Trinity Monday Memorial Discourse 2015 James MacCullagh (1809‐47) Professor James G Lunney FTCD MRIA Provost, Fellows, Scholars, Colleagues, Guests and Friends Great, good, unhappy! For his country’s fame Too hard he toiled; from too unresting brain His arachneaen web of thought he wove The planet‐form he loved, the crystal’s frame Through which he taught to trace light’s tremulous train, Shall be his symbol in the cypress grove. In these words, one of Ireland’s greatest mathematicians, William Rowan Hamilton, responded to the shocking death and the all too short life of his friend, colleague and rival, James MacCullagh. It is an honour and pleasure for me, 168 years later, to try to respond in my turn to MacCullagh’s achievements, by presenting the Trinity Monday Discourse on this gifted mathematical physicist in Trinity College Dublin in the first half of the 19th century. I want to thank the Provost for asking me to give the discourse this year, which is the UNESCO Year of Light. In preparing the discourse, and coming to understand this complex individual, I have been greatly helped by the work of several scholars, in particular Brendan Scaife and David Spearman from this College, Jim Bennett from Oxford, and Oliver Darrigol from Paris, who have all written on the life and work of James MacCullagh. 1 James MacCullagh was born in 1809 into a Protestant family, the eldest of twelve children of James and Margaret, in the townland of Landahussey in the parish of Upper Badoney in the valley of the Glenelly River in Co Tyrone. Five sons and three daughters survived early childhood. The Glenelly River runs westward from Landahussey in a steep‐sided valley for about 2 miles to the small town of Plumbridge. It is a very scenic location that is now classified as an Area of Outstanding Natural Beauty. Though the surroundings were idyllic, winning a living from their hill farm was surely a challenge. Reverend William McGhee, who was the rector of Upper Badoney parish and the clergyman who baptised James MacCullagh described the area: There is neither poverty nor riches, none that arrogate to themselves pre‐ eminence, the equality is uncommon… Their general food, oat bread, potatoes, milk and butter….They make a decent appearance on Sunday, mostly clothed in cloth of their own manufacture,… English and Irish are spoken in common by the Protestants and the Catholics. We all carry well together, no party business, we have neither orange or ribbon men. Though the family circumstances were modest there was a strong interest in education. Two brothers of James were to follow him to Trinity. It seems that James MacCullagh commenced his education at the parish school at Castledamph on the Glenelly Road. While James was still young his father moved the family ten miles to Strabane, seemingly to access better education for him. In a presidential address to the Royal Society shortly after MacCullagh’s death, The Marquis of Northampton, gives the following anecdote of his early education: In Strabane he was, while very young, placed in the only respectable school in the town. Here his genius soon displayed itself. After school hours he was almost constantly employed in solving mathematical problems; yet, it is remembered that when Euclid was first put in his hands he was dissatisfied with the task. He was only required to get the solution to the problem by heart, like a copy of verses, and repeat it. There was no attempt made at explanation. This did not suit the character of his mind, which could not rest until it thoroughly understood the nature of everything that came before 2 it. For some days he was restless, unhappy and puzzled, wandering about with Euclid in his hand. In his perplexity he met a neighbour, a working carpenter, a man of cleverness and talent, who, seeing the boy evidently unhappy, was good enough to ask him what was the matter. He immediately told his good‐natured friend that he was obliged to get by heart a set of strange words, the meaning of which he wanted to understand; at the same time showing him the proposition he was committing to memory for the next day’s task. The carpenter sat down with the puzzled boy, and in a short time showed him what a proof was. This was the way in which Professor MacCullagh first learned to prove a proposition in Euclid. Clearly the problem of rote learning is not new, particularly in mathematics. James MacCullagh entered Trinity College Dublin in November 1824, aged fifteen, as a Pensioner, or fee‐paying student, obtaining second place out of one hundred and thirty candidates. He was successful in the Sizarship examination in June 1825, and was second out of ninety‐five candidates. The College Calendar defined sizars thus: This rank is composed of young men whose means are generally much more limited than their talents; therefore, intellectually, their rank is a high one, as the number of very eminent men who have come from this class sufficiently testifies… The sizars have their Commons, and often their chambers, free of expense; they are likewise exempt from all College and tutors’ fees. MacCullagh took up his rooms in College in June 1826 and resided in College for the rest of his life. Up to the beginning of the 19th century Trinity College was essentially an ecclesiastical institution, where an important function was to train priests for the Anglican Church, which was then the established church in Ireland. In the 1820s and 30s Trinity introduced internal reform in order to take account of new trends in education and to avoid parliamentary interference. James MacCullagh benefitted from the revolution in mathematics in Trinity introduced by Bartholomew Lloyd, who 3 was Professor of Mathematics from 1813 to 1822, and then Professor of Natural Philosophy until 1831, when he was elected Provost. MacCullagh had a very distinguished undergraduate career and was elected to scholarship in June 1827. He took his degree examination in 1829. He was on the honours list, indicating that he had taken the medal examination in which gold medals were awarded to the top candidates in mathematics and classics. In mathematics students were expected to be well grounded in analytic geometry, calculus, mechanics and optics and to be familiar with the continental authors, such as Poisson, Laplace and Lagrange. The next big academic test was examination for Fellowship. The examination was highly competitive. It was conducted in Latin, and in public, with all the candidates participating together. The examination included logic, mathematics, natural philosophy, ethics, classical literature and composition, though by 1828 mathematics and natural philosophy were the primary elements. Somewhat earlier Dionysius Lardner had poked fun at the Fellowship election: Will it be credited abroad, that in the University of Dublin, at the election of Fellows, there is actually held an oral examination in physics and mathematics? The development of a function by the theorem of Taylor or Lagrange, or the introduction of a differential equation effected viva voce, and in Latin, are probably phenomena new to the learned world! MacCullagh was unsuccessful in the Fellowship examinations in 1829 and 1831. He succeeded in 1832 and was elected to Fellowship in June of that year. Tenure was for life. The salary was modest, but he was entitled to rooms, and Commons at High Table, free of charge. In due course he could expect to become a Senior Fellow, which commanded a quite substantial salary and influence in the College. He was appointed junior assistant to Franc Sadlier, the Professor of Mathematics, and to the lecturer in Greek. In this time Fellows were forbidden to marry and nearly all had be ordained as priests in the Anglican Church. He chose not be ordained and requested to be elected to one of the three lay Fellowships; one in medicine and two in law. He was elected Jurista. 4 MacCullagh’s first publications, when he was only 21, were communicated to The Royal Irish Academy in 1830. These were “Geometrical theorems on the rectification of the conic sections” and “On the double refraction of light in a crystallised medium according to the principles of Fresnel”. Optics and geometry were the main themes of his scientific career, though it was his work in optics that was more significant. When James MacCullagh commenced his career in Trinity College the wave theory of light had largely replaced the corpuscular theory that had been dominant until nearly the end of the 18th century. Natural philosophers asserted that some kind of medium was required to support the undulations of light, just as for other kinds of wave. To this mysterious supporting medium they gave the name ether, and many of the scholars of the time devoted much effort to try to discover the properties of this hypothetical substance. Because the velocity of light is so high, the elastic ether needed to have very low density, while at the same time be exceedingly strong; and it not present any hindrance to the passage of solid objects. It was supposed to pervade all space, including material bodies. It was believed that the propagation of light in transparent materials was governed by the way the matter particles interact with the ether. At first it was imagined that the vibrations of the ether were similar to sound waves in a gas where the particle vibration is longitudinal, to and fro along the direction of wave propagation. However, through experiments on double refraction in the mineral, Iceland spar, it became clear that the ether vibration had to be transverse, where the vibrations are perpendicular to the direction of propagation.