Fyodorov (or Fedorov), Evgraf Stepanovich

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Fyodorov (or Fedorov), Evgraf Stepanovich

(b. Orenburg, Russia [now Chkalov, U.S.S.R.], 22 December 1853; d. Petrograd [now Leningrad], U.S.S.R., 21 May 1919)

crystallography, geometry, petrography, mineralogy, geology.

His father, Stepan Ivanovich Fyodorov, came from a peasant family and was a major-general in the Engineer Corps. He was noted for the sharpness of his disposition, which he evidently passed on to his son.

Fyodorov’s mother, Yulia Gerasimovna Botvinko, the daughter of a procurator in Vilna, was a progressive and cultured woman. She gave her son the elements of a musical education and, in particular, imparted a love of reading and accustomed him to steady work and discipline. Fyodorov later said that he was wholly indebted to his mother for his exceptional capacity for work. She made him knit large tablecloths with intricate figures, which probably developed his feeling for symmetry.

Fyodorov’s mathematical abilities appeared very early; when he was five, he had already mastered the rules of arithmetic. At the age of seven he studied with fascination and finished in two days a textbook of elementary geometry. In his own words, the content of the first pages of the text evoked “a resonance in my psyche, so that I was literally carried away.” At the age of ten Fyodorov entered the second class of Annensky College. After the death of his father in 1866, the straitened circumstances of his family forced him to transfer to the military Gymnasium, which he could attend at state expense. Here he joined a small group of friends who were studying natural science and philosophy intensively. At the same time Fyodorov independently immersed himself in the mathematical disciplines, which for him were always invested with an aura of special beauty. In 1869 he transferred to the Petersburg Military Engineering School. There he became an active member of an illegal group devoted to self-education, in which, under the influence of the literary critic, Dmitry Pisarev, the works of the materialist natural scientists were studied.

In 1872 Fyodorov graduated and went to Kiev with the rank of second lieutenant in a combat engineering battalion; the following year he returned to St. Petersburg, and in 1874 he retired completely from military service. As a result of his enthusiasm for natural sciences he became a free auditor at the Military Medical and Surgical Academy. Having passed the necessary examinations, Fyodorov entered the second-year course of the Technological Institute, where he concentrated on physics and chemistry. All his thoughts and interests were already directed toward theoretical mathematics, particularly geometry; this made possible the completion of his important monograph, Nachala uchenia o figurakh, which he had begun at the age of sixteen. In it he touched on symmetry and the theory of crystal structure and set forth the principles of contemporary theoretical crystallography. His work on the theory of mathematical polyhedrons brought Fyodorov to questions relating to natural polyhedrons—the crystals of minerals—and to geometric mineralogy.

Because of his enthusiasm for crystallography Fyodorov chose the specialty closest to this science and in 1880, at the age of twenty-seven, he entered the third-year course at the Mining Institute, where a general course in crystallography and related mineralogy was taught. After graduating from the Mining Institute in 1883 (his name was placed at the top of the list carved in marble), Fyodorov joined a Mining Department expedition to investigate the northern Urals.

Fyodorov married Ludmila Vasilievna Panyutina, a vivacious and purposeful girl who had come from Kungur in the Urals to study medicine in St. Petersburg. She selflessly helped him in his scientific and revolutionary work. Fyodorov’s son, Evgraf Evgrafovich, was a specialist in climatology and later a corresponding member of the Soviet Academy of Sciences.

In childhood Fyodorov had been sickly; in his middle years he was extremely robust. He always worked a great deal and was extraordinarily precise in carrying out the life plan he had set for himself. He went on expeditions to the Urals and other regions, distinguishing himself on them because of his great endurance. Fyodorov traveled under conditions of great privation and worked to the point of exhaustion; on expeditions he was sunburned and thin but cheerful and energetic. In his old age he was often ill.

In 1896 Fyodorov was elected a member of the Bavarian Academy of Sciences and in 1901 an adjunct of the Petersburg Academy of Sciences; but, not having received support for his demands for the creation of a mineralogical institute, he withdrew from the Petersburg academy in 1905. He was elected a member of the Soviet Academy of Sciences in 1919, when an institute in which mineralogy occupied an important place was organized.

Revolutionary activity gave meaning to Fyodorov’s life. In 1876 he became a member of the populist Land and Freedom party; the following year he was commissioned to set up connections with revolutionary organizations in France, Belgium, and Germany, a task which he handled well. His apartment in Petersburg contained an underground revolutionary press.

Fyodorov’s scientific and literary work is distinguished for its richness and extraordinary variety. Most numerous among his more than 500 scientific published works are those on crystallography, followed by geometry, mineralogy, petrography, geology, history of science, and philosophy.

Fyodorov devoted forty-three publications to mineralogy, but the only one to deal with the field as a whole is Kritichesky peresmotr form mineralnogo tsarstva (1903), in which the morphology of minerals is examined relative to crystal structure theory. Fyodorov exerted a very strong influence on the development of mineralogy and opened a new stage in it. He also contributed to the accumulation of significant new factual material and helped to change the methodological approach to the study of minerals. He used the analytical approach and attempted to understand natural processes and phenomena by starting from more general mathematical and physicalchemical principles. Through his work Fyodorov laid the foundations for the analytical period in the development of mineralogy.

The foundation of all of Fyodorov’s scientific work was geometry. Among his first works was the monograph Nachala uchenia o figurakh, and his last article treated questions of the new geometry. Geometrical research led Fyodorov to the brilliant derivation of the 230 space groups—the symmetry groups governing the periodic distribution within crystalline matter. The derivation is the foundation of contemporary mineralogy and the basis of the atomic structure of minerals. His first work was an exposition of all those parts of the theory of figures which constitute the basis of contemporary crystallography.

The period of the first geometrical investigations and publications was crowned by the classic work Simmetria pravilnykh sistem figur (1890), which contained the first deduction of the 230 space groups. The publication in 1891 of Schoenflies’ book with his derivation of the 230 space groups prompted Fyodorov to publish several articles in the Zeitschrift für Kristallogrphie. He compared his results with those of Schoenflies and made a series of essential corrections and notations. In these articles he gave a strict mathematical definition of thirty-two point groups for six crystallographic systems, which still retain their significance. At the basis of this classification he placed a number of single and symmetrically equivalent axes in crystals. This classification led to the working out of a new nomenclature of systems and point group symmetries, accepted throughout the world and known as Fyodorov-Groth nomenclature. For these accomplishments, and at the insistence of such eminent crystallographers as Groth and L. Sohncke, Fyodorov was elected a member of the Bavarian Academy of Sciences in 1896. Fyodorov himself considered these works as belonging to the theory of crystallography, specifically to geometric mineralogy. Fyodorov’s group classifications are, with the aid of X-ray diffraction, at the base of modern mineralogical determinations of the atomic structure of minerals.

In the category of physical crystallography are Fyodorov’s works that explain a universal method of optical research, which played an important role in mineralogy and petrography. In 1889, at a session of the Mineralogical Society, Fyodorov reported on his projected two-circle optical goniometer for the measurement of all angles in crystals with a single setting of the specimen. It differed from previous goniometers, which had only a single axis of rotation. (A two-circle goniometer had been proposed earlier by W. H. Miller.) This produced a revolution in the method of investigating minerals. Following Fyodorov and using his idea, Victor Goldschmidt, S. Czapski, Y. Flint, and others designed two-circle goniometers. Crystallographers and mineralogists throughout the world began to work exclusively with these instruments.

In 1891 Fyodorov proposed to the Geological Committee the construction of a universal stage for the petrographic microscope that would locate the specimen at the center of two glass hemispheres. In essence this method is crystallographic, but its application is to mineralogy and petrography. With what became known as the Fyodorov method the optical constants of minerals could be established and, without resorting to chemical analysis, the composition of the isomorphic lime-soda feldspars (plagioclases) was determined, as were those of other minerals.

Of all the instruments constructed and developed by Fyodorov, the universal stage (also called U-stage or Fyodorov table) has enjoyed the greatest popularity. Special courses in its use are given to students of mineralogy and petrography. Handbooks and special studies on the Fyodorov method have been published by Russian and foreign authors: S. N. Nikitin, M. A. Usov, V. S. Sobolev, L. Duparc, M. Reinhard, M. Berek, and others. The Fyodorov method has allowed researchers to carry out quickly the optical study of plagioclases, pyroxenes, and other minerals, using thin sections of rock. The present Fyodorov table is a refined instrument with five axes of rotation, convenient for the study of minerals in any cross section.

In describing Fyodorov’s activity in petrography and mineralogy, it must be noted that he himself never drew a sharp boundary between these sciences. He considered that all the physical, mathematical, and natural sciences were used in them. He also believed that in the cycle of mineralogical and geological sciences one used the totality of knowledge of the earth—which, in his view, is located in infinite, starry space and interacts with it. These ideas are only now being worked out in detail by his followers in the fields of astrogeology and planetology.

Fyodorov gave much attention to the chemical composition of rocks and their graphic representation, and he introduced symbols of chemical composition, petrographic nomenclature, and rock classification. He conducted important research on the northern Urals, the Bogoslovsky (now Sverdlovsk) district, the coast of the White Sea, the Caucasus, and Kazakhstan. He was one of the first to show the great importance of the apatite resources lying in the depths of the Soviet north (1909).

In one of his first scientific works, the tract “Perfektsionizm” (1906), Fyodorov showed that he was a convinced materialist. Starting from the materialistic principle that natural conditions are in essence conditions of eternal change, he attacked authors who teach the theory of stability and equilibrium in nature. The essence of evolution, in his opinion, is not in the tendency toward a higher order, stability, and equilibrium of organisms but in their life movement. Criticizing the outlook of Herbert Spencer and other partisans of equilibrium in nature, Fyodorov showed that the main effect of such points of view when applied to the evolution of natural history was to give attention to the least changeable. But the creators of these systems of philosophy systematically failed to take into account the fact that equilibrium is attained only at the moment of death. As long as life is active, changing forms are developing. For this reason Fyodorov considered deeply erroneous the introduction into natural philosophy of the concept of the constant and the stable as the supreme mission of life. He asserted that life never finally achieves anything but eternally strives to achieve. It was in this that the true philosophy of nature lay for him.

Later, in published statements, Fyodorov defended science against positivism, which, in his view, reduces the significance of mind to simply a mold for the more convenient organization of material gathered by experimentation. Attacking the attempts of positivists and followers of Ernst Mach to disregard the atomic theory, Fyodorov wished to remove all metaphysical errors from contemporary science and to be led by the clear guide of atomic theory, which has produced so many valuable and stunning developments in contemporary theory.

Fyodorov’s work harmoniously combined the achievements of varied fields of science. Mathematics was the basis of Fyodorov’s theory of structure and symmetry of crystals. He was able to combine the methods drawn from mathematical analysis with the older empirical laws of crystallography and the methods of crystallographic research with descriptive mineralogy; he introduced principles of geometry into petrography; he combined chemistry with crystallography, thus creating crystal chemistry; and he introduced the principles of the new geometry into mine surveying. Fyodorov knew how to make generalizations and find simple solutions in the analysis of natural phenomena. His “simple” theodolite method in crystallography and petrography played a role in the history of these sciences no less than the most profound generalizations and theoretical achievements. Fyodorov presented all his scientific conclusions in mathematical form. He asserted that the crown of man’s conscious activity, of man’s intelligence, was the solution of the questions facing him by means of mathematical analysis.

The enormous Tsarstvo kristallov (“The Crystal Kingdom,” 1920) was the fruit of forty years of work by Fyodorov and his colleagues. In it he noted that strongly developed sciences satisfy the spiritual needs of part of mankind and at the same time provide great power to direct the active forces of nature for man’s use, thus forcing nature to serve man to a great degree. Lately it has become clear that special sciences can master nature in some respects and in certain areas of natural phenomena, directing them according to the wishes of man.


I. Original Works. Fyodorov’s writings include “Teodolitny metod v mineralogii i petrografii” (“The Theodolitic Method in Mineralogy and Petrography”), in Trudy Geologicheskogo komiteta, 10 no. 2 (1893), 1–191; “Iz itogov tridtsatipyatiletia” (“From the Results of Thirty-five Years”), in Rech i otchet, chitannye u godichnom sobranii Moskovskogo selskokhozyaistvennago instituta, 26 sentyabrya 1904 g. (“Speech and Report Given at the Annual Meeting of the Moscow Agricultural Institute, 26 September 1904,” Moscow, 1904), pp. 1–15; “Perfektsionizm” (“Perfectionism”), in lzvestiya S. Peterburgskoi biologicheskoi laboratorii, 8 pt. I (1906), 25–65; ibid., pt. 2, 9–67; “Beloe more kak istochnik materiala dlya selskokhozyaystvennoy kultury” (“The White Sea as a Source of Material for Agriculture”), in Izvestiya Moskovskago selskokhozyaistvennago instituta, 1 (1908), 94–97; “Iz rezultatov poezdki v Bogoslovsky okrug letom 1911 g.” (“From the Results of a Trip to the Bogoslov District in the Summer of 1911”), in Zapiski Gornago instituta Imperatritsy Ekateriny II,3 (1912), 340–348; “Tsarstvo kritallov” (“The Crystal Kingdom”), in Zapiski Rossiiskoi akademii nauk, 36 (1920); and Nachala uchenia o figurakh (“Principles of the Theory of Figures,” Leningrad, 1953).

II. Secondary Literature On Fyodorov or his work, see O. M. Ansheles, “100-letie so dnya rozhdenia velikogo russkogo uchenogo E. S. Fyodorova” (“Centenary of the Birth of the Great Russian Scientist E. S. Fyodorov”), in Vestnik Leningradskogo gosudarstvennogo universiteta, no. 1 (1954), 223–226; N. V. Belov, Chetyrnadtsat reshetok Brave i 230 prostranstvennykh grupp simmetrii (“The Fourteen Bravais Lattices and the 230 Three-Dimensional Groups of Symmetries,” Moscow-Leningrad, 1962); N. V. Belov and I. I. shafranovsky, “Rol E. S. Fyodorov v predistorii rentgenostrukturnoy kristallografii ...” (“E.S. Fyodorov’s Role in the Early Development of X-ray Structural Crystallography . . .”), in Zapiski Vsesoyuznogo mineralogicheskogo obshchestva, pt. 91, no. 4 (1962), 465–471; G. B. Boky, “O zakone raspolozhenia atomov v kristallah” (“On the Law of Arrangement of Atoms in Crystals”), no. 5 in the collection Kristallografiya (Leningrad, 1956), pp.25–36; F. Y. Levinson-Lessing, “Neskolko yubileynykh dat v petrografii (v tom chisle ‘Sorokopyatiletie tak nazyvaemogo universalogo, ili fyodorovskogo metoda v petrografii’)” (“Several Jubilee Dates in Petrography [Including the ‘Fortieth Anniversary of the So-called Universal or Fyodorov Method in Petrography’]”), in Priroda (1938), no. 6, 137–144; I. I. Shafranovsky, Evgraf Stepanovich Fyodorov (Moscow-Leningrad, 1963); and N. M. Sokolov, “O mirovozzrenii E. S. Fyodorov” (“On the World View of E. S. Fyodorov”), in Kristallografiya, no. 5 (Leningrad, 1956), pp. 5–23.

A. Meniailov