. Eri Yagi, “Analytical approach to Clausius’s first memoir (1850)” Historia Scientiarum, the History of Science Society of Japan, Tokyo, No.20, pp.77-94,1981. 3. E.Yagi, “Clausius’s Mathematical method,”Historical Studies in the Physical Sciences, Berkeley, 15;1, pp.177-185, 1984 4. E.Yagi and H.Hayashi, “Clausius’s first and second laws of Thermodynamics with Fourier’s influence, ”Proceedings of the 20th International Congress of the History of Science, July, Liege, 1997: No.24, Working paper (in house), Global Economy Center, Toyo. University, 2002 (15pp.& 2figs.) 5. E.Yagi and R.Tadokoro, “Studies on the history of thermodynamics through a database,” delivered at the British Society for the History of Mathematics, Christmas meeting, Birkbeck College, London,17 December, 1998, Newsletter, No.3, pp.8-9, 1999 (12 pp. & 3 figs. & 1 photo) 6. E.Yagi and R.Tadokoro, “Theory of electricity by Clausius in the development of thermodynamics,” the Volta Conference, September, Como, 1999 (6 pp. & 3 figs.) 7. E.Yagi (1985), English Translation of Clausius’s early German paper “On the light absorption” Ann.d.Phys. (2),72,1847, 294-314.

10 A Historical Approach to Entropy CHAPTER II Clausius at Koszalin, Poland 1. Ref-1) E.Yagi, “R.Clausius’ contribution to the 1st and 2nd laws of Thermodynamics,” Book of Abstracts, 4th Symposium on Vacuum-based Science & Technology, September, Kozsalin, Poland (2009).C1, p.11 (total 1page )

udolf Clausius’ (1822-88) 16 papers on the mechanical theory of heat Rhave been studied through 4 various methods, e.g., traditional text analysis with the help of Clausius’ own manuscripts, mathematical equation analysis, experimental data table analysis, and technical term analysis. The first 3 analyses were briefly summarized while the result of the last technical analysis was explained with such important terms in thermodynamics as Disgregation (Degree of dispersion) and Uncompensirte Verwandlung (Non compensate transformation). These terms played important roles through indicating the micro nature and non (ir) reversible character, respectively before the appearance of the term Entropie (entropy) in Clausius’ famous paper of 1865. Through these analyses, I would like to emphasize Clausius’ Role as the first presenter of the 1st and 2nd laws of thermodynamics in an analytical form. In addition, Clausius also presented the 1st and 2nd laws in the literary expression through the introduction of the new concept “Entropy(Entropie)”in the field of physics.

References: A Historical Approach to Entropy, collected papers of Eri Yagi and her coworkers (International Publishing Institute Tokyo, 2002) and A Supplement.

12 A Historical Approach to Entropy 2. Ref-2) E.Yagi, “R.Clausius’ contribution to the 1st and 2nd laws of Thermodynamics,” Power Point named Yagi at Koszalin 1 (total 15 pages)

R.Clausius’s Contribution to the 1st and 2nd Laws of Thermodynamics

Eri YAGI (Inst. Hist. of Science, NPO GKN Japan)

Sept. 21 2009 (presentation)

Contents • Introduction • Influence(Math) from Clapeyron & Fourier • Clausius’s heat flow calculation (the difference) • Clausius’s 1st and 2nd laws as a related set of equations (Fig.II-1) • Clausius’s experimental table • Clausius’s special technical terms for mechanical theory of heart • Conclusions • References and Notes

CHAPTER II : Clausius at Koszalin, Poland 13 Fourier’ on Clausius

Figure I-2) A similar calculation method by Clausius’ Light flow and Fourier’s heat flow slomg the x-axis

Note : I, II, III equations are similar between Fourier and Clausius.

14 A Historical Approach to Entropy Clausius’s heat flow calculation (taking the difference)

CHAPTER II : Clausius at Koszalin, Poland 15 Clausius’s 1st law (beginning )

( ― )

16 A Historical Approach to Entropy Figure II-1) Clausius’s second and first laws in his papers of 1862, Abhandlung VI, treated as a related set.

Figure II-2) Clausius’s second and first laws in his papers of 1865, Abhandlung IX, treated as a related set.

CHAPTER II : Clausius at Koszalin, Poland 17 Clausius’s experimental table of Carnot’s function C(1850)

Cent.Gr. C nach Clapeyron C nach W. Thomson 35,5 0,733 0,728 78,8 0,828 0,814 100 0,897 0,855 156,8 0,930 0,952

Clausius’s special technical terms

German (original term) English (translation) Aequivalent Equivalent Nicht umkehrbare Weise Non reversible way Verwandlungs Werth Transformation value Uncompensirte Verwandlung Non compensate transformation Disgregation Degree of dispersion Entoropie Entropy

18 A Historical Approach to Entropy Clausius’s special technical-terms in his papers(1850-1865) Appearance:○

1850 1854 1862 1865

Nicht umkehrbar × ○ ○ ○ Verwandlung × ○ ○ ○ Uncompensirte × ○ ○ ○ Verwandlung Disgregation × × ○ ○ Entropie × × × ○ Aequivalent ○ ○ ○ ○

Conclusions

• Through these analyses, I would like to emphasize Clausius’s Role as the first presenter of the 1st and 2nd laws of thermodynamics in an analytical from.

• In addition, Clausius also presented the 1st and 2nd laws in the literary expression through the introduction of the new concept “Entropy(Entropie)” in the field of physics.

CHAPTER II : Clausius at Koszalin, Poland 19 The 1st and2ndlaws of thermodynamics in words

1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum.

References and Notes

References: A Historical Approach to Entropy, collected papers of Eri Yagi and her coworkers (International Publishing Institute, Tokyo, 2002) and A Supplement. Notes: The name Entropy was proposed by R. Clausius as “Entropie” from the Greek language while in China it has been called Shang with one Chinese letter since 1923 (when Planck visited ).

20 A Historical Approach to Entropy Appendix:Clausius’s functional approach to entropy Q/T (reversible process)

• Clausius proposed one “equivalence value” through two kinds of transformation, e.g., 1st kind is between work and heat, Qf(t) 2nd bet. two different temperatures, QF(t1,t2) These two kinds of transformation were treated at the same time by the use of Carnot cycle. Then the “equivalence value” in functional form was determined as Q/T ( in 1854)

• See E. Yagi “Thermodynamics,” p.1177, Companion Ency. of History of Mth. Sci. (Routledge1994)

CHAPTER II : Clausius at Koszalin, Poland 21 3. Ref-3) E.Yagi, “Visiting Poland for the Clausius Tower Project (September 2009) Part 1(total 6 pages)

started my trip from Narita Tokyo Airport to Koszalin on the morning of ISeptember 17th to deliver a lecture on Clausius’s contribution to the 1st and 2nd laws of thermodynamics at the solemn session dedicated to Rudolf J.E. Clausius (born in Koszalin) to be held during the 4th Symposium on Vacuum Based Science and Technology, 8th Annual meeting of the German Vacuum Society, DVG, organized by the Institute of Mechatronics, Nanotechnology and Vacuum Technique, at Koszalin University of Technology in Poland. My round-trip airfare from Narita to Berlin via Amsterdam on KLM was generously paid for by KUT, as well as a car with a professional driver and Mr. Jupi Poldlaszewki, a freelance writer and one of the Clausius Tower Project promoters, picked me up at the Tegel Berlin Airport. During the 4-hour drive to Koszalin, I enjoyed talking with Jupi although it was the first occasion to meet him after a 6-year email correspondence. Here I learned that the current development of strong unification of EU countries in the fields of economy and culture had made it possible to build the Clausius Tower. In particular, the progress of friendly relations between Poland and Germany has played an important role. Jupi told me that the most important key person was physicist Dr. Jan Staskiewicz, Deputy Director for Development and Cooperation with Industry, the Institute of Mechatronics, Nanotechnology and Vacuum Technique, who had been promoting the tower project for the past six years. I told Jupi about the drastic change of political scene in Japan where the new government of Prime Minister Yukio Hatoyama

From Eri YAGI’s Blog, “Visiting Poland: Part 1” (Written Nov. 12, 2009)

22 A Historical Approach to Entropy had come to power through the late August election. And that Mr. Hatoyama had proposed to decrease Japan’s CO2 output to 25% by 2020. We arrived in Koszalin around 11 p.m. (European time, 7-hour difference from Japan time). I finally went to bed about 2 a.m. at the Hotel Club 2CV where I stayed from September 17th to the 19th.

he next morning on the 18th I got up at 8 a.m.and although I had not slept Tproperly due to the jetlag, enjoyed the Polish style breakfast which includes pieces of pickles. After that I walked around the hotel to take in the sun light, and found quite a number of parks with wonderful green trees in the city. I visited a museum near the hotel where such history of Koszalin as the formation of the “old town” before the 13th century was mentioned. About 3 p.m. in the afternoon a cameraperson who worked for KUT came and took a number of pictures of me in the lobby of the hotel. Around 3:30 p.m. people from KUT, Jupi, Jan, and a professor of physics from Torun arrived with a bouquet of flowers for me to discuss our schedule for the Clausius session in the garden at the front of the hotel while the cameraperson took pictures of us. We then went to the main campus of KUT by car where again around a big stone at the front of the building of KUT pictures were taken by the cameraperson and myself. The stone was located there to hold a board of data on the Clausius Tower. In Jan’s car we went to his Institute which, organized two years before, is some distance from the main campus. Jan kindly introduced me inside rooms of the Institute where various facilities to produce a high degree of vacuum conditions were arranged for nanophysics experiments. Through this opportunity I asked Jan why he decided to invite me for the Clausius session, Jan said he had found me through a Google “Rudolf Clausius” search. Borrowing Jan’s room in the Institute, Jupi began to interview me for the local newspaper to be published on the morning of the 21st when my talk was scheduled at the Clausius session. During the interview Jan helped us providing hot drinks. Surprisingly enough, he gave me tea with a beautiful cup, made in Japan! I appreciated his sensitive hospitality.

CHAPTER II : Clausius at Koszalin, Poland 23 Jupi’s interview started with why I had become interested in Clausius as a college student of physics in Japan, and how I came to do research in the history of physics, focusing on Clausius. My answers would be referred to later in connection with my lecture of the 21st. This interview was published on the morning of the 21st through Jupi’s editorial effort in the local newspaper “MIASO“ ZYJE and the title is “Clausius windziany z Japonii” (Clausius, studied by a Japanese woman).

n the afternoon of September 19th I went to the lecture room 101A I(capacity, 200 peopel) at KUT to check the facilities for my talk on the 21st although I had sent my Power-point text (made on a Mac) in advance to the Symposium Chair, Prof Wilter Gulbinskwi who kindly converted it to the Windows format for the use of KUT. After recognizing no problems with my Power-point text presentation, I could try the over-head projector system there, which would be used for my transparent sheets together with the non transparent ordinary sheets. Several university people, including Prof. Gulbinskwi helped me in the room. Finally, the possibility to use a black board was demonstrated for me. Then in the autumn afternoon I enjoyed my way back to the hotel from the top of the hill where KUT is located. Along the way to the hotel a number of plant seeds were floating in air like golden snow dancing around me.

n the 20th, Jan picked me up in his car and brought me to the Aquarius OSpa Hotel, newly built, in Kolobrzeg near the Baltic Sea, where all participants, including me (as an invited guest) of the Conference stayed for 3 nights. In the evening, a welcome reception, sponsored by Vacuum Engineering Works TEPRO S.A. Koszalin was held, where a Swedish buffet style dinner was served. There I enjoyed the company with Jan, Professor Dieter Hoffmann from the Max Planck Institute of Berlin, an invited speaker at the Clausius session, Jupi and his partner, Marga, a physics teacher, who explained to me how to make Japanese style Sushi in Poland.

24 A Historical Approach to Entropy n the morning of the 21st at 9 a.m. all of us started toward KUT in OKoszalin on a community bus, where I sat with Professor Hoffmann with whom I talked about various topics, including Clausius, Mac comput- ers, and the current situations of such former East German cities near the Polish border as Eisenhuettenstd (former Fuerstenberg), the home town of my German conversation teacher and cooking in Tokyo. We arrived at KUT at about 10 a.m. and the opening ceremony of the conference began with a welcome speech by the Rector of KUT, Prof. Tomasz Krzyriski. This was followed by several speeches by representatives from vacuum societies that continued to 10:45 a.m. namely, 15 minutes over the planned schedule. Then the Clausius Session started with my lecture. I began firstly to introduce myself as follows:

My name is Eri Yagi from Japan. It is my great pleasure to deliver my talk on this wonderful occasion since I have been working for the past 20 years on the history of entropy, focusing on Clausius. It was the time of my 4th year at College (Ochanomizu University) where I became strongly attracted by Clausius way of thinking in the field of physics. It was because Clausius included the non-reversible (irreversible) process and un(non)-equal sign of equations while at that time it was more common to deal with the reversible process in the form of symmetry with equations of equal signs in Western physics. Because of sudden social phenomena, namely the Japanese fishermen who were injured by radioactive fallout, caused by American H-bomb experiments near the Bikini Islands in the Pacific ocean in the spring of 1954, my academic plan was changed from becoming a solid state physicist to an external historian of physics. I wanted to propose an ideal scientific organization for the welfare of human beings and world peace. So I started to study the history of scientific institutions. And I entered the Graduate School, Dept. of Physics, University of Tokyo where I began to work on the history of Riken (which was the most famous

CHAPTER II : Clausius at Koszalin, Poland 25 scientific institution for theoretical and experimental nuclear physics in Japan before and during The Second World War) with an excellent coworker, Mr. Kiyonobu Itakura under Professor Hidehiko Tamaki (one of the followers of Yoshio Nishina). Soon, I became interested in Derek Price’s method, e.g., statistical approach to the history of science, recently called “scientometrics”. So I left the University of Tokyo for 3 years to study under Prof. Price at the Dept of History of Science and Medicine, at Yale Graduate School in New Haven. My research along this line was compiled in the book, Science and Society in Modern Japan, edited by myself together with Prof. Shigeru Nakayama and Mr David Swain (published by the University of Tokyo Press and MIT Press in 1974). After coming back from the U.S., I joined the group of Dr K. Itakura and Dr Tosaku Kimura to write a biography of Hantaro NAGAOKA, the first Japanese creative physicist, known for his Saturnian atomic model of 1903. After 10 years of investigation, mainly dealing with Nagaokoa’s scientific papers and manuscripts, our biography, Hantaro Nagaoka was published (by the Asahi Newspaper Publisher in 1973) where I wrote sections of a historical background of Nagaoka’s atomic model and spectroscopy. Through Nagaoka’s research I shifted from being an external historian to an internal historian of physics. It was then that I realized my strong interest in R. Clausius’s mechanical theory of heat and his concept of entropy.

I then went on to say that it was my pleasure to deliver our results with the help of figures and tables through a Power point text. Most of our results had been published in the form of papers, which were compiled as a book, called “A Historical Approach to Entropy, collected papers of Eri Yagi and her coworkers on the occasion of her retirement”(from International Publishing Institute, Tokyo, 2002,186pp). And I said that I would summarize here the results focusing on Clausius’s contribution to the 1st and 2nd laws of thermodynamics. The following is the shortened version of my talk, mentioned above.

26 A Historical Approach to Entropy Eri Yagi, delivering her lecture on September 21 (Photo taken by Dr Jan Staskiewicz of Koszalin University of Technology)

Firstly, through text and MS (located at the Deutsches Museum in Munich) analysis : Fourier’s mathematical influence, shown and along the line of this method, e.g. taking the difference between the flow of “in and out”, Clausius 1st law of thermodynamics was presented in the form of the 2nd order differentials. In detail, taking the difference between the heat flow of “in and out” to the Carnot cycle’s working substance (for example an ideal gas), then Clausius put a ratio between the above heat and work expanded, to be a constant “A (reciprocal to Joule’s J)” e.g., (Heat /Work) equals to A. Secondly, through mathematical equation analysis: Clausius’s attitude to treat the 1st and 2nd laws of thermodynamics as a related set of equations was noticed through a quick glance of our database, which consists of 500 equations from Clausius 16 papers written between 1850 and 1865. (See A Supplement of the Collected Papers of Eri Yagi and her Coworkers, A Database from R. Clausius’s Abhandlungen, Eri Yagi Institute of Science, Kawagoe, 2002, 72pp.) Through this attitude

CHAPTER II : Clausius at Koszalin, Poland 27 Clausius proposed the form of entropy dS(dQ/T) as a complete differential for the reversible process corresponding to energy dU, which was already considered as a complete differential in the field of mechanics. Thirdly, through experimental table analysis: Clausius was interested in experimental data although he did not carry out experiments. himself. We found the same data tables were used in publications by Clausius and by W. Thomson. Fourthly, through technical term analysis (which was currently made and reported at the 23rd International Congress of the History of Science, Budapest, 28 July to 2nd August 2009): among Clausius special technical terms(in1850,1854,&1862) such as “Aequivalent (Equivalent)”, “Uncompensirte Verwandlung (Non compensate transformation)” and “Disgregation (Degree of dispersion)” played important roles before the appearance of the term “Entropie (Entropy)” which was newly proposed in his paper of 1865. Through the above various analyses, it was clearly shown that Clausius was the first presenter of the st1 and 2nd laws of thermodynamics in the form of differentials together with their well known literary expression, below: The 1st law: The energy of the universe is constant. The 2nd law: The entropy of the universe tends to a maximum.

he second speaker, Prof. Hoffmann, delivered ”Rudolf Clausius (1822- T1888) from Koeslin to Berlin & Bonn, from kinetic theory to modern thermodynamics,” which was nicely done with pictures of important physicists and buildings, related to Clausius. The third speaker, Prof Marek Danielewski of AGH University of Technology, Cracow “Mass transport and entropy production at different length scales “ was interesting from the view point of the modern concept of entropy. After the coffee break, the Chancellor of KUT, Dr Artur Wergraf, presented the “Clausius Tower” project. (The Tower, next to the KUT main building, will be established by 2011 in the form of a sea lantern, carrying the

28 A Historical Approach to Entropy light and the Foucault pendulum). Then the ceremony of laying the corner stone for the construction of the Clausius Tower was carried out. As part of the ceremony each of the participants, including myself, was requested to sign their name on a piece of paper, which was put into a hole made in the stone of a spherical shape. A picture of the conference participants, who left the lecture room 101A, was taken at the front of KUT main building for the commemoration. About 100 people had come from all over Poland and 12 European countries. I am the only person to have come from an Asian country. Finally, the stone was placed in the ground, and covered by cement at the front of the big stone with the board of Clausius. We then returned to Kolobrzeg for lunch and the afternoon session on vacuum based science and technology began in the Hotel.

n the evening of the 21st a Banquet was held in the dining room of the Ihotel, where a local band played a variety of music, including Polish tunes. After the banquet Jan and Jupi asked Prof. Hoffmann and me to get together in the lobby in order to discuss the way of promoting the Clausius Tower project in the coming two years. Prof. Hoffmann suggested holding some lecture meetings on Clausius each year. I suggested producing a new website of the Clausius Tower project and organizing people, interested in Clausius in a broader sense, through an e-mail network where the progress of the Tower project would be described. Jan and Jupi also requested me to retune to Koszalin on the occasion of the Tower’s completion in 2011. The exciting day for me ended with joy feeling that I should keep good health in the coming two years.

CHAPTER II : Clausius at Koszalin, Poland 29 Granted “An honorary membership of the Clausius Tower Society” (from Professor Tomasz Krzyzynsk in 2011)

30 A Historical Approach to Entropy CHAPTER III Clausius through various study methods

CHAPTER III : Clausius through various study methods 31 1. Ref.-4) E.Yagi and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods,” (delivered on 29 July) Abstract, XXIII International Congress of History of Science (2009), Budapest, Hungary. (total 1 page)

e have been studying the history of entropy through various meth- Wods.1) Our papers were compiled as a book called “A Historical Approach to Entropy,” in 2002.2) In his book R. Clausius’ 16 papers (1850- 1865) on the mechanical theory of heat were studied through such various methods as text analysis with the help of Clausius’ own manuscripts, mathematical equation analysis by the use of our own database, experimental data table analysis and technical term analysis. It was clearly recognized that the results acquired through the traditional text analysis were greatly expanded thanks to the other analyses. In addition to this expansion, new findings came out as a result of these analyses. They were 1. Clausius’ pair- ing treatment of the first and second laws of thermodynamics through the equation analysis, 2. A sort of existence of experimental data distribution in the inter-European academic community which required Clausius to compare his value, 1/A with Joule’s J (the equivalent of work for the unit of heat) through the experimental data table analysis, and 3. The wider possibility for non-natives of German to study the mechanical theory of heat through technical term analysis. We briefly reported the above results at the annual Conference of the British Society for the History of Science in 2003.3) In the case of the method of the experimental table analysis: Clausius discussed a number of experimental tables in his papers on thermodynamics although he hardly carried out any experiments. We have collected Clausius’ experimental tables to compare them with W. Thomson’s because they both adopted some data from V. Regnault, a famous French experimentalist at the time.

32 A Historical Approach to Entropy Through the experimental table analysis, the existence of three related tables by E. Clapeyron, W. Thomson and R. Clausius was found out. These three tables include the so-called Carnot’s function “C,” the function of temperature, which played an important role in the formation of the second law of thermodynamics. In the case of the technical term analysis: We started to use Clausius’ 12th paper on the theory of electricity. Firstly, frequently appeared names of 10 physicists in the paper of 1853 were discussed rather than actual technical terms. These 10 physicists are interestingly classified in two groups: 1) Physicists in the field of thermodynamics: S. Carnot, Mariotte & Guy- Lussac, Helmholtz, and W. Thomson, 2) Physicists in the field of electricity: Johan Poggendorff (1796-1877). George Ohm (1787-1854), Benjamin Franklin (1706-1790), Thomas Seebeck (1770-1831), and Jean Peltier (1785- 1845). The last two physicists are direct predecessors of the thermoelectric effect (Seebeck effect and Peltier effect). W. Thomson (Kelvin) also belongs to the group of predecessors. At this conference, we would like to report our recent progress along the above line. Particularly, through the two methods, namely, through the experimental data table analysis and the technical term analysis where such technical terms as Verwandlung (transformation), Disgregation, Arbeit (work) and Werk (action) will be considered.

References 1. Eri Yagi, “Studies on the history of thermodynamics through a database”, BSHM Newsletter, 39, pp. 8-9, 1999. 2. Eri Yagi, A Historical Approach to Entropy, Collected Papers of Eri Yagi and her co-workers, at the Occasion of her Retirement, International Publishing Institute, Tokyo, p. 186, 2002, A Supplement of the Collected Papers of Eri Yagi and her co-workers, A Database from R. Clausius’ Abhandlungen I-XVI, Eri Yagi Institute for History of Science, Kawagoe, Japan, 2002. 3. Eri Yagi, “Various mathods to study the mechanical theory of heat,” Abstract: BSHS Annual Conference, York, 2003

CHAPTER III : Clausius through various study methods 33 2. Ref-5) E.Yagi, and Rika (Tadokoro) Okamoto, “A History of Entropy through various Methods: Specially Focused on Technical term Analysis,” Historia Scientiarum, Tokyo, Vol.20-1 (2010) pp.47-56 (total 10 pages) Abstract

udolf Clausius (1822-88)’s 16 papers on the mechanical theory of heat Rhave been studied through 4 various methods, e.g., traditional text analysis with the help of Clausius’s own manuscripts, mathematical equation analysis, experimental data table analysis, and technical term analysis. The first 3 analyses were briefly summarized while the result of the last technical analysis was explained with such important terms in thermodynamics as Disgregation (Degree of dispersion) and Uncompensirte Verwandlung (Non compensate transformation). These terms played important roles through indicating the micro nature and non (ir) reversible character, respectively before the appearance of the term Entropie (entropy)in Clausius’s famous paper of 1865. The result of technical term analysis for his paper on the theory of electricity (1853) by the use of a text mining method is also shown with tables and figures.

Key words: R.Clausius Entropy mechanical theory of heat non (ir) reversible text mining

34 A Historical Approach to Entropy 1. Introduction We have been studying Clausius’s papers, published between 1847 and 1873 under the name of the mechanical theory of heart for the past 20 years, and published a book, in which our research papers were mostly collected in 2002.1,2 On this occasion the results of our studies through 4 important analyses will be mentioned.

1.1 Traditional Text Analysis with Clausius’s own Manuscripts We discovered the strong influence of Joseph Fourier’s work, the analytical theory of heat on Clausius’s mathematical approach. 3 Through studying Clausius‘s own manuscript which was in the style of a note book, called “Aus Waermetheorie von Fourier (1848)” HS 6452 at the Archive section of the Library of the Deutsches Museum in Munich. It was found out that Fourier’s mathematical method was well applied by Clausius, e.g. taking the difference between the heat flow of “in and out” for the case of the Carnot cycle’s working substance (for example an ideal gas), Clausius succeeded in obtaining the heat (the difference) in the form of the 2nd order differentials. Then he calculated a ratio between the above heat and work (produced), to be a constant A (reciprocal to Joule’s “J”). Finally, Clausius ‘s 1st law of thermodynamics was presented in the form of the 2nd order differentials. Detailed discussions were published in our paper.4

1.2 Mathematical Equation Analysis We created a database which consisted of about 500 mathematical equations from Clausius‘s 16 important papers (1850-1865) compiled in his 2 publications (1864 &1867).5 Having glanced over these equations, several significant facts were realized. The most important one was Clausius’s approach for treating the 1st and (pre-) 2nd laws of thermodynamics as a related set of equations, and it was noticed through a quick glance at our database. Through this attitude Clausius proposed the form of entropy dS (dQ/T) as a complete differential for the reversible process corresponding to the (internal) energy dU of the 1st law, which was already considered a

CHAPTER III : Clausius through various study methods 35 complete differential in the field of mechanics. Detailed discussions were published in our paper.6

1.3 Experimental Data Table Analysis Clausius was interested in experimental data although he did not carry out experiments himself. These experimental data were by E. Clapeyron, J. P. Joule, W. Thomson, and H. V. Regnault. We found three related experimental tables by Clapeyron (1834), W. Thomson (read 1849) and Clausius (1850). These tables include the so-called Carnot function C (the function of temperature) for 4 different temperatures, including 100 (Cent Gr.). The function C played an important role in the formation of the 2nd law of thermodynamics. Detailed discussions with these tables were published in our paper.7

2 Technical Term Analysis

2.1 Technical Terms in thermodynamics We picked up 6 special technical terms, used in Clausius’s 4 papers in thermodynamics through the traditional text analysis method. These papers were “Ueber die bewegende Kraft der Wäerme und Gesetze,welche sich daraus für die Wärmelehre selbust ableiten lassen” (1850)8, “Ueber eine veränderet Form des zweiten Hauptsatzes der mechanischen Wäermetheorie”(1854)9, “Ueber die Anwendung des Satzes von der Aequivalentz der Verwandlungen auf die inner Arbeit”(1862) 10, and “Ueber die verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wäermetheorie”(1865). 11 These 6 technical terms are “Aequivalent (Equivalent)”, “Nicht umkehrbar (Nonreversible)”, “Verwandlung (Transformation)”, “Uncompensirte Verwanglung (Noncompensate transformation)”, ”Disgregation (Degree of dispersion)”, and “Entropie (Entropy). The appearance of these terms is shown in this paper by Table 1 with Figure 1 of the chronological table of development by R.Clausius (1822-1888), which was taken from Figure (0-1)

36 A Historical Approach to Entropy in Ref. 1. The term Aequivalent (Equivalent) was used firstly in Clausius’s paper of 1850 to express the principle of the equivalence between heat and work, namely, the 1st law of thermodynamics. Here Clausius wrote that his constant “A” expressed the equivalent of heat for the unit of work. It is worth pointing out that A is reciprocal to Joule’s “J” which expressed the equivalent of work for the unit of heat. (Note that Clausius’s equations of thermodynamics were written in the heat unit while Joule’s were in the work unit). In his paper of 1854, Clausius expanded the usage of the term Aequivalent (Equivalent) together with the term Verwandlung (Transformation). Here he named the transformation from work to heat which was assumed to have the positive equivalent value as the first kind of transformation. In addition to that, the transformation of heat from higher to lower temperatures, also the positive equivalent value, was named as the second kind of transformation. Clausius tried to find the common equivalent value for the above two kinds of transformation. Then he succeeded to find the form of value as Q/T (heat/temperature) which is the mathematical form of Carnot’s law (based on the material theory of heat) for the reversible process. The term Uncompensirte Verwanglung (Noncompensate transformation) indicated Clausius’s interest in the ir(non)reversible process, which started from 1854. The term Disgregation (Degree of dispersion) was used by Clausius from 1862 to show the micro nature of working substances. He mentioned that heat increased the Disigregation of molecules. This expression meant the micro nature of thermodynamics from the beginning before the appearance of the term Entropie (Entropy).

2.2 Technical Term Analysis in the theory of electricity

2.2.1Applying the method of text mining to the analysis on Clausius’s papers We started to investigate Clausius‘s 4 papers (1852-57) on the theory of electricity through the traditional text analysis with the help of our database.

CHAPTER III : Clausius through various study methods 37 Here the 1st and (pre-) 2nd laws of thermodynamics were applied to solve electrical phenomena. Further, the way of approaching small particles of matter was developed. In addition to the above, we began to perform our preliminary studies on the technical term analysis of his 12th paper.12 Now we will describe how we applied “noun analysis” on Clausius’s 12th paper (“Abhandlung XII” in German13). Here we used some basic methods of text mining.

2.2.2 What is “text mining”? Text mining is a method of document analysis, which mainly uses computational and statistical procedures and tools. According to the definition of text mining by Feldman and Sanger14; “Text mining can be broadly defined as a Knowledge-intensive process in which a user interacts with a document collection over time by using a suite of analysis tools.” Text mining is often referred to as a part of data mining, machine learn- ing, and computational linguistics, because basically this method requires such retrieval capability to check the data quantity and quality. It generally requires “machine readable” data and some tools to cleanse objective data, to apply the statistical computation and to draw some graphs. In this paper, we would like to focus on computational and statistical text mining as a text analysis to analyze again Clausius’s 12th paper.

2.2.3 Previous text analysis on “Abhandlung XII” As mentioned above, we have already tried the method of technical term analysis15 on Clausius’s 12th paper (called Abhandlung XII in German). In our previous paper it was realized that the thermoelectric current played an important applicable phenomenon in both the 1st and pre-2nd laws of thermodynamics. Further, the distribution graph of frequently appeared physicists in the paper was interestingly classified into such two fields of people as thermodynamics and electricity. (Shown by Figure. IV-I in Ref.1, p.37.)

38 A Historical Approach to Entropy 2.2.4 Applying the method of text mining to “Abhandlung XII” We applied the method to “Abhandlung XII” again along the following three processes; 1) To analyze entire technical terms in Abhandlung XII, 2) To build a basic technical terms’ list for analyzing all Clausius’s papers in the near future, 3) To renew the knowledge of text mining for the purpose of making a basis for new statistical tools. We have analyzed Clausius’s 16 papers through such various methods as the traditional text analysis, the mathematical equation analysis, and the experimental data table analysis. These 16 papers were compiled in the first edition of his collection of papers (Ref.5, Erste & Zweite Abtheilungen). The subjects of these were thermodynamics, the theory of radiation, thermoelec- tricity, and the gas theory. If we planned to apply the method of text mining to all Clausius’s papers, we would face the difficulties, caused by the data quantity. The reason is because that there is very limiter quantity of public data of Clausius’s papers for the use in the above purpose. So we have to make “machine readable” data at first through the following procedures; (1) scanning papers with a scanner, (2) turning the scanned image into text data through OCR (Optical Character Recognition) software, or input the text data as a computer-readable format by hand, (3) cleansing the data so it is readable by a computer, (4) making a dictionary for the text analysis. Through these procedures, each process itself is very simple but it takes much time and increases each document size and the number of documents. There is some software that can automatically handle the processes (1) to (3). However, cleansing the data (which means eliminating errors of OCR, formatting the text, and correcting words) manually is indispensable for analyzing a document, and also making the dictionary for each purpose by hand.

CHAPTER III : Clausius through various study methods 39 So we have firstly decided to carry out the above procedures for Abhadlung XII, because of its word quantity, which is of a relatively large volume including the same words that appear in other Clausius’s papers. For these procedures, we aim to build our own method of technical term analysis.

2.2.5 Analyzing the Result The following tables and figures were made as a result of our studies: Table 2. Appearance Frequency (Top 20) of the Technical Terms. Table 3. Appearance Frequency of the Technical Terms’ Categories (sub-fields in Physics) in Clausius’s 12th Paper. Note: Each category which is indicated in this table is selected from a proper sub-field in Physics. Each noun in Abhandlung XII is classified by one of this category. Each word, which appears here, has two or more meanings but we selected only one of the meanings. Figure 2. Appearance Frequency graph of Technical Terms from Table 2. Figure 3. Appearance Frequency graph of the Technical Terms’ Categories from Table 3.

2.2.6 Discussion Through the above studies by the text mining, where we used typical nouns as technical terms, the essential character of Clausius’s 12th paper became clearer, e.g. the high appearance frequency are observed (see Table 3) in such 2 sub-fields as thermodynamics and electromagnetism. Figure 3 indicated clearly the close connection between thermodynamics and electromagnetism. However, there are some difficulties, namely, how to classify each noun to a proper category.

3. Remarks & Conclusions On this occasion the results of our studies through the 4 various methods, especially those through the method of technical term analysis were mainly described. Our technical term analysis has two approaches to the

40 A Historical Approach to Entropy original texts: firstly ticking up the technical terms through the traditional method with the help of our database, and secondly doing them trough the appearance frequency with the help of a computer. Both ways of technical term analysis played important roles to expand results rather than only relaying on the traditional text analysis.

Acknowledgements This paper is mainly based on our paper, delivered in the afternoon of the 29th July, 2009, Session 9.2 at the 23rd International Congress of the History of Science, Budapest, Hungary.16 We deeply appreciate the sug- gestive participants of the meeting. Thanks also go to the Editor, Professor Takehiko Hashimoto’s kind invitation to the journal through email correspondence. Our Clausius‘s studies have been strongly encouraged by the Clausius Tower (Project) Society at Kozsalin University of Technology, Kozsalin, Poland, which invited Yagi for the solemn session of the ceremony for the setting of the foundation cornerstone for the new Clausius Tower on September 21st 2009.17 (written on Mar. 15th, 2010)

A List of Tables and Figures Table 1. Clausius ‘s Technical Terms in Thermodynamics. Figure 1. The Chronological Table of R.Clausius (1822-1888). Table 2. Appearance Frequency (more than ten times). Figure 2. Appearance Frequency graph from Table 3. Table 3. Appearance Frequency (sub-fields in Physics). Figure 3. Appearance Frequency graph from Table 4.

Notes *Professor Emeritus, Toyo University, Eri Yagi Institute for History of Science, Kawagoe City (NPO GKN) Japan. Email: [email protected] **Research stuff, Eri Yagi Institute for History of Science, Kawagoe City (NPO GKN) Japan.

CHAPTER III : Clausius through various study methods 41 1. Eri Yagi, A Historical Approach to Entropy, Collected Papers of Eri Yagi and Her Coworkers (Tokyo: International Publishing Institute, 2002) 181pp. 2 Eri Yagi, A Supplement of the Collected Papers of Eri Yagi and Her Coworkers, A Database from R.Clausius’s Abhandlungen I-XVI (Kawagoe Japan: Eri Yagi Institute of Science, 2002) 72pp. 3 J. Fourier, Théorie analytidue de la chaleur (Paris,1822) in Oeuvres de Fourier, part 1(Paris 1887):1-563. 4 Eri Yagi and Haruo Hayashi, “Clausius’s 1st and 2nd laws of thermodynamics with Fourier’s influence,” Proceedings of the 20th International Congress of the History of Science, Liege, 1997, Vol.14, (Belgium, Breopls)pp.132-141. Also in Ref 1, pp.81-98. 5 R.Clausius,Abhandlungen über die Mechanische Wärmetheorie, Erste Abtheilung Abhandlungen I-VIII(1864): Zweite IX-XVI (1867): (Freidrich Vieweg und sohn) 6 Eri Yagi and Rika Tadokoro, ”Studies on the History of Themodynamics through a Database,” delivered at the British Society for the History of Mathematics Christmas Meeting, Berkbeck College , London, 17th December1998, BSHM Newsletter,No.39 (1999):8-9. Keizai-rohshu (Economic Review of Toyo University) Vol.27,Nos.1& 2( 2002):299-310. Also in Ref. 1, pp.99-112. 7 Eri Yagi, Rika Tadokoro and Haruo Hayashi, “ Studies on Clausius various methods,” (2002) in Ref. 1, pp.13-37. 8 R.Clausius, Ann. d. Phys. Vol.79 (1850):368-397 & 500-524. Abhandlung I in Ref. 5, pp.16-78. Phil.Mag. Vol. (4) 2 (1850): 1- 21 & 102 –119. 9 R. Clausius, Ann. d. Phys. Vol.93 (1854):481-506. Abhandlung IV in Ref. 5, pp.127-154. Phil.Mag. Vol. (4) 12 (1854):81-93. 10 R. Clausius, Ann. d. Phys. Vol.116(1862):73-112. Abhandlung VI in Ref. 5, pp.242-279. Phil. Mag. Vol.(4)24 (1862):81-97 & 201-213. 11 R. Clausius,Ann.d.Phys.Vol.125(1865):353-400. Abhandlung IX in Ref. 5, Zweite pp.1-44. R. Clausius (ed. by T. A. Hirst), The Mechanical Theory of Heat (London, Tyler and Francis, 1867): 327-365. 12 Eri Yagi and Rika Tadokoro, “Theory of electricity by R.Clausius in the development of Thermodynamics,” Bicentenary of Invention of the Battery by A.Volta, Volta and the History of Electricity Conference, Como & Pavia, 11-15 September, 1999, Book of Abstracts (1999), p.29, Volta and the History of Electricity, ed. by Fabio B. & E.Gionnetto, pp.299-307 (Hoepli International Publisher, Milan) 2003. Also in Ref.1 , pp.21-22,& pp.113-123. 13 R. Clausius, “Ueber die Anwendung der mechanischen Wärmetheorie auf die thermoelectrischen Erscheinungen, ”Ann.d.Phys.Vol.90(1853):513-544. Abhandlung XII in Ref. 5, Zweite pp.175-201.

42 A Historical Approach to Entropy 14 R. Feldman and J. Sanger, The text mining handbook, Advanced Approaches in Analyzing Unstructured Data (Cambridge University Press, 2007), p.1. 15 Eri Yagi, Rika Tadokoro and Haruo Hayashi, “Studies on R.Clausius through various useful methods,” in Ref.1, pp.21-22. 16 E. Yagi & R. T. Okamoto, “A History of Entropy through various Methods,” Abstract, the 23rd International Congress of the History of Science, Budapest, Hungary (2009). See also Professor Emeritus Yagi’s Blog: http://www.schaft.org/ wp/ 17 E. Yagi, ”R. Clausius’s contribution to the 1st and 2nd laws of thermodynamics,” Book of Abstract, 4th Symposium on Vacuum based Science & Technology, September, Kozsalin, Poland (2009) p.C1. The meaning of the session was described on Professor Emeritus Yagi’s Blog: http://www.schaft.org/wp/

CHAPTER III : Clausius through various study methods 43 3. Ref-6) E.Yagi, “The Important Role of Particles through the Mechanical Theory of Heat,” International Conference for the 3rd Centenary of R.G. Boscovich, Pavia, Italy September, 2011 (to be published in the near future) (total 3 pages)

Preface Through the development of the mechanical theory of heat, the concept of particles, especially originated by Newton and followed by Boscovich played an important role in the 19th century. Rudolf Clausius (1822-88) mentioned an important role of particles in his first paper on thermodynamics, written in 1850. In that he spoke of heat caused through motions of the ultimate particles of the body.. He called such particles as “die kleinst Theile der Koerper” (in Gernan) 1). Later he adopted the term “Disgregation,” which meant the degree of dispersion of particles (molecules) of the body (system) in his paper on thermodynamics of 1862. The term Disgregation played an important role in the paper of 1865, where he proposed the well known concept of Entropy. I would like to discuss the relation between Disgregation and entropy. Here I mean the particle as a perfectly elastic sphere with no inner structure, adopted by James Maxwell 2) .

Introduction of the term Disgregation in 1862 Firstly, Clausius introduced the term Disgregation to show the ability of heat by which distances between molecules of the body were increased3) Namely this term indicated the ability of heat to do work. Here Clausius expressed the Disgregation by “Z” with the following equation (2):

dZ = (AdL) /T

where dL is work while T shows absolute temperature. A is the

44 A Historical Approach to Entropy Clausius’s constant that corresponds to (1/J ) where J is Joule’s constant. For the reversible circular process Clausius wrote the following equation (15):

∫ dZ = 0

while for the non-reversible circular process equation:

∫ (dQ + dH) /T+∫ dZ > 0

Clausius explained in his note to the above VIth paper (added in 1864) the difference between the specific heat and the heat capacity (Wärmecapcität). He mentioned that true heat capacity must be equal for such three different conditions of water: liquid, ice and gas. Then he considered dQ, e.g.the heat given to the body, was distributed into two parts, namely, one part, which remained in the form of heat, indicated the temperature and the other part, which was transferred to work, produced the particle (molecular) movements of the body. The former part meant the true heat capacity by Clausiius. The final equation of the VIth paper ended at that of (29):

Z – Z0 = mc log (T0 / T )

where m indicated mass while c was the true heat capacity.

Development of the concept of Disgregation in connection with that of Entropy in Abhandlung IX (1865). Here Clausius introduced the term dS (= dQ/T) as the differential expression of entropy. He started from the following equation (61):

∫ dQ/T = ∫ dH/T+∫ dZ

and finally arrived at the following equation (64)

CHAPTER III : Clausius through various study methods 45 ∫ dQ/T = S - S0

The above calculation clearly shows that the concept of Disgregation is included in the entropy concept. There might be some reflection from Clausius' s research on the theory of gas (1857,1858,1862) although no references to the term Disgregation were found among those papers4).

Experimental backgrounds of Disgregation Clausius was interested in the experimental data of specific heat of water as mentioned above. In addition, see Appendix B to the VIth paper where a table of specific heats of 35 different gases through 7 columns were listed. These experimental data were by Regnault. Clausius himself published a paper in the Ann. der Chem. und Parm. vol.118, p.14 (1861) with the added 8th column of the true heat capacity of the above gases, which were theoretically reduced from the strongly over-heated vapors.

Additional Notes I have already mentioned the process of Clausius‘s finding of the concept of entropy through a functional analysis for the reversible process: namely he succeeded in finding the perfect differential dS as dQ/T corresponding to the dU (internal energy )5).

Acknowledgements Currently, my research has been stimulated through contact with the Clausius Tower (project) Society at Koszalin University of Technology, Poland whose activities are described on the following website6): http:// www.clausius-tower-society.koszalin.pl/ During the Conference period I was greatly stimulated through discussions with Dr Gus Prince and Dr Roger Anderton. Finally I am deeply grateful to Professor Fabio Bevilacqus and his staff of the International Conference of R.G. Boscovich, Pavia for giving me this wonderful opportunity. (written January 14,2012).

46 A Historical Approach to Entropy References 1. R.Clausius, Abhandlung I, 1850 s.18; from R.Clausius’s collected papers: Abhandlungen Ueber die Mechanischen Waermetheorie,Erste(1864),Zweite (1867),Braunschweig. 2. J.C .Maxwell,Phil.Mag.,Vol 19, p19, (1860); reprinted in The Scientific Papers of Maxwell, Cambridge University Press, 1890, Vol.I, p377. 3. R. Clausius, Abhandlung VI, 1862 s.248. 4. Clausius’s list of publications was published by Eduard Riecke on Rudolf Clausius (geb.2 Januar 1822, gest.24 August 1888) Rede gehalten in der oeffentlichen Sitzung der K.Gesellschaft der Wissenschaften am 1 December 1888,Goettingen,Dieterichsche Verlangs-Buchhandlung,1888, 39pp. 5. Eri Yagi, “Thermodynamics” I.Gratten-Guinnes ed., Encyclopaedia of the History of Philosophy of Mathematical Sciences, 2,Section9.5, pp.1171-1182 (Routledge, London, 1994) ; Eri Yagi, A Historical Approach to Entropy Collected papers of Eri Yagi and her coworkers (International Publishing Institute, Tokyo, 2002) 6. See also Professor Emeritus Eri Yagi’s Blog: http://www.schaft.org/wp/ 7. Our chronological Table:Fig.0-1) from the latter Ref.5) is attached on the next page. Note: here Clausius did not use round d for differential expressions, which he started to be used from his later publications because he recognized the Jacobi’s expression in his note written in 1864 to his Abhandlung I, 1850 s.29.

CHAPTER III : Clausius through various study methods 47 48 A Historical Approach to Entropy 4. Ref-8) Haruo Hayashi ＊ , “Clausius’ 5th paper and the theory of the Steam Engine ＊＊ ” (2013). (total 1page)

ith the great developments in the field of the steam-engine, such as Wappearances of a high pressure engine in the 1840s, more accurate knowledge on steam in the adiabatic expansion became indispensable. Under such circumstances, H. V. Regnault (1810-1878) presented precise experimental data in 1847.(1) However, these data denied the Caloric theory that had been the fundamental theory of heat engineering. At the same time, an important problem was the consistency of the experimental data and a new theory through the construction of the mechanical theory of heat by Clausius and others. The realistic problem in such an engineering area and construction of his mechanical theory of heat existed as important issues for Clausius from the beginning. Although the fifth paper by Clausius has rarely been discussed by histori- ans of physics, it should be highly evaluated as the paper which introduced the conclusion to the theory of the steam engine by applying the results, obtained through his fourth paper with the earlier entropy concept. In the fifth paper, Clausius took up Théorie des Machines á Vapeur (1844, Paris) by de Pambour, which was the main theoretical book on steam-engine engineering, based on the Caloric theory at that time. Clausius compared the numerical values obtained from Pambour’s theory with those numerical values derived from Clausius’ mechanical theory of heat under the same setting and conditions. And Clausius indicated that his theoretical values were in considerably good agreement with experimental data. I would like to emphasize some quantita- tive applications attributable to Clausius for the practical field, and to show that his fifth paper contributed to the great progress of steam engine studies.

* Toyo University, Research Institute of Industrial Technology, Guest Researcher. E-mail: [email protected]

CHAPTER III : Clausius through various study methods 49 ** The full paper to be published in the journal of Japan History of Science Society, Historia Scientiarium. And also this paper was originally delivered at the Annual Meeting of the Physical Society of Japan (2012), at Kwansei Gakuin Univesity on March 25, 2012. (1) H.V. Regnault, Mémoires de L’Academie des Sciences, 21 (1847), 26 (1862) & 37, pat. 1 and 2 (1868, 1870)

50 A Historical Approach to Entropy 5. Ref-9) E.Yagi and Haruo Hayashi, “Clausius’ theory of heat and the steam-engine,” [Abstract: BSHS Annual Conference 2010]. (total 1page)

ogether with my three followers, I have been studying the origin of Tentropy over the past 30 years, and finally published a set of collected papers titles, “A Historical Approach to Entropy” (International Publishing Institute, Tokyo, 2002). We also published the translations of 7 Clausius papers from German to Japanese with comments in 2013. Through these publications the following findings were made clear: Clausius had a strong intention to treat the first and second laws of the mechanical theory of heat (thermodynamics) as a set of analytical equations with the heat unit. This unit expressed by “A” (equivalent of heat for the unit of work) corresponds to 1/J. The Kozalin University of Technology is located in the city where Clausius was born in 1822 and lived before moving to Szczecin High School (presently in Poland). The university has been planning to build a Clausius Tower since 2009 when the first Clausius Session at the Symposium on Vacuum-based Science and Technology was held and where I had the privi- lege of being the first speaker.

CHAPTER III : Clausius through various study methods 51 6. Ref-10) E.Yagi, “Clausius on Nagaoka’s development of his atomic model (1903),” the 24th ICHSTM, Manchester, Program T160, July 25 (2013) p.343. (total 1 page)

Abstract: 1. What is Clausius Virial (equation)? After presenting the first and second laws of mechanical theory of heart (1865), Clarsius proposed the Virial (equation) to indicate relation between heat and mechanical theory in 1870. Here he related the average of total kinetic energy of material particles of the system equals to the average of sum of each material’s Xx + Yy+ Zz. Where x,y,and z indicate the positions on the coordinate of x,y, and z axises while X, Y, and Z the component of the forces. The equation will be shown below. 2. What is Nagaoka’s atomic model? After the discovery of electrons in an atom through the discovery of Zeeman effect (1896), several atomic models were proposed which had electrons. Nagaoka’s model was one of them. He adopted the mechanical stability of the Saturnian ring (used by Maxwell) to his atomic model where a great number of electrons were moving around the central positive charge (a sort of nucleus). Nagaoka showed several physical laws were confirmed even if the material would be consisted from his atomic models. 3. What law was confirmed by Nagaoka? Nagaoka showed the Van der Waals equation was established if the gas would be consisted from his atomic model. Nagaoka’s way of approach is indicated below. 4. What is Nagaoka’s original point? Most of his approach was followed his former teacher Boltzmann although no references. However Boltzmann did not consider the inner structure of atoms while Nagaoka adopted his atomic model with the above mentioned inner structures. 5. What kind of relation between Boltzmann and Nagaoka? Nagaoka

52 A Historical Approach to Entropy (1865-1950) studied in Germany between 1893 and 1896 where he took courses and seminars under Helmholtz, Fucks, Kundt and Boltzmann in Berlin. Then went to Munich for continuous study under Boltzmann. 6. What is other Nagaoka’s contribution? His exact experimental data in spectroscopy started in 1907 and continued to 1924 played the most important role for the discovering of the concept of the spin by Pari and Goudsmit. The exactness was mainly depend on Nagaoka’s strong interests in the inside structure of atoms.

CHAPTER III : Clausius through various study methods 53 7. Clausius on Nagaoka’s Development of his Atomic Model

Clausius on Nagaoka’s Development of his Atomic Model

Eri Yagi Eri Yagi Institute for History of Science (NPO G.K.N. Japan)

Clausius’s Chronological Table

54 A Historical Approach to Entropy Abstract

Clausius proposed the Virial theorem(1870) for the material points whose movements were stationary along the line of his mechanical theory of heart. No inside structure of the material point of which the substance (gas) consisted was assumed. Nagaoka(1905) used Boltzmann’s method of approach to present the Van der Waals equation through Clausius’s Virial theorem. Finally Nagaoka gave a possibility in the case that the substance (gas) consisted of his atomic modes.

What is Clausius Virial (theorem) ?

After presenting the first and second laws of mechanical theory of heat (1865), Clarsius in 1870 proposed the Virial (theorem) to indicate the relation between heat and the mechanical theory.1)

1) R.Clausius ,Sitzungsberichte der niederrheinschen Gesellschft 114-119 (Bonn,1870) “On a mechanical theorem applicable to heat”, Phil. Mag., (4)40, 122-127(1870)

CHAPTER III : Clausius through various study methods 55 What is Clausius’s Virial Theorem

Here he related the sum of the average of total kinetic energy of material particles in stationary motion as corresponding to the sum of the square root of the average of each material‘s Xx + Yy+ Zz. Where x,y, and z indicate the positions on the coordinate of the x,y, and z axes while X, Y, and Z the component of the acting forces. The equation will be shown in the chronological table.

Note: The right-hand side is called “Virial” ( force in Latin).

Clausius’s Virial Theorem(1870) Note:The right-hand side is “Virial”

56 A Historical Approach to Entropy What is Nagoka ‘s atomic model?

After the discovery of electrons in an atom through the discovery of the Zeeman effect (1896), several atomic models were proposed in the early 20th century which had electrons in the atom. Nagaoka’s model was one of these. They went into Rutherford’s nuclear model (at Manchester,1911) and were developed into Bohr’s model (1913) with a stable orbit of electrons.

Nagaoka’s model (detailes)

Nagaoka in 1903 proposed adopting the mechanical stability of Saturnian rings (used by Maxwell) to his atomic model with a great number of electrons moving around the outside of the central positive charge ( a sort of nucleus). 2) Nagaoka qualitatively explained, such physical phenomena as spectrum lines and radioactivity, if the material (gas) consisted of his atomic models.

2)Proc.Tokyo Phys-Math.Soc.,[2]335-340,1905.

CHAPTER III : Clausius through various study methods 57 Van der Waals equation was confirmed by Nagaoka

Nagaoka in 1905 showed that the Van der Waals equation was established if the gas consisted of his atomic models3)4).

3)Eri Yagi, “Development of Nagaoka’s Atomic model(1904-05),”- Japanesen Studies in the History of Science, No.11,73-89, 1972. 4)Eri Yagi, “Hantaro NAGAOKA,” Bictionary of Scientific Biography (New York, Charles Scribner’s Sons) Vol.9(1974)606-607.

What is Nagaoka’s original point?

Most of his approach was followed that of his former teacher Boltzmann although with no references, written by Nagaoka himself.5) Nagaoka studied directly under Boltzmann at Berlin, Munich and Vienna between 1893 and 1894 during his three years in Germany. Clausius and Boltzmann assumed a force between two particles as a simple function of their distance with no inner structure of them.

5) L.Boltzmann, Vorlesungen ueber Gastheorie II,5,Leipzig 1896 &1897,(trans.by B.Brush, Univ.of California Press,1964,p.353)

58 A Historical Approach to Entropy Nagaoka’s original point (continued)

On the other hand, Nagaoka adopted his atomic model with the above mentioned inner structures and wrote more detailed form for the force between two his atomic models.

Firstly after Clausius, Nagaoka wrote the Virial (force) as Wa + Wi where Wa was the well known macro external force due to the pressure p,namely, -3pV. Wi is consisted of the internal forces of W2 and W3.

Nagaoka ‘s culculation

Nagaoka adopted Boltzmann’s result for W2 which is the Virial due to the impact of spherical particles of diameter σ. For W3 Nagaoka used his original result of the Virial due to his atomic models. He showed in his previous paper that the repulsion force between his 2 atomic models was pro- portional to 1/(distance r)4 On the other hand, Boltzmann assumed it as a function of r.

CHAPTER III : Clausius through various study methods 59 Nagaoka and Van der Waals equation

Finally, Nagaoka added all terms, mentioned above, neglected the higher terms, and succeeded in presenting the following Van der Waals equation:

Originally presented by Van der Waals (1873) based on experimental data.

Other Nagaoak’s contribution.

His exact experimental data in spectroscopy which started in 1908 and continued up to 1930 played the most important role in the discovery of the concept of the spin by Pauli (1924)6) and Goudsmit & Uhlenbeck(1925). The high qualitiy of Nagaoka’s experimental data with the improvement of spectroscopy instruments at RIKEN (The Institute of Physical and Chemical Research in Tokyo) were mainly result of his strong theoretical interests in the inside structure of atoms (see Yagi, Itakura & Kimura, H. Nagaoka den (The Asahi P., 1973)).

60 A Historical Approach to Entropy CHAPTER IV Bibliography

CHAPTER IV : Bibliography 61 1. Total list of Clausius’ Papers by Kiyoshi Yoda (total 11 pages from K.Yoda’s list in our Japanese translation of 7 of Clausius’ German papers on the mechanical theory of heat, Entoropie no Kigen (The origin and backgrounds of Entropy) (Tokai University Press, Japan, pp.336-351)

Rudolf Clausius の論文および著書は，八木の『熱力学第二法則の展開』および Historical Approach to Clausius の同名のリストをベースに， Eduard Riecke の Rudolf Clausius (Eduard Rieche, Rudolf Clausius. Redegehalten am 1 December 1888 by in: Abhandlungen der Körniglichen Gesellscaft der Wissenschaften in Göttingen, S 3-39, Berlin; 1843, 1892) の中にある Clausius の著作リストを全面的に採用した．なお論文の冒頭に記載した番号は八木の著作の中にある記述法で，発行年度とその連番である．また，雑誌掲載の論文は各論文末に掲載ページを記入した．これは Riecke の記述法（各論文の最後に総ページ数を記載する）とは異なる．

Magazines

1. Poggendorfs Annalen der Physik und Chemie. 1847 47-1) Ueber die Lichtzerstreunug in der Atmosphäre und Intensitate des durch die Atmo- sphäre reflectirten Sonnelichtes. 72. (1847.) 294-314 1849 49-1) Ueber die Veränderungen, welche in den bisherigen gebräuchlichen Formeln für das Gleichgewicht und die Bewegung elastier fester Körper durch neuere Beobachtungen nothwendig geworden sind. 76. (1849.) 46-67 49-2) Ueber die Natur derjenigen Bestandtheile der Erdatmosphäre, durch welche die Licht- reflexion in derselben bewirkt wird. 76. (1849.) 161-188 49-3) Ueber die blaue Farbe des Himmels und die Morgen- und Abendröthe. 76. (1849.) 188-195

62 A Historical Approach to Entropy 1850 50-1) Ueber die bewegende Kraft der Wäme und die Gesetze, welche sich daraus für die Wämelehre selbst ableiten lassen. 79. (1850.) 368-397 50-2) Notiz über da Einfluss des Druckes auf das Gefrieren der Flüssigkeiten. 81. (1850.) 168-172 1851 51-1) Ueber das Verhalten des Dampfes bei der Ausdehnung unter verschiedenen Umständen. 82. (1851.) 263-273 51-2) Ueber den theoretischen Zusammenhang zweier empirisch aufgestell- ter Gesetze über die Spannung und die latente Wärme verschiedener Dämpfe. 82. (1851.) 274-279 51-3) Erwiderung auf die im Märzheft der Annalen enthaltenen Bemerkungen des Hrn. Holtz- mann (über die bewegende Kraft der Wärme). 83. (1851.) 118-125 51-4) Bemerkungen uber die Erklarung der Morga- und Abendröthe. 84. (1851.) 4 p. 1852 52-1) Ueber die Anordnung der Electricität auf einer einzelnen sehr dunnen Platte und auf den beiden Belegen einer Franclin’schen Tafel. 86. (1852.) 161-205 52-2) Ueber das mechanische Aequivalent einer electrischen Entladung und die dabei stattfindende Erwärmung des Leitungsdrahtes. 86. (1852.) 337-375 52-3) Ueber die bei einem stationären electrischen Strome in dem Leiter gethane Arbeit und erzeugte Wärme. 87. (1852.) 415-426 52-4) Uber die von Grove beobachtete Abhägigkeit des galvanischen Glühens von der Natur des umgebenden Gases. 87. (1852.) 12p. 1853 53-1) Ueber das Vorhandensein von Dampfläschen in der Atmosphäre und deren Einfluss auf die Lichtreflexion und Farben derselben. 88. (1853.) 14 p. 53-2) Ueber einige Stellen der Schrift von Helmholtz über die Erhaltung der Kraft. Bd. 89. (1853.) 16 p. 53-3) Ueber die Anwendung der mechanischen Wärmetheorie auf die ther- moelecrischen Erschei- nungen. 90. (1853.) 513-544

CHAPTER IV : Bibliography 63 1954 54-1) Uber einige Stellen der Schrift von Helmholtz über die Erhaltung der Kraft, zweite Notiz. 91. (1854.) 3 P. 54-2) Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie. 93. (1854.) 481-506 1956 56-1) Ueber die Anwendung der mechanische Wärmetheorie auf die Dampfmaschine. 97. (1856.) 441-476, 513-558 56-2) Notiz über den Zusammenhang zwischen dem Satz von der Aequivalenz der Wärme und Arbeit und dem Verhalten der permanenta Gase. 98. (1856.) 7 p. 1857 57-1) Ueber die Art der Bewegung, welche wir Wärme nennen. 100. (1857.) 28 p. 57-2) Ueber die Electricitätsleitung in Electrolyten. 101. (1857.) 23 p. 1858 58-1) Erwiderung auf einige Bemerkungen des Hrn. Hittorf; (über die Wanderungen der Jonen.) 103. (1858.) 4 p. 58-2) Ueber die Natur des Ozons. 103. (1858.) 9 p. 58-3) Ueber die Zunahme des electrischen Leitungswiderstandes der Metalle mit der Temperatur. 104. (1858.) 2 p. 58-4) Ueber die mittlere Länge der Wege, welche bei der Molecularbewegung gasfömiger Körper von den einzelnen Molecülen zurückgelegt werden, nebst einigen anderen Bemerkungen uber die mechanische Wärmetheorie. 105. (1858.) 16 p. 1862 62-1) Ueber die Wärmeleitung gasfämiger Körper. 115. (1862.) 57 p. 62-2) Ueber die Anwendung des Satzes von der Aequivalenz der Verwandlungen auf die innere Arbeit. 116. (1862.) 40 p. 1863 63-1) Ueber eiaen Grundsatz der mechanischen Wärmetheorie. 120. (1863.) 27 p.

64 A Historical Approach to Entropy 1864 64-1) Ueber die Concentration von Wärme- und Lichtstrahlen und die Gränzen ihrer Wirkung. 121. (1864.) 44 p. 64-2) Ueber den Untershied zwischen activem und gewöhnlichem Sauerstoff. 121. (1864.) 19 p. 1865 65-1) Ueber die Berechnung der Dichtigkeit des gesättigten Wasserdampfes. 124. (1865.) 3 p. 65-2) Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. 125. (1865.) 49 p. 1866 66-1) Ueber die Bestimmung der Disgregation eines Körpers und die wahre Wärmecapacität. 127. (1866.) 8 p. 66-2) Ueber die relativen Intensitaten des directen und zerstreuten Sonnenlichtes. 129. (1866.) 7 p. 1868 68-1) Ueber die von G a u s s angeregte neue Auffassung der electrischen Erscheinungen. 135. (1868.) 16 p. 1869 69-1) Zur Geschichte des Ozons. 136. (1869.) 4 p. 1870 70-1) Bemerkungen zu zwei Aufsätzen von W. v. Bezold und E.Edlund uber electrische Erscheinungen. 139. (1870.) 6 p. 70-2) Ueber einen auf die Wärme auwendbaren meehanischen Satz. 141. (1870.) 8 p. 70-3) Ueber die Zuruckführung des zweiten Hauptsatzes der mechanischen Wärmetheorie auf allgemeine mechanische Princpien. 142. (1870.) 29 p. 1871 71-1) Bemerkungen zu den Prioritätsreklamationen des Herrn Boltzmann. 144. (1871.) 9 p. 1872 72-1) Zur Geschichte der mechanischen Wärmetheorie. 145. (1872.) 16 p. 72-2) Ueber die von Tait erhobenen Einwände gegen meine Behandlung der

CHAPTER IV : Bibliography 65 mechanischen Wärmetheorie. 146. (1872.) 6 p. 72-3) Ueber den Zusammenhang des zweitan Hauptsatzes der mechanischen Wärmetheorie mit dem Hamilton‘schen Princip. 146. (1872.) 12 p. 1873 73-1) Ueber einen neuen mechanischen 8atz in Bezug auf stationäre Bewegungen. 150. (1873.) 25 p. 73-2) Bemerkungen zu einer Aeusserung des Herrn Avenarius in Bezug auf thermoëlec- trische Ströme. 150. (1873.) 2 p. 1874 74-1) Jubelband. Ueber verschiedene Formen des Virials. (1874.) 13 p. 74-2) Ergänzungsband VII. Ueber den Satz vom mittleren Ergal und seine Anwendung auf die Mo1e- cularbewegungen der Gase. (1874.) 65 p. 1875 75-1) Bemerkung zu den meteorologischen Notizen des Hernn Budde. 152. (1875.) 2 p. 75-2) Ueber ein neues Grundgesetz der Electrodynamik. 156. (1875.) 3 p. 1876 76-1) Ueber das Vehalten des electrodynamischen Grudgesetzes zum Princip von der Erhal- tung der Energie und über eine noch weitere Vereinfachung des eateren. 157. (1876.) 5 p. 76-2) Bemerkungen zu dem Aufsatze des Hrn. vou Oettingen über Temperatur und Adiabate. 159. (1876.) 2 p. 1877 77-1) Bemerkungen zu einem Aufsatz von F.Kohlrausch über Thermoëlectricität. 160. 1877. 5p.

2. In Wiedemanns Annalen der Physik und Chemie. 1877 77-2) Ueber die Behandlung der zwischen linearen Strömen und Leitern stattfindenden ponderomotorischen und electromotorischen Kräfte nach dem electrodynamischen Grundgesetz. 1. (1877.) p. 26. 77-2) Nachträgliche Bemerkung. 1. (1877.) 1 p.

66 A Historical Approach to Entropy 77-3) Ueber einen allgemeinen Satz in Bezug auf electrische Influenz. 1. (1877.) 6 p. 77-4) Erwiderung auf die von Zöllner gegen meine electrodynamischen Betrachtungen erhobenen Einwände. 2. (1877.) 13 p. 77-3) Ueber eine von Hrn. Tait in der mechanischen Wärmetheorie angewandte Schlussweise. 2. (1877.) 3 p. 1878 78-1) Ueber einige neue von Hrn. Zöllner gegen meine electrodynamischen Betrachtungen erhobenen Einwände. 4. (1878.) 9 p. 78-2) Ueber die Beziehulg der durch Diffusion geleisteten Arbeit zum zweiten Hauptsatz der mechanischen Wärmetheorie. 4. (1878.) 2 p. 1879 79-1) Ueber das Bekanntwerden der Schriften Robert Mayers. 8. (1879.) p. I-XII 1880 80-1) Ueber das Verhalten der Kohlesäure in Bezug auf Druck, Volumen und Temperatur. 9. (1880.) 2l p. 80-2) Ueber einige neue Untersuchungen über die mittlere Weglänge der Gasmolecüne. 10. (1880.) 11 p. 80-3) Ueber die Vergleichung der electrodynamischen Grundgesetze mit der Erfahrug. 10. (1880.) ll p. 80-4) Ueber die Anwendung des electrodynamischen Potentials zur Bestimmung der ponderomotorischen und electromotorischen Kräfte. 11. (1880.) 30 p. 1881 81-1) Ueber einige Bemerkungen des Hrn. Carl Neumann in Bezug auf Elektrodynamik. 12. (1881.) 5 p. 81-2) Ueber die theoretische Bestimmung des Dampfdruckes und der Volumina des Dampfes und der Flüssigkeit. 14. (1881.) 26 p. 1882 82-1) Ueber die verschiedenen Maassysteme zur Messung electrischer und magnetisder Grössen. 16. (1882.) 23 p. 82-2) Ueber den Zusammenhang zwischen den Einheiten des Magnetismus und der Electricität. 17. (1882.) 7 p.

CHAPTER IV : Bibliography 67 1883 83-1) Zur Theorie der dynamoëlectrischen Maschine. 20. (1883.) 353-390.( 38 p.) 83-2) Zur Theorie der Kraftübertragung durch dynamoëlectrische Maschinen. 21. (1884.) 385-401. ( 13 p.) 1887 87-1) Erwiderung auf eine Bemerkung des Hrn. Lorberg in Bezug auf dynamoëlectrische Maschinen. 31. (1887.) 4 p.

3. Zeitschrift für Mathematik und Physik. 1864 64-3) Ueber den Einfluss der Schwere auf die Bewegungen der Gasmolecüle. 9. (1864.) l p. 1866 66-3) Ueber die Bestimmung der Energie und Entropie eines Körpers. 11. (1866.) 15 p. 66-4) Ueber umkehrbare und nicht umkehrbare Vorgänge in ihrer Beziehung auf die Wärme-theorie. 11.(1866.) 7 p. 1867 67-1) Elkläruug in Betreff einer Bemerkung des Hrn. Bauschinger. 12. (1867.) 1 p. 1870 70-4) Bemerkungen zu zwei Aufsätzen des Hrn. Mohr. 15. (1870.) l p.

4. Journal für die reine und angewandte Mathematik. 1847 47-2) Ueber die Lichtzerstreuung in der Atmosphäre. 34. (1847.) 26 p. 1848 48-1) Ueber die Intensität des durch die Atmosphäre reflectirten Sonennlichtes. 36. (1848.) 3l p. 1876 76-3) Ueber die Ableitung eines neuen electrodynmischen Grundgesetzes. 82. (1876.) 50 p.

68 A Historical Approach to Entropy 1877 77-2) Ueber das Grassmann‘sche Gesetz der ponderomotorischen Kraft. 83. (1877.) l p.

5. Mathematische Annalen. 1871 71-2) Ueber die Anwendung einer von mir aufgestellten mechanischen Gleichung auf die Bewe- gung eines materiellen Punktes um ein festes Anziehungscentrum und zweier materieller Punkte um einander. 4. (1871.) 11 p. 1873 73-3) Ueber die Beziehungen zwischen den bei Centrallbewegungen vorkommen- den characteristi-schen Grössen. 6. (1873.) 25 P.

6. Annalen der Chemie und Pharmacie. 1861 61-1) Ueber die specifische Wärme der Gase. 118. (1861.) 14 p.

7. Electrotechnische Zeitschrift. 1885 85-1) Ueber die von Hrn. Fröhlich aufgestellte Theorie der dynamoelec- trischen Maschine. 6. (1885.) 3 p.

8.Polytechnisches Journa1. 1859 59-1) Ueber die mechanische Wärmetheorie. 150. (1859.) 20 p.

9. Monatsberichte der Berliner Akademie. 1847 47-3) Lichtmenge, welche die Erde durch Reflexion des Sonnenlichtes in der Atmosphäre erhält. 2 p.

CHAPTER IV : Bibliography 69 1850 50-3) Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärme selbst ableiten lassen. 12 p. 1852 52-5) Ueber die Anordnung der Electricität auf einer einzelnen sehr dünnen Platte und auf den beiden Belegen einer Franklin’schen Tafel. 7 p. 52-6) Ueber die mechanische Aequivalent einer electrischen Entladung und die dabei stattfindende Erwärmung des Leitungsdrahtes. 7 p. 1853 53-4) Ueber die Anwendung der mechanischen Wärmetheorie auf die thermoelectrischen Erschei- nungen. 13 p. 1884 84-1) Ueber die zur Erklärung des zweiten Hauptsatzes der mechanischen Wärmetheorie die- nunden mechanischen Gleichungen. 7 p.

10. Nachrichten der Kgl. Ges. d. Wiss. zu Göttingen. 1871 71-3) Ueber die Anwendung einer von mir aufgestellten mechanischen Gleichung auf die Bewe- gung eines materiellen Punctes um ein festes Anziehungscentrum zweiter materieller Puncte um einander. 22 p. 1872 72-4) Ueber die Beziehungen zwischen den bei Centralbewegungen vor- kommeden characteristi- schen Grössen. 47 p.

11. Mittheilungen der niederrheinischen Gesellschaft. 1870 70-5) Ueber einen auf die Wärme anwendbaren mechanischen Satz. 5 p. 1871 71-4) Ueber die Zurückführung des zweiten Hauptsatzes der mechanische Wärmetheorie auf allgemeine mechanische Principien. 22 p.

70 A Historical Approach to Entropy 1873 73-4) Ueber einen neuen mechanischen Satz in Bezug auf stationäre Bewegungen. 18 p. 1874 74-3) Ueber den Satz vom mittleren Ergal und seine Anwendung auf die Molecularbewegungen der Gase. 49 p. 1875 75-3) Ueber ein neues Grundgesetz der Electrodynamik. 3 p Ueber die Theorie der Lichtmühle. 7 p. 1876 76-4) Ueber das Verhältniss des electrodynamischen Grundgesetzes zum Princip von der Erhal- tung der Energie und über eine noch weitere Vereinfachung des ersteren. 4 p. Ueber die Behandlung der zwischen linearen Strömen und Leitem stattfindenden pondero- Motorischen und electromotorischen Kräfte nach dem electrodynamischen Grundgezetz. 24 p. 1880 80-5) Ueber die Anwendung des electrodynamischen Potentials zur Bestimmung der ponderomo- Torischen und electromotorischen Kräfte. 31 p. 1882 82-3) Ueber die verschiedenen Massysteme zur Messung electrischer und magnetischer Grössen. 23 p.

12. Sitzungsberichte der math. naturwiss. Classe der Wiener Akademie. 1863 63-2) Ueber die Molecularbewegungen in gasförmigen Körpern. 2 p.

CHAPTER IV : Bibliography 71 13. Vierteljahrsschrift der naturforschenden Gesellschaft in Zürich. 1857 57-3) Ueber die Entfernung in welcher die von einem Eisenbahnzuge bewirkte Erschütterung noch spürbar ist. 2. (1857.) l p. 1861 61-2) Ueber die Anwendung des Satzes von der Aequivalentz der Verwandlungen auf die innere Arbeit. 7. (1861.) 47 p. 1863 63-3) Ueber den Unterschied zwischen activem und gewönlichem Sauerstoff. 8. (1863.) 22 p. 1865 65-3) Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. 10. (1865.) 59 p.

14. Berichte der deutschen chemischen Gesellschaft. 1871 71-5) Bemerkungen zu einem Aufsatze des Hrn. Mohr über die ungleiche Leitungsfähigkeit der Gase für Wärme. 4. (1871.) 1 p.

15. Philosophica1 Magazine. 1851 51-5) Reply to a note from Mr. W. Thomson on the effects of fluid Friction etc. 2. (1851.) 3 p. 1853 53-5) On the colours of a jet of steam and of the athmosphere. 4. (1853.) 1 p. 1856 56-3) On the discovery of the true form of Carnots function. 11. (1856.) 2 p. 1860 60-1) On the dynamical theory of gases. 19. (1860.) 2 p. 1872 72-5) A necessary correction of one of Mr. Taits remarks. 44. (1872.) 1 p.

72 A Historical Approach to Entropy 16. Archives des sciences physiques. 1857 57-4) Remarques sur la relation entre l’action chimique qui a lieu dans une pile voltaique et les effets produits par le courant. 36. (1857.) 3 p. 1872 72-6) Nouveaux mémoires sur la théorie mécanique de la chaleur. 48. (1872.) 6 p.

17. Comptes rendus de l’Académie des sciences. 1861 61-3) Sur la densité de la vapeur saturée. 52. (1861.) 3 p. 1862 62-3) Sur la fomule pour la vitesse de propagation du son dans l’air donnée par M. Du- hamel. 55. (1862.) 5 p. 62-4) Sur la pression dans l’air pendant la propagation du son. 55. (1862.) 3 p. 1863 63-4) Sur la condensation des vapeurs pendant la détente ou la compression. 56. (1863.) 2 p. 63-5) Sur quelques équations, qui dérivent de la théorie mécanique de la chaleur. 58. (1863.) 3p. 1865 65-4) Sur le second théorème principal de la théorie mécanique de chaleur. 60. (1865.) 2 p 65-5) Remarques sur une loi général relative à la force agissant de la chaleur. 61. (1865.) 6 p. 1870 70-6) Sur une quantité analogue au potentiel et sur un théorème y relative 70. (1870.) 5 p. 1872 72-7) Sur l’équation mécanique dont découle le théorème du viriel. 75. (1872.) 4 p. 1874 74-4) Sur une équation mécanique, qui correspond à 1’équation 78. (1874.) 4 p. 1878 78-3)Sur l’énergie d’un corps et sa chaleur spécifique. 87. (1878.) 1 p.

CHAPTER IV : Bibliography 73 18. Liouville Journal de mathématiques. 1858 58-6) Sur la démonstration de l’équation 3. (1858.) 5 p.

19. Les Mondes. 1864 64-4) Sur les équations fondamentales de la théorie mécanique de la chaleur. 6. (1864.) 8 p. 1875 75-4) Sur la nouvelle manière de considerer les phénomènes électrodynamiques. 39. (1875.) 1 p.

20. La Lumière é1ectrique. 1885 85-2) Sur les dimensions des mo1écules et leur distances relatives. 17. (1885.) 8 p.

21. Annales du Génie civil. 1867 67-2) Introduction à la théorie mathématique de l’électricité. 6. (1867.) 28 p.

22. Bulletin de l’Académie de Belgìque. 1886 86-1) Examen des objections faites par M. Hirn à la théorie cinétique des gaz. 11. (1886.) 20 p.

74 A Historical Approach to Entropy BOOKS 1850 Uebersichtlich Darstellung der das Gebiet der Optik gehörenden Erscheinungen. Grunerts Meteorologische Optik. Bd. I. 1850. (Die Lichterscheinungen der Atmosphäre dargestellt und ertäutert, Leipzig, 1850, 367-462, Zweiter Theil.)

1857 Ueber das Wesen der Wärm verglichen mit Licht und Schall. Zürich 1857.

1859 Die Potentialfunction und das Potential. Leipzig 1859. (II. Auflage. 1867., III. Auflage. 1877., IV. Auflage. 1885. )

1864 Abhandlungen über die mechanische Wärmetheorie. Erste Abtheilung. Braunschweig 1864. Abhandungen, welche Begründung der mechanischen Wärmetheorie, nebst ihrer Anwendung auf die in die Wärmetheorie gehörigen Eigenschaften der Körper und auf die Dampfmaschinentheorie enthalten; vervollständigt durch eine mathematische Einleitung und durch erläuternde Anmerkungen und Zusätze.

1867 Ueber den zweiten Hauptsatz der mechanischen Wärmetheorie. Braunschweig 1867.

1867 Abhandlungen über die mechanische Wärmetheorie. Zweite Abtheilung. Braunschweig 1867. Abhandungen über die Anwendung der mechanischen Wärmetheorie auf die elek- trischen Erscheinungen, nebst einer Einleitung in die mathematische Behandlung der Elektricität, Abhandlungen über die zur Erklärung der Wärme angenommenen

CHAPTER IV : Bibliography 75 Molecularbewegungen und eine auf die allgemeine Theorie bezügliche Abhandlung; vervollständigt durch erläuternde Anmerkungen und Zusätze. ( 2 v. in 1 )

1868 Recension der Mayer’schen Schriften im Litterarischen Centralblatt 1868.

1876 Die mechanische Wärmetheorie. Zweite umgearbeitete und vervollständigte Auflage des unter dem Titel “Abhandlungen über die mechanische Wärmetheorie“ erschienenen Buches.Brannschweig 1876 ( Entwickelung der Theorie, soweit sie sich aus den beiden Hauptsätzen ableiten lässt, nebst Anwendungen. ) (Die Mechanische Wärmetheorie / von R. Clausius ; Bd. 1)

1879 Die mechanische Wärmetheorie. Zweite umgearbeitete und vervollständigte Auflage des unter dem Titel “Abhandlungen über die mechanische Wärmetheorie“ erschienenen Buches. Zweiter Band. Anwendung der mechanischen Wärmetheorie zu Grunde liegenden Principienauf die Electricität. Brannschweig 1879 (Die mechanische Behandlung der Electricität, Braunschweig 1879 ) (Die Mechanische Wärmetheorie / von R. Clausius ; Bd. 2)

1885 Ueber den Zusammenhang zwischen den grossen Agentien der Natur. Bonn1885.

1885 Ueber die Energievorräthe in der Natur und ihre Verwerthung zum Nutzen der Meschheit. Bonn 1885.

1887 Die mechanische Wärmetheorie. Dritte umgearbeitete und vervollstandigte

76 A Historical Approach to Entropy Auflage. Erster Band. Entwickelung der Theorie, soweit sie sich aus den beiden Hauptsätzen ableiten lässt, nebst Anwendungen. Brannschweig 1887. (Die Mechanische Wärmetheorie / von R. Clausius ; Bd. 1)

1889 Die mechanische Wärmetheorie von R.Clausius. Zweite umgearbeitete und ver- vollständigte Auflage des unter dem Titel “Abhandlungen über die mechanische Wärmetheorie“ erschienenen Buches. Dritter Band. Entwickelung der besonderen Vorstellungen von der Natur der Wärme als Art der Bewegung. Herausgegeben von Dr. Max Plank, und Dr. Carl Pulfrich, Brannschweig 1889-1891. ( Die kinetische theorie der Gase. Herausgegeben von Max Planck und Carl Pulfrich. Zweite umgearbeitete und vervollständigte Auflage des unter dem Titel "Abhandlungen über die mechanische Wärmetheorie" erschienenen Buches. Braunschweig, 1889-1891)(Die Mechanische Wärmetheorie / von R. Clausius ; Bd. 3)

CHAPTER IV : Bibliography 77 2. A list of Eri Yagi ‘s papers from 2002 to 2018 (total 2 pages)

2002 Eri Yagi, Haruo Hayashi, Kiyoshi Yoda, & Rika (Tadokoro) Okamoto: A Historical Approach to Entropy –Collected papers of Eri Yagi and her coworkers,International Publishing Institute, Japan, 2002, 186pp.

A Supplement of the Collected Papers of Eri Yagi and her Coworkers — A Database from R.Clausius’s Abhandlungen I – XVI, Eri Yagi Institute for History of Science, Japan, 2002, 72pp.

2003 E.Yagi “Various methods to study the mechanical theory of heat,” British Society for the History of Science. Annual Conference, 17-19 July,2003, York St John College, York, Abstracts (2003), p.15.

2005 E. Yagi (with Ivor Grattan-Guinness, Emeritus Professor of Middlesex University,U.K) “What are Potential and Entropy ? Their historical background,”the7thlecture-meeting,NPO GKN,Yokyo,16 October, 2005, http// gakujutsukenkyunet.org/ekoensummary7th.html

2009 E,Yagi & Rika (Tadokoro) Okamoto “A History of Entropy through various Methods,” (delivered on 29 July) Abstract, XXIII International Congress of History of Science (2009), Budapest, Hungary. See also Professor Emeritus Yagi’s Blog: http://www.schaft.org/wp/

E. Yagi ”R. Clausius’s contribution to the 1st and 2nd laws of thermodynamics,”

78 A Historical Approach to Entropy Book of Abstract, 4th Symposium on Vacuum based Science & Technology, September, Kozsalin, Poland (2009) p.C1.

2010 E. Yagi “On Yagi’s invited lecture for the new Clausisu Tower (project) at Koszalin University of Technology, Poland (in Japanese),” Entoropii (the journal of entropy society of Japan) No.68, March (2010) pp.210- 214. 2010, E.Yagi & R. T. Okamoto “A History of Entropy through various Methods:Specially Focused on Technical term Analysis,” Historia Sientiarum, Tokyo, Vol.20-1 (2010) pp.47-56.

2011 E.Yagi “The Important Role of Particles through the 19th Mechanical Theory of Heat,”, International Conference for the 3rd Centanary of R.G.Boscovich, Pavia, Italy September, 2011 (to be published in the Proceedings in the near future)

2013 E.Yagi “Clausiu on Nagaoka ‘s development of his atomic model (1903),” the 24th ICHSTM, Manchester, Program T160, July 25 (2013) p.343. 2013, Eri Yagi, Haruo Hayashi, Kiyoshi Yoda, & Rika (Tadokoro) Okamoto: The Japanese translation of 7 Clausius’s German papers on the mechanical theory of heat, Entoropie no Kigen (The origin and backgrounds of Entropy) (Tokai University Press, Japan) 376pp.

2014 E.Yagi “Tetsuo Tsuji’s historical studies on thermodynamics & statistical mechanics ( in Japanese),” Abstract of the 69th Annual meeting of the Physical Society of Japan, Vol.69, No.1-2, March 28 (2014) p.451. 2014, E.Yagi, Haruo Hayashi, Kiyoshi Yoda, and Rika Tadokoro Okamoto, “Clausius and the 19th century physics (in Japanese),”Butsuri (the Japanese journal of the Physical Society of Japan) Vol.69, No.4, April (2014) pp.230-232.

CHAPTER IV : Bibliography 79 E.Yag “Tetsuo Tsuji’s historical studies on physics (in Japanese),” Abstract of the 61th Annual meeting of the History of Science Society of Japan, May 25, C17, p.108.

2018 E.Yagi, Naohiko Hiromasa, and Haruo Hayashi, ”Late Professor Emeritus Tsuyoshi Ogawa’s contributions toward the History of Physics (in Japanese),” Abstract of the th 65 Annual meeting of the History of Science Society of Japan, May 27, C34, p.47.

80 A Historical Approach to Entropy Acknowledgments

e wish to thank each editor and organization, for the Wpermission to reproduce our papers and talks in this Second Edition, especially, Witold Gulbinski, Physics, the Koszalin University of Technology, the Clausius Society, Professor Takahiko Hashimoto, the Editor of HISTORIA SCIENTIARUM, and the editor of the British Society for History of Science. Thanks are also due to Mr. Miguel Rivas-Micoud for his valuable suggestions and input in making the English under- standable and to seeing this edition through to publication. The actual publication became possible through the effort of the Aozora Shobo by Mr Eiji Mitachi. In addition to the above, I deeply appreciate Ms Tossi Conrad’s help with the German writing together with the useful advice by Emerita Professor Gertorude Krombholz of the University of Munik. Finally, I would like to express my deep appreciation to the late Dr. Jan Staskiewicz (vacuum experimental physicist, who passed away on the 9th of March, 2013) and also to his friend Mr. Jupi Podlaszewski (Journalist). As the active members of the Clausius Tower Society, they had long been interested in my Clausius research through the Internet and contacted me several years before the special year of 2009. Eri Yagi: Biographical information

Professor Emeritus of Toyo University, Tokyo. Director of Eri Yagi Institute for History of Science, and member of the NPO Gakujutu Kenkyu Network.

Eri Yagi received her undergraduate education in physics at Ochanomizu University, Tokyo. After studying under the late Professor Derek Price at Yale Graduate School for three years (1960-63) on a leave of absence from the Department of physics, the Graduate School of the University of Tokyo, Yagi received a Ph.D. in physics in 1965. The topics of her thesis were a statistical approach to Japanese physics, the internal history of H. Nagaoka's atomic model (1903) and spectroscopy.

For the past 30 years Yagi has been working on Clausius and entropy. In addition to the traditional text analysis, Yagi and her co-workers have been exploring several useful methods: They are the method of mathematical equation analysis, experimental table analysis, and technical term analysis. These results have been collected in the first edition of “A Historical Approach to Entropy”, published in 2002. This second edition includes a similar collection of papers, published between 2002 to 2018.