Beryl May Dent
Beryl May Dent (10 May 1900 – 9 August 1977), was a British mathematical physicist, technical librarian, and a programmer of early analog and digital computers to solve electrical engineering problems. A graduate of the University of Bristol, Dent wrote her master's thesis on the forces between atoms and ions, with the objective of calculating theoretically the properties of carbonate and nitrate crystals. Later work has shown that the results she obtained had direct application to atomic force microscopy by predicting that non-contact imaging is possible only at small tip-sample separations.
Beryl May Dent MIEE | |
---|---|
Dent in 1928. | |
Born | Chippenham, England | 10 May 1900
Died | 9 August 1977 77) Sompting, England | (aged
Alma mater | |
Awards | Ashworth Hallett scholarship |
Scientific career | |
Fields | |
Institutions |
|
Academic advisors | John Lennard-Jones |
In 1930, she joined Metropolitan-Vickers Electrical Company Ltd (Metropolitan-Vickers), Manchester, as a technical librarian for the scientific and technical staff of the research department. She contributed to papers on numerical methods for solving differential equations by the use of the differential analyser that was built for the University of Manchester and Douglas Hartree. She was the first to develop a detailed reduced major axis method for the best fit of a series of data points. Later in her career she became leader of the computation section at Metropolitan-Vickers, and then a supervisor in the research department for the section that was investigating semiconducting materials.
Early life
Beryl May Dent was born on 10 May 1900, at Penley Villa, Park Lane, Chippenham, Wiltshire, the eldest daughter of Eustace Edward Dent (1868–1954) and his wife, Agnes (1869–1967), née Thornley.[1] She was baptised at St Paul's, Chippenham, on 8 June 1900.[2] Her mother, Agnes, was educated at the Harris Institute, Preston, Lancashire, passing examinations in science and art.[3] She was a teacher at Attercliffe School, before moving to Goosnargh School, near her hometown of Preston, where her elder brother and sister, John William and Mary Ann Thornley, were the head teachers.[4] In March 1894, she had applied for the headship at Fairfield School, Cockermouth, making the short list, but the board decided to appoint a local candidate.[5] Agnes and Eustace married at St Mary's Church, Goosnargh, on 27 July 1898.[6]
Her father, Eustace, had been educated at the Halifax Mechanics' Institute, obtaining a first class pass in mathematics.[7][lower-alpha 1] He then enrolled on a degree course at University College, Aberystwyth in the Education Day Training College.[lower-alpha 2] In January 1894, he was awarded a first by Aberystwyth, and a first in the external University of London examinations.[8][lower-alpha 3] He first taught at Coopers' Company Grammar School, Bow, London,[9] before moving to Chippenham, where he was a senior assistant teacher at the County School. After five years at Chippenham, he left in October 1901 to become head teacher of the then recently established Warminster County School, located next to the Athenaeum Theatre.[10] He was chair of the Warminster Urban District Council from 1920 to 1922, and remained as head teacher of the County School until his retirement in August 1929.[11][lower-alpha 4] Eustace was regular cast member of the Warminster Operatic Society; Beryl May Dent and her younger sister, Florence Mary, would often appear with him on stage in such operettas as Snow White and the seven dwarfs and the Princess Ju-Ju.[14][lower-alpha 5]
Education
Dent was educated at Warminster County School, where her father was head teacher. In August 1914, she passed the University of Oxford Junior Local Examination with first class honours. In the following year, she passed the senior examination with second class honours and a distinction in French.[16] She then joined the sixth form and won the school prize for French in December 1916.[17][lower-alpha 6] In March 1918, Dent applied for a scholarship in mathematics from Somerville College, Oxford, one of the first two women's colleges in Oxford. She was highly commended but was not awarded a scholarship for that year, nor an exhibition.[18]
She was accepted on to the general Bachelor of Arts (BA) degree course at the University of Bristol and passed her intermediate degree examinations in June 1920.[lower-alpha 7] For the following academic year, she took the honours course in mathematics at Bristol.[20] After spending the summer of 1921 at her parent's home in Warminster,[21] she returned for the start of the 1921/1922 academic year to find that Paul Dirac had joined the mathematics course.[22][lower-alpha 8] Dent and Dirac were taught applied mathematics by Henry Ronald Hassé, the then head of the Mathematics Department, and pure mathematics by Peter Fraser. Both of them had come from Cambridge.[22] Fraser introduced them to mathematical rigour, projective geometry, and rigorous proofs in differential and integral calculus.[23][lower-alpha 9]
There was a choice of specialisation in the final year; applied or pure mathematics. As the only official, registered fee-paying student, Dent had the right to choose, and she settled on applied mathematics for the final year. The department could offer only one set of lectures so Dirac also had to follow the same course.[25] In June 1923, she graduated with Dirac, gaining a Bachelor of Science (BSc) degree in applied mathematics with First Class Honours.[26][lower-alpha 10] On 7 July 1923, she was awarded the Ashworth Hallett scholarship by the University of Bristol and was accepted as a research student at Newnham College, Cambridge.[28][lower-alpha 11]
Career
University of Bristol
In 1924, the University of Bristol Council set aside a portion of a bequest from Henry Herbert Wills for the Department of Physics where Professor Arthur Mannering Tyndall was building up a staff for teaching and research in the H. H. Wills Physics Laboratory, Royal Fort Gardens.[30][lower-alpha 12] In the same year, Dent returned to Bristol and was appointed a researcher in the Physics Department.[32] From August 1925, John Lennard-Jones, from Trinity College, Cambridge, was elected Reader in Mathematical Physics.[33] In March 1927, he was appointed Professor of Theoretical Physics, a Chair being created for him, with Dent becoming his research assistant in theoretical physics.[34][lower-alpha 13] He pioneered the theory of interatomic and intermolecular forces at Bristol and Dent became one of his first collaborators.[35]
Lennard-Jones and Dent published six papers together between 1926 and 1928, dealing with the forces between atoms and ions, with the objective of calculating theoretically the properties of carbonate and nitrate crystals.[36] Dent's thesis for her master's degree, Dent 1927, Some theoretical determinations of crystal structure, was the basis of the three papers that followed in 1927; Lennard-Jones and Dent (1927), and with Sydney Chapman, Lennard-Jones, Dent, and Chapman (1927a, 1927b).[lower-alpha 14] On 28 June 1927, Dent was awarded a Master of Science (MSc) degree for her thesis and research work.[37] In 1927, the physics laboratory at Bristol had a surplus of funds, and so it was decided that the funds would be used to provide more technical help.[lower-alpha 15] Consequently, Dent was asked to combine her research duties with the post of part-time departmental librarian.[38]
Dent was now living at Clifton Hill House, the university hall of residence for women in Clifton.[39][lower-alpha 16] She represented the University of Bristol Association of Alumni in 1927, and then later, the Manchester branch of the association.[41] She had been appointed honorary secretary of the Bristol Cheeloo Association by March 1926.[42] The association's aim was to raise sufficient funds to support a chair of chemistry at Cheeloo University.[39] In an effort to publicise the cause and raise money, she presented to the local branch of the Women's International League in October 1928.[43] In the same year, Lennard-Jones and Dent published two papers, Lennard-Jones and Dent (1928), and with Sydney Chapman, Lennard-Jones, Dent, and Chapman (1928), that studied the force fields on a thin crystal cleavage.[44]
Around this time, quantum mechanics was developed to become the standard formulation for atomic physics.[lower-alpha 17] Lennard-Jones left Bristol in 1929 to study the subject for a year as a Rockefeller Fellow at the University of Göttingen.[46] With her collaborator and advisor in Germany, Dent wrote one last paper before leaving the physics department at Bristol: Dent (1929) examined the effect of the polarisation of surface ions in decreasing the surface energy of alkali halides.[47] In December 1929, Dent resigned her position and it was accepted with regret by the Council of the University of Bristol.[48] She left Bristol for Stretford, Manchester, to become the technical librarian for the scientific and technical staff in the research department at Metropolitan-Vickers.[49] In 1930, Lennard-Jones returned to Bristol, as Dean of the Faculty of Science, and introduced the new quantum theories to the Bristol group.[50][lower-alpha 18]
Metropolitan-Vickers
Metropolitan-Vickers was a British heavy industrial firm, based at Trafford Park, Manchester. They were well known for industrial electrical equipment and generators, street lighting, electronics, steam turbines and diesel locomotives. They built the Metrovick 950, the first commercial transistorised computer.[53] In 1917, a research department was established at the Trafford Park site, when the care of the library came within the remit of James George Pearce. He made the library the centre of a new technical intelligence section. In 1929, the technical intelligence section was substantially reorganised and expanded, and placed under the directorship of James Steele Park Paton.[54] Dent joined the research department in January 1930 as one of only two women on the senior scientific and technical staff.[55]
By 1933, the Metropolitan-Vickers library had 3,000 engineering volumes and around the same number in pamphlets and patent specifications.[56] Besides covering electrical subjects, the library covered accountancy, employment questions, and subjects of interest to the sales department. It also issued a weekly bulletin, scrutinised patents, handled patents taken out by research staff, and exchanged information with associated companies.[57] From 1931 to 1936, Dent was honorary secretary to the founding committee for the northern branch of the Association of Special Libraries and Information Bureaux (ASLIB).[58] She was also a delegate at the fourteenth International Conference on Documentation and was invited to the Government's conference dinner on 22 September 1938 at the Great Dining Hall of Christ Church, Oxford.[59][lower-alpha 19] She served on various ASLIB committees and made conference presentations detailing the workings of different aspects of the company's library and information service.[60]
Dent continued to publish papers in applied mathematics and contribute to papers on emerging computational technologies. In Dent (1935), On observations of points connected by a linear relation, she developed a detailed reduced major axis (RMA) method for line fitting that built on the work of Adcock (1878) and Kummell (1879).[61] In Myers, Hartree, and Porter (1937) she provided the key numerical integrations for differential equations to aid in the calculation of the space charge limitation of secondary current using a differential analyser.[62] In 1946, she was promoted to section leader of the company's new computation section, and in the latter half of her career, became the section leader for the women in the research department that were working on semiconducting materials.[63] She joined the Women's Engineering Society and published several papers on the application of digital computers to electrical design.[64] She retired from Metropolitan-Vickers in 1960.[65]
Death
Dent's father had died on 24 June 1954 (aged 85), at their shared home, 529 Kings Road, Stretford.[66] Two years after her retirement, Dent and her elderly mother, Agnes, moved from to Stretford to 1 Cokeham Road, Sompting, West Sussex, a village in the coastal Adur District of West Sussex, between Lancing and Worthing.[67] Agnes died on the 5 April 1967 (aged 97) and was cremated at the Downs Crematorium on 10 April 1967.[68]
Beryl May Dent died at her home in Sompting on 9 August 1977 (aged 77).[69][lower-alpha 20] She donated her body for medical examination, with the understanding that her remains would be returned later for a burial service at St Mary's Church, Sompting, and afterwards, cremated at the Downs Crematorium.[71] Dent never married, believing that getting married, and the subsequent pressures of family responsibilities, would be a "wastage" of a woman's training. However, she also believed that women leaving employment (to get married) meant promotion opportunities for other women, and that married women could still return to work in mid-life.[72]
Legacy
Professor Richard J. Smith has stated that Dent, in Dent (1935), On observations of points connected by a linear relation, was the first to develop a reduced major axis method for line fitting that built on the work of Adcock (1878) and Kummell (1879).[61] At the time of publication, Dent's referee, William Edwards Deming, was indifferent to Dent's paper.[73] However, when Deming later developed his own line of best fit for a two-dimensional dataset, now known as Deming regression, this turned out to be a special case of the reduced major axis method developed by Dent.[74] Deming's exposition of his method, in Deming (1964), Statistical Adjustment of Data, does not cite Dent's work, but probably should have under the accepted norms of intellectual honesty.[lower-alpha 21]
In 1928, Lennard-Jones and Dent published two papers, Lennard-Jones and Dent (1928) and Lennard-Jones, Dent, and Chapman (1928), outlining the calculation of force fields on a thin crystal surface.[44] Buckley (1951, p. 178), suggests that the results obtained in Lennard-Jones and Dent (1928), should be treated with caution. For example, the contraction a crystal plane would suffer under the conditions prescribed would not be the same as that of a similar plane with a solid mass of crystal behind it. Another difficulty arises because calculation of crystal surface field force fields are so great that simplifying assumptions have to be made to render them capable of any solution at all.[75] However, later work by Cleveland, Radmacher, and Hansma (1994) has shown that the Lennard-Jones and Dent paper has direct application to atomic force microscopy by predicting that non-contact imaging is possible only at small tip-sample separations.[76]
Considerable research had been devoted to determining a transformer's internal transient voltage distribution. Early attempts were hampered by computational limitations encountered when solving large numbers of coupled differential equations with analog computers.[77] It was not until Dent, Hartill, and Miles (1958b) recognised the limitations of the analog models and developed a digital computer model, and associated program, where any degree of non-uniformity in the transformer windings could be introduced and any form of input voltage applied.[78]
Publications
Year | Title | Co-author(s) | Notes | Ref. |
---|---|---|---|---|
1926 | The forces between atoms and ions. II | John Edward Lennard-Jones | Extends earlier results to provide a complete table of forces between the monovalent and divalent ions of the inert gases. | [79] |
1927 | Some theoretical determinations of crystal structure | Dent's MSc thesis. It formed the basis of the three papers published in 1927. | [80] | |
1927 | Some theoretical determinations of the structure of carbonate crystals | John Edward Lennard-Jones and Sydney Chapman | Discusses the structure of the carbonate anion CO2− 3, a polyatomic ion, in iron(II) carbonate FeCO 3, or ferrous carbonate. |
[81] |
1927 | Some theoretical determinations of the structure of carbonate crystals. II | John Edward Lennard-Jones and Sydney Chapman | Discusses the work required to separate iron(II) carbonate into its constituent iron(II) cations Fe2+ and carbonate anion. |
[82] |
1927 | Some theoretical determinations of crystal parameters | John Edward Lennard-Jones | The surface plane of a face-centred cubic lattice was derived by Lennard-Jones and Dent and has been used extensively in physisorption studies. They simplified the calculation of the Lennard-Jones potential by noting that the ions under study were isoelectronic with inert gas atoms, and thus, there was no need to introduce additional empirical L-J parameters into the equation. | [83] |
1928 | Cohesion at a crystal surface | John Edward Lennard-Jones | Calculation of the surface energy of solids. Shows that for an ionic substrate a charged particle would be most strongly adsorbed, but that the electrostatic forces were very short range, and for greater distances, were smaller than the van der Waals' forces. A dipole would be adsorbed in the same manner as a charged particle but much less strongly. | [84] |
1928 | The change in lattice spacing at a crystal boundary | John Edward Lennard-Jones and Sydney Chapman | Shows that when all alkali metal halide crystals are put under tension along their length, they suffer a lateral contraction of the order of 6 percent. | [85] |
1929 | The effect of boundary distortion on the surface energy of a crystal | The effect of polarization of surface ions in decreasing surface energy of the alkali halide crystals is studied. It is shown that for a series of alkali halide crystals, it is the deformability of the surface ions which largely controls the distortion at the surface. In general, close-packing and wide inter-planar spacing tend to lower the free surface energy in crystals. | [86] | |
1933 | The technical news bulletin and house journal of the Metropolitan-Vickers Electrical Company | |||
1935 | On observations of points connected by a linear relation | Dent was the first to describe and develop a detailed reduced major axis (RMA) method for line fitting. Includes commentary by William Edwards Deming. | [87] | |
1946 | The library and information service of the Metropolitan-Vickers Co. Ltd. | J. S. P. Paton | ||
1946 | What the industrialist expects of an information service | Sir Arthur Fleming | Describes the information service developed during the last thirty years to meet the needs of the research department at the Metropolitan-Vickers Electrical Company. | [88] |
1956 | The digital computer as an aid to the electrical design engineer | B. Birtwistle | ||
1956 | The authors' replies to the discussion on 'Engineering and scientific applications of digital computers' | C. Robinson and others | ||
1958 | Analysis of transformer impulse voltages by digital computer | E. R. Hartill and J. G. Miles | A review of the paper below after it was published as an individual paper in December 1957 and republished in Part A, Power Engineering, Proceedings of the Institution of Electrical Engineers. Hartill and Miles also worked at Metropolitan-Vickers. | [89] |
1958 | A method of analysis of transformer impulse voltage distribution using a digital computer | E. R. Hartill and J. G. Miles | The paper presents a method of impulse voltage calculation in which any degree of non-uniformity in the transformer windings could be introduced and any form of input voltage applied. The derivation of the transformer circuit is discussed, together with a digital computer program for the solution of the resulting differential equations. | [90] |
See also
References
- Ranger 2014, p. 1; Birth certificate 1900.
- Ranger 2014, p. 1.
- Preston Chronicle 2 February 1889, p. 5.
- Preston Herald 27 January 1894, p. 2; Preston Herald 26 July 1899, p. 5.
- West Cumberland Times 17 March 1894, p. 3.
- Lancashire Online Parish Clerks 1898.
- Halifax Courier 31 August 1889, p. 3.
- The Welshman 28 July 1893, p. 6; Carnarvon and Denbigh Herald 19 January 1894, p. 3.
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- Wiltshire Times 1 May 1897, p. 4; Salisbury Journal 26 October 1901, p. 8; The Salisbury Times 22 November 1901, p. 6.
- Wiltshire Times 10 August 1929, p. 2; Wiltshire Times 25 May 1935, p. 4.
- Wiltshire Times 27 December 1930, p. 9.
- Murray 2016.
- Warminster & Westbury journal 29 February 1908; Wiltshire Times 28 November 1914, p. 6; Howell 1987.
- Wiltshire Times 12 June 1926, p. 4.
- Wiltshire Times 11 December 1915, p. 3; Wiltshire Times 29 August 1914, p. 5.
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- University of Bristol 2019.
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- Mehra 2001, p. 671.
- Mehra & Rechenberg 1982, pp. 13–14.
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- Western Daily Press 28 June 1923, p. 7; Mehra & Rechenberg 1982, p. 13, I.3 and Footnote 18.
- Western Daily Press 28 June 1923, p. 7.
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- Mott 1955, p. 175; Mehra & Rechenberg 1982, p. 13, I.3 and Footnote 18.
- Mehra & Rechenberg 1982, p. 13, I.3 and Footnote 18; Mellor 1935, pp. 358–359.
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- Brightman 1956, pp. 204–205.
- The Times 23 September 1938, p. 15.
- Black, Muddiman & Plant 2007, p. 228; Dent 1933, p. 56.
- Smith 2009, p. 477; Choudhary & Nagaraja 2017, p. 41.
- Froese Fischer 2003, pp. 95–96.
- Black, Muddiman & Plant 2007, p. 233.
- The Woman Engineer Summer 1948, p. 216, p. 264 in vol.; The Woman Engineer Autumn 1957, pp. 9–12, pp. 151–154 in vol.
- Reynolds 1960, p. 3.
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- BT Archives 1961, p. 207, Vol. 11; BT Archives 1963, p. 105, Vol. 4.
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- "No. 50671", The London Gazette, 1 October 1986, p. 12718.
- Will 1975, p. 1.
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- Dent, Hartill & Miles 1958b.
- Lennard-Jones & Dent 1926, p. 230.
- Dent 1927, p. 4.
- Mellor 1935, pp. 358–359.
- Mellor 1935, p. 359.
- Sammis 1972, p. 16; Ben-Ephraim & Folman 1984, p. 682–683.
- Weaver 1960, p. 734.
- Davey 1934, p. 383.
- Clark 1934, p. 326; Bickle 1960, p. 111.
- Smith 2009, p. 477.
- Fleming & Dent 1946b, pp. 491–492.
- Dent, Hartill & Miles 1958a, p. 259.
- Dent, Hartill & Miles 1958b, p. 259; Degeneff 2004, p. 396.
Footnotes
- A number of his siblings took the mathematics examination at the same time.[7]
- See Thomas 1978, pp. 249–261 The Day Training College: a Victorian innovation in teacher training.
- A number of major universities originated as university colleges teaching external degrees of the University of London. See University of London Worldwide history of the external examination system.
- The school closed at the end of the summer term 29 July 1931, after the Wiltshire County Council Education Authority built a new secondary school for Warminster.[12]. The building was used as the town library until 1958, and then by Warminster Youth Centre, but is now owned and managed by the Athenaeum Trust.[13]
- Beryl May Dent was known as May Dent by schoolfriends and family.[15]
- Dent's sister, Florence Mary, won the same prize for the year below.[17]
- The University of Bristol was the first higher education institute in England to admit women on an equal basis to men.[19]
- The course of mathematics at Bristol University normally lasted three years, but because of Dirac's previous training, the Department of Mathematics had allowed him to join in the second year.[22]
- Dirac would later say that Peter Fraser was the best teacher he had ever had.[24]
- Dent's sister, Florence Mary, graduated at the same time with a Bachelor of Arts degree.[27]
- The scholarship was open to female graduates of any recognised college or university, and worth £45 at the time.[29]
- Tyndall became the "father" of the School of Physics. A lecturer and then professor who researched the mobility of ions in gases, Tyndall persuaded the Bristol industrialist Henry Herbert Wills to endow a purpose-built physics laboratory.[31]
- This was the first appointment of a professor of theoretical physics in the United Kingdom.[31]
- Professor Sydney Chapman was Lennard-Jones's PhD thesis advisor at Trinity College, Cambridge.[30]
- Despite the fact that the department had acquired a second professor and two research fellows.[38]
- May Christophera Staveley was her warden and tutor at Clifton Hill House. Dent returned to Bristol on 22 December 1934 for Staveley's funeral.[40]
- See the Fifth Solvay Conference in 1927.[45]
- In 1932, Lennard-Jones was elected to the Plummer Chair of Theoretical Chemistry in the University of Cambridge: The first person to hold a Chair of Theoretical Chemistry anywhere in the world.[51] Professor John N. Murrell has described Lennard-Jones as "the father of British quantum chemistry".[52]
- Earl Stanhope, President of the Board of Education, was in the chair at the dinner.[59]
- Dent's sister, Florence Mary, a retired insurance secretary, also lived at the house until her death on 13 September 1986 84).[70] (aged
- For example, compare equations (34) and (35) in Dent (1935, p. 99) with (4), (5), and (6) in Deming (1964, p. 103).
Bibliography
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- Dent, Beryl May (1 October 1929). "LV. The effect of boundary distortion on the surface energy of a crystal". Philosophical Magazine and Journal of Science. London. 8 (51): 530–539. doi:10.1080/14786441008564909. ISSN 1941-5982. Retrieved 15 July 2020. Communicated by Professor J. E. Lennard-Jones.
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- Dent, Beryl May (1957). Cowper-Coles, C. H. (ed.). "Opportunities in the Metropolitan-Vickers Electrical Company's Research Department for Girls of Good Scientific Education". The Woman Engineer. Autumn 1957 (pages 151 to 154 in the volume). London. 8 (6): 9–12. ISSN 0043-7298. Retrieved 15 July 2020.
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- Lennard-Jones, John Edward; Dent, Beryl May; Chapman, Sydney (1 January 1927a). "Some theoretical determinations of the structure of carbonate crystals" (PDF). Proceedings of the Royal Society. Series A. Containing Papers of a Mathematical and Physical Character. London. 113 (765): 673–689. doi:10.1098/rspa.1927.0015. ISSN 0950-1207. JSTOR 94650. Retrieved 15 July 2020. Received 3 November 1926. Chapman provided the calculation of the electrostatic potential energy of an infinite array of electrical charges distributed according to the scheme determined by X-ray analysis.
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- Lennard-Jones, John Edward; Dent, Beryl May (1 May 1927). "CXVI. Some theoretical determinations of crystal parameters". Philosophical Magazine and Journal of Science. London. 3 (18): 1204–1227. doi:10.1080/14786440508564290. ISSN 1941-5982. Retrieved 15 July 2020.
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Miss Beryl May Dent ... who became associates of the Society in 1956.
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May Dent, a Warminster County School fellow scholar and daughter of Mr. E. E. Dent (headmaster).
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On April 5, peacefully, at home 1 Cokeham Road Sompting, Lancing, Agnes Dent 97 years widow of Eustace Edward DENT and beloved mother of Beryl May and Florence Mary. Service at St. Mary Church Sompting, on Monday, April 10, at 2:15 pm followed by cremation at the Downs Crematorium.
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Archives
- BT Archives (September 1961). Manchester and Stoke-On-Trent Telephone Directory. British Phone Books 1880–1984 (Online database). 11. Stretford: BT Heritage. p. 207.
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Further reading
- Byers, Nina; Williams, Gary (2006). Out of the shadows: contributions of twentieth-century women to physics. Cambridge: Cambridge University Press. ISBN 978-0-521-82197-1. OCLC 1050066680.
- Hennessy, Brian Anthony (2005). "The 2ZY Station at Trafford Park, Manchester". The emergence of broadcasting in Britain. Lympstone: Southerleigh. ISBN 978-0-9551408-0-8. OCLC 254929009.