The names of the twelve [junior optimes], who, in the course of the

examination, 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[45]. 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[46]. Although the examination did not occupy more than

three days it must have been a severe 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 frozen in the pots on their desks.

The University was not altogether satisfied[47] with the regulations,

and in 1779[48] 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's _Essay_. It was further announced[49] that a

candidate would not receive credit for advanced subjects unless he had

satisfied the examiners in Euclid's _Elements_ 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-examined with the view of being moved from one bracket to another

is uncertain, but later this also was allowed.

The number of examiners was also 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

examination 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 master of arts 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 a regular custom

for the moderators to invite particular residents 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[50] 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 candidates. 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 _1/D²_ 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 _1/D³_, secondly in a greater

ratio than _1/D²_ but less than _1/D³_, and thirdly in a less ratio

than _1/D²_, 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?

6. In the cubic equation _x³ + qx + r = 0_ which wants the second

term; supposing _x = a + b_ and _3ab = -q_, to determine the value

of _x_. (_sic._)

7. To find the fluxion of _x^r × (y^n + z^m)^{1/q}_.

8. To find the fluent of _aẋ / (a + x)_.

9. To find the fluxion of the _m_^th 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 versatus_, and the

third place to that one who _in scholis sophistarum melius

disputavit_.

At this time there were various 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 playing with a teetotum[51] on the Wednesday (when specified

works by Locke and Paley formed the subjects of examination), and says

this game "was carried on with great spirit ... by considerable

numbers during the whole of the examination."

About this period, 1790, the custom of printing the problem papers was

introduced, but until 1828 the other papers continued to be dictated.

Since then all the papers have been printed.

I insert here the following letter[52] from William Gooch, of Caius,

in which he described 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_ ¼ 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 Rooms this Evening from 7 till 9, I don't know yet;--but

I did above three times as much as the Sen^r 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 must (of course) be very great, I never suspected that his

Partially (_sic_) w^d 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^th or 9^th & Lucas is either 10^th or 11^th.--Poor Quiz Carver is

one of the οἱ πολλοί;--I'm perfectly _satisfied_ that the Senior

Wranglership is Peacock's due, but _certainly_ not so very

undisputably 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

behaviour to me to any one.

Such was the form ultimately taken by the senate-house examination, a

form which it retained substantially 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 senate to

refuse to pass a supplicat for a bachelor's degree in arts 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[53].

Henceforth the examination was compulsory on all candidates pursuing

the normal course for the B.A. degree. In 1791 the University laid

down rules[54] for its conduct, so far 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

_primâ facie_ poll-men.

In 1799 the moderators announced[55] that for the future they would

require every candidate to show a competent knowledge of the first

book of Euclid's _Elements_, arithmetic, vulgar and decimal fractions,

simple and quadratic equations, and selected books by Locke and Paley.

Paley's works seem to be held in esteem by modern divines, and his

_Evidences_, though not his _Philosophy_, still remains (1917) one of

the subjects of the Previous Examination, but his contemporaries

thought less highly of his writings, or at any rate of his philosophy.

Thus Best is quoted by Wordsworth[56] 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 autobiography[57], 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,

but many of the so-called problems were really pieces of bookwork or

easy riders. No problems were ever set to the men in the seventh and

eighth preliminary classes, which contained the poll-men.

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. None of the bookwork papers of this time are now extant,

but it is believed that they contained few, if any, riders. In looking

at these papers to form an opinion of the knowledge current at the

time it is necessary to bear in mind that the text-books then in

circulation were far from satisfactory.

The _Calendar_ of 1802 contains a diffuse account of the examination.

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,

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 οἱ πολλοί.

The young men hear the propositions or questions delivered by the

examiners; 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 o'clock in the morning. At nine 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 dismissed for the day at nine, after eight hours of

examination. 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 was 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

or better than 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 was considered rather ridiculous.

Revised lists were published at eleven, three, and five, 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 in a few hours, but sometimes not

before two or three 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 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[58]

which is sufficiently interesting to bear reproduction:

I shall 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 _Jesuit's_ Newton and

Vince's _Fluxions_; these were all the _books_, but there were

certain MSS. floating about which I copied--which belonged 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 _fluxional_ 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; my _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, Wollaston's chemical, and Farish'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 anyone 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 anyone 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 Walter. You

may judge what my 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 college reputation. It was

said I was more than half of the examination before anyone else. The

two moderators were Hornbuckle, 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, dated 7 August 1869, of Sir Frederick Pollock to these

questions was as follows:

You have put together as _revivers_ five very different men.

Woodhouse 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 everything about it. I have never forsaken my

favourite pursuit; I delighted 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 accuracy, 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[59]. A fifth day was added to the examination. 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 bookwork and seven to problems. The problem papers were

set from six to ten in the evening.

A letter from Whewell, dated 19 January 1816, thus describes his

examination in the senate-house[60]:

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 examination 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 who is at

the head of the list is of Caius 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[61].

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 Woodhouse, later professor in the University,

who stands out as the apostle of the new movement.

It is doubtful if Woodhouse 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 reforms he had suggested. They created an Analytical Society

which Babbage explained was formed to advocate "the principles of pure

_d_-ism as opposed to the _dot_-age of the University." The character

of the instruction in mathematics at the University has at all times

largely depended on the text-books 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[62]. 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 examination;

his colleague, however, continued to use the fluxional notation.

Peacock himself wrote on 17 March 1817 (_i.e._ shortly after the

examination) on the subject as follows[63]:

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 character 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 introduced, 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 immediate effect

on a man's place in the tripos. Thus Whewell[64], 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[65]:

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 every 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[66], but there is

nothing of special interest in it.

Sir George B. Airy[67] gave the following sketch of his recollections

of the reading and studies of undergraduates 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 οἱ πολλοί 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 knowledge 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 established 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 examination 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[68] which came into operation in January 1828,

four days, exclusive of the day of arranging the brackets, were

devoted to the examination; 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 _vivâ voce_ questions, though such

questions "were restricted to asking about 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 _vivâ 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 its traditions.

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[69]. 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 optimes or third class of

the tripos.

In the course henceforth ordained for the poll or ordinary degree, the

examination, later known as "the General," represents that part of the

old senate-house examination which was intended for the poll-men, but

gradually it was moved to an earlier period in the normal course taken

by the men. In 1851 admission to the classical tripos[70] was allowed

to others than those who passed the mathematical tripos, and this

provided another avenue to a degree entirely independent of the old

senate-house examination. 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 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 a degree in arts have been established, and it is now

possible to graduate by showing proficiency in very special, or even

technical subjects.

Further changes in the mathematical tripos were introduced in

1833[71]. 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 examination 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 _vivâ voce_ questions, though permission was

reserved to re-examine candidates if it were found necessary: this

right remained in force till 1848, but in fact 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[72] in 1839. The examination 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 be abolished, but they were discontinued by the

moderators of 1839 without the authority of the senate. The

examination was for the future confined[73] to mathematics.

In the same year in which the new scheme came into force a proposal to

reopen the subject was rejected on 6 March 1839.

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, which

foreshadowed the creation of a Mathematical Board, was rejected by the

senate on 31 March.

A few years later the scheme of the examination was again

reconstructed by regulations[74] 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 bookwork, 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

force till 1873.

In the same year as these regulations came into force, a Board of

Mathematical Studies (consisting of the mathematical professors,

with the moderators and examiners for the current year and the two

preceding years) was constituted[75] by the senate. From that time

forward their minutes supply a permanent 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 mathematical 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 elliptic integrals, Laplace's

coefficients, capillary attraction, and the figure of the earth

considered as heterogeneous, as well as a definite limitation of

the questions in the lunar and planetary theories. In making these

recommendations the board were only recognizing what had become the

practice in the examination.

I may, in passing, mention a curious attempt which was made in 1853

and 1854 to assist candidates to estimate 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 bookwork 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 from 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 members of the senate arrived at 8.0 the moderators

said that the list should not be read until 9.0.

Considerable changes in the scheme of examination were introduced in

1873. On 5 December 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 6 June 1867,

to consider the matter, and a scheme drawn up by them was approved in

1868[76] 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 introduced into the schedule of subjects for the last five

days, and their arrangement in divisions; the total marks awarded to

the questions in each of the five divisions being approximately in a

proportion to the total marks assigned to the questions in the first

three days as 2, 1, 1, 1, 2/3 to 1 respectively. Under these

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 divisions. 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 cover all the ground thoroughly in the time allowed.

The failure was so pronounced that in 1877 another syndicate was

appointed to consider the mathematical studies and examinations of the

University. They presented an elaborate scheme, but on 13 May 1878,

some of the most important parts of it were rejected; their subsequent

proposals, accepted on 21 November 1878 (by 62 to 49), represented a

compromise which pleased few members of the senate[77].

Under the new scheme which came into force in 1882 the tripos was

divided into two portions: the first portion was 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 made[78], the second

part of the examination being moved to the June of the fourth year,

and thrown open to all men who had graduated in the tripos of the

previous June. At the same time the conduct of the examination in

part II was transferred 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 mathematicians; that the distinction of a high place in the

historic list produced on its results tended to prevent the best men

taking it in their second year, though by this time they had read

enough to be able to do so; and that part II was so constructed as to

appeal only to professional mathematicians, and thus the higher

branches of mathematics were neglected in the University 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[79] further changes. These seemed to some members

of the senate to be likely still further to decrease the number of men

who took up the subject as one of general education; and the two main

proposals were rejected, 15 February 1900 by votes of 151 to 130 and

161 to 129.

A few years later, in 1907[80], the board brought forward another

scheme, proposing changes so sweeping as almost to destroy the

identity of the tripos. Under this the examination in part II was

abolished--a change on which all parties were agreed. There was

introduced an examination, called part I, confined to elementary

mathematics, which could be taken as early as the second term of

residence, and for which in certain cases of failure a student could

present himself again, but this, although an examination for honours,

did not qualify for a degree. In the new part II, taken normally at

the end of the third year of residence and qualifying for a degree,

candidates were given some option in the subjects of their

examination, and order of merit was abolished. The first examination

under this scheme was held in 1908.

A remarkable feature in the history of the Cambridge mathematical

school is the fact that for nearly two hundred years most students

were accustomed to rely for preparation for it on work done with a

private tutor or "Coach." Towards the close of the seventeenth century

we first read of these "pupil-mongers" (among whom Laughton of Clare

was the most famous) who made it their business to prepare men for

their "acts."

With the rise of the senate-house examination the importance of this

class of teachers increased, for success in that examination was

regarded as the crown of the academic course, and brought with it, in

the shape of a fellowship, an immediate competence with a reasonable

prospect of an assured career. It was the business of private tutors

to prepare their pupils for the examination, and among those who in

this way came to the front shortly after the middle of the eighteenth

century were Richard Watson, John Wilson whose name is still known by

its association with a proposition in the theory of numbers, and

Robert Thorp. The last named teacher was described, about 1761, as

being "of eminent use to young men in preparing them for the

Senate-House Examinations and peculiarly successful"; and it was added

that "one young man of no shining reputation with the assistance of

Mr Thorp's tuition had stood at the head of wranglers."

In a grace of the senate, passed in 1781, it is stated that almost all

sophs then resorted to private tuition, and for more than a century

subsequently, the practice was well established. These were the men

who really directed the reading of the students. Even non-residents,

if reputed to be successful coaches, drew pupils. Thus John Dawson, a

medical practitioner at Sedbergh, regularly prepared pupils in the

vacations for the senate-house examination, and at least eleven of the

senior wranglers between 1781 and 1800 are known to have studied under

him.

During the nineteenth century the system developed under two

remarkable teachers, William Hopkins, 1793-1866, and Edward John

Routh, 1831-1907, to whom the vast majority of the better known

Cambridge mathematicians of this century owed most of what they learnt

in their undergraduate days. Hopkins in the twenty-two years from

1828-49, had among his pupils one hundred and seventy-five wranglers,

of whom seventeen were senior, forty-four in one of the first three

places, and one hundred and eight in one of the first ten places.

So too Routh, in the thirty-one years from 1858-88, had between six

hundred and seven hundred pupils, most of whom became wranglers,

twenty-seven being senior in the tripos and forty-one Smith's

prizemen. To organize teaching on this scale demanded rare gifts.

Perhaps it may be of interest to describe, by way of example, the

general features of Routh's system. He gave catechetical lectures

three times a week to classes of eight or ten men of approximately

equal knowledge and ability. The work to be done between two lectures

was heavy, and included the solution of some eight or nine fairly hard

examples on the subject of the lectures. Examination papers were also

constantly set on tripos lines (bookwork and riders), while there was

a weekly paper of problems set to all pupils alike. All papers sent up

were marked in public, the comments on them in class were generally

brief, and, to save time, solutions of the questions were circulated

in manuscript. Teaching also was supplemented by manuscripts on the

subjects. Finally to the more able students he was accustomed, shortly

before their tripos, to give memoirs or books for analyses and

commentaries. The course for the first three years and the two earlier

long vacations covered all the subjects of the examination--the last

long vacation and the first term of the fourth year were devoted to a

thorough revision.

Under Hopkins and Routh there was no trace of what is called cramming;

they might say that a particular demonstration was so long that it

could not be required in the tripos, but none the less they expected

their pupils to master it. The system had faults, but it had the merit

of providing a systematic grounding in a wide field of subjects. The

effectiveness of teaching of this kind was dependent on intimate

constant personal intercourse, and the importance of this cannot be

overrated. The scandal of the system consisted in the fact that a man

was compelled to pay heavy fees to the University and his College for

instruction, and yet found it advantageous at his own expense to go

elsewhere to get it.

During the last quarter of the nineteenth century college lecturers

began to share with the coaches the general direction of studies.

Post-graduate work was also to some extent brought under the influence

of professors and university lecturers--these not uncommonly

suggesting subjects for dissertations for fellowships, Smith's prizes,

etc. But the students thus influenced were not numerous, and it still

remains true that the majority of mathematical undergraduates are so

out of touch with the professors in the subject as to be unacquainted

even with their personal appearance.

Such was the mathematical tripos and its history. Whatever its

demerits, it dominated the situation, and Cambridge mathematics and

mathematicians of the nineteenth century were the direct product of

the system it embodied. Judged by the output, I do not think it can

be said to have resulted in failure; and perhaps Cayley, Sylvester,

Adams, Green, Stokes, Kelvin, and Maxwell--to mention no others--were

none the worse for having been compelled to go through the course.

The reconstitution in 1907 of the tripos, and the destruction of many

of its distinctive features must profoundly modify the future history

of mathematics at Cambridge, but forecasts on such a theme would be

useless.

The curious origin of the term tripos has been repeatedly told, and an

account of it may fitly close this chapter. Formerly there were three

principal occasions on which questionists were admitted to the title

or degree of bachelor. The first of these was at the comitia priora,

held on Ash-Wednesday, for the best men in the year. The next was at

the comitia posteriora, which was held a few weeks later, and at which

any student who had distinguished himself in the quadragesimal

exercises subsequent to Ash-Wednesday had his seniority reserved to

him. Lastly, there was the comitia minora, for students who had in no

special way distinguished themselves.

In the fifteenth century an important part in the ceremony on each of

these occasions was taken by a certain "ould bachilour," who sat upon

a three-legged stool or tripos before the proctors and tested the

abilities of the would-be graduates by arguing some question with the

"eldest son," who was selected from them as their representative. To

assist the latter in what might be an unequal contest his "father,"

that is, the officer of his college who was to present him for his

degree, was allowed to come to his assistance.

The discussion took place in Great St Mary's Church, and marked the

admission of the student to a position with new responsibilities,

while the season of Lent was chosen with a view to bring this into

prominence. The puritan party objected to the semi-ecclesiastical

character of the proceedings, and in the course of the sixteenth

century set themselves to bring the ceremony into disrepute. The part

played by the questionist now became purely formal, though a serious

debate still sometimes took place between the father of the senior

questionist and a regent master who represented the University: this,

however, came to be prefaced by a speech by the bachelor, who was now

called Mr Tripos, just as we speak of a judge as the bench, or of a

rower as an oar. Ultimately public opinion permitted Mr Tripos to say

pretty much what he pleased, so long as it was not dull and was

scandalous. The speeches he delivered or the verses he recited were

generally printed and preserved by the registrary, and were known as

the tripos verses: originally they referred to the subjects of the

disputations then propounded. The earliest copies now extant are those

for 1575.

The university officials, to whom the personal criticisms in which

Mr Tripos indulged were by no means pleasing, repeatedly exhorted him

to remember "while exercising his privilege of humour, to be modest

withal." In 1710, says Mullinger[81], "the authorities after

condemning the excessive license of the tripos announced that the

comitia at Lent would in future be conducted in the Senate-House; and

all members of the University, of whatever order or degree, were

forbidden to assail or mock the disputants with scurrilous jokes or

unseemly witticisms. About the year 1747-8, the moderators initiated

the practice of printing the honour lists on the back of the sheets

containing the tripos verses, and after the year 1755 this became the

invariable practice. By virtue of this purely arbitrary connection

these lists themselves became known as the tripos; and eventually the

examination itself, of which they represented the results, also became

known by the same designation."

Mr Tripos ceased to deliver his speech about 1750, but the issue of

tripos verses continued for nearly 150 years longer. During the latter

part of this time they consisted of four sets of verses, usually in

Latin, but occasionally in Greek, in which current topics in the

University were treated lightly or seriously as the writer thought

fit. They were written for the proctors and moderators by

undergraduates or commencing bachelors, each of whom was supposed to

receive a pair of white kid gloves in recognition of his labours. Thus

gradually the word tripos changed its meaning "from a thing of wood to

a man, from a man to a speech, from a speech to sets of verses, from

verses to a sheet of coarse foolscap paper, from a paper to a list of

names, and from a list of names to a system of examination[82]."

In 1895 the proctors and moderators, without consulting the senate,

sent in no verses, and thus, in spite of widespread regret, an

interesting custom of many centuries standing was destroyed. In

defence of this action, it was said that the custom had never been

embodied in statute or ordinance, and thus was not obligatory, and

further that its continuance was not of material benefit to anybody.

Such arguments are not conclusive, and we may well regret the

disappearance of historic ties unless it can be shown that they cause

inconvenience, which of course in this case could not be asserted.

By way of supplement to the foregoing account, I append a list of

those who have held or hold the various university mathematical chairs

and lectureships.

The _Lucasian Professorship of Mathematics_ was founded in 1663 by

Henry Lucas. The successive occupants of the chair have been: Isaac

Barrow, 1664-1669; Isaac Newton, 1669-1702; William Whiston,

1702-1711; Nicholas Saunderson (Sanderson), 1711-1739; John Colson,

1739-1760; Edward Waring, 1760-1798; Isaac Milner, 1798-1820; Robert

Woodhouse, 1820-1822; Thomas Turton, 1822-1826; George Biddell Airy,

1826-1828; Charles Babbage, 1828-1839; Joshua King, 1839-1849;

George Gabriel Stokes, 1849-1903; Joseph Larmor, 1903 _et seq._

The _Plumian Professorship of Astronomy and Experimental Philosophy_

was founded in 1704 by Thomas Plume. The successive occupants of the

chair have been: Roger Cotes, 1707-1716; Robert Smith, 1716-1760;

Anthony Shepherd, 1760-1796; Samuel Vince, 1796-1822; Robert

Woodhouse, 1822-1828; George Biddell Airy, 1828-1836; James Challis,

1836-1883; George Howard Darwin, 1883-1912; Arthur Stanley

Eddington, 1913 _et seq._

The _Lowndean Professorship of Astronomy and Geometry_ was founded

in 1749 by Thomas Lowndes. The successive occupants of the chair

have been: Roger Long, 1750-1771; John Smith, 1771-1795; William

Lax, 1795-1836; George Peacock, 1836-1858; John Couch Adams,

1858-1892; Robert Stawell Ball, 1892-1913; Henry Frederick Baker,

1914 _et seq._

The _Sadleirian Professorship of Pure Mathematics_ was founded, in

1863 from a benefaction given in 1710 by Lady Sadleir. The

successive occupants of the chair have been: Arthur Cayley,

1863-1895; Andrew Russell Forsyth, 1895-1910; Ernest William Hobson,

1910 _et seq._

The _Cavendish Professorship of Experimental Physics_ was founded in

1871 by the University; the laboratory attached being built at the

expense of the then Chancellor, the Duke of Devonshire. The

successive occupants of the chair have been: James Clerk Maxwell,

1871-1879; John William, Baron Rayleigh, 1879-1884; Joseph John

Thomson, 1884 _et seq._

The _Professorship of Mechanism and Applied Mechanics_, with

laboratories and shops attached, was founded by the University in

1875. The successive occupants of the chair have been: James Stuart,

1875-1890; James Alfred Ewing, 1890-1903; Bertram Hopkinson, 1903

_et seq._

Five _Lectureships in Mathematics_ were created in 1882 under the

directions of Royal Commissioners, and subsequently two others (now

reduced to one other) tenable, if desired, with one of the above,

were founded. The successive holders have been: Joseph John Thomson,

1884; Andrew Russell Forsyth, 1884-1895; William Herrick Macaulay,

1884-1887; Richard Tetley Glazebrook, 1884-1898; Ernest William

Hobson, 1884-1910; Joseph Larmor, 1885-1903; Richard Pendlebury,

1888-1901; Henry Frederick Baker, 1895-1914; Augustus Edward Hough

Love, 1898-1899; Hector Munro Macdonald, 1899-1904; Herbert William

Richmond, 1901 _et seq._; George Ballard Mathews, 1903-1905; James

Hopwood Jeans, 1904-1906, 1910-1912; John Gaston Leathem, 1905-1909;

Robert Alfred Herman, 1906 _et seq._; Edmund Taylor Whittaker,

1905-1906; Thomas James I'Anson Bromwich, 1909 _et seq._; John

Hilton Grace, 1901 _et seq._; Godfrey Harold Hardy, 1914 _et seq._;

Arthur Berry, 1914 _et seq._

[Footnote 34: The greater part of this chapter formerly appeared in my

_Mathematical Recreations and Essays_, but a few paragraphs on

"coaching" have been taken from a paper which I wrote for distribution

to those who attended the International Congress of Mathematicians

held in England in 1912. The subject is treated in Whewell's _Liberal

Education_, Cambridge, three parts, 1845, 1850, 1853; Wordsworth's

_Scholae Academicae_, Cambridge, 1877; my own _Origin and History of

the Mathematical Tripos_, Cambridge, 1880; Glaisher's Presidential

Address to the London Mathematical Society, _Transactions_,

vol. XVIII, 1886, pp. 4-38; and my _History of the Study of

Mathematics at Cambridge_, Cambridge, 1889.]

[Footnote 35: _Budget of Paradoxes_, by A. De Morgan, London, 1872,

p. 305.]

[Footnote 36: See grace of 25 October 1680.]

[Footnote 37: _Ex. gr._ see De la Pryme's account of his graduation in

1694, _Surtees Society_, vol. LIV, 1870, p. 32.]

[Footnote 38: W. Reneu, in his letters of 1708-10 describing the

course for the B.A. degree, makes no mention of the senate-house

examination, and I think it is a reasonable inference that it had not

then been established.]

[Footnote 39: _Memoirs of Richard Cumberland_, London, 1806,

pp. 78-79.]

[Footnote 40: Quoted by C. Wordsworth, _Scholae Academicae_,

Cambridge, 1877, pp. 30-31.]

[Footnote 41: _Anecdotes of the Life of Richard Watson_, London, 1817,

pp. 18-19.]

[Footnote 42: See grace of 25 October 1883; and the _Cambridge

University Reporter_, 23 October 1883.]

[Footnote 43: See grace of 11 February 1909, and the _Cambridge

University Reporter_, 8 December 1908.]

[Footnote 44: _The Works of J. Jebb_, London, 1787, vol. II,

pp. 290-297.]

[Footnote 45: "Emulation, which is the principle upon which the plan

is constructed." _The Works of J. Jebb_, London, 1787, vol. III,

p. 261.]

[Footnote 46: _The Works of J. Jebb_, London, 1787, vol. III, p. 272.]

[Footnote 47: See graces of 5 July 1773, and of 17 February 1774.]

[Footnote 48: See graces of 19, 20 March 1779.]

[Footnote 49: Notice issued by the vice-chancellor, dated 19 May

1779.]

[Footnote 50: 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 1786.]

[Footnote 51: H. Gunning, _Reminiscences_, second edition, London,

1855, vol. I, p. 82.]

[Footnote 52: C. Wordsworth, _Scholae Academicae_, Cambridge, 1877,

pp. 322-323.]

[Footnote 53: H. Gunning, _Reminiscences_, second edition, London,

1855, vol. I, p. 182.]

[Footnote 54: See grace of 8 April 1791.]

[Footnote 55: Communicated by the moderators to fathers of colleges on

18 January 1799, and agreed to by the latter.]

[Footnote 56: C. Wordsworth, _Scholae Academicae_, Cambridge, 1817,

p. 123.]

[Footnote 57: _Anecdotes of the Life of Richard Watson_, London, 1817,

p. 19.]

[Footnote 58: _Memoir of A. De Morgan_, London, 1882, pp. 387-392.]

[Footnote 59: See graces, 15 December 1808.]

[Footnote 60: S. Douglas, _Life of W. Whewell_, London, 1881, p. 20.]

[Footnote 61: For a contemporary account of this, see C.A. Bristed,

_Five Years in an English University_, New York, 1852, pp. 233-239.]

[Footnote 62: See _ex. gr._ the grace of 14 November 1827, referred to

below.]

[Footnote 63: _Proceedings of the Royal Society_, London, 1859,

vol. IX, pp. 538-539.]

[Footnote 64: _Whewell's Writings and Correspondence_, ed. Todhunter,

London, 1876, vol. II, p. 36.]

[Footnote 65: S. Douglas, _Life of Whewell_, London, 1881, p. 56.]

[Footnote 66: _Alma Mater_, London, 1827, vol. II, pp. 58-98.]

[Footnote 67: See _Nature_, vol. XXXV, 24 February 1887, pp. 397-399.

See also his _Autobiography_, Cambridge, 1896, chapter ii.]

[Footnote 68: See grace, 14 November 1827.]

[Footnote 69: See grace, 21 May 1828, confirming a report of 27 March

1828.]

[Footnote 70: See grace of 31 October 1849.]

[Footnote 71: See grace of 6 April 1832.]

[Footnote 72: See grace of 30 May 1838.]

[Footnote 73: Under a badly-worded grace passed on 11 May 1842, on the

recommendation of a syndicate on theological studies, candidates for

mathematical honours were, after 1846, 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 14 March 1855, a grace was passed making this clear.]

[Footnote 74: See grace of 13 May 1846, confirming a report of

23 March 1846.]

[Footnote 75: See grace of 31 October 1848.]

[Footnote 76: See grace of 2 June 1868. It was carried by a majority

of only five in a house of 75.]

[Footnote 77: See graces of 17 May 1877; 29 May 1878; and 21 November

1878; and the _Cambridge University Reporter_, 2 April, 14 May,

4 June, 29 October, 12 November, and 26 November 1878.]

[Footnote 78: See graces of 13 December 1883; 12 June 1884;

10 February 1885; 29 October 1885; and 1 June 1886.]

[Footnote 79: See reports dated 7 November 1899, and 20 January 1900.]

[Footnote 80: See the reports of the special board, _Cambridge

University Reporter_, 29 May and 20 November 1906, and the graces of

2 February 1907. The voting on the first grace was 776 placet and 644

non-placet.]

[Footnote 81: J.B. Mullinger, _The University of Cambridge_,

Cambridge, vol. I, 1873, pp. 175-176.]

[Footnote 82: C. Wordsworth, _Scholae Academicae_, Cambridge, 1877,

p. 21.]

INDEX

Abbot, Wm, 263.

Acts, Scholastic, ch XV.

Adams, J.C, 311, 315.

Admonitions, Statutory, 221-4.

Airy, G.B, 173, 293, 315.

Alford, Hen, 174.

Allen, Thos, 34.

All Saints' Ch, Camb, 85.

Alston Tankard, The, 123.

Ambler, John, 224.

Amos, Andrew, 130, 140.

Analytical Society, 290.

Anne of Denmark, 117.

Ansill, Thos, 13.

Apprenticeship, 187, 189.

Arrington Vicarage, 11.

Artistic Treasures, ch VI.

Arts, Students in, 187, 188.

Ascham, Roger, 203.

Assessors, Trin. Coll, 127.

Assistant Tutors, 44.

Athletic Club, Trinity, 125, 126.

Athletic Clubs, 174.

Atterbury, Fras, 68.

Attractions, Theory, 229, 234, 235.

Auditors, Trin. Coll, ch VII.

Aykerod Cup, The, 120.

Babbage, Chas, 290, 315.

Babington, Gervase, 57.

Backhouse, Jas, 42.

Bacon, Arth, 165.

Bacon, Fras, 108, 117, 165.

Baker, H.F, 315, 316.

Balfour, A.J, 112.

Ball, R.S, 315.

Balsham, Hugh de, 191.

Bancroft, Rich, 61, 62.

Bankes Ewer, The, 121.

Barnes, E.W, 43.

Barnes, J.W, 81.

Barrington Vicarage, 12.

Barrow, Isaac, 108, 109, 117, 150, 170, 171, 254, 315.

Beaumont, Robt, 92, 93, 94, 106.

Bedesmen, 18.

Bedwell, Thos, 254.

Bellot Tankard, The, 123.

Bennet, Bishop, 57.

Bennet Ewer, The, 121.

Bensley, Jas, 224.

Benson, E.W, 110, 111.

Bentley, Rich, 41, 67, 68, 98, 111, 134, 135, 172, 239.

Benton, Dan, 212.

Berry, Art, 316.

Best, H.D, 279.

Bill, Wm, 49, 88, 91, 92.

Billingsley, Hen, 254.

Birching, 199-208, 210-214.

Blackburn, Jas, 278.

Blakesley, J.W, 81.

Bland, Tobias, 214.

Blundeville, Thos, 254.

Board, Mathematical, 300, 301.

Boat Club, The, 124, 125, 174.

Bolland, Wm, 285.

Bonnycastle's _Algebra_, 281, 284.

Bottisham Vicarage, 11.

Boude, Wm, 15, 16.

Boxworth Rectory, 12.

Boyle Cup, The, 122.

Boys, Wm, 88.

Brackets, System of, 271-272, 282-288, 295, 300.

Brass, John, 255.

Bridges, Simon, 17.

Briggs, Hen, 254.

Briggs, Simon, 17.

Bristed, C.A, 174, 289.

Bromwich, T.J.I'A, 316.

Brooke, Rich, 128, 129, 131, 132.

Brown, John, 81, 286.

Browne, Galen, 223.

Browne, I. Hawkins, 110, 111.

Buckingham Ewer, The, 120.

Buckley, Wm, 254.

Bulaeus, 182.

Burcham, T.B, 81.

Burials in College, 103.

Burnand, F.C, 174.

Burnell, Edw, 128, 129, 130.

Busby Cup, The, 121.

Busby, Rich, 202.

Butler, H.M, 115, 175.

Butler, Miss, 100.

Butler's _Analogy_, 219, 268.

Byron, Lord, 109, 117.

Calculus, The, 289-292.

Cambridge University, Beginnings of, ch XI.

Camden, Marquess of, 112.

Caroline, Queen, 138.

Cartwright, Thos, 93, 165.

Carus, Wm, 73, 74, 79, 81.

Carver, Chas, 277.

Cavendish Cup, The, 123.

Cavendish Professorship, 316.

Cayley, Art, 110, 111, 176, 311, 315.

Cecil, Sir Wm, 51.

Censer Boat, 87, 118.

Central Forces, ch XIII.

Challenge Plate, 124-126.

Challis, Jas, 315.

Challis MSS, 273.

Chantrey, Fras, 116.

Chapel Attendance, ch IV, 102.

Chapel, Compulsory, ch IV, 204, 206, 207.

Chapel, Trinity, ch V.

Charles I, 96, 168.

Charles II, 96, 107, 117.

Charrington, John, 115.

Cheadle Rectory, 12.

Cheke, John, 4, 5, 17, 191.

Chesterton Vicarage, 11.

Christ Church Westminsters, ch III.

Christopherson, John, 88, 91, 92.

Cipriani, G.B, 116.

Clairaut, A.C, 240.

Clarence, Duke of, 174.

Clark, J.W, 130, 143.

Clarke, Sam, 254.

Clarke's _Attributes_, 268.

Clarkson Cup, The, 120.

Classical Tripos, 295, 297.

Clerke, Gilbert, 254.

Coaches, Private, 307-310.

Coke, Edw, 111, 165.

Colleges, Early, 27, 191, 192.

Colson, John, 315.

Combination Rooms, 167.

Commencement-House, 153.

Commons, Out of, 216, 217, 219.

Confessions, 219, 221.

Conybeare, W.J, 76.

Conyers, Tobias, 212.

Corporal Punishments, 199-208, 210-215.

Cotes, Roger, 98, 172, 254, 267, 315.

Cotton, G.E.L, 76.

Cowley, Abraham, 66, 111, 169.

Cox, Rich, 202.

Craig, John, 254.

Cranworth, Lord, 173.

Creighton, Robt, 39.

Croyland Abbey, 91, 181.

Cumberland, Rich, 262.

Dacres, Art, 254.

Damer Cup, The, 123.

Dance, Nath, 112.

Darwin, G.H, 315.

Dawson, John, 308.

Days, Loss of, 217.

Dealtry, Wm, 285, 286, 287.

Deans, College, 28, 206-8, 219-20.

De Aston, John, 155, 156, 160.

De Bagshot, John, 155, 156.

De Balsham, Hugh, 191.

De Berwick, Rich, 155.

De Beverley, Robt, 155, 160.

Declaratio Computi, 128.

De Croyland, Robt, 84, 85.

De Durnford, Nich, 155.

Dee, John, 254.

De Gretford, Hen, 155.

De Gretford, Ralph, 155.

De Hull, John, 155.

De Immeworth, John, 155.

De Kelsey, John, 155.

De Kingston, Edw, 155, 160.

De la Pryme, Abraham, 259.

De London, Phil, 155.

De Morgan, Aug, 256, 284, 286.

Denman, Geo, 130, 141.

De Nottingham, Walter, 155.

Derby, Henry Earl of, 110, 111.

De Rome, Nich, 155.

De Salisbury, John, 155.

De Salisbury, Rich, 155.

Descartes, René, 227, 236, 237.

De Stanton, Hervey, 87.

De Sutton, Hugh, 155.

De Torterold, Jas, 155.

De Torterold, John, 155.

Devereux, Robt, 108, 165.

Devonshire, Duke of, 316.

D'Ewes, Simon, 208.

De Winchester, David, 155, 160.

De Windsor, Thos, 155.

De Woodstock, John, 155.

Dialectici, 16.

Digges, Thos, 254.

Discipline, ch XII, 27, 32, 33.

Discommonsing, 216, 217, 219.

Dissizaring, 216, 217.

Distribucio Collegii, 13-22.

Dobson, Wm, 81.

Donaldson, J.W, 81.

Douglas, Stair, 288, 292.

Downing, Sir Geo, 131.

Draghswerd, Wm, 155.

Dryden, John, 111, 169, 219.

Duport, Jas, 40, 169.

Duport Salt, The, 121, 122.

Early University History, ch XI.

Earnshaw, Sam, 298.

Eddington, A.S, 315.

Edward II, 84, 154.

Edward III, 84, 115, 117, 163.

Edward IV, 110.

Edward VI, 87, 115, 164.

Edward VII, 174.

Elizabeth of York, 106, 115.

Elizabeth, Queen, 48, 49, 90, 91, 92, 114, 115, 117, 144, 164,

167, 168.

Ellethorpe, 213.

Ellis, Wm, 129, 130, 133.

Emerson, Wm, 268.

Euclid's _Elements_, 271, 279, 281.

Euler, Leonhard, 240.

Essex, Earl of, 108, 165.

Everett, Wm, 174.

Ewing, J.A, 316.

Eworth, Hans, 106, 115.

Expulsions, 221-224.

Fairfax, Sir Thos, 97.

Fakenham Rectory, 11.

Farish, Wm, 285.

Fees, College, in 1570, 36-37.

Fellow-Commoners, 29, 34, 119.

Fellows, Election of, 30.

Fellowship Election in 1659, 39.

Felmersham Vicarage, 11.

Fenn, John, 263.

Ferguson, Jas, 267.

Field, Fred, 81.

Fines, 215-216.

Fiott (Lee), John, 285, 287.

Firebrace Cup, The, 122.

First Trinity Boat Club, 124, 125, 174.

Fitzgerald, Edw, 173.

Fitzgerald Tankard, The, 122.

Flamsteed, John, 230, 254.

Fletcher, Bishop, 57.

Fletcher, W.M, 43.

Flogging, 199-208, 210-214.

Fluxions, 289-292.

Foley Tankard, The, 123.

Forsyth, A.R, 315, 316.

Fort, John, 155.

Foster, Michael, 110, 111.

Foster, Sam, 254.

Foundation of Trinity, ch I.

Franciscan Monastery, 19, 184.

Frazer, Sir Jas, 170.

Frere, John, 265.

Fuller, Thos, 93.

Galileo, 231, 232, 239.

Galton, Fras, 110, 111, 174.

Gating, 218-219.

General Examination, 297.

George I, 259.

George III, 107.

Gerrard, Mark, 115.

Glaisher, J.W.L, 252.

Glazebrook, R.T, 316.

Glomerels, 181, 189-191.

Gloucester, Duke of, 107, 112, 115.

Goad, Roger, 204.

Gooch, Wm, 276.

Goodman, Gabriel, 52.

Gordon, Douglas, 107.

Gouldesborough, Edw, 57.

Grace, J.H, 316.

Graham, Robt, 129, 136.

Grammar, Degrees in, 190, 191.

Grammarians, 15, 16, 17, 28, 181, 189-191.

Grammar School at Trinity, 15-17, 28, 30.

Grammatici, 15, 16, 17, 28.

Granby, Marquess of, 112, 113.

Gravitation, Law of, ch XIII.

Gray, 88.

Greaves Cup, The, 123.

Greaves, Wm, 129, 135, 136.

Greek Authors read in 1570, 37.

Green, Geo, 311.

Grendon Vicarage, 11.

Griffith, T, 133.

Griffon, John, 155.

Griffon, Thos, 155.

Grigson, Thos, 215.

Grote, John, 174.

Grundisburgh Rectory, 12.

Guilds, University, 188.

Gulphing, 264.

Gunning, Hen, 275, 278.

Hacket, John, 61.

Halfhead, 223.

Halifax, Earl of, 110.

Hallam, A.H, 173.

Halley, Edmund, 228, 230.

Hamilton, Hugh, 267.

Hardy, G.H, 316.

Hare, J.C, 173.

Harman, Rich, 15.

Harvey, John, 254.

Harwood, Busick, 285.

Heath, J.M, 81.

Helsham, Rich, 267.

Henry I, 180.

Henry II, 180.

Henry VII, 106, 115.

Henry VIII, 3, 48, 106, 162, 167.

Herbert, Geo, 61, 169.

Herkomer, H. von, 109.

Herman, R.A, 316.

Herschel, John, 290.

Herschel, Wm, 240.

Hill, Thos, 254.

Hitch, Robt, 223.

Hobson, E.W, 315, 316.

Hodges, 213.

Hodson, Wm, 273.

Holbein, 106.

Hon. Optimes, 257, 261, 296.

Hood, Thos, 254.

Hooke, Robt, 228.

Hopkins, Wm, 308-310.

Hopkinson, B, 316.

Hornbuckle, T.W, 286, 287, 288.

Horrox, Jeremiah, 254.

Hort, F.J.A, 110, 111, 176.

Hostels, Private, 27, 29, 192, 193, 195, 198, 199.

Houghton, Lord, 173.

Howson, J.S, 76.

Huddling, 255, 258.

Hughes, Fras, 129, 132.

Humphrey Ewer, The, 120.

Husbands Cup, The, 122.

Hustler, J.D, 285.

Hutton, Archbishop, 57.

Huygens, Christian, 238.

Hydrodynamics, Theory of, 230, 235, 236.

Impositions, 219-221.

Ireland, Rich, 59.

Jacob, Edw, 287, 288, 289.

James I, 54, 64, 66, 114, 117, 168.

James II, 171.

Jeans, J.H, 316.

Jebb, John, 263, 267, 270, 271.

Jebb, R.C, 110, 111, 170, 176.

Jephson, Thos, 285.

Joachim, Joseph, 110.

John, King, 180.

Johnson, 212.

Jones, Thos, 110.

Jurin, Jas, 254.

Kant, Immanuel, 242.

Keate, John, 202.

Keill, John, 267.

Kelvin, Lord, 311.

Kempthorne, John, 285.

Kent Ewer, The, 120.

Kepler's Problem, 234.

King, C.W, 75.

King, Joshua, 315.

King, John, 59.

Kinglake, A.W, 173.

King's Hall, 3, 9-11, 20, 84-86, 144, 154-160, 162, 163.

King's Scholars, _see_ King's Hall.

Kneller, Godfrey, 112.

Knight, Sam, 130, 137.

Lagrange, J.L, 239, 240, 290.

Laplace, P.S, 241, 242, 290.

Larmor, Joseph, 315, 316.

Laszlö de Lombros, P.A, 112.

Latin Authors read in 1570, 37.

Laud, Wm, 94.

Laughton, Rich, 254, 307.

Laurence, R.V, 43.

Lawrence, Thos, 112.

Lax, Wm, 276, 315.

Least Resistance, Solid of, 236.

Leathem, J.G, 316.

Lecture-Rooms, College, 44, 45.

Lectures, College, 44-46.

Lectureships, Mathematical, 253, 316.

Lee (Fiott), John, 287.

Leg, Thos, 93.

Legendre, A.M, 290.

Lever, Thos, 24.

Library, Trinity, ch VIII, 104.

Lightfoot, J.B, 101, 110, 111, 115, 170, 176.

L'Isle, Denys, 129, 134, 135.

Locke's _Essay_, 268, 275, 279.

Lombard, Peter, 181.

Long, Roger, 267, 315.

Lonsdale, John, 112.

Loss of Days or Terms, 218.

Love, A.E.H, 316.

Lowndes, Thos, 315.

Lowndean Professorship, 315.

Lucas, Hen, 315.

Lucas, Rich, 277.

Lucasian Professorship, 315.

Lushington, E.L, 174.

Lyndhurst Cup, The, 123.

Lyndhurst, Lord, 173.

Lyons, Israel, 268.

Macaulay, T.B, 117, 173.

Macaulay, W.H, 316.

Macclesfield, Earl of, 111.

Macdonald, H.M, 316.

Maclaurin, Colin, 267, 268.

Man, Henry, 17.

Mansel, W.L, 112, 217.

Martin, Fras, 81.

Martin, Theodore, 123.

Marvell, Andrew, 169.

Mary, Queen, 48, 88, 91, 108, 115, 164, 167.

Mary of Scotland, 115.

Mathematical Board, 300, 301.

Mathematical Tripos, ch XV.

Mathematics, Cambridge, ch XV.

Mathews, G.B, 316.

Maule, W.H, 173.

Maurice, F.D, 110, 111.

Maxwell, J. Clerk, 110, 111, 176, 311, 316.

Maydew, John, 17.

Mechanics, Theory of, 231-232.

Mechanism Professorship, 316.

Medieval Tutorial System, 27.

Medieval University, Beginnings of, ch XI.

Melbourne, Viscount, 110, 111.

Merit, Order of, in Examinations, 261, 307.

Mexborough Cup, The, 123.

Mey, Wm, 5.

Michael-House, 3, 11-13, 20, 86, 87, 162, 163.

Milner, Isaac, 272, 315.

Milnes, Monckton, 173.

Milton, John, 213.

Moderators, Mathematical, 258, 259, 260.

Monasteries at Cambridge, 180, 181, 184, 185.

Monks at University, 181, 185, 186, 187, 196.

Moreton, Albert, 53.

Morland, Sam, 254.

Moro, Antonio, 106, 108.

Motion, Laws of, 232.

Mullinger, J.B, 179, 188, 313.

Munro, H.A.J, 176.

Murray, Thos, 112.

Nebular Hypothesis, 241, 242.

Neile, Rich, 59.

Nevile Cup, The, 119.

Nevile, Robt, 212.

Nevile, Thos, 53, 55, 58, 59, 60, 61, 62, 114, 149, 166, 167, 168.

Nevile's Court, 151, 152.

Newton, Isaac, 108, 112, 116, 170, 244-251, 267, 268, 281, 284,

287, 315.

Newton, John, 134.

Newton, Sam, 129, 132, 133, 134.

Newton's _Principia_, ch XIII.

Non-Regents, 183.

Northampton, Earl of, 62.

Numbers of Students, 41-44, 188.

Offley, Chris, 223.

Opie, John, 112.

Opponencies, 253.

Optimes, ch XV.

Optimes, Honorary, 257, 261, 296.

Ordines Senioritatis, 261.

Orleans, University of, 182.

Orwell Rectory, 12.

Oughtred, Wm, 252.

Paget, Sir Wm, 6.

Paley, Wm, 265, 275, 279, 299.

Parham, Peter, 213.

Paris, University of, 182, 252.

Parke, Jas, 130, 138, 139, 173.

Parker, Matthew, 4, 5, 6, 7.

Parker, Nich, 155.

Parker, Roger, 155.

Parne, Thos, 215.

Parr, Queen Katherine, 6, 7.

Paston, Clement, 201.

Paulet Tankard, The, 123.

Payne, 255.

Peacock, Geo, 55, 81, 173, 179, 180, 182, 189, 276, 277, 290,

291, 315.

Pearson, John, 108, 111, 170.

Peckitt of York, 116.

Peile, John, 213.

Pell, John, 254.

Penalties, ch XII.

Pendlebury, Rich, 316.

Pensioners, 29, 31, 33, 34.

Pepys, Thos, 217.

Perry, Chas, 76, 78, 79, 81, 82.

Perry Plate, The, 124.

Pheasaunt Tankard, The, 123.

Philip of Spain, 108.

Physwick's Hostel, 86, 87.

Plate, College, ch VI.

Plume, Thos, 315.

Plumian Professorship, 315.

Poll-Men, _see_ ch XV.

Pollock, J.F, 173, 284, 287.

Porson, Rich, 114, 172.

Portraits, College, ch VI.

Pour, Nich, 155.

Pour, Rich, 155.

Pour, Wm, 155.

Pre-elections, 59, 60, 62, 64.

Prime and Ultimate Ratios, 232.

_Principia_ of Newton, ch XIII.

Prior, Matthew, 112.

Private Tutors, 307-310.

Professors' Examinations, 297.

Pull, Nich, 155.

Raeburn, Hen, 109.

Raine, Matthew, 110.

Rait, R.S, 200.

Rashdall, Hastings, 179, 199, 220.

Ray, John, 169, 215.

Rayleigh, Lord, 316.

Rayleigh Prizes, 266.

Record, Robt, 254.

Redman, Bishop, 57.

Redman, John, 5, 9, 11, 13, 20, 24, 88, 92.

Regents, 183.

Religious Students, 27.

Remée, 107.

Reneu, Wm, 259.

Resisting Mediums, 235-236.

Respondents, 253.

Reynolds, Joshua, 107, 112.

Rhetoric, Degrees in, 190, 191.

Richard III, 110.

Richard, Duke of York, 110.

Richardson, John, 65, 66.

Richmond, H.W, 316.

Ring, Mrs, 112.

Rod, Punishment by, 199-208, 210-214.

Romney, Geo, 115.

Rooke, Laurence, 254.

Rose, C.L, 76.

Rosekin, Andrew, 155.

Roubiliac, L.F, 116.

Routh, E.J, 308-310.

Rud, Bishop, 57.

Rustication, 221-224.

Rutherford, Wm, 267.

Sadleir, Lady, 315.

Sadleirian Professorship, 315.

St Mary's Ch, Camb, 11.

St Michael's Ch, Camb, 12, 87, 98, 101.

Salisbury, Earl of, 55, 62.

Sanderson, Nich, _see_ Saunderson.

Sandwich Cup, The, 122.

Saunderson, Nich, 254, 268, 315.

Scholars, Election of, 30, 31.

Scholefield, Jas, 173.

Scot, Major, 97.

Sedgwick, Adam, 81, 110, 111, 173.

Senate-House, 153, 260.

Senate-House Examination, ch XV.

Servant Students, 28.

Seymour, Queen Jane, 106.

Shaw-Lefevre, J.G, 130, 140, 141.

Shepherd, Anth, 315.

Shirley, Walsingham, 61, 223.

Sides, Tutorial, 42, 43.

Sidgwick, Hen, 110, 111, 176.

Simeon, Chas, 74, 112.

Simpson, Thos, 268, 284.

Sizars, 28.

Sloane Tankard, The, 123.

Smith, Elismar, 103.

Smith, John, 315.

Smith, Robt, 111, 172, 254, 265, 267, 315.

Smith, Thos, 4, 5.

Smith's Prizes, 266.

Solar System, ch XIII.

Solomon, Proverbs of, 203.

Somerset, Duke of, 112, 113, 114.

Sophia, Princess, 107, 108.

S.P.C.U. ch IV, 101.

Special Examinations, 297.

Spectrum Analysis, 242-243.

Spedding, Jas, 173.

Spicer, Robt, 129, 132.

Stangs, 214-215.

Statutes, Trinity, 1552, 30, 31.

" " 1554, 33.

" " 1560, 33, 34.

" " 1844, 35, 175,

" " 1861, 35, 175.

" " 1882, 35, 175.

Stephen, Leslie, 174.

Stevinus, Simon, 231.

Still, Bishop, 57.

Stocks, 214-215.

Stokes, G.G, 315.

Stuart, Bernard, 119, 124.

Stuart, Jas, 316.

Stuart, John, 119, 124.

Subsizars, 28.

Sussex, Duke of, 112.

Sylvester, J.J, 311.

Tavel, G.F, 287.

Taylor, Brook, 254.

Taylor Tankard, The, 123.

Taylor, Tom, 174.

Tennyson, Alf, 108, 115, 117, 174.

Tennyson, Chas, 174.

Tennyson, Fred, 174.

Terms, loss of, 217.

Thackeray, W.M, 170, 173.

Thirlwall, Connop, 71, 72, 73, 83, 173.

Thompson, W.H, 81, 109, 114, 174, 175, 176.

Thomson, J.J, 316.

Thomson, Wm, 311.

Thorp, Thos, 73, 81, 307, 308.

Thorwaldsen, Bertel, 117.

Tindal, N.C, 76, 130, 137, 173.

Tisserand, F.T, 241.

Todhunter, Isaac, 302.

Treasures, College, ch VI.

Trench, R.C, 173.

Trentine Disputes, 188, 189.

Trinity Athletic Clubs, 124-126, 174.

Trinity College, Foundation, ch I.

Trinity College, History of, ch X.

Trinity College, Numbers at, 163.

Tripos, Mathematical, ch XV.

Tripos, Origin of Name, 311-314.

Trot, Warin, 160.

Tunstall, Cuthbert, 253.

Turner, Joseph, 286.

Turton, Thos, 315.

Tusser, Thos, 202, 210.

Tutorial System, ch II.

Tutors, College, ch II.

Tutors, Private, 45, 307-310.

Udall, Nich, 202.

Vanderbank, John, 108.

Vandyke, A, 119.

VanSittart, A.A, 130, 140.

Van Somer, Paul, 108.

Vaughan, C.J, 110, 111.

Verdon, Thos, 215.

Verney Cup, The, 122.

Vernon Tankard, The, 123.

Victoria, Queen, 69.

Vince, Sam, 284, 287, 315.

Vortices, Cartesian, 227, 230, 236, 237, 238.

Wakefield, Thos, 17.

Walker, Rich, 99.

Walling, 218.

Wallis, John, 254.

Walpole, Horace, 107.

Walsh, B.D, 81.

Walter, Hen, 285, 286.

Ward, Seth, 254.

Waring, Edw, 263, 277, 281, 286, 287, 315.

Watson, Rich, 264, 279, 307.

Watts, G.F, 108.

Waves, 230, 236.

Wensleydale, Lord, 130, 138, 139, 173.

West, Robt, 93.

Westcott, B.F, 101, 110, 111, 176.

Westlake, John, 110, 111.

Westminster Gowns, 68.

Westminster Scholars, ch III, 248.

Westminster School, ch III.

Whetham, W.C.D, 43.

Whewell, Wm, 69, 72, 73, 81, 108, 110, 111, 117, 174, 175, 221,

252, 287, 288, 289, 291, 292.

Whisson, Stephen, 42.

Whiston, Wm, 254, 315.

Whitgift, John, 36, 51, 93, 94, 165, 166, 210.

Whittaker, E.T, 316.

Wilkins, John, 40, 111, 112.

William I, 179.

Williams, Joshua, 138.

Willis and Clark, 143, 152.

Willis, Robt, 90.

Wilson, John, 287, 307.

Windows, Chapel, 91, 93, 102, 115, 116.

Winthrop, Adam, 128, 129, 130, 131.

Wollaston, F.J.H, 285.

Wood, Jas, 277, 284, 286.

Woodhouse, Robt, 286, 287, 290, 315.

Wordsworth, Chris (1), 71, 72, 73, 74, 81.

Wordsworth, Chris (2), 252, 263, 275, 279, 314.

Wordsworth, John, 81.

Wranglers, ch XV.

Wren, Chris, ch VIII, 228.

Wright, Edw, 254.

Wright, J.M.F, 100, 174, 219, 293.

Yool, G.V, 130, 142.

York, Richard Duke of, 110.

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Transcriber's notes:

Both "primâ facie" and "prima facie" retained in line with the author's

inconsistent usage. Hyphenation of commonwealth/common-wealth not

regularised because the latter form occurs only within a quote from a

seventeenth-century source.

End of Project Gutenberg's Cambridge Papers, by Walter William Rouse Ball