Ewald Thesis Statement

Paul Peter Ewald, FRS[1] (January 23, 1888 in Berlin, Germany – August 22, 1985 in Ithaca, New York) was a Germancrystallographer and physicist, a pioneer of X-ray diffraction methods.[2]


Ewald received his early education in the classics at the Gymnasium in Berlin and Potsdam, where he learned to speak Greek, French, and English, in addition to his native language of German.[3]

Ewald began his higher education in physics, chemistry, and mathematics at Gonville and Caius College in Cambridge, during the winter of 1905. Then in 1906 and 1907 he continued his formal education at the University of Göttingen, where his interests turned primarily to mathematics. At that time, Göttingen was a world-class center of mathematics under the three “Mandarins” of Göttingen: Felix Klein, David Hilbert, and Hermann Minkowski.[4] While studying at Göttingen, Ewald was taken on by Hilbert as an Ausarbeiter, a paid position as a scribe, i.e., he would take notes in Hilbert’s classes, have the notes approved by Hilbert’s assistant – at that time Ernst Hellinger – and then prepare a clean copy for the Lesezimmer – the mathematics reading room.[5] In 1907, he continued his mathematical studies at the Ludwig Maximilians University of Munich (LMU), under Arnold Sommerfeld at his Institute for Theoretical Physics. He was granted his doctorate[6] in 1912. His doctoral thesis developed the laws of propagation of X-rays in single crystals. After earning his doctorate, he was an assistant to Sommerfeld.[3][7]

During the 1911 Christmas recess and in January 1912, Ewald was finishing the writing of his doctoral thesis. It was on a walk through Englischer Garten in Munich, in January, that Ewald was telling Max von Laue about his thesis topic. The wavelengths of concern to Ewald were in the visible region of the spectrum and hence much larger than the spacing between the resonators in Ewald’s crystal model. Laue seemed distracted and wanted to know what would be the effect if much smaller wavelengths were considered. It was not until June of that year that Ewald heard Sommerfeld report to the Physikalische Gesellschaft of Göttingen on the successful diffraction of X-rays by Max von Laue, Paul Knipping and Walter Friedrich at LMU, for which Laue would be awarded the Nobel Prize in Physics, in 1914.[8][9]

With the rise of theoretical physics in the early part of the twentieth century and its foundation in mathematics, David Hilbert decided to lend an organizing hand to formalizing the sciences, starting with physics. In 1912, Hilbert asked his friend and colleague Arnold Sommerfeld[10] to send him a special assistant for physics. Sommerfeld sent Ewald, who was dubbed as “Hilbert’s tutor for physics,”[11] and he performed this function until 1913, when Sommerfeld sent another one of his students, Alfred Landé. The first problem assigned Ewald was to review the controversy in the literature on the constants of elasticity in crystals and report back. A few years later, Max Born, at Göttingen, solved the problem.[7][12]

During Ewald’s stay in Göttingen, he was often a visitor at El BoKaReBo, a boarding house run by Sister Annie at Dahlmannstrasse 17. The name was derived from the first letters of the last names of its boarders: “El” for Ella Philippson (a medical student), “Bo” for Max Born (a Privatdozent) and Hans Bolza (a physics student), “Ka” for Theodore von Kármán (a Privatdozent), and “Re” for Albrecht Renner (a medical student). Richard Courant, a mathematician and Privatdozent, called these people the “in group.” It was here that Ewald met Ella Philippson, who was to become his wife.[1][13]

In the spring of 1913, Niels Bohr, of the Institute for Theoretical Physics at the University of Copenhagen, submitted his theory of the Bohr atomic model for publication.[14] Later that year, Ewald attended the Birmingham meeting of the British Association where he heard accounts and discussions of James Jeans’ review on radiation theory and Bohr’s model.[15] This ignited a major new area of research for Sommerfeld and his students – the study and interpretation of atomic spectra and molecular band spectroscopy and theoretical modeling of atomic and molecular structure.

During World War I, Ewald served in the German military as a medical technician. When he could, he continued to think about the physics of his doctoral thesis, and he developed the dynamical theory of X-ray diffraction, which he was later to use in his Habilitationsschrift. At the conclusion of the war, he returned to LMU as an assistant to Sommerfeld. He completed his Habilitation in 1917,[16] and became a Privatdozent there, while remaining as an assistant to Sommerfeld.[3][17]

In 1921, while still at LMU, Ewald published a paper on the theta function method of analyzing dipole fields in crystals,[18] an offshoot from his earlier work on the dynamical theory of optics and X-rays in crystals, which appeared in three journal publications.[19][20][21] According to Ewald, the impetus for the method came from a skiing holiday in Mittenwald, at Easter, in 1911. It was Sommerfeld’s practice to take his students and assistants on skiing outings in the winter and mountain climbing outings in the summer, where the discussions of physics were as hard as the physical exertion of the outings.[22] Ewald, was having trouble subtracting out of his calculations the field of the test dipole. The solution was provided by Sommerfeld’s assistant and former doctoral student, Peter Debye, in a discussion that took no more than 15 minutes. Ewald’s paper has been widely cited in the literature as well as scientific books, such as Dynamical Theory of Crystal Lattices,[23] by Max Born and Kun Huang.[24]


When Erwin Schrödinger let it be known that he was leaving his position as extraordinarius professor at the StuttgartTechnische Hochschule, to go to the University of Breslau, Ewald was called and accepted the position in 1921. In 1922, he was called to the University of Münster. Ewald used the offer to better his position at Stuttgart to ordinarius professor; however, while Ewald was promoted to ordinarius professor, the established position was actually retained as an extraordinarius professorship.[25] From 1922 Erwin Fues, also a former doctoral student of Sommerfeld, did postgraduate work at the Stuttgart Technische Hochschule, under Ewald; Fues completed his Habilitation in 1924. Also in that year, Ewald became co-editor of Zeitschrift für Kristallographie. In 1929, he received a call to the Technische Hochschule Hanover. Again, he used this call to better his position at Stuttgart by negotiating for a second assistant, the permanent conversion of his position to that of ordinarius professor, and a separate building for his activities. The building was formally opened in 1930 as the Institute for Theoretical Physics, with Ewald as director. The institute was modeled after Sommerfeld’s Institute for Theoretical Physics at Munich, in that it would conduct theoretical work as well as have space and equipment for experimental work.[26] In 1931, Ewald was appointed Director of the Physical Science Division.[27][28][29]

At Göttingen, Richard Courant had taken Hilbert’s lecture notes which were available in the Lesezimmer, edited them and added to them to write a two-volume work. The first volume, Methoden der mathematischen Physik I, was published in 1924.[30] Upon seeing the book, Ewald was compelled to write a detailed review describing it as providing mathematical tools, characterized by eigenvalues and eigenfunctions, for the theoretical physics then being developed.[31] The Courant-Hilbert book fortuitously contained the mathematics necessary for the development of the Heisenberg-Bornmatrix mechanics formulation of quantum mechanics and also for Schrödinger’s wave mechanics formulation, both put forward in 1925!

The main thrust of Ewald’s work was X-ray crystallography, and Ewald was the eponym of Ewald construction and the Ewald sphere, both useful constructs in that field.[32]

In 1929, in order to remove confusion from the proliferation of crystallographic data, Ewald proposed review and collection of the best data into a single publication. The results were published in 1935 as the Internationale Tabellen zur Bestimmung von Kristallstrukturen. Another contribution by Ewald, published in 1931, Strukturbericht Volume I (1913-1928) was edited by Ewald and C. Hermann.[3][33]

Ewald was elected Rector at Stuttgart in 1932. However, due to increasing difficulties with faculty who were members of National Socialism in Germany, he resigned his position in the spring of 1933,[34] one year before his term was due to expire. Ewald continued with his other activities. However, over increasing problems with the Dozentenbund,[35] Wilhelm Stortz, University Rector, asked Ewald to leave.[36] He emigrated to England in 1937 and took a research position in Cambridge, until he was offered and accepted a lectureship at Queen's University Belfast, in 1939. He later became a professor of mathematical physics.[3][27][29]

While lecturing at Duke University in 1937, Hans Bethe, who got his doctorate under Sommerfeld in 1928, bumped into Rose Ewald, who had already emigrated to the United States and was attending the school. They were married in September 1939. Thus Bethe became son-in-law to Paul Peter Ewald.[37]

Near the end of World War II, Sommerfeld organized his lecture notes and began writing the six-volume Lectures on Theoretical Physics. While at the Polytechnic Institute of Brooklyn, Ewald wrote a Foreword to Sommerfeld’s Course, which appeared in the English translation of Sommerfeld’s work.[38]

Also, toward the end of World War II, Ewald was concerned that peace would result in the establishment of multiple, competing national journals of crystallography. So, in 1944, at Oxford, he proposed the establishment of an International Union of Crystallography (IUCr) that would have sole responsibility for publishing crystallographic research. In 1946, he was elected Chairman of the Provisional International Crystallographic Committee, in a London meeting of crystallographers, from 13 countries; he served in this capacity until 1948, when the Union was formed. The Committee also nominated him Editor of the journal to be published by the Union. The first issue of Acta Crystallographica was published in 1948, the same year that Ewald chaired the first General Assembly and International Congress of the IUCr, which was held at Harvard University.[3][39]

In 1952, Ewald was elected President of the American Crystallographic Association. He served on the IUCr Executive Committee from its foundation until 1966, and he was its Vice-President in 1957 and President in 1960, a position he held until 1963. His editorship of its journal Acta Crystallographica extended from its inception in 1948 to 1959.[3][39]

A decade after moving to Belfast, Ewald moved to the United States in 1949 and took a position at the Polytechnic Institute of Brooklyn, as a professor and head of the Physics Department. He retired as head of the department in 1957 and from teaching in 1959.[3][27][29]



  • Paul Peter Ewald Kristalle und Röntgenstrahlen (Springer, 1923)
  • Paul Peter Ewald, Theodor Pöschl, Ludwig Prandtl; authorized translation by J. Dougall and Winifred Margaret DeansThe Physics of Solids and Fluids: With Recent Developments (Blackie and Son, 1930)
  • Paul Peter Ewald Der Weg der Forschung (insbesondere der Physik) (A. Bonz'erben, 1932)
  • Peter Paul Ewald, editor 50 Years of X-Ray Diffraction (Reprinted in pdf format for the IUCr XVIII Congress, Glasgow, Scotland, 1962, 1999 International Union of Crystallography)
  • Peter Paul Ewald On the Foundations of Crystal Optics (Air Force Cambridge Research Laboratories, 1970)

See also[edit]


  • Durward W. J. Cruickshank, Hellmut J. Juretschke, N.` Kato (editors) P. P. Ewald and His Dynamical Theory of X-ray Diffraction: A Memorial Volume for Paul P. Ewald (Oxford University Press, 1992)


  1. ^ abBethe, H. A.; Hildebrandt, G. (1988). "Paul Peter Ewald. 23 January 1888-22 August 1985". Biographical Memoirs of Fellows of the Royal Society. 34: 134. doi:10.1098/rsbm.1988.0006. JSTOR 770049. 
  2. ^Juretschke, H. J.; Moodie, A. F.; Wagenfeld, H. K.; Bethe, H. A. (May 1986). "Obituary: Paul P. Ewald". Physics Today. 39 (5): 101–104. Bibcode:1986PhT....39e.101J. doi:10.1063/1.2815014. Archived from the original on 2018-01-21. 
  3. ^ abcdefghEwald – Memorial
  4. ^Greenspan, 2005, pp. 26-34.
  5. ^Constance Hilbert p. 109.
  6. ^Paul Peter Ewald – Mathematics Genealogy Project. Ewald’s 1912 dissertation title: Dispersion und Doppelbrechung von Elektronengittern.
  7. ^ abAuthor Index: EwaldArchived 2007-02-05 at the Wayback Machine. – American Philosophical Society
  8. ^Ewald 50 Years of X-Ray Diffraction Chapter 4, pp. 37-42.
  9. ^Jungnickel, Volume 2, 1990, pp. 284-285.
  10. ^Both Hilbert and Minkowski, then at Göttingen, had gotten their doctorates under Ferdinand von Lindemann at the University of Königsberg, as had Sommerfeld.
  11. ^Reid Courant, 1996, p. 43.
  12. ^Reid Hilbert, 1996, pp. 129-133.
  13. ^Greenspan, 2005, p. 53.
  14. ^BohrArchived 2007-07-04 at the Wayback Machine. - On the Constitution of Atoms and Molecules
  15. ^Paul Peter Ewald Bericht über die Tagung der British Association in Birmingham, Phys. Zs.14 1298-1307 (1913). Received 19 October 1913. – Paper cited in: Mehra, Volume 1, Part 1, p. 202 and Mehra, Volume 1, Part 2, 2001, p. 770.
  16. ^Mehra, Volume 5, Part 1, 2001, p. 249.
  17. ^Ewald 50 Years of X-Ray Diffraction Chapter 20, p. 456-457.
  18. ^Paul Peter Ewald Die Berechnung optischer und elektrostatischer Gitterpotentiale, Ann. Phys.64 253-287 (1921), as cited in Ewald – University of Pennsylvania.
  19. ^Paul Peter Ewald Zur Begründung der Kristalloptik. Teil I, Ann. Phys.49 1-38 (1916), as cited in Ewald – University of Pennsylvania.
  20. ^Paul Peter Ewald Zur Begründung der Kristalloptik. Teil II, Ann. Phys.49 117-143 (1916), as cited in Ewald – University of Pennsylvania.
  21. ^Paul Peter Ewald Zur Begründung der Kristalloptik. Teil III, Ann. Phys.54 519-597 (1917), as cited in Ewald – University of Pennsylvania.
  22. ^Jungnickel, Volume 2, 1990, p. 284, quoting from references given in Footnote 100 on the page.
  23. ^Max Born and Kun Huang Dynamical Theory of Crystal Lattices (Oxford, Clarendon Press, 1954)
  24. ^Ewald – University of Pennsylvania.
  25. ^EwaldArchived 2007-02-20 at the Wayback Machine. – ITAP University of Stuttgart.
  26. ^Ewald 50 Years of X-Ray Diffraction Chapter 20, p. 460.
  27. ^ abcEwald – IURC. Stuttgart honors Ewald.
  28. ^EwaldArchived 2005-11-03 at the Wayback Machine. – University of Stuttgart
  29. ^ abcEwaldArchived 2007-02-20 at the Wayback Machine. – ITAP University of Stuttgart
  30. ^Richard Courant and David Hilbert Methoden der mathematischen Physik I (Springer, 1968) ISBN 978-3-540-04177-1 [English translation: Richard Courant and David Hilbert Volume 1, Methods of Mathematical Physics (Wiley-Interscience, 1989) ISBN 978-0-471-50447-4].
  31. ^Paul Peter Ewald Ein Buch über mathematische Physik: Courant-Hilbert, Naturwiss.13 384-387 (1925). This article was published in the 1 May 1925 issue. – This reference cited in: Mehra, Volume 5, Part 2, 2001, pp. 582-583 and 897.
  32. ^EwaldkugleArchived 2005-11-03 at the Wayback Machine.
  33. ^Vol. I: Strukturbericht 1913-1928, P. P. Ewald and C. Hermann, editors (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931). After 1939, the reports were published in the United States under the name Structure Reports. See Strukturbericht.
  34. ^Adolf Hitler had become Chancellor on January 30, 1933.
  35. ^The Dozentenbund was an association of National Socialist lecturers at Stuttgart.
  36. ^Ulrich Dehlinger succeeded Ewald.
  37. ^Hans Bethe – New York Times
  38. ^Sommerfeld, Volume I, 1964, pp. v-vii.
  39. ^ abEwald Prize – IUCr


  • Ewald, P. P., editor 50 Years of X-Ray Diffraction (Reprinted in pdf format for the IUCr XVIII Congress, Glasgow, Scotland, Copyright © 1962, 1999 International Union of Crystallography)
  • Greenspan, Nancy Thorndike End of the Certain World: The Life and Science of Max Born. The Nobel Physicist Who Ignited the Quantum Revolution. (Basic Books, 2005) ISBN 0-7382-0693-8
  • Jungnickel, Christa and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925. University of Chicago Press, Paper cover, 1990. ISBN 0-226-41585-6
  • Mehra, Jagdish, and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 1 Part 1 The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld 1900–1925: Its Foundation and the Rise of Its Difficulties. (Springer, 2001) ISBN 0-387-95174-1
  • Mehra, Jagdish, and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 1 Part 2 The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld 1900–1925: Its Foundation and the Rise of Its Difficulties. (Springer, 2001) ISBN 0-387-95175-X
  • Mehra, Jagdish, and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 5 Erwin Schrödinger and the Rise of Wave Mechanics. Part 1 Schrödinger in Vienna and Zurich 1887-1925. (Springer, 2001) ISBN 0-387-95179-2
  • Mehra, Jagdish, and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 5 Erwin Schrödinger and the Rise of Wave Mechanics. Part 2 The Creation of Wave Mechanics: Early Response and Applications 1925 - 1926. (Springer, 2001) ISBN 0-387-95180-6
  • Reid, Constance Courant (Springer, 1996) ISBN 0-387-94670-5
  • Reid, Constance Hilbert (Springer, 1996) ISBN 0-387-94674-8
  • Sommerfeld, Arnold, translated from the fourth German edition by Martin O. Stern Mechanics - Lectures on Theoretical Physics Volume I (Academic Press, 1964)
  • S.G. Podorov, A. Nazarkin, "Wide-Angle X-Ray Diffraction Theory Versus Classical Dynamical Theory" - Recent Res. Devel. Optics, 7 (2009) ISBN 978-81-308-0370-8

External links[edit]

Extract from 50 Years of X-ray Diffraction, edited by P. P. Ewald


Laue's Discovery of X-ray Diffraction by Crystals

4.1. Physics and Crystallography at the University of Munich in 1912

The University of Munich prided itself upon having the chairs occupied by eminent professors, well known beyond the confines of the city and of Germany. In 1912 some of the celebrities were H. Wölfflin for History of Art, L. Brentano for Economics, Amira for History, O. Hertwig for Zoology, P. Groth for Mineralogy and Crystallography, W. C. Röntgen for Experimental Physics and A. Sommerfeld for Theoretical Physics. The last three are of particular interest for our subject and may therefore be characterized in some detail. Each was head of an Institute with Assistants, Lecturers (Privatdozenten) or Assistant Professors (a.o. [= ausserordentlicher] Professor) and other staff attached to it.

a. Rõntgen's Institute was by far the largest of the three and was situated in a separate three-storey building in the main block of University buildings between the Ludwigstrasse and the Amalienstrasse. Besides the science students, the numerous medical students were supposed to go to Röntgen's lecture course and first-year laboratory and this demanded a large number of assistants and lecturers. P. P. Koch was already mentioned above, and E. Wagner will be mentioned later. E. von Angerer, who later became Professor at the Technical University in Munich and is well known as the author of several very useful books on the techniques of physical experimentation, was a third assistant. Röntgen had some 12-15 doctorands who were being looked after by the assistants and himself. As a 'doctor-father' Röntgen was, as in his own work, very exacting and 3-4 years full-time work on the thesis was not unusual. He demanded all possible precautions to be taken against errors and wrong interpretations and the maximum of accuracy to be obtained.

After his appointment to the chair of experimental physics of Munich University in 1900 Röntgen naturally maintained his interest in the clarification of the nature of his X-rays, and among the topics given out by him for thesis work there was usually an important one on X-rays :

  • E. v. Angerer (1905): Bolometric (absolute) energy measurement of X-rays.
  • E. Bassler (1907): Polarization of X-rays.
  • W. Friedrich (1911): Emission by a platinum target.
  • R. Glocker (1914): Study of interference.

Much of Röntgen's own work was spent on the electrical conductivity generated by X-ray irradiation in calcite (published 1907) and in other crystals. The greater part of this painstaking work was done together with A. Joffé, who had come to him after his graduation at the St. Petersburg Technological Institute in 1902, obtained his Ph. D. under Röntgen in 1905, and stayed with him for another year as assistant. It was, however, not before 1913 and 1921, respectively, that Röntgen felt satisfied with the checking of the measurements so as to release them for publication.

That a wide field of interest was covered by the work in Röntgen's institute is obvious to physicists from a list of a few others of the 25 doctorands graduating while Röntgen was director from 1900-22 :

  • P. P. Koch (1901);
  • J. Wallot (1902);
  • A. Bestelmeyer (1902);
  • E. Wagner (1903);
  • R. Ladenburg (1906);
  • P. Pringsheim (1906);
  • P. Knipping (1913);
  • J. Brentano (1914);
  • R. Glocker (1914).

Because of the exceptionally high demands, graduation under Röntgen was attempted only by highly devoted and serious students. They were expected to work independently, and even too much communication from door to door in the institute was not encouraged.

b. Sommerfeld's much smaller Institute for Theoretical Physics was an academic novelty. Sommerfeld had insisted on it before accepting the chair of theoretical physics in Munich which had been vacant for four years following L. Boltzmann's departure to Vienna. It had not been quite easy to overcome the obvious argument that theory demanded a library, and desks, but no experimental facilities. Sommerfeld, however, succeeded in convincing the faculty and the ministry of the necessity for a theoretician to keep in close touch with physical reality if his work was to obtain purpose and inspiration from physics. In contrast to an Institute of Experimental Physics which is equipped for experimenting in any field of physics, the Theoretical Physics Institute would need only special equipment for supporting experimentally the lines of theoretical research.

At first, Sommerfeld's institute was situated in the 'Old Academy' or 'Augustinerstock' in the Neuhauserstrasse in Munich, where the Bavarian Academy of Arts and Science held its meetings and where also the zoological, geological and mineralogical Institutes of the University were housed. With the completion of the University extension along Amalienstrasse, the Institute moved in 1910 to part of the ground floor and basement there, in close proximity to Röntgen's Institute. It consisted of a small lecture theatre for about 60, a museum room for equipment (containing a.o. the models constructed by Sohncke from cigarboxes for demonstrating his 65 point systems), four offices, and, in the spacious basement, a workshop, a dark room, and four experimental and storage rooms. Apart from the occasional preparations of demonstrations for Sommerfeld's lecture course on Theoretical Physics, the main experimental work set up after the move to the new premises was an experimental investigation on the onset of turbulence in fluid motion in an open channel; Sommerfeld had been long interested in the problems of turbulence, and this particular work was performed by his doctorand Ludwig Hopf. In 1911, Sommerfeld appointed W. Friedrich as second assistant in order to make further experimental checks on the theory of X-rays, as mentioned above.

Up to then there had been only one assistant at the Institute, P, Debye, whom Sommerfeld had taken with him from Aachen to Munich, when he accepted the chair. Needless to say to those who know of his later development, Debye was, even then, an outstanding physicist, mathematician and helpful friend. He was, not less than Sommerfeld himself, a centre for the senior students and graduates frequenting the Institute and the Physics Colloquium. Of these about ten were actually working on theoretical subjects under Sommerfeld's guidance, while others, from Röntgen's and other institutes came in for occasional discussions of their problems. Even more efficiently and informally than at the Institute an exchange of views and seminar-like consultation on any subject connected with physics took place in the Café Lutz in the Hofgarten, when the weather permitted under the shade of the chestnut trees, and otherwise indoors. This was the general rallying point of physicists after lunch for a cup of coffee and the tempting cakes. Once these were consumed, the conversation which might until then have dealt with some problem in general terms, could at once be followed up with diagrams and calculations performed with pencil on the white smooth marble tops of the Café's tables - much to the dislike of the waitresses who had to scrub the tables clean afterwards. Sommerfeld and his friend R. Emden (Professor at the Technical University and well known for his pioneer work on stellar atmospheres) and also others like the mathematicians Herglotz, Carathéodory, Schoenflies when they happened to be in Munich, came to this unofficial centre of exchange of physical ideas and news. For the younger members of the group it was most exciting to watch research in the making, and to take sides in the first tentative formulation of experiments and theory. No need to say that Röntgen never came to this informal meeting - nor even to the regularly scheduled Physics Colloquium; he was dominated by a shyness that made him evade personal contacts wherever he could.

In the fall of 1909 Laue joined Sommerfeld's group. He was a pupil of Planck and had obtained his degree in Berlin. After two post-doctoral years in Göttingen he returned as assistant of Planck's to Berlin and became lecturer there for two years. He was Planck's favorite disciple, but for some personal or other reason he asked for being transferred to Munich University and this was arranged. Unmarried, and devoted to Physics as he was, he soon became a leading member in all the group's activities. His interests covered the whole of physics; he wrote the first monograph on the (special) Theory of Relativity, brought from his association with Planck a deep understanding of thermodynamics and the theory of radiation and had done some profound thinking on Optics. Sommerfeld was the editor of Volume 5 of the Enzyklopaedie der mathematischen Wissenschaften which dealt with Physics and contained many very important semi-original contributions such as those by H. A. Lorentz on the Theory of Electrons, by L. Boltzmann on Kinetic Theory of Gases, by Van der Waals on the Equation of State, etc. Laue, having finished his book on Relativity, agreed to write the chapter on Wave-optics, and set to work in 1911. This was also the year that he got married to a very charming and good-looking young girl coming from a Bavarian officer's family. They established themselves in the Bismarckstrasse and kept open house for the younger members of the Physics group.

c. As mentioned above, Groth's Institute for Mineralogy and Mineral Sites was in an old building near the centre of the city. This, originally an Augustine convent, had been taken over by the State during the period of secularization and had housed the Academy of Sciences and the Academy of Fine Arts. The latter obtained a handsome new building of its own at the end of Amalienstrasse, close to the main buildings of the University - see Gottfried Keller's description of its inauguration in Der Grüne Heinrich - whereupon the University, in great need of expanding, was given the vacated premises for some of its Institutes. On entering from the street one passed through a high hall and past covered stairways where the mail coaches formerly discharged their passengers, came to a large quadrangle and mounted on another broad flat stairway to Groth's institute. The balustrade, the stucco ornamentation of the walls, and the high double winged doors showed the typical 'Jesuit Style' of the first half of the eighteenth century. On passing through two very long and very high rooms where the practical classes of crystallography were held, one finally reached the door of the Geheimrat's room. After knocking and being asked inside the visitor would be confronted with a rather picturesque view. Except on the side where the tall windows admitted a flood of light and offered a fine view of roofs and parts of the old buildings near Munich's ancient cathedral, the Frauenkirche, all walls of the room were lined with Jesuit style, glass-fronted, high cases filled to the top with books, journals, manuscripts and occasional crystals. Two or three large tables stood in the room piled up with books, manuscripts, galley proofs and an odd goniometer, Bunsen burner and chemical glassware squeezed in among them. At the wall opposite to where the visitor entered he would finally detect the old-fashioned desk with a small worthy old gentleman facing the wall and turning his back to the visitor while eagerly entering the end of a sentence in a manuscript or a correction in a galley proof. This was the Geheimrat, P. von Groth, then in his early seventies. Once he was summoned from his work, Groth seemed eager to learn all the news his visitor could give him, both personal and scientific. But he was also willing to contribute to the conversation by reminiscing on his own experiences, or conversations he had had, or by offering his advice on problems about which he was consulted. His lively speech, with a strong Saxon intonation, belied his age and made the student lose the sense of distance - in strong contrast to what he felt in talking to Röntgen.

Groth's first great achievement was the classification of minerals according to chemical relationship and simultaneous occurrence in sites. The principles by which he re-arranged the mineralogical collection of the University of Strassburg, while he was professor there, was widely acclaimed. He insisted on including in crystallography not only the naturally occurring minerals, but artificially prepared chemical compounds as well, and in particular he fought for the wide introduction of crystallographic methods in organic chemistry. In order to facilitate this, he wrote a much used textbook Physikalische Kristallographie. In 1877 he founded the first Journal of Crystallography and Mineralogy, omitting from it Geology, Petrography and Palaeontology which at that time were often combined with the first two subjects. His personal relations to crystallographers and mineralogists all over the world were widespread, through correspondence, his own travels, and visits of foreign colleagues of shorter or longer duration to his laboratory. This personal contact as well as the large amount of active work he devoted to the Zeitschrift für Kristallographie und Mineralogie was the reason for his Journal's international success. Groth edited 55 volumes, from 1877 to 1920; only after the Zeitschrift had been firmly established by his work as the leading journal for Crystallography, and only after Crystallography itself had acquired a  new depth through Laue's and the Braggs' work, was it possible to devote the Zeitschrift entirely to Crystallography, leaving the mineralogical part to be absorbed by a number of existing journals of mineralogy.

Groth's most stupendous work was the Chemische Kristallographie


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