CAMBRIDGE.
Universal Language — Purchase Lacroix’s Quarto Work on the Integral
Calculus — Disappointment on getting no explanation of my Mathematical
Difficulties — Origin of the Analytical Society — The Ghost Club
— Chess — Sixpenny Whist and Guinea Whist — Boating — Chemistry —
Elected Lucasian Professor of Mathematics in 1828.
My father, with a view of acquiring some information which might be of
use to me at Cambridge, had consulted a tutor of one of the colleges,
who was passing his long vacation at the neighbouring watering-place,
Teignmouth. He dined with us frequently. The advice of the Rev. Doctor
was quite sound, but very limited. It might be summed up in one short
sentence: “Advise your son not to purchase his wine in Cambridge.”
Previously to my entrance at Trinity College, Cambridge, I resided for
a time at Totnes, under the guidance of an Oxford tutor, who undertook
to superintend my classical studies only.
During my residence at this place I accidentally heard, for the first
time, of an idea of forming a universal language. I was much fascinated
by it, and, soon after, proceeded to write a kind of grammar, and then
to devise a dictionary. Some trace of the former, I think, I still
possess: but I was stopped in my idea of making a universal dictionary
by the apparent impossibility of arranging signs in any consecutive
{26} order, so as to find, as in a dictionary, the meaning of each
when wanted. It was only after I had been some time at Cambridge that
I became acquainted with the work of “Bishop Wilkins on Universal
Language.”
Being passionately fond of algebra, I had instructed myself by means
of Ward’s “Young Mathematician’s Guide,” which had casually fallen
into my hands at school. I now employed all my leisure in studying
such mathematical works as accident brought to my knowledge. Amongst
these were Humphrey Ditton’s “Fluxions,” of which I could make nothing;
Madame Agnesi’s “Analytical Institutions,” from which I acquired some
knowledge; Woodhouse’s “Principles of Analytical Calculation,” from
which I learned the notation of Leibnitz; and Lagrange’s “Théorie des
Fonctions.” I possessed also the Fluxions of Maclaurin and of Simpson.
Thus it happened that when I went to Cambridge I could work out such
questions as the very moderate amount of mathematics which I then
possessed admitted, with equal facility, in the dots of Newton, the
d’s of Leibnitz, or the dashes of Lagrange. I had, however, met with
many difficulties, and looked forward with intense delight to the
certainty of having them all removed on my arrival at Cambridge. I had
in my imagination formed a plan for the institution amongst my future
friends of a chess club, and also of another club for the discussion of
mathematical subjects.
〈PURCHASE THE WORK OF LACROIX.〉
In 1811, during the war, it was very difficult to procure foreign
books. I had heard of the great work of Lacroix, on the “Differential
and Integral Calculus,” which I longed to possess, and being
misinformed that its price was two guineas, I resolved to purchase it
in London on my passage to Cambridge. As soon as I arrived I went to
the French {27} bookseller, Dulau, and to my great surprise found that
the price of the book was seven guineas. After much thought I made
the costly purchase, went on immediately to Cambridge, saw my tutor,
Hudson, got lodgings, and then spent the greater part of the night in
turning over the pages of my newly-acquired purchase. After a few days,
I went to my public tutor Hudson, to ask the explanation of one of my
mathematical difficulties. He listened to my question, said it would
not be asked in the Senate House, and was of no sort of consequence,
and advised me to get up the earlier subjects of the university studies.
〈DIFFICULTIES NOT ANSWERED.〉
After some little while I went to ask the explanation of another
difficulty from one of the lecturers. He treated the question just
in the same way. I made a third effort to be enlightened about what
was really a doubtful question, and felt satisfied that the person I
addressed knew nothing of the matter, although he took some pains to
disguise his ignorance.
I thus acquired a distaste for the routine of the studies of the place,
and devoured the papers of Euler and other mathematicians, scattered
through innumerable volumes of the academies of Petersburgh, Berlin,
and Paris, which the libraries I had recourse to contained.
Under these circumstances it was not surprising that I should perceive
and be penetrated with the superior power of the notation of Leibnitz.
At an early period, probably at the commencement of the second year of
my residence at Cambridge, a friend of mine, Michael Slegg, of Trinity,
was taking wine with me, discussing mathematical subjects, to which he
also was enthusiastically attached. Hearing the chapel bell ring, he
took leave of me, promising to return for a cup of coffee. {28}
〈RESULT OF BIBLE SOCIETY.〉
At this period Cambridge was agitated by a fierce controversy.
Societies had been formed for printing and circulating the Bible.
One party proposed to circulate it with notes, in order to make it
intelligible; whilst the other scornfully rejected all explanations of
the word of God as profane attempts to mend that which was perfect.
The walls of the town were placarded with broadsides, and posters were
sent from house to house. One of the latter form of advertisement
was lying upon my table when Slegg left me. Taking up the paper, and
looking through it, I thought it, from its exaggerated tone, a good
subject for a parody.
I then drew up the sketch of a society to be instituted for translating
the small work of Lacroix on the Differential and Integral Lacroix. It
proposed that we should have periodical meetings for the propagation of
d’s; and consigned to perdition all who supported the heresy of dots.
It maintained that the work of Lacroix was so perfect that any comment
was unnecessary.
On Slegg’s return from chapel I put the parody into his hands. My
friend enjoyed the joke heartily, and at parting asked my permission to
show the parody to a mathematical friend of his, Mr. Bromhead.[4]
[4] Afterwards Sir Edward Ffrench Bromhead, Bart., the author of
an interesting paper in the Transactions of the Royal Society.
The next day Slegg called on me, and said that he had put the joke into
the hand of his friend, who, after laughing heartily, remarked that it
was too good a joke to be lost, and proposed seriously that we should
form a society for the cultivation of mathematics.
〈ANALYTICAL SOCIETY.〉
The next day Bromhead called on me. We talked the subject over, and
agreed to hold a meeting at his lodgings {29} for the purpose of
forming a society for the promotion of analysis.
At that meeting, besides the projectors, there were present Herschel,
Peacock, D’Arblay,[5] Ryan,[6] Robinson,[7] Frederick Maule,[8] and
several others. We constituted ourselves “The Analytical Society;”
hired a meeting-room, open daily; held meetings, read papers, and
discussed them. Of course we were much ridiculed by the Dons; and, not
being put down, it was darkly hinted that we were young infidels, and
that no good would come of us.
In the meantime we quietly pursued our course, and at last resolved to
publish a volume of our Transactions. Owing to the illness of one of
the number, and to various other circumstances, the volume which was
published was entirely contributed by Herschel and myself.
At last our work was printed, and it became necessary to decide upon
a title. Recalling the slight imputation which had been made upon our
faith, I suggested that the most appropriate title would be—
The Principles of pure D-ism in opposition to the Dot-age of the
University.[9]
[5] The only son of Madame D’Arblay.
[6] Now the Right Honourable Sir Edward Ryan.
[7] The Rev. Dr. Robinson, Master of the Temple.
[8] A younger brother of the late Mr. Justice Maule.
[9] Leibnitz indicated fluxions by a _d_, Newton by a dot.
〈ELECTED LUCASIAN PROFESSOR.〉
In thus reviving this wicked pun, I ought at the same time to record
an instance of forgiveness unparalleled in history. Fourteen years
after, being then at Rome, I accidentally read in Galignani’s newspaper
the following paragraph, dated Cambridge:—“Yesterday the bells of St.
Mary rang on the election of Mr. Babbage as Lucasian Professor of
Mathematics.” {30}
If this event had happened during the lifetime of my father, it would
have been most gratifying to myself, because, whilst it would have
given him much pleasure, it would then also have afforded intense
delight to my mother.
I concluded that the next post would bring me the official confirmation
of this report, and after some consideration I sketched the draft of a
letter, in which I proposed to thank the University sincerely for the
honour they had done me, but to decline it.
This sketch of a letter was hardly dry when two of my intimate
friends, the Rev. Mr. Lunn and Mr. Beilby Thompson,[10] who resided
close to me in the Piazza del Populo, came over to congratulate me on
the appointment. I showed them my proposed reply, against which they
earnestly protested. Their first, and as they believed their strongest,
reason was that it would give so much pleasure to my mother. To this
I answered that my mother’s opinion of her son had been confirmed by
the reception he had met with in every foreign country he had visited,
and that this, in her estimation, would add but little to it. To their
next argument I had no satisfactory answer. It was that this election
could not have occurred unless some friends of mine in England had
taken active measures to promote it; that some of these might have been
personal friends, but that many others might have exerted themselves
entirely upon principle, and that it would be harsh to disappoint such
friends, and reject such a compliment.
[10] Afterwards Lord Wenlock.
My own feelings were of a mixed nature. I saw the vast field that
the Difference Engine had opened out; for, before I left England in
the previous year, I had extended its mechanism to the tabulation of
functions having no constant {31} difference, and more particularly
I had arrived at the knowledge of the entire command it would have
over the computation of the most important classes of tables, those
of astronomy and of navigation. I was also most anxious to give my
whole time to the completion of the mechanism of the Difference Engine
No. 1 which I had then in hand. Small as the admitted duties of the
Lucasian Chair were, I felt that they would absorb time which I thought
better devoted to the completion of the Difference Engine. If I had
then been aware that the lapse of a few years would have thrown upon
me the enormous labour which the Analytical Engine absorbed, no motive
short of absolute necessity would have induced me to accept any office
which might, in the slightest degree, withdraw my attention from its
contrivance.
The result of this consultation with my two friends was, that I
determined to accept the Chair of Newton, and to hold it for a few
years. In 1839 the demands of the Analytical Engine upon my attention
had become so incessant and so exhausting, that even the few duties
of the Lucasian Chair had a sensible effect in impairing my bodily
strength. I therefore sent in my resignation.
〈FIRST EXAMINATION.〉
In January, 1829, I visited Cambridge, to fulfil one of the first
duties of my new office, the examination for Dr. Smith’s prizes.
These two prizes, of twenty-five pounds each, exercise a very curious
and important influence. Usually three or four hundred young men are
examined previously to taking their degree. The University officers
examine and place them in the order of their mathematical merit. The
class called Wranglers is the highest; of these the first is called the
senior wrangler, the others the second and third, &c., wranglers. {32}
All the young men who have just taken their degree, whether with or
without honours, are qualified to compete for the Smith’s prizes by
sending in notice to the electors, who consist of the three Professors
of Geometry, Astronomy, and Physics, assisted occasionally by two
official electors, the Vice-Chancellor and the Master of Trinity
College. However, in point of fact, generally three, and rarely above
six young men compete.
〈COURT OF APPEAL.〉
It is manifest that the University officers, who examine several
hundred young men, cannot bestow the same minute attention upon
each as those who, at the utmost, only examine six. Nor is this of
any importance, except to the few first wranglers, who usually are
candidates for these prizes. The consequence is that the examiners
of the Smith’s prizes constitute, as it were, a court of appeal from
the decision of the University officers. The decision of the latter
is thus therefore, necessarily appealed against upon every occasion.
Perhaps in one out of five or six cases the second or third wrangler
obtains the first Smith’s prize. I may add that in the few cases known
to me previously to my becoming an examiner, the public opinion of
the University always approved those decisions, without implying any
censure on the officers of the University.
In forming my set of questions, I consulted the late Dean of Ely and
another friend, in order that I might not suddenly deviate too much
from the usual style of examinations.
After having examined the young men, I sat up the whole night,
carefully weighing the relative merits of their answers. I found, with
some mortification, that, according to my marks, the second wrangler
ought to have the first prize. I therefore put aside the papers until
the day before the decision. I then took an unmarked copy of my
questions, and put new {33} numbers for their respective values. After
very carefully going over the whole of the examination-papers again, I
arrived almost exactly at my former conclusion.
〈REMARKABLE AGREEMENT.〉
On our meeting at the Vice-Chancellor’s, that functionary asked me,
as the senior professor, what was my decision as to the two prizes. I
stated that the result of my examination obliged me to award the first
prize to the second wrangler. Professor Airy was then asked the same
question. He made the same reply. Professor Lax being then asked, said
he had arrived at the same conclusion as his two colleagues.
The Vice-Chancellor remarked that when we altered the arrangement of
the University Examiners, it was very satisfactory that we should be
unanimous. Professor Airy observed that this satisfaction was enhanced
by the fact of the remarkable difference in the tastes of the three
examiners.
The Vice-Chancellor, turning to me, asked whether it might be permitted
to inquire the numbers we had respectively assigned to each candidate.
I and my colleagues immediately mentioned our numbers, which Professor
Airy at once reduced to a common scale. On this it appeared that the
number of marks assigned to each by Professor Airy and myself very
nearly agreed, whilst that of Professor Lax differed but little.
On this occasion the first Smith’s prize was assigned to the second
wrangler, Mr. Cavendish, now Duke of Devonshire, the present Chancellor
of the University.
The result of the whole of my after-experience showed that amongst
the highest men the peculiar tastes of the examiners had no effect in
disturbing the proper decision.
I held the Chair of Newton for some few years, and still feel deeply
grateful for the honour the University conferred {34} upon me—the only
honour I ever received in my own country.[11]
[11] This professorship is not in the gift of the Government. The
electors are the masters of the various colleges. It was founded
in 1663 by Henry Lucas, M.P. for the University, and was endowed
by him with a small estate in Bedfordshire. During my tenure of
that office my net receipts were between 80 _l._ and 90 _l._ a
year. I am glad to find that the estate is now improved, and that
the University have added an annual salary to the Chair of Newton.
I must now return to my pursuits during my residence at Cambridge, the
account of which has been partially interrupted by the history of my
appointment to the Chair of Newton.
Whilst I was an undergraduate, I lived probably in a greater variety
of sets than any of my young companions. But my chief and choicest
consisted of some ten or a dozen friends who usually breakfasted with
me every Sunday after chapel; arriving at about nine, and remaining
to between twelve and one o’clock. We discussed all knowable and many
unknowable things.
〈GHOST CLUB—EXTRACTORS.〉
At one time we resolved ourselves into a Ghost Club, and proceeded to
collect evidence, and entered into a considerable correspondence upon
the subject. Some of this was both interesting and instructive.
At another time we resolved ourselves into a Club which we called The
Extractors. Its rules were as follows,—
1st. Every member shall communicate his address to the Secretary once
in six months.
2nd. If this communication is delayed beyond twelve months, it shall be
taken for granted that his relatives had shut him up as insane.
3rd. Every effort legal and illegal shall be made to get him out of the
madhouse. Hence the name of the club—The Extractors. {35}
4th. Every candidate for admission as a member shall produce six
certificates. Three that he is sane and three others that he is insane.
It has often occurred to me to inquire of my legal friends whether, if
the sanity of any member of the club had been questioned in after-life,
he would have adduced the fact of membership of the Club of Extractors
as an indication of sanity or of insanity.
〈SHYNESS—CHESS.〉
During the first part of my residence at Cambridge, I played at chess
very frequently, often with D’Arblay and with several other good
players. There was at that period a fellow-commoner at Trinity named
Brande, who devoted almost his whole time to the study of chess. I was
invited to meet him one evening at the rooms of a common friend for the
purpose of trying our strength.
On arriving at my friend’s rooms, I found a note informing me that he
had gone to Newmarket, and had left coffee and the chessmen for us. I
was myself tormented by great shyness, and my yet unseen adversary was,
I understood, equally diffident. I was sitting before the chess-board
when Brande entered. I rose, he advanced, sat down, and took a white
and a black pawn from the board, which he held, one in either hand. I
pointed with my finger to the left hand and won the move.
The game then commenced; it was rather a long one, and I won it: but
not a word was exchanged until the end: when Brande uttered the first
word. “Another?” To this I nodded assent.
How that game was decided I do not now remember; but the first sentence
pronounced by either of us, was a remark by Brande, that he had lost
the first game by a certain move of his white bishop. To this I
replied, that I thought he was {36} mistaken, and that the real cause
of his losing the game arose from the use I had made of my knight two
moves previously to his white bishop’s move.
We then immediately began to replace the men on the board in the
positions they occupied at that particular point of the game when the
white bishop’s move was made. Each took up any piece indiscriminately,
and placed it without hesitation on the exact square on which it had
stood. It then became apparent that the effective move to which I had
referred was that of my knight.
Brande, during his residence at Cambridge, studied chess regularly
several hours each day, and read almost every treatise on the subject.
After he left college he travelled abroad, took lessons from every
celebrated teacher, and played with all the most eminent players on the
Continent.
At intervals of three or four years I occasionally met him in London.
After the usual greeting he always proposed that we should play a game
of chess.
I found on these occasions, that if I played any of the ordinary
openings, such as are found in the books, I was sure to be beaten. The
only way in which I had a chance of winning, was by making early in
the game a move so bad that it had not been mentioned in any treatise.
Brande possessed, and had read, almost every book upon the subject.
〈SIXPENNY WHIST.〉
Another set which I frequently joined were addicted to sixpenny whist.
It consisted of Higman, afterwards Tutor of Trinity; Follet, afterwards
Attorney-General; of a learned and accomplished Dean still living, and
I have no doubt still playing an excellent rubber, and myself. We not
unfrequently sat from chapel-time in the evening until the sound {37}
of the morning chapel bell again called us to our religious duties.
I mixed occasionally with a different set of whist players at Jesus
College. They played high: guinea points, and five guineas on the
rubber. I was always a most welcome visitor, not from my skill at
the game; but because I never played more than shilling points and
five shillings on the rubber. Consequently my partner had what they
considered an advantage: namely, that of playing guinea points with one
of our adversaries and pound points with the other.
〈EXPEDITIONS TO THE FENS.〉
Totally different in character was another set in which I mixed. I was
very fond of boating, not of the manual labour of rowing, but the more
intellectual art of sailing. I kept a beautiful light, London-built
boat, and occasionally took long voyages down the river, beyond Ely
into the fens. To accomplish these trips, it was necessary to have two
or three strong fellows to row when the wind failed or was contrary.
These were useful friends upon my aquatic expeditions, but not being
of exactly the same calibre as my friends of the Ghost Club, were very
cruelly and disrespectfully called by them “my Tom fools.”
The plan of our voyage was thus:—I sent my servant to the apothecary
for a thing called an ægrotat, which I understood, for I never saw
one, meant a certificate that I was indisposed, and that it would be
injurious to my health to attend chapel, or hall, or lectures. This was
forwarded to the college authorities.
I also directed my servant to order the cook to send me a large
well-seasoned meat pie, a couple of fowls, &c. These were packed in a
hamper with three or four bottles of wine and one of noyeau. We sailed
when the wind was fair, and rowed when there was none. Whittlesea Mere
was a very {38} favourite resort for sailing, fishing, and shooting.
Sometimes we reached Lynn. After various adventures and five or six
days of hard exercise in the open air, we returned with our health more
renovated than if the best physician had prescribed for us.
* * * * *
〈CHEMISTRY.〉
During my residence at Cambridge, Smithson Tennant was the Professor
of Chemistry, and I attended his lectures. Having a spare room, I
turned it into a kind of laboratory, in which Herschel worked with me,
until he set up a rival one of his own. We both occasionally assisted
the Professor in preparing his experiments. The science of chemistry
had not then assumed the vast development it has now attained. I gave
up its practical pursuit soon after I resided in London, but I have
never regretted the time I bestowed upon it at the commencement of my
career. I had hoped to have long continued to enjoy the friendship of
my entertaining and valued instructor, and to have profited by his
introducing me to the science of the metropolis, but his tragical fate
deprived me of that advantage. Whilst riding with General Bulow across
a drawbridge at Boulogne, the bolt having been displaced, Smithson
Tennant was precipitated to the bottom, and killed on the spot. The
General, having an earlier warning, set spurs to his horse, and just
escaped a similar fate.
〈TRANSLATION OF LACROIX.〉
My views respecting the notation of Leibnitz now (1812) received
confirmation from an extensive course of reading. I became convinced
that the notation of fluxions must ultimately prove a strong impediment
to the progress of English science. But I knew, also, that it was
hopeless for any young and unknown author to attempt to introduce the
notation of Leibnitz into an elementary work. This opinion naturally
{39} suggested to me the idea of translating the smaller work of
Lacroix. It is possible, although I have no recollection of it, that
the same idea may have occurred to several of my colleagues of the
Analytical Society, but most of them were so occupied, first with their
degree, and then with their examination for fellowships, that no steps
were at that time taken by any of them on that subject.
Unencumbered by these distractions, I commenced the task, but at what
period of time I do not exactly recollect. I had finished a portion
of the translation, and laid it aside, when, some years afterwards,
Peacock called on me in Devonshire Street, and stated that both
Herschel and himself were convinced that the change from the dots to
the d’s would not be accomplished until some foreign work of eminence
should be translated into English. Peacock then proposed that I
should either finish the translation which I had commenced, or that
Herschel and himself should complete the remainder of my translation.
I suggested that we should toss up which alternative to take. It was
determined by lot that we should make a joint translation. Some months
after, the translation of the small work of Lacroix was published.
For several years after, the progress of the notation of Leibnitz at
Cambridge was slow. It is true that the tutors of the two largest
colleges had adopted it, but it was taught at none of the other
colleges.
〈COLLECTION OF EXAMPLES.〉
It is always difficult to think and reason in a new language, and
this difficulty discouraged all but men of energetic minds. I saw,
however, that, by making it their interest to do so, the change might
be accomplished. I therefore proposed to make a large collection of
examples of the differential and integral calculus, consisting merely
of the statement of each problem and its final solution. I foresaw
that if such a {40} publication existed, all those tutors who did not
approve of the change of the Newtonian notation would yet, in order to
save their own time and trouble, go to this collection of examples to
find problems to set to their pupils. After a short time the use of
the new signs would become familiar, and I anticipated their general
adoption at Cambridge as a matter of course.
I commenced by copying out a large portion of the work of Hirsch. I
then communicated to Peacock and Herschel my view, and proposed that
they should each contribute a portion.
Peacock considerably modified my plan by giving the process of solution
to a large number of the questions. Herschel prepared the questions
in finite differences, and I supplied the examples to the calculus of
functions. In a very few years the change was completely established;
and thus at last the English cultivators of mathematical science,
untrammelled by a limited and imperfect system of signs, entered on
equal terms into competition with their continental rivals.
{41}