Broader Impacts of Women in Crystallography - Crystal Growth

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Broader Impacts of Women in Crystallography Bart Kahr Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 13 Aug 2015 Downloaded from http://pubs.acs.org on August 14, 2015

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Crystal Growth & Design

For special virtual issue of Crystal Growth and Design in Honor of Professor Margaret Etter

Broader Impacts of Women in Crystallography Bart Kahr Department of Chemistry and Molecular Design Institute, New York University, 100 Washington Square East, New York City, New York, 10003 USA

ABSTRACT: Women made many early and outstanding contributions to X-ray crystallography at a time when they were excluded from most other branches of physical science. The etiology of this bright spot in the social evolution of science is sought in early childhood education, especially the Froebel kindergarten that was rooted in symmetry and lattice building exercises. This connection is explored through the formative educational experiences of eight crystallographers that are compared with those of eight astronomers. Associations with Froebel's pedagogy are ubiquitous in the biographies of the crystallographers and wholly absent in the biographies of astronomers. Creating a more democratic scientific enterprise requires understanding the mechanisms for increasing the participation of members of unrepresented genders and ethnicities. Some of these mechanisms may be found in history. One of the crystallographers profiled, Isabel Ellie Knaggs (1893-1981), made a major contribution to the X-ray analysis of organic compounds by establishing that carbon atoms in isolated molecules adopt tetrahedral coordination geometries. This determination was a capstone on the stereochemistry of the preceding 50 years. Another scientist, working independently, exclusively claimed this discovery. Thus, while studying the general disenfranchisement of women in science, a particular example not heretofore recognized, came into focus.

INTRODUCTION Some years ago, I was discussing with Jeanne Spielman Rubin (1917-2007), music professor emeritus at Kent State University, the mission of the US National Science Foundation to broaden the participation in science and engineering of students of underrepresented genders and ethnicities. I related that scientists and educators were busily searching for strategies to capture those individuals in the so-called STEM (Science, Technology, Engineering and Mathematics) fields. Jeanne replied more or less this way: "I don't know what all the fuss is about. They did the experiment in the nineteenth century and it worked." Jeanne's comment, its context, and meaning, should have a wider audience. Reaching this

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audience on her behalf is the general motivation for this essay. A more particular impetus is the opportunity to test a hypothesis about the crystallographic workforce that I proposed in this journal more than 10 years ago,1 a hypothesis about STEM education and gender that gives legs to Rubin's claim above, and that is suited to a special issue of Crystal Growth and Design in honor of Professor Margaret (Peggy) Cairns Etter (1943-1992) whose career was reviewed in a celebratory Chemistry of Materials article in 1994.2 I knew Rubin as the author of Intimate Triangle: Architecture of Crystals, Frank Lloyd Wright, and the Froebel Kindergarten,3 one of the last publications of the Polycrystal Book Service, a welcome presence for bibliophiles at meetings of professional crystallographers. From Rubin, I learned about the surprising role of crystallography in the invention of kindergarten in the 19th century, and the rigid crystallographic pedagogy that dominated the early kindergartens. So surprised by this history, and confident that Rubin's research would surprise other crystallographers, I wrote in this journal "Crystal Engineering in Kindergarten,"1 an elaboration of the crystallographic content of the kindergarten as prescribed by its inventor, Friederich Froebel (1782 – 1852). Rubin's thesis is that the crystallographic training of the early kindergartners, grounded in symmetry and lattice building exercises, was the geometrical foundation for the explosion of modernism in the visual arts at the turn of the century. Rubin's scholarship was literally grounded in her home in Canton, Ohio,4 commissioned from Frank Lloyd Wright (1867-1959), one of the 20th Century's most influential architects, and a vocal devotee of Froebel's pedagogy. 5,6 One could say that Rubin lived within a manifestation of the crystallographic training that Wright received from his mother Anna, a Froebel kindergarten teacher. Kindergarten and modernism are drawn together even more tightly by Brosterman in Inventing Kindergarten, 7 a comparison of art of 19th-century Froebel kindergartners and acknowledged masters of abstraction including Bart van der Leck (1876-1958), Piet Mondrian (1877-1944), Paul Klee (1879-1940), and Josef Albers (1888-1976). Even a trained eye struggles to distinguish the art of the small children from that of the celebrated adults. Many other pioneering modern artists were deeply indebted to Froebel including Johannes Itten (18881967), a Froebel kindergarten teacher and proponent of the Bauhaus design ethic, as well as Wassily Kandinsky (1866-1944), Theo van Doesburg (18831931), and Le Corbusier (1887-1965).3,7 In our 2004 essay, mindful of the fact that the discovery of X-ray analysis of crystals was a revolution in the architecture of matter coincident with the demise of representation in the visual arts, I asked the following questions: If many of the pioneering artists had their geometric sensibilities inculcated in Froebel kindergartens, it is likely that many of the pioneering X-ray crystallographers had a similar experience. Did the crystallographic content of late nineteenth century kindergarten play a role in the explosion of research into the architecture of crystals? In other words, did the crystallographic content of kindergarten influence the future development of crystallography? Such an investigation would require a


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collection of early childhood biographies of the pioneers of X-ray crystallography.1

If kindergarten crystallography can affect the arts, surely it can affect the sciences. I speculated more particularly: It has often been observed that X-ray crystallography was unique in the physical sciences in the proportion of women among its greatest contributors...Is it possible that many girls were exposed to crystallography in kindergarten, before being systemically shut out of study of the natural sciences by conventional schooling biases?1

I implied that pioneering female X-ray crystallographers may have rediscovered crystallography as adults, long after having unknowingly adopted crystallography as parts of their identities in kindergarten. Crystallography became a branch of science to which they gravitated as mature students, even in the absence of encouragement to do so. I did not pursue these questions, wary that it might not be easy to establish much about the early educations of the female crystallographers, few known outside the profession. I hoped to inspire someone else to look more closely at the link between early Froebel kindergarten education and women in crystallography as many scholars are now actively studying the roles, or lack thereof, of women in science. This has not happened to the best of our knowledge so I take the opportunity here in this celebration of Peggy Etter.

BROADER IMPACTS The US National Science Foundation (NSF) aspires to create a scientific workforce that better represents the American population. Activities that support this democratic goal are said to have "Broader Impacts" because they align science and engineering activities with "societal goals". 8 , 9 The NSF is not proscriptive about how its grantees should actualize the goals of society. It leaves room for the input and invention of individual investigators. But, we can and should ask more often than we do: What are the best ways -- the evidencebased methods -- for increasing the participation of members of underrepresented groups in activities with which they would not otherwise likely engage? Psychologists and sociologists have wrestled with these questions and we should know what wisdom they distilled in the process. Some of what has been discovered has pushed its way out of the specialized social science literature, particularly in the intellectual memoir of Steele 10 who explores the consequences of identity contingencies that certain subgroups of people carry into academic settings.11,12,13,14 ,15 For instance, there is a widely held prejudice that girls are poor at math. If we remind girls in advance of a math exam that they carry this identity-linked expectation, they will indeed perform poorly. In the absence of this trigger of a so-called stereotype threat, girls' performance is the equal of boys'.


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The research cited above emphasized that sustained achievement in a field filled with obstacles both intrinsic to the discipline in question, and extrinsic from prejudicial expectations of others, requires identification with the discipline. The cultivation of an identity associated with STEM fields is the counterweight required to overcome stereotype threats, malicious or otherwise, that are part of the fabric of any culture made up of people of distinct groups with differences in perceived characteristics. People will fight to maintain those qualities they adopt as parts of their identities. When the going gets tough, forces are marshaled to preserve our psyches as we have constructed them. This power can be harnessed for positive social change -- increasing the representation of the underrepresented in STEM fields. (On the other hand, there can also be too much of a good thing: Witness the slaughter of human beings in order to preserve national or religious identities, or less catastrophic, the snobbery that accompanies association with one academic discipline over another, or even one academic sub-discipline over another, as in chemistry.) While most of the professional literature has focused on stereotype threats experienced by college-age students readily evaluated by university professors, there is an increasing realization that younger students are sophisticated enough to be cowed by the contingencies of identity. Researchers observed a surprising difference in math performance in Asian girls, ages five to seven in Boston.16 Subjects asked to color a picture of a girl holding a doll before taking a math evaluation performed measurably worse than a comparable cohort who had been asked to color a picture of a landscape. A reminder to a student of how she tends to be perceived, subtly transmitted through the coloring exercise, is enough to trigger the anxiety of stereotype threat and compromise test scores.17 Something similar was observed in ten-year-old Italian girls.18 By citing the literature on stereotype threats, I do not want to give the impression that the imbalance in representation in STEM fields can be fixed once girls or other underrepresented groups shoulder the responsibility of "fixing" their psychologies. There are broader socioeconomic issues at work. Nevertheless, well-crafted experiments show that girls as young as five can perceive and respond to the limiting contingencies of their gender. Given this truth, where better than kindergarten to instill an identity linked with science and mathematics that can serve to counteract the negative consequence of prejudice? This is what Friederich Froebel achieved, according to Jeanne Spielman Rubin.

THE FROEBEL KINDERGARTEN Friederich Froebel was born in the Thuringian forest in the central part of what is modern Germany. As a young man, he struggled to receive an education and "changed his major" many times. Sporadically, he took courses in botany, chemistry, physics, mathematics, mineralogy, languages, and land surveying. To


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make ends meet, he worked as a teacher and fell under the influence of Johann Pestalozzi (1746-1827) who practiced active learning. Today, we might call Pestalozzi a pioneer of the "flipped classroom." Froebel volunteered to help the Royal Prussian Army defeat Napoleon, after which, through the influence of friends, he was apprenticed to Christian Samuel Weiss (1780-1856), creator of the concept of the crystallographic system,19 in the Mineralogical Museum at the University of Berlin. During this period, Froebel's interests coalesced around the science of crystals. Froebel writes, After the war of the spring of 1813 had interrupted my studies I returned to Berlin in 1814 to resume them and take up a scientific post. My work was to classify and partly to research into crystals. I worked under Weiss as an assistant at the mineralogical museum of the university. I had then attained my aim; for me now theory and its application, life, Nature and mathematics were all to be studied in a single formation, the crystal... It had long been my dearest wish to devote myself to an academic career, for I thought to find in it my vocation, the meaning of my life. But the opportunity to get to know students and see their slight knowledge of the subject, their small feeling for it, and still more their lack of any true scientific spirit made me go back on my purpose...I began to think earnestly again about education and teaching. Therefore, I stayed in my post only for two years, but meanwhile the stones in my hand and under my eyes became forms of life which spoke a language I understood. The world of crystals clearly proclaimed the structure of man’s life to me and spoke of the real life of his world.20

Under Weiss, Froebel experienced a consequential convergence of themes that up until this time ran independently through his peripatetic life. While engaged in cataloging minerals, Froebel recalled, I continually proved to be true what had long been a presentiment with me, namely, that even in these so-called lifeless stones and fragments of rock, torn from their original bed, there lay germs of transforming, developing energy and activity. Amidst the diversity of forms around me, I recognized under all kinds of various modifications one law of development...And thereafter, my rocks and crystals served me as a mirror wherein I might descry mankind, and man’s development and history...Geology and crystallography not only opened up for me a higher circle of knowledge and insight, but also showed me a higher goal for my inquiry, my speculation, and my endeavor.21

“The simplest forms," said Froebel, "which lie at the foundation of the fabric of the world, lay also the foundation in the minds of children for the understanding of the world...These simplest and unarticulated forms are the fundamental forms of crystallization.” 22 An educational philosophy was born from crystal polyhedra. According to one biographer, "Throughout [Froebel's] writings the argument of analogy between the human and the crystalline worlds is to be found, and the distinctive feature of his version of the philosophy of Nature is its presentation in crystallographic and mathematical terms.23 "It is intended", wrote Froebel,


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that man should recognize Nature in her multiplicity of form and shape, and also that he should understand her modes of being and come to a realization of her unity. So in his own development he follows the course of Nature and imitates her modes of creation in his games. He likes to build and to imitate the structuring of form which we find in Nature's first activity, the formation of crystals.24

In 1816, Froebel declined a professorship of mineralogy in Stockholm so that rather he could guide children in an exploration of "Nature's first activity," crystallization. Froebel articulated his educational philosophy in 1826,22 opened his first school in 1831, and created what we now know as "kindergarten" in 1837. Kindergarten became an international movement and spread rapidly through Europe, North America, and parts of Asia.7, 25 The Froebel kindergarten in the first generations focused instruction of girls and boys on 20 so called "gifts", geometric crafts and activities through which children were intended to develop an “inner connection” with the symmetric structures and periodic lattices of his/her construction. For fuller discussions of the gifts see my 2004 summary,1 the contemporary accounts of Rubin3 and Brosterman,7 or an old kindergarten manual.26 Here, I closely examine only the fifth gift, a cube of cubes (Figure 1). Of the 27 sub-cubes, three are halved, diagonally, and three are quartered along two diagonals. Kindergartners were instructed to exhaustively investigate the symmetrical arrangements that could be achieved with the blocks in aggregate. 4m-symmetric arrangements are illustrated in Figure 1. After arranging the components in the plat in the upper right labeled "110", students were instructed by the teacher, Any of the cubes may be changed in its position except the central cube, which remains immovable; but whatever change is made with one cube, the same change must be made with the three corresponding cubes also. For instance: If No. 1 is drawn out, the same must be done with Nos. 33, 6, and 28; and if No. 13 is moved up to No. 8, No. 21 must be moved down to No. 26, No. 15 up to No. 9, and No. 19 towards No. 25, etc. The variety is great, the effect of the kaleidoscopic forms beautiful, and the changes that can be made are almost endless.27

If five-year-old girls were required to solve X-ray crystal structures, this is the kind of training that they would need for decorating special positions with atoms. Is it possible that many girls developed through Froebel's gifts an identity grounded in these crystallographic exercises, such that when they encountered crystallography again at university, they were able to deflect the inevitable stereotype threats, as well as real prejudicial conduct, that they undoubtedly experienced? This thesis can be evaluated only through biographical analyses of the cluster of exceptional female crystallographers who emerged mainly in the British Isles.


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Figure 1. Decorating a site of 4m symmetry with the blocks of Froebel's fifth gift. (No distinctions are intended by black/grey shading, an artifact of scanning.) Adapted from ref. 27.

Peggy Etter did not attend kindergarten, according to her brother and sister. Nevertheless, it is relevant for those readers who may not be familiar with her research, to emphasize here that her most widely appreciated contributions to science involved the recognition and analysis of patterns in crystal structures. Her review on "Encoding and Decoding Hydrogen Bond Patterns in Organic


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Compounds"28 has been cited an eye-popping >3000 times and an elaboration of Etter's observations by Bernstein et al.,29 a review that Etter might have written herself given more time, has been cited >5400 times.30 Such statistics indicate work that has no doubt had a transformative effect on a large scientific community.

WOMEN AND X-RAY CRYSTALLOGRAPHY Recently, Francl noted, "a lot of ink has been spilled trying to understand why comparatively more women are crystallographers." 31 Indeed, a number of scholars have tackled the conspicuous contributions of women to the development of X-ray crystallography in particular. 32 , 33 , 34 Julian provides academic genealogies of women trained in the laboratories of William Henry Bragg (1862-1942), William Lawrence Bragg (1890-1971), and John Desmond Bernal (1901-1971). 35 The women directly trained by the Braggs number 15, those in the second generation 19, including Dorothy Crowfoot Hodgkin (19101994) who further trained 13 women. Despite this accounting, Julian,35 Ferry,36 and Francl31 caution that the contributions of women to X-ray crystallography ought not be overdrawn. As a field, women are, and have always been, in the minority. What is significant is that women were not a vanishingly small minority. Below, I summarize the reasons suggested previously for the apparent anomalous clustering of women at the birth of X-ray analysis. All-Hands-on-Deck. Women tend to appear in new areas of science marked by rapid growth and an urgent need for personnel. 37 In other words, a great vacuum will fill with any gender. "Uncompetitive Societies Tend to be Good for Women". This quote is from Anne Sayre (1923-1998), Rosalind Franklin's (1920-1958) first biographer, as told to Julian.32 Sayre argued that the Braggs were modest, even-tempered, and therefore attractive to women.38 William Henry Bragg's track record at hiring and supporting female coworkers was exceptional for the time.32 Some have recently tried to paint a more equivocal picture of William Lawrence Bragg's inclusiveness, but the evidence given -- for instance, his failure to get James Watson (1928- ) to soften the portrait of Franklin in The Double Helix39 -- is not convincing.38 Bragg should not be judged by what Watson did or didn't do. Service Discipline or "Service Rather than Discipline".32 X-ray crystallography was seen as a helpmate to other disciplines (biology, chemistry, geoscience, and physics), just as women were seen as helpmates to men. As a service discipline, it was less attractive to men and therefore open to women. Communists. Bernal, among many others between the wars, was a "cardcarrying communist".32 Communists tended to believe, in principle, in gender equality in the workplace, a natural consequence of the demise of the bourgeois family. Bernal also believed in practice. Like the Bragg's, he welcomed women in his laboratory. "Ladies Owned Chemistry Sets". In Britain, chemistry sets were designed and


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manufactured for girls of the aristocracy.32 In this way, exposure to crystals was distributed, at least among the well to do.40 Seeding. Like the growth of a crystal, one or two women may create a climate that welcomes others. Seeding in this context requires like-gender for growth. Women path-breakers were crucial.31 Knitting. Before computers, X-ray crystallography required Fourier analysis by pencil and paper. Massive summations were needed to deduce the electron density at each point in space. This repetitive labor was akin to knitting, in the minds of some, and therefore well suited to female talents. 41 Some have suggested that only women would dare engage in such tedium.42 Francl debunks some of these notions by citing other new, collaborative fields in which women were absent. Moreover, she highlights the pinching of Franklin's famous photograph 51 of the B-form of DNA; competition was fierce.31 If all distinguished female physical scientists were sprinkled at random among all of the sub-fields of physical science, we would expect some outlying clusters that beg for explanations but may not warrant them. Perhaps the group of pioneering women in crystallography is nothing other than statistics at work. In the same way that a cluster of cancers in a family or town may be nothing more than outliers in a random distribution, it would be irresponsible for health care workers or public health officials to ignore the possibility of underlying causes. Likewise, if understanding the unusual success of women in crystallography is a key to creating a more representative scientific culture, it would be cavalier if we did not look for this understanding. Are the pioneering X-ray crystallographers a statistical cluster or evidence of meaningful social change that can be comprehended and emulated? Of course, they can be both. Perhaps the first cluster of women in X-ray crystallography in Great Britain, Francl's seeding,31 was a fluke but then conditions were just right for welcoming others. Though there can be no proof in historical studies, experimental science does not permit proof either. In science, we have merely the advantage of building a sense of certainty by doing experiments again and again. Though it is often said that history repeats itself, we cannot rerun the 20th century. Thus, cause and effect in history is tougher sledding. Still, trying to sort it out may be instructive.

EARLY EDUCATIONS To answer the question posed in 20041 and above -- whether girls were exposed to crystallography in school and were thus predisposed to crystallography as young adults? -- we must know more about the early educations of our subjects. I chose eight women to investigate. Our set of case studies includes six from the British Isles, one from the Netherlands, and one from the United States. The scientists whose biographies are considered in the next section include the following: Isabel Ellie Knaggs (1893-1981), Dorothy Wrinch (1894-1976), Kathleen Yardley Lonsdale (1903-1971), Carolina MacGillavry (1904-1993),


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Helen Megaw (1907-2002), Dorothy Crowfoot Hodgkin (1910-1994), Elizabeth Wood (1912-2006), and Rosalind Franklin (1920-1958). As the crystallographic content of the Froebel kindergarten was diminished with each generation as new voices began to inform early childhood education, we are less likely to find an influence on those born more recently and so I restrict our set to scientists born no later than 1920. Isabel Ellie Knaggs (1893-1981) is not the best remembered of the pioneering female X-ray crystallographers. She did not win a Nobel Prize (Hodgkin), write the International Tables (Yardley), battle Linus Pauling (Wrinch), rise to iconic status as the representative of the great achievements and great abuses of women in science (Franklin), write a beloved book about symmetry (MacGillavry), or have an island in the Antarctica named in her honor (Megaw). Nevertheless, she worked to great effect on a challenging problem at the forefront of structural chemistry, the demonstration with X-rays that methane derivatives were tetrahedrally coordinated. Knaggs had studied with William Jackson Pope (1870-1939) at Cambridge from which she brought to Bragg an emphasis on "valency and spatial considerations in determining structures." 43 Arthur Lindo Patterson (1902-1966) sanctioned her approach: "...most of us were determining space groups and obtaining very little structural information. It was only when a molecule had some symmetry that some definite information could be given. This was the case with the work of Knaggs."44 Knaggs joined William Henry Bragg at the Davy-Faraday Laboratory of the Royal Institution where she solved the crystal structure of benzil with Lonsdale,45 and thought early and hard about diffuse scattering. 46 The greatest fraction of her published work was aimed at establishing that carbon in a discrete molecule -- in contrast with the extended network of diamond 47 -- adopted a tetrahedral coordination geometry. I will discuss this work at length in the next major subsection, work that was an outgrowth of her PhD research at Imperial College, University of London on "The Relation between the Crystal Structure and Constitution of Carbon Compounds, with Special Reference to Simple Substitution Products of Methane." 48 At issue was the point symmetry of equivalently tetra-substituted derivatives of methane. Ellie Knaggs was born in Durban, South Africa. Her first school was in England, a private school in Hampstead, according to the Girton College Register. 49 Hampstead was the sight of the first Froebel kindergarten in 1851. After the failed 1848 revolution in Germany, many liberal Germans emigrated to London, bringing with them Froebel's ideas on education.50 We don't know if Knagg's first school was the first Froebel kindergarten in Hampstead. Knaggs next attended the North London Collegiate School founded by Frances Mary Buss (1827-1894). 51 North London Collegiate was modeled after the principles of the Swiss educator, Johann Pestalozzi (1746-1827). Froebel was a student of Pestalozzi and from 1808-1810 lived at Pestalozzi's Institute. The North London Collegiate School Newsletter of 1875 writes of their system of kindergarten derived from Froebel who was "deeply impressed with the truth that education should precede instruction. The child is taught little, it simply produces for itself; the toys of the


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simplest kind are given to it, it is shown how to use them, and becomes an architect and inventor."52 The Head of North London Collegiate while Knaggs attended was Sophie Bryant (1850-1922), a mathematician, the first woman to receive a First Class Honors Bachelor of Science Degree, and the first to receive a Doctor of Science degree in Britain (and one of the first to own a bicycle).53 Bryant, a native of Ireland, was a committed Irish Home Ruler and frequently lectured in Dublin on Irish independence at the Alexandra School, the center of Froebel-thought in Ireland and the alma mater of Megaw (see below). Knaggs later attended the Bedford Training College (part of the University of London). According to school history, Bedford students followed the progressive philosophy of Froebel.54 Knaggs progressed to Girton College at the University of Cambridge to study chemistry. Girton was also a center for Froebelian thinking. Buss 55 played a prominent role in the creation of Girton which stayed true to progressive ideas in education, not only because it admitted women, but also through the efforts of Emily Anne Eliza Shirreff (1814-1897) who, as founder of the Froebel Society in 1876 and its longstanding president, was a pioneer in bringing Froebel's ideas to England. Shirreff was a mistress at Girton and was closely connected with the college throughout her life. Shirreff was also a fundraiser for Knaggs primary school, North London Collegiate. Dorothy Wrinch (1894-1976) received her formal training in mathematics and philosophy and collaborated with rarefied figures such as Bertrand Russell (1872-1970). 56 Her research interests evolved in the 1930s through her associations with a group of pioneering structural biologists including Bernal and Hodgkin. The work of these crystallographers focused Wrinch's mathematical interests on Fourier transforms57 and expressions of the Patterson function.58 Her discussions with crystallographers ultimately led to a mathematically inspired theory of protein structure59 that attracted powerful opponents.60 Wrinch attended the Surbiton High School in Kingston Upon Thames. Eva Kobrak (1922-1982) became the head mistress of this school, long after Wrinch. Kobrak had taken Froebel training according to a family history.61 Closer to home was Wrinch's younger sister, Muriel, who earned a Froebel certificate.60 Both Dorothy and Muriel had strongly held views on early childhood education. Dorothy, writing under the pseudonym Jean Ayling, published The Retreat from Parenthood.62 She argued that full-time motherhood was outmoded and outlined a national system of childcare. Muriel published several books including Mothers and Babies,63 Your Children,64 and Key to Living.65 Following Surbiton, Wrinch entered Girton College. As we discovered in the Knaggs profile, Froebel came to Girton through Buss and Shirreff. Kathleen Yardley Lonsdale (1903-1971) established the planarity of the benzene ring by X-ray crystallography 66 and she was also responsible for creating the first edition of the International Tables with W. T. Astbury (18981961).67


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Yardley, born in Ireland, moved with her family to Essex, England at age five. She attended was the Downshall Elementary School in Ilford, now part of greater London. She graduated to the Ilford County High School for Girls but transferred to the companion school for boys so she could study mathematics and science, subjects not offered at the girls' school. I could find no connection between Downshall or Ilford and Froebel, however, at age 19 Yardley entered the Bedford Training College (part of the University of London). According to school history, Bedford students followed the progressive philosophy of Froebel. 68 This connection is fully developed in the Bedford Training College, 1882-1982: A History of a Froebel College and Its Schools. 69 Lonsdale was thus certainly exposed to the ideas of Froebel at Bedford, but at a comparatively late age. Carolina MacGillavry (1904-1993) used X-rays to gain early insight into the physical properties of the long chain dicarboxylic acids70 and contributed to the development of direct methods. 71 But, for our purposes, I emphasize her fascination with tesselations that resulted in the classic book Fantasy and Symmetry in the Periodic Drawings of M. C. Escher. 72 Teaching space group symmetry to students using the plane groups in her book illustrated by the Dutch graphic artist M. C. Escher (1898-1972) has since become a near universal exercise. Tesselation is "so Frobel." Was she influenced in her professional choices by her kindergarten experience? MacGillavry, as the name implies, was of Scottish descent but she was born and raised in Amsterdam. I could not find any information about her early education. All we know is that she attended the exclusive Barlaeus Gymnasium, with a high school curriculum focused on the classics. That said, the Netherlands was fertile soil for Froebel's kindergarten experiment. By 1900, 50% of kindergartners in the Netherlands were taught the Froebel way. The association of early childhood education with Froebel was so strong in the Netherlands that kindergartens were called Fröbelschools.73 Perhaps Escher himself practiced tesselating planes74 in kindergarten? Escher attended schools in Arnhem and Zandvoort but I was unable to establish what went on in his classrooms. I located a photograph of a Fröbelschool in Arnhem from 1932, long after Escher might have attended.75 It is clear that religious instruction was important. There are statuettes of Christ both inside and outside the same classroom window. And the chalkboard reads RK Fröbelschool Insula-Dei (Roman Catholic Island of God Kindergarten). Below Christ, one can see a wall of tesselations, presumably the works of the students seated. Helen Megaw (1907-2002) studied with Bernal and is best known for her work on the crystallography of ferroelectrics,76 perovskites,77 and ice.78 It is the latter study that earned an Antarctica Island (Megaw Island, 66°55′S 67°36′W) named in her honor. Megaw attended the Alexandra School in Dublin from 1916-1921 that today cites a "philosophy of teaching and learning [that] is child-centered and based on the principles of Friedrich Froebel, the German educator and founder of the Kindergarten method". 79 In collaboration with the Froebel College in Sion Hill, Alexandra College "worked strenuously" to extend Froebel pedagogy to the lower


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economic classes. 80 In the 1920s a Froebel teacher-training department took shape at Alexandra that awarded the Higher Certificate of the National Froebel Foundation. According to a history of the college, "The standard of the kindergarten department increased as the years went by and its students did much to enhance the reputation of Froebel teaching and to spread its influence." However the Froebel department was closed in 1970.81 Megaw next attended the Roedean School in Brighton when her parents moved to Belfast. The Roedean School was founded by Penelope Lawrence (18561932). Lawrence spent part of her youth in Thuringia, Froebel's home, attended the school of one of Froebel's followers, and began work towards a Froebel diploma. After her family returned to England, Lawrence became the third student in Newham College, Cambridge history to pass the Natural Science Tripos. However, women did not have the use of laboratory facilities. Lawrence left Cambridge to provide opportunities in education for girls. 82 She took the position of principal of the Froebel Society's Kindergarten Training College in Tavistock Place from 1881-83.83 Afterward, she joined forces with her half sisters, Dorothy Lawrence (1860–1933) and Millicent Lawrence (1863–1925). The curriculum was infused with Froebel's ideas that Penelope had learned in Thuringia, and at the Tavistock kindergarten. Megaw began her B.Sc. degree at Queen's University in Belfast and finished at Girton, already introduced above as compatible Figure 2. Apophyllite lace designed by H. Webster and A. C. Gill. With permission of Science & Society Picture with Froebel's educational Library, Science Museum Group Enterprises Ltd. ideals. From 1936-43, Megaw taught at Bedford High School and at the Bradford Girl's Grammar School before being "rescued" by Bernal and given a research appointment at Birkbeck College, University of London.34


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Megaw's training at the Alexandra and Roedean schools may be manifest in her work for the Festival Pattern Group, a part of Festival of Britain of 1951. The story of the Festival Pattern Group is told by Lesley Jackson in From Atoms to Patterns 84 , 85 in which Megaw is amply quoted from her papers stored in the Archive of Art and Design at the Victoria & Albert Museum. In 1946, Megaw wrote, "I should like to ask designers of wallpapers and fabrics to look at the patterns made available by X-ray crystallography. I am constantly being impressed by the beauty of the designs which crop up." She wrote to a friend, "I had always had pleasure in patterns." She elaborated on this innate attraction in an unpublished essay, "Pattern in Crystallography", reprinted by Jackson: It is often put forward as a professed aim of science to gain control of the processes of nature by learning to understand their mechanisms; but to most scientists, perhaps, an appreciation, however inarticulate, of the pattern underlying these processes is the driving force of their work. For the crystallographer, these patterns are readily translatable into visual terms. It is hoped that these few examples drawn from such a rich field may suggest to designers ways in which to broadcast to a wider public some of the aesthetic pleasure found in the subject by crystallographers themselves.84,86

Designers and industrialists, organized as the Festival Pattern Group under the auspices of the Council of Industrial Design, embraced these suggestions. They hired Megaw as a consultant to liaise between the industrialists and her crystallographer colleagues including Bernal, the Braggs, Lonsdale, Hodgkin, John Kendrew (1917-1997), Max Perutz (1914-2002) and others. In this way, she supplied the designers with the results of X-ray analyses in graphical form. These structures were then displayed on neckties, curtains, carpets, upholstery, wallpaper, wall tiles, napkins, plates, and drinking glasses. Jackson84 richly illustrates the crystallographically informed work of the Festival Pattern Group and shows periodic structures in a host of media: haemoglobin's structure woven on a Jacquard loom, aluminum hydroxide printed in enamel glaze, screen printed afwillite, zinc hydroxide's network baked into earthenware tiles, apophyliteinspired sheet glass (see apophyllite lace in Figure 2), 87 polythene's atomic connectivity electro-plated in cutlery, mica in polyvinyl sheeting, insulin in linoleum, beryl in lace, cristobalite rendered in pierced metal sheets, and pentaerythritol in machine woven carpet. And what was the Froebel kindergarten? Creating symmetric or periodic patterns out of blocks of wood (3rd, 4th, 5th and 6th gifts), out of paper tablets (7th gift), out of sticks of whatever material (8th gift), out of rings and arcs (9th gift), by drawing with pencil and paper (10th gift), by perforating paper (11th gift), by embroidering (12th gift), by interlacing, braiding and weaving (14th, 15th, 16th, and 17th gifts), by folding (18th gift) or by linking peas and toothpicks (19th gift). The Festival Pattern Group for which Megaw consulted may have been her grown up realization of the habits of a Froebel kindergartner. Dorothy Crowfoot Hodgkin (1910-1994) raised crystal structure solution to new heights of complexity88 with her analyses of penicillin,89 vitamin B-12, 90 and


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insulin. 91 Her 1964 Nobel Prize in Chemistry met risible British newspaper headlines such as The Daily Mail's "Oxford housewife wins Nobel", among others.92 Georgina Ferry's biography of Hodgkin identifies the important role of the Parents National Education Union (PNEU) in her early education. 93 This information appears to be drawn from an interview Hodgkin gave to the BBC. Hodgkin reported: When I was quite young, I think I was ten at the time, I went to a small PNEU class in Beccles. PNEU stands for Parents National Educational Union, and it was founded by a Miss Mason of Ambleside to improve the education of governesses, in a private way, all over the country. They produced small books that would enable the governesses to introduce their pupils to the different sciences in turn. So the small book on chemistry began with growing crystals, which I think is quite a common way to begin chemistry, growing crystals of copper sulphate and alum. I found this fascinating and repeated the experiments at home, when we had a home, which was the following year."

It is remarkable that late in life Hodgkin recalled the name and place of association of the woman behind the philosophy of the grade school she attended. Few can recall such details of their early schooling. Hodgkin was referring to Charlotte Mason (1842-1923). Mason was not a typical acolyte of Froebel. His first generation followers were typically under-employed women of means. Mason was orphaned as teenager, trained to be a teacher, and developed an independent vision of a universal liberal education while working in the classroom. Her activities were organized under the Parents Education Union, which added National to its name only after Mason moved to Ambleside to begin an institution for the training of governesses. While Mason was self-made, her advocacy could not survive independently of the wave of enthusiasm for Froebel that was sweeping across England. Mason's PNEU was overrun with Froebelian's in short order. As such, she needed to praise Froebel, while at the same time distinguishing her creative invention from his. She was equivocal about Froebel's philosophy, despite the fact that there are many similarities between her philosophy and his, especially their emphases on the Natural forms. Mason's philosophy is nevertheless today considered a descendant of that of Froebel.94 It is no coincidence that Mason's writings, reissued in six volumes in contemporary language by Laurio, are all decorated with crystals, 95 a design choice that is baffling in the absence of knowledge of the history of kindergarten. Laurio paraphrased Mason and assumed her voice on "What We Owe to Froebel": We reverence Friederich Froebel. We share many of his great thoughts. What he said wasn't new. Some of it, like the child's relations to the universe, has been around since the days of Plato. Others are common knowledge and experience, which proves that they are true. Froebel collected various thoughts and practices that were scattered and combined them into one system. But even more importantly, he inspired an enthusiasm for childhood that still continues. The classic Froebel


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kindergarten teacher is a true artist. She is inspired in her work, and most sincere teachers catch some of her enthusiasm, her sense of beauty of childhood and her joy with her work.95

Crowfoot had earlier attended another PNEU school in Burgess Hill.93 The Froebel prophet, Anne Shirreff, introduced in the profile of Knaggs, was, incidentally, vice president of the PNEU. Elizabeth Wood (1912-2006) was the first woman to join the scientific staff of Bell Laboratories where she studied crystals with physical properties of potential use.96 She is particularly admired in our laboratory because of her focus on the interactions of crystals and light.97,98 Wood was born in New York City and enrolled in the Horace Mann School in 1918. She graduated from Barnard College in 1933 and received a PhD in geology from Bryn Mawr. Wood was a teacher at Bryn Mawr and Barnard in the 1930s before taking up her post at Bell Labs. Today, The Horace Mann School is an exclusive preparatory high school in the Bronx. In Wood's day, it was the experimental high school of Columbia University's Teachers College and it was located at Morningside Heights in Manhattan. Immediately upon its launch in 1900, the journal of the Teachers College, The Teachers College Record,99,100 put out a steady stream of articles on the virtues of Froebel schooling. The educational reformer Horace Mann had no direct relationship to the school for which he is named, but he was the brother-in-law of Elizabeth Peabody (1804-1894) for whom the Froebel kindergarten "was not simply a method of education but a movement of mystical significance. Her advocacy was an 'apostolate,' kindergartening a religion, a 'Gospel for children.' " 101 Horace married Elizabeth's sister, Mary, but shared Elizabeth's intellectual outlook. "However affectionate we may be" Elizabeth wrote "it is a brother's & sister's love on both sides."102 Rosalind Franklin (1920-1958). The BBC asked its readers whether Rosalind Franklin's photograph 51 of the B-form of DNA was the most important photo ever taken. 103 Irrespective of how we should choose to answer this question, merely the asking marks Franklin's work on the structure of DNA as high class X-ray crystallography that will endure for ages. The story of how this photo was taken by Franklin, and taken in a different way by her competitors, is now the subject of books, plays, and movies too numerous and too easy to find (e.g. YouTube) to warrant enumeration here. Franklin's first schooling was at Norland Place, near Hyde Park.104 Norland Place was founded by Emily Lord (1850-1930) in 1876. It was intended to teach children aged 3-8 according to Froebel precepts. Lord, the first Norland Place principal, was a member of Britain's Froebel Society and studied with one of Froebel's most important disciples in Geneva, Madame du Portugal. Lord translated one of Froebel's books from German. 105 According to the Norland Place website, in 1879 the Froebel Society honored the school with a commendation for its instruction. Subsequently, Lord became a lecturer on behalf of the Society.106


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"THE CARBON ATOM PLAYS THE PART EXPECTED OF IT" We return to the work of Knaggs before advancing past the biographies of crystallographers because it confronts the attribution of credit for an important discovery. On close inspection, a minor Franklin-esque drama comes into focus. According to a 2005 newsletter of the International Union of Crystallography, Isamu Nitta (1899-1984) confirmed by X-ray diffraction the anticipated tetrahedral coordination in methane derivatives. I. Nitta...studied the crystal structure of pentaerythritol C(CH2OH)4 to establish tetrahedral carbon valence bonds. At that time, however, there was a report based on a space group assignment that the central C atom of pentaerythritol in the crystal was (tetragonal) pyramidal. Nitta (1926) found that the reported space group was erroneous and the C atom was actually tetrahedral. This was later verified by a full structure determination, and the tetrahedral carbon valence bonds were established.107

I shared the article, clipped from newsletter, with my research group, engaged as we were at that time in measuring the chiroptical properties of pentaerythritol crystals.108 This was a bit of relevant history that was new to us. This view of the confirmation of the tetrahedral carbon in discrete compounds by X-ray analysis seems to originate with Nitta who recalled in Fifty Years of X-ray Diffraction: My second paper [the first109 was on iodoform but disorder precluded a confirmation of the tetrahedral coordination at carbon], which appeared in the same year [1926], was on the crystal structure of pentaerythritol,110 and contained some comments on the previous investigations of the same crystal by other authors.[119,120] One of the unfortunate conclusions of these authors was due to the inappropriate description of the unipolar, tetragonal symmetry of the crystal given in Groth’s Chemische Kristallographie.[ 111 ] By observing carefully the crystal growth of pentaerythritol from aqueous solution, I realized that crystals frequently grow with their tetragonal axes hanging perpendicular from the surface of the solution, so that the crystals appeared as if they had unipolar, tetragonal axes. Bearing this in mind I chose the space group 4, which enabled the central carbon atom of the molecule to conform with the tetrahedral distribution of the valence bonds.

In fact, this choice was made in 1937, not in 1926 as the discussion suggests. To set stage for further analysis, it is helpful to review some of the milestones in the X-ray structure determination of organic compounds as laid out in Authier's admirable new history. 112 First came the structure of diamond (1913),47 then graphite (1917), 113 hexamethylenetetramine (1923), 114 urea, 115 hexamethylbenzene (Lonsdale 1923), 116 and polycyclic aromatics 117 (naphthalene). While hexamethylenetetramine had tetrahedral carbon atoms, the hydrogen positions were unknown and therefore the carbon coordination


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could not be precisely defined. Diamond was of course built from tetrahedral carbons, but this was considered a special case. Authier paints swiftly over the work I emphasize here: "Only a few structures of aliphatic compounds were determined in the early 1920s, but they confirmed classic organic stereochemistry: the tetrahedral symmetry of bonding for a fourcoordinated carbon atom." It is during this period that both Nitta and Knaggs were independently trying to pin down the tetrahedral carbon in discrete molecules. However, Nitta's 1926 paper110 makes no mention of interfacial growth, and the point symmetry of pentaerythritol is left as an open question: In either case of [4 ] and [ 4] we can arrange four structurally equivalent alcohol radicals CH2OH around the central carbon atom. The minimum possible symmetry of the molecule is that of the point group in the case of , while it is in . It implies that we are dealing with the tetrahedral central carbon atom in the former case and the nontetrahedral one in the latter.

Returning to this question in 1937, Nitta writes,118 The presence of a non-tetrahedral carbon atom in the crystal of pentaerythritol, C(CH2OH)4, has been reported by H. Mark and K. Weissenberg[119] and recently by M. L. Huggins and S. B. Hendricks.[120] Now that there is no other X-ray investigation yet imparted which confirms the presence of such carbon atom in organic crystals, while the theory of the tetrahedral carbon atom has actually offered a great deal of applications to organic chemistry, it seems not insignificant to reexamine if there can never be a possibility of attributing the tetrahedral nature to the central carbon atom of penta-erythritol in crystalline state.

Knaggs might have taken exception to the suggestion that "no other X-ray investigation...confirms the presence of such [a tetrahedral] carbon atom." She chose to focus on pentaerythritol derivatives rather than on pentaerythritol itself. In 1925, in a paper that predates Nitta, she tackles the explosive pentaerythritoltetranitrate.121 But here, she had already settled on the tetrahedral carbon at the center. A consideration of the spacings shows that the only true halvings are for planes (hk0), where (h + k) is odd. The only space-group in the holohedral class of the tetragonal system, which, based on a simple tetragonal lattice, would lead to this result is

[P4/nmm]. This space[122] group has 16-fold symmetry, and, since it has been shown that there must be four molecules per unit cell, each molecule must have four-fold symmetry.[122] Two types of four-fold symmetry are possible in this case: (1) the molecule may have two planes parallel to (100) and (010) respectively intersecting in a digonal axis, or (2) a plane parallel to (110) with a digonal axis at right angles to it. Only by assuming the molecular symmetry (1) was it found possible to obtain a reasonable structure for the crystals. This structure is, moreover, in accordance with the known facts, as far as they can be interpreted.

Condition (1) describes molecules with C2v symmetry sitting on Wyckoff positions


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d in space group 129. Knaggs recognized that polar site symmetry is not inconsistent with tetrahedral coordination because the conformation of the side chains can obviate an improper rotation axis. As of 1947,123 we know that the

axes in the space group 42 . The four molecules in the unit cell sit on 4 authors of this more refined structure claim that Knaggs picked a centered cell, but she did not, albeit her cell was twice as large, it was still primitive. Some features of her structure were correct (tetrahedral coordination), some features were incorrect (molecular and space group symmetry). All in all, her answer is quite good given that she recorded only 11 intensities! Who among us would dare so much with so little. Knaggs picked a local symmetry characterized by intersecting planes, a perfectly reasonable judgment assuming the highest possible molecular symmetry consistent with her limited observations. Knaggs reported to Girton College, by May of 1927, her results on the symmetry of pentaerythritoltetraacetate 124 whose crystallographic study parallels that of pentaerythritol. But, by the time her paper was published in 1929, Gerstäcker, [P4/n] with Möller and Reis had already assigned the crystals to space group

125 Z=2 and place the molecules on the proper fourfold axes. Knaggs recognized that the molecules in such a crystal could not be tetrahedral. She wrote, "It does not seem that the authors have put forward any evidence which could justify the adoption of a molecular form departing so completely from what would be expected from physical and chemical consideration." 126,127 Knaggs revised the symmetry from

[P4/n] to

[P42/n]. The distinction required the diffraction condition (00l) l=2n in the latter case. Knaggs concludes forcefully, "[In] the space-group is

, there is no longer any possibility of a molecule with a simple fourfold axis of symmetry, the only possible molecular symmetry then being a fourfold alternating axis...On this view, therefore, the carbon atom plays the part expected of it."126 This is the first unequivocal statement derived from X-ray data that a methane derivative has tetrahedral coordination as far as I am aware. Knaggs rebutted the Gerstäcker et al.125 structure head on for emphasis in 1929.128 Nitta's earliest work on pentaerythritol110 postdates Knaggs earliest work of the tetranitrate.121 It is equivocal about symmetry and lacks the force of discovery. He did not decide between pentaerythritol molecules sitting on a proper or improper fourfold axes until 1937,118 well after all of Knaggs' papers on the pentaerythritol derivatives. Moreover, Knaggs papers from the 1920s went much further than do Nitta's; she attempted structure solutions. In 1920s, researchers had not yet broached two-dimensional Fourier syntheses. But, Knaggs nevertheless tried to fix the orientation of the side chains by judging the relative intensities of hk0 and h0l reflections. In this way, Knaggs produced atomic models as shown in Figure 3. The models are imperfect because the nitrate and ester oxygen atoms take linear coordination, but this is a comparatively small infelicity for the time. The first edition of Pauling's The Nature of the Chemical Bond was published in 1939129 and valence shell electron pair repulsion theory was not considered before 1940.130


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Figure 3. (a) Knaggs' model of pentaerythritoltetranitrate (ref. 120) and (b) pentaerythritoltetraacetate (ref. 123) with corresponding views of the crystal structures (c) and (d) respectively, viewed along the rotational axes. (e and f) are examples from the kindergarten manual of Kraus-Boelte and Kraus (ref. 27) showing how to use Froebel's third gift. Eight oblong blocks are arrayed symmetrically (e) and dis-symmetrically (f). Making distinctions of this kind were the work of kindergartners and may have been the work of Knaggs at the North London Collegiate School.

Why are the capstone contributions of Knaggs to the theory of the tetrahedral carbon atom wholly forgotten? It may depend on who writes the histories. Of the 36 contributors to Fifty Years of X-ray Diffraction, two are women, Lonsdale and Wood. Nitta wrote three chapters, more than all the chapters written by women combined, including the following: "In Memorium: Shoji Nishikawa", 131 "Isamu Nitta: Personal Reminiscences", 132 and "Schools and Regional Development: Japan". 133 The latter two refer to the pentaerythritol triumph. Knaggs is never mentioned in these essays or cited in the technical papers from Japan. In 1938, Goodwin and Hardy went further with the structure of pentaerythritoltetraacetate. 134 But this time, the standard involved twodimensional Fourier synthesis (aka knitting). They noted that Knaggs correctly deduced the space group for which tetrahedral coordination was required, but gave the impression that Knaggs work was otherwise a failure. Miss Knaggs (1929) showed that the space group had been incorrectly deduced, that it was, in fact, P42/n (

), and that the molecular symmetry is fourfold alternating, the valencies of the central carbon being directed from the centre to the apices of a tetragonal bisphenoid. Whether the chemical theory that this bisphenoid is a regular tetrahedron is correct can only be ascertained by the determination of the co-ordinates of the atoms adjacent to the central one. Although Miss Knaggs did not do this,


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she did suggest a tentative structure for the molecule, but as this structure differed radically from that found by us and as it was not supposed to be final no good purpose would be served by discussing it here.

Shown in Figure 4 is the two-dimensional Fourier synthesis of Goodwin and Hardy.134 The reader may judge whether Knaggs' structure in Figure 3d is indeed radically different and not worthy of discussion. In fact, Knaggs did indeed place the atoms, albeit not by Fourier synthesis, but by combining chemical logic with intensities of selected reflections. Her structure is not perfect. But, in 1928, no one had yet succeeded in calculating electron density in planes from diffraction photographs. X-ray diffraction was a fast moving field, and to dismiss the structural analysis 15 years into the development of that science by the standards ten years hence is hardly sporting, especially when the old work was a significant step in the right direction. Denigrating someone else's work to elevate your own is a strategy that should not stand up to scrutiny. The collective dismissal of the work of Ellie Knaggs succeeded. I had not known of her contributions and became aware of her name only as a result of the work of scholars who have been reconstructing the climate for women in 34 the early years of X-ray crystallography. There, Knaggs is acknowledged for her structure determination of cyanuric triazide.135 But this is a comparatively minor, one-off structure. She raced to publish two notes about the compound, only because W. H. Bragg spoke about her work at the Faraday Society, thereby revealing her discovery that the azide group was linear,136 and because another scientist published in the interim a study of lesser quality showing that the -N3 group is bent by 15°.137 It is not. Knaggs was again correct. Figure 4. Electron density section of Goodwin and Hardy (ref. 133) for pentaerythritotetraacetate "Fourier projection on (001) showing arrangement of atoms in the {520} planes."

Knaggs' most significant body of work, stemming from her doctoral thesis, was the structure determination of symmetrically substituted methane derivatives, and it is here that she should have been recognized for making a lasting contribution. By 1923, both Knaggs and Nitta began assaults on the coordination at carbon in methane derivatives by X-ray diffraction. Knaggs solved the problem first and more completely in our estimation.


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According to Megaw, as cited in ref. 34, "Ellie Knaggs was a kind and gentle person, rather shy. She attended scientific meetings, but did not put herself forward." Still, her published work should speak for itself. To honor her achievement, I sought a photo of the 1913 class at Girton College, Figure 5.

Figure 5. Top: First year students at Girton College. Ellie Knaggs is an the left end of the second row from the top. Bottom: Knaggs enlarged. Published with the permission of The Mistress and Fellows, Girton College, Cambridge.


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ASTRONOMICAL CONTROL EXPERIMENT What shall we make of the many connections between female crystallographers and Friederich Froebel, highlighted previously and summarized in Table 1? Not much in the absence of a control experiment of some kind. Perhaps every conspicuous cluster of high achieving women in physical science round the turn of the 20th Century was likewise marked by exposure to Froebel's crystallographic pedagogy, being widespread at that time. If so, there would be no special connection that we could attribute to early childhood crystallography and a return to crystal analysis in adulthood, albeit we might be buoyed by the notion that Froebel helped to produce scientists generally speaking. I chose seven distinguished astronomers mainly associated with the Harvard College Observatory, 138 and one other from Yale, whose biographies were intended to serve as a control. These women included the following: Williamina Paton Fleming (1857-1911), Annie Jump Cannon (1863-1941), Antonia Maury (1866-1952), Henrietta Swan Leavitt (1868-1921), Ida Barney (1886-1982), Cecilia Payne-Gaposchkin (1900-1979), Helen Sawyer Hogg (1905-1993), and Ellen Dorrit Hoffleit (1907-2007). The astronomers are on average one generation older than the crystallographers, making for an imperfect comparison. However, we are restricted to the characters that are delivered by history. Should we expect that this generational difference was impactful? Kindergarten came to England in 1851 and to the United States in 1856. It quickly became widespread. By 1885 there were 545 American kindergartens following the Froebel model.7 Still, the spread of kindergarten, however rapid, took a finite amount of time and the astronomers, especially the oldest, were less likely to be exposed. Nevertheless, earlier Froebel training, had it occurred, was likely to be more significant because as more and more voices began to inform the kindergarten curriculum, it gradually lost its crystallographic, geometrical character. We must be careful not to place too great an emphasis on the fact that the name "Froebel" appears in the biography of any one scientist. As we saw, in the Netherlands Froebelschool became a simple synonym for kindergarten. Moreover, in some places, educators were strident to remove the "Germanness" from kindergarten. While "slavish imitation" of Froebel's methods served the kindergarten movement at the start, it was feared in the United States that the determination of teachers to follow Froebel "to the letter" would kill the spirit of kindergarten and quash the possibility of universalization.139 On the other hand, the schism between the old and new was not as sharp in England.140 Of course, there is no perfect control experiment. All we can do is ask whether Froebel intrudes in the biographers of the astronomers as he clearly does in the biographies of crystallographers. Williamina Paton Fleming (1857-1911) discovered the Horsehead Nebula, one of the most dramatic objects photographed by the Hubble Space Telescope, in a photograph taken by Henry Pickering (1858-1838), the brother of Edward Pickering (1846-1919) who was the director of the Harvard College Observatory.


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Fleming's main labor was cataloging spectra of some 10,000 stars previously photographed. Fleming was born in Scotland. We do not know anything about her early education. She settled in Boston with a child and a husband who later abandoned the family. To make ends meet, she took a job as a maid in the home of Edward Pickering. Apparently, Pickering's observatory was in greater disarray than his home. Fleming was hired to work at the office as a clerk, filing star data. In Scotland, she had been a schoolteacher. Her education, and outsized intelligence were not lost on Pickering.141 Fleming's efforts went beyond record keeping to major astronomical discoveries and classification schemes. Her journey to observational astronomy does not seem to have been directed by her early education but rather by an improbable chain of events prompted by the need to support her family. Antonia Maury (1866-1952) refined Fleming's stellar classification scheme based on spectra. However, her system was too complex and fussy for Pickering's taste and they had a falling out. Maury was the granddaughter of John William Draper (1811-1882) who made the first photograph of the moon. Draper was the first scientist at New York University, and he founded the American Chemical Society at the site of the author's laboratory. John's son, Henry Draper (1837-1882), made the first spectrum of a star. Maury was exposed to science at an early age through her famous relatives. Since the age of four, she assisted her uncle Henry in his laboratory with chemistry experiments. Maury was otherwise educated at home. After she graduated from Vassar College,142 her father arranged for her work at the Harvard College Observatory with Pickering. By this time, Henry's wealthy widow, Antonia's aunt, was supporting Pickering's astronomical researchers in husband Henry's memory. The star catalog to which Maury contributed, and which Fleming helped to classify, is named for her uncle.143 Annie Jump Cannon (1863-1941) succeeded Maury, though three years older. Cannon synthesized the two schemes of Fleming and Maury, keeping the best features of each. With only the necessary complexity, she won Pickering's long-lasting confidence. Cannon was remembered as genius for recognizing stellar spectra at a glance and through her labors she increased the Henry Draper Catalog to some 400,000 stars.144 Cannon was devoted to astronomy before she attended school because her mother taught her to identify the constellations. She ultimately attended the Wilmington Conference Academy, a preparatory school in Dover Delaware. The Academy was founded in 1873 to promote interest in the Methodist denomination by creating a "first class academy for boys." The next year, it admitted "40 boarders and 35 day students, 10 of whom were young ladies." 145 Despite welcoming women from the start, in part due to financial necessity and in the face of opposition to coeducation, the Wilmington Conference Academy instruction was traditional. Afterwards, Cannon studied physics and astronomy at Wellesley.


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Henrietta Swan Leavitt (1868-1921) recognized that the log of the period of stars with oscillating luminosities was linearly related to the log of their brightness. Gross violations of this log-log plot led Edwin Hubble (1889-1953) to the discovery of stars beyond our galaxy; Leavitt's work was the basis for a magnificent expansion of the size of the universe from 100,000 light years to more than two million light years.146,147 It has grown much more since. Leavitt was the daughter of a minister and attended public schools in Cambridge, Massachusetts. Her family relocated to Ohio briefly after which she enrolled in Oberlin College,148 but she ultimately returned to Cambridge and graduated from the Society for the Collegiate Instruction of Women (now Radcliffe). Leavitt's interest in astronomy was piqued by a course in that subject during her senior year. She then volunteered her services to the observatory. For Leavitt, a Cambridge Massachusetts native and local college graduate, proximity was surely a factor in her career in astronomy at the Harvard College Observatory. Ida Barney (1886-1982) spent the majority of her career at Yale as a Research Assistant or Research Associate where from 1922-1959 she was a major contributor to 22 volumes of the Transactions of the Yale University Observatory. In all, she contributed to establishing the accurate positions and motions of nearly 147,000 stars.149 She never worked at Harvard. Barney was born in New Haven, Connecticut, the daughter of a Yale Professor of Civil Engineering. We do not know how she was educated before attending Smith College, and receiving a PhD in mathematics from Yale. After several brief positions teaching math at women's colleges (Rollins, Smith, Lake Erie, and Meredith) she was appointed as a research associate at the Yale observatory where she stayed throughout her life.149 She never had a formal association with the Harvard College Observatory. Cecilia Payne-Gaposchkin (1900-1979) was a pioneer in stellar composition and evolution. She derived temperatures of stars from their spectra consistent with the degrees of ionization of the elements predicted by theory.150 ,151 Much later she refined our understanding supernovae 152 and the evolution of galaxies.153 Payne, like Cannon, was first exposed to astronomy through her mother when together they happened to see a meteor streaking in the sky above the woods near her home in Wendover. She first attended school by chance because one opened up across the street from her house.154 The school was characterized by strict discipline and memory exercises. At age twelve, Payne's family moved to London. Cecilia attended the St. Mary's College, Paddington (1916-1918), and then St. Paul's Girls School in London (1918-1919) to prepare for university exams. The St. Paul's Girls school was described as an anti-kindergarten, in the Froebel sense: "In place of the casual games, there was conventional training and discipline for 500 girls."155 But, for Payne, this was thrilling compared with the dreary St. Mary's School; St. Paul's had science classes.154 Payne went on to Newnham College, Cambridge. She moved to Harvard, expecting more opportunities for female astronomers, where she earned her PhD and ultimately


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was appointed to the faculty. Helen Sawyer Hogg (1905-1993) continued studying and cataloging variable stars in the tradition of Leavitt, greatly extending the period-luminosity relationship, and using it to analyze globular clusters, spherical star aggregates drawn together by gravity.156,157 Sawyer graduated at age 15 from Lowell High School in Massachusetts and then attended Mount Holyoke College before receiving her PhD in astronomy from Radcliffe for work at the Harvard College Observatory on star clusters in collaboration with Cannon, and Harlow Shapley (1885-1972), Pickering's successor.158 Halley's comet in 1910 sparked Sawyer's interest in astronomy.159 Sawyer Hogg's own account attributes her commitment to the observation of the total eclipse of January 24, 1925, which "locked me into astronomy for the rest of my life." 160 Table 1. Educational institutions and family members of crystallographers and astronomers connected to the pedagogical principles of Friederich Froebel Crystallographers

Astronomers

Knaggs

North London Collegiate School

Bedford Training College

Girton College

Fleming

N/A

Wrinch

Surbirton High School

Girton College

sister Muriel trained as Froebel teacher

Cannon

N/A

Yardley

Bedford Training College

Maury

N/A

MacGillavry

N/A

Leavitt

N/A

Megaw

Alexandra School

Barney

N/A

Hodgkin

Parent's National Education Union

PayneGaposchkin

N/A

Wood

Horace Mann School

Hogg

N/A

Franklin

Norland Place School

Hoffleit

N/A

Roedean School

Girton College

We do not know if Sawyer attended kindergarten or where she attended grade school but it was somewhere within the public system of Lowell, her hometown.161 There is superficial connection between Lowell and Froebel; Milton Bradley (1836-1911), 162 likewise a graduate of Lowell High School, but long


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before Sawyer, was evangelical when it came to Froebel. Bradley translated and published Froebel's writings, manufactured and sold Froebel's gifts through his toy company, and opened Massachusetts' first kindergarten in Springfield where he taught with his wife. Kindergarten spread to Lowell, but the city did not sustain its 19th century enthusiasm for this institution. As expenditures per pupil began to rise after 1900, enrollment in kindergarten sharply declined in the city.101 Ellen Dorrit Hoffleit (1907-2007) succeeded Barney at Yale. She compiled and edited The Bright Star Catalog,163 a listing of those stars that can be seen with the naked eye, an invaluable resource to both professional and amateur astronomers. Hoffleit also coauthored the General Catalog of Trigonometric Parallaxes164 that contributed to our understanding of the structure of the Milky Way. Hoffleit's materal grandfather was a physics teacher in Königsburg. Hoffleit, we learn from her autobiography, attended public schools in Alabama and Pennsylvania. 165 She earned a PhD in astronomy from Radcliffe after Payne. Hoffleit worked at the Harvard College Observatory but moved to Yale in 1956 where she worked for decades after her formal retirement.166 Connections to Froebel were persistently identifiable in our biographical research on X-ray crystallographers. I found nine different institutions and one person with large roles in the biographies of crystallographers that were directly linked to Froebel's pedagogy. I found no such connections for the astronomers. These data are summarized in Table 1. One need not look for special circumstances that led to many of the careers in astronomy. Proximity, family history, and luck were at work. Fleming was by chance Pickering's maid. Maury's career was arranged through family connections; her interest in astronomy was a birthright. Barney, a Yale researcher, was the daughter of a Yale Professor. Hoffleit was the granddaughter of a physics teacher. Cannon, Payne, and Sawyer cite early experiences with constellations, meteors, and eclipses as responsible for their adult choices. We know little about Leavitt's early schooling. Leavitt's interest in astronomy was piqued at Radcliffe, in Cambridge Massachusetts, her hometown. By happenstance the best observatory in the United States at that time was a short walk away when she was looking for an occupation. Sawyer and Hoffleit also came through Radcliffe, a magnet for talented women at the time and a funnel to the observatory. In the aggregate, this was our best effort -- imperfect, incomplete, and lacking the force of statistics -- to concoct a control experiment through case studies. Froebel was as absent from the biographies of astronomers, as he was present in the biographies of crystallographers.

SUMMARY Others scholars50, 167 now embrace the idea of Rubin3 and Brosterman7 that Froebel's kindergarten unleashed modernism in the arts. If we concede that


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Froebel's crystallography was a powerful influence on proto-visual artists as children, it must have likewise been a powerful influence on youthful protoscientists. It has been recognized among scholars in the history of education that the ideas of Froebel played a general role in exposing women to science at the turn of the 20th century.168 But, did crystallography receive a special boost in female participation, our investigation herein, because of the crystallographic pedagogy of the Froebel kindergarten? Perhaps. But, establishing causality in history is hard. Sociologists have tried to develop methodologies for drawing strong judgments from focused samples. This is the science of qualitative research. I do not know much about it, and suspect that it would be difficult for the crystallographers in our study to embrace such an approach. After all, we crystallographers like statistics, weighted R-values. The "R-value of this study" is pretty high. Still, lack of certainty is preferable to pejorative comments about knitting. Peggy Etter's colleagues in the crystallographic community -- I count myself in this group but unfortunately for a comparatively short time -- are aware that she battled back more than pejorative comments. She couldn't likewise battle back an illness that also took the lives of Kathleen Lonsdale and Dorothy Hodgkin. Elizabeth Wood commented in the International Union for Crystallography newsletter dedicated to "Women in Science and Crystallography" that, "Kathleen Lonsdale wrote to me about a visit from Dorothy Hodgkin when [Lonsdale] was terminally ill with cancer of the bone marrow. She said that when she asked Dorothy what bone marrow did, Dorothy replied, 'I am afraid it does quite a lot.' "

169

If we wish to see social change in the time that we have, we must be proactive. But, we must be effective as well as proactive. The National Science Foundation has sponsored proactivity to increase women and others in STEM disciplines. However, we must implement the right kinds of interventions to actually change the face of the scientific workforce. Figuring out precisely how to change is more difficult than adopting liberal intentions. This is because social science is complicated. It is much harder than crystallography. Therefore, we must seek best practices wherever we might find them, even in the tesselations of small children of the last century, and evaluate their effectiveness. To make a more democratic scientific enterprise, we have to understand the mechanisms for making a more democratic scientific enterprise. Some of the answers may lie in history, waiting to be picked up and carried forward.

AUTHOR INFORMATION E-mail: [email protected]

Notes The author declares no competing financial interest.


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ACKNOWLEDGMENTS This work was supported by the NYU MRSEC Program of the National Science Foundation under Award Number DMR-0820341 as well as from the NSF through DMR-1105000. Many thanks to Hannah Westfall, archivist at Girton College, Cambridge, Karen B. Morgan, archivist of the North London Collegiate School, and Rosemary Davis, Chair of the Old Girl's Association of the Woodford County High School for Girls, as well as Georgina Ferry for her play about Dorothy Hodgkin. Thanks also to Pedro Noguera for introducing the author to the work of Claude Steele. Joel Bernstein made some transformative suggestions. Bill Ojala in St. Paul tracked down an important email address so that we could connect with Peggy's sister and brother, Elizabeth Reveal and John Cairns.

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40.

There were not only chemistry sets for girls in Britain, there were guides for the study of crystals. As Francl indicates in ref. 31, the critic John Ruskin (1819-1900) was a strong advocate for teaching science to women in England and lectured to school children on mineralogy. These lectures were collected in The Ethics of the Dust [Smith, Elder and Co. London, 1865] a dialog between an old lecturer and girls at a boarding school. Ruskin was the intended guide to crystallography for Froebel kindergarten instructors. The Kindergarten Magazine instructs, in conjunction with an introduction to Froebel's second gift, the cube, the cylinder and the sphere: Here the teacher suggests crystallizing of alum, sugar, salt etc. All the forms of the Kindergarten material are taken and considered as under the laws of crystallization. "Ethics of the Dust" by Ruskin is suggested as a timely reading and "Dana's Book on Mineralogy" [!] recommended as a reference book [Schwedler, F. E. The Kindergarten for Teachers and Parents, 1889, 2, 85.] Or the following: "...she was looking into the wonders of crystallography; and I looked and listened, and learned, too. Looking, I saw the models of crystals which she had made from cardboard of various tints -- blue, cherry, primrose, salmon, lilac, court-gray -- all the forms of each system being of one tine. Marvels of dainty work they were; but more than that, for, by thus manufacturing these natural crystal forms, our coming Kindergartner has applied the law, "Learn by doing" to her study of crystallography, and has thus gained a clearer knowledge of crystalline form than she could have gained in any other way. The reading recommended in connection with this subject, was Ruskin's "Ethics of the Dust" and the article in "Appleton's Encyclopedia," and the text-books from which some of the notes were take were Cook's "Chemistry" and Dana's "Manual of Mineralogy" [Poulsson, E. The Kindergarten-primary Magazine, 1890, 2, 42.]

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100. Mills, H. M. The Teachers College Record, 1904, 5, 72. 101. Lazerson, M. Hist. Ed. Quart. 1971, 11, 115. 102. Good, C. A. Founding Friendships: Friendships between Men and Women in the Early American Republic, Oxford University Press, Oxford UK, 2015. 103. Walsh, F. BBC News, 15 May 2012; http://www.bbc.com/news/health-18041884 104. Maddox, B. Rosalind Franklin: The Dark Lady of DNA, Harper Collins, London, 2003. 105. Froebel, F. Mother’s Songs, Games and Stories (trans. Lord, F.; Lord, E.) London: William Rice, 1920. 106. www.norland.co.uk/pages/aboutus/EWhistory1.htm 107. Tsukihara, T. International Union of Crystallography Newsletter, 2005, 13(2). 108. Claborn, K.; Herreros Cedres, J.; Isborn, C.; Zozulya, A.; Weckert, E.; Kaminsky, W.; Kahr, B. J. Am. Chem. Soc. 2006, 128, 14746. 109. Nitta, I. Sci. Papers, Inst. Phys. Chem. Res. Tokyo, 1926, 4, 49. 110. Nitta, I. Bull. Chem. Soc. Japan, 1926, 1, 62. 111. Groth, P. Chemische Kristallographie, Wilhelm Engelmann: Leipzig, 1919 112. Autheir, A. Early Days of X-ray Crystallography, Oxford University Press, 2013. 113. Debye, P.; Scherrer, P. Phys. Zeit. 1917, 18, 291.. (Juno 1917). 114. Gonell, H. W.; Mark, H. Zeit. Phys. Chem. 1923, 107, 181. 115. Mark, H.; Weissenberg, K. Z. Physik. 1923, 16, 1 116. Lonsdale, K. Nature, 1928, 122, 810. 117. Robertson, J. M. Proc. Roy. Soc. London, 1933, 142, 674. 118. Nitta, I.; Watanabé, T. Nature, 1937, 140, 365. 119. Mark, H.; Weissenberg, K. Z. Physik. 1923, 17, 301 120. Huggins, M. L.; Hendricks, S. B. J. Am. Chem. Soc. 1926, 48, 164. 121. Knaggs, I. E. Min. Mag. 1925, 20, 346. 122. Note that Knaggs is referring to the multiplicity of the Wyckoff symmetry. Further in the paragraph when she says, "four-fold symmetry", she is referring to Wyckoff


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positions d, e, and f, with four-fold multiplicities but only two-fold rotational symmetry. 123. Booth, A. D.; Llewellyn, F. J. J. Chem. Soc. 1947, 837. 124. Knaggs, I. E. Proc. Roy. Soc. London, 1929, 122, 69. 125. Gerstäcker, A.; Möller, H.; Reis, A. Zeit. Krystallogr. 1928, 66, 355. 126. Knaggs, I. E. Nature, 1928, 121, 616.

symmetry (Wyckoff a and b in P4/n) would have been a perfectly 127. In fact, 4 appropriate choice of site symmetry, but this was discounted on the premature grounds of packing considerations. 128. Knaggs, I. E. Zeit. Krystallogr. 1929, 70, 185. 129. Pauling, L. The Nature of the Chemical Bond, Cornell University Press: Ithaca NY, 1939. 130. Sidgwick, N. V.; Powell, H. M. Proc. Roy. Soc. A, 1940, 176, 153. 131. Nitta, I. Fifty Years of X-ray Diffraction, Ewald, P. P. ed.; International Union for Crystallography: Utrecht, The Netherlands, 1962; pp. 328-334. 132. Ibid. pp. 484-492. 133. Ibid. pp. 608-611. 134. Goodwin, T. H.; Hardy, R. Proc. Roy. Soc. London. Ser. A, Math. Phys. Sci. 1938, 164, 369. 135. Knaggs, I. E. Proc. Roy. Soc. London, 1935, 150, 576. 136. Bragg, W. H. Nature, 1934, 134, 138. 137. Hughes, E. W. J. Chem. Phys. 1935, 1. 138. Mack, P. in Women of Science: Righting the Record, Kass-Simon, G.; Farnes, P.; Nash, D. eds.; Indiana University Press, Bloomington, 1990. 139. Beatty, B. in Wollons, R. ed. Kindergartens and Cultures: The Global Diffusion of an Idea, Yale University Press, New Haven, CT: 2000; pp 42-58. 140. Woodham-Smith, P. in Friederich Froebel and English Education, Lawrence, E. ed. Routledge: London, 1969; p. 91. 141. Powell, J. H. Harvard University Gazette, 19 March http://news.harvard.edu/gazette/1998/03.19/ReachingfortheS.html

1998;

142. Vassar Encyclopedia: www.vcencyclopedia.vassar.edu/alumni/antonia-maury.html 143. Pickering, E. C. ed. The Draper Catalog of Stellar Spectra, John Wilson and Son: Cambridge, 1890. 144. Cannon, A. J.; Pickering, E. C. The Henry Draper Catalogue, Volumes 21, Harvard College Observatory: Cambridge MA, 1924. 145. Powell, L. P. A History of Education in Delaware, Washington, Government Printing Office, 1893. 146. Johnson, G. Miss Leavitt's Stars, W. W. Norton, New York, 2006.


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147. Bill Bryson comments on the relative merits of the scientific work of the men and women who worked at the Harvard College Observatory: “At the time Leavitt was inferring fundamental properties of the cosmos from dim smudges on photographic plates, the Harvard astronomer William H. Pickering, who could peer into a firstclass telescope as often as he wanted, was developing his theory that dark patches on the Moon were caused by swarms of seasonally migrating insects." Bryson, B. A Short History of Nearly Everything; Black Swan: London, 2004; p. 171. 148. Oberlin was named for the Alsatian pastor, Johann Friederich Oberlin (1740-1826) who is considered in education histories as a forerunner of Pestalozzi and Froebel. Perhaps Leavitt was exposed to some of Froebel's ideas during this time, but she was an adult at this time. 149. Hoffleit, E. D. The Committee on the Status of Women in Astronomy, American Astronomical Society, June 1990: retrieved from www.aas.org/cswa/status/status_june1990.pdf 150. Payne Gaposchkin, C. H. Stellar Atmospheres: A Contribution to the Observational Study of High Temperature in the Reversing Layers of Stars, The Observatory, Cambridge, MA, 1925. 151. Payne Gaposchkin, C. H.; Shapley, H. On the Distribution of Intensity in Stellar Absorption Lines, The Observatory, Cambridge, MA, 1926. 152. Payne Gaposchkin, C. The Galactic Novae, Dover, New York, 1957. 153. Baade, W. Evolution of Stars and Galaxies, (Payne Gaposchkin, C. ed.) Harvard University Press, Cambridge MA, 1963. 154. Haramundanis, K. Cecelia Payne-Gaposchkin. An Autobiography and Other Recollections, Cambridge University Press, Cambridge UK, 1984. 155. O'Sullivan, V. Long Journey to the Border: A Life of John Mulgan, Penguin, New Zealand, 2003. 156. Hogg, H. S. A Third Catalogue of Variable Stars in Globular Clusters Comprising 2119 Entries, University of Toronto, Toronto, 1973. 157. Clement, C. M.; Muzzin, A.; Dufton, Q.; Ponnampalam, T.; Wang, J.; Burford, J.; Richardson, A.; Rosebery, T.; Rowe, J.; Hogg, H. S. Astronom. J. 2001, 122, 2587. 158. Maisel, M.; Smart, L. Helen Sawyer Hogg. Retrieved from Women in Science: A Selection of 16 Significant Contributors (1997): http://www.sdsc.edu/ScienceWomen/credits.html 159. Tiede, T. The Argus-Press, Owosso, Michigan, August, 13, 1985; p. 6; Retrieved from http://news.google.com/newspapers?nid=1988&dat=19850813&id=z2MiAAAAIBAJ &sjid=yasFAAAAIBAJ&pg=4416,3717172. 160. Interview of Helen Sawyer Hogg by David DeVorkin on August 17, 1979, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, http://www.aip.org/history/ohilist/4679.html 161. Clement, C.; Broughton, P. J. Roy. Astronom. Soc. Canada, 1993, 87, 351.


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162. Shea, J. J. The Milton Bradley Story, Newcomen Society in North America: New York: 1973. 163. Hoffleit, D. E.; Carlos, J. The Bright Star Catalog, Yale University Observatory: New Haven, 1982. 164. van Altena, W. F.; Lee, J. T.; Hoffleit, D. E. General Catalog of Trigonometric Parallaxes, 4th Ed. Yale University Observatory: New Haven, 1995. 165. Hoffleit, E. D. Misfortunates as Blessings in Disguise: The Story of My Life, American Association of Variable Star Observers: Cambridge, MA, 2002. 166. Pearce, J. Obituary, The New York Times, April 23, 2007, 167. Olson, M. Children's Culture and the Avant-Garde: Painting in Paris, 1890-1915, Taylor and Francis: New York, 2013. 168. Watts, R. Women in Science. A Social and Cultural History, Routledge: London, 2007. 169. Wood, E. International Union of Crystallography Newsletter, 2000, 8(3). The quote finishes: "It is to the credit of all crystallographers that women are welcomed in their field more than in other science fields, with the possible exception of astronomy. What matters in any field is that the person comes to it with interest and competence. Gender is irrelevant."


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Broader Impacts of Women in Crystallography - Crystal Growth

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