Mathematics in Edinburgh University in 1883

Staff in the Mathematics Department

Professor of Mathematics: George Chrystal appointed 1879.
Assistant to the Professor of Mathematics: R E Allardice.

Professor of Natural Philosophy: Peter Guthrie Tait appointed 1860.
Assistant to the Natural Philosophy: C G Knott.

The Examiners: The Professors and, in addition for Mathematics, Alexander Macfarlane D.Sc. appointed 1881.



First Class - 12 to 1.

Theory of Arithmetic; Plane Geometry. equivalent to Euclid, Books i., ii., iii., iv., and vi., (in the lectures the arrangement of the Syllabus of Plane Geometry, prepared by the Association for the Improvement of Geometrical Teaching, is followed more or less closely) ; Solid Geometry, equivalent to Euclid, Book xi.; Geometrical Conic Sections ; and Elementary Algebra.

Second Class.- 10 to 11.

Algebra, including the elements of the Theory of Equations, and of Determinants ; Plane Trigonometry; Conic Sections, treated geometrically and analytically; and the Elements of Modern Geometry.

Third Class.- 9 to 10.

On Mondays, Wednesdays, and Fridays - Higher Algebra, Analytical Geometry, Differential and Integral Calculus, Calculus of Finite Differences.

Additional lectures on Quaternions, and other special subjects may be given occasionally.

Tutorial Classes.- In addition to the ordinary class lectures in the First and Second Classes, occasional lectures are given by the Class Assistant. The attendance on these is voluntary, and the time is devoted to the repetition of parts of the class lectures and to the working of examples.

Home Exercises are prescribed weekly in all the classes.

Written Examinations on the class lectures are held monthly during the Session. The class honours are determined solely by these examinations.

Text-Books.- As a rule special text-books are not prescribed; but the student is recommended to select from the following list:-

Geometry.- Wilson's Elementary Geometry, or Todhunter's or Playfair's edition of Euclid's Elements.

Algebra.- Kelland, or Todhunter.

Solid Geometry and Conic Sections.- Wilson.

Trigonometry.- Todhunter or Snowball.

Analytical Geometry. - Todhunter's or Smith's Analytical Conic Sections; and Dyer's Exercises in Analytical Geometry. Students intending to take the Third Class are recommended to get Salmon's Conic Sections.

Higher Algebra and Theory of Equations, etc.- Todhunter's or Burnside and Panton's, Theory of Equations; Thomson's Introduction to Determinants; and Salmon's Higher Algebra for those who mean to read for Mathematical Honours.

Differential and Integral Calculus.- Williamson's Treatises.




The subjects embraced in the Course of Natural Philosophy are the following:-

1. Properties of Matter - including Inertia, Gravitation, and Molecular Forces.

2. Abstract Dynamics - including Kinematics, Statics and Kinetics of Solid, Liquid, and Gaseous Bodies, with their applications.

3. Sound, and Wave-propagation in general.

4. Heat, with its application to the Steam-Engine, etc.

5. Light (Geometrical and Physical Optics).

6. Electricity, including Frictional and Voltaic Electricity, Thermo- and Magneto-Electricity, Electro-Dynamics, and Magnetism, with their practical applications to the Telegraph, &c.

7. Conservation of Energy.

8. Plane and Physical Astronomy.

9. Meteorology.

Properties of Matter, Abstract Dynamics (commonly called Mechanics), and Conservation of Energy, together with two or three others of the above divisions of the subject, are treated in detail every Session, the remainder being necessarily discussed in a more superficial manner, as it is impossible to enter at length into all in the course of a single Session.

It is intended that in Session 1883-84, in addition to Sections 1, 2, and 7, Sections 5 and 6 shall form the more detailed part of the Course.

The whole Class is examined at short intervals during the Session upon the subjects already treated in the Lectures; and a prize is given for the best answering. In these examinations no Mathematics are requisite, except the most elementary portions of Arithmetic, Algebra, and Geometry.

In the months of January and March there are special Examinations upon prescribed subjects; and, on these two occasions only, the Class is divided into two parts - the division depending mainly upon the students' proficiency in Mathematics. In the Lower Division, the elements of Algebra and Geometry alone are required; in the Higher Division, Algebra, Geometry, and the Geometry of the Conic Sections, are necessary.

[In former years, the Ordinary Class was arranged in three divisions, but the introduction of the Advanced Class (see below) has rendered the highest of these three superfluous.]

The Prizes in each division of the Class are determined by adding the marks obtained in the two sets of Examinations above described. No Student who has obtained a Prize in either Division of the Class can be allowed to compete, in a subsequent Session, for a Prize in the same or in a Lower Division.

The Text-Book for the Course will be Thomson and Tait's Elements of Natural Philosophy (Pitt Press, Cambridge, 2nd edition, 1879.) But, as the first volume only has yet been published, for the remainder of the subject the student may consult Balfour Stewart's Lessons in Elementary Physics, and Tait's Recent Advances in Physical Science.

Throughout the experimental part of the course, constant references will be made to Tait's Sketch of Thermodynamics (Second Edition, 1877), which has been prepared as a Text-Book to serve till the second volume of Thomson and Tait's Elementary Treatise on Natural Philosophy is published.

The special Examinations in January 1884 will be on the following subjects :

Higher Division.

Newton's "Three Sections" (Goodwin's Course of Mathematics," Frost's " Newton," or any good edition of the Principia).

Lower Division.

Herschel's Astronomy, in Lardner's Cyclopaedia, omitting the chapter on Perturbations. A series of explanatory lectures will be given by the Class-Assistant before the examination.

The subjects for the March Examinations will be announced soon after the commencement of the Session.

Subject of Voluntary Essay to be given in before the end of March 1884 - "The connection between Heat and Current Electricity."


For the benefit of Engineering Students, and of Arts Students wishing to Graduate with Honours in the Department of Mathematics, Professor Tait has opened an Advanced Class. Three lectures are given per week, and the subjects are -

Dynamics (generally),
Theory of Heat,
Theory of Electricity,

all treated specially with regard to their practical applications.


At the request of the Medical Faculty, Prof. Tait, in the years 1875-76, tried the experiment of opening an elementary class of Experimental Physics in the Summer Session, chiefly for Medical Students. The formation of this class is now made conditional upon its being shewn, by the enrolment of at least So names during the first week of May, that there is a real demand for a Summer Course of Natural Philosophy on the part of Students who are unable to attend the ordinary Winter Class.


This has been introduced with the view of affording Students a practical knowledge of the construction of, and manner of using, physical apparatus, with the mode of conducting experimental inquiries. The Laboratory is open for five or six hours daily during the Winter and Summer Sessions, under the personal superintendence of the Professor and his Class-Assistant. Fee, £6, 6s. for the Winter Session. It is hoped that, with the valuable collection of apparatus in the Museum, results of real use to science may be obtained.

A practical class, for the instruction of beginners in the elementary processes of measuring Time, Mass, Length, Angle, Force, etc., will be formed in the Winter and also in the Summer Sessions. The course, in each case, will extend over about three months. The fee is £2 2s. The Professor reserves to himself the right of admitting free, to general laboratory work, such members of the practical class as may show special diligence and aptitude.

In 1883 the University of Edinburgh had an "Ordinary Certificate in Arts for Women" and an "Honour Certificate in Arts for Women". The regulations state that:

Candidates, before they can receive the certificates, must have studied in at least three of the Classes of the "Edinburgh Association for the University Education of Women," that are recognised by the Senatus Academicus; and they must also have passed the Local Examinations of the University of Edinburgh, or of one of the other Scottish Universities, or of the Universities of Oxford or Cambridge.

The mathematics examinations topics for the Ordinary Certificate for October 1883 was:

Arithmetic, Euclid, Books I., II., III., IV., and VI., or their equivalent. Algebra to Quadratics equations, including the Progressions.

The mathematics examinations topics for the Honour Certificate for October 1883 was:

Euclid, I., II., III., IV., VI., and XI., or their equivalent; The advanced portions of the Elements of Algebra, Trigonometry, and Conic Sections, treated geometrically and analytically.

Here are some examination questions set at Edinburgh University in Mathematics and in Natural Philosophy.

JOC/EFR February 2008

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