Quod nisi quisquam in Euclidis Geometria Elementis et in notissimis Philosophiæ Naturalis partibus versatissimum se exhibuerit, altiora Matheseos nequicquam se assecutum sciat: Quodque in toto Scientiæ Campo Eruditionem limatam perspicuamque potius quam diffusam Honores Academici maneant.

"Postremo ut Regulæ jam sancitæ in omni examinatione in posterum publicè in Senatu habendâ pro Gradu Baccalaureatûs in Artibus serventur."

210 The main subject of the University's solicitude hitherto appears to have been those students who were candidates for honours; the few; but in 1791, we find an important Grace, which contemplates the case of the many, and establishes a classification of the sophists who fell below the Junior Optimes. These are familiarly called the Polloi; and we shall take the liberty of using this name. The Grace by which they are recognized is as follows:

1791. Ap. 8. "Cum in solenni Sophistarum Examinatione

complures Sophistarum quotannis reperiantur de quibus non satis cautum sit ut Honores Academicos aut mereantur aut optent: cavendum sit tamen ut nequis temere ignominiâ notetur:

"Placeat vobis ut duo Examinatores anni præcedentis constituantur denuo Examinatores qui Sophistas honoribus Academicis non insigniendos examinent et eorum nomina in quatuor classes videlicet quartam, quintam, sextam, et septimam pro merito distributa publici juris faciant; ita tamen ut nomina in quâcunque classe ordine alphabetico, si ita examinatoribus placeat, recenseantur, et ut septima vel sexta vel etiam quinta classis vacare possit, si eorum omnium merita vel sextam vel quintam vel quartam videantur vindi-` care."

It is provided that the rights of Proctors, Moderators, Regents, Non-Regents to take part in the Examinations are not to be diminished.

It is added,

"Placeat vobis ut dictorum Sophistarum nomina ne prelo committantur."

211 So far as I am aware, this law of the Univer

sity has not been superseded by any subsequent Grace. Its directions are very plain :—that the polloi are to be divided into classes not more than four; that in each class, the names are to be arranged alphabetically; and that the names, though published, are not to be printed; that is, not printed by authority, as those of the first three classes are. These are very proper and reasonable directions; for an arrangement of the polloi according to merit in greater detail, can hardly be effected. The amount of their performances does not allow of an arrangement of each person according to merit; and any attempt to effect such an arrangement, can hardly fail to perplex the Examiners, and mislead the public. If there be 200 of the polloi, there cannot be 200, nor 100, nor 50 distinguishable shades of merit among them; and to throw them into four alphabetical classes, is sufficient for their encouragement and guidance. Yet, in this respect, the Grace has been habitually neglected in modern times. I do not know whether it was ever literally obeyed; but, of late years, the whole body of the polloi have been arranged in an asserted order of merit, man by man. I believe the inconvenience and difficulty of this proceeding have recently become matter of general notice; and I hope the Examiners in future will remedy these evils by conforming to the law of the University; which, as I conceive, they are bound to do, or, at least, fully justified in doing.

The direction, that the names of the 4th, 5th, 6th, and 7th classes were not to be printed, was suggested, I presume, by the belief that such a notification of these classes would put them too much upon a level with the mathematical Honours. The names are not printed on the Tripos Papers, as those of the Wranglers, Senior Optimes, and Junior Optimes are; or in the Cambridge Calendar. It would, probably, be neither necessary nor easy to prevent lists of the other

classes being circulated in print, now when every thing is printed. But the Examiners may easily, and with great public advantage, conform to the Grace so far as their own conduct is concerned.

212 The Disputations of the Sophs, at this period regulated, as we have seen, the Classes before the Examination, and had a great share in determining academical reputations. They were a matter of great general interest; and this interest it was wished to maintain. They had hitherto been held after dinner, that is, from two o'clock in the afternoon till four; and it was a common habit of students and of graduates to resort to the Schools after dinner, to witness these exercises. But when the general dinner-hour became later, a corresponding alteration was made in the hours of the disputations by a Grace, which thus begins:

1792. Feb. 14.

"Cum Academiæ nostræ plurimum intersit ut sophistarum disputationes quam maxime frequententur, tempora autem hisce peragendis assignata parum convenientia et opportuna jamdiu evaserint :"And it provides that thenceforth these exercises shall take place from three o'clock to five in the afternoon.

213 The next step of legislation on the subject implies a growing importance in the Examinations. It is as follows:

1808. Dec. 1. "Cum visum sit plerisque eorum qui nuper in annuâ sophistarum examinatione versati sunt, tempus examini accurate habendo vix sufficere, atque etiam in ratione examinis instituendi quædam in melius mutari posse: Placeat vobis ut Ds Procancellarius, Mr J. Wood, Mr Tavel, Mr Hudson, Mr Barnes (Coll. Regin.), Mr Hornbuckle, Mr Woodhouse, una cum duobus hujus anni moderatoribus, sint syndici vestri, qui collatis inter se sententiis videant utrum aliquid de hâc re vestris suffragiis stabiliendum proferre expediat."

This Syndicate offered recommendations which were confirmed by a Grace, Dec. 15. A fifth day was added

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