The study of mathematical sciences underwent something of a revival in the first half of the nineteenth century when the subject became recognised as essential to an education and understanding of the world.  Commerce, trade, military training, surveying, navigation and astronomy were all impossible to undertake without an adequate grasp of mathematics. 

In Aberdeen at the beginning of the century the Arts Degree Examination required students at King’s College and even at the more relatively progressive Marischal College to have studied only the basics of the subject.  However, the growing emphasis on the teaching of mathematics at both these institutions paralleled the development of the subject as a whole and the mathematics curriculum increased in volume and complexity.  By the middle of the century, Aberdeen was producing students well-equipped enough in the subject to go on to become wranglers at Cambridge (a student who has completed the third year at Cambridge (called Part II) of the Mathematical Tripos with first class honours).

At both King’s and Marischal, the foundation mathematics course concentrated very much on the practical applications of the subject; mathematics to be applied as a tool for a wide range of situations from the every-day commonplace to the latest scientific advancement.

The texts on display are by no means a fully representative sample from the hundreds of nineteenth-century mathematical books in the University Library’s collections, but they do exemplify what was being published and what was available to professors and students alike.  Many illustrate the application of mathematics to practical problems encountered at the time, and thus also serve as fascinating sources for social history.

Illustration: Example VIII. “The crew of a ship …p. 181J. B. Florian-Jolly An elementary course on the sciences and philosophy….  (London, 1806).  This is an excellent example of an introductory mathematics text for all, not just those in academic institutions.  In the introduction to this two-volume work, highly acclaimed at the time, Florian-Jolly makes comment on the status of the teaching of mathematics in Britain.  He refutes the claims of Dr. Johnson that “the knowledge of external nature, and of the sciences which that knowledge requires of includes, is not the great or frequent business of the human mind …” by saying: “the REAL TRUTH is, that painting, architecture, navigation, mechanics, manufactures, agriculture; military, financial, or even commercial operations; require a constant application of mathematical and physical knowledge: that it is impossible to make any considerable progress in the most liberal and ornamental parts of education… without being previously acquainted with the geometrical principals upon which those sciences are founded.”  Florian-Jolly also makes a case for the education of women in the sciences: “let them be equally able to manage their private affairs, or the domestic concerns of a family; equally qualified to enjoy affluence, live content with little, or earn a competency if obliged to support themselves.”

Florian-Jolly’s work, published at the beginning of the 19th century reflected a growing realisation in the importance of mathematics and physical sciences in the education of all.  Echoing trends in the development of mathematics as a discipline, nationally and internationally, this text has a strongly practical emphasis stressing the application of mathematics to many and varied subjects with questions applied to the problems of the age.

Illustration: Charles Hutton. A course of mathematics in three volumes.  Title of vol. 2 with Tulloch’s signature and notes. SB 5102 Hut 4A course of mathematics (London, 1811) and A complete treatise on practical arithmetic and book-keeping (Alnwick, 1828) are both by the eminent mathematician, Charles Hutton (1737–1823).  Throughout his career, Hutton produced, in addition to many other publications, a number of mathematical teaching aids, raising the standard of mathematical literacy at both school and university level.  This copy of a Course of mathematics belonged to John Tulloch who was professor of mathematics at King’s College from 1812-1851.  Tulloch presided over a huge advance in the teaching of mathematics at King’s increasing the quantity and complexity of the mathematics curriculum.  Hutton’s Course was a standard text throughout academic institutions in Britain.  Originally written for military cadets at the Royal Military Academy at Woolwich, it was also the core text for the United States Military Academy at West Point.  Editions of the work continued to be published after his death and this appears to be part of Tulloch’s own working copy, with his notes covering the fly-leaf and title-page.

In content, the Course concentrates on the practical application of mathematics as does Practical arithmetic and book-keeping.  The importance of the calculatory sciences and good accounting became increasingly necessary during the 18th century with the rapid rise of trade and commerce.  Hutton’s work concentrates on accountancy both for commercial and for personal finance and emphasises the necessity in educating everyone in these skills.  These pages illustrate how a gentleman’s finances may be kept accurate using double-entry book-keeping.

Commerce and trade were hindered at the start of the 19th century by the lack of a standard in weights and measures.  The universal calculator, or, the merchant’s, tradesman’s and family’s assistant  … by John Thomson (Edinburgh, 1805) is a fine example of the practical application of mathematics.  In addition to tables of interest and the calculation of salaries, there are tables “intended to render trade less complicated and its transactions more expeditious and correct … shewing at one view, the amount or value of any number or quantity of goods or merchandise.”  It also illustrates the problem, universally acknowledged at the time, caused by the many local, national and international weights and measures that were used for trade.  This is illustrated here by a list of the comparative weights and measures of Scotland and England.

As illustrated by the work of Charles Hutton, mathematics as a practical tool had been, and was, a vital component of military training.  Many of the advances in mathematics and physical sciences in the nineteenth century came about through the need to advance military science during the Napoleonic wars.  The advent of peace saw the experience of many gained in surveying and navigation put to a new purpose enabling many to follow full-time scientific careers.

Illustration: Table XXII. Table of tangent practice with a long 24-pounder gun. p. 307A straightforward illustration of the need for basic mathematical knowledge can be seen in General Howard Douglas’ (1776–1861 ) Treatise on naval gunnery. (London, 1820).  Douglas’ treatise came about after he had witnessed the appalling standard of gunnery and drill aboard some British warships during the Napoleonic wars.  As a result of his many experiments in charging and directing cannon, he produced what was to become a core text of naval training.  His experiments and subsequent analysis of data resulted in a basic, theoretical, training for naval gunners involving analysis of the force and effect of gunpowder; dimensions of cannon bore; proportions of cannon and ball; the computation of angles of projection; impetus and velocity of the projection and resistance.

The advances made in many branches of the physical sciences through the work of scientific military servicemen in navigation and surveying were used to advance further study during peacetime.  In particular, many became involved in the quest to establish the size of the earth (and a standard of length based on a natural constant) through, for example, pendulum studies and terrestrial magnetism.

Edward Sabine (1788–1883) spent the early years of the 1800’s on active service in the Royal Artillery.  Once in civilian life, however, he became a regular member on a number of scientific surveys, in particular, those in the Artic where through his studies with the pendulum and on magnetism, he was able to calculate a figure for the ellipticity of the earth.  Such studies were built again on the strongly practical emphasis given to mathematics and were strongly empirical, relying on the gathering of vast quantities of data and the primary use of observation before theory.

Illustration: Plate Balances and weighing machines; compensation pendulums.p. 302.Such calculations were impossible without the parallel advances in the invention and development of scientific instruments used to record such data.  Henry Kater (1777–1835), another ex-serviceman, became (amongst his many other roles) advisor to the Royal Society on the use of instruments for many scientific voyages.  In addition to inventing scientific instruments himself, he published a number of detailed papers on the subject.  However, in common with many mathematicians of the time, he was involved in the publication of more basic instructive texts.  He contributed to this small volume, Mechanics (London, 1831) was published as part of the Cabinet Cyclopaedia, edited by the Reverend Dionysius Lardner, another prolific writer of mathematical texts.  Kater’s chapters include one on balances and pendulums, of which he was the leading authority of the day.

A practical approach to the subject of mathematics is and was not the only or even desirable way to teach it, but it proved a successful and instructive way to provide a decent grounding in the subject.  By the time of the union of the two Colleges of Marischal and Kings in 1860, a comprehensive and challenging mathematics curriculum had been developed, with mathematics a compulsory component of the arts degree and many students pursuing the subject to honours level.

References:
Miller, David Philip. The revival of the physical sciences in Britain, 1815-1840. Osiris, 2nd Series, Vol. 2. (1986), pp. 107-134.

Ponting, Betty. Mathematics at Aberdeen: developments, characters and events, 1717-1860. Aberdeen University Review no. 162, (Autumn 1979), pp. 162-176.

H. M. Chichester, ‘Douglas, Sir Howard, third baronet (1776–1861)’, rev. Roger T. Stearn, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Oct 2007 [http://www.oxforddnb.com/view/article/7888]

Niccolò Guicciardini, ‘Hutton, Charles (1737–1823)’, Oxford Dictionary of National Biography, Oxford University Press, 2004 [http://www.oxforddnb.com/view/article/14300]

Gregory A. Good, ‘Sabine, Sir Edward (1788–1883)’, Oxford Dictionary of National Biography, Oxford University Press, Sept 2004; online edn, Jan 2008 [http://www.oxforddnb.com/view/article/24436]