Barlow, William

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Barlow, William

(b. Islington, London, England, 8 August 1845; d. Great Stanmore, Middlesex, England, 28 February 1934)


Barlow, a privately educated genius, was perhaps one of the last great amateurs in science. It was only when he was in his early thirties, however, after he attained the leisure afforded by an inheritance from his father, that he began to study and work in crystallography. His original view of the nature of crystalline matter united the mathematical system of symmetry, for which he wrote his own final chapter in the 1890’s with an anticipation of the new determinations of atomic structure that were to follow after 1910, and also with certain speculations on the relation of symmetry to structure that have not yet been fully elucidated.

The nineteenth century saw a succession of researches into the reason for the order exhibited by crystals. It was a search joined not only by mineralogists from C.S. Weiss to E.S. Fedorov, but also by mathematicians, notably Auguste Bravais, Louis Jordan, and Artur Schönflies.

Barlow’s theories of the properties of crystals were based on the close packing of atoms. His first paper (1883) in some respects marked no great departure from earlier theories—some dating from the time of Kepler—in which a crystal was regarded as resembling an orderly stack of cannonballs. Barlow was probably unaware of these earlier theories, for by his time a considerable body of chemical theory emphasized the association of atoms into the molecular groupings of compounds. Nearly all of the twoelement crystals that Barlow knew, principally the alkali halides, formed cubic crystals, whatever their chemical composition. As he stated in his introductory sentence of “Probable Nature of the Internal Symmetry of Crystals” (p.186), this “...led him to believe that in the atom-groupings which modern chemistry reveals to us the several atoms occupy distinct portions of space and do not lose their individuality.” Thus, by treating the atoms as individual spheres, Barlow was able to stack them in five arrangements1 that he considered to be the only “very symmetrical” ones; these correspond to structures known today as body-centered cubic, simple cubic, face-centered cubic (cubic closest-packed), bodycentered hexagonal (hexagonal closest-packed), and one kind of double hexagonal (but not closest-packed). Leonhard sohncke criticized Barlow for including the last structure, claiming that it did not fulfill a strict definition of homogeneous symmetry around each sphere (the spheres in alternate layers are surrounded by different configurations). In this Sohncke was correct, but Barlow here showed for the first time that not all the atoms in a symmetrical structure need correspond to a single set of symmetrically equivalent points.

In his first paper, Barlow also recognized that body-centered cubic and simple cubic structures admit packing of spheres of two kinds (but of equal size), and are therefore suited to be structures of the alkali halides. Not until his definitive paper on structure, read before the Royal Society of Dublin in 1897, did Barlow explicitly display the variations possible in making the two kinds of spheres of two corresponding sizes. This was a correct guess for the structure of alkali halides, and through Barlow’s collaboration with W.J. Pope, later professor of chemistry at Manchester, this structure was suggested by Pope to W.L. Bragg, who in 1913 confirmed it with the first structure determination by X-ray diffraction.

Barlow also suggested that face-centered cubic and body-centered hexagonal structures admitted of two kinds of spheres in the ratio 2:1, and ascribed the latter structure first to ice (wrong!) and then to calcite and aragonite only by writing the composition CaC2O3 = Ca2Co3(worse!).2 In this paper he also tentatively introduced the idea that while a structure might be nearly close-packed, slight changes of the groupings might be important for symmetry. His proposed structure for quartz was not borne out by X-ray diffraction, because quartz is not in the class of crystals that approximate close-packing. But he was on the right track when he used his hypothesis to explain the circular polarization in quartz, recognizing that a spiral of atoms could be left-handed or righthanded in similar structures. This was characteristic of Barlow’s approach; he attempted to explain the widest range of crystal phenomena with his structures: cleavage, such polar properties as pyroelectricity, varieties of crystal growth, solid solution, and chemical reactivity. Most of those explanations were in principle correct, if not entirely original, and contributed to the unraveling of crystal physics in the ensuing thirty years.

Today it is clear that only a small fraction of crystalline species can be regarded as close-packed; most, but not all, are elements or simple compounds of dominantly ionic bonding. But many more crystals are nearly close-packed with interatomic distances and angles slightly deformed by covalent bonding. Barlow saw clearly that deformation of his “root forms” was necessary, and ascribed it to an unequal contraction of interatomic distances during crystallization from a more symmetrical but more loosely packed liquid. This led to the important concept of what is today known as pseudosymmetry, which Barlow used as a structural explanation of twinning, polymorphism, oriented overgrowth, and anomalous birefringence in crystals. Similar ideas were developed by E.S. Fedorov and T.V. Barker, between 1900 and 1930, into an elaborate system of “syngony” relating the morphology of crystals to similar but not equivalent angles Although this system has had little direct use, the general basis set out by Barlow is still fundamental to the understanding of these crystal properties.

In his first paper, it seems that Barlow was not aware of symmetry theory beyond the most elementary description of crystal systems. He was brought up short, apparently, by Sohncke’s comments (1884), and a couple of years later took a course in crystallography from H.E. Armstrong and also began associations with H.A. Miers and W.J. Pope. In 1879 Sohncke published his “Entwickelung einer Theorie der Krystallstruktur,” in which he expanded the work of Bravais to sixty-five infinite groups of equivalent points that might be possible in crystals. Since Sohncke confined himself to congruent equivalence, however, he could not explainn the many known crystals with polar symmetry. Barlow realized the importance of this general mathematical approach, and in his usual independent and original fashion he set about fitting it into his models of structure. At the British Association for the Advancement of Science, on 26 August 1891, he “... concludes his paper by referring to some geometrical properties of the symmetrical systems of the crystallographer which he has discovered by an extension of the methods adopted by Bravais and by Sohncke, and which have greatly facilitated his work in finding symmetrical groupings to fit the forms and composition of a variety of different substances” (p.582). For ten years, apparently unknown to Barlow, Fedorov had also been working (and publishing) on the problem of explaining crystal symmetry by systems of points, taking his departure form A.V. Gadolin and including both congruent and mirror-image (enantiomorphous) equivalence. In January 1891, Fedorov had published in Russian his complete derivation of the 230 space groups. Artur Schönflies, professor of applied mathematics at Göttingen, was also pursuing this problem independently, and following an exchange of letters with Fedorov, he published his version of the 230 space groups later in 1891 in the Zeitschrift für Krystallographie. Barlow did not get into print with his own derivation of the 230 space groups until 1894. In answering a criticism of his work that was published in the same journal in 1895, he complained that he did not have access to the original works of Schönflies and Fedorov.3

The differences in method by which the three authors derived the 230 space groups are no longer of much interest—both more elegant and simpler systems have since been published. Barlow was the last of the three to publish, and consequently has had little credit. In contrast with Fedorov and Schönflies, however, Barlow had as his goal nothing less than a total explanation of crystals in terms of structure. His long paper on crystal structure appeared next, in 1897, and incorporated his work with space groups. He could not go further in solving the puzzle without one very important piece of information, however: the size, or at least the relative size, of the atoms. He had at one point assumed, on the model of Rudjer Bošković, that atoms were points with surrounding fields of attraction and repulsion; but the forms of these fields, or the corresponding sizes of the corresponding atoms, were illusory. For the next fifteen years, then, he worked with W.H. Pope in assembling data on solid-solution substitutions and the variation of the morphological axial ratios that should reflect variations in atomic size. While this approach was a valid one, it still contained a minimum ambiguity, which led Pope and Barlow to postulate that ionic volumes were proportional to valency. These papers were published in the Journal of the Chemical Society between 1906 and 1910; after only a few years, results from X-ray diffraction were sufficient to show that volumes of ions were, if anything, related to negative charge. But even in late (7 December) 1916 Barlow was still inclined to say, in a letter to G.F. Herbert Smith of the British Museum (Natural History), “...I regard the Paper in the Philosophical Magazine, so far as it relates to the Law of Valency Volumes, as a ʿmare’s nestʾ indeed feel confident that the x-ray results instead of weakening will greatly strengthen the case for the Law of Valency Volumes” (letter in files of the Mineralogical Laboratory).

Barlow was elected to the Royal Society in 1908 and was president of the Mineralogical Society in 1915–1918. His career spanned a critical stage in the development of crystallography. His self-educated guesses were sometimes off the mark, but often clear and to the point, and always provocative. In his obituary of Barlow, Pope says:

Although X-ray analysis has increased our knowledge of crystal structure in an astounding way and has proved a most useful tool, it has not led to a mechanical theory of crystal structure; it reveals the atomic arrangement but offers no reason why the component atoms seem to be closely packed in some crystalline structures and often loosely in others. The required mechanical theory of crystal structure may be found in some kind of generalisation of Barlow’s conception of equilibrium conditions [Journal of the Chemical society, p. 1330].


1. A sixth close-packed structure was added in his second paper (1886).

2. Corrected in his second paper, wherepacking of three kinds of atoms (still all the same size) was discussed.

3. “Meine einzige Quelle zur Zeit der Abfassung meiner Abhandlung war der Auszug von Fedorow’s Arbeit in dieser Zeitschr. 20 , 25, und dieser bot mit durch seine Kürze gewisse Schwierigkeiten dar. Was schoenfliesʾ Darstellung betrifft, so konnte ich sie damals nur aus zweiter Hand erehalten, und hierdurch ist es veranlasst, dass ich Demselben einen Ausdruck zuschreib, welchen er nicht gebraucht hat...” Yet Barlow’s 1894 paper quotes Schönfliesʾ book, citing page numbers, as well as Fedorov’s discussion of SChönflies, which appeared in Zeitschrift für Krystallographie, 20 (1892), 25–75.


1. Original Works. Barlow’s most important publications appeared in journals. Inasmuch as a proper bibliography has never been published, the main papers are listed here, in three groups.

(1)Papers on crystal structure and physical properties: The most important is “A Mechanical Cause of Homogeneity of structure and symmetry Geometrically Investigated; With Special application to Crystals and to Chemical Combination,” in Sciencific Proceedings of the Royal Society of Dublin, 8 (1897), 527–690, still in print in 1958. The earlier papers are “Probable Nature of the Internal Symmetry of Crystals,” in Nature29 (1883–1884), 186–188, 205–207, 404; “A Theory of the Connection Between the Crystal Form fand the atoim Composition of chemical compounds,” in Chemical News, 53 (1886), 3–6, 16–19, abstracted in Report of the British Association for the Advancement of Science (1885), 983–984; “On Atomgrouping in Crystals,” ibid., (1890), 754–755; and “On the Connection Between the Crystal Form and the Chemical Composition of Bodies. The Symmetry of Crystals accounted for by the Application of Bosecovich’s Theory of Atoms to the Atoms of the Chemist,” ibid., sec. A(1891), 581–582.

(2) Papers on space groups and other aspects of symmetry: The principal work is “Ueber die geometrischen Eigenschaften homogener starrer Structuren und ihre Anwendung auf Krystalle,” in Zeitschrift für Krystallographie, 23 (1894), 1–63. Other discussions are “The Relation Between the Morphological Symmetry and the Optical Symmetry of Crystals,” in Report of the British Association for the advancement of science(1895), 617–619; “The Relations of Circular Polarization, as Occurring Both in the Amorphous and Crystalline states, to the Symmetry and Partitioning of Homogeneous Structures, i.e., of Crystals,” in Philosophical Magazine, 43 (1897), 110–117; “Nachtrag zu den Tabellen homogener Structuren und Bemerkungen zu E. von Fedorow’s Abhandlung über regelmassige Punktsystme,” in Zeitschrift für Krystallographie, 25 (1896), 86–91; “On Homogeneous Structures and the Symmetrical Partitioning of Them, With Application to Crystals,” in Mineralogical Magazine, 11 (1896), 119–136; and “Partitioning of Space Into enantiomorphous Polyhedra,” in Philosophical magazine, 46 (1923), 930–956. In collaboration with H. A. Miers and G.F.H. Smith, Barlow published a critical-historical review of the symmetry and structure of crystals, “The structure of Crystals: Part I. Report on the Development of the Geometrical Theories of Crystal structure, 1666–1901,” in British association for the advancement of Science, Glasgow Meeting, Sec. C (1902). Part II was to deal with what Barlow calls the mechanical theory of structure, but it was never prepared. The modern reader will need a guide to the diverse nomenclaure used buy the various authors dealing with space groups at this time. A concordance is H. Hilton, “A Comparison of various Notations employed in ‘Theories of crystal structure,’” in Philosophical Magazine, 6th ser., 3 (1902), 203–212; this includes the Schönflies notation, which in turn may be compared with the HermannMauguin notation in the modern International Tables for X-ray crystallography, I(Birmingham, 1952), 545.

(3)Papers on the valency-volume theory: With W.J. Pope, Barlow wrote “A Development of the Atomic Theory Which Correlates Chemical and crystalline structure and Leads to a Demonstration of the Nature of Valency,” in Journal of the Chemical society, 89 (1906), 1675–1774, and, with other titles, 91 (1907), 1150–1214; 93 (1908), 1528; 97 (1910), 2308–2388. By himself he wrote “Crystallographic Relations of Allied Substances Traced by Means of the Law of Valency Volumes,” in Mineralogical Magazine, 13 (1916), 314–323.

Barlow also published a book, New Theories of Matter and of Force (London, 1885), but it apparently did not have much circulation or impact, for it was never cited, even by Barlow. It detailed his speculations on the nature Of the ether, chemical elements, electricity, and the subjects; these preceded his work in crystallography but were not particularly pertinent to it.

The British Museum (Natural History) has several models of crystal structure made by Barlow, and a few of his letters, but otherwise his papers and MSS do not appear to have been preserved.

II. Secondary Literature. Commentaries on specific papers of Barlow’s were published by Sohncke, Lord Kelvin. Sollas, and Federov, among others. He is mentioned briefly in most histories of crystallography. Obituary notices are W.J. Pope, in Journal of the Chemical society (1935), 1328–1330; in Nature, 133 (1934), 637–638; and in Obituary Notices of Fellows of the Royal society, 1 (1935), 367–370. with portrait; G.F.H. Smith, in Quarterly Journal of the Geological Society of London, 91 (1935), lxxxv-lxxxvi; and L.J. Spencer, in Mineraqlogicai Magazine, 24 (1936). 277–279. See also G.T. Moody and W. Mills’s obituary of w.J. Pope, in Journal of the Chemical Society (1940). 697–715.

William T. Holser