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