1837. Feb. 22. Their Report confirmed:-Subjects for Ordinary Degrees: The Acts: one of the Greek and one of the Latin Classics: Paley's Moral Philosophy: and Mathematics according to a Schedule: previous Notice of the Classical Subjects to be given: the Examinations to commence on the Wednesday preceding the first Monday in Lent Term: a Schedule given of Arithmetic, Algebra, Euclid; Mechanics; Hydrostatics: Four Examiners to be elected in October for Classics, The Acts, and Paley: The Moderators of the next but one preceding year to be Examiners in Mathematics.

223 New alterations were made.

1838. May 16. "Placeat vobis ut Ds Procancellarius, Dr French, Dr Graham, Prof. Peacock, Prof. Miller, Mr Whewell, Mr Hymers, Mr Hopkins, Mr Philpott, Mr Thurtell, Mr Phillips, Mr Steventon, Mr Mills, Syndici vestri constituantur qui consilium ineant et deliberent utrum expediat aliquid immutare in modo Quæstionistas examinandi qui honores Academicos ambiunt:" to report before division.

May 30. Their Report confirmed: A Sixth day added: the Examinations to commence on the Monday preceding the first Monday in Lent Term: the previous Classes to be discontinued: the same questions to be proposed "to all whom the Moderators shall judge, from the public exercises in the Schools, to be qualified for examination as Candidates for Mathematical Honours."

The same rules as before are enjoined respecting the easier subjects on the earlier days, and the number of questions in each paper. The result to be published on the Friday; and if any doubt exists, re-examination to take place.

224 The Examinations have since been administered as thus constituted. But still, some dissatisfaction arose in the University respecting the Elementary part of the examination. It was conceived that the portions of Mathematics which have in England commonly been called "Natural Philosophy," were too much superseded by now the more favourite analysis. Hence the following Grace was passed.

1840. Mar. 18. The former Syndicate re-appointed "quo consilium ineant utrum expediat leges accuratiores præscribere de parte examinationis elementariâ et præsertim de numero et naturâ questionum e partibus Philosophiæ Naturalis simplicioribus selingendarum:"-to report by May 16.

This Syndicate did not report by May 16. On May 20, a Grace was proposed for extending the time to June 1, but was refused in the Caput, on the ground that the Syndicate was extinct.

225 It will be seen, that from 1827 to 1838, these acts of the University made a series of changes, all in the same direction. The previous Classes, which had been framed merely upon the performances of the Disputants in the Schools, and which were subject to different examinations, were gradually abolished. In 1827, these Classes were reduced from six to four; and the examiners were enabled, when they thought fit, to give the same examination to all. In 1832, the examination for the first four days was ordered to be the same for all, and the Classes were divided only on the fifth day. In 1838 the Classes were discontinued, and the same questions were to be proposed to all the candidates.

226 A great ground of the disposition to abolish these Classes was the difficulty which was experienced in doing justice to the different Classes, in comparison with one another. The Examiners, in giving different questions to different Classes, endeavoured to proportion the difficulty of the questions to the attainments of

the Class; and again, to proportion the credit to the difficulty, in judging the answer. The credit was generally estimated in marks, and a certain scale of marks allowed to each class. If the questions proposed to the lower Classes were proportionably too easy, the members of those Classes obtained more marks than those who, being in the higher Classes, had probably read higher parts of mathematics than they had. And undoubtedly it must always be difficult to combine, into one arrangement, the result of different examinations. An examination such as that which was finally established, in which the same questions were proposed to all the candidates, has, in that respect a very great advantage, as a means of forming a just list of merit.

227 Another series of changes which took place was, that the length of the examination was gradually increased. In 1779, as we have seen, a fourth day was added to the examinations. In 1808, a fifth. In 1827, two days more were added; making the days for the Mathematical Examinations the Friday, Saturday, Monday, and Tuesday preceding the final Friday, on which the Brackets were to appear. In 1832, five days, instead of four, were appointed for the Mathematical Examination; and in 1838, a sixth day was added to this part of the examination; and so stands the law and the practice at the present time. The length of the examination, however, on each day was diminished in the course of the changes.

228 While more time was assigned to the Candidates to write, more time was also required for the Examiners to read what was written. From 1808 to 1827, when the examinees were set to write during Monday, Tuesday and Wednesday, on an average for six hours a day; and the Examiners had, besides attending at the times of examination, to read and judge the whole mass of answers, so as to bring out the Brackets on Friday morning, their labour was very [PT. I.]

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severe, and could rarely be gone through without devoting to it many hours of the night. Since that period, the beginning of the Examination has been shifted earlier and earlier; and is now (in practice) sixteen days previous to the final Friday, in the case of candidates for mathematical honours.

229 There is another series of changes noticeable in the Graces which I have quoted. The additional time assigned to the Examination is almost entirely appropriated to "Questions from Books," to the exclusion of "Problems." In 1827, five hours were added to the time employed in answering Questions from Books, while the time for Problems remained unaltered. In 1832, four hours were added to the time for Questions, half an hour for Problems. Up to 1827, there had been given by each class about ten hours to Questions and eight hours to Problems (for those who were willing to take so much.) At present, in an examination of six days, and of 5 hours each day, only 8 hours are given to Problems, and the remaining 24 to Questions from Books.

230 We may further remark, as running through all those acts of legislation, a solicitude which we have already noticed as existing in the governors of the University; namely, that the more elementary portions of mathematics should not be neglected in the attention given to the higher portions. The Grace of 1827 refers to the Grace of 1779, which is to this effect; and directs that the Examination on the first two days shall exclude the higher and more difficult parts of mathematics. On the first day, the Differential Calculus is altogether excluded; on the second day, its simpler applications only are to be admitted. The same direction is given in 1832. And the same disposition, I believe, prompted the Grace of 1840, which, as we have seen, led to no result.

I believe the same wish to avoid recondite and dif

ficult parts of mathematics led the Syndicates to appropriate the time which they added to the Examination to Questions from Books, rather than Problems. It was supposed that the former were more likely to test the Candidates' knowledge of the Principles of the Subjects of Examination. Perhaps this is not universally the case. A person may answer by rote a Question from a Book: in order to solve a Problem by means of a Principle, he must see the Principle with some degree of clearness.

231 One cause of the difficulty of securing due attention to the Elementary portion of Mathematics is the want of books upon those subjects recognized among us as the standards of our course of study. It appears to have been thought that the establishment of such standards might be left to the general tacit understanding and tradition of Examiners and Tutors. The Syndicate of 1827 expresses its hope, that by the adoption of its scheme, the questions (hitherto delivered vivá voce, but thenceforth printed) might be more generally known, the students might be better directed in their reading, the studies of the University might become more fixed and definite, and an opportunity might be afforded of seeing that all the subjects were duly introduced. The viva voce Examination, as it had till then been called, was to include only "propositions contained in the mathematical works commonly in use in the University, or simple explanations and examples of such propositions." Moreover in order to discourage the examinees from picking out, in each Examination paper, the higher and passing over the Elementary parts, each Paper of Questions was not to contain a greater number of questions than could be properly answered in the assigned time. The same rules were repeated in the Grace of 1838, the last of those which regulate our Examinations. Notwithstanding these provisions, the Grace of 1840 instituted