Berkeley and Byrne

Whilst the physical Library is closed, research on the collections continues apace. In our latest post Dr Clare Moriarty, IRC Postdoctoral Fellow in Philosophy, writes about her research into the intersection between maths and art and the early nineteenth-century Irish mathematician Oliver Byrne, the ‘Matisse of Mathematics’.

Clare will also be presenting at the The Art + Science Reading Group on 18 June at 6.30pm and registration is via this link. The group is now a virtual gathering of thinkers, researchers and the incurably curious. Organised by PhD candidates Amelia McConville (School of English and Institute of Neuroscience) and Autumn Brown (School of Education and Science Gallery Dublin) and supported by Science Gallery Dublin and the Trinity Long Room Hub, the series will explore the evolutionary and revolutionary kinship between two approaches to understanding the universe and our place within it.

Clare writes;

One is a name familiar to all who know the university: George Berkeley. Berkeley was an 18th century philosopher, Anglican bishop, mathematical malcontent, and Trinity student and tutor. The second, Oliver Byrne, is a different creature altogether. Born in 1810 near Avoca in Wicklow, Byrne mixed a life-long devotion to mathematics and mathematics education with: circulating tracts in America detailing close-combat styles (!) to be used in pursuit of Irish Independence, inventing something called the Byrnegraph, writing colourfully against phrenology, and basically living the hard life of an inventor-cum-educator with his wife Eleanor, who was herself a brilliant meteorologist. Byrne had a connection of sorts to Trinity. He claimed he learned his mathematics here. However, he is not recorded as ever having matriculated. So, we have two figures, a century apart, from very different worlds, but united by lifelong preoccupations with mathematics (regard Berkeley’s ‘Of Infinites’, an essay presented to the Dublin Philosophical Society in 1707).

Byrne—if he is known by people at all—is known for his majestic edition of Euclid’s Elements.

Here, Byrne uses coloured diagrams to present that Junior Cert syllabus treasure, the Pythagorean Theorem. This is not “art for art’s sake”; Byrne had a serious pedagogical insight into the difficulties of teaching maths and believed using colours could more judiciously represent the abstract properties of geometric objects.

Example: It’s a mistake to think of a geometric line as having any breadth. When concentrating on a line in its own right Byrne brings this into focus by using two colours bumping up against each other, to suggest a one dimensional boundary, rather than anything with suggested thickness.

Byrne shows a distinctive philosophy of education here: grappling with overcoming the problems of representing necessarily abstract geometric objects in a 3-dimensional learning scenario.

Byrne continued to use colour as a conceptual tool in his instruction. In the little-known work ‘The Young Geometrician’, which lives in Early Printed Books, Byrne expands his method to describe geometric constructions, or, how things need to move when setting up various geometric problems. This time colour is used to mark fixed versus moving parts. So, in these diagrams, Byrne conveys that the moving one of two set squares is the red one.

The process starts out simply, but we can see that it quickly develops into a procedure for fairly sophisticated direction.

TCD Manuscripts are the custodians of box of treasures given to the university by Byrne’s wife, Eleanor. It includes the beautiful manuscript of Byrne’s last book, The Trinal Calculus. The elaborate pictorial frontispiece suggests that Eleanor Byrne prepared the document.

And again, we have fascinating mathematical connections to Berkeley whose infamous 1734 tract The Analyst criticised the foundations of calculus, and inflamed what became a near-century long search for more rigorous logical foundations. Byrne’s strange treatise is (1) dedicated to solving Berkeley’s problems:

And when we look to see what Byrne provided by way of an appendix, it’s just his copy of The Analyst.

The above shows the possibility of demonstrating significant links between two key thinkers with a few key resources. Distance from primary material during Covid-19 is challenging. Now that archive access is not a short-term option, I find myself reminded that the sources that first struck me as relevant—those that first caused me to photograph them for personal use—are very likely the ones that epitomise the project.

Dr Clare Moriarty

IRC Postdoctoral Fellow, Philosophy, TCD

The Moon Landing and Sir William Rowan Hamilton

Space exploration would be unthinkable without the contribution of the Trinity College graduate, mathematician, poet and Professor of Astronomy William Rowan Hamilton (1805-1865), best known as the inventor of quaternions. Quaternions provide a mathematical notation for representing orientations and rotations of objects in three dimensions – essential for space flight. They are routinely employed by NASA, and were used in simulations and in plotting the orbit of the missions to the moon. These equations are also used in many other established and emerging technologies, from the computer games industry to molecular dynamics.

Among the Library’s manuscript collections is the tiny notebook which contains Hamilton’s earliest surviving workings-out of the quaternion equation. As he recounted to Peter Guthrie Tait in a letter of 15 October 1858, ‘[I] felt the galvanic circuit of thought close; and the sparks which fell from it were the fundamental equations between i, j, k; exactly such as I have used them ever since. I pulled out on the spot a pocket-book, which still exists, and made an entry’.

The first ‘written’ recording of the quaternion equation was a piece of graffiti scratched by Hamilton on Broome Bridge in Dublin. In a letter to his son, Hamilton recalled the circumstances around his ‘discovery’ on 16 October 1843, ‘which happened to be a Monday, and a council day of the Royal Irish Academy – I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal…yet an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance … nor could I resist – unphilosophical as it may have been – to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula … but of course, as an inscription, has long since mouldered away’.

Although the inscription degraded within Hamilton’s lifetime the site is now commemorated with a plaque. 

Mathematicians and scientists from around the world (some with NASA connections) have made pilgrimages to see the little notebook in the Manuscripts & Archives Reading Room. The manuscript was also filmed for tomorrow’s RTE broadcast ‘The day we landed on the Moon’, where Professor Peter Gallagher, Adjunct Professor of Astrophysics at Trinity and Head of Astronomy and Astrophysics at DIAS, will explain the direct relationship with the Apollo missions.

Hamilton’s significance for the moon landing itself was recognised by Neil Armstrong when he visited the Library of Trinity College Dublin a few years ago. Whilst being shown around the Old Library he stopped at the marble bust of Sir William Rowan Hamilton and discussed the role of such calculations in the control of spacecraft.

Estelle Gittins



What is Life? Celebrating Erwin Schrödinger and the science collections in the Library of Trinity College Dublin

In 1943, Erwin Schrödinger (1887-1961), Nobel-prize winning physicist and Director of Dublin Institute for Advanced Studies (DIAS), delivered three public lectures entitled What is Life? at Trinity College Dublin as the DIAS statutory lecture. The lectures were published as a book in 1944 and had an immediate and powerful impact on the development of molecular biology including inspiring the discovery of DNA.

To mark the anniversary, and to coincide with the major international conference ‘What is Life?’ Schrӧdinger at 75 – the Future of Biology, Archivist Estelle Gittins has collaborated with Professor Luke O’Neill, one of the conference organisers, to curate an exhibition now on show in the Old Library of Trinity College Dublin. The exhibition, and accompanying online exhibition, showcase some of the Library’s most significant scientific and mathematical collections.

At the outbreak of World War II, Schrӧdinger was invited to Dublin by President Éamon de Valera to become Director of the School of Theoretical Physics at Dublin Institute of Advanced Studies, where he stayed until 1956. The exhibition examines what attracted him to Dublin; one of the reasons was the chance to walk in the footsteps of one of his heroes, Ireland’s most renowned scientist Sir William Rowan Hamilton (1805-1865).

Hamilton made numerous advances in maths and science reflected in the vast collection of his papers held in the Library, but he is most famous for developing Quaternions, the mathematical notation for representing orientations and rotations of objects in three dimensions. Quaternions are essential for calculating orbital rotation in space flight; they are routinely employed by NASA, and are also relied upon by the computer gaming industry. The exhibition includes the tiny notebook containing Hamilton’s first scribbled recording of the Quaternion equation made as he walked by the Royal Canal at Broome Bridge in Dublin. The display also includes poetry and sketches that provide a glimpse of the private man as well as the genius. Schrödinger has been described as the scientific heir to Hamilton and made use of the Hamiltonian operator in his wave equation.

Whilst in Dublin, the sociable Schrödinger joined a circle of intellectuals sheltering in neutral Ireland including Irish physicists Shelia Power and Kathleen Lonsdale who had returned from Edinburgh and London respectively. The exhibition includes the papers of some of those friends and colleagues, including a first edition of What is life? inscribed by Schrödinger for his close friend and Trinity College Provost Albert McConnell (1903-1993). Schrödinger also spent time with fellow Nobel-prize winner, Ernest Walton (1903-1995). Walton, a Trinity graduate and lecturer, is most famous, (along with John Cockcroft), for the splitting of the atom in 1932, which constituted the physical demonstration of Einstein’s law E=mc. On display is Walton’s first communication of the breakthrough, an understated letter to his fiancée Freda Wilson confiding, ‘Cockcroft and I made what is in all probability a very important discovery in the lab … It opens up a whole new field of work which may go a long way towards elucidating the structure of the nucleus of the atom’. This is displayed alongside Walton’s Nobel medal. Ernest Walton very generously donated his scientific and personal papers to the Library in 1993.

The exhibition also looks at the important academic and cultural legacy of the What is life? lecture series including the 40th anniversary commemorations where an older Professor Walton met a younger Professor Hawking. There is also a selection of the literary and artistic works inspired by the notion of ‘Schrödinger as a Dubliner’ such as the musical Improbable Frequency produced by the Rough Magic Theatre Company, whose own archives were donated to the Library in 2017.

The conference Schrödinger at 75: the future of Biology will be streamed live on the website

The exhibition What is Life? Celebrating Erwin Schrödinger and the science collections in the Library of Trinity College Dublin will be on display in the Long Room of the Old Library until 31 October and the online version can be accessed here

Estelle Gittins

With thanks to Prof Luke O’Neill, Prof David Wilkins, Dr Jane Maxwell, Aisling Lockhart, Gillian Whelan, Greg Sheaf and Clodagh Neligan

To Aleppo Gone

'The Prospect of Aleppo' from Henry Maundrel 'Journal of a Journey from Aleppo to Jerusalem 1697' Fag.4.33

‘The Prospect of Aleppo’ from Henry Maundrel Journal of a Journey from Aleppo to Jerusalem 1697 Fag.B.4.33

For anyone who watches current news footage from Aleppo, it is hard to imagine what this ancient city once was. For centuries it was a peaceful, vibrant, multi-cultural centre with a strong relationship with the West based on trade and tourism. These unique items from the Library’s Research Collections reflect the cultural intersections between East and West once nurtured in Aleppo.

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Galbraith’s Account of the Foucault Pendulum Experiment in Dublin

In 1851, Léon Foucault amazed the world by demonstrating the rotation of the earth using a simple pendulum. As the earth spins, the swing-plane of a pendulum turns around. Within a month or so, the experiment was repeated in Dublin by two Irish scientists, Joseph Galbraith and Samuel Haughton, both fellows of Trinity College and both members of the Royal Irish Academy.

Engraving in L’Illustration of Foucault’s pendulum in the Panthéon, Paris

Engraving in L’Illustration of Foucault’s pendulum in the Panthéon, Paris

Galbraith kept a diary, which is now in the Manuscripts and Archives Research Library (TCD MS 3826). The entries for the months April to July, 1851 give us a day-by-day account of the activities of Galbraith and Haughton. The first relevant entry is for 17 April, recording that the two scientists were in Ringsend with Wilfred Haughton, Samuel’s cousin. Wilfred was Chief Engineer of the Dublin & Kingstown Railway, and the engine factory beside Grand Canal Basin, with its lofty roof, was an ideal location for the experiments. The pendulum length was 35.4 feet or 10.8 metres.

Following preliminary testing, six experiments were carried out, each lasting between 15 and 30 hours. The azimuthal angle of the pendulum, that is, the angle between the swing-plane and a north-south line, was recorded every 20 minutes, requiring one of the team members to be present throughout each experiment. The precession of the pendulum occurs slowly, taking well over a day to complete a full circle.

TCD MS 3826 diary entry for 17 April 1851

TCD MS 3826 diary entry for 17 April 1851

There are about 25 diary entries relevant to the experiments. They detail who was present during various periods. In the final experiment, a full rotation was achieved in a time of 28 hours and 26 minutes. The theoretical period is 28 hours and 21 minutes, not far from the observed period. According to an article in the Philosophical Magazine, “Messrs Galbraith and Haughton have pursued their research with all imaginable precautions”. Their impressive results confirm this assessment.

A full account of the experiments appears in the Proceedings of the Royal Irish Academy, Volume 116C, pages 1-15. Appendix A of this report contains a list of all the relevant entries from Galbraith’s diary. A copy of the report is available online.

Peter Lynch, School of Mathematics and Statistics, UCD


  • Lynch, Peter, 2016: Replication of Foucault’s pendulum experiment in Dublin. Proc. Roy. Irish Acad., 116C, 1-15. doi:10.3318/PRIAC.2016.116.03. (PDF:
  • Manuscripts and Archives Research Library, Trinity College Dublin, TCD MS 3826, Diary of Joseph Galbraith for April and May 1851.