## Mathematics at Aberdeen 3

**Betty Ponting**published a two-part article on the history of Mathematics at Aberdeen in

*The Aberdeen University Review.*Both parts appeared in volume

**XLVIII**(1979-80), the first part on pages 26-35 and the concluding part on pages 162-176. We give a version of the article below. We have divided the article into four web pages. On this page we give the first part of the second of the two articles. Here are links to the other parts:

Mathematics at Aberdeen, Part 1

Mathematics at Aberdeen, Part 2

Mathematics at Aberdeen, Part 4

**Developments, Characters and Events, 1717-1860**

This article continues the story of the gradual growth of mathematics in the two universities in Aberdeen and of the people mainly concerned, starting in 1717 when both colleges were recovering from the disruptions of the 1715 rebellion and finishing in 1860 when the union of the two finally ended the long period of uncertainty as to their future. Beginning with Marischal College the article contains a short account of each of the occupants of the chair of mathematics with some of the changes during his period of office, followed by a review of the corresponding events at King's College.

In 1717 a modified regent system was in use for the four year Arts course in both institutions. The professor of Greek took the bajan or first year, then for the remaining three years a regent or professor of philosophy moved on with his class, teaching the entire course. A professor received a small salary and class fees from individual students. These, who usually entered in their early teens, often obtained extra instruction from private tutors during or outside the five months session and many attended only a few classes. Mathematics held a special position at Marischal where the foundation in 1613 of the Liddell Chair of Mathematics, under the patronage of the Town Council, had opened the way for separate classes. An attempt to set up a similar system at King's in 1703 had met with little success, Thomas Bower, the Regius Professor of Mathematics there, finally resigning in 1717 due to the

*'mean and precarious'*nature of his salary. The chair at Marischal was also vacant following the removal from office of George Liddell for Jacobite sympathies.

**MARISCHAL COLLEGE**

**Colin Maclaurin**

Anxious to replace the deposed professor, the Town Council issued a

*'program'*in May 1717 inviting candidates to present themselves for a competitive trial at the end of August. Two applicants, Colin Maclaurin and Walter Bowman, were examined over ten days by Charles Gregory, Professor of Mathematics at St Andrews, and Alexander Burnet, a regent at King's, both candidates making a favourable impression.

*'In the inferior pairts of the Mathematicks ther wes no great odds. Only in*Euclid

*Mr Bowman wes much readier and distincter, and in the last tryall Mr M'Laurine plainly appeared better aquainted with the speculative and higher pairts of the Mathematicks, ... Mr Bowman only hath applyed himselfe to those things that are commonly taught and Mr M'Laurine hath made further advances'.*In appointing the nineteen year old Maclaurin the Town Council brought to Aberdeen, for an annual salary of £504 Scots, one of the most outstanding mathematicians of his day.

Colin Maclaurin was a minister's son, born at Kilmodan, Argyll, in 1698, but left an orphan he was brought up by an uncle, minister at Kilfinan. He entered Glasgow University at the age of eleven where he developed an interest in geometry and graduated at fifteen with a publicly defended thesis

*On the power of gravity.*After a year as a divinity student he returned to his uncle's house, devoting himself to research in mathematics and philosophy until his appointment at Aberdeen.

His wide interests and enthusiasm for both pure and applied mathematics soon showed in his work. As well as a private course to students, given in his own chamber, he gave some public lectures and was responsible for buying apparatus for experimental philosophy (using, with government sanction, money from salaries unpaid during the rebellion). At the same time he furthered his already considerable research in geometry. He extended ideas of Isaac Newton on curves generated by the intersections of rotating lines and did elaborate work on pedal curves and chains of such curves. (A pedal curve is one traced by the feet of the perpendiculars from a fixed point to the tangents to a given curve.) He published early results in two papers in the

*Philosophical Transactions: Of the construction and measure of curves*in 1718 and

*A new method of constructing all kinds of curves*in 1719. Eager for new experiences and delighted to have

*'an office that allowed me one half of the year to dispose of at my pleasure',*he spent the summers of 1719 and 1721 in London. During the first of these he met Sir Isaac Newton, was elected Fellow of the Royal Society and made arrangements for the publication, in 1720, of his first major book

*Geometria Organica.*In 1721 (after travelling to London in an experimental ship, which was attempting, unsuccessfully, to carry live salmon in its false bottom), Maclaurin made several useful contacts and, on the eve of his return, accepted with alacrity the offer of a post as travelling tutor to Lord Polwarth's son.

Maclaurin's own account of the sequel is in the University archives. He returned to Aberdeen in December expecting no difficulty in getting leave of absence for two or three years, relying on the influence of a political friend 'Mr B.' He left at the end of May, without the required permission, hoping that Mr B, who had advised waiting until after the September magisterial elections, would deal with the matter. Shortly before leaving he received an anonymous letter, which he deduced came from Mr B's son,

*'full of scurrilous reflections'*on some mutual friends and decided to confide in one of the family concerned. The next part is tantalizingly missing but from later references it seems that word had reached Mr B who was no longer willing to satisfy the council on Maclaurin's behalf. Undeterred, Maclaurin eventually settled with his charge in Lorraine where he produced work on the percussion of bodies (which gained him a prize from the French Academy of Sciences in 1724) and continued his geometrical researches. Failure to publish the latter for some ten years was to lead to a very acrimonious dispute over priority with an Edinburgh mathematics teacher, Brakenridge, who was also working independently on pivots and linear guides.

Meanwhile in December 1724 the Aberdeen Council, not unreasonably annoyed by several letters containing unfulfilled promises of return and an absence now approaching three years

*'whereby the students had suffered considerable loss by their not being taught mathematicks as formerly',*appointed Daniel Gordon, a regent with experience in teaching the subject at St Andrews, to give two hours instruction per day. When Maclaurin finally reappeared in January 1725, after the death of his pupil, he found himself suspended

*'Untill he should give some reasonable satisfaction and acknowledgement. First, For his going away without Liberty from the Counsell. Second, For his being so long absent from his Charge and not attending the same'.*It was said in his defence that he had brought honour to the town and college by carrying their names far abroad; but it was not until the end of April, after protracted negotiations, that he

*'compeared in Counsell and acknowledged that he was sorrie the Magistrats and Counsell had taken offence and promised to be carefull of his Charge hereafter, wherewith the Magistrats and Counsell were satisfied and appointed such Sallarys as were due to the said Professor to be payed to him'.*Maclaurin stayed in Aberdeen only long enough to get involved in a quarrel with the Principal over his right to vote in rectorial elections. By November of the same year he was in Edinburgh, appointed conjunct professor with the ageing James Gregory, a post negotiated for him by Newton who had offered to pay twenty pounds a year towards his salary. Maclaurin apparently omitted to inform Aberdeen of the change. The Council, learning of it only

*'by the Publict News Prints',*indignantly declared his office vacant on 12 January 1726.

Maclaurin held the chair in Edinburgh for twenty years, gaining a reputation as an able teacher with a wide interest in practical science and public affairs. His numerous published works include books on fluxions, algebra and Newton's Philosophy. He took a leading part in organizing the defences of Edinburgh against the Jacobites in 1745. When the city fell he fled to York but his efforts had damaged his health. He died in Edinburgh on 14 June 1746 shortly after his return home, and was buried in Greyfriars churchyard.

**John Stewart**

A competitive examination for Maclaurin's successor was arranged for July 1726, but was postponed when the Crown claimed part of the patronage. The Town Council refused a friendly settlement and the members sought legal confirmation of their one hundred year old exclusive right. It was not until August 1727 that, with a decreet of the Lords of Council and Session in their favour, they quietly arranged to test a young 1726 graduate, John Stewart, son of a former provost. Daniel Gordon and Maclaurin's examiners, Gregory and Burnet, reported unanimously that

*'he may be a very sufficient Professor of Mathematicks'.*The omission of any advertisement and competition was swiftly challenged. An Aberdeen advocate, Alexander Charles, protested vehemently to the Council and University, with the threat of legal action, that his son George, as a near relation of the founder, ought to have the chair or at least the opportunity to dispute for it. The University's reply ruthlessly denied both the son's case and the father's right to act for him, threatening counter action if he persisted.

Stewart, known affectionately to his students as John Triangles, proved to be a capable teacher, renowned for his humanity and compassion. He realized that many students found mathematics difficult but believed it valuable in developing habits of accurate reasoning as well as being an essential tool for natural philosophy. To help and encourage beginners he published much expanded translations of two of Newton's tracts, on quadrature and series. Stewart's thirty nine years of office were marked by the growing importance of mathematics and science. An attempt had been made in 1726 to establish a

*'Compleat Course of Experimental Philosophy',*given by the professors of Medicine, Philosophy and Mathematics. Despite a promise of simplicity so that

*'even those who have not made progress in Mathematicks may understand some of the most usefull and pleasant Parts of Natural Philosophy',*a public appeal for money brought little response. The heaviest outlay occurred on 30 October 1727,

*'For the experimental room ... eight bottles of ale 12/-'.*However, a collection of apparatus was gradually built up, using contributions from graduating students. Regenting was finally abolished in 1753 and the curriculum for all except the first year completely reorganized. Less time was spent on Logic and Moral Philosophy, which were moved to the magistrand (fourth) year, thus recognizing the advantages of studying the rapidly expanding factual subjects first. Geography, Chronology and Natural and Civil History in the semi (second) year were accompanied by a compulsory Mathematics course consisting of Arithmetic, Euclidean Geometry, Plane Trigonometry, Practical Geometry and Elementary Algebra, in preparation for Natural Philosophy in the tertian (third) year. A second mathematical course in that year covered Spherical Trigonometry, Conic Sections, Astronomy and Higher Algebra. Interested students could go on to the Professor's optional third class of Advanced Algebra, Quadrature and Fluxions (Newton's approach to Calculus), with parts of Newton's

*Principles of Philosophy.*

Stewart was the first member of staff to be made Dean of Faculty, in contravention of the Foundation Charter which had made it an external appointment. He held the office from 1761 until March 1766 when his wife, eldest daughter and he himself died of

*'fever'*within three days, leaving six other children.

**William Trail**

The Town Council, apparently determined to avoid any grounds for complaint this time, despite the opinion of the Principal and Masters that a sufficiently qualified person might be found locally, arranged an open competition for the chair in August 1766. Four examiners, from St Andrews, Glasgow, King's and Marischal, were chosen to test the six candidates who had first to submit

*'sufficient Attestations of their moral Characters'*to the Town Clerk. The trial covered a detailed list of mathematical topics and included any original work. The order of both proposing and answering oral questions was decided by lot and names were cut off written papers by a clerk before the examiners received them. For an ordeal which lasted eleven days, the victims must have been relieved that

*'As the Examinators apprehend the presence of Spectators may be apt to disconcert the Candidates and even to hurt the attention of the Examinators, they are of opinion the Trial should be in the presence of the Examinators and their Clerk only'.*Marks awarded ranged from 16 to 126, the top score and appointment going to William Trail, a young man newly graduated from Glasgow. The runners up, with 119 and 90 respectively, were Robert Hamilton, who joined the staff later and John Playfair, afterwards professor at Edinburgh. Details of Hamilton's actual questions may be found in the University archives.

Although Trail began his duties in October, the Town Council paid his annual £50 professorial salary only from Whitsunday 1767, retaining the balance to defray

*'the great expense incurred by the comparative Tryal of the Candidates'.*Meanwhile he presumably had to live on his class fees, estimated at about £70 for the session. By this time the earlier system of appointing post graduate teaching bursars to help with arithmetic and elementary geometry had been abandoned as no longer necessary. Trail, responsible for all Mathematics, taught

*'above twelve times a week'.*His widely used

*Elements of Algebra,*which he published for his students in 1770, ranged from first principles to equations of all orders and included applications to problem solving, physics and geometry. In 1776, at Trail's request, John Garioch, a physician in Aberdeen, was appointed his assistant and successor. Garioch died six months later and was not replaced. During the session 1778-9, in Trail's absence, the higher branches of mathematics were taught by Patrick Copland, Professor of Natural Philosophy since 1775. At the end of that session Trail resigned for service in the church in Ireland. His continuing interest in mathematics was shown in an account of the life and work of his former Glasgow professor, Robert Simson, published in 1812. He died in 1831 aged eighty-four.

On Trail's resignation Copland applied to the Town Council for his post and was immediately appointed. Robert Hamilton, second in the 1766 competition, received the Crown nomination for the vacated Natural Philosophy chair. Hamilton lacked aptitude for a practical class and after one session, during which

*'he broke much of the apparatus of glass',*he and Copland exchanged duties. Copland, whilst retaining the title and higher salary of Professor of Mathematics, built up a large collection of apparatus and established a reputation as an outstanding teacher of Natural Philosophy.