The Syndicate are authorized to announce to the Senate that, should the Regulations contained in the foregoing Report be adopted, the Regius and Lady Margaret Professors of Divinity and the Regius Professor of Hebrew, in consideration of the length of time which must elapse before the plan marked No. 4 can come into operation, will commence in the Michaelmas Term of 1843, and continue in the corresponding Term of each of the two following years, Examinations somewhat similar to those proposed in that plan.

A Grace to confirm the above Report passed the Senate May 11, 1842.

XII.

(Published May 19, 1849.)

THE VICE-CHANCELLOR begs leave to publish to the University the following REPORT, in accordance with the Regulation D. adopted by the SENATE Oct. 31, 1848.

THE BOARD OF MATHEMATICAL STUDIES beg leave to lay before the VICE-CHANCELLOR the following REPORT:

WITH the view of carrying out the intention of the University in appointing a Board of Mathematical Studies, the present Members commenced their duties by making regulations for holding meetings and conducting the discussion of the questions that might require their consideration, and for keeping minutes of their proceedings to serve as an authentic record for future reference. The existing state of the Mathematical Studies of the University has been the subject of mutual communications and discussions, which have resulted in their agreeing upon certain recommendations which will be found in the latter part of this Report.

I. The Board conceive that the objects intended to be secured by an annual Report on the state of our Mathematical

Studies may be promoted, and a basis formed for future suggestions, by bringing under review in this first Report, (1) the changes that have been made from time to time by Graces of the Senate in the regulations for conducting the Mathematical Examinations; (2) the progressive steps by which new modes of treating the subjects of examination, and new subjects, have been introduced into the course of Mathematical Study.

(1) In 1808, the Examination of the candidates for Honours commenced on the first Monday in the Lent Term; three days were devoted to Mathematics; and the candidates having been arranged in Brackets according to the result of the examinations on those days, the order of their merit was finally determined by examinations of the Brackets on the following Friday. Each candidate was examined 18 hours in the course of the three days, of which 11 hours were employed in answering questions from books, and the remaining 7 in the solution of Problems. The number of candidates that obtained Honours in that year was 38. In 1828, when the number had increased to 90, the examination commenced on the Friday preceding the first Monday in the Lent Term, and extended over four days, exclusive of the day of examining the Brackets; the total number of hours of examination was 23, and the time assigned to Problems remained the same as in 1808. By regulations which took effect in January 1833, the commencement of the examination was placed a day earlier, the duration was five days, and the hours of examination on each day were 53. Thus 4 hours were added to the whole time of examination, 4 of which were appropriated to the answering of questions from books, and the remaining half-hour to the solution of Problems. The successful candidates in that year amounted to 105. In 1835 the number was 117, and the examination, for the convenience of the examiners, began on the Wednesday of the same week, without alteration in other respects. In January 1839 there were six days of examination, beginning on the Monday preceding the first Monday in the Lent Term, and the total number of hours of examination was 33, of which 8 were given to

Problems. The first day of examination was altered in 1841 to the Wednesday week preceding the first Monday in the Lent Term. The number on the list of Honours in 1840 was 146.

Of the alterations relating to the classification of the candidates and the mode of proposing the questions, the following are those of chief importance. Previous to January 1828, the candidates were divided into six classes, determined by the Exercises in the Schools; different printed Problems and vivâ voce questions were proposed to different classes, generally taken two together, and the only questions proposed to all in common were the Evening Problems. In the year above named, important regulations, confirmed by Grace of the Senate, Nov. 13, 1827, came into operation. The classes were reduced to four, determined as before by the Exercises in the Schools. On the first two days all the candidates had the same questions proposed to them, inclusive of the Evening Problems; and the examination from books on those days excluded the higher and more difficult parts of mathematics, with the view of securing an object which, in the opinion of the Syndicate on whose recommendation these regulations were adopted, was highly desirable, viz.: "That the Candidates for Honours may not be induced to pursue the more abstruse and profound mathematics to the neglect of more elementary knowledge." Accordingly, on the first day (Friday), the questions from books extended to such parts of pure Mathematics and Natural Philosophy as do not require the Differential Calculus, and on the Saturday were added parts of Natural Philosophy somewhat more advanced, and the simpler applications of the Calculus. On Monday, the first and second classes were examined together, and the third and fourth together, in questions from books and in Problems; and on Tuesday, the second and third were examined together, and the first and fourth separately, in questions from books. The questions which had previously been given out vivâ voce, were printed, in order to make generally known the questions proposed in each year, and, by thus directing the reading of the students, to produce more fixity and definiteness in the mathematical studies of the University. The printed papers also

[PT. II.]

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afforded the opportunity of ascertaining by inspection that the examination embraced in due proportion all the ordinary subjects of mathematical study. No change was made in the substance of the examination; the questions inserted in the papers being, like those which had been proposed vivâ voce, propositions contained in the mathematical works commonly in use in the University, or simple examples and explanations of such propositions. For the purpose of preventing those who had attended to a part only of the subjects from having any undue advantage by this mode of conducting the Examination, it was especially recommended that "there be not contained in any paper more questions than students well prepared have been generally found able to answer within the time allowed for such paper." At the same time a discretionary power was given to the Examiners of proposing additional questions vivâ voce, if any candidate should before the end of the time have answered all the questions in the paper. This power, however, was not continued in the regulations of 1833, nor in any subsequent regulations. With this exception, the preceding regulations may be said to have determined the principles on which in the main the examinations have been since conducted; and for this reason it has been thought right to insert them at some length in this Report.

By regulations which came into force in January, 1833, the same questions were proposed to all the classes during the first four days. The order of difficulty of the questions on the first three days was the same as it had previously been on the first two days; but on the fourth day the examination extended to subjects of greater difficulty, care, however, being taken to insert into the papers some questions suitable to the lower classes. On the fifth day the examination was conducted according to classes.

In January, 1839, the division into classes was discontinued, and the same questions were proposed throughout the examination to all whom the Moderators judged, from the public Exercises in the Schools to be qualified for examination as candidates for Mathematical Honours. The order of difficulty

of the questions was regulated nearly as before, questions selected exclusively from the higher parts of the subjects being proposed only on the sixth day of the examination.

The most recent alterations came into force in January, 1848. As these are of an important character, and the Board may be expected to give some account of their operation in the last two examinations, it will be necessary to state the regulations in some detail. The examination commences on the first Thursday after the first day of January. Questions and Problems are proposed to the candidates on eight days, instead of six as formerly, the first three days being assigned to the elementary, and the last five to the higher parts of mathematics. After the first three days there is an interval of eight days, and on the seventh of these days the Moderators and Examiners declare what persons have so acquitted themselves as to deserve Mathematical Honours. Those who have so acquitted themselves, and no others, are admitted to the examination in the higher parts of mathematics, and after the examination the Moderators and Examiners, taking into account the examination of all the eight days, arrange those who have been declared to deserve Mathematical Honours in the order of merit in the usual manner. The three classes of Wranglers, Senior Optimes, and Junior Optimes, are published on the Friday morning preceding the general B.A. admission, and no provision is made for any further examination corresponding to the examination of the Brackets, which formed part of the previous scheme, but had in practice been discontinued for several years. A principal feature in the new scheme is the limitation by a Schedule of the subjects and parts of subjects of examination in the first three days, and of the manner in which the questions are to be answered. The subjects are, the portions of Euclid usually read; Arithmetic; parts of Algebra, embracing the Binomial Theorem and the Principles of Logarithms; Plane Trigonometry, so far as to include the solution of Triangles; Conic Sections, treated geometrically; the elementary parts of Statics and Dynamics, treated without the Differential Calculus; the First three Sections of Newton, the