active teachers (regents) acting with the concurrence of the
chancellor who represented the bishop of Ely; their grouping in
faculties was an obvious development, and probably took place early in
the thirteenth century. Resident graduates who had ceased to teach
(non-regents) were allowed a voice on matters of property, rights, and
privileges. The establishment of monasteries and colleges with
administrative officers tended to retain in residence graduates who
were not lecturing; through them the house of non-regents grew in
power, and finally in many questions obtained concurrent jurisdiction
with that of the regents--the result was a very complex constitution.
At first the University had no buildings of its own; the regent and
non-regent houses met in St Benet's or St Mary's church, and lectures
were given wherever accommodation could be obtained. After this
digression I return to the position of the students in the early
University.
Numerous monasteries were established in Cambridge during the
thirteenth century, and from this I infer that the number of members
of the religious Orders studying in the University steadily increased
during that century. Of monastic Houses in Cambridge previous to the
foundation of the University I have already mentioned those of the
Augustin Canons, founded in connection with St Giles' church, about
1092, and moved in 1112 to Barnwell where their priory became in time
one of the largest conventual buildings in England, and of the Austin
Brethren of Frost's or St John's Hospital, built about 1135 on ground
now occupied by St John's College. Shortly after the organization of
a studium in the town, five important Orders established Houses here.
These were the Franciscan or Grey Friars, who, from their first home
situated near the present Divinity Schools and used from 1224 to 1294,
removed in 1294 to a site now occupied by Sidney Sussex College, where
their church was one of the conspicuous architectural features of
medieval Cambridge; the Dominican or Black Friars, who built in 1274
on ground now occupied by Emmanuel College; the Carmelite or White
Friars, who, having previously lived in houses at Chesterton and
Newnham, removed in 1290 to a site now occupied by Queens' and King's
Colleges; the Augustine Friars, who built, about 1290, a home on or
near ground now occupied by the university examination halls and
lecture rooms, in the basement of which some fragments of the old
friary may be found; and the Sempringham or White Canons, who about
1290 obtained possession of St Edmund's Priory which had been built
before 1278 near the Trumpington Gate. The Houses of the Bethlehem
Friars, opened in 1257, of the Friars of the Sack, opened in 1258, and
of the Friars of St Mary, opened in 1273, were suppressed in 1307, and
probably were never important foundations. I believe that the presence
in Cambridge of these great establishments, always housing a certain
number of students, gave stability to the nascent University, and
tended to prevent its dissipation in times of stress: this is a point
in our early history which is sometimes overlooked. Students from
Houses of the Benedictine or Black Monks were also sent to Cambridge,
but until 1428 they seem to have had no special home of their own: in
that year the Order built for them a hostel known as Buckingham House
which now forms part of the first court of Magdalene College.
These conventual Houses were outside town and university authority,
but their wealth and position made them influential. Striking evidence
of this is afforded by the facts that they secured to their members
the right to proceed direct to degrees in divinity without graduating
in arts--a privilege not granted to students in law or medicine--and
that at every congregation of the University the senior religious
doctor present could veto the offer of any grace and so block all
business. These privileges suggest that monastic students were the
dominant class in the early days of the University. They were,
however, naturally distrusted by other students, for admittedly they
owed allegiance to outside bodies, and no man can serve two masters.
By the end of the thirteenth century the monastic movement had spent
its force, and thenceforth the religious students took a constantly
decreasing share in university activities; of course they disappeared
at the reformation, when the monasteries throughout the country were
suppressed.
I come next to the question of the secular students in arts, most or
all of whom would be clerks in major or minor orders. Rejecting the
migration theory of the origin of the University, I do not suppose
that in its earliest days these secular students were numerous, for
the vicinity cannot have provided many such men, but as soon as the
University acquired reputation as a centre of higher teaching they
would be attracted to it from a wide area, and their numbers would
be increased by many glomerels who would continue their course as
students in arts. In the course of the thirteenth century these
secular students became strong enough to assert themselves against the
position and privileges assumed by the religious students, and after
that century graces were constantly passed (_ex. gr._ in 1303) to
prevent monastic interference in academic affairs, or (as in 1369) to
limit the number of monastic graduates.
A non-graduate student in arts was, before admission, expected to
know Latin, and, on admission, apprenticed to a master or doctor who
acted as a tutor in scholastic matters: in 1276 this system of
apprenticeship was made compulsory. The full medieval course lasted
several years. Students who entered as boys stayed, if they took the
full course, till they were grown men, gradually taking up teaching as
part of their course of study. The bachelors may have assisted in the
education of the younger arts students and of the glomerels who are
mentioned below, but normally instruction in the arts course was given
by masters, and in the higher faculties by doctors. The degree of
master was a license to teach, and newly created masters were required
to teach and to reside for two years (or later at least one year) for
that purpose. This pre-reformation scheme is in marked contrast to the
modern plan where the students enter as young men, all of about the
same age, with a normal course lasting three years or so, and with
their studies sharply differentiated from those of a limited number
of post-graduate and research students and of a separate body of
teachers. Mullinger estimated that during the medieval period the
number of resident regents varied from one hundred to two hundred, and
the number of students (apparently exclusive of monastic students)
never exceeded two thousand of whom the great majority were of humble
birth; no doubt there were wide variations in the numbers at different
times.
The history of Guilds in the University cannot be given with any
certainty. It may be that in the early years of the University most
secular students and teachers from any particular locality were
associated together as a guild, and perhaps every student on arrival
was expected to join his local guild, and through it become a member
of the University. The guilds imposed on their members definite rules
for their conduct in relation to one another, and enforced such
regulations by means of money fines, refusal of assistance, and in
extreme cases expulsion. The relations between the members of
different guilds were, however, often unfriendly or worse; in
particular there was constant friction between the guilds connected
with localities north and south of the Trent. It has been suggested
that at one time one of the proctors represented the cis-trentine
guilds and the other the trans-trentine guilds: this seems to have
been the case at Oxford, but there is no evidence of such a custom at
Cambridge where, according to Peacock, these trentine disputes were
less violent than at the sister University.
We may take it that the master to whom a secular non-graduate student
was apprenticed looked after his studies, and probably officers of the
guild to which he belonged looked after him when sick or maltreated.
In other matters, however, he was left to take care of himself, and
thus was constantly liable to extortion. To meet this evil, the
University early obtained powers enabling it to settle, without
consulting the citizens, various local matters such as the prices of
lodging and food.
Besides students in arts there was also another class of secular
students consisting of boys, known as glomerels (grammarians) and
rhetoricians, who were under a special officer of the University
called the master of glomery. I conjecture that originally these were
the boys at the local grammar-schools, that after the foundation of
the University such boys were regularly treated as glomerel members of
it, and that for this reason we hear nothing more of the local
grammar-schools which had at first supplied them: most students of
this type must have lived at home and come from the town or immediate
neighbourhood. I suppose that in later times the number of glomerels
was swollen by the entry among them of students who had come to
Cambridge, and were found to be ignorant of Latin grammar, and so
inadmissible to the arts faculty.
The chief study of a glomerel was Latin grammar, and on attaining
reasonable proficiency in it he could change over to the arts faculty
if he wished. If a student continued in the glomerel faculty, the
degree of master in grammar (or rhetoric) was open to him, but in
processions of the University, such graduates took a lower place than
students in arts, and their inferior position was emphasized by a
statute which, while regulating the attendance of regents at the
funeral of a regent master or student in arts, stated that graduates
and scholars in grammar were not entitled to such recognition--_Illis
tantummodo exceptis, qui artem solam docent vel audiunt grammaticam,
ad quorum exequias nisi ex devotione non veniant supradicti_.
The ceremony of graduation in grammar has often been described: it
involved the beating openly in the schools of a shrewd boy obtained by
the university officers for the purpose, and the presentation to the
new master of a ferule: this suggests that the course was regarded as
a training for a schoolmaster's career, it also facilitated admission
to orders. As time passed, the glomerels, originally forming a large
and important section of the University here and at Oxford, decreased
in numbers, and in the latter half of the fifteenth century they
ceased to be of much importance in academic life. The faculty of
rhetoric was constituted on similar lines to that of grammar, and
practically treated as part of it. The last degrees in rhetoric and
grammar of which we have notice were conferred in 1493 and 1548
respectively: probably the office of master of glomery fell into
disuse about the beginning of the sixteenth century, though it is
possible that it was held by Sir John Cheke as late as 1547.
The evils consequent on allowing inexperienced students, some of whom
were quite young, to fend for themselves in all matters outside the
schools were obvious, and it was not long before steps were taken to
improve matters by the foundation of colleges and the licensing of
private hostels.
Colleges were designed for selected scholars partly to provide
assistance for them, and partly to protect them from pressure to join
a monastic Order: the advantages offered being shelter, a common
sitting room properly warmed, regular meals, the use of books, and
general supervision. The earliest attempt to provide aid and
protection of this kind for certain scholars was made, about 1275,
by Hugh de Balsham, who arranged for their reception as members of
Frost's Hospital; but there were constant quarrels between the two
sides of the House, and in 1284 he dissolved the union and moved the
secular students to a building (Peterhouse) of their own. Other
similar foundations were soon created: the King's Scholars (later
incorporated as King's Hall) in 1317, Michael-House in 1324, Clare in
1325, Pembroke in 1347, Gonville in 1348, Trinity Hall in 1350, and
Corpus Christi in 1352. Every new college that was established
provided fresh definite ties with the locality, and rendered less
likely the break-up of the University and the scattering of its
members--a serious risk to which in early days it was always subject.
Then came an interval of nearly a hundred years, but in the fifteenth
century the collegiate movement recommenced, and we have the
foundation of God's House in 1439, of King's in 1441, of Queens' in
1448 and 1465, of St Catharine's in 1473, and of Jesus in 1496. In the
sixteenth century we have the larger and more ambitious foundations of
Christ's in 1505, St John's in 1511, Magdalene in 1519, Trinity in
1546, Emmanuel in 1584, and Sidney Sussex in 1596.
The colleges were intended for picked scholars. In the course of the
fourteenth century the problem of the care of other students was taken
up, and they were forbidden to live in lodgings selected by themselves
and under no external supervision. To provide for them, the University
licensed private hostels which were managed by masters of arts on
lines somewhat similar to boarding houses in public schools to-day.
Thenceforth throughout the middle ages the majority of undergraduates
resided in these hostels. Caius gave the names and sites of
twenty-seven private hostels which he had known and all of which
closed their doors during his life, the last in 1540: Fuller
enumerated thirty-four hostels and two "inns" while his editor
mentioned fourteen other hostels, but some of these certainly ought
not to be included under the term. Perhaps we may say that the number
open at anyone time rarely exceeded thirty or fell short of twenty:
some were cheap, some expensive; some were well managed, others not
so. After the development of these hostels the guilds decreased in
importance, and finally disappeared.
With the establishment of colleges and private hostels the University
was fairly launched on its career in a form which lasted till the
middle half of the sixteenth century. My object was to state how, in
my opinion, it originally took shape, and I do not propose here to
follow its history further.
[Footnote 31: Most of the known facts are given in Mullinger's
excellent histories, Peacock's _Observations on the Statutes_, and
Rashdall's _Universities of Europe in the Middle Ages_--but all the
views of the last-named writer are not universally accepted.]
[Footnote 32: See _passim_ G. Peacock, _Observations on the Statutes_,
London, 1841, p. xxxv.]
CHAPTER XII.
DISCIPLINE.
This paper contains some extracts from my notebooks on the way in
which university and college discipline was maintained in former days
at Cambridge. The records on the subject are scanty, but I think the
facts are worth putting together in a connected form. There is no
reason to suppose that the practices of different colleges varied
materially, and if in the later period I have taken examples from the
records of Trinity it is only because I have had easier access to
them.
In the history of university discipline and social customs abrupt
changes are not to be expected, and none such are noticeable in the
transition from the medieval period, _circ._ 1200 to 1525, through
the renaissance, _circ._ 1525 to 1640, and the period of stagnation,
_circ._ 1660 to 1820, to the present age of reconstruction and
extension. I begin naturally with discipline in medieval Cambridge.
In the early days of the University the students lodged in the town
and were of all ages from twelve or thirteen upwards. Except in
strictly academic matters, there was little or no supervision of their
conduct, and, outside the schools, grave disorders were common; the
University, however, claimed power, when it chose, to take cognizance
of all offences contrary to good manners, and at any rate in later
days did so in serious cases. The regulations at Cambridge and Oxford
were so similar that we may fairly draw illustrations from either
University, and the records of the chancellor's court at Oxford in the
fifteenth century show that fines, imprisonment, and, in extreme
cases, expulsion were customary penalties for serious offences against
university regulations and customs. I have no doubt that earlier
records, if extant, would be of the same general character.
The first college to be founded at Cambridge was Peterhouse which took
its final form in 1284, and during the next century several other
similar Houses were established: these societies were intended for
selected scholars. The problem of the control of other students was
met in the course of the fourteenth century by preventing them from
living in private lodgings chosen by themselves, and thenceforth,
throughout the middle ages, those who came from a distance were
generally required to reside in private hostels run by masters of arts
on lines somewhat similar to boarding houses in public schools to-day.
Besides the lay and secular students accommodated in colleges, private
hostels, and at their homes, there were also in the medieval
University a considerable number of "religious" students who were
housed in monasteries or monastic hostels. Some of the colleges in
later medieval times received as paying members a few wealthy
pensioners, parochial priests in middle life, and even monks from
distant convents, but probably the number of such favoured students
was never large. With the establishment of colleges and the
organization of private hostels discipline improved; inside their
walls as well as in the monastic hostels it is probable that order was
well maintained, but outside them, at least among the students at
private hostels, discipline was left to the university authorities who
did little or nothing in the matter.
The colleges took seriously their responsibilities for discipline, and
all things contrary to good manners and morals were prohibited. For
the gravest offences, such as contumacy, crimes of violence, and
heresy, expulsion was usually ordered. Among less serious
delinquencies, explicitly forbidden and therefore we may assume not
unknown, were bringing strangers into the house, sleeping out, and
absence without leave; using insulting language, drunkenness,
gambling, and frequenting taverns; keeping company with loose women;
throwing missiles and carrying arms; and the keeping of dogs, hawks,
falcons, and ferrets. In the regulations of many colleges, a course
of study was indicated, and directions given that idleness was to be
punished. Regular attendance at religious exercises was assumed, and
was explicitly directed on certain occasions: I suppose that students
performed such duties without much external pressure, and I know no
record of the infliction of any penalty in early times for
non-attendance. In the middle ages Latin was the language generally
enforced, though occasionally French was permitted; this remained the
rule until the seventeenth century. Conversation during dinner and
supper was forbidden in many colleges, and of course was impossible in
those cases where some book was then read aloud. At King's College,
jumping and ball throwing, and at Clare College meetings in bedrooms
for feasting and talking were also forbidden. At a somewhat later date
Caius ordered his students to be in bed by eight o'clock at night, but
they made up for this by rising very early in the morning. In general
the punishment for minor faults was left to the discretion of the
authorities. This was only reasonable, for a medieval college was a
mixed community of lads and men, the members being of all ages from
about fourteen or fifteen upwards; and rules enforced on boys of
fourteen could not be applied to men of twenty-three or twenty-four,
who were in fact already taking part in the teaching of the junior
scholars.
For all members, the ultimate penalty for the gravest offences was
expulsion. For less serious misconduct, fines, restrictions on the
food supplied, impositions, and confinement within the walls, are
believed to have been common penalties, at any rate for adolescents;
but, as I explain below, I think that corporal punishment was
constantly inflicted on non-adults in lieu of a fine, which indeed
boys would have had considerable difficulty in paying. As far as the
younger students and the bachelors at colleges were concerned the
extant regulations in regard to their exercises, amusements, incomings
and outgoings, suggest that they were treated much like the junior and
senior boys in a rather strict public school in the first half of the
nineteenth century; and perhaps the senior graduate members were
treated somewhat like residents in colleges at the same period.
Membership of a college was a privilege confined, in general, to
scholars specially nominated, and no doubt the standards of work and
discipline there were higher than in the private hostels. Naturally we
know less of life in these hostels, but it is likely that disciplinary
rules were originally made by or with the approval of the elder
residents, and that the normal discipline in them was of the same
general character as that exercised in colleges, though, as the
members paid for themselves, money fines were possible and usual
penalties, especially in the case of the older members. There must
have been more variety in the discipline of hostels than of colleges,
and we may safely say that some hostels were well conducted, others
not so.
It is possible that finally the University claimed the right to
examine and supervise the internal regulations of the hostels. A set
of rules, thus enforced on an unendowed hall at Oxford in the
fifteenth century, has been discovered and printed by Rashdall: they
do not differ much from those usual at a college, except that some of
the penalties specified are pecuniary, and that the principal was
given explicit permission, if he wished, to flog a student, even
though the lad's own master (_i.e._ the master to whom he had been
apprenticed) had certified that he had already corrected him or was
willing to do so.
Was corporal punishment commonly used in medieval times? Until
recently it was accepted without argument that this was the case; and
certainly in the fifteenth century and later when we get detailed
information on the subject, the younger students were subject to it.
Rashdall, however, has argued that the absence of its mention in
earlier times implies that the birch was unknown in the ordinary
university regulations till towards the end of the sixteenth century
or later, though he admits in various places that glomerels were
liable to it: his authority is accepted by Rait. It is true that in
the statutes given in the thirteenth and fourteenth centuries,
birching is not mentioned explicitly, but, since the punishments for
petty offences are rarely specified in detail, this proves nothing. In
the fifteenth century corporal punishment is mentioned as a recognized
penalty. For instance, the statutes given by Henry VI to King's
College, Cambridge, prescribed that scholars and young fellows might
be punished by stripes, and a year or two later, the statutes of
Magdalen College, Oxford, directed that the demies should be subject
to flogging. In later regulations of various colleges, to some of
which I refer below, whipping is mentioned as a recognized punishment,
but often as one to which only the younger students were liable.
I have already argued that in medieval colleges discipline must have
varied according to the age of the offender, and I conjecture that
adults were never regularly subject to corporal punishment, but that
boys were always so, and that the use of the rod was regarded as
needing no explicit statutable authority. Its employment was no
strange thing, for adult offenders against the law, apprentices, and
boys at school, were all flogged at times. And what else, it has been
well asked, could the authorities do with a troublesome boy of
fourteen? In general a fine was impossible for he had no
pocket-money. Most of the colleges were designed for poor scholars,
and in such foundations usually the allowance for commons was so small
that without risk to health any reduction for more than a day or two
was difficult; little leisure was allowed for recreation or exercise,
and thus heavy impositions were impossible; and confinement to the
precincts of the House was so common that gating was no punishment. A
lad of seventeen or eighteen had more liberty and privileges, and in
general on reaching that age was as safe from the chance of corporal
punishment as was a boy of the same age at a public school fifty years
ago.
Somewhat similar arguments apply to the private hostels, and the
regulations of an unendowed hall at Oxford, to which I have already
referred, show that the use of the rod or birch was recognized there.
If as I suppose is likely, Clement Paston was at a private hostel, we
have a definite instance of the similar use of the rod at Cambridge,
for among the Paston letters is one dated 28 January 1458 from Dame
Agnes Paston, about her boy, Clement, in which she says "prey
Grenefeld to send me feythfully word by wrytyn who (how) Clement
Paston hathe do his dever i lerning. And if he hathe nought do well,
nor wyll nought amend, prey him that he wyll trewly belassch (_i.e._
flog) him tyll he wyll amend, and so ded the last Maystur and ye best,
that ev' he hadd at Cambrege." Clement was born in 1442, so he was
then fifteen years old.
I asserted above that school-boys in the middle ages were liable to
the birch or cane. I suppose this will not be questioned, but by way
of parenthesis I add that this liability seems to have been a
well-established practice for centuries. It goes back to classical
times for in the schools of Rome the less serious offences were
punished by the cane applied to the hand, and graver faults by the
birch applied to the back; and there is a curious fresco at
Herculaneum of the application of the latter to a boy, horsed by one
schoolfellow and with his feet held by another. The royal whipping
boys in the courts of Western Europe remind us that, at least
vicariously, princes were subject to this discipline as well as
commoners.
In more recent times the deeds of Busby and Keate at Westminster and
Eton respectively are preserved in tradition, while the reputation of
Udall at an earlier time, _circ._ 1530, may be gathered from the
remarks of Thomas Tusser, a choirboy at St Paul's Cathedral, who
subsequently went to Eton: Tusser says, "From Paul's I went, to Eton
sent, To learn straightways the Latin phrase Where fifty-three stripes
giv'n to me, at once I had. For faults but small, or none at all, It
came to pass thus beat I was." The similar vigour of Udall's
successor, Cox, is mentioned by Ascham. In short, the old saw: "Spare
the rod, and spoil the child, Solomon said in accents mild, Be it boy
or be it maid, Whip 'em and wallop 'em Solomon said" represented the
current belief and practice of former days; though the dictum
attributed to that king is stronger than the passage in Proverbs,
xiii, 24 warrants.
In the sixteenth century the colleges opened their doors to the
admission of pensioners and fellow-commoners. Collegiate teaching and
arrangements were superior to those of the private hostels, and before
the middle of the century the latter had disappeared: their revival
was rendered impossible by a regulation that membership of the
University should be confined to those who were members of a college.
Shortly afterwards it became the custom not to require residence for
degrees after the baccalaureate, and thus a course limited to three or
four years became usual for the average student. These changes were of
far-reaching importance.
In the course of this century new statutes were given to the
University and colleges, and subsequently we possess records, fairly
complete, of the domestic life of students. Early in the following
century, the average age of entry began to rise, and before its close,
it had become common for students to defer entry until about seventeen
years old.
University decrees regulating the conduct of students in many matters
now appear, notably one in 1595 by Goad, then vice-chancellor, which
gives a summary of what was expected. Expulsion, suspension from
degrees, and refusal of leave to graduate until after a specified
time, were normal punishments for serious offences, for trivial
misconduct fines are now constantly prescribed, and physical
punishments for non-adults are also directed in many cases.
In colleges, the Tudor statutes generally enjoined good conduct on all
students. The regulations about the punishment of offences were mostly
concerned with grave matters for which admonitions, and finally
expulsions, were the recognized punishments. Penalties for the
non-performance of religious exercises now appear: thus, at Christ's
College, Cambridge, and at Balliol College, Oxford, whipping was
prescribed as a penalty for absence from chapel, though probably
restricted to the younger students; so too at Peterhouse, students
over eighteen who were absent from prayers were to be fined, while
younger students so offending were to be deprived of dinner, and if
persistent in their neglect flogged in hall.
As in medieval times, the authorities were generally left a free hand
in settling the regulations for the maintenance of normal discipline.
Probably fines, impositions, restrictions on the food supplied, and
gatings continued to be ordinarily used. Reading the bible aloud at
meal times in hall, dining apart on bread and water, and being
deprived of commons, are definitely mentioned in the 1520 statutes of
St John's College, Cambridge, as possible penalties; similarly at
Corpus Christi College, Oxford, being compelled to eat alone at a
small table in the middle of the hall and restriction to bread and
water are specified as suitable punishments.
The use of the birch was now constantly prescribed, though probably
in practice always confined to lads. Thus, at Christ's College,
Cambridge, a whipping for lads and a fine for adults; and at
Brasenose, Oxford, a fine or a flogging, at the discretion of the
principal, were statutable punishments for various faults, including
at the latter College the making of odious comparisons in
conversation. At other Houses too, for instance, at Corpus Christi,
Oxford, Wolsey (Christ Church), Oxford, Trinity College, Cambridge,
and Gonville and Caius, Cambridge, the use of the cane or birch is
sanctioned in the case of lads. I have no doubt this was also the
general rule in earlier days, and nothing in the Tudor codes indicates
that any material change was made in the existing practice, but on the
whole I conjecture that the regulations were more humane, and I am
inclined to think, contrary to Rashdall's view, that discipline was
less severe after the renaissance than before it. In colleges the
deans were and are the chief officers responsible for discipline; in
the University, the proctors.
A part of the fifth chapter of the Trinity statutes of 1560 relating
to the office of deans may be summarized as indicating what was then
customary, or at any rate desired, in the matter of chapel attendance
and in certain questions of petty discipline. The statute, which is in
Latin, is to the following effect:
In every community regard should be paid to correctness of morals
and general probity of life, accordingly there shall be two deans to
give their sedulous attention to these objects; at least one of such
deans shall be a bachelor of divinity and chosen from the eight
senior fellows, and the other, a master of arts or a bachelor of
divinity.
The deans shall provide for the fitting performance of public
worship; see that all fellows, scholars, pensioners, sizars, and
subsizars attend on Saints' days and Sundays at morning and evening
prayers, the litany, the communion, and sermons; and see that the
same persons are on other days regularly present at prayers between
five and six o'clock in the morning. Every fellow who is absent
shall be fined three half-pence, and if he comes in late or goes out
early, one half-penny. The fine for a bachelor scholar who is absent
shall be one penny, and for one who comes in late or goes out early,
one half-penny. Every undergraduate scholar, and every pensioner,
sizar, and subsizar who is absent shall, if his age exceeds eighteen
years be fined one half-penny, and if he comes in late or goes out
early, one farthing; but if such student has not attained this age,
he shall be chastised with rods in the hall on the following
Friday. Those are to be deemed as coming late who at evening prayers
arrive after the first psalm; at morning prayers, after the
_Venite_; at the Litany, after the words _O Holy Blessed and
Glorious Trinity_; and at the communion service after the recital of
the commandments: anyone who, during service, remains in the
antechapel is to be punished as if he had been absent.
Each week on Friday, at seven o'clock in the evening, the deans
shall chastise non-adult offenders. All scholars (bachelors
excepted), pensioners, sizars, and subsizars shall be present during
the infliction of such corporal punishment, and anyone who does not
answer to his name when called, and does not stay until all the
punishments are finished, shall, if an adult, be fined one penny,
and if non-adult be flogged on the next day.
Each week on Thursday, the deans shall appoint two monitors from
among the bachelor scholars for noting offences of bachelors; and
six monitors [from among the undergraduate scholars], two for noting
offences of undergraduates at public worship, and four for noting
those who fail to speak Latin: the monitors shall prepare lists of
all who offend in these particulars. The deans shall also appoint
each week six scholars and four sizars for service at the fellows'
table, and one sizar for the organ.
In order to ensure the decorous celebration of public worship, the
deans shall bring with them to the first vespers of every festival
a written schedule of the duties of everyone concerned in that
festival, and shall further appoint an inquisitor who shall remind
everyone of the duty so assigned to him. Anyone who shall fail in
such duty shall, if a non-adult, be whipt, and, if an adult, be
fined fourpence.
One half of all fines inflicted shall go to the College, the other
half shall be kept by the deans.
The Tudor statutes generally remained in force till the middle of the
nineteenth century, though in time the practices of the colleges came
to differ materially from what was there directed. Briefly we may say
that in the sixteenth century the standard of medieval discipline and
study sank; but in the early years of the seventeenth century things
improved until the civil disturbances threw academic work into
confusion. With the establishment of the commonwealth the age of entry
rose, and thus the use of corporal and puerile punishments died out,
and with the disappearance of boys as members of the University, rules
intended only for young lads became obsolete and inoperative. Most of
the students henceforth were adolescent. The few who were younger were
dealt with like school-boys, but the comparison is rather with
school-boys of recent years than with those of their own period.
As far back as Sir Simon D'Ewes's time--and he entered Cambridge in
1618--the majority of the students were regarded as responsible, and
capable of conducting themselves rationally. They reflected the
virtues and foibles of their time, but they were a select class, and
compare favourably in manners and morals with their contemporaries
elsewhere. Almost without exception they speak warmly of their
development in college from lads to young men, of friendships formed
with their elders as well as their contemporaries, of the abiding
influence of the place, and of their affection for it.
From the restoration to the regency was a period of stagnation.
Discipline deteriorated, and if we may trust contemporary accounts
drunkenness and immorality were far from uncommon. No doubt there were
always some residents who maintained high traditions and ideals, but
on the whole the records of the social life prevalent then at
Cambridge and Oxford make but sorry reading.
The sixteenth century codes indicate lofty aims, but statutes and
rules are not always observed literally, and it may be thought that
those mentioned represented only old customs, perhaps already
obsolete, or what was deemed desirable but was not enforced. It may be
well then to turn to contemporary evidence, to regulations passed on
specific occasions, and to records of definite punishments--though we
can expect the latter to have been preserved only in grave cases, and
cannot hope to learn from them much about discipline in petty matters.
Contemporary evidence would serve us best if we could get it, but the
diarists and letter-writers are mostly silent on the subject. From
this, however, I conclude that generally the disciplinary regulations
were thought sensible. Life in the University may have been hard and
probably was so, but I do not believe that discipline was
unreasonable. All the evidence is to the contrary. Thus the
above-mentioned Tusser, a student of no special brilliancy, who
entered at Trinity Hall in the early half of the sixteenth century
speaks thankfully of leaving school, and says: "To Cambridge thence
... I got at last, There joy I felt, there trim I dwelt, There heaven
from hell, I shifted well, With learned men, a number then, the time I
passed."
Coming now to definite punishments, I mention successively corporal
punishments, such as birching, the use of the stocks, and stanging;
fines, direct and indirect; deprivation of days or standing; gatings;
impositions; declaratory confessions; and rustications and expulsions.
_Birching, Flogging._ Birching remained a recognized punishment for
the younger students in the sixteenth and seventeenth centuries, but I
think that in practice it was not often inflicted except on boys. One
or two examples of orders directing it will suffice.
On 8 May 1572, the Vice-Chancellor, Whitgift, issued an order which is
so detailed that I write it at length. Here it is:
If any scholar shall go into any river, pool, or other water in the
county of Cambridge; by day or night, to swim or wash, he shall, if
under the degree of bachelor of arts, for the first offence be
sharply and severely whipped publicly in the common hall of the
College in which he dwells, in the presence of all the fellows,
scholars, and others dwelling in the College, and on the next day
shall be again openly whipped in the public school, where he was or
ought to be an auditor, before all the auditors, by one of the
proctors or some other assigned by the Vice-Chancellor, and for the
second offence every such delinquent shall be expelled his College
and the University for ever. But if he shall be a bachelor of arts,
then for the first offence he shall be put in the stocks for a whole
day, in the common hall of his College, and shall, before he is
liberated, pay 10s towards the commons of the College, and for the
second offence shall be expelled his College and the University. And
if he shall be a master of arts, or bachelor of law, physic or
music, or of superior degree, he shall be severely punished, at the
judgment and discretion of the Master of his College.
From this it is clear that at that time undergraduates, even of mature
age, were liable to be flogged as a part of the ordinary discipline of
the University and College, but probably it was unusual to inflict the
penalty.
Thirty years later, after the disturbances of 20 February 1607,
following the performance of a comedy in King's College, an order was
issued that thereafter every ringleader in any similar disturbances
should be banished from the University: and every less responsible
offender should, if a graduate, pay for the harm done, be suspended
from his degree, and for one year refused leave to take a further
degree; and if a non-graduate should for one year be refused leave to
graduate, and further, if non-adult, be corrected in the schools by
the rod, and, if adult, make an open confession of his guilt in the
schools: also the offender if not a scholar should be set in the
stocks at the bull ring in the market place. Here, it will be noticed,
the punishment by the rod is restricted to those non-adulti.
In a list of punishments inflicted at Corpus Christi College in 1622,
quoted by Lamb, admonitions, fines, suspensions, and whippings are
mentioned. Even as late as 1648 there is a record of "Benton per
Tutorem suum Magistrum Johnson virgis castigandis."
In 1648 an undergraduate bible-clerk of Peterhouse, age about
seventeen, Tobias Conyers by name was "corrected publicly"--which,
I take it, means flogged--for toasting the king. But times were
abnormal, and if Conyers ventured into the stirring field of politics,
he had to take the consequences.
The liability to a flogging still existed after the restoration.
Thus in the _Poor Scholar_, by R. Nevile, London, 1662, there are
references to it in Act ii, Scene 6, and Act v, Scene 4, as being
still in use in colleges though whether adults were so liable is
uncertain. If the author's statements refer to contemporary matters
and are trustworthy it would seem that the punishment was then
common, the culprits being mounted on barrels, and the flogging
inflicted at the butteries. The birch was also still occasionally used
in university discipline, for on 20 March 1674, the vice-chancellor
ordered Ellethorpe of St John's, and Hodges of Sidney Sussex to be
whipped for having been rude to the junior proctor, Peter Parham, of
Caius College: neither of the offenders had matriculated.
These references provide the strongest evidence with which I am
acquainted for the assertions that flogging was a usual punishment at
Cambridge during the seventeenth century. There is a widely spread
tradition that when at Christ's College, Milton was flogged, but Peile
has shown that there is no satisfactory evidence for it, and it is
intrinsically improbable. In a disciplinary order of Corpus Christi
College in 1684, the only punishments mentioned are discommonsings,
admonitions, rustications, deprivation of seniority, and refusal of
college testimonials, so, comparing this with the orders of 1622 and
1648 which I have quoted above, perhaps we may take it that the use of
the rod there had become obsolete.
The above extracts are sufficient to show that corporal punishment was
recognized under the Elizabethan codes, though it seems probable that
public opinion was against its use, unless the students were quite
young; perhaps this was always the practice, and thus, as the age of
entry rose, the use of the birch died out. Incepting bachelors and
senior students were usually punished for serious offences by
deferring their admission to degrees, loss of terms, or rustication:
being adult, they were in effect regarded as not subject to corporal
punishment.
_Stocks. Stangs._ A couple of other physical punishments--ignominious
and sometimes painful--may be mentioned in passing.
One of these was confinement in Stocks. To this allusion has already
been made in the orders of 1572 and 1607. Another instance is to be
found in the records of Corpus Christi College, where about 1580, one
of the students, Tobias Bland, who had libelled the master, was
compelled to confess his fault publicly, next put in the stocks, and
then expelled. In the old dining hall of Trinity College there were
stocks in the minstrel's gallery, but there is no evidence that they
were re-erected when the hall was rebuilt in 1605; perhaps the
punishment was then becoming unusual, though against this may be set
the fact that there are references to the college stocks in 1610 at
King's, in 1625 at Christ's, and in 1642 at Emmanuel. The stocks at
King's and Emmanuel, like those at Trinity, were in the hall.
Allusions to their use are rare. The punishment continued to be
inflicted after the restoration, for on 10 April 1680, Thomas Grigson,
who had been rude to the junior proctor, Thomas Verdon of St John's
College, was ordered to be "sett fast in the stocks, by the heeles for
one whole houre, which was presently effected by the Constable of
Saint Bennett's Parish in Cambridge." He had partially atoned for his
offence by begging pardon on his knees, and so escaped a worse
punishment.
The Stang was a wooden pole on which the luckless culprit was tied,
and carried ignominiously through the courts of his college. In John
Ray's _Collection of English Words not Generally Used_, London, 1674,
it is said that the "word is still used in some colleges in the
University of Cambridge; to stang scholars in Christmas, being to
cause them to ride on a colt-staff or pole for missing of chappel."
References to the place where the pole was kept occur in the
account-books of Trinity, St John's, Queens', and Christ's. In Parne's
unpublished manuscript history of Trinity College, allusion is made to
stanging as though at the beginning of the eighteenth century it had
become recently obsolete. From his language it would seem also that
undergraduates themselves inflicted the punishment on those of their
members who declined to take part in the Christmas revelries.
_Fines._ Pecuniary fines have been used to enforce discipline from
the earliest times by the University as well as by the colleges: after
the renaissance, the increasing age and means of students made fines a
suitable penalty for many of the less serious offences, such as
participation in forbidden amusements, visits to places out of bounds,
walking across the grass in college courts, smoking in public places,
the failure to wear academic dress when required, non-attendance at
lectures, chapel, hall, etc. Probably grave misconduct was punished
otherwise, or by fines combined with additional penalties. A fine, if
heavy, presses unequally on men of different means; and thus a system
of fines on a fixed scale cannot be regarded as equitable. Fines are
still used as penalties for the infraction of rules.
_Discommonsing. Dissizaring._ To be put out of commons was a
well-recognized penalty, applicable chiefly to scholars and sizars,
part of whose emolument consisted of a right to dine in hall and, in
some cases, to have commons (bread, butter, and beer) to a limited
amount each day. To deprive such a student of the right to dine in
hall or of his commons was equivalent to a pecuniary fine, and in the
case of a poor scholar might be a severe, though not a satisfactory,
punishment; probably a modicum of bread and beer was supplied to
students even when discommonsed. In some comments, published in 1768,
on university education at Cambridge, discommonsing is described as
"one of the most idle and anile punishments ... inflicted rather on
the parent than on the young man, who being prohibited to eat in Hall
is driven to purchase a dinner at a tavern or coffee house."
Here is an example of an order of discommonsing at Trinity in the
seventeenth century: "Agreed that Cassill should be punisht a monthes
commons.... Agreed at the same time that Pepys besides a monthes
commons, should have an admonition and pay the charges of the
chirurgion for the healinge Cassil's head w^h he broke with a key."
(Conclusion, 1 August 1643.) Its preservation is due to the fact that
Pepys' punishment was combined with an admonition, and evidence that
an admonition had been given might be required if subsequently a
question of expulsion arose. The culprit in question was Thomas Pepys
(B.A. 1645) and not the Samuel of immortal memory.
In 1815, Mansel, master of Trinity and bishop of Bristol, was
accustomed to put men out of sizings and commons if they appeared in
hall in trousers instead of knee breeches, and it would seem then that
to be put out of sizings further deprived the student of obtaining
private supplies from the college kitchens. Half a century ago the
penalty was still in use at Trinity, being imposed on scholars in
waiting, who failed to appear after hall to say grace.
_Loss of Days._ To qualify for a degree and for an emolument, it is
and has been generally necessary to keep a certain number of days by
residence in each of certain specified terms. At one time a common
form of punishment was to cancel a certain number of days already
kept. Thus the student would be obliged to stay at Cambridge for so
many additional days to make up for the requisite number which had to
be kept in the course of that term. In the seventeenth century the
authorities went further and sometimes cancelled terms that had been
kept. I believe this form of punishment has long been obsolete.
_Gating. Walling._ Continuous confinement within the walls of the
college (walling) or confinement during certain hours (gating) was
another form of punishment. A case of walling occurred at one of the
smaller colleges in Cambridge in 1872, but I know of no more recent
instance. Gating is still in force. It causes some social
inconvenience. As far as it goes, it promotes regular hours and
economy, and it has no indirect ill-effects. Accordingly it serves
well to mark dissatisfaction and act as a warning.
Here is an old-time example from the records of Trinity, 19 July 1652,
of the infliction of this and other penalties interesting from the
name of the scholar on whom it was inflicted:
Agreed that Dryden be put out of commons for a fortnight at least,
and that he goe not out of the colledg during the time aforesaid,
excepting to sermons, without express leave of the master or
vice-master; and that at the end of the fortnight he read a
confession of his crime, in the hall, at the dinner time; at the
three fellowes tables.
His offence was disobedience to the vice-master, and his contumacy in
submitting himself to discipline.
_Impositions._ Another tolerably obvious punishment was the setting of
impositions. The imposition might be the learning of lines by heart or
the delivery of a declamation on some given subject, or the production
in writing of so many lines of a classical work or of an analysis of
some book. Impositions in writing were constantly done vicariously,
and if so, the punishment was little more than a fine: apparently this
abuse of the practice was well known.
The tasks set were very heavy. In the _Gradus_, 1803, the learning by
heart of the first book of the _Iliad_ is mentioned as a possible,
though very severe imposition. Similarly, according to J.M.F. Wright,
a thousand lines of Homer would have been regarded in 1815 as an
unusually sharp punishment, but such as might have been given in lieu
of rustication. Other impositions mentioned are the learning by heart
of a satire of Juvenal, and the production of an analysis of Butler's
_Analogy_.
At Trinity the deans were provided with long sheets of paper on which
were printed in double columns forms such as the following:
... to transcribe ... lines of Virgil's Aeneid, beginning at line
... book ..., and to deliver it to the Junior Dean after morning
Chapel on Tuesday.
... to transcribe ... lines of Homer's Iliad, beginning at line ...
book ..., and to deliver it to the Senior Dean after Morning Chapel
on Thursday.
... to repeat ... lines of ... by order of the Junior (or Senior)
Dean.
These were filled up by the deans, cut off, and distributed by the
chapel-clerk to the men concerned. Customarily in Trinity the senior
dean gave impositions from the _Iliad_ to be delivered on a Thursday,
an the junior dean from the _Aeneid_ to be delivered on a Tuesday.
Forms for putting men out of commons, and admonishing them were
printed in the same way on sheets, to be used as occasions arose.
Impositions were set at Trinity as late as 1830, but I believe the
custom had died out before 1840, though I am told it was still used in
certain Cambridge colleges as late as 1855. At Oxford the practice
continued rather later and indeed at a few colleges seems to have been
in force till near the close of the nineteenth century, for Rashdall,
writing in 1895, speaks of the practice as having been in force there
until recently.
A century ago there seems to have been a sort of recognized scale of
penalties for cutting lectures or chapel. First, a reprimand was given
at an interview or sent in writing by a servant; second, an imposition
was set; third the offender was deprived of commons and sizings. If
these steps were ineffective, the matter might be regarded as a
serious offence against college discipline, and lead to "hauling" by
the tutor, a gating, an interview with the master, a formal
admonition, and in extreme cases to rustication.
The theory of these petty punishments was set out by Whewell in his
_Principles of English University Education_, 1837. A punishment,
according to him, was to be regarded as the visible expression of
college dissatisfaction with certain conduct: as an infliction it
might be slight, but it emphasized the discontent expressed, and acted
as a definite warning. He suggested a most severe scale; namely, for
the first offence, forfeiture of one month's commons; for the second,
of three months' commons; and for the third, expulsion; but there is
no reason to think that this was ever the practice.
_Confessions._ A public confession was another form of punishment once
used: I believe that this ceased to be employed by the middle of the
eighteenth century.
_Statutory Admonitions. Rustication. Expulsion._ For the graver
offences, a statutory admonition, rustication (temporary removal from
the college), or expulsion were reserved.
A formal admonition was intended to act as a serious warning, and it
served as a statutory prelude to expulsion. For this reason it was
usually recorded, and in former times an additional sting was added by
compelling the culprit to make also a public or written confession of
his fault. Admonitions are not very common in the records of Trinity:
some thirty or forty occur in the sixteenth and seventeenth century,
only a few in the eighteenth century, and they are rare in the
nineteenth century save for a few relating to irregularity of
attendances at chapel or lectures. The last admonition at Trinity was
given in 1881, shortly before the new statutes of 1882 became
operative. Here are typical instances of the record of admonitions.
Whereas heretofore I have received an admonition from the Master of
the College for my lewd and outrageous behaviour within the same,
and have since that time for like rioting and swaggering in the Town
received another admonition from him before the Vice-Master of the
College and my Tutor and also therewith all public correction, if
these admonitions together with due punishment do not work
reformation in me hereafter, I do likewise willingly acknowledge
that I am incorrigible and worthy for the next like offence to be
expelled the College. Galen Browne. Circ. 1601. [Browne was elected
to a scholarship in 1602, and graduated B.A. and M.A. in due course,
so presumably he amended his ways.]
Whereas I have very unadvisedly and rashly stricken one Mr Halfhead,
a College servant, to the shedding of blood, I do acknowledge myself
to have received an admonition for that fault tending to expulsion.
Thomas Shirley, 22 February, 1621. [Halfhead was the manciple.
Shirley was a fellow and master of arts, so the offence was the more
serious, but perhaps the provocation was great. Shirley was
subsequently junior bursar and tutor.]
I, Christopher Offley, do confess that often time and many ways I
have offended against the Statute _de Modestia Morum_ to the
displeasure of God, hurt to myself, the evil example of others, and
discredit of the College, and also have broken mine oath taken when
I was preferred scholar in unreverent behaviour towards some of the
fellows and specially in giving scandalous and contumelious speeches
to Mr Hitch, being the Minister and Fellow of this College for which
misdemeanors and undutiful carriage I am unfainedly sorry and
heartily desire forgiveness both of God, and him, or any other whom
I have offended, and confess I have received a just admonition of
the Master and Seniors by setting my date to this writing. Circ.
1622. [Offley graduated B.A., 1624, and M.A., 1627, so presumably he
amended his ways.]
Whereas we whose names are underwritten, on the fourth of April
last, were guilty of grave irregularity and misbehaviour by
insulting the Vice-Master, the Dean, and other officers of the
College and thereby gave just offence to the Society, we do profess
ourselves heartily sorry for the same and acknowledge the lenity of
the Master and Dean in suffering us to return so soon from
rustication. And we do hereby engage to be strictly observant of our
duty for the future and take this as our first admonition in order
to expulsion. James Bensley, John Ambler. 29 May, 1754. [Bensley
graduated in due course and was elected to a fellowship: Ambler did
not graduate.]
Ordered that ..., for irregular attendance at lectures and neglect
of impositions, be admonished a second time previous to rustication
or expulsion. 29 May, 1844.
Temporary or permanent removal from the College were penalties
reserved for the gravest offences. They are still recognized as
possible punishments. The fact that there are but few records of the
infliction of these extreme penalties indicates how easily discipline
has always been maintained.
My readers may well think that the results of these notes are somewhat
scanty, but if that nation is happy which has no history, surely
universities and colleges are to be congratulated whose records of
punishment are so few. To sum up the matter, the general effect left
on my mind is that most of the common offences were due only to
youthful exuberance of spirits and not to deliberate mischief making;
and that the rules and sanctions, judged by the standard of their
time, have been neither harsh nor unreasonable, and have usually been
approved by public opinion in the University.
CHAPTER XIII.
NEWTON'S _PRINCIPIA_.
Newton's _Principia_ is one of the few scientific books which has
sensibly affected the methods of scientific research and the ideas of
men about the universe. It is on this aspect of the subject I propose,
in this paper, to make a few remarks. The work itself is a classic in
the history of mathematics: the exposition of the subject, the
enunciation of the principle of prime and ultimate ratios, the
creation of mechanics as a science resting on experiments, and the
theory of universal gravitation with concrete applications to the
solar system, make it a masterpiece. Here I avoid all technicalities,
and confine myself to a general description of its genesis and
contents and the reason why its publication affected scientific
thought and methods.
Newton's exposition arose from an investigation of the cause of the
motion of the planets round the sun, and this in due course led to the
enunciation and establishment of the Newtonian theory of attraction.
The origin of this theory has been often told, but will bear
repetition. The fundamental idea occurred to Newton in 1665 or 1666,
shortly after he had taken his degree at Cambridge, when, as he wrote
later, "I was in the prime, of my age for invention, and minded
Mathematicks and Philosophy more than at any time since." His
reasoning was as follows. He knew that gravity extended to the highest
hills, he saw no reason why it should cease to act at greater heights,
accordingly he believed that it would be found in operation as far as
the moon, and he suspected that it might be the force which retained
that body in its path round the earth.
This hypothesis he verified thus. If a stone is allowed to fall near
the surface of the earth, the attraction of the earth causes it to
move through sixteen feet in one second: also Kepler's Laws, if
accurate and applicable, involve the conclusion that the attraction
of the earth on a distant body varies inversely as the square of its
distance from the earth. Now the radius of the earth and the distance
of the moon were known to Newton, and therefore, on this hypothesis,
he could find the magnitude of the earth's attraction on the moon.
Further, assuming that the moon moved in a circle, he could calculate
the force required to retain it in its orbit. At this time his
estimate of the radius of the earth was inaccurate, and, when he made
the calculation, he found that this force was rather greater than the
earth's attraction on the moon. The discrepancy did not shake his
faith in his theory, but he conjectured that the moon's motion was
also affected by other influences, such for example, as the effect of
a resisting medium which might itself be in motion as supposed by
Descartes in his hypothetical vortices.
In 1679 Newton knew with approximate correctness the value of the
radius of the earth. He repeated his calculations, and found the
results to be in accordance with his former hypothesis. He then
proceeded to the general theory of the motion of a particle under a
force directed to a fixed point, and showed that the vector to the
particle would sweep over equal areas in equal times. He also proved
that, if a particle describes an ellipse under a force directed to a
focus, the law must be that of the inverse square of the distance from
the focus, and conversely, that the orbit of a particle projected in
free space under the influence of such a force must be a conic. The
application to the solar system was obvious, since Kepler had shown
that the planets describe ellipses with the sun in one focus, and that
the vectors from the sun to them sweep over equal areas in equal
times. This investigation was made for his own satisfaction and was
not published at the time. In it he treated the solar bodies as if
they were particles, and he must have realized that the results could
be taken as being only approximately correct.
In 1684 the subject of the planetary orbits was discussed in London
by Halley, Hooke, and Wren. They were aware that, if Kepler's
conclusions were correct, the attraction of the sun or earth on a
distant external particle must vary inversely as the square of the
distance, but they could not determine the orbit of a particle
subjected to the action of a central force of this kind. It was
suggested that Newton might be able to assist them. Accordingly in
August, Halley went to Cambridge for a talk on the subject, and then
found that Newton had solved the problem some five years previously,
and that the path was necessarily a conic. At Halley's request Newton
wrote out the substance of his argument, and sent it to London.
Halley at once realized the importance of the communication, and later
in the autumn returned to Cambridge to urge Newton to prosecute the
theory further. He found that Newton had already done something in the
matter, the results being contained in a manuscript which he saw.
Probably this reference is to the holograph manuscript, still
preserved in the University Library at Cambridge, of Newton's lectures
in the Michaelmas Term, which served as the basis of his memoir sent
to the Royal Society a few months later. The great value of these
investigations was recognized, and Newton was persuaded to attack the
more general problem. His results are given in the _Principia_.
As yet Newton had dealt with the problem as if the sun and the planets
might be regarded as heavy masses concentrated at their centres.
Clearly at the best this was only an approximation, though considering
the enormous distances involved it was not unreasonable. In January or
February, 1685, he considered the question of the attraction of bodies
of finite size, and found, to his surprise and gratification, that
a sphere or spherical shell attracts an external particle as if
condensed into a heavy mass at its centre. Hence the results he had
already proved for the relative motion of particles were true for the
solar system, save for small errors due partly to the fact that the
bodies were not perfectly spherical and partly to disturbances caused
by the planets attracting one another. It was no longer a question of
rough approximation: the problem was reducible to mathematical
analysis, subject to the introduction of minute corrections, which,
given the necessary observations, could be calculated very closely.
This was a new discovery of first-rate importance, and initiated the
modern theory of attractions.
The first book of the _Principia_ was finished before the summer of
1685. It deals with the motion of particles or bodies in free space
either in known orbits or under the action of known forces. In it
the law of attraction is generalized into the statement that every
particle of matter attracts every other particle with a force which
varies directly as the product of their masses and inversely as the
square of the distance between them. Thus gravitation was brought into
the domain of Science.
The second book was completed by the summer of 1686. It treats of
motion in a resisting medium and of various problems connected with
waves. At the end of it, it is shown that the Cartesian theory of
vortices is inconsistent with the laws of motion, and necessarily
leads to incorrect results. This book opened another world to the
application of mathematics and, in effect, created the science of
hydrodynamics.
The third book was finished in March 1687. In this, the theorems
previously established are applied to the chief phenomena of the
universe, and briefly we may say that all the facts then known about
the solar system and, in particular, the motion of the moon with its
various inequalities, the figure of the earth, and the phenomena of
the tides, were shown to be in accord with the theory. Much of the
material for these calculations was collected by Flamsteed and Halley.
The _Principia_, as I have said, is a classic. Like other books to
which that compliment is paid, it is rarely read: indeed, I doubt
whether there are a dozen men in Cambridge who have glanced all
through it, even in a cursory manner. When I was an undergraduate the
course for the Tripos involved five sections (1, 2, 3, 9, and 11) of
the first book, but now, probably with good reason, even this slight
acquaintance with the work is no longer required, and to-day the
character of these investigations is unfamiliar to most
mathematicians, while the fact that it is written in Latin tends to
diminish the number of its readers. I will, then, with your
permission, describe briefly its frame-work.
First, however, let me remark on how different was the knowledge of
mathematics, even among experts, at the time it was written from
that current to-day. In the geometry of the circle and conics
mathematicians were familiar with the methods of Greek science, and in
their application Newton was unrivalled among his contemporaries, but
outside geometry methods of investigation were far to seek. Analysis
had been but little developed; algebraic notation had only recently
taken definite form; trigonometry was still used mainly as an adjunct
to astronomy; analytical geometry had been invented by Descartes, but
no text-books on it of modern type were available; while nothing about
the calculus had been published. Mechanics, however, had recently been
treated as a science--statics by Stevinus and dynamics by Galileo--and
this paved the way for Newton's investigations. In particular,
Galileo had established principles which foreshadowed the first two
laws of motion, and had deduced formulae in linear motion like
_v² = 2fs_, _s = ½ft²_, and in circular motion like _f = v²/r_.
Newton prefaced the _Principia_ by explaining that the earliest
problems in natural philosophy which attract attention are connected
with the phenomena of motion, and it was with motion that the book
dealt. To discuss motion effectively, it was necessary to give
precision to the language used, and accordingly he propounded
definitions of mass, momentum, inertia, and so on, which have settled
the language of the subject. He next enunciated his three well-known
laws of motion, and described the experiments on which he based them.
He followed this up by deducing rules for the composition and
resolution of forces, and discussed relative motion.
This preliminary matter is followed by the first book, concerned with
the motion of bodies in an unresisting medium. It is divided into
fourteen sections containing ninety-eight propositions with various
interpolated lemmas, corollaries, and scholia.
The first section is on the method of prime and ultimate ratios, by
the use of which Newton was able, in effect, to integrate. He applied
this to the curvature and the areas of curves, and proved that, at
the very beginning of the motion of a body from rest under any force,
the space described is proportional to the force and the square of the
time.
The second section is concerned with the motion of a particle under a
central force. It contains the well-known propositions that if the
force is central the area swept out by the vector to the centre is
proportional to the time, and conversely that if such area is
proportional to the time the particle is acted on by a central force.
Newton further discussed particular cases of circular, elliptic, and
spiral motion. In the third section he dealt with motion in a conic
under a central force to the focus, showed that in this case the force
must vary inversely as the square of the distance, and conversely that
if a particle be projected from any point in any direction with any
velocity under such a force it must describe a conic about the centre
of force as a focus, and that in such elliptic orbits the periodic
times are in the sesquiplicate ratio of the major axes of the
ellipses. He also explained how to treat the problem if disturbing
forces are introduced. These two sections solved the problem of
planetary motion if the planets could be treated as particles and did
not disturb one another's motions.
The fourth and fifth sections are given up to the proof of certain
geometrical propositions in conics required for subsequent
discussions: in particular the construction of a conic when a focus
and three other conditions or when five points on it or five tangents
to it are given.
In the sixth section Newton returned to the problem of the motion of a
particle in an ellipse under a central force to a focus, and discussed
how to determine the position of the particle at any given time.
(Kepler's Problem.)
The seventh and eighth sections are devoted to the motion of a
particle under a central force which is any function of the distance.
The geometrical treatment of these problems is ingenious, but
necessarily more involved than when modern analysis is used.
In the ninth section Newton dealt with the motion of particles in
orbits which are revolving about the centre of force, and on the
motion of the apses of such orbits: this introduced the theory of
disturbing forces. The tenth section is concerned with constrained
motion, and particularly with the motion of pendulums. The eleventh
section deals with the motion of particles under their mutual
attractions and incidentally with the problem of three bodies. These
three sections afford a notable illustration of Newton's analytical
powers.
The twelfth and thirteenth sections deal with the attraction under
various laws of force of spherical bodies, circular laminae, and
solids of revolution. These sections brought the problem of the solar
system, consisting of solid bodies of finite size and approximately
spherical in form, into the domain of mathematics, and led up to the
generalization that all particles of matter attract one another with a
force proportional to the product of their masses and inversely
proportional to the square of the distance between them, from which
law it would seem that all the known phenomena of the motions of the
solar system can be deduced.
The fourteenth section is concerned with the motion of minute
corpuscles, with applications to the corpuscular theory of light.
The second book is devoted to the discussion of the motion of bodies
in resisting mediums: there are fifty-three propositions besides
lemmas, scholia, etc.
In the first section, Newton considered the motion of a particle or
sphere moving in a medium whose resistance varies as the velocity of
the particle: in the second section the resistance is assumed to vary
as the square of the velocity: and in the third section the resistance
is supposed to consist of two terms, one varying as the velocity and
the other as the square of the velocity. The fourth section is on
spiral motion caused by resistance of the medium.
The fifth section deals with the density and pressure of liquids and
gases at rest (Hydrostatics).
The sixth section treats of the motion of pendulums in a resisting
medium; and the seventh section is concerned with the motion of
fluids, and the resistance they offer to the motion of projectiles.
The latter section contains the celebrated statement of the form of
the solid of least resistance, whose demonstration proved a puzzle to
mathematicians until the invention of the calculus of variations.
Newton's solution is in the Portsmouth papers, and elsewhere I have
published it: it involves the use of fluxions, and it is probable that
it was his failure to translate this demonstration into geometrical
language that led him to give the result without a proof.
The eighth section deals with the motion of waves with applications to
the theory of sound and the undulatory theory of light; and the ninth
section deals with vortices; it is here shown that the theory of
vortices suggested by Descartes to explain the motion of the solar
system is untenable.
This book created the theory of hydrodynamics. Much of it is
incomplete, but it is astonishing that Newton proved as much as he
did; of course to-day no one would suggest that the best way of
attacking these problems is by Newtonian geometrical methods.
The third book contains the practical application of the propositions
in the two earlier books to the solar system. I need not describe this
in detail. In order to justify this application, Newton commenced by
laying down four rules which have since been accepted as binding in
scientific investigations. These, as given in the third edition, are
to the following effect: (1) We are not to assume more causes than are
sufficient and necessary for the explanation of observed facts.
(2) Hence, as far as possible, similar effects must be assigned to the
same cause; for instance, the fall of stones in Europe and America.
(3) Properties common to all bodies within reach of our experiments
are to be assumed as pertaining to all bodies; for instance,
extension. (4) Propositions in science obtained by a wide induction
are to be regarded as exactly or approximately true, until phenomena
or experiments show that they may be corrected or are liable to
exceptions. The substance of these rules is now accepted as the basis
of scientific investigation. Their formal enunciation here serves as a
landmark in the history of thought.
As soon as the Copernican view of the solar system was accepted, it
was natural for men to seek to explain the reason why the planets
moved as they did. Descartes, in 1644, had suggested that the
explanation might be found in the existence of vortices in space. This
conjecture, although based on arbitrary assumptions, and in fact
untenable, played an important part in the history of the subject,
for it accustomed men to think that planetary phenomena might be
explicable by the same laws as are found to be true on the earth.
That this was so was established by Newton in his _Principia_, where
all the motions of the solar system were made to depend on one
assumption as to the law of attraction. The question whether this law
could itself be deduced from some more fundamental assumption was
raised by Newton, but he could not devise a satisfactory hypothesis.
It has been discussed again and again since his time, and the problem
is still unsolved.
Newton's conclusions were immediately accepted in Britain, and very
rapidly by the leading mathematicians in Europe: indeed Huygens came
expressly from Holland in order to make the personal acquaintance of
a writer whose work promised to revolutionize the history of science.
The refutation of the Cartesian hypothesis ran, however, counter to
the sentiments and wishes of a certain number of philosophers, and
some few years elapsed before the truth of the gravitation theory was
universally admitted, but it would be ungracious to dwell further on
this. In Britain the work exercised a profound influence in philosophy
as well as in science, and educated men of all schools of thought
acquainted themselves with the general line of Newton's reasoning and
his deductions.
That men of science and philosophers should have approved Newton's
theory is not surprising, but it is somewhat curious that it excited
so little opposition among theologians. Galileo's discoveries of
hills, vales, and (supposed) seas on the moon and planets had already
suggested that life might exist there, and in the popular (but
illogical) view this involved the idea of the existence of beings with
spiritual and intellectual faculties not unlike those of men. Newton's
results seemed to show that there was nothing in the nature of things
to differentiate the earth from the other planets, and therefore
considerably strengthened the view that life might be found on them.
It might well be asked whether such life, and indeed whether the
mechanism of the solar system as expounded by Newton, was in
accordance with Scripture. That these difficulties were not pressed
against Newton's conclusions is, I think, attributable to the fact
that his theory was explicitly concerned only with non-organic matter.
His own opinion was that the extension of the reign of law was an
additional argument in favour of a divine creation: this view, set out
at the end of the _Principia_ and in his five letters to Bentley in
1692-93, was generally accepted by the leaders of religious thought in
Britain.
Lagrange more than once remarked that Newton was not only the greatest
mathematician of former days, but the most fortunate, since, as there
is but one universe, it can happen to but one man in the world's
history to be the interpreter of its laws. It is true that Newton
applied his theory only to the solar system for which alone he had the
necessary data, but after the publication of the _Principia_, no one
doubted that gravity extended to the most distant regions of space.
The work of Sir William Herschel and that of all later astronomers on
binary and other systems rests on this hypothesis.
The influence of the _Principia_ on dynamical astronomy has been
permanent. It is not too much to say that when it was published, the
theory, as there set out, had outstripped observation, but during the
succeeding century large numbers of new facts were collected, and
applications of the theory to new problems were made, notably by
Clairaut, Euler, and Lagrange. All these researches tended to confirm
it.
The demonstrations in the _Principia_ are expressed in the language of
classical geometry, and, though unnecessarily concise and difficult,
their correctness is unimpeachable. That Newton could carry his
calculations so far with the limited mathematics then at his command
is not the least wonderful part of the performance, but it is the
prerogative of genius to get great results with but scanty equipment.
Newton's methods, which even in the seventeenth century were archaic,
became in time quite out of date. This reason, the growth of the
subject, and the development of analysis made it desirable to expound
dynamical astronomy afresh. Towards the end of the eighteenth century
the task was undertaken by Laplace in his _Mécanique Céleste_. This is
far more than the translation of the _Principia_ into the language of
modern analysis, for it greatly extends the theory of some branches of
the subject which had been left incomplete by Newton, either on
account of his not having the requisite analysis at his command or
because the necessary facts were not available. Laplace acknowledged
his debt to Newton, and expressed his deliberate opinion that the
_Principia_ was pre-eminent over every previous production of human
genius--"so near the gods, man cannot nearer go." A century later a
fresh exposition of the subject embodying the discoveries of the
nineteenth century was given by F.F. Tisserand in his _Mécanique
Céleste_; this presents the subject in its modern form.
Newton had applied his theory to the solar system as it existed, and
had not investigated its origin. We owe to Laplace the enunciation of
a hypothesis as to its evolution. According to this conjecture, the
solar system originated in a quantity of incandescent gas rotating
round an axis through its centre of mass. Laplace assumed that as this
gas cooled, it would contract, and that successive rings would break
off from its outer edge; these rings in their turn would cool, and
finally condense into the planets with their satellites; while the sun
represents the central core which would be left. Recent investigations
show that this cannot be taken as correct without numerous
modifications. Moreover every extension of our knowledge requires the
introduction of alterations in the hypothesis, and this clearly
suggests that the conjecture is untenable. It played, however, a
useful part in its day, as suggesting a common origin for all members
of the system. Perhaps I ought to add that a nebular origin had been
previously outlined by Kant, who had also suggested meteoric
aggregations and tidal friction as agents concerned, but these were
little more than vague conjectures.
The _Principia_ convinced its readers that the laws of mechanics,
discovered by experiment on the earth, were operative throughout the
solar system. It was reserved for the nineteenth century to extend the
reign of law to other celestial phenomena. Newton and his successors
had proved that the law of gravity extends through all parts of space
where observations are possible. That the sun, stars, and planets are
constituted of similar materials was generally believed; and this has
now been confirmed by the use of the spectroscope which has enabled us
to calculate the temperature of gaseous stars, and specify the
chemical elements comprised in them. Thus the composition of
far-distant suns has been reduced to problems to be settled in our
laboratories. The scientific world, however, in admitting the validity
of the theory of universal gravity had implicitly accepted the
principle that the reign of law, as investigated on the earth, extends
throughout the universe. Thus the daring which permits us, living on a
medium-sized planet attached to one of the smaller suns, to analyse
the universe is, I venture to say, the direct outcome of the genius of
Newton as displayed in his _Principia_.
CHAPTER XIV.
ISAAC NEWTON ON UNIVERSITY STUDIES.
Among the Portsmouth papers in the University Library at Cambridge[33]
is a memorandum by Isaac Newton, drawn up, I conjecture, towards the
close of the seventeenth century, on the organization of the studies
and on the discipline of the University.
Conditions then differed so widely from those now in force that the
value of the memorandum is only historical, but notwithstanding this,
its interest is considerable. I have no reason to suppose that it was
formally brought before the regent or the non-regent house, and
possibly the plan never got beyond discussion by a few friends. I have
modernized the spelling, made the use of capitals uniform, allowed
myself to break paragraphs, and sometimes inserted punctuation or
altered it--otherwise the paper is as originally written. I give it
without further comment.
_Newton's Memorandum._
"Undergraduates to be instructed by a Tutor, a Humanity Lecturer, a
Greek Lecturer, a Philosophy Lecturer, and a Mathematic Lecturer.
"The Tutor to read logic, ethics, the globes and principles of
geography and chronology in order to understand history, unless the
Lecturers have time for any of these things.
"The Humanity and Greek Lecturers to set tasks in Latin and Greek
authors once a day to the first year, and once a week to the rest; and
to examine diligently and instruct briefly; and to punish by exercises
such faults as concern lectures; and to appoint the reading of the
best historians.
"The Philosophy Lecturer to read first of things introductory to
natural philosophy--time, space, body, place, motion and its laws,
force, mechanical powers, gravity and its laws, hydrostatics,
projectiles solid and fluid, circular motions and the forces
relating to them. And then to read natural philosophy, beginning with
the general system of the world, and thence proceeding to the
particular constitution of this earth and the things therein--meteors,
elements, minerals, vegetables, animals, and ending with anatomy if he
have skill therein. Also to examine in logic and ethics.
"The Mathematic Lecturer to read first some easy and useful practical
hings; then Euclid, spherics, the projections of the sphere, the
construction of maps, trigonometry, astronomy, optics, music, algebra,
etc. Also to examine and (if the Tutor be deficient) to instruct in
the principles of chronology and geography.
"Several sciences which depend not on one another are all learnt in
less time together than successively, the mind being diverted and
recreated by the variety, and put more upon the stretch. And
therefore divers of these Lecturers may proceed together: suppose the
Tutor's [lectures] after morning chapel, the Greek or Philosophy
Lecturer's two hours after, and the Humanity and Mathematic
[Lecturers'] in the afternoon. The Tutor to accompany his pupils to
the philosophy and mathematic lectures, and to examine them the next
morning both in those lectures and in his own, and make them
understand where they hesitate. These two Lecturers to read five days
in the week and with the other two [Lecturers] to examine the sixth.
Each Lecturer to read the same day successively to two or three years
[_i.e._, to Freshmen, Junior Sophs, or Senior Sophs as the case may
be] under [their] several Tutors. Their lectures to begin with [the]
Michaelmas Term and continue till the Commencement [_i.e._ the end of
the Easter Term]: the Tutors to begin the Commencement before. The
Greek and Humanity Lecturers to set bigger tasks in the vacations than
in the reading-time, proportionally to the spare hours of the
students.
"A Monitor to note those who miss lectures, and give their names to
the Humanity Lecturer, who shall punish them, not by pecuniary mulcts,
but by tasks [, such as] by making verses, themes, epistles, or
getting anything without book. All pecuniary mulcts of Undergraduates
to be abolished; and exercises, admonitions, recantations, and
expulsions (according to the nature of the crime) to succeed in their
room.
"In the Long Vacation, between the Commencement and Michaelmas, the
Tutor shall take care that his Pupils read over all the last year's
lessons again by themselves, and at the end of the vacation they shall
be examined again, and those, who are at any time found not fit to go
on, turned down to the lectures of the year below, that they do not
retard the Lecturer and be an ill example to others.
"The Lecturers to be chosen every three years, and the elections after
the first institution to be on this manner. All those who have at any
time been Lecturers shall choose four out of their number, one for
each office, and the Master and Seniors of the College shall choose
other four who have not yet executed the office, and those eight with
the Master shall, by balancing, choose four out their number. [There
shall be] no regard to seniority or anything but merit. The Lecturers
to choose yearly a Public Tutor, and to reprehend or displace him if
there be reason. This Tutor without a new election to take none but
those admitted in his year of office until their course of lectures be
gone through. No Private Tutor to take two years together. All sizars,
poor scholars, and scholars of the House to be under Public Tutors,
except Westminster scholars of Trinity College when the Tutor is of
another school.
"For encouraging able and fit men to accept of the Readers' places,
their fellowships during their office shall be doubled by the
addition of four other fellowships kept vacant for the purpose, one,
for each, unless some other competent provision be made for any of
them. And because the Philosophy and Mathematic Lecturers' office is
laborious, for encouraging them to diligence none shall be compelled
to come to their lectures, but all that will be auditors shall offer
each of them a quarterly gratuity; suppose of 10s. the sizar, 12s. or
15s. the pensioner, and 20s. or 25s. the fellow-commoner. And to
encourage auditors those shall be preferred to scholarships and
fellowships which are best skilled in all sciences, _caeteris
paribus_, and shall have seniority of those that come not to lectures.
This institution to begin in the greater colleges, and be carried on
in the rest as men qualified and revenues can be had. In smaller
colleges the Mathematic Lecturer may be omitted, and only a power
granted the College of instituting one when they can. Also the Greek
Lecturer's office may be supplied by the Humanity Lecturer when it
shall be thought fit. A gratuity to be given by all the first year to
the Greek and Humanity Lecturers.
"For securing the Tutor and making his office desirable by fit
persons, every student at his admission to deposit caution money in
the hands of the bursar of the College; suppose £10 or £12 the sizar,
£16 or £20 the pensioner, and £30 or £40 the fellow-commoner. And in
case any pupil at the end of any quarter be in his Tutor's debt, and
do not discharge it within six weeks after his receipt of the quarter
bill, the Bursar to discharge it, and return back the residue upon
demand, and the Tutor forthwith upon pain of forfeiting his office, to
send home the pupil. Yet may the pupil be received again with a new
supply of money. This institution to be universal. The Master and
Seniors to regulate the expenses of all under tuition by certain
limits common to them all, and the Senior Dean to read over and sign
all their quarter bills. Extravagant pupils, after one admonition,
to be sent away.
"Fellow-commoners to perform all exercises in their courses, and to be
equally subject to their Tutors and Governors with other scholars and
alike punishable by exercises, and those who are resty or idle to be
sent away lest they spoil others by their bad example. They shall read
geography, chronology, and mathematics the first year.
"All students who will be admitted to lectures in natural philosophy
to learn first geometry and mechanics. By mechanics I mean here the
demonstrative doctrine of forces and motions, including hydrostatics.
For without a judgment in these things a man can have none in
philosophy.
"Whenever the major part of the Mathematic Lecturers in the University
shall desire [it] a Master [shall be appointed] to teach
fellow-commoners and others arithmetic and designing. The University
shall allow him £10 yearly out of their Common Chest, and he shall
observe the orders of the Mathematic Lecturers and be placed or
displaced by the major part of them at pleasure.
"All graduates without exception found by the Proctors in taverns or
other drinking houses, unless with travellers at their inns, shall at
least have their names given in to the Vice-Chancellor, who shall
summon them to answer it before the next Consistory.
"The Deans to visit the chambers of all undergraduates once at least
every week, upon pain of forfeiting 10s. to the Lecturers for every
omission.
"Fasting nights have a shadow of religion without any substance. 'Tis
only supping more pleasantly out of the public hall. And this does
great mischief by sending young students to find suppers abroad, where
they get into company and grow debauched. Whether would it not be
better to license undergraduates to sup together in such places as the
Dean shall appoint, with a Monitor to note the names of the absent?
"All these lectures to consist in extemporary explications of books in
such an easy, short, and clear manner as may be most profitable to the
auditors. And if any Lecturer or other person shall compose any
treatise which shall be preferred and used by the major part of the
Mathematic or Philosophic Lecturers, the University shall give the
author either £20, or if those Lecturers request it, £30, £40 or £50,
out of their Common Chest.
"Commissioners to be appointed for some years to set on foot, inspect,
and amend the institution.
"No oaths of office to be imposed on the Lecturers. I do not know a
greater abuse of religion than that sort of oaths: they being harder
to be kept than the Jewish Law, so that yearly absolutions have been
instituted. The papists, who believe such absolutions, might be
excused for instituting such oaths, but we have no such doctrine, and
yet continue their practices. Admonitions and pecuniary mulcts for
neglect of duty are less cruel punishments than the consequence of
perjury, and may be as effectual."
[Footnote 33: Camb. Univ. Library, Newton MSS. section viii, No. 5.
Add. 4005/6, A.]
CHAPTER XV.
THE HISTORY OF THE MATHEMATICAL TRIPOS.
The Mathematical Tripos has played so prominent a part in the history
of education at Cambridge and of mathematics in England, that a sketch
of its development[34] may be interesting to general readers.
So far as mathematics is concerned the history of the University
before Newton may be summed up very briefly. The University was
founded towards the end of the twelfth century. Throughout the middle
ages, the instruction given to students was organized on lines similar
to those current at Paris and Oxford, and to qualify for a degree it
was necessary to perform various exercises, and especially to keep a
number of _acts_ or to oppose acts kept by other students. An act
consisted in effect of a debate in Latin, thrown, at any rate in
later times, into syllogistic form. It was commenced by one student,
the _respondent_, stating some proposition, often propounded in the
form of a thesis, which was attacked by an _opponent_ or _opponents_,
the discussion being controlled by a senior graduate. The teaching was
largely in the hands of young graduates--every master of arts being
compelled to reside and teach for at least one year--though no doubt
colleges and private hostels supplemented this instruction in the case
of their own students.
The reformation in England was largely the work of Cambridge divines,
and in the University the renaissance was warmly welcomed. In spite of
the disorder and confusion of the Tudor period, new studies and a
system of professional instruction were introduced. The earliest
lectureships created by the University seem to have been one in Latin
established in or before 1492 and one in mathematics established in or
before 1501: they mark the beginning of the system of teaching by
experts which has superseded the medieval system of compulsory
teaching by all regent masters. The fact that one of these
lectureships was in mathematics shows that as early as 1500 the
subject was regarded as important. Tunstall, subsequently the most
eminent English arithmetician of his time, migrated in 1496 from
Oxford to Cambridge, and most of the subsequent English
mathematicians of the Tudor period were at Cambridge; of these I may
mention Record (who migrated, probably about 1535, from Oxford), Dee,
Digges, Blundeville, Buckley, Billingsley, Hill, Bedwell, Hood,
Richard and John Harvey, Edward Wright, Briggs, and Oughtred. Under
the Elizabethan statutes of 1570, notwithstanding many disadvantages,
the mathematical school continued to grow. Horrox, Seth Ward, Foster,
Rooke, Gilbert Clerke, Pell, Wallis, Barrow, Dacres, and Morland may
be cited as prominent Cambridge mathematicians of the succeeding
century.
Newton's mathematical career dates from 1665; his reputation,
abilities, and influence attracted general attention to the subject.
He created a school of mathematics and mathematical physics, among the
earliest members of which I note the names of Laughton, Samuel Clarke,
Craig, Flamsteed, Whiston, Saunderson, Jurin, Taylor, Cotes, and
Robert Smith. Since then Cambridge has been regarded as, in a special
sense, the home of English mathematicians, and from 1706 onwards we
have fairly complete accounts of the course of reading and work of
mathematical students.
Until less than a century ago the form of the method of qualifying for
a degree remained substantially unaltered, but the subject-matter of
the discussions varied from time to time with the prevalent studies
of the place.
After the renaissance some of the statutable exercises were "huddled,"
that is, were reduced to a mere form. To huddle an act, the proctor
generally asked some question such as _Quid est nomen?_ to which the
answer usually expected was _Nescio_. In these exercises considerable
license was allowed, particularly if there were any play on the words
involved. For example, J. Brass, of Trinity, was accosted with the
question, _Quid est aes?_ to which he answered, _Nescio nisi finis
examinationis_. It should be added that retorts such as these were
only allowed in the pretence exercises, and a candidate who in the
actual examination was asked to give a definition of happiness and
replied, "An exemption from Payne"--that being the name of his
questioner--was plucked for want of discrimination in time and place.
In earlier years even the farce of huddling seems to have been
unnecessary, for it was said in 1675 that it was not uncommon for the
proctors to take "cautions for the performance of the statutable
exercises, and accept the forfeit of the money so deposited in lieu of
their performance."
In medieval times acts had been usually kept on some scholastic
question or on a proposition taken from the _Sentences_. About the
end of the fifteenth century religious questions, such as the
interpretation of biblical texts, began to be introduced. Some fifty
or sixty years later the favourite subjects were drawn either from
dogmatic theology or from philosophy. In the seventeenth century the
questions were usually philosophical, but in the eighteenth century,
under the influence of the Newtonian school, a large proportion of
them were mathematical.
Further details about these exercises and specimens of acts kept in
the eighteenth century are given in my _History of Mathematics at
Cambridge_. Here I will only say that they provided an admirable
training in the art of presenting an argument, and in dialectical
skill in attack and defence. The mental strain involved in keeping a
contested act was severe. De Morgan, describing his act kept in 1826,
wrote[35]:
I was badgered for two hours with arguments given and answered in
Latin--or what we call Latin--against Newton's first section,
Lagrange's derived functions, and Locke on innate principles. And
though I took off everything, and was pronounced by the moderator to
have disputed _magno honore_, I never had such a strain of thought
in my life. For the inferior opponents were made as sharp as their
betters by their tutors, who kept lists of queer objections drawn
from all quarters.
Had the language of the discussions been changed to English, as was
repeatedly urged from 1774 onwards, these exercises might have been
retained with advantage, but the barbarous Latin and the syllogistic
form in which they were carried on prejudiced their retention.
About 1830 a custom arose for the respondent and opponents to meet
previously and arrange their arguments together. The discussions then
became an elaborate farce, and were a mere public performance of what
had been already rehearsed. Accordingly the moderators of 1839 took
the responsibility of abandoning them. This action was singularly
high-handed, since a report of 30 May 1838, had recommended that they
should be continued, and there was no reason why they should not have
been reformed and retained as a useful feature in the scheme of study.
On the result of the acts, a list of those qualified to receive
degrees was drawn up. This list was not arranged strictly in order of
merit, because the proctors could insert names anywhere in it, but by
the beginning of the eighteenth century this power had become
restricted to the right reserved to the vice-chancellor, the senior
regent, and each proctor to place in the list one candidate anywhere
he liked--a right which continued to exist till 1828, though it was
not exercised after 1792. Except for the names of these "honorary
optimes," this final list was, until 1752, arranged in order of merit
into wranglers and senior optimes, junior optimes, and poll-men;
after 1752, the wranglers and senior optimes were placed in separate
classes. The bachelors on admission to their degrees took seniority
according to their order on this list. The title _wrangler_ is derived
from these contentious discussions; the title _optime_ from the
customary compliment given by the moderator to a successful disputant,
_Domine ..., optime disputasti_, or even _optime quidem disputasti_,
and the title of _poll-man_ from the description of this class as οἱ
πολλοί.
The final exercises for the bachelor of arts degree were never
huddled, and until 1839 were carried out strictly. University
officials were responsible for approving the subject-matter of these
acts. Stupid men offered some irrefutable truism, but the ambitious
student courted reputation by affirming some paradox. Probably all
honour men kept acts, but poll-men were deemed to comply with the
regulations by keeping opponencies. The proctors were responsible for
presiding at these acts, or seeing that competent graduates did so.
In and after 1649 two examiners were specially appointed for this
purpose. In 1680[36] these examiners were appointed by the senate with
the title of moderator, and with the joint stipend of four shillings
for everyone graduating as a bachelor of arts during their year of
office. In 1688 the joint stipend of the moderators was fixed at £40
a year. The moderators, like the proctors, were nominated by the
colleges in rotation.
From the earliest times the proctors had the power of questioning a
candidate at the end of a disputation, and probably all candidates for
a degree attended the public schools on certain days to give an
opportunity to the proctors (or any master who liked to take part in
the examination) to examine them[37], though the opportunity was not
always used. Such examinations were conducted in Latin, and originally
different candidates attended on different days. Soon after 1710[38]
the moderators or proctors began the custom of summoning on one day in
January all candidates whom they proposed to question, and conducting
the examination in English and in public: the examination did not last
more than one day, and was partly on philosophy and partly on
mathematics. It was from this examination that the Mathematical Tripos
developed.
This introduction of a regular oral examination seems to have been
mainly due to the fact that when, in 1710, George I gave the Ely
library to the University, it was decided to assign for its reception
the old senate-house--now the catalogue room in the library--and to
build a new room for the meetings of the senate. Pending the building
of the new senate-house the books were stored in the Schools, which
thus were rendered unavailable for keeping acts. In consequence of
this, considerable difficulty was found in arranging for all the
candidates to keep the full number of statutable exercises, and
obtaining opportunities to compare them one with another: hence the
introduction or extension of a supplementary oral examination. The
advantages of this examination as providing a ready means of testing
the knowledge and abilities of the candidates were so patent that it
was retained when the necessity for some system of the kind had passed
away, and finally it became systematized into an organized test to
which all questionists were subjected.
In 1731 the University raised the joint stipend of the moderators to
£60 "in consideration of their additional trouble in the Lent Term."
This would seem to indicate that the senate-house examination had then
taken formal shape, and perhaps that a definite scheme for its conduct
had become customary.
As long as the order of the list of those approved for degrees was
settled on the result of impressions derived from acts kept by the
different candidates at different times and on different subjects, it
was impossible to arrange the men in strict order of merit, nor was
much importance attached to the order. But, with the introduction of
an examination of all the candidates on one day, much closer attention
was paid to securing an accurate classification, and more confidence
felt in the published order. It seems to have been consequent on this
that in and after 1748 the final lists were regarded as authoritative
and important and that the names of the honorary optimes were
definitely indicated: the lists from this time appeared in the
_University Calendars_. The lists from 1748 to 1910, with the earlier
Ordines Senioritatis from 1499 to 1747, are printed in the _Historical
Register of the University_.
Of the detailed history of the examination until the middle of the
eighteenth century we know nothing. From 1750 onwards, however, we
have more definite accounts of it. At this time, it would seem that
all the men from each college were taken together as a class, and
questions passed down by the proctors or moderators till they were
answered: but the examination remained entirely oral, and technically
was regarded as subsidiary to the discussions which had been
previously held in the schools.
Each class contained men of very different abilities, and to meet
difficulties thus caused, a custom grew up by which every candidate
was liable to be taken aside to be questioned by any master of arts
who wished to do so, and this was regarded as an important part of the
examination. The examination now continued for two days and a half,
the subjects, as before, being mathematics and philosophy. At the
conclusion of the second day the moderators received the reports of
those masters of arts who had voluntarily taken part in the
examination, and provisionally settled the final list. The last
half-day was used in revising and rearranging the order of merit.
Richard Cumberland has left an account of the tests to which he was
subjected when he took his bachelor degree in 1751. Clearly the
disputations still played an important part, and it is difficult to
say what weight was attached to the subsequent senate-house
examination; his reference to it is only of a general character. After
saying that he kept two acts and two opponencies he continued[39]:
The last time I was called upon to keep an act in the schools I sent
in three questions to the Moderator, which he withstood as being all
mathematical, and required me to conform to the usage of proposing
one metaphysical question in the place of that, which I should think
fit to withdraw. This was ground I never liked to take, and I
appealed against his requisition: the act was accordingly put by
till the matter of right should be ascertained by the statutes of
the university, and in the result of that enquiry it was given for
me, and my question stood.... I yielded now to advice, and paid
attention to my health, till we were cited to the senate house to be
examined for our Bachelor's degree. It was hardly ever my lot during
that examination to enjoy any respite. I seemed an object singled
out as every man's mark, and was kept perpetually at the table under
the process of question and answer.
It was found possible by means of the new examination to differentiate
the better men more accurately than before; and accordingly, in 1753,
as above stated, the first class was subdivided into two, called
respectively wranglers and senior optimes, a division which is still
maintained.
The semi-official examination by masters of arts was regarded as the
more important part of the test, and the most eminent residents in the
University took part in it. Thus John Fenn, of Caius, 5th wrangler in
1761, wrote[40]:
On the following Monday, Tuesday, and Wednesday, we sat in the
Senate-house for public examination; during this time I was
officially examined by the Proctors and Moderators, and had the
honour of being taken out for examination by Mr Abbot, the
celebrated mathematical tutor of St John's College, by the eminent
professor of mathematics Mr Waring, of Magdalene, and by Mr Jebb of
Peterhouse, a man thoroughly versed in the academical studies.
This irregular examination by any master who chose to take part in it
constantly gave rise to accusations of partiality.
In 1763 the traditional rules for the conduct of the examination 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 the other candidates for honours, and the last two
classes consisted of poll-men only. Practically anyone placed in
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 _vivâ 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
Watson, of Trinity, claimed that this change was made by him when
acting as moderator in 1763. He said[41]:
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 that examination
was regarded as the most important honour open to undergraduates.
In 1768 Robert 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[42]. Additional prizes, awarded at the same time, and
associated with the name of Lord Rayleigh[43], were founded in 1909.
Until about 1770, the senate-house examination had been oral, but it
began now 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
interruptions 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 was given by Jebb[44]:
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.
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,
Rutherforth, 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 fluxional
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 till 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.
The "fathers" of the respective colleges, zealous for the credit of
the societies, of which they are the guardians, are incessantly
employed in examining 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 presence
of the vice-chancellor, and of the assembled university.