part in it constantly gave rise to accusations of partiality.

In 1763 the traditional rules for the conduct of the examin- ation took more definite shape. Henceforth the examiners used the disputations only as a means of classifying the men roughly. On the result of their " acts," and probably partly also of their general reputation, the candidates were divided into eight classes, each arranged in alphabetical order. The subsequent position of the men in the class was determined solely by the Senate- House Examination. The first two classes comprised all who were expected to be wranglers, the next four classes included
* Quoted by C. Wordsworth, Scholae Academicae, Cambridge, 1877, pp. 30—31.
256 THE MATHEMATICAL TRIPOS [CH. XI
the other candidates for honours, and the last two classes con- sisted of poll-men only. Practically anyone placed m either of the first two classes was allowed, if he wished, to take an aegrotat senior optime, and thus escape all further examination: this was called gulphing it. All the men from one College were no longer taken together, but each class was examined separately and vivd voce ; and hence, since all the students comprised in each class were of about equal attainments, it was possible to make the examination more effective. Richard \Vatson, of Trinity, claimed that this change was made by him when acting as moderator in 1763. He says*:
There was more room for partiality... then [i.e. in 1759] than there is now; and I attribute the change, in a great degree, to an alteration which I introduced the first year I was moderator [i.e. in 1763], and which has been persevered in ever since. At the time of taking their Bachelor of Arts' degree, the young men are examined in classes, and the classes are now formed according to the abilities shown by individuals in the schools. By this arrangement, persons of nearly equal merits are examined in the presence of each other, and flagrant acts of partiality cannot take place. Before I made this alteration, they were examined in classes, but the classes consisted of members of the same College, and the best and worst were often examined together.
It is probable that before the examination in the Senate-House began a candidate, if manifestly placed in too low a class, was allowed the privilege of challenging the class to which he was assigned. Perhaps this began as a matter of favour, and was only granted in exceptional cases, but a few years later it became a right which every candidate could exercise ; and I think that it is partly to its development that the ultimate predominance of the tripos over the other exercises for the degree is due.
In the same year, 1763, it was decided that the relative position of the senior and second wranglers, namely, Paley, of Christ's, and Frere, of Caius, was to be decided by the Senate- House Examination and not by the disputations. Henceforward distinction in the Senate-House Examination was regarded as the most important honour open to undergraduates.
* Anecdotes of the Life of Richard Watson by Ilimselff London, 1817, pp. 18—19.
CH. Xl] THE MATHEMATICAL TRIPOS 257
In 1768 Dr Smith, of Trinity College, founded prizes for mathematics and natural philosophy open to two commencing bachelors. The examination followed immediately after the Senate-House Examination, and the distinction, being much coveted, tended to emphasize the mathematical side of the normal University education of the best men. Since 1883 the prizes have been awarded on the result of dissertations*. Additional prizes, awarded at the same time, and associated with the name of Lord Rayleighf, were founded in 1909.
Until now the Senate- House Examination had been oral, but about this time, circ. 1770, it began to be the custom to dictate some or all of the questions and to require answers to be written. Only one question was dictated at a time, and a fresh one was not given out until some student had solved that previously read : a custom which by causing perpetual inter- ruptions to take down new questions must have proved very harassing. We are perhaps apt to think that an examination conducted by written papers is so natural that the custom is of long continuance, but I know no record of any in Europe earlier than the eighteenth century. Until 1830 the questions for the Smith's prizes were dictated.
The following description of the Senate-House Examination as it existed in 1772 is given by JebbJ.
The moderators, some days before the arrival of the time prescribed by the vice-chancellor, meet for the purpose of forming the students into divisions of six, eight, or ten, according to their performance in the schools, with a view to the ensuing examination.
Upon the first of the appointed days, at eight o'clock in the morning, the students enter the senate-house, preceded by a master of arts from each college, who... is called the "father" of the college, ...
After the proctors have called over the names, each of the moderators sends for a division of the students: they sit with him round a table, with pens, ink, and paper, before them : he enters upon his task of examination, and does not dismiss the set till the hour is expired. This examination has now for some years been held in the english language.
* See Grace of October 25, 1883 ; and the Cambridge University Beporter^ October 23, 1883.
t See Grace of February 11, 1909, and the Cambridge University Reporter, December 8, 1903.
J The Works of J. Jcbb, London, 1787, vol. ii, pp. 290—297,
B. R. 17
258 THE MATHEMATICAL TRIPOS [CH. XI
The examination is varied according to the abilities of the students. The moderator generally begins with proposing some questions from the six books of Euclid, plain {sic) trigonometry, and the first rules of algebra. If any person fails in an answer, the question goes to the next. From the elements of mathematics, a transition is made to the four branches of philosophy, viz. mechanics, hydrostatics, apparent astronomy, and optics, as explained in the works of Maclaurin, Cotes, Helsham, Hamilton, Eutherforth, Keill, Long, Ferguson, and Smith. If the moderator finds the set of questionists, under examination, capable of answering him, he proceeds to the eleventh and twelfth books of Euclid, conic sections, spherical trigonometry, the higher parts of algebra, and sir Isaac Newton's Principia ; more particularly those sections, which treat of the motion of bodies in eccentric and revolving orbits; the mutual action of spheres, composed of particles attracting each other according to various laws ; the theory of pulses, propagated through elastic mediums ; and the stupendous fabric of the world. Having closed the philosophical examination, he sometimes asks a few questions in Locke's Essay on the human understanding, Butler's Analogy, or Clarke's Attributes. But as the highest academical distinctions are invariably given to the best proficients in mathematics and natural philosophy, a very superficial knowledge in morality and metaphysics will suffice.
When the division under examination is one of the highest classes, problems are also proposed, with which the student retires to a distant part of the senate-house, and returns, with his solution upon paper, to the moderator, who, at his leisure, compares it with the solutions of other students, to whom the same problems have been proposed.
The extraction of roots, the arithmetic of surds, the invention of divisers, the resolution of quadratic, cubic, and biquadratic equations ; together with the doctrine of fluxions, and its application to the solution of questions " de maximis et minimis," to the finding of areas, to the rectification of curves, the investigation of the centers of gravity and oscillation, and to the circumstances of bodies, agitated, according to various laws, by centripetal forces, as unfolded, and exemplified, in the fiuxional treatises of Lyons, Saunderson, Simpson, Emerson, Maclaurin, and Newton, generally form the subject matter of these problems.
When the clock strikes nine, the questionists are dismissed to breakfast : they return at half-past nine, and stay till eleven ; they go in again at half-past one, and stay tiU three ; and, lastly, they return at half -past three, and stay till five.
The hours of attendance are the same upon the subsequent day.
On the third day they are finally dismissed at eleven.
During the hours of attendance, every division is twice examined in form, once by each of the moderators, who are engaged for the whole time in this employment.
As the questionists are examined in divisions of only six or eight at a time, but a small portion of the whole number is engaged, at any particular hour, with the moderators ; and, therefore, if there were no further examination, much time would remain unemployed.
But the moderator's inquiry into the merits of the candidates forms the least material part of the examination.
CH. Xl] THE MATHEMATICAL TRIPOS 259
The "fathers" of the respective colleges, zealous for the credit of the societies, of which they are the guardians, are incessantly employed in ex- amining those students, who appear most likely to contest the palm of glory with their sons.
This part of the process is as follows :
The father of a college takes a student of a different college aside, and, sometimes for an hour and an half together, strictly examines him in every part of mathematics and philosophy, which he professes to have read.
After he hath, from this examination, formed an accurate idea of the student's abilities and acquired knowledge, he makes a report of his absolute or comparative merit to the moderators, and to every other father who shall ask him the question.
Besides the fathers, all masters of arts, and doctors, of whatever faculty they be, have the liberty of examining whom they please ; and they also report the event of each trial, to every person who shall make the inquiry.
The moderators and fathers meet at breakfast, and at dinner. From the variety of reports, taken in connection with their own examination, the former are enabled, about the close of the second day, so far to settle the comparative merits of the candidates, as to agree upon the names of four-and-twenty, who to them appear most deserving of being distinguished by marks of academical approbation.
These four-and-twenty [wranglers and senior optimes] are recommended to the proctors for their private examination ; and, if approved by them, and no reason appears against such placing of them from any subsequent inquiry, their names are set down in two divisions, according to that order, in which they deserve to stand ; are afterwards printed ; and read over upon a solemn day, in the pres'^uce of the vice-chancellor, and of the assembled university.
The names of the twelve [junior optimes], who, in the course of the examina- tion, appear next in desert, are also printed, and are read over, in the presence of the vice-chancellor, and of the assembled university, upon a day subsequent to the former. . . .
The students, who appear to have merited neither praise nor censure, [the poll-men], pass unnoticed : while those, who have taken no pains to prepare themselves for the examination, and have appeared with discredit in the schools, are distinguished by particular tokens of disgrace.
Jebb's statement about the number of wranglers and senior optimes is only approximate.
It may be added that it was now frankly recognized that the examination was competitive*. Also that though it was open to any member of the Senate to take part in it, yet the determination of the relative merit of the students was entirely in the hands of the moderators f. Although the examination did not occupy more than three days it must have been a severe
* "Emulation, which is the principle upon which the plan is constructed." The Works of J. Jebb, London, 1787, vol. in, p. 261.
t Tlie Works of J. Jebb, London, 1787, vol. in, p. 272.
17—2
260 THE MATHEMATICAL TRIPOS [CH. XI
physical trial to anyone who was delicate. It was held in winter and in the Senate-House. That building was then noted for its draughts, and was not warmed in any way : and, according to tradition, on one occasion the candidates on entering in the morning found the ink in the pots on their desks frozen.
The University was not altogether satisfied* with the scheme in force, and in 1779 f the scheme of examination was amended in various respects. In particular the examination was extended to four days, a third day being given up entirely to natural religion, moral philosophy, and Locke. It was further announced J that a candidate would not receive credit for advanced subjects unless he had satisfied the examiners in Euclid and elementary Natural Philosophy.
A system of brackets or " classes quam minimae " was now introduced. Under this system the examiners issued on the morning of the fourth day a provisional list of men who had obtained honours, with the names of those of about equal merit bracketed, and that day was devoted to arranging the names in each bracket in order of merit: the examiners being given explicit authority to invite the assistance of others in this work. Whether at this time a candidate could request to be re-ex- amined with the view of being moved from one bracket to another is uncertain, but later this also was allowed.
Under the scheme of 1779 also the number of examiners was increased to four, the moderators of one year becoming, as a matter of course, the examiners of the next. Thus of the four examiners in each year, two had taken part in the examination of the previous year, and the continuity of the system of ex- amination was maintained. The names of the moderators appear on the tripos lists, but the names of the examiners were not printed on the lists till some years later.
The right of any M.A. to take part in the examination was not affected, though henceforth it was exercised more sparingly, and I believe was not insisted on after 1785. But it became
* See Graces of July 5, 1773, and of February 17, 1774.
+ See Graces of March 19, 20, 1779.
t Notice issued by the Vice-Chancellor, dated May 19, 1779.
CH. Xl] THE MATHEMATICAL TRIPOS 261
a regular custom for the moderators to invite particular M.A.s to examine and compare specified candidates. Milner, of Queens', was constantly asked to assist in this way.
It was not long before it became an established custom that a candidate, who was dissatisfied with the class in which he had been placed as the result of his disputations, might challenge it before the examination began. This power seems to have been used but rarely ; it was, however, a recognition of the fact that a place in the tripos list was to be determined by the Senate- House Examination alone, and the examiners soon acquired the habit of settling the preliminary classes without exclusive reference to the previous disputations.
The earliest extant paper actually set in the Senate-House, to which we can with certainty refer, is a problem paper set in 1785 or 1786 by W. Hodson, of Trinity, then a proctor. The autograph copy from which he gave out the questions was luckily preserved, and is in the library* of Trinity College. It must be almost the last problem paper which was dictated, instead of being printed and given as a whole to the candi- dates. The paper is as follows :
1. To determine the velocity with which a Body must be thrown, in a direction parallel to the Horizon, so as to become a secondary planet to the Earth ; as also to describe a parabola, and never return.
2. To demonstrate, supposing the force to vary as — , how far a body must
fall both within and without the Circle to acquire the Velocity with which a body revolves in a Circle.
3. Suppose a body to be turned (sic) upwards with the Velocity with which it revolves in an Ellipse, how high will it ascend ? The same is asked supposing it to move in a parabola.
4. Suppose a force varying first as ^-^ , secondly in a greater ratio than .=-^
but less than y-g , and thirdly in a less ratio than ■=-, , in each of these Cases to
determine whether at all, and where the body parting from the higher Apsid will come to the lower.
5. To determine in what situation of the moon's Apsid they go most forwards, and in what situation of her Nodes the Nodes go most backwards, and why ?
• The Challis Manuscripts, iii, 61. There are two copies almost identical, one dated 1785, the other 1786. Probably the paper printed in the text was set in 178d.
262 THE MATHEMATICAL TRIPOS [CH. XI
6. In the cubic equation x^ + qx + r = 0 which wants the second term ; sup- posing x = a + b and Sab= - q^ to determine the value of x. {sic.)
7. To find the fluxion of o:^ x (y** + 2"^)a .
•
8. To find the fluent of -^ .
a+x
9. To find the fluxion of the vi^^ power of the Logarithm of x,
10. Of right-angled Triangles containing a given Area to find that whereof the sum of the two legs AB + BC shall be the least possible. [This and the two following questions are illustrated by diagrams. The angle at B is the right angle.]
11. To find the Surface of the Cone ABC. [The cone is a right one on a circular base.]
12. To rectify the arc DB of the semicircle DBV.
In cases of equality in the Senate-House Examination the acts were still taken into account in settling the tripos order : and in 1786 when the second, third, and fourth wranglers came out equal in the examination a memorandum was published that the second place was given to that candidate who dialectis magis est versatvs, and the third place to that one who in scholis sophistarum melius disputavit.
There seem to have been considerable intervals in the examination by the moderators, and the examinations by the extraneous examiners took place in these intervals. Those candidates who at any time were not being examined occupied themselves with amusements, provided they were not too boisterous and obvious: probably dice and cards played a large part in them. Gunning in an amusing account of his examination in 1788 talks of games with a teetotum* in which he took part on the Wednesday (when Locke and Paley formed the subjects of examination), but " which was carried on with great spirit... by considerable numbers during the whole of the examination."
About this time, 1790, the custom of printing the problem papers was introduced, but until 1828 the other papers con- tinued to be dictated. Since then all the papers have been printed.
* H. Giinning, Reminiscences, second edition, London, 1855, vol. r, p. 82.
CH. Xl] THE MATHEMATICAL TRIPOS 26
•">
I insert here the following letter* from William Gooch, of Caius, in which he describes his examination in the Senate- House in 1791. It must be remembered that it is the letter of an undergraduate addressed to his father and mother, and was not intended either for preservation or publication: a fact which certainly does not detract from its value.
Monday | aft. 12.
We have been examin'd this Morning in pure Mathematics & I've hitherto kept just about even with Peacock which is much more than I expected. We are going at 1 o'clock to be examin'd till 3 in Philosophy.
From 1 till 7 I did more than Peacock ; But who did most at Moderator's Kooms this Evening from 7 till 9, 1 don't know yet ;— but I did above three times as much as the Sen' Wrangler last year, yet I'm afraid not so much as Peacock.
Between One & three o'Clock I wrote up 9 sheets of Scribbling Paper so you may suppose I was pretty fully employ'd.
Tuesday Night.
I've been shamefully us'd by Lax to-day ; — Tho' his anxiety for Peacock mu?t (of course) be very great, I never suspected that his Partially {sic) w"^ get the better of his Justice. I had entertain'd too high an opinion of him to suppose it. — he gave Peacock a long private Examination & then came to me {I hop'd) on the same subject, but 'twas only to Bully me as much as he could, — whatever I said (tho' right) he tried to convert into Nonsense by seeming to misunderstand me. However I don't entirely dispair of being first, tho' you see Lax seems determin'd that I shall not. — I had no Idea (before I went into the Senate-House) of being able to contend at all with Peacock.
Wednesday evening.
Peacock & I are still in perfect Equilibrio & the Examiners themselves can give no guess yet who is likely to be first ; — a New Examiner (Wood of St. John's, who is reckon'd the first Mathematician in the University, for Waring doesn't reside) was call'd solely to examine Peacock & me only. — but by this new Plan nothing is yet determin'd. — So Wood is to examine us again to-morrow morning.
Thursday evening.
Peacock is declar'd first & I second, — Smith of this Coll. is either 8'^ or 9'^ & Lucas is either 10'^ or ll*'^. — Poor Quiz Carver is one of the ol ttoWoI; — I'm perfectly satisfied that the Senior Wranglership is Peacock's due, but certainly not 80 very indisputably as Lax pleases to represent it — I understand that he asserts 'twas 5 to 4 in Peacock's favor. Now Peacock & I have explain'd to each other how we went on, & can prove indisputably that it wasn't 20 to 19 in his favor ; — I cannot therefore be displeas'd for being plac'd second, tho' I'm provov'd {sic) with Lax for his false report (so much beneath the Character of a Gentleman.) —
N.B. it is my very particular Request that you dont mention Lax's be- haviour to me to any one.
* C. Wordsworth, Scholae Academicae, Cambridge, 1877, pp. 322—323.
i>64 THE MATHEMATICAL TRIPOS [CH. XI
Such was the form ultimately taken by the Senate-House Examination, a form which it substantially retained without alteration for nearly half-a-century. It soon became the sole test by which candidates were judged. The University was not obliged to grant a degree to anyone who performed the statutable exercises, and it was open to the University to refuse to pass a supplicat for the B.A. degree unless the candidate had presented himself for the Senate-House Examination. In 1790 James Blackburn, of Trinity, a questionist of exceptional abilities, was informed that in spite of his good disputations he would not be allowed a degree unless he also satisfied the examiners in the tripos. He accordingly solved one " very hard problem," though in consequence of a dispute with the authorities he refused to attempt any more*.
It will be recollected that the examination was now com- pulsoiy on all candidates pursuing the normal course for the B.A. degree. In 1791 the University laid down rules f for its conduct, so ffir as it concerned poll-men, decreeing that those who passed were to be classified in four divisions or classes, the names in each class to be arranged alphabetically, but not to be printed on the official tripos lists. The classes in the final lists must be distinguished from the eight preliminary classes issued before the commencement of the examination. The men in the first six preliminary classes were expected to take honours ; those in the seventh and eighth preliminary classes were primd facie poll-men.
In 1799 the moderators announced J that for the future they would require every candidate to show a competent knowledge of the first book of Euclid, arithmetic, vuglar and decimal fi-actions, simple and quadratic equations, and Locke and Paley. Paley's works seem to be held in esteem by modern divines, and his Evidences, though not his Philosophy, still remains (1905) one of the subjects of the Previous Examination, but his contemporaries thought less highly of his writings, or at any
* H. Gunning, Beminiscences, second edition, London, 1855, vol. i, p. 182. t See Grace of April 8, 1791.
X Communicated by the moderators to fathers of Colleges on January 18, 1799, and agreed to by the latter.
CH. Xl] THE MATHEMATICAL TRIPOS 265
rate of his Philosophy. Thus Best is quoted by Wordsworth* as saying of Paley's Philosophy, " The tutors of Cambridge no doubt neutralize by their judicious remarks, when they read it to their pupils, all that is pernicious in its principles": so also Richard Watson, Bishop of Llandaff, in his anecdotal autobio- graphy-|-, says, in describing the Senate-House Examination in which Paley was senior wrangler, that Paley was afterwards known to the world by many excellent productions, " though
there are some principles in his philosophy which I by
no means approve."
In 1800 the moderators extended to all men in the first four preliminary classes the privilege of being allowed to attempt the problem papers : hitherto this privilege had been confined to candidates placed in the first two classes. Until 1828 the problem papers were set in the evenings, and in the rooms of the moderator.
The University Calendars date from 1796, and from 1802 to 1882 inclusive contain the printed tripos papers of the previous January. The papers from 1801 to 1820 and from 1838 to 1849 inclusive were also published in separate volumes, which are to be found in most public libraries. No problems were ever set to the men in the seventh and eighth preliminary classes, which contained the poll-men. None of the bookwork papers of this time are now extant, but it is believed that they contained but few riders. Many of the so-called problems were really pieces of bookwork or easy riders: it must however be remembered that the text-books then in circulation were inferior and incomplete as compared with modern ones.
The Calendar of 1802 contains a diffuse account of the ex- amination. It commences as follows :
On the Monday morning, a little before eight o'clock, the students, generally about a hundred, enter the Senate-House, preceded by a master of arts, who on this occasion is styled the father of the College to which he belongs. On two pillars at the entrance of the Senate-House are hung the classes and a paper denoting the hours of examination of those who are thought most competent to contend for honours. Immediately after the University clock has struck eight,
* C. Wordsworth, Scholae Academicae, Cambridge, 1877, p. 123.
+ Anecdotes of the Life of Richard IVutson by Himself, London, 1817, p. 19.
266 THE MATHEMATICAL TRIPOS [CH. XI
the names are called over, and the absentees, being marked, are subject to certain fines. The classes to be examined are called out, and proceed to their appointed tables, where they find pens, ink, and paper provided in great abundance. In this manner, with the utmost order and regularity, two-thirds of the young men are set to work within less than five minutes after the clock has struck eight. There are three chief tables, at which six examiners preside. At the first, the senior moderator of the present year and the junior moderator of the preceding year. At the second, the junior moderator of the present, and the senior moderator of the preceding year. At the third, two moderators of the year previous to the two last, or two examiners appointed by the Senate. The two first tables are chiefly allotted to the six first classes ; the third, or largest, to the ol iroWoi.
The young men hear the propositions or questions delivered by the ex- aminers ; they instantly apply themselves ; demonstrate, prove, work out and write down, fairly and legibly (otherwise their labour is of little avail) the answers required. All is silence ; nothing heard save the voice of the examiners ; or the gentle request of some one, who may wish a repetition of the enunciation. It requires every person to use the utmost dispatch ; for as soon as ever the examiners perceive anyone to have finished his paper and subscribed his name to it another question is immediately given
The examiners are not seated, but keep moving round the tables, both to judge how matters proceed and to deliver their questions at proper intervals. The examination, which embraces arithmetic, algebra, fluxions, the doctrine of infinitesimals and increments, geometry, trigonometry, mechanics, hydrostatics, optics, and astronomy, in all their various gradations, is varied according to circumstances : no one can anticipate a question, for in the course of five minutes he may be dragged from Euclid to Newton, from the humble arithmetic of Bonnycastle to the abstruse analytics of Waring. While this examination is proceeding at the three tables between the hours of eight and nine, printed problems are delivered to each person of the first and second classes ; these he takes with him to any window he pleases, where there are pens, ink, and paper prepared for his operations.
The examination began at eight. At nine o'clock the papers had to be given up, and half-an-hour was allowed for breakfast. At half-past nine the candidates came back, and were examined in the way described above till eleven, when the Senate-House was again cleared. An interval of two hours then took place. At one o'clock all returned to be again examined. At three the Senate-House was cleared for half-an-hour, and, on the return of the candidates, the examination was continued till five. At seven in the evening the first four classes went to the senior moderator's rooms to solve problems. They were finally dis- missed for the day at nine, after eight hours of examination.
CH. Xl] THE MATHEMATICAL TRIPOS 267
The work of Tuesday was similar to that of Monday: Wednesday was partly devoted to logic and moral philosophy. At eight o'clock on Thursday morning a first list was published with all candidates of about equal merits bracketed. Until nine o'clock a candidate had the right to challenge anyone above him to an examination to see which w^as the better. At nine a second list came out, and a candidate's right of challenge was then confined to the bracket immediately above his own. If he proved himself the equal of the man so challenged his name was transferred to the upper bracket. To challenge and then to fail to substantiate the claim to removal to a higher bracket w^as considered rather ridiculous. Revised lists were published at 11 a.m., 3 p.m., and 5 p.m., according to the results of the examination during that day. At five the whole examination ended. The proctors, moderators, and examiners then retired to a room under the Public Library to prepare the list of honours, which was sometimes settled without much difficulty in a few^ hours, but sometimes not before 2 a.m. or 3 a.m. the next morning. The name of the senior wrangler was generally announced at midnight, and the rest of the list the next morning. In 1802 there were eighty-six candidates for honours, and they were divided into fifteen brackets, the first and second brackets containing each one name only, and the third bracket four names.
It is clear from the above account that the competition fostered by the examination had developed so much as to threaten to impair its usefulness as guiding the studies of the men. On the other hand, there can be no doubt that the carefully devised arrangements for obtaining an accurate order of merit stimulated the best men to throw all their energies into the work for the examination. It is easy to point out the double-edged result of a strict order of merit. The problem before the University was to retain its advantages while checking any abuses to which it might lead.
It was the privilege of the moderators to entertain the proctors and some of the leading resident mathematicians the night before the issue of the final list, and to communicate that
268 THE MATHEMATICAL TRIPOS [CH. XI
list in confidence to their guests. This pleasant custom survived till 1884. I revived the practice in 1890 when acting as senior moderator, but it seems to have now ceased.
In 1806 Sir Frederick Pollock was senior wrangler, and in 1869 in answer to an appeal from De Morgan for an account of the mathematical study of men at the beginning of the century- he wrote a letter* which is sufficiently interesting to bear reproduction :
I shcall write in answer to your inquiry, all about my books, my study, and my degree, and leave you to settle all about the proprieties which my letter may give rise to, as to egotism, modesty, &c. The only books I read the first year were Wood's Algebra (as far as quadratic equations), Bonnycastle's ditto, and Euclid (Simpson's). In the second year I read Wood (beyond quadratic equations), and Wood and Vince, for what they called the branches. In the third'year I read the Jesidfs Newton and Vince's Fluxions ; these were all the books, but there were certain mss. floating about which I copied — which be- longed to Dealtry, second wrangler in Kempthorne's year. I have no doubt that I had read less and seen fewer books than any senior wrangler of about my time, or any period since ; but what I knew I knew thoroughly, and it was completely at my fingers' ends, I consider that I was the last geometrical and fiuxional senior wrangler ; I was not up to the differential calculus, and never acquired it. I went up to college with a knowledge of Euclid and algebra to quadratic equations, nothing more ; and I never read any second year's lore during my first year, nor any third year's lore during my second ; ray forte was, that what I did know I could produce at any moment with perfect accuracy. I could repeat the first book of Euclid word by word and letter by letter. During my first year I was not a ' reading ' man (so called) ; I had no expectation of honours or a fellowship, and I attended all the lectures on all subjects — Harwood's anatomical, Woollaston's chemical, and Parish's mechanical lectures — but the examination at the end of the first year revealed to me my powers. I was not only in the first class, but it was generally understood I was first in the first class ; neither I nor any one for me expected I should get in at all. Now, as I had taken no pains to prepare (taking, however, marvellous pains while the examination was going on), I knew better than any one else the value of my examination qualities (great rapidity and perfect accuracy) ; and I said to myself, 'If you're not an ass, you'll be senior wrangler' ; and I took to 'reading' accordingly. A curious circumstance occurred when the Brackets came out in the Senate-house declaring the result of the examination : I saw at the top the name of Walter bracketed alone (as he was) ; in the bracket below were Fiott, Hustler, Jephson. I looked down and could not find my own name till I got to Bolland, when my pride took fire, and I said, ' I must have beaten that man, so I will look up again ' ; and on looking up carefully I found the nail had been passed through my name, and I was at the top bracketed alone, even above
* Memoir of A. de Morgan, London, 1882, pp. 387—392.
CH. Xl] THE MATHEMATICAL TRIPOS 269
Walter. You may judge what mj feelings were at this discovery; it is the only instance of two such brackets, and it made my fortune — that is, made me independent, and gave me an immense coDege reputation. It was said I was more than half of the examination before any one else. The two moderators were Hornbuclde, of St John's, and Brown (Saint Brown), of Trinity. The Johnian congratulated me. I said perhaps I might be challenged; he said, •Well, if you are you're quite safe — you may sit down and do nothing, and no
one would get up to you in a whole day.'
Latterly the Cambridge examinations seem to turn upon very different matters from what prevailed in my time. I think a Cambridge education has for its object to make good members of society — not to extend science and make profound mathematicians. The tripos questions in the Senate-house ought not to go beyond certain limits, and geometry ought to be cultivated and encouraged much more than it is.
To this De Morgan replied :
Your letter suggests much, because it gives possibility of answer. The branches of algebra of course mainly refer to the second part of Wood, now called the theory of equations. Waring was his guide. Turner — whom you must remember as head of Pembroke, senior wrangler of 1767 — told a young man in the hearing of my informant to be sure and attend to quadratic equations. • It was a quadratic,' said he, ' made me senior wrangler.' It seems to me that the Cambridge revivers were [Woodhouse,] Waring, Paley, Vince, Milner.
You had Dealtry's mss. He afterwards published a very good book on fluxions. He merged his mathematical fame in that of a Claphamite Christian. It is something to know that the tutor's ms. was in vogue in 1800-1806.
Now — how did you get your conic sections? How much of Newton did you read? From Newton direct, or from tutor's manuscript?
Surely Fiott was our old friend Dr Lee. I missed being a pupil of Hustler by a few weeks. He retired just before I went up in February 1823. The echo of Hornbuckle's answer to you about the challenge has lighted on Whewell, who, it is said, wanted to challenge Jacob, and was answered that he could not beat [him] if he were to write the whole day and the other wrote nothing. I do not believe that Whewell would have listened to any such dissuasion.
I doubt your being the last fluxional senior wrangler. So far as I know, Gipps, Langdale, Alderson, Dicey, Neale, may contest this point with you.
The answer of Sir Frederick Pollock to these questions is dated August 7, 1869, and is as follows :
You have put together as revivers five very different men. Woodhonse was better than Waring, who could not prove Wilson's (Judge of C. P.) guess about the property of prime numbers; but Woodhouse (I think) did prove it, and a beautiful proof it is. Vince was a bungler, and I think utterly insensible of mathematical beauty.
Now for your questions. I did not get my conic sections from Vince. I copied a ms. of Dealtry. I fell in love with the cone and its sections, and
270 THE MATHEMATICAL TRIPOS [CH. XI
everything about it. I have never forsal in such problems as two spheres touching each other and also the inside of a hollow cone, &c. As to Newton, I read a good deal (men now read nothing), but I read much of the notes. I detected a blunder which nobody seemed to be aware of. Tavel, tutor of Trinity, was not ; and he argued very favourably of me in consequence. The application of the Principia I got from mss. The blunder was this: in calculating the resistance of a globe at the end of a cylinder oscillating in a resisting medium they had forgotten to notice that there is a difference between the resistance to a globe and a circle of the same diameter.
The story of Whewell and Jacob cannot be true. Whewell was a very, very considerable man, I think not a great man. I have no doubt Jacob beat him in accui-acy, but the supposed answer cannot be true; it is a mere echo of what actually passed between me and Hornbuckle on the day the Tripos came out — for the truth of which I vouch. I think the examiners are taking too practical a turn ; it is a waste of time to calculate actually a longitude by the help of logarithmic tables and lunar observations. It would be a fault not to know how, but a greater to be handy at it.
A few minor changes in the Senate-House Examination were made in 1808*. A fifth day was added to the exami- nation. Of the five days thus given up to it three were devoted to mathematics, one to logic, philosophy, and religion, and one to the arrangement of the brackets. Apart from the evening paper the examination on each of the first three days lasted six hours. Of these eighteen hours, eleven were assigned to book- work and seven to problems. The problem papers were set from 6 to 10 in the evening.
A letter fi'om Whewell dated January 19, 1816, describes his examination in the Senate-House f.
Jacob. Whewell. Such is the order in which we are fixed after a week's examination... I had before been given to understand that a great deal depended upon being able to write the greatest possible quantity in the smallest time, but of the rapidity which was actually necessary I had formed the most distant idea. I am upon no occasion a quick writer, and upon subjects where I could not go on without sometimes thinking a little I soon found myself considerably behind. I was therefore surprised, and even astonished, to find myself bracketed off, as it is called, in the second place ; that is, on the day when a new division of the classes is made for the purpose of having a closer examina- tion of the respective merits of men who come pretty near to each other, I was not classed with anybody, but placed alone in the second bracket. The man
* See Graces, December 15, 1808.
t S. Douglas, Life of W. Whewell, London, 1881, p. 20.
CH. Xr] THE MATHEMATICAL TRIPOS 27 1
who is at the head of the list is of Cains College, and was always expected to be very high, though I do not know that anybody expected to see him so decidedly superior as to be bracketed off by himself.
The tendency to cultivate mechanical rapidity was a grave evil, and lasted long after Whewell's time. According to rumour the highest honours in 1845 were obtained by assiduous practice in writing*.
The devotion of the Cambridge school to geometrical and fluxional methods had led to its isolation from contemporary continental mathematicians. Early in the nineteenth century the evil consequence of this began to be recognized ; and it was felt to be little less than a scandal that the researches of Lagrange, Laplace, and Legendre were unknown to many Cambridge mathematicians save by repute. An attempt to explain the notation and methods of the calculus as used on the Continent was made by R. Woodhouse, who stands out as the apostle of the new movement. It is doubtful if he could have brought analytical methods into vogue by himself; but his views were enthusiastically adopted by three students, Peacock, Babbage, and Herschel, who succeeded in carrying out the re- forms he had suggested. They created an Analytical Society which Babbage explained Avas formed to advocate "the principles of pure d-ism as opposed to the dot-Sige of the University." The character of the instruction in mathematics at the University has at all times largely depended on the text-books then in use, and the importance of good books of this class was emphasized by a traditional rule that questions should not be set on a new subject in the tripos unless it had been discussed in some treatise suitable and available for Cambridge students *!■. Hence the importance attached to the publication of the work on analytical trigonometry by Woodhouse in 1809, and of the works on the differential calculus issued by members of the Analytical Society in 1816 and 1820.
In 1817 Peacock, who was moderator, introduced the symbols
for differentiation into the papers set in the Senate- House
* For a contemporary account of this see C. A. Bristed, Five Years in an English Univenity, New York, 1852, pp. 233—239.
t See ex, gr. the Grace of November 14, 1827, referred to below.
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Examination. But his colleague continued to use the fluxional notation. Peacock himself wrote on March 17 of 1817 {i.e. shortly after the examination) on the subject as follows*:
I assure you... that I shall never cease to exert myself to the utmost in the cause of reform, and that I will never decline any office which may increase my power to effect it. I am nearly certain of being nominated to the office of Moderator in the year 1818-19, and as I am an examiner in virtue of my office, for the next year I shall pursue a course even more decided than hitherto, since I shall feel that men have been prepared for the change, and will then be enabled to have acquired a better system by the publication of improved elementary books. I have considerable influence as a lecturer, and I will not neglect it. It is by silent perseverance only that we can hope to reduce the many-headed monster of prejudice, and make the University answer her char- acter as the loving mother of good learning and science.
In 1818 all candidates for honours, that is, all men in the first six preliminary classes, were allowed to attempt the problems : this change was made by the moderators.
In 1819 Peacock, who was again moderator, induced his colleague to adopt the new notation. It was employed in the next year by Whewell, and in the following year by Peacock again. Henceforth the calculus in its modern language and analytical methods were freely used, new subjects were in- troduced, and for many years the examination provided a mathematical training fairly abreast of the times.
By this time the disputations had ceased to have any im- mediate effect on a man's place in the tripos. Thus Whewell *[*? writing about his duties as moderator in 1820, said :
You would get very exaggerated ideas of the importance attached to it [an Act] if you were to trust Cumberland ; I believe it was formerly more thought of than it is now. It does not, at least immediately, produce any effect on a man's place in the tripos, and is therefore considerably less attended to than used to be the case, and in most years is not very interesting after the five or six best men : so that I look for a considerable exercise of, or rather demand for, patience on my part. The other part of my duty in the Senate House consists in manufacturing wranglers, senior optimes, etc. and is, while it lasts, very laborious.
Of the examination itself in this year he wrote as follows J :
* Proceedings of the Royal Society, London, 1859, vol. ix, pp. 538—539. t WhewelVs Writings and Correspondence, ed. Todhunter, London, 1876,
vol. II, p. 36.
J S. Douglas, Life of Whewell, London, 1881, p. 56.
CH. Xl] THE MATHEMATICAL TRIPOS 27S
The examination in the Senate House begins to-morrow, and is rather close work while it lasts. We are employed from seven in the morning till five in the evening in giving out questions and receiving written answers to them; and when that is over, we have to read over all the papers which we have received in the course of the day, to determine who have done best, which is a business that in numerous years has often kept the examiners up the half of 3very night ; but this year is not particularly numerous. In addition to all this, the examination is conducted in a building which happens to be a very beautiful one, with a marble floor and a highly ornamented ceiling; and as it is on the model of a Grecian temple, and as temples had no chimneys, and as a stove or a fire of any kind might disfigure the building, we are obliged to take the weather as it happens to be, and when it is cold we have the full benefit of it — which is likely to be the case this year. However, it is only a few days, and we have done with it.
A sketch of the examination in the previous year from the point of view of an examinee was given by J. M. F. Wright*, but there is nothing of special interest in it.
Sir George B. Airyf gave the following sketch of his recol- lections of the reading and studies of undergj-aduates of his time and of the tripos of 1823, in which he had been senior wrangler :
At length arrived the Monday morning on which the examination for the B.A. degree was to begin.... "We were all marched in a body to the Senate-House and placed in the hands of the Moderators. How the "candidates for honours" were separated from the ol iroWoi I do not know, I presume that the Acts and the Opponencies had something to do with it. The honour candidates were divided into six groups: and of these Nos. 1 and 2 (united), Nos. 3 and 4 (united), and Nos. 5 and 6 (united), received the questions of one Moderator. No. 1, Nos. 2 and 3 (united), Nos. 4 and 5 (united), and No. 6, received those of the other Moderator. The Moderators were reversed on alternate days. There were no printed question-papers : each examiner had his bound manuscript of questions, and he read out his first question ; each of the examinees who thought himself able proceeded to write out his answer, and then orally called out "Done." The Moderator, as soon as he thought proper, proceeded with another question. I think there was only one course of questions on each day (terminating before 3 o'clock, for the Hall dinner). The examination continued to Friday mid-day. On Saturday morning, about 8 o'clock, the list of honours (manuscript) was nailed on the door of the Senate-House.
It must be remembered that for students pursuing the normal course the Senate-House Examination still provided the only avenue to a degree. That examination involved a
* Alma Mater, London, 1827, vol. ii, pp. 58—98.
t See Nature, vol. xxxv, Feb. 24, 1887, pp. 397—399. See also his Auto- biography, Cambridge, 1896, chapter ii.
B. R. IS
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loiowledge of the elements of moral philosophy and theology, an acquaintance with the rules of formal logic, and the power of reading and writing scholastic Latin, but mathematics was the predominant subject, and this led to a certain one-sidedness in education. The evil of this was generally recognized, and in 1822 various reforms were introduced in the University curriculum ; in particular the Previous Examination was estab- lished for students in their second year, the subjects being prescribed Greek and Latin works, a Gospel, and Paley's Evidences. Set classical books were introduced in the final examination of poll-men ; and another honour or tripos examin- ation was established for classical students. These alterations came into effect in 1824; and henceforth the Senate-House Examination, so far as it related to mathematical students, was known as the Mathematical Tripos.
In 1827 the scheme of examination in the Mathematical Tripos was revised. By regulations* which came into opera- tion in January, 1828, another day was added, so that the examination extended over four days, exclusive of the day of arranging the brackets ; the number of hours of examination was twenty-three, of which seven were assigned to problems. On the first two days all the candidates had the same questions proposed to them, inclusive of the evening problems, and the examination on those days excluded the higher and more difficult parts of mathematics, in order, in the words of the report, " 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, only such questions as could be solved without the aid of the differential calculus were set on the first day, and those set on the second day involved only its elementary applications. The classes were reduced to four, determined as before by the exercises in the schools. The regulations of 1827 definitely prescribed that all the papers should be printed. They are also noticeable as being the last which gave the examiners power to ask viva voce questions, though such questions were
* See Grace, November 14, 1827.
CH. Xl] THE MATHEMATICAL TRIPOS '^ 275
restricted to " propositions contained in the mathematical works commonly in use at the University, or examples and explanations of such propositions." It was further recommended that no paper should contain more questions than well-prepared students could be expected to answer within the time allowed for it, but that if any candidate, before the end of the time, had answered all the questions in the paper, the examiners might propose additional questions viva voce. The power of granting honorary optime degrees now ceased ; it had already fallen into abeyance. Henceforth the examination was conducted under definite rules, and I no longer concern myself with the traditions of the examination.
In the same year as these changes became effective the examination for the poll degree was separated from the tripos with different sets of papers and a different schedule of subjects*. It was, however, still nominally considered as forming part of the Senate-House Examination, and until 1858 those who obtained a poll degree were arranged in four classes, described as fourth, fifth, sixth, and seventh, as if in continuation of the junior op times or third class of the tripos. The year 1828 therefore shows us the Senate-House Examination dividing into two distinct parts ; one known as the Mathematical Tripos, the other as the poll examination. Historically, the examination known as "the General" represents the old Senate-House Examination for the poll-men, but gradually it has been moved to an earlier period in the normal course taken by the men. In 1851 admission to the Classical Tripos f was allowed to others than those who passed the Mathematical Tripos, and thus provided a separate avenue to a degree. In 1852 another set of examinations, at first called " the Professor's Examinations," and now somewhat modified and known as " the Specials," was instituted for all poll-men to take before they could qualify for a degree. In 1858 the fiction that the poll examinations were part of the Senate- House Examination was abandoned, and subsequently they have been treated as providing an independent
• See Grace, May 21, 1828, confirming a Eeport of Maixb 27, 1828. t See Grace of October 31, 1849.
18—2
276 THE MATHEMATICAL TRIPOS [CH. XI
method of obtaining the degree : thus now the Mathematical Tripos is the sole representative of the old Senate-House Examination. Since 1858 numerous other ways of obtaining the degree have been established, and it is now possible to get it by showing proficiency in very special, or even technical subjects.
Further changes in the Mathematical Tripos were introduced in 1833*. The duration of the examination, before the issue of the brackets, was extended to five days, and the number of hours of examination on each day was fixed at five and a half. Seven and a half hours were assigned to problems. The ex- amination on the first day was confined to subjects that did not require the differential calculus, and only the simplest applications of the calculus were permitted on the second and third days. During the first four days of the examination the same papers were set to all the candidates alike, but on the fifth day the examination was conducted according to classes. No reference was made to viva voce questions, and the preliminary classification of the brackets only survived in a permission to re-examine candidates if it were found necessary. This per- missive rule remained in force till 1848, but I believe that in fact it was never used. In December, 1834, a few unimportant details were amended.
Mr Earnshaw, the senior moderator in 1836, informed me that he believed that the tripos of that year was the earliest one in which all the papers were marked, and that in previous years the examiners had partly relied on their impression of the answers given.
New regulations came into force f in 1839. The examina- tion now lasted for six days, and continued as before for five hours and a half each day. Eight and a half hours were assigned to problems. Throughout the whole examination the same papers were set to all candidates, and no reference was made to any preliminary classes. It was no doubt in accordance with the spirit of these changes that the acts in the schools should
* See Grace of April 6, 1832. + See Grace of May 30, 1838.
CH. Xl] THE MATHEMATICAL TRIPOS 277
be abolished, but they were discontinned by the moderators of 1839 without the authority of the Senate. The examination was for the future confined* to mathematics.
In the same year in which the new scheme came into force a proposal to again reopen the subject was rejected (March 6).
The difficulty of bringing professorial lectures into relation with the needs of students has more than once been before the University. The desirability of it was emphasized by a Syndicate in February, 1843, which recommended conferences at stated intervals between the mathematical professors and examiners. This report foreshadowed the creation of a Mathematical Board, but it was rejected by the Senate on March 31.
A few years later the scheme of the examination was again reconstructed by regulations f which came into effect in 1848. The duration of the examination was extended to eight days. The examination lasted in all forty-four and a half hours, twelve of which were devoted to problems. The first three days were assigned to specified elementary subjects; in the papers set on these days riders were to be set as well as book- work, but the methods of analytical geometry and the calculus were excluded. After the first three days there was a short interval, at the end of which the examiners issued a list of those who had so acquitted themselves as to deserve mathematical honours. Only those whose names were contained in this list were admitted to the last five days of the examination, which was devoted to the higher parts of mathematics. After the conclusion of the examination the examiners, taking into account the whole eight days, brought out the list arranged in order of merit. No provision was made for any rearrangement of this list corresponding to the examination of the brackets. The arrangements of 1848 remained in torce till 1873.
* Under a badly-worded Grace passed on May 11, 1842, on the recommencla- tion of a syndicate on theological studies, candidates for mathematical honours were, after 1840, required to attend the poll examination on Paley's Moral Philosophy, the New Testament and Ecclesiastical History. This had not been the intention of the Senate, and on March 14, 1855, a Grace was passed making this clear.
t See Grace of May 13, 1846, confirming a report of March 23, 1846.
278 THE MATHEMATICAL TRIPOS [CH. XI
In the same year as these regulations came into force, a Board of Mathematical Studies (consisting of the mathematical professors, and the moderators and examiners for the current year and the two preceding years) was constituted* by the Senate. From that time forward their minutes supply a per- manent record of the changes gradually introduced into the tripos. I do not allude to subsequent changes which only concern unimportant details of the examination.
In May, 1849, the Board issued a report in which, after giving a review of the past and existing state of the mathe- matical studies in the University, they recommended that the mathematical theories of electricity, magnetism, and heat should not be admitted as subjects of examination. In the following year they issued a second report, in which they recommended the omission of elliptical integrals, Laplace's coefficients, capillary attraction, and the figure of the earth considered as hetero- geneous, as well as a definite limitation of the questions in lunar and planetary theory. In making these recommendations the Board were only giving expression to what had become the practice in the examination.
I may, in passing, mention a curious attempt which w^as made in 1853 and 1854 to assist candidates in judging of the relative difficulty of the questions asked. This was effected by giving to the candidates, at the same time as the examination paper, a slip of paper on which the marks assigned for the book-work and rider for each question were printed. I mention the fact merely because these things are rapidly forgotten and not because it is of any intrinsic value. I possess a complete set of slips which came to me fi'om Dr Todhunter.
In 1856 there was an amusing difference of opinion between the Vice-Chancellor and the moderators. The Vice-Chancellor issued a notice to say that for the convenience of the University he had directed the tripos lists to be published at 8.0 a.m. as well as at 9.0 a.m., but when the University arrived at 8.0 the moderators said that they should not read the list until 9.0.
Considerable changes in the scheme of examination were
* See Grace of October 31, 1818,
CH. Xl] THE MATHExMATICAL TKIPOS 279
introduced in 1873. On December 5, 1865, the Board had recommended the addition of Laplace's coefficients and the figure of the earth considered as heterogeneous as subjects of the examination; the report does not seem to have been brought before the Senate, but attention was called to the fact that certain departments of mathematics and mathematical physics found no place in the tripos schedules, and were neglected by most students. Accordingly, a syndicate was appointed on June 6, 1867, to consider the matter, and a scheme drawn up by them was approved in 1868* and came into effect in 1873. The new scheme of examination was framed on the same lines as that of 1848. The subjects in the first three days were left unchanged, but an extra day was added, devoted to the elements of mathematical physics. The essence of the modification was the greatly extended range of subjects intro- duced into the schedule of subjects for the last five days, and their arrangement in divisions, the marks awarded to the five divisions being approximately those awarded to the three days in proportion to 2, 1, 1, 1, 2/3 to 1 respectively. Under the new regulations the number of examiners was increased from four to five.
The assignment of marks to groups of subjects was made under the impression that the best candidates would concentrate their abilities on a selection of subjects from the various divi- sions. But it was found that, unless the questions were made extremely difficult, more marks could be obtained by reading superficially all the subjects in the five divisions than by attaining real proficiency in a few of the higher ones : while the wide range of subjects rendered it practically impossible to thoroughly cover all the ground in the time allowed. The failure was so pronounced that in 1877 another syndicate was appointed to consider the mathematical studies and examina- tions of the University. They presented an elaborate scheme, but on May 13, 1878, some of the most important parts of it wtre rejected and their subsequent proposals, accepted on
* See Grace of June 2, 1868. It was carried by a majority of only five in a house of 75.
280 THE MATHEMATICAL TRIPOS [CH. XI
November 21, 1878 (by 62 to 49), represented a compromise which pleased few members of the Senate*.
Under the new scheme which came into force in 1882 the tripos was divided into two portions : the first portion wns taken at the end of the third year of residence, the range of subjects being practically the same as in the regulations of 1848, and the result brought out in the customary order of merit. The second portion was held in the following January, and was open only to those who had been wranglers in the preceding June. This portion was confined to higher mathematics and appealed chiefly to specialists. The result was brought out in three classes, each arranged in alphabetical order. The moderators and examiners conducted the whole examination without any extraneous aid.
In the next year or two further amendments were madef, moving the second part to the June of the fourth year, throwing it open to all men who had graduated in the tripos of the previous June, and transferring the conduct of the examination in Part II to four examiners nominated by the Board : this put it largely under the control of the professors. The range of subjects of Part II was also greatly extended, and candidates were encouraged to select only a few of them. It was further arranged that Part I might be taken at the end of a man's second year of residence, though in that case it would not qualify for a degree. A student who availed himself of this leave could take Part II at the end either of his third or of his fourth year as he pleased.
The general effect of these changes was to destroy the homogeneity of the tripos. Objections to the new scheme were soon raised. Especially, it was said — whether rightly or wrongly — that Part I contained too many technical subjects to serve as a general educational training for any save mathe- maticians ; that the distinction of a high place in the historic list produced on its results tended to prevent the best men
* See Graces of May 17, 1877; May 29, 1878; and November 21, 1878: and the Camhridge University Reporter, April 2, May 14, June 4, October 29, November 12, and November 26, 1878.
t See Graces of December 13, 188o; June 12, 1884; February 10, 1885; October 29, 1885 ; and June 1, 1886,
CH. Xl] THE MATHEMATICAL TRIPOS 281
taking it in their second year, though by this time they had read sufficiently to be able to do so ; and that Part II was so constructed as to appeal only to professional mathematicians, and that thus the higher branches of mathematics were neg- lected by all save a few specialists.
Whatever value be attached to these opinions, the number of students studying mathematics fell rapidly under the scheme of 1886. In 1899 the Board proposed* further changes. These seemed to some members of the Senate to be likely to still further decrease the number of men who took up the subject as one of general education. At any rate the two main proposals were re- jected, February 15, 1900, by votes of 151 to 130 and 161 to 129.
A few years later f the Board brought forv\^ard another scheme, proposing changes so sweeping as almost to destroy the identity of the Tripos. Under this the examination in