to the Examinations: the Moral Philosophy was made the subject of the fourth day, instead of the third; and the Brackets were arranged and examined on the fifth day, instead of the fourth.

214 About this time, or soon after, a new cause of change began to work extensively in the University; namely, the introduction of new mathematical methods among the students of mathematics. The state of mathematics, as then existing in the University, was by no means unsatisfactory, at least, as an instrument of Education. At a period somewhat earlier,-I suppose, soon after the rise of paper examinations, Manuscript Treatises; privately circulated, had been the main subjects of dependence and study; a result likely to follow from paper examinations. And this state of things produced its natural consequence. The ingenuity and energy of the students was employed, not in overcoming the real difficulties of a standard course of mathematics, but in trying to divine and prepare for the line which the examination would take. But before 1800, this evil had been, in a great measure, remedied by the publication of standard works, and their general acceptance in the University. Such works were Dr Wood's Algebra, Mechanics, and Optics; works admirably constructed for their purpose. About the same time Professor Vince published his Trigonometry, his Fluxions, his Hydrostatics, and his Astronomy: but these were works deficient in the judicious selection and simple exposition which belonged to Dr Wood's books; and their influence was much more limited and short-lived.

Besides these works of Wood and Vince, the Mathematical Course at Cambridge might be considered to include the works of Cotes and Attwood, and the Principia of Newton. And these works, well studied, were, as I have said, by no means a bad system of mathematical education. Those who had mastered

these works, had overcome the main difficulties of the subject; had possessed themselves of a great store of beautiful examples of mathematical logic and mathematical ingenuity; and could solve most problems of the kind with which English mathematicians had commonly dealt. A person who, at this period, obtained a high mathematical honour, had commonly acquired a command of certain mathematical methods, and a love of mathematics, which he retained through life.

215 But about the time of which I am speaking, the most active-minded English Mathematicians began to perceive that the methods of the French analysts were more powerful, or, at least, more general and symmetrical, than their own and this perception made them discontented with some of the treatises in common use, which I have mentioned. As this feeling grew stronger and more diffused, it led to the publication of Treatises, on various parts of mathematics, of a more analytical character than those which were previously in use. The processes contained in these Treatises gradually made their way into the University Examinations; and, in the end, displaced altogether the former standard course. Among the most important of the works which produced this effect, I may mention the Trigonometry of Professor Woodhouse, and the Translation of Lacroix's Elementary Treatise on the Differential and Integral Calculus, by Messrs Herschel, Peacock, and Babbage. I cannot avoid noticing also my own works on Mechanics; since the number of editions through which they have gone, and the form given to the subject in more recent Treatises by other authors, show that they had a share in this change, notwithstanding their great defects, of which I am well aware.

216 The persons who produced this revolution in the mathematical literature of Cambridge, laboured in

an honest zeal, with the object of substituting, as they conceived, a better kind of mathematics in the place of a worse. But their success in this respect was a source of considerable inconvenience to the University, with regard to her Educational System. For the standard of her mathematics being again unsettled, while her main machinery was mere Examinations, she was driven towards the peculiar evils belonging to such a combination; the reign of manuscript treatises, or of printed books quite as transient in their circulation; and the universal dependence upon private Tutors.

Moreover, the nature of the new kind of mathematics, addressing itself, as analysis does, to the eye, and difficult to express in an oral form, made the disputations in the Schools much less intelligible and interesting, and gave an increased importance to the paper Examinations.

217 We have, in the following Grace, an indication of a tendency to some alteration, as early as 1818; although the great change did not take place till nine years later.

1818. Dec. 4. "Placeat vobis ut Ds Procancellarius, Regii

Professores Sacræ Theologiæ, Legum, Medicinæ, et Græcarum Literarum, Prof. Calvert, Prof. Sedgwick, Mr Bridge, Mr Woodhouse, Mr Turton, Mr French, Mr Griffith, Syndici vestri constituantur, qui deliberent annon examinationes pro Gradibus novari et amplificari expediat ; et si illis aut eorum majori parti (quorum unus semper sit Procancellarius) videatur bonum, qui regulas ad vos referant quibus nova examinatio administretur."

In the Syndicate thus appointed, there prevailed great diversity of opinion upon some particulars; and, through an anxiety felt by the Syndics to satisfy every scruple entertained in the University, the Proposal resulting from their deliberations, fell far short of the general expectation, and did not reach the views of the

Syndics themselves, as one of them* informed the public.

218 In the course of a few years, the Examinations became the only part of the University exercises in which any interest was taken: the disputations, as I have already said, fell into neglect. At the same time the evils of the want of a Standard of study, fixed and known, were felt; and the old evil so forcibly described in the Grace of 1779, was still complained of;-that students, neglecting the Elementary parts of Mathematics, sought to obtain distinction by lucky hits in the higher portions.

The Grace by which it was attempted to remedy these evils, may be considered as the foundation deed of our present system. In order to understand it fully, it may be mentioned, that there had been much discussion in the University respecting the advisableness of introducing other subjects, as well as Mathematics, into the University Examinations. In 1821, Dr Wordsworth, the Master of Trinity, then Vice-Chancellor, proposed a plan for examining the students in Classics and Theology, which met with considerable support, but was rejected by the majority of voices in the Non-Regent House. But in 1822, the "Classical Tripos was established, as I shall afterwards have to mention ; and in this same year, it was also directed by a Grace that those who were not candidates for mathematical honours, should be examined on the fourth day, in the first six books of the Iliad and of the Æneid. It is to be recollected, also, that in the mathematical examination for honours, as then existing, certain hours for each class were assigned to the solution of "problems" proposed on paper, and certain hours to the answering of questions from books," which questions were pro

66

* Dr Monk, in a pamphlet published under the name

of Philograntus.

posed vivá voce, though the answers were given on paper. The previous classes determined, at least in supposition, by the exercises performed in the Schools, were at this time six in number.

219 I proceed to give the Grace of which I have spoken and the concomitant Graces.

1827. Mar. 30. Quoniam experientiâ recentiore compertum sit quod examinationes pro gradu Baccalaureatûs in Artibus minus commodè constitutæ sint, tam propter hodiernam Academiæ frequentiam quam propter studiorum ipsorum mutationem:

"Placeat vobis ut Ds Procancellarius, Dr Wood, Dr French, Domini Procuratores et Moderatores, Mr Peacock, Mr Gwatkin, Mr Whewell, Mr Graham, Mr Chevallier et Mr King, Syndici vestri constituantur, qui de his examinationibus ordinandis consulant et ad vos intra tres menses referant."

Jan. 30.

The Syndicate was continued: and was directed to report before the end of Lent Term, 1828.

Nov. 14. The Report of the Syndicate was confirmed; To this effect: Two days to be added to the Examination: five hours added to the time employed in answering Questions from books: the time for Problems unaltered:

Four previous Classes to be made instead of six the Examiners enabled, when they think fit, to give the same examination to all: the first two days to exclude the higher and more difficult parts of mathematics: the Grace of 1779 is referred to.

The Examinations on Friday to exclude the Differential Calculus: on Saturday, to include the simpler applications of the Calculus. The Questions hitherto proposed vivá voce to be printed. It was hoped, as the Syndics stated, that by this means, the questions might be more generally known, the