## Mathematics at Aberdeen 2

**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 second part of the first of the two articles. Here are links to the other parts:

Mathematics at Aberdeen, Part 1

Mathematics at Aberdeen, Part 3

Mathematics at Aberdeen, Part 4

**Developments, Characters and Events, 1495-1717 - Continued**

**King's College in the seventeenth century**

Although King's College nominally accepted the new foundation in 1597 its ideas were only partially carried out, in particular, regenting continued. A commission of 1619 which found the affairs of the College in a state of neglect and the buildings ruinous, virtually restored the old foundation. The political upheavals of the seventeenth century affected King's even more than Marischal, with oscillations between the ideas of the old and new foundation. Many members, including three principals, were removed from their posts with the changing fortunes of the country's leaders. In the early years of the century the average entry was less than twenty students and was only about twelve in 1638 at the height of the Troubles.

From 1628 regents were fixed to a certain year of the course. During this period two of the regents, Andrew Strachan and later David Leech are referred to as Professors of Physiology and Lower Mathematics. The old system of regenting was restored in 1641. The syllabus then included Arithmetic and Geometry in the second year, the Sphere and Astronomy in the fourth.

A Commission of 1642 advocated a uniform course for all Scottish Universities and some work was done towards this end. A committee of representatives of the various universities met in Edinburgh in 1647 to discuss progress. Aberdeen (King's and Marischal were officially, if ineffectually, united as King Charles' University for twenty years from 1641) was allotted the task of drawing up the sections on Mathematics and Ethics. Details of the syllabus then taught at King's show that the Logic, Philosophy and Physics of Aristotle still formed a large part of the course. Arithmetic was taught in the second year, some elements of Geometry in the third. The Sphere of Sacrobosco with the beginnings of Geography and insight into globes and maps represent the nearest approach to Mathematics in the fourth year.

An attempt to improve standards came under John Row who was appointed Principal in 1652. During the following year he issued a code of laws to cover all parts of the students' college life. He was a firm believer in the advantages of regenting, considering it desirable that the students should not have to change their teachers every year and that the regents should be familiar with the whole course. Under his regime Arithmetic appeared in the first year and Geometry in the second. Chronology and Optics came in the third with Geography and Astronomy in the final year.

A General Commission, appointed by Parliament in 1690 sat for ten years and did much to revitalize the Scottish Universities. It revived the idea of a uniform course which would be printed to avoid the dictating and writing of notes. Regents were only to be elected after public competition and until the printed course was ready, were to submit their lectures to the Principal for approval before the beginning of the session. The students were to be examined publicly at the beginning and end of each session. The library has a set of lecture notes on the elements of Geometry written in 1693, his second year at King's by William Gordon, second Earl of Aberdeen. These show that the Geometry he was then taught came from the first six books of Euclid. The course continued with some Trigonometry. The basic definitions given were sine, tangent and secant and their application to the resolution of triangles was discussed. A final section covered the use of Naperian logarithms to simplify calculations.

The commission recommended that

*'every year the regents of the severall classes shall be oblidged to teach their students some rudiments of the Mathematicks with their courses'.*In 1700 a regulation fixing one of the regents to teach Greek in the first year, opened the way towards a modification of the regenting system and specialist teaching.

**The first professor of Mathematics at King**'s

The Minute Book of 4 May 1703 records that

*'The Principall and remanent masters taking to their serious consideration how much it may be for the advancement of learneing & interest of the said University that Mathematicks should be professed and taught therein'*appointed Thomas Bower to teach the subject both publicly and privately in the College. Like all the masters he would receive class fees from his students but owing to the low estate of the College revenues they could only offer him a yearly salary of 200 merks and that

*'in case onely that it appeare after cleareing the yeirly Procurator Accounts that the balance can beare the same & no otherwise'.*At least he was to be given his meals in college.

Bower does not appear to have been content with these conditions. Two months after his appointment he was asking permission to visit Edinburgh to try to get funds for his salary and was away for over a year. In 1705 he went off to spend the winter in London. He reappeared in Aberdeen to compete for the Marischal chair when George Liddell was deposed in 1706. When the trial was cancelled on Liddell's reinstatement, Bower took legal action against the Town Council for cost, skaith and damage occurred in coming from London, finally appealing to Parliament.

The Scottish Parliament at this time was indebted to Bower as he, with James Gregory, Professor of Mathematics at Edinburgh, had been responsible for calculating the Equivalent in preparation for the Union of Parliaments. (The Equivalent was compensation paid to Scotland to offset extra taxes etc. These calculations proved highly generous to the Scots.) In an Act of 1707 they gave New Aberdeen the right to continue collecting a local tax of two pence on each pint of ale brewed and sold in the New town and extended it to the Old Town, College Bounds, Spittal and Seaton. From the revenue New Aberdeen was to pay £40 sterling in way of salary to the Professor of Mathematics at King's. On the same day a similar privilege was extended to Kirkaldy, of all places, on condition that it added a further annual sum of £10 sterling to this salary. Despite this Bower still seems to have been frequently out of town. The Old Town brewers objected to paying a tax to New Aberdeen, particularly when the Professor was obviously not carrying out his duties.

He attended College meetings in 1711, arguing with the Principal over his right, as a professor confirmed by Parliament, to vote in them, particularly at the election of a new regent. Bower took his case to the Lords of Session in Edinburgh, despite a warning from the Principal that this would bring a counter action against him as

*'a raiser of factions and disturber of the peace'.*The Lords found in Bower's favour but the Principal refused to accept defeat appealing repeatedly and unsuccessfully against their judgment and eventually taking the case to the Queen and Parliament. The argument was brought to an end by the events of the 1715 rebellion following which the Principal was deposed. Bower himself failed to appear before the Commission of 1716-17 who recorded that he had not been in Aberdeen

*'this three years past'.*He did not return to Aberdeen and finally demitted in 1717.

Although 1717 found both colleges without professors of mathematics some progress had been made and the possible need for specialist teaching recognized. Many of the students entered college at the age of only twelve or thirteen and at King's particularly came from country areas. The Foundation had recognized their lack of opportunity to acquire fluent Latin, the language of instruction, by providing a grammarian. Still less were they likely to have had much grounding in arithmetic so it was necessary to provide basic courses. The ideas of the Reformation had led to the swing away from Aristotle and an increase in the amount of Mathematics, especially Geometry and Trigonometry, taught. Despite the difficulties occasioned by the political instability of the seventeenth century, many changes had been introduced and Mathematics had become recognized as a fundamental part of the Arts curriculum. The Universities were now ready to go forward in the eighteenth century with the great advances in Mathematics resulting from the introduction of Analytical Geometry and Calculus.