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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



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