Beryl May Dent

Beryl May Dent MIEE (10 May 1900 – 9 August 1977) was a British mathematical physicist, technical librarian, and a programmer of early analogue and digital computers to solve electrical engineering problems. She was born in Chippenham, Wiltshire, the eldest daughter of schoolteachers. The family left Chippenham in 1901, after her father became head teacher of the then recently established Warminster County School. She graduated from the University of Bristol in 1923 with First Class Honours in applied mathematics. She was awarded the Ashworth Hallett scholarship by the University of Bristol and was accepted as a postgraduate student at Newnham College, Cambridge.

Beryl May Dent MIEE
Dent in 1928.
Born	10 May 1900 Chippenham, Wiltshire, England
Died	9 August 1977 (aged 77) Sompting, West Sussex, England
Nationality	British
Alma mater	University of Bristol (1927: MSc) Newnham College, Cambridge
Awards	1923: Ashworth Hallett scholarship
Scientific career
Fields	Computer-aided engineering Molecular physics Regression analysis Other fields Intermolecular forces Semiconductor materials Technical library services Thin films Valency
Institutions	University of Bristol Physics Department Metropolitan-Vickers Electrical Company Ltd
Academic advisors	John Lennard-Jones

Dent returned to Bristol in 1925, after being appointed a researcher in the Physics Department at the University of Bristol, with her salary being paid by the Department of Scientific and Industrial Research. In 1927, John Lennard‑Jones was appointed Professor of Theoretical Physics, a chair being created for him, with Dent becoming his research assistant in theoretical physics. Lennard‑Jones pioneered the theory of interatomic and intermolecular forces at Bristol and she became one of his first collaborators. Lennard‑Jones and Dent published six papers together from 1926 to 1928, that were the foundation of her master's thesis, dealing with the forces between atoms and ions. Later work has shown that the results they obtained had direct application to atomic force microscopy by predicting that non-contact imaging is possible only at small tip-sample separations.

In 1930, Dent joined Metropolitan-Vickers Electrical Company Ltd, Manchester, as a technical librarian for the scientific and technical staff of the research department. She became active in the Association of Special Libraries and Information Bureaux (ASLIB) and was honorary secretary to the founding committee for the Lancashire and Cheshire branch of the association. She served on various ASLIB committees and made conference presentations detailing different aspects of the company's library and information service. She continued to publish scientific papers, contributing 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. Dent joined the Women's Engineering Society and published papers on the application of digital computers to electrical design. She retired in 1960, with Isabel Hardwich, later a fellow and president of the Women's Engineering Society, replacing her as section leader for the women in the research department. In 1962, she moved with her mother and sister to Sompting, West Sussex, and died there in 1977.

Early life

The family lived at Boreham Road before moving in 1907 to 22 Portway, Chippenham.

Beryl May was born on 10 May 1900, at Penley Villa, Park Lane, Chippenham, Wiltshire, the eldest daughter of Agnes Dent (1869–1967), née Thornley, and Eustace Edward (1868–1954).[1] She was baptised at St Paul's, Chippenham, on 8 June 1900.[2]^:1 Agnes Thornley and Eustace Edward Dent had married at St Mary's Church, Goosnargh, near Preston, Lancashire, on 27 July 1898.[3] Thornley was educated at the Harris Institute, Preston, passing examinations in science and art.[4] She was a teacher at Attercliffe School, in northeast Sheffield, 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.[5][6] In March 1894, she had applied for the headship at Fairfield School, Cockermouth, making the shortlist, but the board decided to appoint a local candidate.[7]

On 18 March 1889, Eustace Edward Dent was appointed to a teaching assistant position at Portland Road School, in Calderdale, Halifax, after completing a teaching apprenticeship with the school board.[8][9] In the same year, Florence Emily Dent, Eustace's elder sister and Dent's aunt, was appointed head teacher at West Vale girls' school, Stainland Road, Greetland, moving from the Higher Board School at Halifax.[10] In August 1889, Eustace obtained a first class pass in mathematics from the Halifax Mechanics' Institute.[11][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.[13][14][lower-alpha 3] His first teaching post was at Coopers' Company Grammar School, Bow, London,[15] before moving to Chippenham, where he was a senior assistant teacher at the Chippenham County School. After five years at Chippenham, he left in October 1901 to become head teacher of the then recently established Warminster County School, that adjoined the Athenaeum Theatre in Warminster.[16][17][18][lower-alpha 4] He was chair of the Warminster Urban District Council from 1920 to 1922,[lower-alpha 5] and remained as head teacher of the County School until his retirement in August 1929.[22][21][lower-alpha 6]

After moving from Chippenham, the Dent family lived at Boreham Road, Warminster, where houses were built in the early 19th century.[25][26][lower-alpha 7] In April 1907, the family moved to 22 Portway, Warminster, situated a short distance from the County School and the Athenaeum.[20]^:264[27] Eustace was a regular cast member of the Warminster Operatic Society at the Athenaeum and other venues. 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 (The Golden Amulet), a Japanese operetta in three acts by Clementine Ward.[28][29][30] In Princess Ju‑Ju, she played La La, one of the three maidens attendant on the Princess Ju‑Ju, and sang the first act solo, She must be demure.[31][32] In act two of the same musical, she performed in the fan dance, Spirits of the Night.[29][32][lower-alpha 8] She also acted in a scene from Tennyson's Princess at the County School's prize giving day on 16 December 1913.[35][lower-alpha 9]

Education

Warminster County School

Former Warminster County School, where Dent was educated and her father was head teacher.

Dent was educated at Warminster County School, where her father was head teacher. At school, she was close friends with her neighbour at Portway, Evelyn Mary Day, the eldest daughter of Henry George Day, a former butler to Colonel Charles Gathorne Gathorne‑Hardy, son of Gathorne Gathorne-Hardy, 1st Earl of Cranbrook.[36][37][lower-alpha 10] In August 1914, she passed the University of Oxford Junior Local Examination with first class honours, and on the strength of her examination result, she was awarded a scholarship by the County School. In 1915, she passed the senior examination with second class honours and a distinction in French, and subsequently, her scholarship was renewed.[38][39][40] She then joined the sixth form and won the school prize for French in December 1916.[41][lower-alpha 11] In March 1918, she 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 nor an exhibition.[42]

University of Bristol

Paul Dirac, Dent's fellow student on the honours course in mathematics at Bristol.

In 1923, Dent was accepted as a postgraduate research student by Newnham College, Cambridge.

Dent 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 12] For the following academic year, she took the honours course in mathematics at Bristol.[44] After spending the summer of 1921 at her parent's home in Warminster,[45] she returned for the start of the 1921 to 1922 academic year to find that Paul Dirac had joined the mathematics course.[46][lower-alpha 13] 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.[46] Fraser introduced them to mathematical rigour, projective geometry, and rigorous proofs in differential and integral calculus.[47][lower-alpha 14] Dent studied four courses in pure mathematics:

• Geometry of conics; Differential geometry of plane curves
• Algebra and trigonometry; Differential and integral calculus
• Analytical projective geometry of conics
• Differential equations; Solid geometry.[48]

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.[49][lower-alpha 15] Dent studied four courses in applied mathematics:

• Elementary dynamics of a particle and of rigid bodies
• Graphical and analytical statics; Hydrostatics
• Dynamics of a particle and of rigid bodies
• Elementary theory of potential with applications to electricity and magnetism.[48]

Newnham College, Cambridge

In June 1923, she graduated with Dirac, gaining a Bachelor of Science (BSc) degree in applied mathematics with First Class Honours.[50][46][lower-alpha 16] On 7 July 1923, she was awarded the Ashworth Hallett scholarship by the University of Bristol and was accepted as a postgraduate student at Newnham College, Cambridge.[49][51][52][lower-alpha 17] Dent spent a year at Cambridge, leaving in 1924 without further academic qualification, prior to being appointed to a temporary position teaching science at Barnsley Girls' High School, Huddersfield Road, Barnsley.[52] Before 1948, Cambridge University denied women graduates a degree, although in the same year as Dent left Cambridge, Katharine Margaret Wilson was the first woman to be awarded a PhD at Cambridge.[54][lower-alpha 18]

Career

University of Bristol Department of Physics

H. H. Wills Physics Laboratory, University of Bristol, where Dent worked as a researcher.

John Edward Lennard‑Jones, Dent's advisor and co-author at Bristol in the 1920s.

In 1925, Dent was appointed a researcher in the Physics Department at the University of Bristol, with her salary being paid by the Department of Scientific and Industrial Research, the forerunner of the Science and Engineering Research Council (SERC).[56]^:107[52][lower-alpha 19] In 1924, the University of Bristol Council had set aside a portion of a bequest from Henry Herbert Wills for the Department of Physics where Arthur Mannering Tyndall was building up a staff for teaching and research in the H. H. Wills Physics Laboratory, Royal Fort House Gardens.[58][lower-alpha 20] From August 1925, John Lennard‑Jones, Trinity College, Cambridge, was elected Reader in Mathematical Physics.[60][58] In March 1927, Lennard‑Jones was appointed Professor of Theoretical physics, a chair being created for him, with Dent becoming his research assistant in theoretical physics.[61][62]^:24[63][lower-alpha 21] Lennard‑Jones pioneered the theory of interatomic and intermolecular forces at Bristol and Dent became one of his first collaborators.[58][46]

Lennard‑Jones and Dent published six papers together from 1926 to 1928, dealing with the forces between atoms and ions, with the objective of calculating theoretically the properties of carbonate and nitrate crystals.[46][64] Dent's thesis for her master's degree, Some theoretical determinations of crystal structure (1927), was the basis of the three papers that followed in 1927; with Lennard‑Jones, Crystal parameters, and with Lennard‑Jones and Sydney Chapman, Structure of carbonate crystals (1927) and Part II. Structure of carbonate crystals (1927).[lower-alpha 22] On 28 June 1927, she was awarded a MSc degree for her thesis and research work.[65] 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 23] Consequently, Dent was asked to combine her research duties with the post of part-time departmental librarian, the first appointment of librarian in the Department of Physics.[62]^:26[1][lower-alpha 24]

Dent was now living at Clifton Hill House, the university hall of residence for women in Clifton.[66][lower-alpha 25] She had been appointed honorary secretary of the Bristol Cheeloo Association by March 1926.[69] The association's aim was to raise sufficient funds to support a chair of chemistry at Cheeloo University.[66] 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.[70] In 1927, she was one of eleven people elected to the standing committee of the University of Bristol's Convocation, the university's alumni association, and later, represented the Manchester branch of the association.[71][72][67] In 1928, Lennard‑Jones and Dent published two papers, Cohesion at a crystal surface (1928), and with Sydney Chapman, The change in lattice spacing at a crystal boundary (1928), that studied the force fields on a thin crystal cleavage.[73][74] Around this time, quantum mechanics was developed to become the standard formulation for atomic physics.[lower-alpha 26] Lennard‑Jones left Bristol in 1929 to study the subject for a year as a Rockefeller Fellow at the University of Göttingen.[76]

With her collaborator and advisor in Germany, Dent wrote one last paper before leaving the physics department at Bristol: The effect of boundary distortion on the surface energy of a crystal (1929) examined the effect of the polarisation of surface ions in decreasing the surface energy of alkali halides.[77] In December 1929, she resigned her position and it was accepted with regret by the Council of the University of Bristol.[78] She left Bristol for Stretford, Manchester, to become the technical librarian for the scientific and technical staff in the research department at Metropolitan-Vickers.[79]^:232 In 1930, Lennard‑Jones returned to Bristol, as Dean of the Faculty of Science, and introduced the new quantum theories to the Bristol group.[76][58][lower-alpha 27] Marjorie Josephine Littleton was appointed as Dent's replacement on the 1 February 1930. She was the daughter of a local Bristol councillor and a graduate of Girton College, Cambridge. She was later Sir Neville Mott's co-author and research assistant in the Physics Department.[81][82]^:517

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.[83] In 1917, a Research and Education Department was established at the Trafford Park site, when the care of the library came within the remit of James George Pearce, a former engineer in the Transformer Department.[lower-alpha 28] 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.[79]^:193[84] In January 1930, Dent joined the senior scientific and technical staff in the research at department Metropolitan-Vickers.[62]^:49[79]^:193 Technical librarianship emerged as a new scientific career in interwar Britain and rapidly became one of the few types of professional industrial employment that was routinely open to both women and men.[85]^:301

By 1933, the Metropolitan-Vickers library had 3,000 engineering volumes and around the same number in pamphlets and patent specifications.[86] 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.[87] From 1931 to 1936, Dent was honorary secretary to the founding committee for the Lancashire and Cheshire branch of the ASLIB.[88]^:204–205 In 1932, the branch had twenty six members and had organised four meetings, including one addressed by Sir Henry Tizard, the then President of ASLIB. After the war, it formed the basis for the Northern Branch of the association.[89]^:412 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.[90][lower-alpha 29] She served on various ASLIB committees and made conference presentations detailing different aspects of the company's library and information service.[79]^:228[91]

Differential analyser designed by Douglas Hartree, at the Science and Industry Museum in Manchester.

Dent continued to publish papers in applied mathematics and contribute to papers on emerging computational technologies. In On observations of points connected by a linear relation (1935), she developed a detailed reduced major axis method for line fitting that built on the work of Robert Adcock and Charles Kummell.[92][93] For Myers, Hartree, and Porter, in The Effect of Space-Charge on the Secondary Current in a Triode (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.[94] In 1946, she was promoted to section leader of the company's new computation section. Her knowledge of higher mathematics meant that she was often asked to check the mathematics in papers for publication by engineers at Metropolitan-Vickers. For example, Cyril Frederick Gradwell, a graduate of Trinity College, Cambridge, asked her to scrutinise the algebraic part of his work in The Solution of a problem in disk bending occurring in connexion with gas turbines (1950).[95][lower-alpha 30]

In the latter half of her career, Dent became the section leader for the women in the research department that were working on semiconducting materials.[79]^:233 She performed the Fourier analysis in Shorting and Field Corrections in Hall Measurements (1954), that developed a method for correcting the measured Hall effect in semiconductors for inhomogeneities in the applied magnetic field.[97] In 1958, she carried out computer calculations for the mechanical engineering team at the Nuclear Power Group, Radbroke Hall. Their paper outlined a procedure for calculating the theoretical deflection (bending) of a circular grid of support girders for a graphite neutron moderator in a gas-cooled reactor.[98] A general expression was derived from the central deflection of the grid and the maximum bending moment on the central cross-beam for a range of grid diameters.[99]

Dent joined the Women's Engineering Society and published papers on the application of digital computers to electrical design.[100][101] With Brian Birtwistle, she wrote programs for the Manchester University Ferranti Mark 1, that demonstrated that high speed digital computers could provide considerable assistance to the electrical design engineer.[102] Birtwistle would later have an extensive career in the computer industry, working at, amongst others, Honeywell Information Systems and ADP Network Services.[103] She retired from Metropolitan-Vickers in May 1960, with Isabel Hardwich, later a fellow and president of the Women's Engineering Society, replacing her as section leader for the women in the research department.[104][105]^:243

Later life and death

Church of St Mary the Blessed Virgin, Sompting.

Worthing Crematorium.

Dent's funeral was held at St Mary's and a memorial to her is located in the Hospitallers' Room there. Her ashes are interred at Worthing Crematorium.

Dent's father died on 24 June 1954, at their shared home, 529 King's Road, Stretford, with the funeral service taking place at St Matthew's Church, Stretford.[106] Dent had close links to St Matthew's; from 1956 to 1962, she served as a school manager for St Matthew's Church of England Primary School at Poplar Road, Stretford.[52] In 1962, she and her elderly mother, Agnes, moved from Stretford to 1 Cokeham Road, Sompting, a village in the coastal Adur District of West Sussex, between Lancing and Worthing.[107][108] Agnes died on 5 April 1967 and was cremated at the Downs Crematorium on 10 April 1967.[109][lower-alpha 31]

Dent died at her home in Sompting on 9 August 1977 (aged 77).[112][113] She donated her body for medical examination, on the understanding that her remains would be returned for a funeral service at St Mary's Church, Sompting, followed by cremation.[114] Her ashes were interred at Worthing Crematorium, in the Gardens of Rest, towards the Spring Glades, and her entry in the Book of Remembrance at the crematorium states:[115][116][lower-alpha 32]

Beryl May Dent 1900 – A real Christian loved by all – 1977.

There is also a memorial to her in the Order of St John, Hospitallers' Room, at St Mary's Church, where a carver chair bears a brass plaque with the following inscription:[117][lower-alpha 33]

In loving memory of Beryl Dent 1900 – 1977.

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 would mean promotion opportunities for other women, and that married women would still be able to return to work in mid-life.[118] Her Christian faith is perhaps not surprising, given her father's work for the church in Warminster, and the era she grew up in, where religion pervaded social and political life.[119][120] However, it is notable that she remained a committed Christian while pursuing a scientific career. According to Steven Weinberg, science offers no support for belief in God, and that belief in God is unnecessary; a view shared by other scientists. However, Steve Ball, in an article that supports the science of prominent atheistic scientists, states that physics can actually fit well with biblical faith.[121][122]^:2[lower-alpha 34]

Legacy

Atomic force microscopy

An atomic force microscope on the left with controlling computer on the right. Dent's work had direct application to the development of atomic force microscopy.

In 1928, Lennard‑Jones and Dent published two papers, Cohesion at a crystal surface (1928) and The change in lattice spacing at a crystal boundary (1928), that for the first time, outlined a calculation of the potential of the electric field in a vacuum, produced by a thin sodium chloride crystal surface.[73][74] They gave an expression for the electric potential produced by a system of point charges in vacuum (although not a real cubic sodium chloride ionic lattice).[123]^:796–797 The expression for the potential in vacuum, ${\displaystyle \varphi _{0}\left(r\right)}$, at the point r = {x, y, z}, near the cubic lattice of point ions with different signs, the charge ${\displaystyle e_{k}}$, and the period a (a crystalline solid is distinguished by the fact that the atoms making up the crystal are arranged in a periodic fashion), can be represented in the form:[123]^:797

${\displaystyle \varphi _{0}\left(r\right)={\frac {2\pi }{a^{2}}}\sum _{l,m}\sum _{s}{\frac {\left(-1\right)^{s}\exp \left[-\left({\frac {2\pi }{a}}\right){\sqrt {l^{2}+m^{2}}}\left(z+z_{s}\right)\right]}{\left|k_{l,m}\right|}}\times \sum _{k}e_{k}\cos \left[k_{l,m}\left(r_{\parallel }-r_{k}\right)\right]}$

(1)

${\displaystyle r_{\parallel }=\left\{x,y\right\}}$ is the lateral vector that fixes the observation point coordinates in the sample plane.

${\displaystyle k_{l,m}}$ is the reciprocal lattice vector.

s is the number of planes to be calculated inside the crystal; s set to zero would calculate the surface plane.

The expression sums the set of potential static charges for the surface and lower layers of the crystal. Lennard‑Jones and Dent showed that this expression forms a rapidly convergent Fourier series.[123]^:797 Harold Eugene Buckley, a crystallographic researcher at the University of Manchester until his death in 1959,[124]^:481 had suggested that the results obtained in Cohesion at a crystal surface (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 a solution.[125] However, later work by Cleveland, Radmacher, and Hansma, in Atomic Scale Force Mapping with the Atomic Force Microscope (1994), has shown that the Lennard‑Jones and Dent paper had direct application to atomic force microscopy by predicting that non-contact imaging is possible only at small tip-sample separations.[126]

Reduced major axis regression

Richard J. Smith has stated that Dent, in On observations of points connected by a linear relation (1935), was the first to develop a reduced major axis (RMA) regressiom method for line fitting that built on the work of Robert Adcock in A Problem in Least Squares (1878) and Charles Kummell in Reduction of observation equations which contain more than one observed quantity (1879).[92][93] The theoretical underpinnings of standard least squares regression analysis are based on the assumption that the independent variable (often labelled as x) is measured without error as a design variable. The dependent variable (labeled y) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Therefore, the underlying least squares regression assumptions can be violated. RMA regression is specifically formulated to handle errors in both the x and y variables.[127]^:1 If the estimate of the ratio of the error variance of y to the error variance of x is denoted by 𝜆, then the reduced major axis method assumes that 𝜆 can be approximated by the ratio of the total variances of y and x.[128] RMA minimizes both vertical and horizontal distances of the data points from the predicted line (by summing areas) rather than the least squares sum of squared vertical (y-axis) distances.[127]^:2

Linear regression attempts to model the relationship between two variables by fitting a linear equation (straight line) to observed data.

Maurice Kendall and Alan Stuart showed that the maximum likelihood estimator of a likelihood function, depending on a parameter ${\displaystyle \theta }$, satisfies the following quadratic equation:[129]^:387

${\displaystyle \theta ^{2}x^{T}y+\left[\lambda x^{T}x-y^{T}y\right]\theta -\lambda x^{T}y=0}$

(2)

where x and y are the ${\displaystyle \mathbf {X} }$ and ${\displaystyle \mathbf {Y} }$ vectors in a covariance matrix giving the covariance between each pair of x and y variables.

Using the quadratic formula to solve for the positive root (or zero) of (2):[130]

${\displaystyle \theta _{ML}\equiv {\frac {y^{T}y-\lambda x^{T}x+{\sqrt {(y^{T}y-\lambda x^{T}x)^{2}+4\lambda (x^{T}y)^{2}}}}{2x^{T}y}}}$

(3)

Inspection of (3) shows that as 𝜆 tends to zero, the positive root tends to ${\displaystyle \theta _{y}}$ equal to ${\displaystyle {y^{T}y}/{x^{T}y}}$, and as 𝜆 tends to plus infinity, the root tends to ${\displaystyle \theta _{x}}$ equal to ${\displaystyle {x^{T}y}/{x^{T}x}}$.[130] Dent had solved the maximum likelihood estimator in the case where the covariance matrix is not known, that is, when the variances in the x and y variables are unknown.[131]^:1049 Dent's maximum likelihood estimator is the geometric mean of ${\displaystyle \theta _{x}}$ and ${\displaystyle \theta _{y}}$, equal to:[130]

${\displaystyle {\sqrt {\left({y^{T}y}/{x^{T}x}\right)}}}$, where ${\displaystyle x^{T}y}$ is positive.

Dennis Lindley repeated Dent's analysis and stated that Dent's geometric mean estimator is not a consistent estimator for the likelihood function, [132]^{:235–236, 241} and that the gradient of the estimate will have a bias, and this remains true even if the number of observations tends to infinity.[133]^:15 Kenneth Alva Norton, a former consulting engineer with the then National Bureau of Standards, responded to Lindley, stating Lindley's own methods and assumptions lead to a biased prediction.[134] Furthermore, Albert Madansky noted that Lindley took the wrong root for the quadratic in (2) for the case where ${\displaystyle x^{T}y}$ is negative.[135]^:201–203 Subsequently, Theodore Anderson pointed out that the likelihood function has no maximum in this case, and therefore, there is no maximum likelihood estimator.[136]^:3

Although Dent's solution has its theoretical limitations, it is of practical importance, as it likely represents the best a priori estimate if nothing is known about the true error distribution in the model. It is generally much less reasonable to assume that all the error, or residual scatter, is attributable to one of the variables.[133]^:3[128]

Electrical design using digital computers

In the 1950s, British electrical engineers would rarely use a digital computer, and if they did, it would be to solve some complicated equation outside the scope of analogue computers. To a certain extent, engineers were deterred by the difficulty and the time taken to program a particular problem. Furthermore, the varied and often unique problems that arise in electrical design practice, together with the degree of uncertainty of the numerical data of many problems, accentuated this tendency. On 10 April 1956, Dent and Brian Birtwistle presented their paper, The digital computer as an aid to the electrical design engineer (1956), to the Convention on Digital Computer Techniques at the Institution of Electrical Engineers.[137] The paper was intended to show, by describing three relatively simple applications, that the digital computer could be a very useful aid to the electrical design engineer. The three example problems were:

• Impulse voltage distribution on transformer windings
• Supply frequency ripple on transductor performance
• Starting torque of a synchronous motor.[138]

Illustration of transformer windings.

The Manchester University Ferranti Mark 1 computer was used for the calculations in the three problems. Dent was allowed to use the University's library of subroutines, from which the following were taken and incorporated into the programs:[139]

Input of instructions. Input of numerical data in decimal form. Output of results in decimal digits and tabular form.

Mathematical functions. Division. Exponential. Sine and cosine. Square root. Solution of simultaneous equations. Inversion of matrices. Integration of differential equations by Runge–Kutta methods.

Their paper was one of the first to recognise that high speed digital computers could provide considerable assistance to the electrical design engineer by carrying out automatically the optimum design of products.[102] 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 analogue computers.[140] It was not until Dent, with Hartill and Miles, in A method of analysis of transformer impulse voltage distribution using a digital computer (1958), recognised the limitations of the analogue models and developed a digital computer model, and associated program, where non-uniformity in the transformer windings could be introduced and any input voltage applied.[141]

Publications

Selected papers and academic articles

Table of selected papers and academic articles

Year	Title	Co-author(s)	Notes
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.[142]
1927	Some theoretical determinations of crystal structure	Dent (sole author)	Dent's MSc thesis. It formed the basis of the three papers published in 1927.[143]
1927	Some theoretical determinations of the structure of carbonate crystals	John Edward Lennard‑Jones and Sydney Chapman	Test tube with a sample of brown-red Ferrous carbonate. Discusses the structure of the carbonate anion CO^2− 3, a polyatomic ion, in iron(II) carbonate FeCO 3, or ferrous carbonate.[64]
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 Fe^2+ and carbonate anion.[64]
1927	Some theoretical determinations of crystal parameters	John Edward Lennard‑Jones	Simple cubic Body-centred cubic Face-centred cubic Comparison of crystal cubic lattice structures. 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. In rock-salt or sodium chloride (halite) structure, each of the two atom types forms a separate face-centred cubic lattice. Examples of compounds with this structure include sodium chloride itself, along with the other alkali halides, and divalent metal oxides, sulphides, selenides, and tellurides.[144]^:16[145][146]^:682–683
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.[73]
1928	The change in lattice spacing at a crystal boundary	John Edward Lennard‑Jones and Sydney Chapman	Shows that when alkali metal halide crystals are put under tension along their length, they suffer a lateral contraction of the order of 6 percent.[74]
1929	The effect of boundary distortion on the surface energy of a crystal	Dent (sole author)	The effect of polarisation 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.[77][147]
1933	The technical news bulletin and house journal of the Metropolitan-Vickers Electrical Company	Dent (sole author)	The conference was held at the Wills Hall, University of Bristol. There were eight contributors to the subject "the preparation and production of information bulletins, house journals and reports", which was presented at the general session of the tenth annual conference of the ASLIB on the morning of the 23 June 1933.[lower-alpha 35] James George Pearce, Dent's former technical director at Metropolitan-Vickers, was in the chair. Dent described the technical news bulletin and the house journal of Metropolitan-Vickers. The bulletins and journals contained references to current literature, abstracts, news of current interest, and select bibliographies. They were often duplicated owing to the prohibitive cost of printing: "Don't press the printers" was the advice of Dent.[148][149]
1935	On observations of points connected by a linear relation	Dent (sole author)	Dent was the first to describe and develop a detailed reduced major axis method for line fitting. The paper was sent to the Physical Society by Henry Ronald Hassé, Dent's former professor of applied mathematics at Bristol, on 10 July 1934. The paper was refereed by Alexander Aitken, and at the time of publication, commented on by William Edwards Deming.[92][150]
1946	The library and information service of the Metropolitan-Vickers Co. Ltd.	James Steele Park Paton	Describes the information service developed during the last thirty years to meet the needs of the research department at the Metropolitan-Vickers Electrical Company. In response to a request from the senior staff, a weekly "Industrial Digest" was produced from 1945. The digest contained about fifty brief abstracts on factory processes and workshop practice.[151]
1946	What the industrialist expects of an information service	Sir Arthur Fleming	The Polytechnic (now the University of Westminster) on Regent Street, where Dent and Fleming presented at the twenty first annual conference of ASLIB. On 14 September 1946, Dent and Fleming presented at the twenty first annual conference of ASLIB in the Fyvie Hall at the Polytechnic, Regent Street. They stressed the importance of new knowledge and ideas in industry as a condition of progress, and that industry required rapid, accurate, and comprehensive information.[152]
1956	The digital computer as an aid to the electrical design engineer	Brian Birtwistle	The value of the digital computer as an aid to the electrical design engineer is discussed in the light of the authors' extensive use of the Ferranti Mark 1 computer.[lower-alpha 36] Three examples are described:[137] Impulse voltage distribution on transformer windings.[lower-alpha 37] Supply frequency ripple on transductor performance. Starting torque of a synchronous motor.
1956	The authors' replies to the discussion on 'Engineering and scientific applications of digital computers'	Brian Birtwistle	Replies to questions on the digital computer as an aid to the electrical design engineer. Douglas Hartree suggests using an extension of Numerov's method to reduce the time taken to solve the second-order differential equations. Dent and Robinson also support Dr. Robert Kenneth Livesley's recommendation that engineering courses should take into account modern developments with regard to the application of digital computers to engineering practice.[153]
1958	Analysis of transformer impulse voltages by digital computer	Eric Raymond Hartill and James George 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.[154][lower-alpha 38]
1958	A method of analysis of transformer impulse voltage distribution using a digital computer	Eric Raymond Hartill and James George Miles	The paper presents a method of impulse voltage calculation in which non-uniformity in the transformer windings could be introduced and 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.[141][140]

Publications detail

Dent

• Birtwistle, Brian; — (April 1956). "The digital computer as an aid to the electrical design engineer". Proceedings of the Institution of Electrical Engineers. Part B. Radio and Electronic Engineering. London. 103 (1S): 47–53. doi:10.1049/pi-b-1.1956.0008. ISSN 2054-0434. Paper No. 2092 M. The paper was first received 30 January 1956, and in revised form, 5 March 1956. It was published in March 1956 and was read at the Convention on Digital-Computer Techniques on 10 April 1956.
• Birtwistle, Brian; — (April 1956). "The authors' replies to the discussion on 'Engineering and scientific applications of digital computers'" (PDF). Proceedings of the Institution of Electrical Engineers. Part B. Radio and Electronic Engineering. London. 103 (1S): 82–83. doi:10.1049/pi-b-1.1956.0013. ISSN 2054-0434. Retrieved 15 July 2020.
• — (1927). Some theoretical determinations of crystal structure. 25, 13 leaves (MSc). Bristol: University of Bristol Physics Library. OCLC 931574568. DM1961. Retrieved 15 July 2020.
• — (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. Communicated by J. E. Lennard‑Jones.
• — (January 1933). "The technical news bulletin and house journal of the Metropolitan-Vickers Electrical Company". Report of Proceedings of the 10th Conference of the Association of Special Libraries and Information Bureaux. London: ASLIB. 10: 56–58. OCLC 652436848.
• — (1 January 1935). "On observations of points connected by a linear relation". Proceedings of the Physical Society. London. 47 (1): 92–108. Bibcode:1935PPS....47...92D. doi:10.1088/0959-5309/47/1/307. ISSN 0959-5309. Retrieved 15 July 2020. Communicated by Henry Ronald Hassé on 10 July 1934. Includes discussion by William Edwards Deming.
• —; Hartill, Eric Raymond; Miles, James George (1 May 1958). "Analysis of transformer impulse voltages by digital computer". Proceedings of the Institution of Electrical Engineers. London. 4 (41): 259–261. doi:10.1049/jiee-3.1958.0116. ISSN 2054-0612.
• —; Hartill, Eric Raymond; Miles, James George (October 1958) [First published December 1957]. "A method of analysis of transformer impulse voltage distribution using a digital computer". Proceedings of the Institution of Electrical Engineers. Part A. Power Engineering. London. 105 (23): 445–459. doi:10.1049/pi-a.1958.0080. ISSN 2054-040X.
• —; Paton, James Steele Park (1946). Libraries Committee, City Council. "The library and information service of the Metropolitan-Vickers Co. Ltd". Manchester Review. Public Library Review Autumn. Manchester: Manchester Public Libraries. 4: 236–238. ISSN 0025-2026. OCLC 1014381852.
• Fleming, Arthur; — (September 1946). Sanger, Margaret (ed.). "What the industrialist expects of an information service". Report of Proceedings of the 21st Conference of the Association of Special Libraries and Information Bureaux. London: ASLIB. 21: 47–56. OCLC 652436848. Held at Fyrie Hall, the Polytechnic, London, 14–15 September 1946.
• Lennard‑Jones, John Edward; — (3 August 1926). "The forces between atoms and ions. II". Proceedings of the Royal Society. Series A. Containing Papers of a Mathematical and Physical Character. London. 112 (760): 230–234. Bibcode:1926RSPSA.112..230L. doi:10.1098/rspa.1926.0107. ISSN 0950-1207. JSTOR 94629. Retrieved 15 July 2020. Communicated by Sydney Chapman FRS. Received 8 June 1926.
• Lennard‑Jones, John Edward; —; Chapman, Sydney (1 January 1927). "Some theoretical determinations of the structure of carbonate crystals". Proceedings of the Royal Society. Series A. Containing Papers of a Mathematical and Physical Character. London. 113 (765): 673–689. Bibcode:1927RSPSA.113..673L. doi:10.1098/rspa.1927.0015. ISSN 0950-1207. JSTOR 94650. 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.
• Lennard‑Jones, John Edward; —; Chapman, Sydney (1 January 1927). "Some theoretical determinations of the structure of carbonate crystals. II". Proceedings of the Royal Society. Series A. Containing Papers of a Mathematical and Physical Character. London. 113 (765): 690–696. Bibcode:1927RSPSA.113..690L. doi:10.1098/rspa.1927.0016. ISSN 2053-9150. JSTOR 94650. Received 17 November 1926.
• Lennard‑Jones, John Edward; — (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.
• Lennard‑Jones, John Edward; — (1928). "Cohesion at a crystal surface". Journal of the Chemical Society, Faraday Transactions. London. 24: 92–108. doi:10.1039/tf9282400092. ISSN 0014-7672. Retrieved 15 July 2020. Received 10 November 1927.
• Lennard‑Jones, John Edward; —; Chapman, Sydney (1 November 1928). "The change in lattice spacing at a crystal boundary". Proceedings of the Royal Society. Series A. Containing Papers of a Mathematical and Physical Character. London. 121 (787): 247–259. Bibcode:1928RSPSA.121..247L. doi:10.1098/rspa.1928.0194. ISSN 2053-9150. JSTOR 95072. Retrieved 23 August 2020.

Dent as mathematician and programmer

• Edwards, John Charles Manson; Gill, Samuel Sidney; Perkins, Stanley (December 1958). "A Method of Calculating the Deflection of the Graphite Support Grid for a Gas Cooled Reactor". Civil Engineering and Public Works Review. London: Lomax, Erskine & Company Ltd. 53 (630): 1400–1402. ISSN 0009-7861. OCLC 220831595.
• Flanagan, William Francis; Flinn, Paul Anthony; Averbach, Benjamin Lewis (1 June 1954). "Shorting and Field Corrections in Hall Measurements". Review of Scientific Instruments. 25 (6): 593–595. Bibcode:1954RScI...25..593F. doi:10.1063/1.1771138. ISSN 0034-6748.
• Gradwell, Cyril Frederick (1 July 1950). "Asymmetrical Bending of Tapered Disks: The Solution of a problem in disk bending occurring in connexion with gas turbines". Aircraft Engineering and Aerospace Technology. 22 (7): 209–212. doi:10.1108/eb031926. ISSN 0002-2667.
• Myers, David Milton; Hartree, Douglas Rayner; Porter, Arthur (1937). "The Effect of Space-Charge on the Secondary Current in a Triode". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 158 (893): 23–37. doi:10.1098/rspa.1937.0002. ISSN 0080-4630. JSTOR 96742.

ASLIB

• Fleming, Arthur; — (5 October 1946). Gale, Arthur James Victor (ed.). "Association of Special Libraries and Information Bureaux. Annual Conference" (PDF). Nature. London. 158 (4014): 491–492. doi:10.1038/158490b0. ISSN 1476-4687. S2CID 4099552. Retrieved 15 July 2020.

Women's Engineering Society

• — (1957). Cowper-Coles, Constance Hamilton (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.

See also

• Arthur Fleming
• Ferranti Mark 1
• Isabel Hardwich
• Metropolitan-Vickers
• Cecil Frank Powell and Herbert Wakefield Banks Skinner were colleagues of Dent at the Wills Physical Laboratory, Bristol, in the late 1920s
• University of Bristol

Footnotes

1. His siblings took the mathematics examination at the same time.[11]
2. See The Day Training College: a Victorian innovation in teacher training.[12]
3. Aberystwyth originated as a college teaching external degrees of the University of London. See University of London Worldwide history of the external examination system.
4. In 1897, the Government Education Inspectors insisted the Athenaeum must expand if it was to continue as a centre of learning. An initial plan to add a floor to the building was rejected in favour of adding a new adjoining building at a cost of £3,000. The new school also made use of the first floor classrooms in the Athenaeum.[19][20]^:263
5. There is a portrait photograph of Eustace, as chair of the council, in the cafe area of the Civic Centre in Sambourne Road, Warminster.[21]
6. 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.[23] 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.[24]
7. A Warminster town guide of 1924 described Boreham Road as a modern residential quarter of semi-detached villas, pretty gardens, with a tree lined footpath blending the rural with the urban.[26]
8. 

   Market Place in Warminster.
   At the end of the musical, the national anthem of Japan was sung, followed by the British national anthem, and the flags of the Allies were waved from the stage.[29] The Belgian flag was held by a young refugee, Alphonse Cambier, who, with three others, were attending the County School.[29] Germany had invaded Belgium on 4 August 1914, forcing Belgians to flee, with the United Kingdom home to 250,000 Belgian refugees during World War I. Lord Bath placed his vacant houses in the district at their disposal. Amongst others, two large houses in Warminster were made available, one in the Market Place, and one in Silver Street.[33][34]
9. Probably a scene from Princess Ida, the comic opera adaptation by Gilbert and Sullivan.
10. Dent was a bridesmaid at Evelyn's wedding to Maurice Philip Young, a pharmacist, at the Minster Church of St Denys, Warminster, on 7 June 1926. At the time of her marriage, Evelyn was an assistant mistress at the Central County School, Church Road, Bexleyheath. Dent wore printed silk, with a shaded hat to match, and pink pearls, the gift of the bridegroom. She was known to friends and family as May Dent.[36]
11. Dent's sister, Florence Mary, won the same prize for the year below.[41]
12. The University of Bristol was the first higher education institute in England to admit women on an equal basis to men.[43]
13. 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.[46]
14. Dirac would later say that Peter Fraser was the best teacher he had ever had.[46]
15. Her relations with Dirac were strictly formal; they seldom spoke to each other.[48]
16. Dent's sister, Florence Mary, graduated at the same time with a Bachelor of Arts degree.[50]
17. The scholarship was open to female graduates of a recognised college or university, and worth £45 at the time.[53]
18. Wilson later became a successful writer and poet. Wilson's dissertation, Music and English Poetry, featured at The Rising Tide: Women at Cambridge exhibition from October 2019.[54][55]
19. Paul Dirac was also in receipt of a Research Council grant at this point with his research interests listed under Dent's entry in the Research Council's report for the year 1925 to 1926.[57]
20. 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.[59]
21. This was the first appointment of a professor of theoretical physics in the United Kingdom.[59]
22. Sydney Chapman was Lennard‑Jones's PhD thesis advisor at Trinity College, Cambridge.[58]
23. Despite the fact that the department had acquired a second professor and two research fellows.[62]^:26
24. The library had been named after Maria Mercer, the last surviving daughter of John Mercer, a Lancashire weaver who taught himself sufficient chemistry to be elected to a Fellowship of the Royal Society in 1852.[56]^:3 Mercer was the inventor of the process of treating cotton known as mercerisation, and had amassed a considerable fortune. When Maria died, on 22 February 1913 at Clayton-le-Moors, aged 93, her trustees offered "not less than £5,000" to the University of Bristol, towards the endowment of a Chair of Chemistry.[56]^:3
25. May Christophera Staveley was her warden and tutor at Clifton Hill House. Dent returned to Bristol on 22 December 1934 for Staveley's funeral.[67] Dent was a member of the Clifton Hill House Old Students Association.[68]
26. See the Fifth Solvay Conference in 1927.[75]
27. 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.[58] John Murrell has described Lennard‑Jones as "the father of British quantum chemistry".[80]
28. Pearce was later a liaison engineer for European and American companies at Metropolitan-Vickers. He was also Director and Secretary of the British Cast Iron Research Association.[84]
29. Earl Stanhope, President of the Board of Education, was in the chair at the dinner.[90]
30. Along with Dent, Cyril Gradwell was one of the first programmers of the Ferranti Mark 1 computer. He wrote system software routines (for example Input G and Reciprocal G) that had advantages over the original versions written by Alan Turing. He wrote Mark I programs for Ferranti's guided missile work for the Royal Aircraft Establishment (RAE) at Farnborough, and on cotton spinning applications for the British Cotton Industry Research Association's Shirley Institute at Didsbury.[96]
31. Dent's sister, Florence Mary, also lived at the house until her death on 13 September 1986 (aged 84).[110] The move to Sompting was likely made after Florence retired from working life on 22 September 1961. She had been a secretary for the Withington Friendly Burial Collecting Society, Withington, and after its takeover in 1954, for Liverpool Victoria.[111]
32. Dent is interred in row 11, plot 32, on a mowed lawn area, where the markers are in the form of small brass plaques set into the lawn, approximately 15 by 10 cm (6 by 4 in) in size. Dent's sister, Florence Mary, is also interred at the crematorium.[116]
33. Similarly, Dent's mother, Agnes, is remembered on a brass plaque at the east end of the choir stall.[117]
34. See also Has Physics Made Philosophy and Religion Obsolete? (2012) by Ross Andersen and David Albert's review of A Universe From Nothing: Why There Is Something Rather Than Nothing (2012) by Lawrence Krauss.
35. The conference was held at the Wills Hall, University of Bristol, with Dent returning to Bristol for the first time since 1929 after resigning her position in the Physics Department.[148]
36. See also the history of the transistor computer.
37. See the 1958 paper, A method of analysis of transformer impulse voltage distribution using a digital computer.
38. James George Miles served in the electrical branch of the Royal Naval Reserve, before studying at Brighton Technical College, graduating in 1948. After a college apprenticeship with Metropolitan-Vickers, he joined their staff at Manchester. He was awarded an Associated Electrical Industries Fellowship in 1950, and spent one year studying power-system analysis with British Thomson-Houston, before returning to Manchester.[155]

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Bibliography

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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.
• Fleming, Arthur Percy Morris; Churcher, Brian Andrew Graham; Davies, Leonard John (28 February 1952). "The research laboratories of Associated Electrical Industries Ltd". Proceedings of the Royal Society. B — Biological Sciences. 139 (895): 208–235. Bibcode:1952RSPSB.139..208F. doi:10.1098/rspb.1952.0008. PMID 14911826.
• Hennessy, Brian Anthony (2005). "The 2ZY Station at Trafford Park, Manchester". The emergence of broadcasting in Britain. Lympstone: Southerleigh. pp. 190–204. ISBN 978-0-9551408-0-8. OCLC 254929009. Retrieved 3 October 2020.
• Napper, Brian (2003). "The Ferranti Mark 1". Computer 50: The University of Manchester Celebrates the Birth of the Modern Computer. Manchester: University of Manchester. Archived from the original on 10 February 2020. Retrieved 4 September 2020.
• Swinton, Jonathan (4 March 2019). "Women At The Console". Alan Turing's Manchester. Manchester. Archived from the original on 27 August 2020. Retrieved 27 August 2020.

External links

• Four women who changed the face of physics by Helen Briggs, BBC News Online.
• Magnificent Women Engineers is dedicated to women in engineering from the past 100 years.
• History of the School of Physics at the University of Bristol.
• The "Manchester TC" transistor computer at the Computer History Museum.
• Metropolitan-Vickers Electrical Co. Ltd. 1899–1949 by John Dummelow.
• Works by Beryl May Dent at WorldCat.
• Beryl May Dent at zbMATH.
• The Park of Industry is a documentary produced by REELmcr that tells the story of Trafford Park, through a series of filmed interviews with ex-employees and residents.