Science at St Andrews by Herbert Westren Turnbull

Herbert Westren Turnbull, Regius Professor of Mathematics at the University of St Andrews, wrote an article Men of Science: General in James B Salmond (ed.), Veterum Laudes (Oliver and Boyd, Edinburgh, 1950), 108-119. We give a version of his article describing the history of science at the University of St Andrews:


The story of the sciences in the College of St Salvator is rooted in the still earlier history of the University. It goes back to Laurence of Lindores, who was one of the first professors and the master of the College of St John. His commentary on the Physics was in use throughout the universities of Central Europe until the time of Copernicus, and served to introduce the new philosophy of its founder William of Ockham and of his disciple Jean Buridan, who became Rector of the University of Paris in 1327.

Up to the end of the eighteenth century the science of the University is confined to Mathematics and Natural Philosophy. It was part of the liberal education which each regent gave to his pupils, a course based upon the time-honoured Pythagorean quadrivium of knowledge. Archbishop Schevez, the Chancellor of the University from 1478 to 1496, who was of European repute as an astronomer and astrologer, doubtless followed Laurence of Lindores by encouraging his own studies at St Andrews. Indeed one, Jasper Laet, in 1491, dedicated to him a booklet on the "sentiments of astronomers concerning the eclipse of the Sun," commending him for having "brought from the darkness of obscurity into the light of day the mathematical sciences which through the negligence of the Scotch had become nearly forgotten." A second year student in 1572, James Melville, describes his studies at the sister College of St Leonard's, and mentions the "Primarius, a guid, peacable, sweit auld man, who luiffed me weill, teached the four speaces of Arithmetik and sum thing of the Sphere." In his third and fourth years Melville heard the "aught buikis of Physiks" and "lerned the buikis de Coelo and Mateors, also the Sphere, more exactlie teachit be our awin Regent."

On the establishment of the University of Glasgow, Andrew Melville, who had matriculated at St Mary's College in 1560, was chosen to be Principal, and later returned from Glasgow to become Principal of his old college, St Mary's. A man of exceptional ability and charm he had already travelled widely and had studied at Paris under Ramus. This celebrated mathematician and philosopher was the Martin Luther among the men of science, refuting the logic of Aristotle, and siding with the practical geometer against Euclid. Following this lead, Melville set about reforming the courses first at Glasgow, then at St Andrews, establishing a four years curriculum, and insisting that, instead of the ancient arrangement "the naturell philosophie, metaphisicks and principis of mathematicks" in this order, arithmetic and geometry should be taken first. His zeal for reform roused opposition, and the consequent reaction led to the neglect of mathematics. The eclipse of Andrew Melville and the rise of George Buchanan caused a reversion to the traditional state of things. According to a curious custom that had grown up in Scotland and long survived, the same regent took the class from beginning to end. Melville however insisted on choosing men to teach according to their talents. What was to be taught, first as a general foundation and then in particular subjects such as law and mathematics, was laid down by Act of Parliament, when in 1579 it was declared that after a prescribed course in Latin, Greek, and elocution "the fourth Regent sall teach in Greek samekle of the phisikis as is neidfull in the spheir," and that "the mathematician now in St Salvator's college sall reid within the same four lessons ouklie in the mathematick sciences in sic dayis and houres as sall be appointed." It would seem that the allusion is to Homer Blair, who entered the college as a fellow-bejant with John Napier and later became a lecturer in mathematics.

It is probable that Andrew Melville's schemes were only carried out imperfectly, for in 1621 the last vestiges of his reforms were swept away. On the ground that it had "bred confusion in the professions of sciences," Parliament revoked the ratification of 1579 and "restored the first foundations of the said colleges." As Professor Burnet writes: "The fact that the medieval curriculum survived both the Revival of Learning and the Reformation without substantial change is the cardinal fact in the history of St Andrews University."

Nevertheless this was the time when, according to David Hume, there lived and worked the greatest genius Scotland had produced. In the 500th year of the College we also celebrate the 400th anniversary of the birth of John Napier, whose invention of logarithms was the first essentially new mathematical advance that took place since the time of the ancient Greeks. The construction of the seven-figure tables involved far more than the devoted study of twenty years; it involved the imagination to lay bare, and then to organise, those concepts of relative motions and rates of changes that only became clear and distinct a hundred years later through the work of Newton and his contemporaries. The work was carried out in the seclusion of Merchiston, Napier's baronial home near Edinburgh, from 1594 to 1614. As a lad of thirteen he had lost his mother, and shortly afterwards was sent to "the triumphant college of St Salvator" where he matriculated. In those days, as we may well suppose, the College was no home of quiet academic studies; accordingly his uncle (Adam Bothwell, Bishop of Orkney), who took a kindly interest in the lad, advised a change. "I pray you, schir," he wrote to John's father, "to send your son Jhone to the schuyllis; over to France or Flanderis; for he can leyr na guid at hame, nor get na proffeit in this maist perullous worlde." So abroad John went: and during his sojourn he eagerly studied the history of the Arabic number notation and traced it to its Indian source, but it was during the year at St Andrews that his interest had been aroused in both arithmetic and theology. The preface to his Plain Discovery of the Whole Revelation of St John which was published in 1593, contains a reference to his "tender yeares and barneage in Sanct Androis" where he first was led to devote his talents to the study of the Apocalypse. The students were exercised once a week in theological discussions, at which one of the masters presided, and the rest were present and took a share in the debate. Napier, who throughout all his life was characterised by singleness of heart and the gentlest disposition, seems nevertheless to have been able to hold his own and even "to play a conspicuous part in the gladiatorship of intellect affected by his youthful competitors."

A change in the prospects for the newer learning and experimental philosophy came in the middle of the seventeenth century, when in 1668 James Gregory was appointed by King Charles II to the newly-founded Chair of Mathematics in St Salvator's College. This was due to Sir Robert Moray who, according to tradition, had been a student in the University. He was accomplished and versatile, a zoologist, geologist, chemist, mathematician and musician; a recluse yet a man of affairs, who had great influence at Court, having previously joined Charles II in his exile. Moray shares with Theodore Haak the credit for persuading the King to found the Royal Society: and there is still a tradition in Scotland that the choice of St Andrew's Day for the Anniversary meeting in London is a compliment to Robert Moray, who presided at the earliest gatherings. During those fertile years, Moray conducted a long and varied scientific correspondence with Huygens in the Netherlands, and his frequent journeys between London and Scotland afforded him an opportunity of keeping friends north of the Border in touch with the world of science. This intercourse was particularly acceptable to James Gregory: but for this, as he put it, "he would be lost to the world." Nor was the traffic in new ideas all one way: a copy of a letter from Huygens to Moray, written from the Hague and stimulated by the recent discovery of Robert Boyle on the "spring of air," is still preserved in our University Library. It in turn stimulated Gregory to prove mathematically the correctness of Huygens' surprising appeal to Napier in his logarithmic interpretation of atmospheric pressure.

For six years (1668-1674) there worked in the College this man of genius who in an era of exceptional brilliancy was held to be second only to Isaac Newton. James Gregory was the greatest in a family who for 200 years had occupied university Chairs upon twenty-two occasions, representing mathematics, medicine, chemistry, history and philosophy at St Andrews, Edinburgh, Aberdeen and Oxford. On leaving St Andrews, James Gregory went to Edinburgh as her earliest mathematical professor, to be succeeded a year later, after his untimely death at the height of his powers, by his nephew, David, who subsequently in 1692 went to Oxford at the recommendation of Isaac Newton. Meanwhile, James, a younger brother of David, was appointed at the age of twenty to the Chair of Philosophy at St Andrews (1685-91), but succeeded to the vacancy in Edinburgh where he remained as mathematician till 1725. In due course a third and younger brother, Charles, held the Chair at St Andrews (1707-39) and was succeeded by his son David who occupied the Chair until 1765. Among the direct descendants of the elder James Gregory a talent for medical sciences and for philosophy was conspicuous, but mathematics once more reappeared at the fifth generation in Duncan Farquharson Gregory (1813-44) who became a Fellow of Trinity College, Cambridge.

James Gregory arrived in St Andrews (1668) at the height of his creative activity and in his thirtieth year. He had already written four short books of deep originality, the first in Aberdeen five years previously, then two at Padua where he drew his inspiration from the school of Galileo and Cavalieri and then a fourth at London during the summer when he was on his way home from Italy. In the Optica Promota (1663) he gave an account of mirrors and lenses that revealed high geometrical skill and made the original proposal for constructing a reflecting telescope. With this, a modest affair only a few feet long, he hoped to replace the refracting telescopes that had grown to prodigious lengths as a result of Galileo's initial invention. With a simple diagram Gregory explained how the light rays on passing along the cylindrical tube would strike a large parabolic mirror and be reflected through a focus to a small concave mirror standing on the central axis of the tube, from which by a second reflexion they resume their course and pass out at a central aperture in the first mirror to an eye-piece.

In the same year Gregory set out for Padua, and on his way through London persuaded Rieve, who was an expert craftsman, to try to fashion a mirror suitable to the design: but with the tools available nothing better was achieved than a crude polish with cloth and putty. Gregory accordingly gave the matter up but not without interesting Hooke, that prince of experimenters, who eventually succeeded in making such a telescope twelve years later. Meanwhile and independently, Newton, who was four years Gregory's junior, had devised and constructed a reflecting telescope in 1668, though it differed from Gregory's by directing the rays after the second reflexion into a path at right angles to the axis, the eye-piece being consequently set at the side and not at the end of the tube. Then in 1672 Cassegrain devised and constructed a model on the Gregorian pattern, but with a convex secondary mirror replacing the original concave.

In Italy Gregory, inspired by the recent advances of the Italian and French schools, made his first discoveries in the differential and integral calculus, probably quite unaware that Barrow and Newton were doing the like at Cambridge. On returning to London in 1668 Gregory learnt from his friend Collins of a new method for expanding a logarithm by an infinite series that had just been published by Mercator. From this event mathematics in its modern form may be said to date. Gregory at once divined its importance and admitted that "it was a hard matter in this age to write a booke that should presently be rendered naught." It supplied the one weapon that was lacking in his armoury, and thus equipped he arrived at the College of St Salvator in the autumn of 1668.

During his three months stay in London before he travelled north Gregory was elected Fellow of the Royal Society, where he took an active part in the meetings. In one communication he offered queries on motion and light, upon the effect of heat and cold on weight, and of loadstones on the flight of falling bodies, and of reflexion and refraction on gunfire: "to mak experiments of refractions it might be convenient to shoot guns well fixed at several inclinations into wooden vessels, full of liquor cowered ower with fin linnen." He was searching for an analogy to the path of light particles. The volcanic booklet, the Exercitationes that he wrote at London in reply to Huygens who had criticised the Vera Quadratura, one of his earlier books, drew from Moray the remark: "Mr Gregory is truly well versed in mathematics but the fire of his youth needs some softening," and he went on to apportion praise and blame impartially to the combatants. Despite its pugnacity the booklet is a tour de force, with a bewildering variety of novel ideas concealed in a verbiage of medieval geometry, yet containing a forthright solution of a problem on the rhumb line that had mystified men for a century. The mystery concerned the surprising likeness between a table of meridional parts upon a nautical chart and a table of logarithms. Edward Wright had constructed the former fifteen years before the appearance of Napier's work, and, as Collins had remarked, Wright "made a table of logarithms before logarithms were invented and printed, but did not know he had done it." Mercator proposed to wager "a good sum of money against whoso would fairly undertake" to resolve the puzzle. Gregory's answer amounted to integrating the trigonometrical function called the secant of an angle and from it producing a logarithm.

The six years that Gregory spent at St Andrews were a period of great intellectual activity, enhanced at the end of the first year by news from Collins that a young pupil of Barrow's at Cambridge, Isaac Newton by name, was performing wonders in the analyticks. The occasional visit of Moray, the letters from Collins, with the newly-instituted Philosophical Transactions and now and then a book, kept Gregory in touch with friends in England and abroad. In this way he learnt of Newton's telescope and thereupon entered into a friendly correspondence on the merits of the two patterns. He received an occasional formula but no sustained account of Newton's mathematical advances. But by a strange accident Gregory received two copies of Transactions No. 79 and not one of No. 80 which contained Newton's own account of his experiments with the spectrum. The misunderstanding and criticism that followed the publication of this epoch-making discovery had a deplorable effect upon Newton. An unwillingness to impart, which Collins had noticed at their first meeting, now grew to be a sheer refusal. How different might have been the sequel had the facts been known to Gregory at the outset, as he was both open-handed and competent when confronted with novel and startling evidence.

This period of discovery culminated for Gregory in the central expansion theorems of interpolation and the differential calculus, the former of which he announced in a letter to Collins, November 1670, and the latter of which he exemplified in the following February by half a dozen examples and again a year later by the solution of Kepler's problem - on determining the theoretical position in its orbit of a planet at a given time - which Gregory solved by invoking the properties of the cycloid and repeated differentiation. As was customary in those days, the results were communicated without a hint of how they were reached. Happily the rough notes on which the work was based have been preserved: they are written on the blank spaces of the letters he received, usually on those from Collins, but in this case on a letter from Gideon Shaw, a bookseller in Edinburgh who supplied him with paper from Holland: and paper was scarce. In this performance Gregory anticipated Brook Taylor, to whom this particular method has hitherto been attributed, by forty-five years. Alluding to a new edition of his Quadratura, Gregory wrote to Collins: "I purpose to add to it several universal methods, as I imagine as yet unheard of in mathematics, both in geometrie and analyticks: I am afraid I can have it but naughtilie done here: and therefore I humbly desire your concurrence to try how I can have it done in London, and advertise me the first occasion. ... I derive from that same ground an universal method of resolving equations numerically but without tables. ... Ye need not be so close-handed of anything I send you: ye may communicate them to whom you will, for I am little concerned if they be published under other's name or not."

Unfortunately Gregory never published this, his crowning achievement, and the progress of mathematics was needlessly retarded thereby. For Gregory withheld the revision, on learning from Collins that Newton had anticipated him. He generously waited - and waited in vain - for Newton to break the silence. How close Gregory and Newton were in mathematical thought may be judged from the fact that on one occasion independent statements of the same discovery - the infinite series for the inverse sine - crossed in the post.

Gregory did not exaggerate when he spoke of his universal methods as yet unheard of in mathematics. What he and Newton were doing simultaneously at St Andrews and Cambridge was fundamentally to inaugurate a revolution in mathematics, comparable to that effected in arithmetic by the introduction into Europe of the Arabic numerals. To reckon with Ramus in sixties, as was done of old in Babylonia and Greece, or to continue to write in Roman numerals, would have rendered logarithm tables impossible: it is to the decimal system that we owe the vast contributions of Napier and Kepler. It was the transference of the precision and controlled approximation, which are manifest in the great medieval numerical tables, to the formulae of algebra, that was the decisive step, into the unknown, taken by these two men of genius.

Gregory took energetic steps to set up an observatory in St Andrews - the first to be erected in Britain. He worked in the lengthy upper room of the University Library with its unbroken view of the country to the south. He gained the confidence of men of goodwill who helped to provide the necessary instruments: and on one occasion he persuaded the townsfolk of Aberdeen to hold a church-door collection for this purpose. He sought expert advice from Hooke and from Flamsteed, then a young and enthusiastic astronomer at Derby. "Having a commission for such a noble design," he wrote in a letter (1673) to Flamsteed where he freely admitted his ignorance and inexperience "in ye most considerable things belonging to it, I have 2 Pendulum clocks makinge with long swinges, vibrating seconds; and pointinge houres, minits and seconds without striking, and also one little Pendulum clock, with a short Pendulum, vibrating 4 times a second, also without striking, for discerning small Intervalls when there may be a pointe of a seconde in Question: as for Telescopes Mr Tock is makinge one of an 100 foot, which I mind to take, if Mr Hook can show me to mannage it, as he Promiseth. I think our Steeple [St Regulus Tower] which I lately mentioned may helpe me in this. Mr Tock hath one (as he saith to me) - by him, of 50 foot, which I also mind to take, for I think it can be mannaged upon a platforme above the Observatorye."

Gregory proposed to erect this as a third storey of the Parliament Hall, "being as we all judge the fittest place and least expense," immediately above the upper hall which the three clocks continue to adorn, and on the floor of which there slants his line running truly north and south: for, as he stated to Flamsteed, the walls of the building diverge 9 or 10 degrees from the meridian. The boards have perished upon which Gregory marked the line but the position is preserved. So, too, is the wall-bracket beside the window that held his quadrant or telescope, and also the trident standing upright upon what was then a bare hill top to the south and in full view from the window.

The observatory was planned to have six tall windows facing north, south, and east in pairs, with a still higher platform above it all for making observations towards the north over the intervening buildings. But the scheme collapsed: and in 1674 Gregory accepted a call to the Chair of Mathematics in the University of Edinburgh. He had met with discouragement and prejudice among his colleagues "because some of their scholars, finding their courses and dictates opposed by what they had studied in the mathematics, did mock at their masters, and deride some of them publicly. After this, the servants of the college got orders not to wait on me at my observations: my salary was kept back from me; and scholars of most eminent rank were violently kept from me, contrary to their own and their parents' wills, the masters persuading them that their brains were not able to endure it. These, and many other discouragements, oblige me to accept a call here to the College of Edinburgh, where my salary is nearly double, and my encouragement otherwise much greater."

Besides the three clocks there remain at St Andrews very few traces of Gregory's astronomical instruments. There is no evidence that the great astrolabe of Humphrey Cole, the finest extant Elizabethan scientific instrument, was part of Gregory's collection. The Department of Natural Philosophy, where the astrolabe is still exhibited, has long possessed apparatus for astronomical and physical demonstrations: some of it may date from the time of Homer Blair: its small Gregorian telescope is an eighteenth century model. As for the observatory, a small building was certainly erected before the year 1713 on a site at the extreme south end of West Burn Lane, but according to the University Minutes, vol. 4, it was dismantled in 1736 and remained a ruin for another century. It was marked on the plan of the city that appeared in local guide books as late as 1845. A telescope and stand belonging to the Department of Mathematics were presented by Professor Fischer about 1870.

The family of Gregory has been equally renowned for mathematics and medicine. The first trace of this double interest occurs in the inaugural oration at St Salvator's College of James Gregory, the nephew. After a broad survey of existing knowledge he described medicine as the most uncertain of the natural philosophies, but he called on men to extend the analytical method to all those problems to which its genius can be extended: and he looked for a universal analysis that, for example, could be applied to problems dealing with the mind.

A small book on practical mathematics in manuscript at the University Library bears the name of James Gregory, Professor of Mathematics in St Andrews, and the date 1696, which is puzzling, because James the nephew occupied the Chair in Edinburgh at that time.

There were two later successors in the Chair at St Andrews, Charles and David Gregory, father and son. Little is known of Charles, but David left several interesting papers, including a copy of a very early unpublished work by his uncle David upon the history of fluxions prior to the celebrated controversy between Newton and Leibniz: and also a yearly record of the names of students attending the mathematical classes. Among many of these students, who rose to fame, was James Glenie, a mathematician of considerable power. He was one of the first to give a formal proof of the binomial theorem that had been discovered independently by Newton and Gregory a century earlier. During a military career he gained applause by rendering "one of the most important political services that was ever directly performed by a mathematician." He had composed an essay "on the Modes of Defence best adapted to the situation and Circumstance of this Island"; and the use of his arguments turned the scale by a casting vote in a Parliamentary Debate on the projected defence of the Portsmouth and Plymouth dockyards. Glenie had, it would seem, saved the nation from a scheme that "was calculated for the subjugation of this country and the subversion of its constitution."

The study of Natural Philosophy is coeval with the foundation of St Salvator's College in 1450, but the Chair that carries the title, Natural and Experimental Philosophy, dates from the union of the Colleges of St Salvator and St Leonard in 1747, when David Young of St Leonard's was appointed to fill it. The addition of the words "and experimental" to the title of the Chair is significant: how far Young carried his experiments we do not know. But it was he who initiated the proposal to confer an honorary degree in 1759 upon Benjamin Franklin, a man eminent alike in public life and for his electrical studies. Young was also one of the original group of gentlemen golfers who formed the Golf Club in 1755, and so was his brother John who was Professor of Moral Philosophy from 1733 to 1772. A torn scrap of paper bearing an invitation to Professor Nicolas Vilant from the gentlemen golfers to a Ball in 1800 marks the place in a volume of trigonometrical notes that survives.

William Wilkie, who succeeded Young, is one of the picturesque figures of his century: he is better known for his epic poem, the Epigoniad, than for his natural philosophy, but, to judge from contemporary accounts, he was master of his science, a well-read philosopher, original, a brilliant conversationalist, a farmer at heart, a disciple of Bacon and an admirer of Don Quixote. As a teacher he excelled: now and then he would lose the thread of his lecture. Then after a short pause, he would not hesitate to say, "I have been bewildered. I have been speaking nonsense" - and would proceed with a new demonstration. He possessed that entire simplicity of character by means of which a man puts himself out of the question and fixes his eye only on what is true and what is right. Wilkie has been called the Homer of Scotland, but in his character and interests he is more akin to the writer of the Georgics. He was at home with peasant, poet, or philosopher. His friends mentioned Lucretius as a successful scientific poet. "Lucretius," said Wilkie, "reminds me of a cobbler I once knew, who would now and then take up his fiddle and play himself a tune, but soon throw it aside, and fall a hammering again on his last."

Among others, who have an honoured place in the ranks of the sciences, is George Martine, the younger (1702-1741), physician. On the occasion of the 1715 Jacobite rebellion he headed a riot of students of the college, who rang the college bells on the day that the Pretender was proclaimed. After studying in Edinburgh and Leyden, he settled down to practise at St Andrews. He enriched natural philosophy by correcting temperature scales and studying the rates of change and relative distributions of heat among different substances. John Leslie (1766-1832), a native of Largo and a student at St Andrews, became Professor of Natural Philosophy at Edinburgh. In 1810 he succeeded in freezing water by artificial evaporation. He is the father of refrigerators, and all manner of appliances for producing low temperatures. A fellow-student, James Ivory (1765-1842), a native of Dundee, became an outstanding mathematician of his day. He contributed to the history of gravitation as it was shaping under Colin Maclaurin, Lagrange and Laplace, on the foundation of Newton's Principia. Edinburgh also claimed James Playfair (1748-1819) of Benvie near Dundee, who was a student at 14 years of age under Wilkie and Gregory, and became a notable mathematician and geologist. Others came to St Andrews with their reputation already made, such as David Brewster (1781-1868) Principal of the United College (1838-59) who brought a high repute in the study of light and its polarization, had in 1831 helped to found the British Association for the Advancement of Science, and who wrote a life of Isaac Newton.

His successor as Principal (1859-68) was James David Forbes (1809-1868) who restored the College Church of St Salvator and whose last public act was to lay the foundation stone of the St Leonard's Hall. He was a versatile geologist and had been the first to set foot on the summit rocks of Sgurr nan Gillean and again to detect and to measure the movements of glacier flow. His son, George Forbes, who shared his love of adventure and of science, was a student at St Andrews and then at Cambridge, a world-wide traveller who had crossed the Desert of Gobi. It is quite in character that at an evening reception after his honorary graduation at St Andrews he should produce a fragment of the summit rock of the Matterhorn from his pocket. He was physicist, astronomer, and engineer of eminent powers, and once carried out a long series of experiments, from 1876 to 1880, in Pitlochry and across the Firth of Clyde by means of arc lamps for directly measuring the velocity of light. He pioneered and supervised the hydro-electric scheme for harnessing the power of Niagara to supply Buffalo and other cities, and then the Huka Falls in New Zealand and the cataracts of the Nile. Of his father a kinsman had said. "his sense of right amounted to chivalry": the same stern code of honour descended to the son. Old age found him a very poor man living at one time in a shed (as he liked to call it) built mostly by his own hands at the edge of a Highland wood, surrounded by books, the better part of his father's library, which piety and honour forbade him to sell: rare books by Copernicus, Gilbert, and many others, autographed copies of the Difesa of Galileo, of Daniel Bernoulli, and of Boscovich. He bequeathed this magnificent family collection of scientific volumes to our University Library.

Among other teachers and students of the sciences who are memorable are Thomas Duncan and Lyon Playfair, whose portraits hang in the College Hall, Balfour Stewart, John Adams, William Fischer and George Chrystal: Adams, the astronomer, who occupied Gregory's Chair - for one year only until Cambridge claimed him - and who shared with Le Verrier the honour of discovering the planet Neptune. Fischer who had come from Berlin had been fourth wrangler at Cambridge in the year when William Thomson (Lord Kelvin) was placed second. He was a greatly respected teacher in the Chairs, first of Mathematics and next of Natural Philosophy. A Cambridge friend of James Stuart (afterwards Rector, 1898) describes an episode of the Dundee meeting of the British Association in 1867: "On Saturday I went with an excursion to St Andrews where I slunk away from a geological walk which I would hardly tell you if I had not the excuse of the company of Maxwell and two Scotch Professors and Thomson the electrician. Maxwell, Thomson and Tait, all mathematicians, lunched at Professor Fischer's ... and I was there and heard shop talked abundantly." In this meeting, prominent among the young zoologists was William Carmichael McIntosh who communicated three papers to the proceedings. Fifty years later and long after retiral from the Chair of Natural History he was still an active and devoted worker in the Gatty Marine Laboratory. The courtly presence of the old man of ninety, rosy, erect and supple, appearing at each formal assembly dressed in his uniform of the Fife Battalion of the Volunteers recalling bygone days, was a symbol of the eternal youth of the University.

Our most distinguished Professor of Natural Philosophy is William Swan, who occupied the Chair 1859-1880. His name is still associated with the Swan spectrum, a display in the flame of a bunsen burner that is due to hydrocarbon vapour. The prism photometer is his invention. There is evidence that in his time experiments were carried out by the students. Under his successor, Arthur Stanley Butler (a nephew of Montague Butler, Master of Trinity College, Cambridge), a small room for practical work was fitted up (which is now the Mathematical Class Library): and in 1900 the first physical laboratory was erected. The new physical laboratories were opened by Sir William Bragg in 1925, during the tenure of the Chair by Herbert Stanley Allen, who promoted and carried out research on the secondary spectrum of hydrogen and the band spectrum of water vapour. His outstanding pupil is Gordon Sutherland of Dundee who is now in America, having been assistant director of research in the Department of Colloid Science at Cambridge, and one of the leading authorities in the world on infra red analysis. In 1949 Sutherland became a Fellow of the Royal Society, as was his teacher from whom he drew his first inspiration: and also the two successors in the Chair. First, John Turton Randall who invented the magnetron and promoted radio-location: then again in 1949 John Frank Allen who follows in the steps of John Leslie by probing to the lowest possible temperatures. He and his team use devices that no longer appeal to the imagination through the ordinary arithmetical scale of degrees, but require a framework decreasing by logarithmic steps. Thus the original concept of the logarithm, as Napier held and asserted it, is strangely apposite: and the words of genius bear a wider application than the thought which first prompted them.

Many a student, man or woman, who has held the time-honoured degree in Mathematics and Natural Philosophy has gone out from the College into the world of teaching, or of public life, in all its variety, at home and abroad. Among those who were drawn towards mathematics were Duncan M Y Sommerville and William Saddler, each of whom won a Berry Scholarship, joined the mathematical staff at the College, and later occupied a Chair in New Zealand. Each is distinguished as a geometer; and Sommerville was led in a deep and scholarly way, particularly to the bypaths of Non-Euclidean Geometry years before the advent of relativity brought it into prominence.

Two hundred years and more had passed since Gregory proposed his telescope and his observatory. The time for the fulfilment of his dreams was now at hand. In 1879 Peter Redford Scott Lang, a pupil of Tait, was elected to the Chair of Mathematics which he held until his retirement in 1921. Many successive generations of students Scott Lang taught with fidelity and diligence: but his interests were in practical rather than in abstract mathematical thought; and in the broader world of college and public life he made notable contributions. He instituted the Common Dines for students, a step which essentially led to the restoration of a collegiate residential system that had lapsed for a century. As in other things that he undertook, an unpretentious beginning proved to be of great significance. He had an instinct for collecting books and manuscripts of importance: his publication (1926) of the memorandum and account book of Duncan Dewar gives a vivid picture of student life a century earlier: and his institution of the Andrew Lang Lectureship is a yearly reminder of the many-sided talents of a great St Andrean. He enlarged the class Library, begun by Duncan and Fischer, with volumes of great historic interest. But his two chief contributions to the sciences were the discovery - how and where we know not - of the forgotten manuscripts of James Gregory, and the endowment of a lectureship and an astronomical observatory. At the beginning of this century Scott Lang presented the letters to the University Library and initiated the task of deciphering them, a work that was finally completed by his successor just before the Gregory celebration in 1938. Gregory had died at the height of his powers: Newton at the same age had not written the Principia. The project of the observatory had come to naught. Whether Scott Lang had this in mind, when he founded the Napier lectureship, we cannot tell: he certainly sought to perpetuate something that Napier began. In 1938, and, as a fitting sequel to the celebrations, an astronomer was appointed - Dr Findlay Freundlich, at the recommendation of Sir Arthur Eddington who had been the first to introduce into Britain the general theory of relativity. Then there came the war; and the newly-built observatory was taken into a system of coastal defence.

During the enforced inactivity, an idea was born, that of prefixing to a Gregory Cassegrain telescope a Schmidt plate, a thin sheet of glass that would indeed anticipate the errors of the instrument before the light struck the object mirror: and this would provide clear definition over a wide field of view in place of the square inch of exactness which is all that may be expected even of the 200-inch reflector at Palomar. This idea occurred to Dr Freundlich during a conversation in America with Shapley, who was experimenting with a Schmidt plate, fitted to a reflecting telescope, but without the secondary mirror characteristic of the three original designs: instead there was to be a photographic plate in the place of the secondary mirror, and the plate must needs be curved and also inaccessible for direct observation, which complicated its use. A friendly rivalry was set up on both sides of the Atlantic: for on returning to St Andrews, and soon after the war was ended, Freundlich put his idea into practice by finding the artificer, then forging the appliances and next constructing the instrument. It is an instrument of 20-inch diameter fitted with a Schmidt plate, and it has been completed in the new year of 1950: it is the pilot model of a larger telescope, and is the first of a kind that promises to revolutionise the search into the depths of space. This same year, too, the Napier lectureship has become a Chair of Astronomy, with Dr Freundlich as its first occupant. Thus is fulfilled after a break of 260 years the interrupted work of Gregory on the eve of celebrating the quincentenary of collegiate history; and thus may such discoveries be continued, and in the spirit of humility, mutual trust and adventure may grow from strength to strength.

HERBERT W TURNBULL


JOC/EFR July 2012

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