Memoir of Augustus De Morgan

AUGUSTUS DE MOEGAN

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MEMOIR

OF

AUGUSTUS DE MOEGAN

BY HIS WIFE

SOPHIA ELIZABETH DE MORGAN

WITH SELECTIONS FROM HIS LETTERS

LONDON
LONGMANS, GKEEN, AND CO.

1882

All rights reserved

QA

PKEFACE.

I NEED hardly say that in the following pages I have not
attempted a scientific memoir. My object has been to
supply that part of my husband's life the material for
which would not be within the reach of another biographer.

The selection from his letters might have been much
larger, if I could in all cases have inserted those of his
correspondents. Without these many would have been
incomprehensible. As it is, I may have over-estimated the
attention which readers will be disposed to give to them.
My rule in choosing the letters has been to take those
which are most characteristic of the writer, and in this
way to give to readers already acquainted with him through
his writings a more familiar knowledge of him as a man.

His connection with University College, and the events
which led to his leaving it, are necessarily made promi-
nent. So long a time has elapsed since their occurrence,
and I have known so little during that time of the Institu-
tion, that I cannot even surmise how the present Council
would in like circumstances share the convictions or con-
firm the action of its predecessors. After the lapse of
sixteen years I trust that the narrative will provoke no
revival of the somewhat acrimonious controversy which
ensued. It might perha.ps have been in some ways

vi PREFACE.

better that Mr. De Morgan should have published a
fuller statement of his views at the time, and have thus
left less to be done by his biographer. But he had several
reasons for not doing this. He refrained partly from
reluctance to add to the censures which were being pro-
nounced on the College, perhaps too emphatically, even by
well-wishers, and re-echoed by its enemies with uncon-
cealed satisfaction ; partly by the feeling that he had
made no sacrifice of a pecuniary nature in resigning his
Professorship ; but, as I think, chiefly from weariness and
disappointment, and from a desire to have done with the
Institution as soon as possible. Nothing, not even a dis-
tinct recantation of the measure which made him leave,
would have induced him to resume his chair, for he would
have held such a recantation to be but another concession
to expediency in deference to the storm unexpectedly
raised.

Should any portion of what I have written appear un-
called for, it must be remembered that I could not touch my
husband's side of the question without placing the whole
before my readers. The insertion of the lengthy justifica-
tion of the Council by members of the Senate will, I
trust, exempt me from the charge of having suppressed
arguments on the other side.

SOPHIA ELIZABETH DE MORGAN.

Row,

, 18*2.

CONTENTS.

SECTION I.
FROM 1806 TO 1827.

PAGE

Place of Birth — Voyage to England — Family — Schools and School
Days — Early Religious Teaching — Trinity College, Cam-
bridge— Reading and Study — Mother's Anxiety — Teachers —
College Friends — Choice of Profession — Degree — Lincoln's
Inn ... 1-18

SECTION II.
FROM 1827 TO 1831.

William Frend — Religious Discussions — Stoke Newington — Can-
didature for Professorship — University in London — Its
Foundation — Its Principle — Opening of Classes — Introductory
Lecture — Disagreements between Professors and Council —
Paris — Colonel Briggs — East India Service — Dr. Briggs'
Ghost Story — Opening of Session — Differences renewed —
Letter of Remonstrance— Resignation of Chair . . 19-40

SECTION III.
FROM 1831 TO 1836.

Residence in Guilford Street — Astronomical Society — Efforts
to raise Astronomy— Baily— Herschel— Airy— De Morgan
elected Hon. Secretary—Astronomical Society's Charter-
Captain Smyth — Sir James South — Friendships in Astro-
nomical Society — Mr. Baily 's House— Sir James South's
Quarrels — Nautical Almanac — Standard Scale — ' Elements of
Arithmetic ' — Charles Butler— Archdeacon Thorp — Book-
collecting — Hachette — Amicable Assurance Company -
Troughton v. South— Challenges— Maps of the Stars— Return
to Mathematical Chair . • 41-74

a

Vlll CONTENTS.

SECTION IV.

PAGE

CORRESPONDENCE FROM 1831 TO 1836 . 75-84

SECTION V.
FROM 1836 TO 1846.

Death of his Sister — His Religious Feelings and Opinions — His
Mother's Anxieties — Church Bates — Marriage — Friends —
Lady Noel Byron — Mrs. Fry — Introductory Lecture — Uni-
versity of London — 'Theory of Probabilities' — 'Essay on
Probabilities '—Dickens' Works— Women's Rights—4 Philo-
sophers ' — Metaphysics — Lecturing — Distinguished Pupils —
Cram — Outbreak of Students — Testimonial — Jewish Pupils —
George Long — James Tate — * Northern Lights ' — Francis
Baily — The Cavendish Experiment — Blackheath — Death of
William Frend — Obituary Notice — Commission on Standard
Scale — Standard of Length — Henry Hallam — Birth of George
Campbell De Morgan — Dr. Whewell — Cambridge Tracts —
'Differential and Integral Calculus' finished — Limits and
Series— John Stuart Mill— Berkeley's Philosophy— Mill's
Writings — Comte's System — Birth of Edward Lindsey
De Morgan — Death of Francis Baily — His Epitaph — His
Bust — Richard Sheepshanks — Micrometer Observations —
Removal from Gower Street to Camden Street — Incapacity
of a Professor— Class taken by Mr. De Morgan— Students'
Gift— Malby's Globes— Mr. John Taylor's Astronomy and
Work on the Pyramid — Old Mathematical Society — Historical
Society of Science — Rev. Samuel Maitland — The Easter
Question— Lord Brougham— Discovery of Neptune— Recep-
tion of Discovery 85-138

SECTION VI.
CORRESPONDENCE FROM 1836 TO 1846 139-156

SECTION VII.
FROM 1846 TO 1855.

Formal Logic — Dr. Whewell — Cecil Monro's Remarks —
Rev. Dr. Logan— The Hamilton Controversy— Mr. Herbert

CONTENTS. ix

PAUK

Spencer — Berkeley's Metaphysics —Professor Boole — His
System of Logic — Psychology — Chief Baron Pollock — Intro-
ductory Lecture— Our Competitive Examination— Opinions
of Friends— Astronomical Society— Admiral Smyth— Presi-
dency— Royal Society — Acquaintance and Friends — Ladies'
College — Over-teaching — Sir Rowland Hill — Postage —
Museum Catalogue — Guglielmo Libri — Libri accused of
Theft— De Morgan's Advocacy— Death of Thomas Galloway
— Obituary Notice — Address on Negro Slavery — Cambridge
Examinations — Physiology — Vivisection — University College
— Dr. Peene's Legacy — Letter of Remonstrance to Council —
Our Eldest Child's Death— City of London School— Death of
Richard Sheepshanks— His Funeral— Anne Sheepshanks —
Memoir — Table-turning — Mr. Faraday's Lecture on Mental
Training — De Morgan's Criticism — Mr. Faraday's Indi-
cator 157-193

SECTION VIII.
CORRESPONDENCE FROM 1846 TO 1855 194-232

SECTION IX.
FROM 1856 TO 1865.

His Mother's Death— Her Sons— Accident to Shoulder— Decimal
Coinage — History of the Movement — Government Commis-
sions— Decimal Association — Deputation to Mr. Gladstone —
Deputation to Board of Trade — Debate on Question — Sum-
mary in ' Westminster Review ' — Articles in ' Companion to the
Almanac ' — Lecture on Coinage — Lord Overstone's Questions
— Replies — Death of Mr. William Brown — Memoir of Newton
— Brewster's Life of Newton— The Kaleidoscope— M. Biot—
Catherine Barton — Lord Halifax — Article for ' Companion to
Almanac* rejected— Savings Bank— Public Playgrounds —
Rev. David Laing— Letter of Charles Dickens— Removal to
Adelaide Road— Cab Drivers— Drinkwater Bethune— Ram-
chundra — Hindoo Algebra — Non-acceptance of LL.D.
Degree — International Statistical Congress — Retirement
from Astronomical Society— Farewell Letter— Death of Biot
—Foundation of Mathematical Society— Death of George
Campbell De Morgan ... . 233-286

SECTION X.
CORRESPONDENCE FROM 1856 TO 1866 287-335

X CONTENTS.

SECTION XI.

PAGE

FROM 1866 TO 1871.

University College— Chair of Mental Philosophy — Rev. J. Mar-
tineau — Unitarians on Council — Report of Senate — Requisi-
tion to Council — Appointment of Mr. Groom Robertson —
Letter of Resignation — Acceptance of Resignation — Statement
of Fifteen Professors to Proprietors — Annual Meeting —
De Morgan's Last Visit to College — Letters of Old Pupils —
H. C. Robinson— His Books— His Breakfasts— Death of
George Campbell De Morgan — Mathematical Society — Illness
and Removal to Merton Road — Latest Occupation and
Interests— Greek Testament — The Free Christian Union —
Christian Belief — Rationalism — Prayer — Death of Christiana
De Morgan— Last Hours— Death— Extract from Will . 336-368

SECTION XII.

CORRESPONDENCE FROM 1867 TO 1870 369-400

LIST OF WRITINGS 401

INDEX . .... 417

MEMOIR

OP

AUGUSTUS DB MORGAN.

SECTION I.

AUGUSTUS DE MORGAN was born in the year 1806 at 1806.
Madura, in the Madras Presidency. His father Lieu-
tenant-Colonel De Morgan had held appointments, some
of them staff situations, at several stations in India ; and
at the time of his fifth child's birth had chosen Madura
in preference to Yellore on account of its comparative
quietness. This choice was fortunate, for the battalion
of Colonel De Morgan's regiment commanded by Colonel
Fanshawe was at Yellore during the time of the mutiny
of the native troops ; and thus escaped the terrible out-
break in which several English officers lost their lives,
and Colonel Fanshawe was murdered. Even at the
quieter stations there was cause for alarm from the
general disaffection of the native troops, and my hus-
band's mother told how she, being then near her con-
finement, saw Colonel De Morgan, when the sentries
were changed, creep out of bed to listen to the Sepoys,
that he might learn if any plot were in agitation,
about which information might be given with the pass-
word.

When Augustus was seven months old his father and "Voyage to
mother came to England with three children, two
daughters and the infant. They sailed in the Duchess

B

2 MEMOIR OF AUGUSTUS DE MORGAN.

1807. of Gordon, one of a convoy of nearly forty ships. The
Commodore, Captain (afterwards Admiral) Sir John Beau-
fort, was on friendly terms with my husband in after life.
But Mr. De Morgan had no suspicion of having sailed
under his convoy until after Mrs. De Morgan's death,
when the notice of it was found in her journal. When
Admiral Beaufort heard of this he wrote, in a letter dated
Oct. 10, 1857, five weeks before his own death, —
Admiral < Qur co-residence for three or four months, not in the

Beaufort.

same street or village or county, but in the same track
along the ocean, is an amusing link in our two life-
threads ; but not the less flattering to me as being claimed
by you, and as finding myself one of the dramatis personce
in your mother's journal of the Jane, Duchess of Gordon.
You most correctly picture us as being ' at the two ends
of the chain,' for while it was my post to lead that
gigantic fleet of upwards of thirty large vessels, I well
remember that she was in all cases the sternmost, in spite
of the number of hoarse hints that were given her
through our guns. Passengers, even ladies, are never
very tender in their criticisms on the poor commodore,
and it would be charming to see how your mother retali-
ated for his above coarse language by her sharp and witty
castigation.'

isos. Colonel De Morgan settled at Worcester with his wife

and children, but returned to India in 1808 alone.
Some disturbances in the Madras Army, causing the sus-
pension from command of several officers, including him-
self, gave him much trouble and anxiety far some time ;
but the affair, which was settled by an inquiry at the
India House, resulted in his complete and honourable
acquittal. On his return to England in 1810, the family
lived in the north of Devonshire ; first at Appledore, then
at Bideford, then at Barnstaple. In 1812, one daughter
having died, and two sons been born, they settled at
Taunton in Somersetshire. The father again left England
for Madras, and took the command of a battalion at

EARLY EDUCATION. 3

Quilon. Being ordered home ill with liver complaint, he 1816.
left Madras in 1816, and died near St. Helena, on his way
to England.

In a list given of his schools and instructors by Mr.
De Morgan, his father's name occurs as his first teacher.
He was then four years old, and learnt ' reading and nu-
meration.' The heading of one column in this list, ( Age
of the Victim,' shows in a half- serious, half-humorous
way the idea ' the Victim ' retained of his early schooling.
He did not mean that it was worse in his case than in
that of other boys, and he always spoke gratefully of his
father; but he was no exception to the rule that most
children, especially those of great intellectual promise, are
more or less victims to our unenlightened methods of
education. Of these exceptional children I have heard
him say that those have the best chance who have the
least teaching.

At Barnstaple he learned,, from a Miss Williams, 1813.
reading, writing, and spelling; at Taunton, being be- Teachers-
tween seven and eight, from Mrs. Poole, reading, writing,
arithmetic, and (very) general knowledge. He always
retained a painful remembrance of this school. The Rev.
J. Fenner, a Unitarian minister, was for a short time
his teacher. The pupil was at that time about nine
years old, and added Greek and Latin to his other studies.
Mr. Tenner was the uncle of Henry Crabb Eobinson, who
died in 1867, aged ninety-one, and who had been at one
time a pupil in the school. The next two teachers were, at
Blandford, the Eev. T. Keynes, Independent minister ; and
at Taunton, the Eev. H. Barker, Church of England
clergyman, at whose school he was taught Latin, Greek,
Euclid, Algebra, and a little Hebrew. His last school-
master, a clever man, and one of whom, though he was not
a high mathematician, his pupil always spoke with respect,
was the Eev. J. Parsons, M.A., formerly Fellow of Oriel.
At Mr. Parsons' school, at Eedland, near Bristol, Latin,
Greek, and mathematics were taught. Mr. De Morgan

B 2

4 MEMOIR OF AUGUSTUS DE MORGAN.

1820. was at this school from the age of fourteen to sixteen and a
half, and at this period of his life his mathematical powers
were first developed. It was strange that among so many
teachers the germ of mathematical ability should have
been so long unnoticed. It could not be quite latent or
quite unformed in the brain of a boy of fourteen ; it can
only be supposed that the routine of school teaching
Mathema- smothered and hid it from observation. Education means
drawing out ; it often is keeping in, and it is well when
it is no worse. In this case it was good for the pupil
and for mathematics that the early germ should be left
to its own resources of natural growth, uncrippled and
undistorted by mistaken systems of teaching. It was
accidentally developed, and indeed made known to its pos-
sessor by the observation of a dear old friend, Mr. Hugh
Standert, of Taunton. Seeing the boy very busy making
a neat figure with ruler and compasses, and finding that
the essence of the proposition was supposed to lie in its
accurate geometrical drawing, he asked what was to
be done. Augustus said he was drawing mathematics.
' That's not mathematics,' said his friend ; * come, and I
will show you what is.' So the lines and angles were rubbed
out, and the future mathematician, greatly surprised by
finding that he had missed the aim of Euclid, was soon
intent on the first demonstration he ever knew the mean-
ing of. I do not think, from what I have heard him say,
that Mr. Standert was instrumental in further bringing
out the latent power. But its owner had become in some
degree aware of the mine of wealth that only required
working, and as some mathematics was taught at Mr.
Parsons' school, the little help that was needed was soon
turned to profit. He soon left his teacher behind, and
from that time his great delight was to work out ques-
tions which were often as much his own as their solu-
tion.

I can only find one little mention of his first going to
his school in his own handwriting. In a letter to Dean

SCHOOL EXPERIENCES. 5

Peacock in 1852, he says apropos of Robert Young, of 1820.
whom he had been writing, —

* When I was sent to school near Bristol in 1820, I Mr%par-
was consigned to R. Young, who especially warned me
not to walk in my sleep, as there were no leads outside
the windows ; they had been removed. The consequence
was, that though I never walked in my sleep before or
since that I remember, I was awakened by the wind
blowing on me, and found myself before the open window,
with my knee on the lower ledge. I crept back to bed,
leaving the window open, and the family being alarmed
by the noise, came into my room, and found me asleep and
the window open, so that as their fenestral logic did not
reason both ways, they forgot that the leads were not there,
and searched the whole house for thieves.'

Mr. Eobert Reece, his old schoolfellow and constant
friend of forty years, writes concerning these early school
days : —

' I entered Mr. Parsons' school at Redland, near
Bristol, on August 12, 1819. I think dear De Morgan
came among us at the latter end of the following year, or
in January 1821.

' He was certainly a fine stout fellow for his age, and at
once took a high place in the school. He had a grievous
infirmity, the loss of one of his eyes,1 which provoked all
kinds of gibes and practical jokes among the boys.'

Mr. Reece has told me how these cruel practical jokes
were put an end to. One lad was in the habit of playing
a trick upon his schoolfellow which deserves a worse
name than thoughtlessness. He would come up stealthily
to De Morgan's blind side, and holding a sharp-pointed
penknife to his cheek, speak to him suddenly by name.
De Morgan on turning round received the point of the
knife in his face. His friend Reece agreed with him that
until the aggressor should receive a sound thrashing he

1 From birth. Both eyes were affected with the ' sore eye ' of
India, and the left was saved.

6 MEMOIR OF AUGUSTUS DE MORGAN.

1820-21. would never desist from his cruelty. 'But how/ said the
School tormented lad. ' can I catch him to thrash him ? I cannot

days.

see him. He comes up, and is gone before I can lay
hands on him.5 'But you shall* said Reece; and the
arrangement was made. Reece, knowing that when his
friend was quietly reading, as he often did, at a desk so
placed that his blind side was near the door, the enemy
would be likely to approach, hid himself in such a way
that when the boy entered he could shut the door and
prevent escape. All happened as he expected. De
Morgan sat down at his desk with a book before him.
Very soon the cowardly aggressor came quietly in, pointed
his knife at his cheek, and said suddenly, ' De Morgan ! '
His intended victim did not turn round as he had done
before, and in a moment the lad, a stout boy of fourteen,
was seized behind by Reece, who gave him over to receive
the ' sound thrashing ' which De Morgan administered,
and which proved effectual in making him keep the peace
from that time.

Mr. Reece tells how he and his friend, with another
boy of similar tastes, contrived a late reading party, un-
sanctioned by the master. One of the three asked Mr.
Parsons to lend them Scott's poems, at that time just
published. Having got ' The Lady of the Lake,5 they
waited till all the other boys were in bed, the lights out,
and all things quiet ; then De Morgan produced a match
pistol and a tinder, snapped a spark and lit the candle,
and then read to his two companions till all three were
too sleepy to take an interest in Ellen and Roderick Dhu.
I do not mention this as an example to be followed, but I
hope my readers will forgive them.

Mr. Reece says, * I was impressed with his wonderful
ability from the first, and I courted him, and gave him
my admiration and my love. In return, he became at-
tached to me, and invited or permitted me to sit by him
in play-hours. He never joined in the sports of the boys,
owing to his infirmity. He had a remarkable talent for

CHOICE OF^ STUDIES. 7

drawing caricatures, of the kind that Gilray was so 1822.
famous for. I took great interest in these drawings, and Carica-
I had the privilege of suggesting a subject now and then.
Two of them I remember— the one, "Charon's boat,"
with figures; the other, "The Devil," with the three
black graces, Law, Physic, and Divinity. It seems an odd
thing to record, but I well remember that I was advanced
in " Bland's Quadratic Equations " when De Morgan took
up that well-known elementary book, " Bridge's Algebra,"
for the first time. But it was so. He read Bridge's
book like a novel. In less than a month he had gone
through that treatise and dashed into Bland, and so got
out of sight, as far as I was concerned. It is scarcely
necessary to say that all his school work was admirably
performed. Mr. Parsons had the highest opinion of him.' 1

Mr. Parsons being a good classical scholar, his aim
was rather to make his boys good classics than mathe-
maticians. If the mathematical power had not made
itself apparent, and taken the place of all other interests
in the pupil's mind, his studies would probably have
taken the direction desired by his master. As it was, he
was a good Greek and Latin scholar, and his classical
reading was wide and varied. The teaching at Redland
School was good, but abuses creep in everywhere. Here
is an account of a way of saying the lessons, given to
me by my husband in explanation of some remarks I
had written on education. Like the midnight entertain-
ment before mentioned, the story will afford hints to
teachers rather than an example for pupils : —

6 An ingenious application of the logical fallacy of a
part for the whole was invented by schoolboys by the
help of Providence, to moderate a mischief which would
otherwise have been severely felt. It was thought neces-
sary that boys should learn by heart Latin and Greek

1 The writer of the above died two years after his friend, his
affection for whom was one of the strongest feelings in his mind while
consciousness remained.

8 MEMOIR OF AUGUSTUS DE MORGAN.

1822. verses, to strengthen the memory. The poor ignorant
Schoolboy Virgil and Homer scanners, and their subordinate Euclid
and algebra drillers, had not the smallest idea that a
'memory is an adjunct of each faculty, that the training of
one is of little or no help to another, and that the
memory of words, which they over-cultivated, differs
widely among young people. The allowance was forty
lines a day, Latin and Greek alternately, for five days in
the week, the whole two hundred to be repeated in one
lot on Saturday. There was as much difference between
the boys in the rapidity of committing to memory, as
between the two pilgrims who went peashod to Loretto,
the one with hard peas, the other with boiled, in his
shoes. But the boys had the sense to learn their parts, as
the actors do, and again, like the actors, they learnt the
cues. This was carried on, at a school at which I was,
year after year, without a single detection. Even the
contretemps which arose when a boy was ill on a Satur-
day, or when one who had been ill on a week-day came in
on the Saturday, were adroitly got over. I am perfectly
satisfied that the master, an old Fellow of Oriel, was a
party to the whole proceeding, as a means of reconciling
the appearances demanded by opinion with the amount
of word-catching which he thought sufficient. And judg-
ing by what I have heard of other schools, I suspect that
such connivance was not infrequent.'

The boys of Mr. Parsons' school attended St. Michael's
Church, Bristol. Having heard something from Mr. De
Morgan of his juvenile delinquencies, arising from think-
ing more of mathematics than of the scarcely audible
sermon, I searched out the school pew during a visit to
Bristol, and there found, neatly marked on the oak wain-
scot partition, the first and second propositions of Euclid
and one or two simple equations, with the initials A.
DE M. They were made in rows of small holes, pierced
with the sharp point of a shoe-buckle, and are by this
time probably repaired and cleaned away.

EARLY DISPOSITION. 9

The testimony of Mr. Eeece to the affection felt for 1822.
their schoolfellow by most of his companions has been
confirmed to me by one or two of the few who remain in
this world, and I find in letters from friends many little
confirmations.

6 1 have known more of you than you of me,5 his friend
Mr. Leslie Ellis wrote to him during the long and suffer-
ing illness which preceded his death. 'Even while you
were yet at Mr. Parsons' and I was a child I had heard of
you, and of course in later years I have heard of you very
often ; but though everybody spoke well of you, I was left
to find out for myself how kind you could be to a sick
man — how kind, I think I must infer, to all about you.'

And another time, —

6 1 had, since your recollection of Parsons, two
brothers there, and I remember my father speaking of
having seen you, and saying that the usher complained
that you were " such a glutton," meaning in the matter
of reading; but I cannot recollect whether he spoke of
mathematical or classical reading, or of both.'

But the boy was probably, at school, very like what he
was at home, when his mother, who loved him fondly,
described him as a quiet, thoughtful boy, occasionally but
not often irritable, and never so well pleased as when he
could get her to listen to his reading and explanations, and
' always speculating on things that nobody else thought
of, and asking her questions far beyond her power to
answer.'

One element of his early teaching strongly tinged his
character in after life. Col. De Morgan, who was a
strictly religious man, of a rather evangelical, as it is
falsely called, turn of feeling, was premature, seeing the
sensitiveness and grasp of the mind he had to deal with,
in inculcating rigid doctrines, and insisting on formal
observances. The religious training of his son thus begun,
was continued, after his father left England, by his
excellent mother, who, with the best intentions in the

10 MEMOIR OF AUGUSTUS DE MORGAN.

1822. world, was unable to adapt the spiritual food to the needs
Religious of the recipient. He was made to learn by heart and

education. , , ., .

repeat long Scripture lessons, so chosen that their mean-
ing and connection with each other and with himself
were quite imperceptible ; indeed, I have heard him say
that, from frequent repetition, the words and phrases be-
came meaningless to him. He was taken to church twice
in the week, three times on Sunday, and required to
give an abstract of every sermon he heard. Being thus
administered, religion could not fail to become a source of
misery. Sunday was the one wretched day of the week,
to be got over somehow, and church was a place of
penance. A worse result of the system even than this
was the confusing together in an honest young mind all
ideas of right and wrong, truth and falsehood, in con-
nection with religion. The awful description of the
Devil and his doings, and the eternal burning to be under-
gone by all who did not believe what he could not then,
and never was able to believe in the prescribed form,
were set in the boy's mind against Jesus Christ's declara-
tion that His Father was a God of love, and that repent-
ance was the only condition of forgiveness. For a boy
like Augustus De Morgan, whose clear perceptions, love of
truth, and readiness to venerate, rendered him sensitive
to every word spoken by those whom he loved, or who
were in authority over him, such mental antagonisms
must have been the cause of great anguish, and he could
only escape, after he once began to think, by dismissing
the whole from his mind. The problem of how to recon-
cile the Divine idea of God's love with the human notion
of God's justice was a harder one than he ever met with
in after life, and he gave it up as insoluble. Not being
yet able to detect the logical fallacies and critical errors
which formed part of the arguments used to convince
him, he could only receive those arguments in silence, but
without assent. Happily the evil corrected itself, and no
harm was done in the end. His innate sense of relation-

ENTERS THE UNIVERSITY. 11

ship to his heavenly Father was too strong to allow him 1822.
to become atheistical, and his reasoning power too sound
to allow him to be sceptical as to the Christian revelation.
But the process of pulling down and building up took
time, and it was years before the impressions of his child-
hood could pass away, and the natural, healthy working
of the religious spirit could begin. Such an experiment
is a dangerous one for parents to try, and the greater the
early indications of religious feeling in a child, the more
cautious and forbearing should they be in their direction
of it.

One lasting injury done to him by the compulsory at-
tendance so often at public worship, was his inability in
after life to listen for any time to speaking or preaching.
He said that the old troubles of the three services on
Sunday, and the ' dreary sermons ' came back to him, and
to get rid of these memories he thought of something
different from what was being said.

In February 1823 he entered Trinity College, Cam- 1823.
bridge. His old schoolmaster, Mr. Parsons, with other
friends, had counselled his pupil's reading for honours in
Classics ; and Mrs. De Morgan's wish was that her son
should enter the Church as an Evangelical clergyman. She
had had all the responsibility of her children's education,
and, looking to the success of her eldest at Cambridge as
a most important element of his future welfare, naturally
trusted to the advice of her friends, and believed that all
attention given to Mathematics beyond what was needed
for his examination would be so much labour lost. He Age on
was but sixteen years and a half old when he went to
Cambridge, entering at a by -term. Though always
studious and persevering, yet at his first examination,
when his attention had been divided between the classical
reading he had forced himself to attend to, and the
Mathematics which he loved, he stood at the top of the
second class only. But his failure, as she considered it,
caused his mother great anxiety, and her letters to him

12

MEMOIR OF AUGUSTUS DE MORGAN.

1*23.

1824.
Tutor a
opinion of
his capa-
bilities.

at the time are filled with earnest entreaties f not to dis-
regard good advice,5 ' not to be so wilful,' &c.

It is certain that her exhortations were not needed.
He had exerted himself, as his tutor's letter to him shows :
' I am sorry that I cannot congratulate you on being in
the first class, though your merits and exertions richly
deserved it.' We may remember that he was at this time
under seventeen, that he had been at college only three
months, and that he beat by many places his competitor
of his own year, two years his senior in age. Moreover, he
had been urged by his tutor, against his own conviction,
to go in for examination at this time.

It appears from some of his mother's letters that he
had in reply assured her that he would comply with her
wish with respect to his reading. But it cannot be
wondered at that the University lectures opened the field
into which he had long desired to enter. It was like new
life to him when he listened to Dr. Peacock's explanations,
and followed up the study he loved under the guidance of
one who knew how to show the way. From the conflict
between his own inclinations and the wishes of his friends
it is certain that his path could not be quite smooth, but
happily the University courses made it better during the
second than in the first year. A greater amount of Mathe-
matics was then required in the college examination, and
he was found at the head of the first class. Mr. Higman,
his tutor, wrote to his mother : ' Notwithstanding my
disappointment last year, I had formed such a very
favourable opinion of Mr. De Morgan's talent, and was so
much pleased with his industry and the implicit attention
he paid to every direction that I gave him, that I felt per-
fectly assured that he would, on the next trial, when less
depended on Classics, distinguish himself in a very extra-
ordinary manner. Nor have my prognostics with regard
to his success proved deceitful ; he is not only in our first
class, but far, very far, the first in it.'

For the first two years of his Cambridge life, owing to

RELIGIOUS PERTURBATIONS. 13

the difficulty of getting rooms in Trinity College, he was ^1824.
in lodgings. After this his rooms were over the gateway.
At this time his mother wrote to him : ' I hope I am mis- His
taken in supposing from your letter that you go entirely

to " the chapel," and not with Mr. and Mrs. , to

hear the Gospel on Sundays. . . . You are very young, my
love, and will be likely to go wrong from being left to
yourself so soon if you do not take advantage of the
experience of those who hare gone before you. I have
less fear for you than I should have for many youths of
your age, because you are studious and steady, because
you love your mother tenderly, but above all, because you
are the child of many prayers ; but I shall be most
anxious if you do not hear dear Mr. Simeon.'

In another letter she says, speaking of the same
friends who had assisted him in small money arrangements

at Cambridge : ' Mrs. tells me you are like a man of

fifty in settling your accounts with her for things she has
bought. Dear own son of your father and mother, go on
through life with the same scrupulous punctuality ; it will
be a means of keeping you from spending extravagantly ;
it will make you respected and beloved, and preserve you
from that sort of carelessness which brings many young
men to ruin.'

I would not put on record expressions showing- the
intense anxiety of a most energetic and loving mother for
a beloved child, except to afford an instance of how the
very best intentions may be acted on in such a way as to
frustrate their own fulfilment. Mrs. De Morgan had put
some books, of what would now be called a ' Low Church'
tendency, into a box with other things for her son,
accompanying them with a letter, from which I extract
the following : —

* I am so anxious that you should read occasionally the Religious
books I send (unknown to you), and was so fearful you r
might endeavour to persuade yourself and me that you
had no time for such studies, that I thought the best way

14 MEMOIR OF AUGUSTUS DE MORGAN.

•

1824. would be to say nothing about it viva voce, but to send
Doctrines them uninvited ; and, having determined on that, an

of salva- ' _ _ _ _ 4

tion. explanatory note became necessary. I beseech you, for my

sake, to read with attention these books, to utter a prayer
over them whenever you open them, "that they may be
blessed to you as they have been to thousands," many of
whom are now rejoicing in heaven, where you wish to go,
but where you never can go while you remain wilfully
ignorant of your state by nature, and of your need of a
Saviour. Your believing an atonement necessary in a
general sense * will not avail you. You must go ly your-
self and for yourself to Christ for pardon and grace, and
until you do this you may rest assured you are in a most
awful state — liable to be hurled into everlasting torment
by every little accident, every disease, nay, even by a
crumb of bread going the wrong way. Can you wonder
that a mother, doting as I do on you, feels miserable when
she contemplates a beloved child wantonly sporting on the
edge of so tremendous a precipice ? . . . Can you picture
to yourself any agonies like those which would take posses-
sion of your mind were you assured that before to-morrow
morning you would be standing at the tremendous bar of
an angry God ? '

The young man thus appealed to was dutiful and
affectionate, and these exhortations troubled him much.
His reason and instinctive love of God told him that they
must arise from misinterpretations of Scripture, and from
human notions of Divine things. In many less logical and
fearless minds they would have produced disgust with
religion altogether ; but the intellect of the future logician
was too clear to confound the thing itself with its abuses,
or with the misrepresentations of ill-judging advocates.

1 From this expression, and from what I have heard, I conclude
that Mr. De Morgan had assured his mother of his belief in the atone-
ment in the Scripture sense, namely, the reconciliation or at-one-ment
of sinning and repentant man to a loving God, not the reconciling
c >f an angry God to mankind, in consequence of intellectual belief.
This was his creed in after life.

DISCURSIVENESS IN STUDY. 15

These had not even the effect of making him dismiss the 1825.
matter from his mind, for during the whole of his college
life his mind was actively employed on questions con-
nected with theology and philosophy. He never saw the
gospel in any other light than as a professing declaration
of God's love and mercy, but it was some time before he
was convinced of its historical truth and supramundane
origin.

In 1825 Mr. De Morgan was again high in his class.
He had had an illness, perhaps from reading too much
and too late at night ; and his mother, whose gratification
was damped by her great anxiety about his health, writes
to him : ' You are much higher than I expected from
your humble account of yourself, and I rely on your letting
me know if you should suffer materially.' In April Schoiar-
a Trinity scholarship was awarded him. After this time
some friends must have made his mother anxious by
accounts of his general and discursive reading, for she
writes : ' I have heard of you lately as a man who reads
much, but who is not likely to do much, because he will not
conform to the instructions of those who could assist him.'
The indocility to which she refers consisted in extensive
Mathematical reading beyond the bounds marked out by
his tutors, and in the study of Metaphysics, Mental Philo-
sophy, and even Theology. Berkeley's writings attracted
him strongly; the immateriality of Berkeley's doctrine
being suited to a mind instinctively resting upon a
spiritual Father, and believing that we depend on His
sustaining power as well for absolute existence as for
support and guidance through life. It is far from im-
probable that Berkeley's speculations, falling in in a great
degree with his own, gave a strong bias to his subsequent
thoughts on metaphysical questions.

He never forgot what he owed to his teachers in the
University. These were, as entered in his own book, his
college tutor J. P. Higman, Archdeacon Thorp, Gr. B.
Airy, A. Coddington, H. Parr Hamilton (Dean of Salis-

16 MEMOIK OF AUGUSTUS DE MORGAN.

1825. bury), G. Peacock (Dean of Ely), and W. Whewell (after-
wards Master of Trinity). With all of these gentlemen he
kept up a friendship and correspondence during their
joint lives.

Early His college friends of nearly his own age were William

Heald, William Mason, Arthur Neate, and Thomas
Falconer, all of Trinity College. Among those whose
friendship he valued, none were more esteemed by him
than his teachers — Dean Peacock, Dr. Whewell, Mr. Cod-
dington, and Dr. Thorp, afterwards Archdeacon Thorp.
Mr. Heald, afterwards Eector of Birstal, in Yorkshire,
died in 1875. Mr. Mason, Eector of Pickhill, near
Thirsk, died in 1873, and his companion and chum of
Trinity College days, Arthur Neate, died at his rectory,
Alvescot, near Oxford, in 1870.

Some peculiarities in his college life were well known
to Cambridge men of his year. The habit of reading
through great part of the night, and, in consequence,
getting up very late the next day, was notorious ; and
fellow-collegians, coming home from a wine party at four
in the morning, might find him just going to bed. One
of these, better known in the University for rows than for
reading, has told me how often he himself, being late next
day from a different cause, has gone into De Morgan's
rooms, just below his own, and begged for an air on the

Love of flute to ' soothe a headache.' His flute, which he played
exquisitely, was a great source of pleasure to himself and
his friends. He was a member of the ' Camus,' a musical
club so called from the initials of its designation — Cam-
bridge Amateur Musical Union Society ; and their
meetings, and those at the houses of a few musical
families, were his chief recreation. He was a born
musician. His mother said that when listening to the
piano, even when, a very little child, a discordant note
would make him cry out and shiver. I must not omit
to record his insatiable appetite for novel-reading, always
a great relaxation in his leisure time, and doubtless a

UNIVERSITY DEGREE. 17

useful rest to an over-active brain in the case of one who 1826-27.
did not care for riding or boating. Let it be good or bad
in a literary point of view, almost any work of fiction was
welcome, provided it had plenty of incident and dialogue,
and was not over-sentimental. He told me that he soon
exhausted the stores of the circulating library at Cam-
bridge. Like his schoolfellows, his college friends loved
him for his genial kindness, unwillingness to find fault,
and quiet love of fun, always excepting practical jokes,
with which he had no patience at all.

During the last year and a half of his stay at Cambridge intention
Mr. De Morgan had some thoughts of becoming a phy- medicine,
sician. With his views on religion, his ordination was
out of the question ; but he liked the study of medicine,
and some friends advised him to read it with a pur-
pose. This intention did not last long. His old friend,
Mr. Hugh Standert, of TauntQn, knew by experience
what was generally needed for success in medical practice,
and an acquaintance from infancy made him believe
that Augustus was not pliant enough, and could not, or
would not, be sufficiently ready to adapt himself to the
fancies and peculiarities he would meet with to make him
a popular doctor. Whether or not he had any special
genius for medicine is uncertain. His mother agreed
with Mr. Standert, and urged upon her son that his
success in medicine might depend on an amount of tole-
ration for ignorance and folly which, with his e hatred of
everything low,' he would find a great trial. She begged
him to ' throw physic to the dogs,' and to turn his
thoughts to law. He complied, but did not like his des-
tination. Events proved that he was right, that he had
not found his proper place in the world's workshop.

In 1827 he took the degree of fourth wrangler, 1827.
the order being Gordon, Turner, Cleasby, De Morgan.
This place, as one of his scientific biographers truly
says, ( did not declare his real power, or the exceptional
aptitude of his mind for mathematical study.' He had

c

18 MEMOIR OF AUGUSTUS DE MORGAN.

1826. been expected to be senior or second wrangler, and his
lower degree was attributed by his contemporaries and
competitors to the wide mathematical reading by which
he was often led away from the course prescribed for
examination. This failure, in a possibly fallacious test,
was his own early, but unintentional, protest against
competitive examinations ; for which he felt excessive
disapprobation even before his experience as a teacher
showed him not only their mischievous effect upon mind
and health, but their insufficiency to determine the real
worth of a candidate for honours. In saying this I do
not detract from the merit of the gentlemen who stood
above Mr. De Morgan in the Tripos of 1826. All three
distinguished themselves in after life, but as he was un-
doubtedly the first in mathematical ability, it is likely
that their precedence of him might be due to the fact
that his love of the study led him to read more widely
and discursively than his friends on the very subject on
which excellence was to be tested.

At the time of his taking his B.A. degree he came to
live with his two brothers, mother, and sister in London.
He had determined to go to the Bar, and was beginning his
legal studies, but he very much preferred teaching mathe-
matics to reading law. Something like the objection
urged by his friends to medicine was uppermost in his
mind, and he feared or imagined that in practising at the
Bar he might find it difficult to satisfy both his clients
and his conscience. But these scruples were overcome,
and he entered at Lincoln's Inn.

19

SECTION II.

1827 TO 1831.

IT was at this time that he became acquainted with my 1827.
father, William Trend. They first met at the office of William
the Nautical Almanac, of which their common friend,
Lieutenant Stratford, E.N., had been recently appointed
Comptroller. Mr. Trend and Mr. Stratford were both
members of the old Mathematical, and subsequently of
the Astronomical Society. Though iny father was, even
at that time, far behind Mr. De Morgan as a mathe-
matician, the two had a good deal of mathematics in
common. My father had been second wrangler in a year
in which the two highest were close together, and was, as
his son-in-law afterwards described him, an exceedingly
clear thinker and writer. It is possible, as Mr. De
Morgan said, that this mental clearness and directness
may have caused his mathematical heresy, the rejection
of the use of negative quantities in algebraical operations ;
and it is probable that he thus deprived himself of an
instrument of work, the use of which might have led him
to greater eminence in the higher branches. This same
heresy gave occasion to many amusing arguments and
discussions. But between these two sympathy in matters
of morals and principle formed a stronger bond than
similarity of pursuit. My father had sacrificed good
prospects as a clergyman to his conscientious scruples
about the doctrines of the Established Church, as ex-
pressed in the Creeds and Articles, and had been through
life an earnest advocate of religious liberty. These cir-

c 2

20 MEMOIR OF AUGUSTUS DE MORGAN.

1827. cumstances won for him at once the respect and esteem
Family of of Mr. De Morgan, who, like himself, had thrown off the
restraints of a creed which he could not hold, and which
he refused to profess without holding. I think my father,
who was a good Hebrew scholar, afterwards helped him to
clear away some of the doubts and difficulties resulting
from mistranslations of Scripture, and fostered by the
early teaching of a sect not critically learned.

We were living at Stoke Newington, in one of those
old houses with wooded grounds, of which so few remain
near London. It had formerly belonged to Daniel Defoe,
and Isaac Watts had inhabited it. In my father's time it
was the scene of many a pleasant gathering of men and
women of all degrees of intellectual ability, and of almost
every shade of political and religious opinion. The spot
where the old house stood has become the centre of a
district of streets and shops, built where the tall trees
grew, and nothing now remains to commemorate its
existence but the name of Defoe Street.

Mr. De Morgan first came to our house with Mr.
Stratford. He then looked so much older than he was
that we were surprised by hearing his real age — just
twenty-one. I was nineteen. We soon found out that
this c rising man/ of whom great things were expected in
science, and who had evidently read so much, could rival
us in love of fun, fairy tales, and ghost stories, and even
showed me a new figure in cat's cradle. He was in
person very like what he continued through life, but
paler, probably from the effects of his recent Cambridge
reading. His hair and whiskers were very thick and
curly; he was not bald till thirty years after. I re-
member his having a slight pleasure in saying things
which startled formal religionists, but which we, who
were not formal, soon understood to mean what they ex-
pressed, and no more. These sayings were humorous, and
like the half-mischievous jests of a very young man. It
was easy to see that a deep religious feeling underlay the

STOKE NEWINGTON.

21

contempt for observance which, his early training had 1827.
caused, and that his consciousness of the care and father-
hood of the Almighty was a sacred thing belonging to
himself alone, not to be profaned by contact with human
forms or inventions. My father, who, like people who
have made their own belief, was a little impatient in argu-
ment, at first thought him an unbeliever ; and so, in a
certain sense, he was ; but it was only in such things as
he could not find a reason for believing. I mention re-
ligious questions because they entered much into our
thoughts and conversation at that time. As to the Gospels,
he waited for a better and more critical understanding of
them than could be gained from his first instructors, and
this a rather extensive reading of theology enabled him to
acquire before he left this world. When I first knew him,
I was puzzled by such books as Volney's * Ruins of Em- Antiqua-
pires,' Sir. W. Drummond's writings, and other works of
antiquarian research, to which a great interest in our
friend Godfrey Higgins's investigations had led me. Mr.
De Morgan showed me the scientific errors of some of
these writers, and the insufficiency of their theories to
account for all that they have tried to explain. He was
well informed in Eastern astronomy and mythology, and
saw that much of modern doctrine has gained something
of its form, at least, from ancient symbolism.1 Lieut.-
Col. Briggs, his uncle by marriage, had begun his
' Ferishta,' and his nephew's interest in the work had
brought him much into the society of Oriental scholars.
The ancient grandeur and simplicity of the East at once
excited and satisfied his imagination. He sometimes
said that India with its skies and mountains ' might
be really worth looking at,' whereas he never saw any

1 All scholars must see that the time is approaching when a better
knowledge of ancient religions will show that they have been misunder-
stood, and that they are not entirely fictitious or entirely astronomical.
If this were the place it would not be difficult to show the connection
of all,

MEMOIR OF AUGUSTUS DE MORGAN.

1827.

Music.

London
University

scenery in England than which he could not picture
to himself something infinitely grander. He was proud
of his birth in the sacred city of Madura, and at one
time longed to visit his native country, and fancied
that every one had the same instinctive desire. Luckily,
his doing so when young was prevented by the defect
of sight which justified his mother in refusing a cadet-
ship for him.

During the ten years which preceded our marriage,
his delightful flute, accompanied by my sister on the
piano, was a great pleasure to us. I lost the gratification
of accompanying him then, and it was afterwards a
sorrow to me that I was not a musician. Our acquaint-
ance began just before he became a candidate for the
Professorship of Mathematics, but he, like my father,
took an interest in the foundation of the new University,
of which, indeed, my father had been one of the first
projectors.

It has been observed that when the time is ripe for
bringing forward any measure, ideas come at the same
time to more than one mind fitted to receive them, and it
is often difficult to find the author of the first suggestion.
This is especially true in the case of the foundation of
large institutions. In what follows I do not mean to
assert that my father was the first suggester of a college
or university in London, but, being one of the few persons
now living who can remember the beginning of University
College and the expressed designs and hopes of its
founders, I venture to give, more in detail than the scope
of a biography would justify, a short account of its origin;
and in thus contributing my share of its history I must
speak of that part which I best remember.

About or before the year 1820, some liberal-minded
men, after long pondering on the disabilities of Jews and
Dissenters in gaining a good education, came to the con-
clusion that as the doors of the two Universities were
closed against them, the difficulty could best be met by

THE NEW LONDON UNIVERSITY. 23

establishing a University in which the highest academical 1827.
teaching should be given without reference to religious First sug-
differences. As this could not be done in an institution g
in which the pupils resided without excluding religion
altogether from education, a necessary condition of the
establishment was the daily attendance of students on
college lectures, so that while living under their parents'
roof they might be brought up in the religion of the
family.

My father's ideas of the proposed institution had been
embodied in some letters signed 6 Civis,' and published in
a monthly periodical1 edited by Mr. John Thelwall, some-
where about 1819, which did not survive a third number.
The writer was well qualified by his own academical status,
and by the subsequent abandonment of Church prefer-
ment which led him into connection with intelligent Dis-
senters, to estimate the value of University training, and
the great loss and deprivation sustained by young men
every way qualified to profit by it who were unable from
religious belief to receive it. He looked forward to the
day when all forms of religion should be held equal within
the walls of the noble institution which he contemplated,
in which good conduct and compliance with rules should
be the only conditions of admission.

A short time after the publication of the letters re-
ferred to, Mr. Thomas Campbell, the poet, first visited their
writer, and informed him that Lord Brougham (then Mr.
Brougham) and Dr. Birkbeck, with himself and one or two
others, believed that the time for making the attempt
was come. I was about twelve years old when Mr.
Brougham dined with my father to consult upon it. Some
meetings took place, other liberal men joined them, and
after some delay the first active committee was formed.

Mr. Trend was prevented by long and severe illness

1 I have tried in vain to find the title of this periodical, which is
not in the British Museum. It must have appeared between 1818
and 1822.

24 MEMOIR OF AUGUSTUS DE MORGAN.

1827. from taking an active part in the first movements, but he
joined the general committee on his recovery, became a
shareholder, and on the election of a council and officers
was appointed one of four auditors.

The establishment of University College, called at first
the London University, promised to fulfil the hopes of all
friends of education, and was hailed as a forerunner of
religious freedom. My father naturally took the liveliest
interest in its progress. Mr. De Morgan welcomed the
opening of the College, as not only meeting a great
want of the time, but as offering to himself a prospect of
leaving the study of Law, which he did not like, for the
teaching and pursuit of Science. When the time came
for the appointment of Professors he sent his name in as
a candidate for the Mathematical chair. He was one of
thirty-two candidates. The committee for examining tes-
timonials found among his the highest certificates from
Dr. Thorp, Dr. Peacock, Professor Airy, Professor Cod-
dington, and others, his Cambridge teachers. He was
much younger than any of his competitors, but his election
to the chair of Mathematics was made unanimously, and
afterwards confirmed by the Council on February 23, 1828,
being formally communicated -to him without delay.
Election to It was a little characteristic incident connected with
ship. the appointment of the future Mathematical Professor,

that while the election was going on in one part of the
college, and he with some others of the candidates were in
the common room, he took up a volume lying on the table,
•which proved to be Miss Porter's ' Field of the Forty
Footsteps.' The scene of this novel is laid in the fields
which formed the site of the building and its surround-
ings. It was said that, some years before, the marks of
the weird c forty footsteps ' might still be seen in the
ground, but builders and stonemasons had effectually
removed them, and fanciful comparisons were drawn
between the effacement of these marks of the brothers'
rivalry and the barbarity of their lady love as the new

NEED OF A LIBERAL UNIVERSITY. 25

foundations arose, and the disappearance of crime and 1827.
ignorance under the work which the College had to do.
The love of fiction was strong enough in the candidate's
mind to make him forget his interest in what was going
on, and he had run through the volume before a whisper
reached his ears as to the result of the election.

In looking at the past history of an institution it is
useful to trace not only the successes, but the mistakes
which have caused failure and disturbance; for even in
cases where present prosperity may lead to imitation, a
statement of errors committed and corrected will be as a
chart of the rocks to be avoided hereafter. I shall try to
give a truthful sketch of the early history of the College;
not entirely omitting those elements in its formation which
created discord in the first years, and which had some
share long after in the disastrous termination of my hus-
band's connection with it. Had he lived long enough he
would have himself done this, far better than any one else.
His pen was held for a time by consideration for con-
temporaries, most of whom are now gone. Circumstances
connected with his memory have arisen since he was
taken from us which make it imperative on me to do the
work which he left undone.

To learn this history fairly we must look back to the state of
state of education, and to the needs and disabilities which at this time.
led to the foundation of the London University. These
disabilities and needs were felt, not so much by highly
educated academical men wishing for a cheap school for
their sons, as by the great body of enlightened Jews and
Dissenters, held back by religious tests from sharing in
University advantages, but intelligent enough to perceive
the value of what they lost, and rich enough to supply
the want for themselves. The wealth of this party was
of course represented by commercial men. To these must
be added some parents living in London and the neigh-
bourhood who could not afford to send their sons to
college, and to whom the attendance on daily lectures

26 MEMOIR OF AUGUSTUS DE MORGAN.

1828. while living at home seemed more desirable. A few of
the most liberal thinkers of the time gave their best help
to the completion of the design, but the large body of
men who had been trained under University discipline
held aloof from an institution from which religious tests
were excluded, and which might at some time compete
with the two Universities, bound up as they were by old
usage with the interests of the Established Church, whose
foundations were laid in the time of a church older still.

Thus, with the exception of the few enlightened
scholars who generally held out a hand to their less
Founders of fortunate brethren, the founders of the London Uni-
uSvereity. versity were either liberal politicians, not always familiar
with the details of academical discipline, or mercantile
men, who, with the best possible intentions, had no ex-
perience of the best way of securing concord and due
balance in the relations of governing body, teacher, and
pupil.

The Deed of Settlement of the London University
bears date 1826. The Institution was a proprietary one,
the funds being raised partly by shares, partly by sub-
Constitu- scriptions. The management was vested in a council of
twenty-four gentlemen chosen from among the proprie-
tors, and a general meeting of proprietors formed the
highest court of appeal. The Professors were elected by
the Council; and a Warden, who was to be the medium of
communication between the Council and Professors, and
superintendent of the household department, was ap-
pointed. The duties of the Professors were confined to
their class-rooms, in which, as it afterwards appeared,
they were not absolute.

It would have been well for the infant institution if a
piece of advice given by Mr. De Morgan long after, and
in a different connection,1 could have been acted on at
this time. * Never begin,' he said, ' by drawing up con-

1 On the establishment of the Ladies' College, Bedford Square.

INTENTIONS OF ITS FOUNDERS. 27

stitutions. They are sure to prove clogs on the wheel. 1828.
Let the work begin in good earnest, and with no needless
machinery. If it is done well you will soon see what is
wanted, and the constitution will be formed by meeting
the needs as they arise.' The founders of University
College, as of other public institutions, had not grasped
the idea of this natural growth, and the effect of their
arrangements was to put a clog upon the wheels, which
shook the whole vehicle, and well-nigh overturned it at
first going off.

As I cannot enter into the history of this institution
farther than is necessary to explain my husband's connec-
tion with it, no names except those which belong to that
part of the history will be brought forward.

The design of the London University, as set forth in
pamphlets, speeches, and the general understanding of
the time, and repeated many years later in an official
document,1 was to provide a liberal education in Classics,
Mathematics, Physical Science, and Medicine, without
regard to religious distinction either in teacher or pupil.

The teaching was to be given in lectures attended
daily by students, and the only condition of entry, beside
the fee, was good conduct and compliance with the rules
laid down for the maintenance of order in the college.

In conformity with this avowed principle of religious
neutrality we find, among the Professors first chosen, Professors.
three Clergymen of the Church of England, one Inde-
pendent minister, a Jewish gentleman, who in his place
of Hebrew professor taught the reading of the Old Tes-

1 No reference whatever is made to religion in the Deed of Settle-
ment, Regulations, or By-Laws. In these it is stated that the object
of the University is to afford an education in Mathematical and Phy-
sical Science, Classics and Medicine. The absolute determination to
leave the subject of religion entirely untouched appears negatively
from these documents, but positively from all the addresses given in
the institution, in newspaper articles, and in the general understanding
of all the parties connected with it, a great number of whom, being
rich Dissenters, watched the proceedings with a jealous eye.

28

MEMOIR OF AUGUSTUS DE MORGAN.

1828.

Letter to
Mr. Frend.

Appoint-
ment

tament, and other gentlemen nominally churchmen, but
whose religious views were known to vary from strict
orthodoxy to the widest latitudinarianism.

The appointment to the Mathematical Professorship
pleased some of Mr. De Morgan's Cambridge friends, who
spoke and wrote of it as a boon to the London University
and to himself. It would be untrue to say that all his
friends rejoiced in it, for his own family and near rela-
tions, who had anticipated a brilliant success for him at
the Bar, felt that to take a position as yet doubtful, with
a greater doubt of fitting remuneration, was really a
sacrifice on his part. My father shared in this feeling,
and, in reply to the expression of it, Mr. De Morgan
wrote : —

e You seem to fancy that I was going to the Bar from
choice. The fact is, that of all the professions which are
called learned, the Bar was the most open to me ; but my
choice will be to keep to the sciences as long as they will
feed me. I am very glad that I can sleep without the
chance of dreaming that I see an "Indenture of Five
Parts," or some such matter, held up between me and the
Mecanique Celeste, knowing all the time that the dream
must come true.'

One false step due to the tendency in young asso-
ciations to frame constitutions before their needs are
known, was the appointment of a Warden for the new
University. The next error arose from the same cause,
and showed the inability of the governing body to per-
ceive what was due to men of worth and education, if
they meant such men to give them the weight of their
character and influence. As a good friend to the new
College wrote to Mr. De Morgan, speaking of two influen-
tial members of Council : ' A. believes that the University
depends on the Professors, B. that the Professors depend
on the University.' Unfortunately the A.s were in the
minority.

Mr. De Morgan received the official notice of his

FOEMAL APPOINTMENT TO PROFESSORSHIP. 29

appointment on the day of the election, and was informed 1828.
at the same time that c a formal certificate of appoint-
ment will be prepared, in which the duties of the Pro-
fessors will be specified, and they will be required to sign
an acceptance of the authority of the Council and of the
rules of the University on receiving them.'

These conditions and obligations were not such as could Undue re-
be accepted by men accustomed to academical discipline, Professors.
and who knew the value of their work. They were the
work of a governing body new to its own duties, and
to the claims and rights of those for whom they were
composed. But after a strong remonstrance the Pro-
fessors were enabled to hold their diplomas on a simple
declaration of adherence to the constitution as set forth
in the Deed of Settlement. The classes opened on the
following November, and on the 5th the Professor of
Mathematics gave his introductory lecture, when, as he
says, he * began to teach himself to better purpose than
he had been taught, as does every man who is not a fool,
let his former teachers be what they may.5 1

This lecture ' On the Study of Mathematics ' takes a introduc-
much wider view of that study, and its effects upon the ture. ec
mind, than its title alone would imply. It is an essay
upon the progress of knowledge, the need of knowledge,
the right of everyone to as much knowledge as can be
given to him, and the place in mental development which
the culture of the reasoning power ought to hold. It is
not only a discourse upon mental education, but upon
mind itself. It was the work of a young man of twenty-
two years and four months old, and the earnestness and
sanguineness of youth may be seen in the strong deter-

1 In this year he published a translation of the first three chap-
ters of Bourdon's Algebra. This was afterwards superseded in his
class-room by his own Arithmetic and Algebra. In his own copy
of Bourdon is inscribed, after his name, 'Aged 22 years and 2
months, being the first work he ever published. — A. De M., Aug. 26,
1846.'

30 MEMOIR OF AUGUSTUS DE MORGAN.

1828. ruination with which his work was begun, and the high
hopes which he felt of the work the University had to do.
How well his part was done, after years, and the con-
senting voice of many pupils whose own work bore the
fruit of his teaching, have given proof.

What part he had in obtaining for the College its
subsequent reputation it is not for me to say. How he
was repaid, the judgment of the future must deter-
mine.

The Mathematical class during the first session con-
sisted of nearly one hundred pupils. In the next year
there was an increase of numbers. The Professor gave
two lectures every day, the first from nine till ten A.M.,
the second from three to four in the afternoon. After
each lecture he remained for a time at his desk, in order
that pupils who had found any part obscure might come
to him to have their difficulties cleared up. In this way
the two lectures occupied about three hours in the day,
and the pupils' exercises which were to be examined
rather less than an hour more.

Day school. Various proposals had been made by the most active
among the Professors for improving the condition of the
institution; among those which were carried into effect
were the foundation of a day school in connection with
the University, and the annual distribution of prizes and
honours. But, as might be expected from the elements of
which the new institution was founded, it could not go on
long smoothly. Troubles began soon after the opening,
due to arrangements which resulted from the forma-
tion of a constitution and laws before the working neces-
sities of the institution could be known ; and all the mis-
apprehensions which soon arose among the component
members were traceable to this cause. These were set
forth chiefly in the following pamphlets, printed for
private circulation : —

1. ' A Letter to the Shareholders and Councillors of
the University.'

VISIT TO PARIS. 31

2. ' Statements respecting the University of London, 1828.
prepared at the desire of the Council by Nine of the Pro-
fessors.'

3. ' Letter to the Council of the University of London,
by Leonard Homer, Warden of the University.'

4. ( Observations on a Letter, &c., by L. Horner, Esq.,
&c., &c., by Nine Professors.'

During the vacation of 1829, Mr. De Morgan spent a 1829.
few weeks in Paris, chiefly at the house of Colonel, after-
wards General John Briggs, of the Madras Army. Col. Colonel
Briggs and his father, Dr. Briggs, also of the Indian Briggs'
army, had married two Miss Dodsons, sisters of Mr. De
Morgan's mother. They were, therefore, his uncles by
marriage. Col. Briggs, who, as a young man, had served
under Sir John Malcolm during the time of the dissolu-
tion of the Mahratta Confederacy, afterwards held suc-
cessively a diplomatic post in Persia, and that of Resident
at Nagpoor, and finally, for a short time, the place of
Senior Commissioner of Mysore. He was an able officer
and an indefatigable student of Eastern language, history,
and Science. His work on the Land Tax of India was
one of the earliest protests against some points of British
misrule in the East. In the bringing out of this work his
nephew Augustus gave him a good deal of assistance.
Besides this work, General Briggs was the author of
' Letters on India,' an excellent guide for young men
entering the army, even now when the army is under
different rule ; and besides the ' Ferishta,' already men-
tioned, he translated the work by Ghulam Hussein on
the ' Decay of the Mogul Empire.' His knowledge of
Eastern languages and Science had brought him and
our friend Godfrey Higgins into intimate acquaintance.
They visited my father together at Stoke Newington,
and their animated discussions were always amusing
and often instructive, though the two had a tendency to
differ about Hindoo temples and topes and remains, which
Mr. Higgins declared had been built and decorated

32 MEMOIR OF AUGUSTUS DE MORGAN.

1829. according to his theory of ancient Astronomy, and Colonel
Briggs as firmly maintained were not so when he last saw
them.

Acquaint- The visit to Paris was paid just before Colonel Briggs
ParS.m left for India. It was a time of great enjoyment, and
besides the society of his uncle's family and the pleasures
of Paris life, then quite new to him, whose time had been
altogether given to study, he made acquaintance with
many of the scientific men and scholars of the time.
Among these were MM. Hachette (with whom he corre-
sponded till M. Hachette's death in 1832), Biot, Chladni,
the Due de Broglie, and others. With M. Quetelet he
became acquainted two years later. M. Bourdon, whose
work on Algebra he had translated, was in Paris, but the
two never met. .

India. My husband's interest in his birthplace had always

been kept alive by intercourse with his many relations
there, some of whom were in the Madras army, some in
the Civil Service. It is well known how frequent were the
disputes and jealousies among the servants of the East
India Company. Col. De Morgan had suffered much from
accusations made against -him by superior officers, for
which the later justice done to him hardly compensated.
Col. Briggs, who was acknowledged to be an able and well-
informed officer, had his share of trouble. In 1829, great
difficulties arose in the government of the Mysore, owing
partly to the mixture of native rule, and partly to the
province being under the direction of the Governor of
Madras, who appointed Commissioners for it. Owing to
these disorders, Lord W. Bentinck, the Governor-General,
determined to separate the Mysore from the Madras
Presidency, and appointed Col. Briggs and another officer
Commissioners, with full powers over the province. Of
these Col. Briggs was the chief. This appointment
displeased the Governor of Madras, who left no stone
unturned to reverse it, and after a year and a half
succeeded in getting Col. Briggs removed, and another

COLONEL BRIGGS. 33

officer put in his place. The difficulties and real hardships 1829.
(for he was then ill) which Col. Briggs underwent during this
time were communicated to his sympathising nephew and
friend in England, who gave what help he could by calling
the attention of the Directors of the Company to the case.
Nothing could be done, however, and Mr. James Mill
writes, 'From all I hear, I believe Col. Briggs' friends
have reason to rejoice in his dismissal.' l

The session of 1829-30 began nearly as the last

1 Dr. Briggs' ghost story, well known in the Madras Presidency
ninety years ago, was one of the best authenticated incidents of the
kind I ever heard. I give it here as it was told me, first by Mr.
De Morgan, who heard it from his mother ; afterwards by General
Briggs, who had it when a young man from Sir John Malcolm. His
father could not be induced to speak of it.

When my informant was a very young infant, Dr. Briggs, who was
quartered with his regiment somewhere (I forget the place) in the hill
country, used to hunt once or twice a week with the officers and others,
whose custom it was to breakfast at each other's houses after the sport
was over. On a day on which it was Dr. Briggs' turn to receive his
friends, he awoke at dawn, and saw a figure standing beside his bed.
He rubbed his eyes to make sure that he was awake, got up, crossed
the room, and washed his face well with cold water. He then turned,
and seeing the same figure, approached it and recognised a sister
whom he had left in England. He uttered some exclamation, and
fell down in a swoon, in which state he was found by the servant who
came to call him for the hunt. He was of course unable to join his
friends, who, when at breakfast on their return, rallied him on the
cause of his absence. While they were talking he suddenly looked up
aghast and said trembling, * Is it possible that none of you see the
woman who stands there ? ' They all declared there was no one. ' I
tell you there is,' he said. ' She is my sister. I beg you all to make
a note of this, for we shall hear of her death.' All present, sixteen in
number, of whom Sir John Malcolm was one, made an entry of the
occurrence and the date in their note-books, and by the first mail
which could bring the news from England the sister's death at the
time was announced. She had, before leaving this world, expressed a
wish that she could see her brother and leave her two young sons to
his care. Dr. Briggs was a man of great nerve and courage, and one
to whom the idea of a spirit's appearance would, until that time, have
been utterly ridiculous. The death of General Briggs some years
since, at the age of ninety, makes it allowable to publish the story,
which, however, he gave me for the purpose forty years ago.

P

34 MEMOIR OF AUGUSTUS DE MORGAN.

1829-30. had ended, and the dissensions in the institution were
publicly known. In March 1830 the Mathematical Pro-
fessor's share of the difficulties became serious, and a
correspondence between himself and the Warden resulted
in some modifications of the functions of that officer.
But the disturbances on the Medical side continued
through the year, the result of a series of alternate mis-
takes on the part of the authorities and remonstrances on
that of the Professors. One of these remonstrances is con-
tained in a letter written by Mr. De Morgan, who had been
asked by some members of the Council to lay before that
body the views he had expressed in a conference with a
Committee appointed to examine into some complaints pre-
ferred by the Anatomical class against their instructor,
Professor Pattison : l —

Letter to GENTLEMEN, — In compliance with the wish expressed by you

committee, when I had the honour of an interview with you, I lay before
you the views which I entertain on a subject most essentially
connected with the welfare of the University, viz., the situation
which the Professors ought to hold in the establishment. This
question is of the highest importance, inasmuch as upon the
manner in which it shall be settled depends the order of education
and merit which will be found among the Professors in future,
and the estimation in which they will be held by the public.

In order to induce men of character to fill the chairs of the
University, these latter must be rendered highly independent
and respectable. No man who feels (rightly) for himself will
face a class of pupils as long as there is anything in the character
in which he appears before them to excite any feelings but those
of the most entire respect. The pupils all know that there is a
body in the University superior to the Professors ; they should
also know that this body respects the Professors, and that the
fundamental laws of the institution will protect the Professor as
long as he discharges his duty, as certainly as they will lead to
his ejectment in case of misconduct or negligence. Unless the
pupils are well assured of this they will look upon the situation
of Professor as of very ambiguous respectability, and they will

1 I have avoided entering into details, leaving the principles at
issue to be inferred from Mr. De Morgan's letter,

LETTER TO COMMITTEE OF COUNCIL, 35

only be wrong inasmuch as there will be no ambiguity at all in 1831.
the case.

With the public the situation will be altogether as bad.
Wherever the Professor goes, he will meet no one in a similar
situation to his own — that is, no one who has put his character
and prospects into the hands of a number of private individuals.
The clergyman, the lawyer, the physician, the tutor or Professor
in the ancient Universities, will all look down upon him, for they
are all secured in the possession of their characters. Nothing but
the public voice, or the law of the land, can touch them, and a
security as good must be given to the Professor of the London
University before he can pretend to mix in their society as their
equal.

If these were the sentiments of one individual only, they
would merit little attention ; but if they be the opinions of a
majority of the present Professors, or even of a large minority,
the committee may be sure that they are prevalent among the
class of men from which the University ought to expect to draw
its Professors. The sense of the Professors on this subject can be
readily ascertained, and the committee will incur a heavy moral
responsibility should they, without the most attentive examina-
tion, propose a change which may place the Professors, present
or future, in the situation I have described. For mark the con-
sequences. If I am right, every man who has the feelings of a
gentleman will abandon the University in disgust ; the same
feeling will prevent any person of considerable attainments from
offering himself for the vacant chairs ; and the University, in the
general school at least, will sink into the most paltry of all estab-
lishments for education, if, indeed, it long continue to exist. I
am not mentioning my own opinions alone ; such deductions are
very common at present. I hardly meet one of my friends who
does not seriously advise me to resign my situation on these very
grounds.

The committee has done me the honour to ask my opinion
as to the principles to be laid down for the future regulation of
the Professorships. I will state, in few words, my own convic-
tions on the subject.

The University will never be other than divided against itself
as long as the principle of expediency is recognised in the dis-
missal of Professors. There will always be some one who, in
the opinion of some of his colleagues, is doing injury to the
school by his manner of teaching ; and there will always be

P 3

36 MEMOIR OF AUGUSTUS DE MORGAN.

•1831. attempts in progress to remove the obnoxious individual. The
medical school is peculiarly subject to this evil, owing to the very
frequent jealousies of one another which arise among the mem-
bers of that profession. No man will feel secure in his seat ;
and, consequently, no man will feel it his interest to give up his
time to the affairs of his class. And yet this is absolutely
necessary in the general school at least, for from the moment
when a class becomes numerous the preparation, arrangement,
and conduct of a system of instruction is nearly the business of
a life ; at least, I have found it so. If a Professor is easily
removable, he will endeavour to secure something else of a more
certain tenure ; he will turn his attention to some literary under-
taking, or to private pupils, while he remains in the institution,
in order that he may not be without resource if the caprice of the
governing body should remove him — and this to the manifest
detriment of his class, which, when it pays him well, ought to
command his best exertions. In addition to this, he will al-
ways be on the watch to establish himself in some less precarious
employment, which he will do even at pecuniary loss, since,
especially if he have a family, it must be his first object. In this
way the University will become a nursery of Professors for
better conducted institutions of all descriptions, since no man,
or body of men, desirous to secure a competent teacher in any
branch of knowledge, will need to give themselves the trouble to
examine into the pretensions of candidates as long as any one
fit for their purpose is at the University of London. The conse-
quence will be a perpetual change of system in the different classes
of the University, and the eventual loss of its reputation as a place
of education. These evils may be very simply avoided by mak-
ing the continuance of the Professors in their chairs determinable
only by death, voluntary resignation, or misconduct either in
their character of Professors or as gentlemen, proved before a
competent tribunal, so framed that there shall be no doubt in the
public mind of the justice of their decision.

But this, it has been said, will be to give the Professors a
vested interest. I assert that, in the proper sense of the words
vested interest, it ought so to be. Who have more interest in
the well-being of the University than I and my colleagues ? Is
it the Proprietary and the Council, on account of the capital
invested by them, and their zeal for the advancement of educa-
tion ? In the latter we yield to none of them ; and as to
pecuniary risks, I, for example, have invested the whole results

LETTER TO COMMITTEE OF COUNCIL. 3*7

of an expensive education, for the original outlay of which I 1831.
might buy fifty shares at the market price ; and even omitting
this, I have invested here my time, character, and prospects, all
and every one of which is as truly an investment of capital as
that made by any proprietor — with this addition, that it is my all ;
whereas the portion of any proprietor is a very small part of his.
Can it be expected, then, that the Professor should be the only
person in the institution who has no interest in it ? and that he,
merely on account of the important part he has to play, should
be placed in a situation not so respectable as that of a domestic
servant ? These are truths which cannot but have the greatest
weight with every person who shall hereafter think of embarking
his fortunes here ; and the only way to secure proper Professors
on the whole is to respect these truths, and not to let incidental
advantages, even supposing them such now, be considered of
more importance than general results.

An institution such as ours is a machine meant to last for
centuries, but this it cannot do if those who manage it are content
to avail themselves of expediency, which is made for the day,
in preference to fixed principle, which will never wear out.

I have written these sentiments because I feel no trouble too
great when the end proposed is so truly useful. Personally I
feel but slightly interested, for I cannot conceal from myself that
the chance of resuming my duties in the University is very small.
The opinions which I have here given will be the guide of my
conduct, and, I have reason to believe, of that of others also.
But should the result of the present proceedings be that a
Professor of the University of London need not hold down his
head for shame when he hears his situation mentioned, and the
terms on which he holds it, no one is more ready than myself to
stand or fall with this institution. This is, I fear, not an un-
meaning pledge, for past events have so fixed in the minds of
men an impression unfavourable to our prospects, that I fear our
number of pupils will be seriously diminished in the ensuing
session.

In conclusion, gentlemen, I have to thank you for the polite
attention with which I was received by you when I took an
opportunity of laying these sentiments before you in person, and
I beg to subscribe myself,

Your obedient servant,

AUGUSTUS DE MORGAN.
90 Guilford Street, July 15, 1831.

38 MEMOIR OF AUGUSTUS DE MORGAN.

1831. Mr. De Morgan also wrote the following letter, offi-

cially addressed to the Council through the Warden : —

SIR, — I beg leave to address the Council through you on a
subject which I approach with great reluctance.

It is well known to the Council that I have often differed
from them on matters connected with the management of the
University, and that, when I have done so, I have never hesitated
to declare my opinions in the plainest language. The Council
will therefore believe me when I say that I am convinced that they
and the Professors have during the last session been coming to
such an understanding as would have made the supremacy of the
former quite consistent with the respectability and independence
of the latter. A third body has, however, interfered in the ques-
tion, whose declared intentions, if carried into effect, will render
it impossible for me to continue in the situation I at present hold.

Should the result of the labours of the Select Committee be
the abrogation of the by-laws alluded to at the General Meeting,
I respectfully inform the Council that it is my intention to seek
elsewhere the subsistence and character which I had hoped to
gain in the University of London alone. At the same time I
feel it would not be dealing fairly with the Council if I let them
remain in ignorance of my determination, considering that the
deliberation of the Proprietors may possibly be pushed to a late
period in the vacation, when a proper choice of a successor to
my chair may be rendered difficult by the shortness of time re-
maining for that purpose. Having announced my intention, I
am therefore in the hands of the Council ; should they consider
it unfair in me to offer a conditional resignation dependent on cir-
cumstances over which they have no control, I will, on intimation
to that effect, offer an absolute resignation immediately. My
wish is decidedly to remain in the University, if that can be done
consistently with my own notions of what is due to my character.
Having thus shortly stated the predicament in which I find my-
self placed, I leave the matter to the decision of the Council.
I have the honour to remain, sir,

Your obedient servant,

AUGUSTUS DE MORGAN.

90 Guilford Street, July 1831.

The whole was brought to a crisis a few days after by
the dismissal of the Professor of Anatomy, the resolution

FIRST RESIGNATION OF PROFESSORSHIP. 39

for which concluded with these words : — 'Kesolved — That, 1831.
in taking this step, the Council feel it due to Professor
Pa,ttison to state that nothing which has come to their
knowledge with respect to his conduct has in any way
tended to impeach either his general character or profes-
sional skill and knowledge.'

Immediately on hearing of this resolution, Mr. De
Morgan sent in the following letter of resignation : —

To the Council.

GENTLEMEN, — I have just seen Mr. Pattison, who has informed
me of his removal from his chair, and has also shown me a reso-
lution, of which this is a copy. [Copy of resolution as above.]
Here is distinctly laid down the principle that a Professor may
be removed, and, as far as you can do it, disgraced, without any
fault of his own.

This heing understood, I should think it discreditable to hold
a Professorship under you one moment longer.

I have, therefore, the honour to resign my Professorship, and
to remain, gentlemen,

Your obedient servant,

90 Guilford Street, A. DE MORGAN.

Sunday, July 24, 1831.

The answer came in the words, ' The Council accept your

In reply to a letter from my father, he wrote : —

90 GuUford Street, July 29, 1831.

DEAR SIR, — I have just received your kind note, which I Letter to
hasten to answer.

The Council, in a session held after the meeting on Saturday,
deprived Mr. Pattison of his Professorship, alleging at the same
time, in vindication of themselves, I suppose, that nothing which
had ever come to their knowledge had any tendency to lower
their opinion either of Mr. Pattison's general character or of his
professional skill and knowledge ; thus laying down the principle
that a Professor might be deprived of his office without any fault
of his own, and even under a fire of encomiums from the Council.

I had long fully made up my mind not to hold any office
whatever which was not absolutely my own during good be-
haviour— not even in the service of Government, should such a

40 MEMOIR OF AUGUSTUS DE MORGAN.

1831. thing ever fall in my way. Immediately, therefore, on seeing
the minute of Council containing the aforesaid removal, together
with their most sufficient reason for the same as a rider, I ad-
dressed a letter to the Council that, under the principle there
advocated, I should consider it discreditable to hold their Pro-
fessorship one moment longer. The resignation was of course
accepted, and I have done with them.

This step will be against my pecuniary interest should the
University ultimately succeed very well, which the present pro-
ceedings of the Council will not allow any man to think who
knows how much such an institution depends on public opinion.
For the present moment, and up to the present time, I shall be
no loser, since I know that by my own private exertions I can
gain as much as, thanks to the dissensions in the University and
the conduct of the Council regarding them, I have ever done in
my public capacity.

With regard to an accusation and a hearing supposed by you
necessary previous to the removal of a Professor, I must en-
lighten you on a principle discovered in the University of London
by the Council, and faithfully acted on by them up to the present
moment ; viz., that a Professor in their institution is on the same
footing with regard to them as a domestic servant to his master,
with, however, the disadvantage of the former not being able to
demand a month's wages or a month's warning. The proprietors,
by their sense expressed at public meetings, have agreed with
them, it appears to me.

I have still some interest in the University on account of some
valued friends who remain behind, having what the advertise-
ments call encumbrances. They, however, have expressed their
determination to remain only one session longer ; and feeling, as
I do, that I never could send a ward of mine to an institution
where it has been thus admitted by precedent that the student is
a proper person to dictate the continuance and decide the merits
of a Professor, I cannot wish the University to succeed, because
I feel it ought not to succeed upon those principles.

If there be a large body of the Proprietary really interested
in the moral as well as intellectual part of education, their efforts
may yet save that fine institution. As a proprietor of it I would
gladly lend my humble aid.

Yours most sincerely,

A. DE MORGAN.

41

SECTION III.

1831 TO 1836.

AT the time when he left the College, Mr. De Morgan 1831,
was living with his family in Guilford Street, but re-
moved in the autumn of 1831 to 5 Upper Gower Street,
where he lived till our marriage in 1837. His only sister
had been married the year before to Mr. Lewis Hensley,
a surgeon of ability and good practice. My own family
left Stoke Newington and settled at 31 Upper Bedford
Place, Eussell Square, in 1830.

In May 1828, shortly after his first coming to London,
Mr. De Morgan had been elected a Fellow of the Astro-
nomical Society, and in February 1830 took his place on
the Council. Of the state of Science just before that |»te of
period, Sir John Herschel said: ' The end of the eighteenth
and the beginning of the nineteenth century were re-
markable for the small amount of scientific movement
going on in this country, especially in its more exact
departments. . . . Mathematics were at the last gasp,
and Astronomy nearly so — I mean in those members of
its frame which depend upon precise measurement and
systematic calculation. The chilling torpor of routine
had begun to spread itself over all those branches of
Science which wanted the excitement of experimental
research.'

In 1820 the Astronomical Society was founded by
Mr. Baily in conjunction with Dr. Pearson, and from the
time of its formation the joint efforts of many earnest
intellectual men were given to raise the higher sciences

42 MEMOIR OF AUGUSTUS DE MORGAN.

1831. from the state of depression and inactivity described by
Sir John Herschel. The work, however, had not been
uninterrupted, and the difficulties attending their task
were increased by some injudicious persons who liked
better to attack old errors and abuses than to work
harmoniously with those whose only aim was to introduce
better methods and measures.

This was inseparable from a condition of reconstruction
— the same spirit of change and reconstruction that was
at work in the political world — and the obstacles thrown
in the way of reform by men whose efforts went either
in the wrong direction or too far in the right direction,
were not felt only in science. Of this time my husband
wrote some years after : c I first began to know the Scien-
tific world in 1828. The forces were then mustering for
what may be called the great battle of 1830. The great
epidemic which produced the French Revolution, and
what is yet (1866) the English Reform Bill, showed its
effect on the scientific world.' The nature and extent of
the scientific works begun before this time and carried
out to completeness during the half-century which fol-
lowed, can be but slightly mentioned. Mr. Francis Baily
had effected the improvement in the f Nautical Almanac,'
and compiled the Society's ' Catalogue of Stars.' Sir
John Herschel was engaged on his ' Catalogue of Double
Stars,' to complete which he left England for the Cape of
Good Hope nearly three years later. The Royal Observa-
tory, Greenwich, was in full operation, under the direction
of Professor, now Sir George Airy. Astronomy was
rapidly approaching that height on which it now stands,
and the efforts of the Astronomical Society — a body of
men working with earnestness and unanimity — did much
to raise it to its present state.

Mr. De Morgan was elected honorary secretary in
1831. He entered with zeal into every question brought
before the Society, and his place was not a sinecure. It
is not easy to say how much of the usefulness and pros-

THE ASTRONOMICAL SOCIETY. 43

perity of the Society during the years in which Mr. De 1831.
Morgan filled this place was due to his incessant energy
and effort, and to his steady judgment at difficult junctures.

His work at the Society brought him into immediate Astrono-
contact with all its transactions and with all concerned in
thorn, and as he never left London, and was known to be
always at hand, much more than the routine duties of an
honorary secretary would have fallen to his share, even if he
had not voluntarily taken them upon himself. He drew up
documents, wrote letters, and arranged for the meetings and
the publication of memoirs. His obituary notices, written
as one after another of his fellow- workers left the world,
are biographical photographs, taken with a skill that
makes the sunlight bring out all the finest as well as the
most characteristic lines of the face.

In the year 1831, the second of Sir James South's
presidency, a royal charter was granted to this Society.
It was made out in the name of the President, owing to a
legal formality, which would have involved greater expense
to the Society if others of the Council had been included.
But though no mention of differences of opinion appears
on the minutes of the Society, there was certainly any-
thing but unanimity as to the manner of receiving this
grant, for Mr. De Morgan has preserved the following
letter from Captain, afterwards Admiral Smyth, in answer
to the requisition officially made for another Council meet-
ing to re-discuss the question. The style of the formal
letter contrasts strongly with the friendly effusions to the
' Esteemed Sec.' and ' Dear Mentor ' of after times : —

In answer to the requisition for a Conncil to meet on Satur-
day next to re-discuss the subject of the charter, I regret to say
that indispensable occupations prevent my attendance; but, I
must add, if leisure were at my command I should still strongly
object to being called away from employment on account of the
whims of an individual.

I consider the point in question to have been already as well
considered as the true spirit of our association requires ; that
any objection that has been started is more specious than valid ;

44 MEMOIR OF AUGUSTUS DE MORGAN.

1831. and that any further alteration will be merely a distinction
without a difference. I firmly believe that every member of the
Council has acted to the best of his ability and opportunity, and
also feel that the Council, as a body, has ever shown itself more
zealous about substance than about quibbling forms ; but they
might as well frame laws and institutions for Mars or Jupiter as
for those who are predetermined to be dissatisfied.

I therefore trust, in order that the vigour of the Society
may not be fettered, that the Council will take effectual steps to
repel every disorderly attempt to impute motives or impugn its
conduct, as well as to stifle their rancorous disputes, which can
only engender an atrophy of moral work. If this is not insisted
on, the meeting, which was purely instituted for the propagation
of Science, will quickly degenerate into a spouting club, in which,
instead of the adduction of undistorted facts, we shall be exposed
to all the artillery of premisses without conclusions, and conclu-
sions without premisses, added to the iteration of undigested
thoughts in all the turgidity of ill-taste; and even were the
reasoning powers among us more perfect, we should only be
making much noise and little progress, leaving the good uncer-
tain and remote, while the evil would be certain and immediate.
Moreover, the disputatious system, being both irritable and irri-
tating, is altogether as absurd for astronomers as would be the
dramatising of Newton's Principia.

I therefore firmly hope that a perfect union in the cause we
are embarked on will distinguish our efforts, for the straightfor-
ward course of duty is as perfectly practicable as it is desirable.
I have the honour to be, sir,

Your obedient servant,

W. H. SMYTH.

Professor De Morgan, Sec. Ast. Soc.

Who the individual was whose ( whims' Captain
Smyth refers to I cannot say. But it is a significant fact
that Sir J. South, whose Presidency had not expired when
the charter was granted, was not re-elected in the new
staff of officers, nor does his name appear on the Council
after this time.

Mr. De Morgan's acquaintance with his colleagues on
the Council of the Astronomical Society became in several
cases intimate friendship. His friends were Mr. Baily,

FRANCIS BAILY. 45

Sir John Herschel, the Astronomer Royal, Lord Wrottesley, 1831 ,
Rev. Richard Sheepshanks, Admiral Manners, Mr. Gallo-
way, and a few others. Mr. Sheepshanks and Mr. Galloway
had houses in the immediate neighbourhood of Gower
Street, and Mr. Baily lived at 37 Tavistock Place— a
pleasant house in a garden sheltered by sycamores. This
house, rendered famous by the repetition of the Cavendish
experiment, had formerly belonged to Mr. Perry, of the
6 Times.' In it my mother had met Porson, and heard
him repeat Greek poetry.1

Mr. Baily was well fitted by his clear-headed steadiness
of character, as well as by his excellent temper and
geniality, to form the centre of a knot of friends sharing
in the same pursuits. The same qualities made him an
excellent host, and a better President of the Astronomical
Society than if he had been a more brilliant talker. His
kindly, simple bearing gained the love of those who could
only look at his work with wonder. I remember feeling
proud of having played a game of chess, in which I was of
course beaten, with him. His house and appointments were
just what they should be, made perfect to his friends by the
cordiality of his reception. After his sister came to live
with him, when this welcome was extended to his friends'
wives and sisters, no house in London, I suppose, had held
more happy parties than 37 Tavistock Place.

I find an anecdote showing his characteristic order and
neatness in a letter left by my husband for the Institute
of Actuaries. The proposal referred to was made in 1835,
and related to the Cavendish experiment.

' That every rule must have its exceptions is true even
of Baily 's accuracy, though I should have thought the
assertion must have failed if I had not known the con-
trary. Few persons, however, know that this assertion
contradicts itself. For, if it be a rule that every rule has
its exception, this rule must have its exception ; that is,

1 This house was left by Miss Baily to Sir J. Herschel, and until
very lately was inhabited by Mr. Digby Wyatt.

46 MEMOIR OF AUGUSTUS DE MORGAN.

1831. there must be a rule without exception. Leaving this bone
for logicians to pick, I go on with my story. About 1835
the Government made an important proposal to the
Astronomical Society. Mr. Baily, the President, stated
that he had summoned the Council to consider a com-
munication from the Lords of the Admiralty, which he
would forthwith read. He then put his hand in his pocket,
and the paper was not there. This almost excited remark,
for that Mr. Baily should not remember in which pocket
what he looked for was to be found, was a very unlikely
thing. But the other pockets also answered in the negative,
and the end of it was that Baily announced that he must
have left his papers behind him. The announcement of
a comet with satellites would not have created half the
surprise which followed. There was nothing for it but to
take a cab and get back as quick as possible, leaving the
Council to decide nem. con., though it could not be entered
on the minutes, that they liked the President all the
better for being, to absolute demonstration, a man of like
failings with themselves.'

In the Supplement to the ' Penny Cyclopaedia ' Mr. De
Morgan wrote of Mr. Baily : —

( The history of the astronomy of the nineteenth cen-
tury will be incomplete without a catalogue of his labours.
He was one of the founders of the Astronomical Society,
and his attention to its affairs was as accurate and
minute as if it had been a firm of which he was the chief
clerk, with expectation of being taken into partnership.'

Sir John Herschel, the most distinguished in general
estimation of these co-workers, was not so often among
them at this time. He left England for the Cape of Good
Hope in 1833, and was of course unable during his absence
to take part in the practical business of the Society. My
husband's letters to him show how little his colleagues
liked to consider him absent. This correspondence began
in the year 1831, when Mr. De Morgan, as secretary,
addressed him with official formality, and continued till

EICHAKD SHEEPSHANKS. 47

1870, having for many years become the expression of 1831.
affectionate friendship.

The Astronomer Eoyal and Mrs. Airy were among the
most welcome of this circle of friends, who often met at
the house of Mr. Sheepshanks, where the presence of his
sister, a woman full of genial kindness, made all feel wel-
come and happy. All were fond of music, and Mrs. Airy's
and her sister's ballads, sung with a spirit that gave them
a character equal to Wilson's, were sometimes accompanied
by Mr. De Morgan's flute, and are still among my
pleasantest remembrances.

Mr. De Morgan had a strong regard for Mr. Sheep- Richard
shanks. Among many descriptive remarks, he says of shanks.
him in the MS. before mentioned, ' He was the man
from whom I learnt more than from all others of the
way to feel and acknowledge the merits of an opponent. I
have known many men cheerfully and candidly admit the
good points of an antagonist, but hardly another, besides
Sheepshanks, who would, in the course of opposition,
systematically select them, bring them forward, maintain
them against those of his own side ; and this always, year
after year, when engaged in warm opposition as well as in
jocose conversation, when in public discussion with several
as well as in private conversation with a single friend.'
And that which must be noticed is the vigorous and prac-
tical character of his friendship. His active and unwearied
assistance was as surely to be reckoned on as a law of
nature, especially if to the cause of his friend was attached
the opportunity of supporting some principle, or aiding
some question of science. ISTor was his kindness of feel-
ing limited to his friends. It showed itself in real and
thoughtful consideration for all with whom he came in
contact. Had he been a physician, his fanciful and self-
tormenting patients would have thought him the worst of
their ills, his milder cases of real suffering would have
been cheered by his bantering kindness, while severe and
dangerous malady would have felt the presence of the

48 MEMOIR OF AUGUSTUS DE MORGAN.

1831. sympathy which money cannot buy, shown with a delicacy
which benevolence itself cannot always command.

The reference to an opponent points to Sir James
South, who had become before this time a general oppo-
nent of most of his scientific friends. He joined Mr. Bab-
bage, who had accused some members of the Astronomical
Society of being in a conspiracy against him, and this
accusation elicited from Mr. De Morgan the following
description of his own relations with three of his
friends : —

The con- < The only conspirators named were MM. Airy and

Sheepshanks. These two and myself lived together in
intimate friendship, officers of the Astronomical Society
through a long course of years, ... we three, and each
for himself, deciding that he was a rational and practi-
cable man, and that the other two, no doubt worthy and
rational, were a couple of obstinate fellows. Francis
Baily thought the same of all three. I suppose we were
an equi-tenacious triangle. But never a sharp word, I am
sure, passed between any two of the four. Men of Science
are not always quarrelsome ; and, as often happens when
obstinate persons are reasoners, we were generally of one
line of action, with occasional repudiation of each other's
views. In all the many pleasant laughs we have had
together about the doings of the two common assailants,
nothing ever emerged which gave me the least impression
of the existence of any common purpose in the two other
minds, with reference to the eccentric anomalies of the
Astronomical world.'

Captain, afterwards Admiral Smyth, soon after this
time came from Bedford, and took up his abode in
Cheyne Walk, Chelsea. He, assisted, I have heard, by his
bowl of punch, was the life of the Astronomical Club, a
little meeting of chosen friends who repaired after the
business of the Society to the Piazza Coffee-house.
Captain Smyth was a genial companion and a quaint,
pleasant writer, devoted to Astronomical science. He also

ASTKONOMICAL SOCIETY. 49

gave a good deal of attention to antiquarian research, pub- 1831.
lished a quarto volume on the coins and other antiquities
of Hartwell House, whither he went some years after to '
take charge of Dr. Lee's observatory. I think that my
husband's intercourse with his co-secretary, Admiral
Manners, was at first chiefly official ; but in after years
we saw more of him, and he continued till death our
cordial friend.

Mr. and Mrs. Bishop were living at South Villa, George
Eegent's Park. Mr. Bishop was at one time President
and for many years treasurer of the Eoyal Astronomical
Society. His love of science never abated while he lived,
and it led him to undertake a difficult study at an age
when most men hold elementary learning out of the
question. Shortly after this time he came to Mr. De
Morgan for lessons in algebra, in order to read the
Mecanique Celeste. The little observatory in the Eegent's
Park was rendered famous by Mr. Hind's discovery of
many asteroids.

It was at Mr. Baily's suggestion that in the year 1827 Nautical
or 1828, the state of the Nautical Almanac was made the
subject of Government inquiry. This ephemeris, which
was under the management of the Admiralty, had not, as
to the information it aiforded to navigators, kept pace with
Continental works of the same character ; and its defects
and errors were great in comparison with theirs. The
Board of Longitude had suggested improvement, but this
Board was dissolved in 1827, and there seemed to be no
hope that the work, upon which the navigation of the
country greatly depended, should be brought to that
degree of perfection which the amount of scientific know-
ledge in England rendered possible. A strong remon-
strance from Mr. Baily drew attention to the matter, and
after some discussion in various quarters, the Commis-
sioners of the Admiralty entrusted to the Astronomical
Society the task of revising and remodelling the Nautical
Almanac. A committee was appointed and a Eeport

E

50

MEMOIR OF AUGUSTUS DE MORGAN.

1831.

1830-31.
Seconds
pendulum.

1881-32.
Useful
Knowledge
Society.

drawn up by Mr. Baily, who had given the subject un-
remitting attention. The recommendations of this Eeport
were adopted by Government, and the Nautical Almanac,
in its improved state, was the result. Lieutenant Strat-
ford was appointed Superintendent.

The pendulum experiments had been repeated by Mr.
Baily in 1828, under conditions which precluded any but
an almost imperceptible amount of error. Many other
determinations depended on these, a most important one
being the national standard of length ; for, in the event of
the standard yard being lost, the length of vibration of
the seconds pendulum was the only source from which a
new measure could be constructed. In 1832 a new scale
was formed by the Astronomical Society under Mr. Baily's
superintendence. This, which was rigorously tested, was
compared with the imperial standard, and with another
made by Bird in 1758. It was well that this work was
completed, as both these scales, as well as the national
standard of weight, were destroyed by fire in the Houses
of Parliament in 1834.

In all these works, after 1828, Mr. De Morgan took a
deep interest, but he was not an experimenter. He had a
great love for scientific instruments, and in his various
writings described their construction and work in such a
way as to make them readily understood by any person of
average intelligence. But his want of sight prevented his
using them himself, and his share of the work done at this
time of revival was, at least as to applied Science, that
of an expounder and historian. I believe that every dis-
covery, or determination of fact, of any importance, was
made as clear to the world as the subject allowed in his
articles in the ' Companion to the Almanac,' ' The Penny
Cyclopaedia,' and many other works.

The institution of the London University had been an
effect of that quickening of thought and action which ac-
companied what Mr. De Morgan called the social pot-boil-
ing. Another result in the same direction was the formation

POPULAR SCIENCE. 51

of the Society for the Diffusion of Useful Knowledge. It was 1831-32.
founded in 1826 by Lord Brougham, Mr. J. Hume, M.P.,
and others, most of whom had also taken part in the
establishment of the University. The object was to spread
scientific and other knowledge, by means of cheap and
clearly written treatises by the best writers of the time.
Partly from the character of free thought ascribed to
some of its founders, partly perhaps from its designation —
for there is much in a name, and * Diffusion of Useful
Knowledge ' sounded to some undistinguishing ears like
a parody of ' Promotion of Christian Knowledge ' — the
Society was held by some timorous lookers on to be a
sort of conspiracy to subvert all law and religion ; and
the publication of the ' Saturday Magazine,' a markedly
religious periodical, just after the appearance of the ' Penny
Magazine ' of the Society, showed the feeling of opposi-
tion that was in people's minds. One reason given for
this rival publication was that the ( Penny Magazine,'
like the other works of the Society, was too dry and
scientific for general readers. As for the Magazine itself,
it spread far and wide, and the ' Penny Cyclopaedia,' one
volume of which appeared at the end of the first year,
had a great circulation, and has taken its place as a high-
class book of reference. The charge of dryness is not so
easy to get rid of as regards some of the tracts ; but then
it would not be easy to make light and popular reading of
the higher branches of Mathematics, Chemistry, Hydro-
statics, or the Polarisation of Light. The Society did
good to its adversaries by making them give a better and
sounder character to their own works of professedly reli-
gious aim. A few words from the ' Address of the Com-
mittee' in the year 1846,1 when the Society's labours
came to an end, will give an idea of the principles on

1 This address was drawn up by Mr. De Morgan; Lord Brougham,
Sir Isaac Goldsmid, and one or two others made a few slight altera-
tions, amounting to about twenty lines, in his proof.

9 2

52 MEMOIR OF AUGUSTUS DE MORGAN.

1831-32. which it was founded, and to which it adhered through-
out.

Aims of the ' At its commencement the Society determined with
obvious prudence to avoid the great subjects of religion
and government, on which it was impossible to touch
without provoking angry discussion. At a time when
the spirit which produced the effects of 1828, 1829, and
1832, was struggling with those who, not very long
before, had tried to subdue it by force ; when religious
disqualification and political exclusion occupied the daily
attention of the press, and when the friends of education
were themselves divided on the best way of adjusting these
and other matters of legislation, any interference with
theology or politics would have endangered the existence
of a union which demanded the most cordial co-operation
from all who wished well to the cause. That the Society
took an appearance of political colour from the fact that
almost all its original supporters were of one party in
politics, is true ; but it is as true that if the committee
had waited to commence operations until both parties had
been ready to act together the work would have been yet
to begin, and the good which so many of the Society's
old opponents admit that it has done would have been
left undone. But the committee remember with great
satisfaction that this impossibility of combining different
views in support of a great object extended only to
politics. From the commencement the Society consisted
of men of almost every religious persuasion. The harmony
in which they have worked together is sufficient proof
that there is nothing in difference of doctrinal creed
which need prevent successful association when the object
is good and the points of dispute are avoided.'

Tracts. Mr. De Morgan, who became a member of the com-

mittee in the year 1843, was from the first a very large
contributor to its publications. His work ' The Differ-
ential and Integral Calculus ' formed a portion of the
series of tracts. The long list of articles in the ' Penny

USEFUL KNOWLEDGE SOCIETY. 53

Cyclopsedia,' amounting in all to nearly one- sixth of the 1831-32.
whole work, were begun by him at the outset, and con- Penny Cy-
eluded with the last volume of the Supplement, in 1858.

That his labours in this direction were fully appreciated
is certain. He gave time, advice, and help in every way to
the Society's work.1 I find on the title-page of the
Address from which the extract is made, in his own
handwriting, —

'This Address was drawn up by me ; even as to p. 17,
I had to blow my own trumpet, because those who
insisted on its being blown, and proposed to do it for me,
were going to blow louder than I liked.

6 A. DE MOKGAN.

'Aug. 26, 1852.'

P. 17 contained, to the best of my recollection, his
own modified version of the laudatory expressions inserted
in the rough draft by the President and Vice-President,
who had taken it home for inspection.

Private pupils occupied a good deal of the time which
Mr. De Morgan had before spent in lecturing in Univer-
sity College. He was also engaged in writing for the
' Quarterly Journal of Education ' of the Useful Know-
ledge Society, of which the first volume appeared in 1831.
It was carried on for five years under the editorship of Mr.
George Long, formerly Professor in University College.

The ' Companion to the Almanac ' for this year con-

1 In 1867, Mr. Coates wrote to Mr. De Morgan, in answer to his
inquiry as to the place where the relics of the Society were deposited, —

' Take my word for it, that I have the liveliest recollection of the
U.K.S., mingled with some pride, that for twenty years of my life I
was not altogether useless to mankind. Nor have I been since, as to
that matter, in spite of your innuendoes.7

' The archives, or papers of the Society, were deposited by Conolly
in (I suppose the cellars of) University College ; in two boxes or chests,
as I have heard.

' The process was after my dynasty was closed. The common seal
is in my hands, locked up in a little brass box, whereof Sir Isaac
Goldsmid had one key and Lord Brougham had another. The original
charter is, I suppose, in one of the two chests aforesaid.'

54 MEMOIR OF AUGUSTUS DE MORGAN.

1831. tains an article on Life Assurance, the first of a series of
twenty-five articles contributed annually by Mr. De Morgan
to this work.

In this year the ' Elements of Arithmetic ' was first
published. The author's old pupil, Mr. Eichard Hutton,
says of this book : —

Elements ' The publication of his " Arithmetic," a book which
has not unnaturally been more useful to masters than to
scholars, began a new era in the history of elementary
teaching in England ; devoting, as all his books did, far
more space and labour to the logical processes by which the
various rules are demonstrated than to the more technical
parts of the subject, though of these too, in their proper
place, the writer was never unmindful, spending the
greatest care on teaching the art of rapid and accurate
computation, no less than of the true science of number.
His exposition of the theory of limits, from the earliest
stage at which it entered into algebraical conception, was
so masterly and exhaustive, that it haunted his pupils in
the logical tangle of their later lives, and helped many a
man through the puzzle of Dr. Mansel's conundrum-
making as to ' the Infinite,' in his * Limits of Eeligious
Thought.' '

These few lines indicate the place which this book, an
early fruit of his own methods of reasoning, held in rela-
tion to the later writings, and show how, in his most
elementary teaching, he laid the foundation of principles
which were afterwards fully developed, and which fur-
nished a guide to thought on subjects whose connection
with them was not at first apparent.

He liked puzzles about numbers, as he liked riddles,
and, when very good, plays upon words and puns. So all
puzzles were referred to him, and gradually all attempts
to do the impossible, by circle squarers and trisectors. One

1 For a list of all Mr. De Morgan's works see Appendix. The
articles on education for the U. K. Society were reprinted in a book
entitled The Schoolmaster, edited by Charles Knight, London, 1836.

CHARLES BUTLER. 55

of the puzzles had a pleasant result. Mr. Charles 1832.
Butler, the Roman Catholic author of e The Revolutions of Charles
the Germanic Empire,' &c., an old friend of my father's,
was not only a very learned, but a very kind and genial
man. He dabbled (by his own account not very deeply) in
Mathematics, and was fond of algebraical and geometrical
questions. He gave me one, declaring that he had puzzled
over it in vain, and never yet had found a person who
could solve it. The following in Mr. De Morgan's writing
will tell the rest : —

' Mr. Charles Butler betted Miss Frend a coifee party A wager.
that she could not find a Mathematician who could make
out a certain difficulty. Miss Trend referred it to Mr.
De Morgan, who solved it. This letter is for the settle-
ment of the bet.'

'Mr. Butler presents his compliments to Mr. De
Morgan. ... He has perused with great pleasure Mr.
De Morgan's solution of the question proposed to Miss
Frend. It is certainly satisfactory in the highest degree.
Mr. Butler's great professional employment has prevented
his giving the attention he wished to the exact sciences,
but he has always entertained the greatest regard for them,
lamented his inability to prosecute them, and looked with
a holy envy on those who have time and talents to cultivate
them. The proposed coffee party has been changed into
a dinner party. It is fixed for Saturday, the 18th inst., at
Mr. Butler's house, 44 Great Ormond Street. Mr. Butler
requests Mr. De Morgan will do him the honour to join
the party.

'February 11, 1832.'

The party, a pleasant one, as the few now living
who remember Mr. Butler will readily believe, dined
together as appointed, and the solver of the problem was
duly honoured.

Everything belonging to education commanded Mr.
De Morgan's attention from the time when he began
to think. Many circumstances of his own University

56 MEMOIR OF AUGUSTUS DE MORGAN.

1832. career had shown him how much was needed in the Cam-
bridge system to adapt the methods and processes of in-
struction to the wants of learners of every degree and
variety of ability. His own place in the tripos of his year
was an evidence of the inadequacy of the competitive sys-
tem, faulty as it was then, and as it is now, to ascertain
the quantity or quality of mental power. Before he left
this world he saw that the method of crowding so much
learning into a short time, at an age when the brain needs
vital strength to bring it to maturity, was not the right
way to secure future excellence. Its results, too, were
beginning to be seen in nervous and other diseases ; but
he felt, and often said, that remonstrance as yet would
be useless, and that those who saw the evil only too
plainly must wait till the conviction of its reality should
be forced upon all. I have not been able to get his letters
Archdeacon to his old tutor, Dr. Thorp, but, judging by the replies, he
must have felt and expressed this belief at an early period.
The answers generally announce the reception of an essay
or book, or a new pupil sent by the old one to a teacher to
whom he held himself indebted. In one Dr. Thorp says :—

Yon will see that I have taken some pains to attend to the
spirit of yonr wishes about your young friend. "We are going
upon the plan of discouraging private tuition as much as possible,
for the sake both of tutors and pupils, as I hold that a lecture-
room ought to supply all that is necessary ; but as long as such
a various crew is sent up to us as we get every year, part re-
quiring the highest kind of scholarship and part unacquainted
with the rudiments, the latter must avail themselves of some
extra help to bring them up to the comprehension of such lectures
as the former require.

Surely the means and appliances now at work to pre-
pare young men for Cambridge ought to make private
tuition even less wanted than it was in 1832 ; and if stu-
dents were examined only 011 the real knowledge legiti-
mately gained in the lecture-room, which, as Dr. Thorp
says, ought to supply all that is necessary, what would

COMPETITIVE EXAMINATIONS. 57

become of cramming and coaching 91 If any supplementary 1832.
teaching is needed, it should be only to explain difficulties
in the lectures, not to introduce new subjects.

At another time Dr. Thorp writes from Cambridge : —

Believe me, my dear friend, I fully sympathise in the pleasure
you derive from reading classics in your own way only and for
information, and would like nothing better than to keep pace
with you in studying Aratus, Theon, and Euclid in the original ;
though I doubt whether young men would be made better mathe-
maticians, or as good classics or logicians hereby, as by the study
of authors more remarkable for system, and for the perfection of
language and of art. . . . You should come down and see us
oftener, to prevent your losing the knowledge of our streets.
Our streets, however, are not much more changed than our ways.
Have you seen our Trinity lecture-rooms, which we built at a Trinity
cost of 4,OOOZ. (besides a hole in the tutor's pocket, which a C
tutor in ancient times little thought of), and without asking any-
body ? It would make you a scholar to see the men going in
crowds every morning to be taught by fourteen tutors (that is
our number : I have got four, viz., myself, Martin, Law, and
John Wordsworth, on my side), each of whom gives two, and
some three lectures a day.

I rejoice to think that we have so much in common as — 1, some
affection for the University ; 2, something to do with preparing
young men for it ; and 3, some contempt for ' politics and stuff.'
But, believe me, it gives me sincere pleasure to see a few friendly
and familiar lines from one whom, though I have no right to claim
much merit for — which was his fault, not mine — I am not a little
proud to speak of as my old pupil. Ever, dear De Morgan,

' Your attached friend,

' T. THORP.'

This letter is dated 1833.

1 During the tune in which this has been written, several cases
have occurred which sadly confirm my assertions. One will suffice.
A young man, a very high wrangler, full of intellectual power and
aspiration, was obliged to give coaching lessons to undergraduates.
The exhaustion which followed his taking his degree and his subsequent
hard work led him to recruit his strength with stimulants, first opium,
then liquor. He drank himself to death. Had he not done so, in all
probability he would have been a victim to disease in some other
form, the result of exhausted vitality. This would have been less dis-
graceful perkaps, but equally lamentable.

58 MEMOIR OF AUGUSTUS DE MORGAN.

1832. With his keen interest in books and their history Mr.

De Morgan had a great love for collecting rare or ancient
ones. His little library was begun soon after he left
Cambridge, and the Theon, Aratus and Euclid, of which
he so much enjoyed the reading, were among the first he
bought, and are now with his other books in the library
of the University of London, in Burlington House.1 I
have heard him say that he never laid out a shilling on a
book which was not repaid with interest, even as a money
transaction, from the use he made of the purchase. Had
he been rich his collection would have been very large
and valuable, but he was soon obliged to deny himself the
luxury of buying, except the chance treasures which fell
in his way at bookstalls. The first English book which
he bought when a boy was ' The Pilgrim's Progress.' His
researches in bibliography, which afterwards resulted in
the ' Arithmetical Books,' the ' Budget of Paradoxes,' and
many of the tracts, date from the time of his beginning to
collect.

Visitors to the University Library, who take down any
of these works from the shelves, will almost certainly light
upon some of the numerous marginal notes and illustra-
tions, serious or otherwise, with which their former owner
embellished them. The fly-leaves and insides of the covers
are decorated with pictures from periodicals, notably Punch,
and other collectanea, always having some reference to
the contents of the work, although, to those unacquainted
with the peculiarities of Mr. De Morgan's mind and style,
the appropriateness of some of them may not at once
appear obvious.

M. Ha- M. Hachette, the French mathematician, whom Mr.

De Morgan had visited in his stay at Paris two years

1 This Institution must not be confused with University College,
Gower Street. The University of London is for granting degrees
only. It was founded in 1836. The books were bought of me, after
my husband's death, and presented to the University by Lord Over-
stone.

FRENCH CORRESPONDENTS. 59

before, was one of those who felt strongly on the struggle 1832.
for freedom and enlightenment. The two authors had
exchanged scientific brochures, and after thanking Mr.
De Morgan for some sent in 1831, M. Hachette asks
this question relating to the invention of the steam-
engine : —

VOTIS me ferez bien plaisir de m'eclaircir sur un fait relatif a M. Ha-
la construction de la machine a vapenr. Je lis dans 1'ouvrage de
M. Partington, * An Historical and Descriptive Account of the
Steam Engine,' London, 1822, p. 7, que Sir Samuel Morland
etait fils du baronet de meme nom, qui suivit Charles II. dans
son exil ; d'autres disent que ce baronet est le mecanicien qui a
le premier mesure la densite de la vapeur d'eau ; cependant M.
Partington est, dit-on, le bibliothecaire de 1'Institution Royale ;
il n'a pas ecrit sans preuve un fait de cette importance. Tachez
done de savoir la verite. Pour 1'honneur de la science, et de
Fhumanite, je desire que le mecanicien ne soit pas celui qu'on
accuse d'avoir trahi le parti constitutionnel.

I have not Mr. De Morgan's answer, but it appears
not to have settled his correspondent's doubts, though
they were afterwards in some measure set at rest.

In return for the answer to his own question, M. Vieta's
Hachette made some inquiries for Mr. De Morgan touch-
ing a missing book, the * Algebra Nova ' of Vieta. In the
letter giving what information he had gained I find the
first mention of Count Guglielmo Libri, author of the
6 History of Mathematics.' The last communication made
by M. Hachette touching the lost work of Vieta is as
follows : —

. . . J'ai recu la lettre que vous m'avez fait 1'honneur de
m'ecrire le 16 Juillet.

Le fait concernant le manuscrit du Harmonicon Celeste,
prete par Bouillaud au Prince Leopold de Medicis, est consigne
dans les MSS. de Bouillaud, et M. Guglielmo Libri, savant geo-
metre, m'en a donne 1'assurance. Les omissions de Montucla,
ou les erreurs de Delambre, nous prouvent qu'il faut chercher
dans les manuscrits, ou dans les ouvrages publics par leur auteur,
la verite de 1'histoire. . . .

Paris, Aout 15, 1832.

60 MEMOIR OF AUGUSTUS DE MORGAN.

1832. The remainder of the letter contains a comparison of

dates and facts, recurring again to his object of proving
that Morland the mechanician was not the Koyalist.
M. Hachette was probably the more satisfied in some de-
gree by the references Mr. De Morgan gave him, as I find
in the Penny Cyclopaedia article, founded on those au-
thorities, that the history of Morland's relations with the
Royalists is very doubtful.

His last letter to Mr. De Morgan is dated September 30,
1832.

Mr. De Morgan had, I think, met M. Quetelet in
Paris in 1830, but M. Quetelet had not remembered this
when he wrote to Mr. De Morgan in 1833, —

Mon cher Monsieur, — Je vons remercie beaucoup pour 1'obli-
geance que vous avez eue de m'addresser la table que vous m'avez
promise, et vos ouvrages que j'ai parcourus deja avec le plus
grand plaisir. La methode que j'ai trouvee dans vos livres
elementaires augmente encore le prix que j 'attache aux suffrages
honorables que vous avez bien voulu exprimer pour les miens.

Je suis tres charme que notre ami commun, M. Babbage,
m'ait procure le plaisir de faire votre connaissance : je desire
beaucoup le cultiver. Je regrette de ne pouvoir aller moi-meme
vous exprimer mes remerciments, mais, comme je vais aujonr-
d'hui, j'ai du me borner a vous ecrire, comptant bien sur votre
indulgence.

Recevez, je vous prie, mon cher monsieur, 1'expression de
mes sentimens distingues.

Tout a vous,

QUETELET.

Amicable The place of registrar of the Amicable Assurance

Office.ance Office having become vacant about this time, Mr. De
Morgan sent in his name as a candidate. He was of
course well qualified for the situation, and it was a lucra-
tive one, but he would not have liked the work so well as
he did teaching and writing, and he had, as he afterwards
told me, but one reason for wishing to succeed. Our
friend Mr. Thomas Galloway, a distinguished Mathe-
matician, and Fellow of the Astronomical Society, a man

TROUGHTON AND SIMMS V. SOUTH. 61

every way suited for the place, was appointed, and held 1833.
it until his death in 1851.

The ' opponent ' referred to in Mr. De Morgan's little
sketch of Mr. Sheepshanks was Sir James South, known
as the owner of the Campden Hill Observatory, and having
some name as an Astronomer on account of his dexterity
in using his very fine instruments. In the year 1833 a
trial of a curious character, in which Sir James South was
the defendant, commenced. With other scientific men
Mr. De Morgan was greatly interested in this affair, and
has left the following notice of it : —

'Mr. Sheepshanks's visits to Campden Hill were in
discharge of his duty as scientific adviser on the side of
Messrs. Troughton and Simms, who in 1833 brought an
action against Sir James South to recover payment for
mounting equatorially a large object-glass. While the
work was going on, Sir James thought it would not do,
insisted on beginning again upon a new plan, with offer
of payment of money out of pocket, and, on refusal, shut
Messrs. Troughton and Simms out of his observatory.
The Court of course recommended arbitration ; and this
arbitration, which extended over 1833-1838, is the most
remarkable astronomical trial which ever took place in
England. The arbitrator was Mr. Maule, afterwards
judge, the senior wrangler of 1810, a powerful Mathema-
tician, and a man of uncommon sharpness of perception.
The counsel for Troughton and Simms was Mr. Starkie,
the senior wrangler of 1803, with Mr. Sheepshanks, who
was a witness, for his scientific adviser. The counsel for
Sir James South was Mr. Drinkwater Bethune, a well-
known Mathematician, and a high wrangler of 1823, as
sharp as Mr. Maule. Mr. Babbage was a witness and a
sort of scientific adviser. The arbitrator began by insist-
ing that Troughton and Simms should be allowed to
finish the work; he also permitted certain additions to
the plan proposed by Mr. Sheepshanks, on condition that
they should only be paid for if they succeeded. The

62 MEMOIR OF AUGUSTUS DE MORGAN.

.1833. instrument was made serviceable in the opinion of the
arbitrator, and the whole claim was awarded, additions
included. Sir James did not let the instrument remain to
shame the arbitrator and the opponent witnesses; he
broke it up, sold the materials by auction, and placarded
the walls with a bill, headed " Observatory, Kensington ; "
and addressed to " shy cock toy makers, smoke-jack
makers, mock coin makers, &c. &c.," and stating that
" several hundredweight of brass, &c., being the metal
of the great equatorial instrument made for the Ken-
sington Observatory by Messrs. Troughton and Simins,
were to be sold by hand on the premises ; the wooden
polar axis of which, by "the same artists, with its botchings
cobbled up by their assistants, Mr. Airy and the Rev. E.
Sheepshanks, was purchased by divers vendors of old
clothes, and dealers in dead cows and horses, with the
exception of a fragment of mahogany specially reserved,
at the request of several distinguished philosophers, on
account of the great anxiety expressed by foreign astro-
nomers to possess them, was converted into snuff-boxes as
a souvenir piquant of the state of the art of Astronomical
instrument making in England during the nineteenth

century, will be disposed of at per pound."3

I do not mention these things with any wish to throw
blame on one who, as after events proved, was in a state
of mind which rendered eccentricity excusable. But at
that time this was not known, and, as so often happens,
that which would form an excuse for foolish conduct, and
ought to give others the right of restraining it, was not
suspected. The troubles arising from this cause among
men of science, and reaching public associations, were as
real as if they had been the result of wicked designs
rather than of morbid impulse. The Astronomer Eoyal,
who wished to visit Campden Hill for the inspection of
Groombridge's transit circle, begged that no reference
might be made during his visit to the trial then pending.
Sir James insultingly accused him of having changed his

SIR JAMES SOUTH. 63

opinions on that question, &c. On Mr. Airy's declining 1834.
farther correspondence till assured that no disrespect was
meant. Sir James * waited on a military officer of high sir James
rank in her Majesty's service,' who, however, either refused South-
to accept the office offered to him, or quietly stopped the
aggression. Sir James afterwards published the whole
account as an advertisement in the Times of Nov. 29,
1838, in an attack upon the Admiralty. But all persons
who had taken part with the prosecutors in the arbitra-
tion, or who had expressed an opinion contrary to that of
Sir James, were held by him as enemies. Mr. De Morgan,
as the intimate friend of Mr. Sheepshanks, and honorary
secretary of the Astronomical Society, was one of these.

Meeting him one day at the rooms of Lieut. Stratford,
then assistant secretary, Sir James, in a loud voice, asked
the latter to show him the time when and recommenda-
tion on which Mr. De Morgan had been elected a Fellow
of the R.A.S., and added something about 'those gentle-
men ignorami' by whom the election had been made.
Mr. De Morgan took no notice of this, but afterwards
addressed a temperate note to the speaker, saying that it
had appeared to him that Sir James South asking in his
presence for the time, &c., when he became a member of
the Society was not in accordance with the sort of
courtesy which parties who wish to behave distantly
towards each other usually observe when they meet in
private. He asked whether this was to be imputed to
forgetfulness, or to a desire to convey the impression that
Sir James had no wish to practise towards himself that
negative courtesy with which a stranger is usually treated.
He begged for an answer, that he might know how to
behave towards Sir James in case they should meet again,
4 since, in any case,' he says, ' I should not consider such
a breach of etiquette worth any further consideration.'

Sir James South's answer is curious. It ends with —
' As to how you regulate your demeanour towards myself
if we should happen to meet again, that is a point which,

64 MEMOIR OF AUGUSTUS DE MORGAN.

1834. though it may concern yourself, is to me a matter of the
completest indifference.

* After conduct such as I have recently received, and
in which you have borne, I am told, no inconsiderable
part, I beg to decline further correspondence with you,
and must refer you for any further information you may
require to my friend Captain Francis Beaufort, R.N., to
whom I have confided the preservation of my character
as a man, and my honour as a gentleman.

( I remain, sir, your obedient servant,

' J. SOUTH.

' Observatory, Campden Hill,
' March 15, 1834.'

Captain Beaufort being thus referred to, Mr. De
Morgan wrote to that gentleman, stating the circum-
stances, and saying that he was by no means sure that any
offence was intended.

His letter was quiet and temperate, and Captain Beau-
fort and Lieut. Eaper, who, I have been told, were satisfied
that whatever allusions to gunpowder might be made, it
was certain that any waste of that article was not really
contemplated by Sir James, were soon authorised by him
to assure Mr. De Morgan that no offence had been meant.
The affair passed off. In these days, when good sense and
good feeling are generally found more effectual in keeping
the peace than ' the laws of honour,' we may remember,
that although duels were lamented and reprobated forty
years ago, it was often more easy to fight than to avoid
one. But it must not be forgotten that had the required
assurance not been given by Sir J. South, it would have
been almost impossible for Mr. De Morgan as Secretary of
the Society to have afterwards met him.

The death of M. Hachette at Paris occurred at this
time. Mr. De Morgan, who had a strong sympathy with
and regard for this excellent man, had already received
the news before hearing as follows from Dr. Gregory :—

DEATH OF HACHETTE. 65

You have probably heard of the death of onr friend M. 1834.
Hachette at Paris. It took place in January last, but I did not Letter froti
learn it till about a fortnight ago, in a letter from M. Quetelet.
... I have met with very few men of science whom I have so
much admired and esteemed as M. Hachette. He had an ardour
in the pursuit and promotion of science not to be extinguished
by the shameful treatment which for years he met with ; and
his gentleness, kindness, single-heartedness, and generosity were
particularly engaging. . . .

I quite share your feelings of indignation, not only on
account of the shameful treatment experienced by M. Hachette
for so many years, but also on account of the chary and meagrely
doled out measure of justice he has received since his death. As
a man of Science he was truly estimable, and laid Science under
many obligations not yet acknowledged ; and as a man among
French men of Science his character was altogether unique. I
am glad that you so decidedly intend doing him justice.1

I am glad to know that you are about a work on the Dif-
ferential Calculus upon the principles to which you refer. I
have long felt that recourse to algebraical expansions in series,
in establishing the principles, is exceedingly illogical, and have
therefore long been perplexed to know what book to employ as
a text-book. In my own class here I have principally employed

Francoeur in the second vol. of his Mathematiques Pures

The anomalies which you specify are exceedingly curious, and
serve still further to confirm me in my long-cherished persuasion
that the fashionable process is hollow and unstable, and referable
to no irrefragable principle. I wish you complete success accord-
ing to your views of what the logic and metaphysics of first
principles require in your important and interesting undertaking.
. . . And I am,

Yours very cordially,

OLINTHUS GREGORY.

Early in the year 1836 The Connexion of Number and
Magnitude was published. It is an attempt to explain
the fifth book of Euclid. In the Preface the author says,
' The subject is one of some real difficulty, arising from the
limited character of the symbols of Arithmetic considered
as representatives of ratios, and the consequent iutroduc-

1 In the Astronomical Obituary Notices.
F

66 MEMOIR OF AUGUSTUS DE MORGAN.

1834. tion of incommensurable ratios, that is, of ratios which
have 110 arithmetical representation. The whole number of
students is divided into two classes : those who do not
feel satisfied without rigorous definition and deduction ;
and those who would rather miss both than take a long
road, while a shorter one can be cut at no greater expense
than that of declaring that there shall be propositions
which arithmetical demonstrations declare there are not.
This work is intended for the former class.'

Most of his books were illustrated after his own fashion.
The connexion of Number and Magnitude is shown by a
gigantic father having the contents of his pocket rifled by
a crowd of dwarfish children, one meaning of which I
understand to be, to represent the properties of magnitude
analysed by the aid of number.

The author made a great descent in his next book, as
he tells a correspondent. The Useful Knowledge Society,
which, notwithstanding the Rev. Dr. Folliott's low esti-
mate of the ' learned friend ' in Peacock's ( Crotchet
Castle,' was a most useful instrument in raising the
objects and methods of thought of both those who had,
and those who had not thought before, out of a foggy
region of half-knowledge into a comparatively clear and
systematised state, had published 6 Maps of the Stars,' for
students of Astronomy, together with smaller ones for
popular use, and six maps of the Earth. Mr. De Morgan
wrote for the Society an explanation of all these maps.1

Mr. Lubbock furnished some of the materials for the
' Explanation,' &c., in the account of the selection of
objects, the authorities, and the notation employed.

On the back of the title-page is written by the author,
' Ce coquin de livre a etc* commence pendant 1'ete de 1833,
et n'a ete fini que dans le mois de Mai 1836.'

1 Entitled An Explanation of the Gnomonic Projection of the Sphere,
1 and of such points of Astronomy as are most necessary in the use of
Astronomical maps; being a description of the construction and use of the
smaller and larger maps of theU.K.S. ; also of the six maps of the Earth.'

USEFUL KNOWLEDGE SOCIETY'S PUBLICATIONS. 67

This book is exceedingly clear, and even popular. 1836.
The treatise on and explanation of different projections of
the sphere, with the reasons for rejecting Mercator's, are
given in the first chapter. A great deal of bibliogra-
phical knowledge appears in the reference to early Astro-
nomers, and not only much knowledge of Astronomy, but
much of the history of it may be gained from the work.
Astronomical Science in England in the sixteenth century
is represented by an explanation of the constellations
given by T. Hood in 1590 :—

Scholar. I marvell why,- seeing she (Ursa Major) hath the Astronomy
forme of a beare, her taile should be so long. sixteenth

Master. I imagine that Jupiter, fearing to come too nigh century,
unto her teeth, layde hold of her tayle, and thereby drew her
up into the heaven, so that shee of her selfe being very weigh tye,
and the distance from the earth to the heavens very great, there
was great likelihood that her taile must stretch. Other reason
know I none.

A passage from the book adds interest to one of the
letters to Sir John Herschel : —

The figures of the constellations are of no use to the -Astro- Forms of
nomer as such ; a star is sufficiently well known when its right
ascension and declination are given ; and if letters referring to
the constellations are used, such as ft in Orion, y in Draco, &c.,
it is not now to direct the attention to any imaginary figure of
an armed man or a dragon, but to a particular region of the
heavens, which might with equal propriety have been called
region A or region B. It is to the mythological antiquary that
the figures are useful, as sometimes throwing light upon his pur-
suits. Every ancient people has written its own account of the
singular fables, which are common to all mythologies, upon
groups of stars in the heavens, and it might have been thought
that some feeling of congruity, if taste were too much to expect,
would have prevented the burlesque of mixing the utensils of
modern life with the stories of the heroic age, presenting much
such an appearance as the model of a locomotive steam-engine
on the top of the Parthenon. But the Lacailles, the Halleys, and
the Heveliuses have arranged it otherwise ; the water-bearer pours
a part of the stream which should wash the southern fish into a

F 2

68 MEMOIR OF AUGUSTUS DE MORGAN.

1836. sculptor's workshop ; a carpenter's rule has got between old
Chiron and the altar on which he was going to sacrifice a wolf;
and the lion and the hydra, whose juxtaposition has made more
than one speculator imagine he has found a key to the whole
allegory, are in truth two Astronomers fighting for a sextant,
\\hich Hevelius has placed at their disposal. A great deal of
the southern sphere is laid out in mathematical instruments.
If figures are to be drawn at all, it is, as we have said, for the
historian, and not for the Astronomer; and we imagine the
former will think it no loss that in our maps the heavens of
Ptolemy have been restored, and in no one drawing exceeded.
The names only, and boundaries of the modern constellations are
given ; but all the figures are those of Ptolemy, so arranged as
to represent his catalogue.

The constellations are fortunately not in danger of
being renamed before the origin and meaning of the old
signs and symbols are well understood. Many Astro-
nomers, however, were then watching the names of heavenly
bodies newly discovered with a jealous eye, fearing more
mathematical instruments or other incongruities.

Mr. Temple Chevalier wrote to my husband some time
after : — ' Can there not be some proper protest a.gainst the
introduction of earthly names among the heavenly bodies ?
The heathen mythology, independently of lending itself to
analogy, is exactly fitted to the purpose, by lending itself
to allusions, <j>w>vsvra O-VVSTOLCTI. Such are those contained
in Parthenope, Hygeia, Calliope, Irene, and others.
When a planet shall be discovered at Oxford, " Isis " will
be another name of the same kind. In the Comptcs
Rendus it appears that " Lutetia " was given because no
one exclaimed against " Massilia." It seems high time to
avoid more mud being thrown into the skies ; or are we to
have Lugdunum Batavorum, and other equally barbarous
incursions ? '

Perhaps, barbarous as it is, the plan of calling constella-
tions and planets after continental towns and scientific
instruments is less mischievous as regards antiquarian
research than mixing mythological words, ' lending them-

NAMES OF CONSTELLATIONS. 69

selves to allusions ' without reference to time, system, or 1836.
symbol, with the ancient names, all of which bear some
reference to the religions and philosophies of the earliest
times, and furnish a key to some of the deepest mysteries
of past ages.

The death of one of my sisters in March 1836, while Death ^ot
we were at 31 Upper Bedford Place, called out all our sister. &
friend's sympathy and kindness. He had a very affectionate
regard for her, and his warm-hearted friendship was deeply
felt by my family in this time of sorrow.

We left London in the autumn, to spend some months
in the west of England. Mr. De Morgan undertook to
forward letters, and in many other ways to give that
useful help which those at home can always render to the
absent. This occasioned frequent communications; and
in allusion to my own love for the country being about
equal to his for town, his letters contained many ironical
contrasts between our desolate condition in Devonshire
and his own enviable life in empty London. Part of this
time he was confined to the house by an illness which,
however, was not dangerous, and which did not interfere
with his writing. This illness occurred in August, and
prevented his visiting us at Clifton during the Bristol
meeting of the British Association.

Before the end of this year he again took his place as
Professor of Mathematics in University College. In October
1836, Mr. White, his successor, who had been spending Death of
the vacation in the Channel Islands, ventured, with his White,
wife and child, to cross from Guernsey to Jersey in a small
sailing boat. The sea was unusually rough, and the re-
monstrances of the boatmen were unheeded. The boat
capsized, and all on board were lost. This grievous event
took place at the end of the College vacation. The classes
were to open immediately, and the Mathematical chair — in
some respects the most important of all, as, independently
of its own importance, that of Natural Philosophy de-
pended on it — was without a Professor, and the difficulty of

70

MEMOIR OF AUGUSTUS DE MORGAN.

1836.

Invitation
to return to
University
College.

Letter to
Sir H.

Nicolas.

filling it, either for a time or permanently, was greater
than it would have been at another season of the year,
when the authorities would have been in London.

Mr. De Morgan felt the great emergency of the case,
and immediately offered to supply the want until the
Christmas following. Only one who, like himself, had
filled the chair before, could have taken it on so short a
notice, and I am certain that in acting on his first impulse
he consulted the needs of the Institution, without any
thought of the chances of a permanent return. But, once
installed in his old place, it was foreseen by all his friends
that an effort would be made to keep him there ; and he
judged, from the changes which had been made in the
management, that his former objections to holding office
in the College would not recur. An intimation soon came
that the offer would be made, unless it should be distinctly
understood that it would be rejected. His thoughts on
this occasion were set forth in a letter to his friend Sir
Harris Nicolas, by whose opinion as a lawyer he deter-
mined to abide.

MY DEAR SIR HARRIS, — I will not make any apology for asking
of your friendship to consider the following case, and to give me
your advice ; firstly, because I believe yon will willingly give me
your opinion ; and secondly, because I do not even make you run
the risk of incurring the ordinary odium which unfortunate
advisers are sure to meet with if they do not turn out to be
right. For I do not want you to advise me what is right or
what is wrong, or what is safe or what is unsafe ; but I only
want to ascertain the effect upon the mind of an unprejudiced
person produced by the following account, without reference to
the question whether such effect could or could not be made the
basis of safe and honourable rule of action.

The London University opened in 1828, and I was one of the
Professors. The tenure of the Professorships amounted to this,
that they were removable by the Council with or without reason
assigned, having right of appeal against such dismissal to the
Court of Proprietors ; a body, as it afterwards turned out, not
without materials for agitation, but the numerical strength of
which could always be swayed by the Council, partly owing to

PROPOSED RETURN TO PROFESSORSHIP. 71

its consisting of men of business, who could not, or would not, 1836.
take any great interest, partly by the system of voting by proxy, Letter to
the Council holding, as might be supposed, a great number of Sir **•
proxies.

Shortly after the commencement of the Institution various
causes of irritation arose between the Council and Pro-
fessors, partly owing, in my belief, to the desire of power and
influence in an individual who stood in an ill-defined position ;
partly to the jealousy of some members of the Council whose
political bias led them to think the best way of preventing an
administrative officer from going wrong was to tie him up so
tight that he could neither go right nor wrong, but very much
from a feeling among the Professors that their position was not
safe, and in particular a suspicion, which suppose well founded,
that the Council intended to divide the Professorships as soon as
the income became considerable.

In the course of the years 1828 and 1829 the Professors —
that is, a considerable number of them — made such representa-
tions to the Council of their unwillingness to remain in so
ambiguous a position, backed with a declaration of their inten-
tion to retire, as induced that body to subject themselves to by-
laws in regard to dismissal of a Professor, requiring long notice,
considerable attendance, and decided majority before a Professor
could be dismissed. It is to be noticed that these by-laws,
though rescindible at the pleasure of the body which imposed
them, were honourably adhered to in the subsequent matters,
and that no technical difficulties were thrown in the way of the
appeal to the Court of Proprietors.

This matter being settled for the present, though no great
confidence in either body existed on the part of the other, disturb-
ances arose in the Anatomical class, the pupils questioning the
competency of their Professor. Suppose it admitted that these
disturbances were excited in the first instance by insinuations
of two other Professors in their lectures, and were culpably
fomented by the individual already alluded to, and by certain
members of the Council ; suppose also that repeated investiga-
tions into the competency of the Professor in question failed in
establishing anything against him, and that he was finally dis-
missed in consequence of the Council not being able to quell the
disturbance, and of the interference of the Court of Proprietors,
under the name of a Select Committee, which resolved to the
effect that there could be no peace in the University while

72 MEMOIR OF AUGUSTUS DE MOIlGAN.

1836. Mr. remained, and then denied that they had recommended

Letter to his dismissal ?

Nicolas ^n ^is dismissal, within twenty minutes of hearing it

authenticated, I retired from the University, writing the follow-
ing letter to the Council.1

This took place in July or August 1831.

In consequence of the retirement of other Professors, and of
the severe loss sustained by the classes, as I suppose, a different
system of management was finally adopted. It is detailed in the
printed paper enclosed, of which the parts in question are scored
in black ink where they relate to the Professor and Council, and
in red ink where they relate to the Professor and his pupils.2

My successor has, most unfortunately for the University,
been lost at sea, which was communicated to me very suddenly
by one of my old colleagues. My first impulse was to offer to
perform the duties till Christmas, which I accordingly did, look-
ing at the moment only to the inconvenience and probable loss
which would be sustained by the institution opening without
one of its most material chairs.

But on looking out into the world in this new character of
a pro tempore substitute of my former self, I find in the first
place a wish on the part of all I have spoken to (or rather, who
have spoken to me) that I should return to my old post per-
manently, mixed, I suspect, with a strong notion that such is
my desire. I am, therefore, if I do not choose finally to make
any overture on this subject, or to allow any to be made, in a
position to be supposed to have coquetted with this divorcee of
mine, and unsuccessfully. This I mean to avoid by taking a
very early opportunity of stating to anybody who thinks it worth
while to ask the question, whether I will take it or not. I want
the opinion of an unprejudiced person, who knows the world, on
the following questions : —

1. Do the regulations here submitted amount to bond fide
moral security that Professorships in the University of London
are offices tenable during good behaviour, and not held at
pleasure ?

2. In addition to the practical security, supposing it to exist,
do they offer that exterior show of being so held which would
place the holders in that advantageous position as to respect-
ability which a gentleman (meaning only by education and

1 See p. 39.

'2 The document itself is much too long for insertion.

LETTER TO SIR HARRIS NICOLAS. 73

sentiments, for God knows all the rest is but leather and 1830
prunella) requires, one who believes that no independent man
can hold at the pleasure of any individual or corporation, except
perhaps the Crown, and then only because usage has made laws ?

3. Does the regulation relating to that case provide the security
which a prudent man would think requisite against the subdivi-
sion of the Professorship in the event of its becoming lucrative ?

We will suppose it comparatively immaterial what shall or
shall not be good behaviour, and who shall decide, presuming on
the check of public opinion, which operated strongly though not
effectually on a former occasion. And, on the one hand, let the
affirmative of the question (1) have all the advantage of its
having been found very difficult to remove a Professor, even
under the old regime ; while, on the other hand, it must have all
the disadvantage of the appeal to the Court of Proprietors being
utterly worthless.

Your opinion should be given on no supposition of the
affirmative being desired, if possible.

Should I accept any offer (for I shall certainly not be a
candidate) I should rather lose than gain for the time ; and I do
'not consider the prospect of ultimate gain as greater than that I
now have. The advantage would be the resumption of an occu-
pation which is in itself pleasant to me, and which has some few
pleasing associations. But in a thing so nearly indifferent to
myself, the notion of what people in general would think would
have some weight.

If your answers are such as would not please any parties con-
cerned, I will keep this communication entirely secret, and
remain,

Yours sincerely,

A. DE MORGAN.
5 Upper Gower Street, Oct. 10, 1836.

N.B. — The appeal to the Court of Proprietors is abolished ,
which must be considered as increasing the respectability of the
Professorships, since, entre nous, a body of commercial English -
men got together upon a point of trade (and with these gentlemen,
as was sufficiently evident before, the honour and character of a
Professor was avowedly, and almost ipsissimis verbis, made a
question of trade) knows neither right from wrong, nor reason
from anything else.

The answer must have been such as would please all

74 MEMOIR OF AUGUSTUS DE MORGAN.

1836. parties, for when, immediately after, an offer of the
Mathematical chair accompanied the thanks of the Coun-
cil for Mr. De Morgan's considerate kindness, the offer was
accepted, and the Professor once more settled in his old
place. I dare not, in the face of his and my firm
belief that all things are ordered for us by a wiser judg-
ment than our own, express regret that this should have
been ; but the six-and-thirty years of intense labour which
followed, ill paid at the time, and terminated by a disappoint-
ment which broke his heart, may well make me hesitate to
record his return with satisfaction. But he loved his
work, and his pupils were endeared to him by the interest
they took in his teaching, and their efforts to profit by it.

75

SECTION IV.

CORRESPONDENCE FROM 1831 TO 1836.

To Sir J. Herschel

5 Upper Gower Street, Oct. 16, 1832.

MY DEAR SIR JOHN, — I have just duly received your Cata- 1832.
logue, which must in course of things be the first paper ordered
for press, after those already so disposed of. I shall be very
much obliged to you for all you have offered on the Catalogue,
the Comet, and the Herscheliana. The crumbs which fall
from a rich man's table are good — astronomically, whatever they
may be gastronomically.

Have you got, or do you know anything of, Bouillaud's
or Bullialdi's Astronomia PTiilolaica ? There is a copy in the
British Museum which wants the Prolegomena, which is the
very part I want. The matter has reference to Vieta's Har-
monicon Celeste, which has been supposed to be lost, and which
I have a faint hope might be recovered. Bouillaud is reported
to say that somebody stole it from Mersenne, and certainly
Vossius quotes words to that effect from the Prolegomena. But
my good friend M. Hachette assures me that this is a mistake,
and that Bouillaud, in his unpublished MS. at Paris, says that
he himself lent Vieta's MSS. to Leopold, Duke of Tuscany. If
this be true, some library at Florence may yet contain it. I am
the more inclined to hope this, as Schootten, in the Preface
to Vieta, gives as his reason for omitting the Harmonicon
Celeste, not that no copy was to be had, but that the only one
he could get appeared imperfect. Neither Montucla, Delambre,
nor Kastner is to be trusted implicitly — at least with regard to
Vieta. Neither of them was aware of the fact that Vieta
during his life published a collection of his works, or rather I
should say that the first publication of his works was in the form
of a collection, and that they did not appear severally, but were

76 MEMOIR OF AUGUSTUS DE MORGAN.

1832. afterwards severed by editors, as Ghetaldi and others. The name
of this book, which was quite lost, was Restituta Mathematica
Aiialysis, and it contained, among other things, the first seven
books of the Restituta Mathematica^ which all the above his-
torians agree are lost. Perhaps this book may yet turn up
somewhere. I would hope from these circumstances that people
will think it worth while to look a little more into these points.
I remain, my dear Sir John,

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

5 Upper Gower Street, Dec. 27, 1833.

MY DEAR SIR JOHN, — I have a young relation going your way,
and though my lucubrations generally speaking are little worth,
yet as I know paper direct from England acquires a certain
value by crossing the sea, I shall try to fill up this sheet with
English news, or rather with what must pass for such in stag-
nation of better. Thank you, in the first place, for your paper
on nebulae, which I duly received, proving that you never went
to look after the southern hemisphere till you had pretty well
rummaged the northern. . . .

I have written a note to Mr. Baily, informing him of this
opportunity, but as I have only had twelve hours' notice of it, I
am not sure that you will hear from him. In any case, he is in
good health, and thriving as no man better deserves to be. The
same as to predicaments of the Astronomical. Your papers,
namely, Catalogues and observations of Uranus, duly received,
and will be read in course. I shall take care of the proofs, and
Mr. Baily also. The Royal has had several meetings about
their funds. It appears that they are obliged to sell out to
pay arrears, and also that their estimated expenditure exceeds
their income. They do not seem to know where to reduce. I do
not know whether you left England before or after Captain Ross
returned. He was at the Astronomical in November in high
feather. -To judge by his case, the northern latitudes must be
good for consumptive people.

I am not aware whether you know Mr. I , though I sup-
pose you do. A paper by him was read at the Astronomical,
containing an account of Flamsteed, &c. As Captain Ross was
there, the penny-a-liners got hold of the Astronomical, and com-

CORRESPONDENCE, 1831-36. 77

mitted paragraph ology. They spelt Halley, Nalley, whereupon 1833.
Mr. I wrote to Captain Beaufort, whom he had no acquaint-
ance with, and asked him whether the Astronomical had been
attacking anybody under fictitious surnames. Captain Beaufort
answered, I believe, that the paper would be published and he
might see, and thereupon sent him our abstract when it appeared.

Mr. I then said that the whole was an attack upon him, as

having copied from Professor Airy in his paper on ' Physical
Astronomy,' and reasoning very correctly, said it would have
been much better in the Royal to have refused to print his paper
in that case than to have suborned the Astronomical to attack
him, &c.

* From this and several other things I have heard I am very
much afraid that he (I ) is decidedly wrong in his head.

Of course you have heard of your medal from the Institute.
How could they be so imprudent as to risk annihilation at the
hands of Captain Forman ? l

Health and prosperity to you and all yours. Catalogy to the
nebulae of the southern hemisphere,

I remain, dear Sir John,

Yours truly,

A. DE MORGAN.

To Sir J. Herschel.

MY DEAR SIR JOHN, — The bearer, Mr. Templeton, now going
to the Cape, has offered .to take this, whereupon I have ad-
vertised Mr. Baily of the same, and his letter accompanies it.
We have not up to this date heard of your arrival, or even of
MacClear's, which I suppose we hardly could.

I wrote you a gossiping letter by Mr. W. Bird, which I hope
you got duly. Great is your loss if you missed it, for it was
replete with on dits. I presume Mr. Baily has made you
acquainted with all that has passed, which, as far as I know,
amounts to very little. The anniversary of the Astronomical
Society takes place on Friday (this is Wednesday), and I am
just come from a preparatory meeting of Council. There is an
old proverb that when the nose itches some one is talking of the
wearer. I hope for your sake that the converse is not true ; but
a very good way to test it will be to look in your diary, if you

1 An irrepressible paradoxer.

78 MEMOIR OF AUGUSTUS DE MORGAN.

1834. keep one, for the state of your nasal economy on February
14th.

Yonr excellent friend, Captain Forraan, has got a rise in the
world. Sedgdwick has mentioned him in the notes to a pub-
lished sermon' on the studies at Cambridge ; not, indeed, as an
individual, but as the representative of a class, ' The Formans '
of the day. You know the story of Louis XIV., who noticed a
merchant very much, and thereby emboldened him to ask for
letters of nobility, which he got, and the King never spoke to
him after, saying, ' You were the first of your class, now you are
the last.' Would you rather be the first of the Formans or the
last of the savans ?

Your paper on Uranus and Co. is in course of reading at the
Astronomical. The observations of Captain Foster will nearly
fill Volume VII. of our Memoirs ; but if any paper is added to
them, it must be your Test Objects which has been read, and this.
You will therefore receive them before long. I forget at this
moment whether you ordered extra copies, but I have your last
letter and shall look ; I shall also ask Mr. Baily. I should not
have troubled you with such a scrawl had I not Mr. Baily's
letter to send, to which this shall be scum or dregs, according as
you think it most flighty or stupid.

Yours very truly,

A. DE MORGAN.

5 Upper Gower Street,

Wednesday, Feby. 14, 1834.

To William Frend.

Sept. 1, 1834.

MY DEAR SIR, — I was not surprised to find on my return to
town on Friday that yon had decamped, seeing that you take
pleasure in the wilderness. Neither must you be astonished that
I did not exceed by a single day my estimate of the time I could
bear the viridity of extra-urban scenery. I suppose you will let
me know how to direct to you before long. While my health is
recovering from the effects of the raw atmosphere I have been
breathing, I write this in preference to more serious occupation.
This is no joke, I assure you ; whenever I return from the coun-
try I am knocked down for some days, and could be ill with
very little contrivance or external instigation, which never hap-
pens if I stay in town. And yet I have been only two days
regularly in the wilds. To give you some account of my progress,

CORRESPONDENCE, 1831-36. 79

I went to stay with a clerical friend,1 who lives six miles from 1834.
any town or village, except the thing he calls his parish, and a
lone house he calls his rectory. So, he having no vehicle except
a four-legged apparatus called a pony, we slung my baggage
across the beast, and crossed the country on foot like a gipsy
migration, talking Mathematics over his head to his very great
edification. Indeed he, the quadruped, looked as wise and pro-
fited as much as some of my preceding pupils have done. How
people live in such lone houses I know not. Conceive me
reduced to clip hedges to pass away the time till dinner, which
1 did with great gout, seeing that it is reducing trees to some-
thing like regularity, and diminishing the sum-total of foliage.
From thence I went to Oxford, where I was thrown upon my
resources for a whole evening. The only incident worth notice
was that, having strolled out and picked up some second-hand
books at a book-stall, rather Cornelius Agrippa looking sort of
things, a good-looking old gentleman (a stout Church and State
man, I'll swear) was so astoucded that he changed his table to
increase his distance, and looked at me as if he expected to see
me carried away by an Avatar of the evil principle. Thence got
I to Bedford, where I stayed some days with Captain Smyth,
heard all the town politics, saw a jail with two men in it, father
and son, charged with cutting the tails off fifteen pigs, dined
with a clericus, and did various other things, not forgetting seeing
a play acted by little children. Captain Smyth's observatory
is the most beautiful little thing imaginable, mounting a 5-foot
transit, a 3-foot circle (belonging to our Society), and an 8-foot
equatorial. We had no very fine night, so that I could not know
all the merits of the latter; but judging from what I saw, it
must be a very capital instrument of its kind. Thence got I to
Cambridge inside a coach with a lady, whose history I wormed
out of her, agreeably to a talent I have for doing those things
when I like, which you will admit when I tell you that in a ride
of twenty-five miles I ascertained that she had married when
very young an officer of 1st Light Dragoons, with him had gone
to India, was stationed at Bangalore, where she travelled ; how
he died, she came home, and married the vicar of some place
which I now forget ; and, having stayed at some place, which I
equally forget, was now moving, with furniture following in a
waggon, and husband deposited outside the coach, to take pos-
session of his living, first stopping to dine with a friend, whose
1 Rev. Arthur Neate.

80 MEMOIR OF AUGUSTUS BE MORGAN.

1834. name I forget. I also ascertained which of all my cousins in
India she had danced with in her day, which was instructive to
know. These, and a great many other things, did I ascertain ;
so you may see that if I am not communicative myself, I know
how to make other people so when they do not know what I am
at. At Cambridge I found Sheepshanks, Peacock, and several
new buildings, the former of whom drove me to Madingley, a
place I never saw ig^ my life before, so you may judge how far
my walks extended as an undergraduate. Came home as tired
as a city mouse of hedgerows and cottages, and was more
nearly in a good humour with the fiddler who stands opposite
my window on a Saturday night than I could previously have
thought possible. If the locomotives ever come to go so quick
that one tree shall not be distinguishable from another, then, and
not before, do I become a traveller. Mr. Stephenson (engineer)
says he shall never be satisfied till two hours take us from
London to Liverpool. Blessings on his heart, but either he or,
better still, one of the minority who can be spared, shall try it
first. I have not got a large organ of caution for nothing. I am
delighted with the House .of Lords for throwing out the hard
bargain of 80 per cent, of Irish tithes to be secured upon the
land. The I. P.1 will never get so good a composition again. I

perfectly agree now with Lord that the Commons would

sometimes blunder if it were not for the Lords. Can you. imagine

Lord , the quondam Liberal, instigating the House of

Lords to put it in the power of Commissioners to hinder any
pauper's religious instructors from having access to him unless
he were of Parliament principles ? No letters from you, from
which I conclude that your thoughts are of trees, only interrupted
by the slopping of the waves, which are always fiddling at the
sand till I long to give them a thump, and tell them to be easy.
The prettiest thing about the sea is the straight horizon and the
isochronism of the waves in deep water, but near the shore they
do not keep time like my pendulum. . . . We have got our
rooms (in part) given up to me, and about the end of September
shall begin to stir in getting them ready. All the people are out)
of town except myself, and they might as well make me Secretary
of State as set me painting, plastering, and whitewashing*
Stratford is gone to Ramsgate with Mrs. S (as he calls her — I
abominate initial letters) tratford, Baily to Edinburgh, Hender-
son, &c., ditto. There is not a soul left that I know of, which is

1 Quaere Irish People ? I cannot interpret these political allusions.

CORRESPONDENCE. 8 1

a great advantage of being in town in the summer ; for, saving 1834.
your absence, it is a good thing to be thrown upon oneself for a
month or two, to say nothing of the quantity of work one does.
I was very sorry to find when I came home tthat Mr. Woolgar
had been very uncourfceously received by B^^'with my note.
That unfortunate man will never rest until he succeeds in getting
nobody's good word. He calculates very wrong (for a calculating
machine maker) if he thinks such a thrower of stones as himself
can stand alone in the world. It takes all his analysis and his
machine to boot to induce me to say I will ever have any com-
munication with him again, which nothing should induce me to
do except the consideration that men of real knowledge should
have more allowance made for them than some charlatans I
know. I make no doubt Mr. Woolgar will detail to you the
reception he received. . . .

Apropos of logarithms, give my kind regards to all your
circle, and believe me, dear sir,

Yours sincerely,

A. DE MORGAN.

5 Upper Gower Street.

To William Frend, Hastings.

DEAR SIR, — I have nothing whatever in the nature of news
to tell you, except that the Astronomical Society has ob-
tained possession of its rooms l and moved into them, with
nothing remarkable except that one of the secretaries, whom you
know, had an opportunity of confirming an observation he has
often made, that upholsterers, carpenters, and all concerned in
furniture, are laudatores temporis acti, whatever may be their age.
The bookcases of the Society are ' such as are not made now ; '
and even the old orange chests, bought for a trifle to put books
in, are ' such as they doesn't make nowadays,' according to one
of the workmen. However, the race of men are not degenerated,
for four of them took up in their arms our large iron safety
affair, and carried it slick right away into a van, whereas five
men took two hours with iron rollers, &c., to get it into the
chambers a year ago.

I have got the care of all the churches upon me now ; that is,
builders' estimates, &c., with a hitch as to prices. Mr. Baily is
out of town, and workmen must be in the premises on Wednes-
day at latest. We are in this condition. The Royal Society,

1 In Somerset House.
G

82 MEMOIR OF AUGUSTUS DE MORGAN.

1836. which owns the upper storey, has cat a floor through what was
a staircase, so that our rooms in part present a section like the fol-
lowing.1 .... However, I suppose it will come right somehow or
other. Our meeting- room will hold from ninety to a hundred com-
fortably. Our largest meeting hitherto has been eighty.
Give my kind regards all round, and believe me,

Yours sincerely,

A. DE MORGAN.
5 Upper Gower Street.

To Dean Peacock.

DEAR SIR, — I send you herewith my series, corrected and
revised in the newest manner. The result is so much generalised
from that in the Calculus of Functions, that I think it may be
considered as new matter.

I send also a small work with a new kind of title, being an
endeavour to make the fifth book of Euclid somewhat readable.
It is meant to be the first part of a book on Trigonometry. The
astronomical world here has been enlightened by a starlight
Knight,2 at the Royal Institute. What Young and Faraday
have there said of physics has been completely outdone. I did
not hear the lectures, but ani told that if I had I should have
known how George III., surrounded by his Astronomers, went
to Kew to see an occultation, foregoing the stag-hunt which
was going on ; how a cloud hid the moon, and how the pious
King, without a single murmur against Providence (a point dwelt
upon as remarkable), turned the telescope at the hunters, and
saw the stag killed, between the two horizontal wires. The second
lecture was closed by a description of the unfitness of Mathema-
ticians to be practical Astronomers, with the exception of Bessel.
Now Sir James would have lectured at Cambridge with half the
pains which were taken to get Airy.

I remain, dear Sir,

Yours very sincerely,

A. DE MORGAN.
Upper Gower Street, April 25, 1836.

To Sir J. Herschel

MY DEAR SIR JOHN, — Some months ago, when the Calculus
of Functions which I now send you was published, I marked

1 The reader's imagination will easily supply the omitted sketch
from the context.

2 Sir Jaincs South.

CORRESPONDENCE. 83

one for you, which has been lying waiting opportunities. I am 1836,
glad now of the delay, as I am enabled to send with it some
maps of the stars which I have been charged to present to you
in the name of the Committee of the Society for the Diffusion of
Useful Knowledge. They are the first maps, I believe, in which
Sir William's nebulae and your own are laid down from the
Catalogue.

You will find a great deal of new speculation about an old
subject of yours in the Calculus of Functions, and in particular
a discussion which concerns you in § 252, &c.

The two books on Algebra and Number and Magnitude con-
tain various metaphysical points, which I heartily wish were
more attended to. I have not written your name in them be-
cause non constat that it is reasonable to expect you to bring
elementary books home again to England, where other copies
will be much at your service. Present them, therefore, to any
person or institution whom they will be of use to.

We are getting up a pictnre of Mr. Baily by subscription,
and the same is limited to a guinea. It has struck me that I do
not remember that anybody has put your name down, and that
you would not be pleased to be left out in any association which
is to do honour to such a man. I shall therefore take care that
the omission is remedied. The picture is to be presented to
the Astronomical Society.

Your sixth Catalogue has been printed, or will be struck off
shortly. Tbfe extra copies shall be forwarded to Mr. Stewart.
There is very little stirring in our world. You will have heard
that Captain Smyth had already asserted that the two stars
y Virginis were in peri-one-another, and was laughed at by some-
body for his assertion, which laughter your letter has turned on
his side.

I should suppose you now can almost fix the time of your re-
turn. I take it for granted you have learned the extraordinary
discoveries you have made in the moon. It was a dull joke to
republish the book in England, and I suspect in America it
was done to raise the wind. I flatter myself I did just as clever
a thing, which, however, has failed through Mr. Warren's want of
understanding ; at least, I have not seen it in print. I sent him
anonymously the following: —

' Sir John Herschel.' — This distinguished Astronomer writes
this to a friend from the Cape of Good Hope : — ' The climate here
is so bad that my mirrors tarnish immediately. I do not know

a 2

84 MEMOIR OF AUGUSTUS DE MORGAN.

1836. what I should have done if I had not taken the precaution to
bring out with me a large supply of Warren's jet blacking, pre-
pared at his manufactory, 30 Strand, the polish of which is so
exquisite that I can see the faintest stars in the haziest evenings.'
With best wishes, I remain,

Yours very truly,

A. DE MORGAN.
5 Upper Gower Street, July 10, 1836.

N.B. — The Southern Hemisphere on the maps looks tolerably
empty of nebulas. There is ample space and room enough the

characters of He 1 to trace, whence it follows that you may

mark the year and mark the night ; that is, dot down nebulas
through all the twenty-four hours of R.A., and the year and
night will be near enough as to time. Do you not find it
an awfully unromantic change to get out of the land of Hercules,
Draco, Cepheus, &c., into that of Pyxis Nautica, Cesium
Sculptoris, &c. ? If you have to make any new constellations,
remember that the president and other officers of the Astrono-
mical Society have an official claim. Presses Societatis Astro-
nomicas would look pretty; and a Press., or /3 Secret., would not
be amiss in a list of moon culminating stars.

Please to give my kind regards to Maclear and young
Smyth when you see them. Maclear's paper on the opposition
of Mars has reached the Astronomical Society duly, but we wait
about printing it till we hear of his observations. Of course
you know Bachelier, the mathematical bookseller at Paris. All
his stock has been burnt, and that of others at the same time. I
wanted Libri's ' History of Mathematics ' in July, and find it is
all gone in the flames.

85

SECTION V.

1836 TO 1846.

SOON after Mr. De Morgan's return to the college a great 1836.
affliction befell the family in the sudden death of his sister
Mrs. Hensley in her confinement. Her brother had left his
home in Go wer Street, satisfied that she was doing well, and
on his return in the afternoon inquired as he entered the
house how she was going on. The servant replied that
Mrs. Hensley was dead. It had been quite unexpected,
and was a terrible blow to her mother, her husband, and
brothers. Mrs. Hensley left three daughters and the
infant son whose birth immediately preceded her own
death. It was many months before her brother Augustus
recovered from the shock he received in hearing so sud-
denly of the event. In writing to my mother of the affliction
of his own, he added, c As for me, I am stunned, and
hardly know what I write.' And it was far longer before
the grief caused by this, his first experience of the death
of one whom he loved most affectionately, abated.

The religious doubts and difficulties created in his
mind by the doctrinal teaching of his early years were not
the only troubles arising from the same cause. It was
natural that a mother, so anxious and true-hearted as his,
should not see without pain anything like what she thought
carelessness in religious matters, and that her anxiety
to produce a belief like her own should be intensified
by her recent sorrow. His sister had shared her anxiety.
They looked upon him, of whose intellectual powers they
were proud, and who had been enabled to give such loving

86 MEMOIR OF AUGUSTUS DE MORGAN.

1836. and dutiful help to his family, as one perhaps doomed to
endless torment, because, using the power of head and inte-
grity of heart which made him so dear to them, he rejected
some orthodox creed, and the belief that his Father in
heaven was more cruel and unjust than any earthly father.

After his sister's death, his mother wrote to him with
painful earnestness on this subject, begging him to read
some writings left by his sister. His reply shows both
what he thought of the question and what he felt on the
sorrowful occasion which called it forth.1

From this letter it may be gathered that his opinions
at this time were Unitarian, according to the meaning
originally given by that word, and to the belief held by
those who first bore the name.2 There is now so much
confusion of ideas as to this, that it is necessary for
me to say what I mean in calling my husband a Unitarian.
He believed that Jesus Christ, the Son of God by the
gift of the Holy Spirit without measure, was, as to his
nature, a man like ourselves, except in His power of receiv-
ing the Spirit of God. That His divinity was not, like
that of the Father, the Source of all things, underived and
self -existent. That the Father spoke through Him by the
same Spirit, sending the message and the means of redemp-
tion or bringing back erring man to God. That the
mission was attested by His words and miraculous works,
and that He rose from the dead, and was seen to rise to
Heaven, from whence He sends the Spirit to those who are
able to receive it.

Mr. De Morgan never joined any religious sect, but I
think he had most respect for the Unitarians, as being
most honest in their expression of opinion, and having
most critical learning. The writer's belief in the supremacy
of reason to sift and interpret revelation, and his implicit

1 See correspondence following this section.

2 When a proposal was made to require the insertion in the census
return of the various religious denominations, he declared that he
should describe us as * Christians unattached.'

REASON AND FAITH. 87

faith, sufficient evidence having been obtained, are shown in 1836.
the letter, The two are results of the same mental
power, for reason enables us as well to interpret testi-
mony as to judge of its value. This only applies to that
religion which is of the head. My husband had a deep
instinctive spring of faith in his own soul, but with this,
the bond of union between his heavenly Father and him-
self, the world had nothing to do. Years after this letter
was written, he was supposed to have accepted, on slight
and insufficient grounds, facts pronounced unworthy of
examination by less profound thinkers. It may be that
the time will come when his guarded judgment of these
phenomena will be in turn condemned as too cautiously
expressed.1

Early in 1837, a measure for the abolition of Church 1837.
rates, and the application of Church property to meet rates.
the expenses for which they were levied, was proposed by
the Government. Large calculations were, of course,
necessary to show in what way the property could be
so managed as to meet the necessities of the Church,
without injustice to those dignitaries who were its present
holders, and actuaries were engaged to make these calcu-
lations, both on the part of the Ministers and on that of
the Opposition. Lord Ellenborough, then in office, applied
to Mr. De Morgan as follows : —

Mr. Finlaison, not being authorised to communicate with
Lord Ellenborough with respect to the details of the new plan
for the management of Church property, has had the goodness
to recommend to Lord Ellenborough that he should request the
assistance of Mr. De Morgan as the ablest of actuaries in the
elucidation of the subject, &c.

A very intricate calculation was gone through involv-
ing the values of leases for various terms of years, of
the fines levied on change of holder, and of every part of
the complicated question. Lord Ellenborough, between

1 See Preface to From Matter to Spirit.

MEMOIR OF AUGUSTUS DE MORGAN.

1837.

Marriage.

Settled in

Gower

Street.

whom and Mr. De Morgan several letters had passed,
wrote (March 14) : —

When the bill is printed and farther information is obtained,
I may have to trouble yon again with further questions ; but in
the mean time I cannot delay offering my acknowledgment to
you for the most valuable assistance you have already afforded.

This calculation occupied as many hours of several
days as could be spared from his two lectures and his
other work, and he had to sit up more than one night to
complete it. The Bill was lost, and with it Mr. De Mor-
gan's time and trouble.

In the vacation of this year we were married. Mr.
De Morgan's religious views are by this time well known
to the reader. I had been brought up in my father's
belief, but had not adhered to it without much modifica-
tion. My husband's objection to the marriage ceremony
was much stronger than my own, but my respect for his
scruples made me willing to comply with his wish that we
should not be married by the form prescribed by the
Church of England. We were married at the registrar's
office by the Rev. Thomas Madge, and by a form of words
differing from that in the prayer book only by the omis-
sion of the very small part to which we could not assent
with our whole hearts, and of the long exordium of St.
Paul on the duties of husbands and wives.

After a short tour in Normandy we settled at our first
home, 69 Gower Street. The books, which were then
tolerably numerous, had been taken from 5 Upper Gower
Street, a few weeks before, when his mother went to
a larger house in Manchester Street, Manchester Square.
Our house was so near the college that my husband could
come home in the intervals between his morning and
afternoon lectures, instead of remaining away from 8 A.M.
till 5 P.M., as he was obliged to do afterwards when we
lived at a greater distance from Gower Street.

My father was living in Tavistock Square at the time

EARLY MARRIED LIFE. 89

of our marriage. My husband had long known almost all 1837.
my father's circle of acquaintance. One exception — a
dear and early friend of mine whom he did not know per-
sonally till shortly before our marriage — was Lady Noel
Byron, whose health kept her much at home, and whom
he accompanied me to see at her house near Acton.
She soon became as truly his friend as she had been
mine. Lady Byron was always shy with strangers, es-
pecially with those who excited her veneration. This
shyness gave her an appearance of coldness, but she and
my husband soon knew each other's worth, and she never
lost an opportunity of showing her regard for him and
trust in his judgment. He was rather surprised to find in
one commonly reputed to be hard and austere, qualities
of quite an opposite nature. She was impulsive and affec-
tionate almost to a fault, but the expression of her
feelings was often checked by the habitual state of re-
pression in which the circumstances of her life had placed
her. I had known her from my childhood. My father,
whom she always held in the highest esteem, had taught
her Mathematics, as a friend, before her marriage. My
husband afterwards gave her daughter, Lady Love-
lace, then Lady King, much help in her mathematical
studies, which were carried farther than her mother's had
been. I well remember accompanying her to see Mr.
Babbage's wonderful analytical engine. While other
visitors gazed at the working of this beautiful instrument
with the sort of expression, and I dare say the sort of
feeling, that some savages are said to have shown on first
seeing a looking-glass or hearing a gun — if, indeed, they
had as strong an idea of its marvellousness — Miss Byron,
young as she was, understood its working, and saw the
great beauty of the invention. She had read the Differen-
tial Calculus to some extent, and after her marriage she
pursued the study and translated a small work of the
Italian Mathematician Menabrea, in which the mathe-
matical principles of its construction are explained.

90 MEMOIR OF AUGUSTUS DE MORGAN.

1837. Mr. Babbage's ' Ninth Bridgwater Treatise/ at this

time going through the press, contained the development
of an idea suggested by the working of the engine. In
the series of numbers presented by the rotation of the
cylinders, a regular order, which has continued for a long
time, is suddenly interrupted by the appearance of a new
number. The old series is again resumed, and at another
interval a number bearing relation to the first interrup-
tion makes its appearance. This process suggested to
Mr. Babbage a reply to Hume's argument against miracles,
founded on the experience of the world in the sequence of
events. The idea of the intervention of a higher law in the
processes of nature is now more familiar to the world than
it was when Mr. Babbage gave his beautiful illustration.
By theologians the book was condemned as heretical, as
doing away with what was held to be the nature of
miracle — an arbitrary suspension of the laws of nature.
By some thoughtful men, who did not consider science
and revelation incompatible, the suggestion was held
valuable. My husband took a lively interest in the work,
and the author, who was then on friendly terms with him,
was a visitor at our house.

Elizabeth In this year we made the acquaintance and gained

the friendship of Elizabeth Fry ; of whom my husband
speaks in the Budget of Paradoxes as ' one of the noblest
of human beings.' Lady Noel Byron, who had heard of a
scheme for a female benefit society and home, which
seemed to promise great usefulness, and in which Mrs.
Fry took an interest, introduced her to my husband for
the sake of his advice on the calculations, and to us both,
as likely to enter warmly into the design. He found the
calculations utterly worthless, and loss or even ruin was
prevented by the reference to him, for the projector had
obtained promises of money for shares from persons who
could ill afford to lose it; her vexation on the over-
throw of her scheme was very plainly shown. Mrs. Fry
allowed me to accompany her in a visit to this person. It

- OPENING OF COLLEGE SESSION. 91

was like witnessing an interview between an angel and the 1837.
opposite character, and I could only compare the steady
gentleness with which Mrs. Fry replied to the sharp, shrill

arguments of Miss to sunshine clearing away a black

frost. My husband, who was very sensitive on such
points, was charmed with Mrs. Fry's voice and manner
as much as by the simple self-forgetfulness with which
she entered into this business ; her own very uncom-
fortable share of it not being felt as an element in the
question, as long as she could be useful in promoting good
or preventing mischief. T can see her now as she came into
our room, took off her little round Quaker cap, and laying
it down, went at once into the matter. ' I have followed
thy advice, and I think nothing further can be done in
this case ; but all harm is prevented.' In the following
year I had an opportunity of seeing the effect of her most
musical tones. I visited her at Stratford, taking my little
baby and nurse with me, to consult her on some articles
on prison discipline, which I had written for a periodical.
The baby — three months old — was restless, and the nurse
could not quiet her, neither could I entirely, until Mrs.
Fry began to read something connected with the subject
of my visit, when the infant, fixing her large eyes on the
reader, lay listening till she fell asleep.

On the occasion of the opening of the Faculty of Arts Introduc-
my husband was appointed to deliver the introductory tufe.
lecture.

The establishment of the University of London had
altered the relations of University College with the public
and with education generally, and, as Mr. De Morgan
said, ' the circumstances under which this College (Univer-
sity College) reopens its courses of instruction are more
remarkable than any in which it has been placed since the -
commencement of its career.'

The University of London had been founded in the
year 1836 by Government j and to prevent the confusion
consequent on similarity of name, the institution which

92 MEMOIR OF AUGUSTUS DE MORGAN.

1838. had been called the London University took the name of
University College. There were then two Colleges in
London affiliated to the newly established university,
which bore that name with more propriety, its object
being not to give education, but to examine and confer
degrees upon the pupils of Colleges.

This lecture, given nine years after his first, shows the
working of the same thought developed and extended over
a wider field. He disclaimed being in any way the organ
or representative of the College. The ideas were his own ;
and the principles he laid down upon public education
might be consulted now with advantage in this present
stage of opinion on academical training.

Our eldest child was born the year after our marriage.
In the autumn of that year Lady Byron lent us her house,
Fordhook, near Acton ; and for the ten weeks of our
stay my husband was able to go on with his writing more
easily than he could have done at a greater distance from
London. During the years 1836 and 1837 he had been
Theory of engaged in writing his Theory of Probabilities. This is the
biiities. description taken from the agreement made with the pub-
lishers of the ( Encyclopaedia Metropolitana,' published in
January 1838. CA Mathematical Treatise on the Theory
of Probabilities; containing such development of the
application of Mathematics to the said Theory as shall
to him (the Author) seem fit, and in particular such a
view of the higher parts of the subject as laid down by
Laplace in his work entitled Theorie des Probabilites, as
can be contained in a reasonable compass, regard being
had to the extent and character of the Mathematical por-
tions of the said work.' !

During the time which we spent at Fordhook, he
completed the small volume entitled ' Essay on Probabi-

1 From a pamphlet published in 1838, hereafter mentioned. The
extract is given here for the same purpose for which the pamphlet
was written, to show the difference between the scientific treatise and
the popular Essay on Probabilities, in the Cabinet Cyclopaedia.

DISPUTE WITH PUBLISHERS OF ENCYCLOPAEDIA. 93

lities, and on their application to Life Contingencies and 1838.
Insurance Offices,' which appeared in Lardner's ' Cabinet Essay on
Cyclopsedia' in September 1838. The advertisement of bilities.
the 6 Essay ' alarmed the editor of the c Encyclopaedia
Metropolitana,' who, being unable to understand that a
profound Mathematical work full of definite integration
was altogether a different thing from a popular essay
requiring only decimal fractions, and mainly devoted to
life contingencies, accused the writer of having infringed
the rights of the proprietors of the Encyclopedia, by
publishing what he said ' might be deemed a second
edition of the treatise,' and threatened, or implied a threat
of prosecution. The author, who was more amused than
annoyed by this want of perception in the publisher, ex-
plained to him very clearly the respective characters of the
works, but failed to make him understand how widely they
differed. He then proposed arbitration, he being willing
to pay whatever damages should be judged proportionate
to their loss to the supposed injured parties; or, in the
event of the decision being in his favour, that a sum of
money should be given by them to some charity, as amends
for the trouble given and the false aspersions made. This
last proposal being rejected, the author of the Treatise and
Essay published a little pamphlet in explanation, which
showed to all who cared to understand the question that
the publisher's ignorance of its nature had led him into
what my husband called ' wasting a good deal of good
grumbling,' but which was in truth an unjust imputation
on himself.

The great amount of work which he did at this time, Dickcns'a
as at all times while his strength lasted, filled the day, so senals>
that I had but little of his society. We both naturally
regretted this, but it could not be helped. He liked read-
ing to me when he could get anything likely to ploase us
both, so I heard several of Dickens's novels from beginning
to end. They came out in monthly parts, and he would
say, 'We shall have a Pickwick (or whatever it might

94 MEMOIR OF AUGUSTUS DE MORGAN.

1838. be) to-morrow;' and on the first day of the publication
we had read and commented on it. c Punch ' about that
time was in the meridian, and Mrs. Caudle's Curtain
Lectures threw terrible weapons into the hands of hus-
bands. Accordingly, these last were read to me with a
view to my improvement, the reader dwelling with special
emphasis on any of Mrs. Caudle's most outrageous sayings
which were supposed to be particularly suitable to the
case. He said, ' Every man's mother is Mrs. Nickleby,
and every man's wife is Mrs. Caudle.' We had more
time in the vacations, but I was afterwards always parted
from him for a few weeks in the autumn, as it was neces-
sary to take the children out of town for health.

He seldom entered into any serious discussion, but
liked to tell of any interesting fact which he had come
across in his investigations either in reading or thinking ;
and many valuable bits of knowledge, which were after-
wards expanded and published, were talked of first in
this way. Matters of less importance, obscure deriva-
tions of words, and unsuspected translations, the origin
of old customs, versions of nursery rhymes, and, above
all, riddles, good and bad, were generally welcome.
Ideas about I must not conceal the fact that in the earlier part of
his life he held man-like and masterful views of women's
powers and privileges. Women, he thought, ought to have
everything provided for them, and every trouble taken off
their hands ; so the less they meddled with business in any
form the better. But these very young notions gave way,
as he saw more of life, to wiser and more practical ones.
He found that women were not utterly helpless, and his
love of justice, combined with his better opinion of their
powers, made him quite willing to concede to them as
much as he would have desired for himself, namely, full
scope and opportunity for the exercise of all their faculties.
This was shown by his giving lectures gratuitously in the
Ladies' College for the first year after its foundation, and

PHILOSOPHERS. 95

by the interest lie felt in the success of those brave women 1838.
who first attempted the study of medicine.

In society he seldom entered into discussion on
abstract questions, except with those of whose compre-
hension he felt sure, but he would sometimes listen to the
debates of others. I once saw him stand by, with a half-
amused, half -interested look, while a discussion was going
on between two learned professors on matter and spirit, the
future life, and a Creator, in which the two last were on
the losing side, without uttering a word. When I asked
him what he thought of the arguments, he said, c I don't
understand them, but then I'm not a Philosopher.' l

1 He has left some definition of Philosophers : ' The word "Philo-
sopher " is one which has had meanings so different from each other,
and has been in such demand for all manner of uses, that a person who
should read the writings of one period with a notion of this word
derived from the writings of another period would be in actual con-
fusion about matters of fact and opinion both. Some movable words
are understood as such : a good man sometimes means a just man,
sometimes a benevolent man, sometimes a religious man, a rich man,
or, as at Cambridge, an (undergraduate) man who is well up in his
subject (of examination). This is pretty well understood, but nine-
tenths of the educated think that the Philosopher is one kind of
person, throughout all ages and countries.

' A Philosopher, in Greek, was originally a person who desired and
sought after wisdom, especially the knowledge of man in the widest
sense ; of his constitution, his capabilities, and his duties. But in
history may be found this variety of meanings : 1. The original sense
just described. 2. The votary of a school of opinions on man, or on
nature, or on morals. 3. An ascetic, who denies himself the good
things of the world. 4. A person whose temper is not easily put out.
5. A person who despises his fellow- creatures. 6. One who cares not
what is said about him. 7. An academically educated man. 8. An
atheist. 9. An infidel as to revelation. 10. An inquirer into the
material phenomena of the universe. I need not say that this list
does not include the true Philosopher, a genus of species innumerable,
nor the technically adjectived Philosopher, as the moral Philosopher,
the chemical Philosopher, &c., meaning a person who looks into
morals, chemistry, &c. , in a thoughtful and speculative way. These
would be more rightly called Philosophic moralists, Philosophic
chemists, &c. The dreadful bore who did the moral business in

96

MEMOIR OF AUGUSTUS DE MORGAN.

1838.

Conversa-
tion.

Lectures.

Mr. Richard

Button's

sketch.

Then he repeated laughingly to himself a few words
uttered by one of the speakers, and said, ' Poor - — , he
does not see that if what he said were true, he would not
be here to say it.5 As he wrote, he ' had 110 objection to
Metaphysics, far from it, but if a man takes a candle to
look down his own throat, he must take care not to set his
head on fire.' And this sense of the danger of fire, coupled
with the fact that his own thoughts ran in new channels,
made him unwilling to speak on Metaphysical questions
except to the few who were already familiar with his
ideas. Logic and Mathematics were different, being in
some degree out of the reach of ' fire.' But his beliefs in
mental and physical science were founded on that of a
constantly producing and constantly sustaining Creator ;
and he was never found assenting to systems based only
on observation of material nature. It mighb be that
observation had not gone far enough when it resulted in
such expressions as ( forces inherent in matter,' but he
said such expressions were only a step in the road to
atheism. The present state of scientific belief in some
measure justifies this.

The Diorning lecture and explanation lasted from
9 A.M. till 10.30, when he came home, but only to attend
to work of different kinds, or to a private pupil, of whom
two or three came to him while we lived in Gower Street,
and afterwards in Camden Street. The afternoon lecture
was from 3 to 4.30, when he returned to dinner, and for
the little rest he allowed himself before a long evening of
writing, only interrupted by an hour's talk with me, or
occasionally with some friend who might visit us.

As I cannot describe my husband in his character of
Professor, I thankfully give two little sketches of his mode

children's books of forty years ago was a Philosopher ; he was
sententious ; he said, " From this we may learn, and let us all
take warning," and he had a " small but well-selected library
(may it perish with him), containing no poets except Young and
Akenside."' . . . (Unfinished.)

COLLEGE LECTURES AND PUPILS. 97

and system of teaching, taken by pupils for whom he had 1838.
a sincere regard, and who both loved and venerated their Mr; IIut-
old master, — Mr. Richard Hutton and Mr. Sedley Taylor, lections.
Mr. Hutton says, —

' Few men have had more eminent pupils than your
husband, and few have done more to cultivate the intel-
lects of those whom they taught. As you know, in Mr. De
Morgan's time, the Mathematical classes of University
College were quite as much classes in Logic, at least in the
Logic of number and magnitude, as in Mathematics ; but
of my own fellow-pupils very few have, I think, since
become eminent in the world. The present Master of
the Eolls (Sir George Jessel) was, I believe, your husband's
pupil a year or two before my time, as was the late Mr.
Jacob Waley, who, after being his pupil, became his col-
league at University College. Mr. Walter Bagehot, whose
books on the working of our political constitution and on
the early forms of national government have attracted
the attention of most thoughtful men, was a fellow-
student with me, and one of the chief subjects of discus-
sion between us used to be the logical questions raised in
the Mathematical classes, especially in your husband's
lectures on the theory of limits, the theory of probabili-
ties, the calculus of operations, and the interpretation of
symbols applied, with a new and extended meaning, to
cases which were not within the scope of their original
definition. Professor Stanley Jevons, of Owen's College,
Manchester, who has always prized very highly your
husband's teaching, was his pupil many years after I had
left the College, and no one has made better use of the
time passed in those delightful classes ; and every book
he publishes bears witness to the help he has derived from
your husband's teaching.

6 One thing which made his classes lively to men who
were up to his mark, was the humorous horror he used
to express at our blunders, especially when we took the
conventional or book view instead of the logical view.

H

98 MEMOIR OF AUGUSTUS DE MORGAN.

1838. The bland " hush ! " with which he would suppress a sug-
gestion which was simply stupid, and the almost grotesque
surprise he would feign when a man betrayed that, instead
of the classification by logical principles, he was thinking
of the old unmeaning classification by rule in the common
school-books, were exceedingly humorous, and gave a life
to the classes beyond the mere scope of their intellectual
interests. I think all my fellow-pupils would agree that
never was there a more curious mixture of interests than
the prepared discussions of principle in his lectures, and
the Johnsonian force and sometimes fun of his part in the
short dialogues with his pupils which occurred from time
to time.'

A pupil who came rather later than those mentioned,
and in whose success his teacher greatly rejoiced, was Mr.
Robert Bellamy Clifton, now Professor of Physical Science
in Oxford. My husband early perceived talents in Mr.
Clifton which had been ignored by former teachers, and
the result justified his advice and predictions. Professor
Clifton continued a valued friend through Mr. De Morgan's
life, and gave me much kind assistance with the library,
&c., after his death.

Mr. Sediey The work in the Mathematical lecture room, and the
recoilec- Prof essor's manner of doing it, are also well described by
his pupil and friend, Mr. Sediey Taylor of Trinity College,
Cambridge — one who, like him self, held conscience to be
above all things, and gave up his position as a clergyman
of the Church of England because he could not assent
with his whole heart to her doctrine. The following is
extracted from Mr. Taylor's notice of his old teacher in the
Cambridge University Reporter :—

'As Professor of Pure Mathematics at University
College, London, De Morgan regularly delivered four
courses of lectures, each of three hours a week, and last-
. ing throughout the academical year. He thus lectured
two hours every day to his College classes, besides giving
a course addressed to schoolmasters in the evening during

DESCRIPTIONS OF LECTURES. 99

a portion of the year. His courses embraced a systematic 1838.
view of the whole field of Pare Mathematics, from the
first book of Euclid and Elementary Arithmetic up to the
Calculus of Variations. From two to three years were
ordinarily spent by Mathematical students in attendance
on his lectures. De Morgan was far from thinking the
duties of his chair adequately performed by lecturing only.
At the close of every lecture in each course he gave out a
number of problems and examples illustrative of the sub-
ject which was then engaging the attention of the class.
His students were expected to bring these to him worked
out. He then looked them over, and returned them
revised before the next lecture. Each example, if rightly
done, was carefully marked with a tick, or if a mere inac-
curacy occurred in the working it was crossed out, and the
proper correction inserted. If, however, a mistake of
principle was committed, the words c show me ' appeared
on the exercise. The student so summoned was expected
to present himself on the platform at the close of the
lecture, when De Morgan would carefully go over the point
with him privately, and endeavour to clear up whatever
difficulty he experienced. The amount of labour thus
involved was very considerable, as the number of students
in attendance frequently exceeded one hundred.'

6 De Morgan's exposition combined excellences of the
most varied kinds. It was clear, vivid, and succinct — rich
too with abundance of illustration always at the command
of enormously wide reading and an astonishingly retentive
memory. A voice of sonorous sweetness, a grand forehead,
and a profile of classic beauty, intensified the impression
of commanding power which an almost equally complete
mastery over Mathematical truth, and over the forms of
language in which he so attractively arrayed it, could not
fail to make upon his auditors. Greater, however, than
even these eminent qualities were the love of scientific
truth for its own sake, and the utter contempt for all

H 2

100 MEMOIR OF AUGUSTUS DE MORGAN.

i Q->Q counterfeit knowledge, with which he was visibly possessed,
and which he had an extraordinary power of arousing and

Mr.Sedley ... ... ., mi u i , i *•

Taylor's sustaining in his pupils. The fundamental conceptions of
Sons1* each main department of Mathematics were dwelt upon
and illustrated in such detail as to show that, in the judg-
ment of the lecturer, a thorough comprehension and mental
assimilation of great principles far outweighed in import-
ance any mere analytical dexterity in the application of
half-understood principles to particular cases. Thus, for
instance, in Trigonometry, the wide generality of that
subject, as the science of undulating or periodic magnitude,
was brought out and insisted on from the very first. In
like manner the Differential Calculus was approached
through a rich conglomerate of elementary illustration, by
which the notion of a differential coefficient was made
thoroughly intelligible before any formal definition of its
meaning had been given. The amount of time spent on
any one subject was regulated exclusively by the import-
ance which De Morgan held it to possess in a systematic
view of Mathematical science. The claims which Uni-
versity or College examinations might be supposed to
have on the studies of his pupils were never allowed to
influence his programme in the slightest degree. He
laboured to form sound scientific Mathematicians, and, if
he succeeded in this, cared little whether his pupils could
reproduce more or less of their knowledge on paper in a
given time. On one occasion, when I had expressed regret
that a most distinguished student of his had been beaten,
in the Cambridge Mathematical Tripos, \)j several men
believed to be his inferiors, De Morgan quietly remarked
that he "never thought - - likely to do himself justice
in THE GREAT WRITING RACE." All cram he held in the
most sovereign contempt. I remember, during the last
week of his course which preceded an annual College exa-
mination, his abruptly addressing his class as follows : " I
liotice that many of you have left off working my examples
this week. I know perfectly well what you are doing ;

COLLEGE LECTURES. 101

YOU ARE CRAMMING FOR THE EXAMINATION. But T will Set 1839.

you such a paper as shall make ALL YOUR CRAM of no
use." '

His pupils' affection was not gained by any laxity of Enforce-
discipline, for he was strict, especially as to quietness and punctu-
punctuality. His own morning lecture began at nine. allty'
That on Natural Philosophy followed it immediately, and
punctuality in the first comers, to secure its full time, was
important. Some of the pupils had fallen into the
slovenly habit of coming into the theatre a few minutes
after the bell had rung, and in this way lost, and prevented
those present from hearing, the first sentences of the
lecture. For the want of punctuality they could hardly
be blamed, as an example was set by several of the Pro^
fessors, whose entrance was delayed, as they said, Ho give the
lads time to assemble.' Mr. De Morgan, after duly enjoin-
ing punctual attendance, gave notice that if the pupils
came in after he had commenced, they would find the
door locked, which threat after two or three days' trial was
put into effect. A few enterprising youths kicked and
knocked at the door, trying to burst it open, but on the
appearance of a policeman, and a threat of ' the Council,'
which might mean removal, they were brought to order.

At the end of this session nine pupils presented their
Professor with a handsomely bound copy of Macaulay's
Essays, with a letter begging his acceptance of it as ' A
small expression of gratitude for the liberal and most
efficient assistance which his course of mathematical lec-
tures had afforded them in preparing to pass the examina-
tion for the degree of Bachelor of Arts in the University of
London.' Among these nine gentlemen were three of the
insurgents, and among the other six names were those of
Jacob Waley and James Baldwin Browne. Some time had
always been given after each lecture to clearing up diffi-
culties, and rather more than usual was necessary after
the outbreak, as those concerned in it were in greater
need of help to make up for lost time.

102 MEMOIR OF AUGUSTUS DE MORGAN.

1839. Very soon after the establishment of the London

University, young men of Jewish parentage began to
distinguish themselves by their rapid acquirement of
knowledge, thus justifying the hopes of their co-re-
ligionists who had contributed so liberally to the founda-
tion. During the years in which my husband was Professor,
many Jews took the highest honours ; and among his
most attached and valued Jewish pupils, the late Mr.
Numa Hartog was the last, and Mr. Jacob Waley the
first. Mr. Hartog's career, unhappily cut short before
he had applied his talents to the work of life, was a bril-
liant one. After taking all the honours that could be
given in University College, he went to Cambridge, and
took his degree as Senior Wrangler. But the mental
work was too much for his strength, and an attack of
small-pox in 1872 left him too weak to rally.

Jacob Mr. Jacob Waley, afterwards Professor of Law, was

one of the first Jewish students, after my husband's return
to his Professorship, of whom the College had reason to be
proud. He was not only a successful student in class, but
a diligent private pupil, and from the time of which I
write till his death in 1873 a valued friend. His lessons
at our house in Gower Street were pleasant to both teacher
and pupil, and even to myself, for he would come to me
when they were done, for a little talk about books, or
a reading of his favourite writer Macaulay's Lays or
Essays. Mr. Waley was the first M.A. of the University
of London, which in 1836 was ready to confer degrees on
students of its affiliated Colleges in London and else-
where. Some of us now living may remember Lord
Brougham's reference to this pupil in a speech made at a
distribution of prizes at the time, and possibly too some
may remember how the speaker dwelt upon the fact (which
was a fact then, and we had heard it so often that we were
tired of hearing it) that within those walls men of every
religion were received, whether as teacher or student,
without any reference to their beliefs or non-beliefs. The

GEORGE LONG. 103

time at which these assertions were made was spoken of 1839.
by my husband as c before the Fall.'

At the time of our marriage Mr. George Long, who had George
resigned his Professorship of Greek in the University when
Mr. De Morgan retired, was living with his family in
Camden Street, Camden Town. He was editor of the
Penny Cyclopcedia, and others of the works of the Diffu-
sion Society, and the work brought him and Mr. De Morgan
much together. The two had several qualities in common, — •
integrity of purpose and simplicity of character, indefati-
gable industry, and a love of fun which brightened hard ,
work and kept us always amused. Mrs. Long took great
credit to herself for the fulfilment of her predictions on
the subject of our marriage, which she declared she had
foreseen from time immemorial. I believe her prophecies
really dated from the year 1831, when my acquaint-
ance with her began. It lasted as warm friendship till
the year 1841, when to the great sorrow of all her friends
she was taken from us.

Among other visitors not connected with the College
was Mr. Leslie Ellis, who left on my mind the impression of
an almost perfect moral nature. This impression was
confirmed when, some time after, his scientific studies
were interrupted by an illness, which he bore for years
with unexampled patience, trying to alleviate the intensity
of his sufferings when possible by mental work, and when
that was impossible, awaiting the end with perfect resig-
nation. Dr. Logan, a learned Mathematician and after-
wards Professor at the Catholic College of Oscott, was
among our friends. When Mr. Leslie Ellis's sister left
him on the occasion of her marriage with Dr. Whewell,
the Master of Trinity, our friend Dr. Logan took her
place near the sufferer, and attended him with unremit-
ting friendship and affection till his death. I have none
of my husband's letters to Dr. Logan, but I know that
the correspondence was large. Mr. De Morgan was in-
debted to him for the volume of Ploucquet which was

104 MEMOIll OF AUGUSTUS DE MORGAN.

183P. afterwards of such essential service in his logical contro-
versy with Sir William Hamilton.

Rev. James Another and an older friend not connected with the
College was James Tate of Richmond, Yorkshire, who
at this time was living with his family at the residence
as Canon of St. Paul's, Amen Corner. His own story
was nearly connected with that of my mother's family.
Mr. Tate, like so many of his own scholars — ' northern
lights,' as they were called — was of obscure or rather
poor parentage. Archdeacon Blackburne,1 who lived at
Richmond, wanted a lad to act as amanuensis, and to
read to him. Mr. Christopher Wyvill, his friend and
contemporary, a noted Whig reformer of the time, re-
quired a young man in the same capacity. Two lads
were recommended by Mr. Temple, the head-master of
Richmond School. These were James Tate and Peter
Eraser, the last a poor boy, but a lineal descendant of the
beheaded Lord Lovat. My great-grandfather engaged
young Tate, and Mr. Wyvill took Fraser. The two lads
proved well deserving their appointments. Archdeacon
Blackburne became greatly attached to his young amanu-
ensis, and found the means of sending him to Cambridge,
Pupils of where he gained honours as a classic. Mr. Wyvill sent his
School!*11' protege to the University, with nearly the same success.
In due time young Tate was ordained, and afterwards
appointed to a tutorship in the school at Richmond, of
which at Mr. Temple's death he became head-master.
Some of the most distinguished men of the beginning of
this century were his pupils ; many of them, like him-
self, owing all to their own ability and industry. Of
these were Dean Peacock, Professor Adam Sedgwick,
Professor Whewell, Richard Sheepshanks, and many
others.

1 Archdeacon of Cleveland. His work The Confessional gave him
a distinguished place among the writers on Divinity of his time. Mr.
Fraser afterwards married his granddaughter, and died rector of Keg-
worth in Leicestershire.

ARRANGEMENT OF STUDY. 105

Many as were our friends, we had but very little I83U.
visiting, my husband's time being so fully filled with Orderl
his work. The last was done with exceeding order and habits,
punctuality. He has himself described Mr. Baily's habits
of order ; and his own, though less apparent, were equally
characteristic. He had the faculty of arrangement in an
unusual degree, but it showed itself more in classification
than in tidiness. In looking at any undertaking for scien-
tific or practical purposes, he could not go on till all
his materials were ready and arranged. This faculty is
seldom so well proportioned to the power of carrying out
the work projected. Mr. Baily had order of every sort,
from the classification of formulse or facts to the perfect
arrangement of his house and appointments. In Mr. De
Morgan it showed itself differently. Not having the
means to indulge in the luxuries enjoyed by richer and
more affluent writers or experimentalists, he could rot
furnish his library with all the writing appliances and
handsome bindings that ornament rich men's studies,
and his old table and desk, and other cheap contrivances,
looked shabby enough. Any one who went into his room
would be struck at first by the homeliness of the whole,
and the quantity of old and unbound books and packets of
papers. But when it was seen how the books were ar-
ranged and the papers labelled and put into their proper
places according to subjects, the adaptation of means to
ends became as apparent as in the clearness and precision
with which he laid down principles, and showed what
was to be done before making a beginning on his work.
His contrivances in the way of inkstand, penholder, and
blotting-block, had none of them a new or unused look,
but all showed that every contingency had been carefully
provided for. After gutta-percha came into use he
employed it in every possible way, moulding it into pen-
holders, caps, covers, and all sorts of fastenings. He
says, in The Budget of Paradoxes, fc I never could spell
the word, but if cowchoke goes, I go too ; ' and being

106 MEMOIR OF AUGUSTUS DE MORGAN.

1839. once disrespectfully told that he would fasten on a head,
an arm, or a leg, if he lost one, with gutta-percha, he said,
' I should like to see you do as much.'

When the repetition of the Cavendish experiment was
undertaken by Mr. Baily in the year 1837 at his house
in Tavistock Place — a house thereby rendered memorable
— Mr. De Morgan gave so many clear descriptions of it
and its object, that Mr. Baily's work in 1838 and 1839
requires a longer notice than I have given to those Astro-
nomical achievements with which my husband had less
to do. A grant of 500Z. had been made by Government,
at the representation of the Astronomical Society, for
defraying expenses. The forerunners of this effort to
ascertain the mean density of the earth are mentioned by
Mr. De Morgan in the Life of Maskelyne, written some
time before, and will give some idea of the nature and
objects of the undertaking.

Cavendish c The labour of deducing an approximation to the

earth's mean density was undertaken by Dr. Button. By
getting the best possible estimate of the materials of which
Schehallien is composed, and comparing what we must
call the weight of the plumb-line towards the mountain
with its weight towards the earth, it appeared that the
mean density of the latter is about five times that of
water. This, considered as a numerical approximation,
alone and unsupported, would have been worth little,
owing to the doubt which must have existed as to the
correctness of the -estimation of the mountain's density.
It would prove that there was attraction in the mountain,
but would give no very great probability as to the value
of the earth's density as deduced. But a few years after-
wards Cavendish made an experiment with the same
object, and by an entirely different method. By producing
oscillations in leaden balls by means of other leaden balls,
and by a process of reasoning wholly free from astro-
nomical data, he inferred that the mean density of the

REPETITION OF CAVENDISH EXPERIMENT. 107

earth was five and a half times that of water. The ex- 1839.
periment of Cavendish was published in 1798. It is much
to be wished that it should be repeated on a larger scale,
but the expense of the apparatus will probably deter in-
dividuals from the attempt.5

In a pencil note in the margin of the same page I
find-

6 This was, I believe, the remote cause of the repetition First sug.
of the experiment. Being, a few months afterwards, in
the year 1335, on the Council of the Astronomical Society,
something was said about the mean density of the earth,
and I happened to say, " I wish Cavendish's experiment
could be repeated." Mr. Airy immediately said, "Ah,
that would be a good thing." Others agreed, and a
committee was appointed on the spot " to consider of the
practicability," &c. The result was the repetition of the
experiment.'

The history, the nature of the formulse for the calcu-
lations, and the results of the discovery, are all given
by Mr. De Morgan in the articles ' Attraction/ ' Caven-
dish Experiment,' ' Weight of the Earth,' and others,
in the Penny Cydopcedia, and in a sufficiently popular
form in an article in the Companion to the Almanac for
1838.

Mr. Baily's repetition, commenced in 1838, was carried
on in a small upper room twelve feet by twelve, as
far removed as possible from the noise and shaking of
street traffic. It was, of course, an object of interest to
all scientific friends, and Mr. Baily's genial kindness in
explaining his beautiful apparatus and showing his pro-
gress was one of the pleasant accompaniments of his
important work. The apparatus designed and con-
structed by Mitchell, who did not live to use it, had
been used by Cavendish, and afterwards by Mr. Baily,
but so greatly improved and added to by the last ex-
perimenter that it could hardly be called the same. I saw

108 MEMOIR OF AUGUSTUS DE MORGAN.

1839. the progress of the experiment, and my husband's visits
were frequent to the little room in which the world was
weighed.

The Life of Maskelyne, from which the mention of
my husband's suggestion is taken, is one of a series of
lives of Astronomers written by him for the Gallery of
Portraits, published by C. Knight two or three years
before this time. They are those of Bradley, Delambre,
Descartes, Dolloiid, Euler, Halley, Harrison, W. Herschel,
Lagrange, Laplace, Leibnitz, and Maskelyne. They are
bound up together, and illustrated in his own way, under
the title of ' Mathematical Biography, extracted from the
Gallery of Portraits, by Augustus De Morgan, H.O.M.O.
P.A.U.C.A.R.U.M. L.I.T.E.R.A.R.TJ.M.' The letters of
his literary tail were only B.A., F.R.A.S., besides 'those
expressing membership of one or two lesser Scientific
societies. On account of the declaration of belief at that
time required by the University he never took his M.A.
degree.

In November our eldest son, William Frend De
Morgan, was born.

We had spent five weeks at Boulogne in the summer.
I hoped that, as my husband always liked the sea,
a French watering-place would be less irksome to him
than English country or sea- coast ; but he soon got tired
of it, and felt glad to get back to his work.

1840. He bore a few weeks at Blackheath next year with

equanimity. He was near the Observatory, and Mr. and
Mrs. Airy were good neighbours, so were Mr. (afterwards
Lord) Wrottesley and Mrs. Wrottesley, the former being
on the Council of the Astronomical Society, and, be-
sides his other excellent social qualifications, being a
good musician. My husband liked the steamboats, of
which he made much use ; but the heath, which he called
desolation, was a trial to him. After this summer he
begged me to take the children without him ; and I found
that this arrangement, which I disliked, was the best.

DEATH OF AUTHOR'S FATHER. 109

He required a letter, reporting health, &c., and sent me 1840.
one in return, every day.

On our return to Gower Street I went with my two little
children to Highgate for a very short time to be near my
father, who had had a stroke of paralysis.

He died early in the next year, 1841, at the age of 1841.
84. His Cambridge life and early difficulties on the
subject of religion have been slightly referred to. He
had taken his degree as Second Wrangler, and had after-
wards had a Fellowship and a College living till scruples
of conscience led him to leave the Church ; and his sub-
sequent publication of a pamphlet entitled Peace and
Union was the cause of a prosecution by the University.
He was tried and sentenced to non-residence, but he re-
tained his Fellowship till his marriage with my mother, a
granddaughter of Archdeacon Blackburne. He had been
a pupil of Dr. Paley, for whom he always retained an
affection ; and among his own pupils were Dr. Edward
Daniel Clarke, the traveller, Lord Lyndhurst, afterwards
Lord Chancellor, and Mr. Mai thus, in whose social tenets
he entirely disclaimed any share. My father's political
opinions, as set forth in Peace and Union, were held
to be extreme eighty years ago ; they are as milk for babes
in comparison with the strong stimulants given by the
Liberal party now.

He was after he left Cambridge a friend of Sir Francis
Burdett during the reforming portion of his life, of Home
Tooke, and of other reformers. What place he would have
taken in politics had he lived till now I can only conjecture.
He was a good Hebraist, and was trustee for Mr. Robert
Tyrwhitt's Hebrew Scholarship at Cambridge. His largest
work was on popular Astronomy as it was known then.
This book, entitled Evening Amusements, came out, a
volume every year, for nineteen years ; each volume show-
ing the relative positions of all the heavenly bodies for
every month in the year.

My father's ideas on Algebra were peculiar; his re-

110 MEMOIR OF AUGUSTUS DE MORGAN.

1841. jection of the use of negative quantities in algebraic
operations being probably the result of the same straight-
forwardness and clearness rather than great depth of
intellect, which had led him, with more show of reason, to
reject the doctrine of the Trinity in the form in which he
had received it.

He was an upright and noble-minded man, generous
and disinterested to a fault, if that can be, with a vigorous
perceptive mind, but little imagination. His religion was
real and practical ; and his death was an event to which
he had always looked forward with cheerfulness and happy
anticipation. My husband wrote a short biography for
the Athenceum, and a longer one to the Astronomical
Society's Obituary Notices.

Mr. De Morgan was at this time, I think, consult-
ing actuary to the Family Endowment Assurance Office,
which afterwards merged with another office in the
Mutual. I do not think he held this place more than two
years.
Accident to During this summer an accident occurred which nearly

Francis

Baiiv. proved fatal to our friend Mr. Francis Baily. He was
crossing Wellington Street, Strand, when a man on horse-
back, riding furiously, knocked him down and stunned
him. He was taken in an unconscious state to the Charing
Cross Hospital, and was found to have a severe scalp
wound and to be a good deal bruised. As soon as he
could bear the removal he was taken home to Tavistock
Place ; and after a few weeks his recovery seemed to be
complete, though he remained weak for some time. But
the injury to the head left more serious results than were
expected, for it is most probable that the disease of which
he died three years after, and which is now believed to be
often the result of a shock to the nervous system, was
caused by this blow. My husband was, as were all Mr.
Baily 's friends, extremely anxious as to the possible con-
sequences ; but their anxiety was allayed when he got up
again, received his friends, resumed bis work on the

HALLAM'S HISTORY OF LITERATURE. Ill

Cavendish experiment, and even took some part in the 1841.
Report on the Commission for restoring the National
Standards, to which he had devoted so much time and
thought. This Commission was appointed in 1838. The
Report was sent in in 1841. On the appointment of a
new Commission in 1843 to reconstruct the Standard
Scales, Mr. Baily recovered sufficiently to undertake the
Standard of Length, but did not live to complete it.

Mr. Hallam's History of the Literature of the Middle
Ages was at this time coming out, and after the publica-
tion of the first edition Mr. De Morgan sent the author
some observations on the history of the Mathematicians
of the period embraced in the first volume. What his
criticisms were can only be guessed by Mr. Hallam's reply,
as I have not his own letter.

Dec. 12, 1841.

I am much obliged by your correction of some inaccuracies
in the first volume of my History of Literature, which will be
of use to me in the new edition which I am now preparing. I
am always thankful for such communications, which are at least
a sign that the book is thought worthy of them.

In reply to further criticism, further correspondence
took place two years later, Mr. Hallam's letter touching
on the subject of Logic, which had assumed so definite
and important a form in Mr. De Morgan's thoughts,
and which was afterwards treated in connection with
points of original discovery in his Formal Logic.

I shall pay all attention to them (your remarks) in any new H. Hallam.
edition, and will look again at some of the works in which your
more expert eye has detected rny errors. I certainly searched
in vain for the triangle of forces so called in Stevinus, and I was
a little more led to doubt of his using it, as Montucla says, be-
cause the only demonstration with which I am acquainted
involves the third law of motion ; but that, according to the
general opinion, was not laid down till long afterwards. Perhaps
Stevinus might assume it on metaphysical principles without
experiment.

112 MEMOIR OF AUGUSTUS DE MORGAN.

1841. The early history of algebra is a very interesting subject,

and I shall be glad to return to it again with more leisure. I
was forced to copy writers of credit, not always seeing the full
force of what they said. But it seemed to me that a sound
mathematician would find that field not exhausted. . . .

As to your observation about logic — that is, the syllogistic
logic — perhaps I was a little influenced by the impression that
more attention was paid to it at Oxford. That, I believe, is now
much less the case. Bat though what I have written on it is
inconveniently concise, and leaves more for the reader than an
ordinary author has a right to expect, I thought I had given to
that logic what it can best claim, its quality of perfect demon-
stration ; all geometrical demonstration being, in fact, one species,
or rather one application, of the fundamental principle. Nor
did I distrust the usefulness, to a certain degree, of an acquaint-
ance with syllogism, though I have not found that the best
reasoners are very familiar with it. However, if I have gone
too far in lowering this art or science — for it is not settled which
— I am very willing to retract. Let me add that I have received
much pleasure from some of your writings, such as are most
familiar to me, especially that on the ' Connection of Number
and Magnitude.' You need not fear going ultra crepidam, for
your crepida is very extensive.

Believe me, dear sir,

Your much obliged servant,

HENRY HALL AM.

In October our second son, George Campbell, was
born. We lost him at the age of twenty-six, not before
his mathematical talents were developed sufficiently to
entitle him to notice in his father's scientific history. Of
this I must speak later. He was a lovely and seemingly
healthy child, sweet-tempered, quiet, and thoughtful ; and
though sound and certain in all, he was not quite so
quick in learning as his sister and brother.

Our society was diminished by the loss of Mr. Sheep-
shanks, who left London to live at Reading with his
sister.

The correspondence with Dr. Whewell, which had
begun soon after the pupil left Cambridge, related at first

DIFFERENTIAL CALCULUS. 113

to Mathematical questions. But when Mr. De Morgan 1841.
began to make the application of Mathematical principles Cambridge
to Logic, Dr. Whewell was naturally one of the first Tracts*
to whom his ideas were communicated. In many in-
stances the letters were written on the occasion of sending
tracts to the Cambridge Philosophical Transactions. The
first of these, 'On the General Equation of Surfaces of
the Second Degree/ is dated 1830; * On the Foundation
of Algebra/ No. L, read 1839; Nos. II. and III, 1843;
No. IV., 'On Triple Algebra/ 'On the Structure of
the Syllogism, and on the Application of the Theory of
labilities to Questions of Argument and Authority/

The work on the Differential and Integral Calculus 1842
which had been published by the Useful Knowledge
Society, appeared in 1842 in his complete work, a
bsely printed octavo volume of 770 pages. The series
which had commenced in the year 1836, consists of
twenty-five numbers, each containing thirty-two pages
and to the book is added an appendix and two num-
bers of elementary illustrations which had been pub-
lished by the Society before. Of the work he says in
the preface : —

The method of publication in numbers has afforded
tune to consult a large amount of writing on the different
branches of the subject; the issue of the parts has ex-
tended over six years, during two of which circumstances
with which I had nothing to do stopped all progress The
first number was preceded by a short advertisement, which
should desire to be retained as part of the work, for I
have no opinion there expressed to alter or modify nor
have I found occasion to depart from the plan then con-
templated.

'The principal feature of that plan was the rejection

the whole doctrine of series in the establishment of the

fundamental parts both of the Differential and Integral

Calculus. The method of Lagrange, founded on a very

114 MEMOIR OF AUGUSTUS DE MORGAN.

1842. defective demonstration of the possibility of expanding
<f> (x + h) in whole powers of h, had taken deep root in
elementary works ; it was the sacrifice of the clear and
indubitable principle of limits to a phantom, the idea that
an Algebra without limits was purer than one in which
that notion was introduced. But, independently of the
idea of limit being absolutely necessary even to the proper
conception of a convergent series, it must have been
obvious enough to Lagrange himself that all application
of the science to concrete magnitude, even on his own
system, required the theory of limits. Some time after
the publication of the first numbers of this work, four
different treatises appeared in the French language, all of
which rejected the doctrine of series, and adopted that of
limits. I have, therefore, no occasion to argue further
against the former method, which has been thus abandoned
in the country which saw its birth, and will certainly lose
ground in England when it is no longer maintained by a
supply from abroad of elementary treatises written upon
its principles.'

The doctrine of series in opposition to that of limits
was practically overthrown before the completion of the
work, and the new principle had engaged the attention of
Mathematicians. As might be expected, a volume embody-
ing them, important in its bearing upon metaphysical
as well as mathematical thought, excited great interest
in the minds of the few who could enter into the question.
Of these Dr. Whewell, who had written on it in 1838, was
one of the most pronounced. But with one exception the
ideas of cotemporary thinkers must be gathered from the
letters.1 A full review of the subject, if it were within
my power to make it, would not be in place here, and an
imperfect one would be useless. But some of the bearings
of the principles developed in my husband's Differential
Calculus were thus referred to by Mr. John Stuart Mill,

1 See next Section.

INFINITELY SMALL QUANTITIES. 115

thirty years later, in an admirable article ' On Berkeley's 1842.
Life and Writings : ' l —

It is difficult to read without parti pr is 'The Analyst,' and
the admirable rejoinder to its assailants, entitled 'A Defence
of Free-thinking in Mathematics,' and not to admit that
Berkeley made out his case. It was not until later that the
Differential Calculus was placed on the foundation it now stands
on — the conception of a limit, which is the true basis of all Differential
reasoning respecting infinitely small quantities, and properly Calculus-
apprehended, frees the doctrine from Berkeley's objections.
Nevertheless, so deeply did those objections go into the heart of
the subject, that even after the false theory had been given up,
the true one was not (so far as we are aware) worked out com-
pletely in language open to no philosophical objection by any
one who preceded the late Professor De Morgan, who combined
with the attainments of a mathematician those of a philosopher,
logician, and psychologist. Though whoever had mastered the
idea of a limit could see, in a general way, that it was adequate
to the solution of all difficulties, the puzzle arising from the
conception of different orders of differentials — quantities infinitely
small, yet infinitely greater than other infinitely small quantities
— had not (to our knowledge) been thoroughly cleared up, and
the meaning that lies under those mysterious expressions
brought into the full light of reason by any one before Mr. De
Morgan.

My husband died shortly before this was written. He Berkeley's

J J Philosophy.

had, as his letters show, a sincere respect and regard for
the writer, though they had met only on one occasion, and
he had corresponded with Mr. James Mill, his father. But
though, as was truly said, his mathematical reasoning
had deprived Berkeley of an argument drawn from the
mystery of infinitely small numbers, his sympathies were
in many ways more on the side of Bishop Berkeley than
on that of Mr. Mill.2 The works of Berkeley had been, as

1 Fortnightly Review, Nov. 1871.

2 I am aware that the principles of Berkeley's philosophy have
been found by some thinkers to lead to a pantheistic materialism.
Much depends upon words, but more on the minds of those who use
the n, and a spiritual pantheism must be a near approach to truth.
When the words spiritual, material, theistic, pantheistic, and atheistic

i 2

116 MEMOIR OF AUGUSTUS DE MORGAN.

1843. aforesaid, among his earlier studies, and his absolute con-
viction, or, as he said, consciousness, of the fatherly care of
God was directly opposed to the scepticism (I use the
word as expressing doubt, not disbelief) of one whose work
in many directions he valued highly. He wrote with
great respect of Mr. Mill's Logic, and the essay on
Liberty had his cordial admiration. The essay on
Comte, too, he thought very valuable. His own ideas
about this great fabricator of society may easily be con-
jectured. I should like to give them in his own words,
but can only remember their import. Just in proportion
to the strength of that part of a system which is founded
on the principle of love to the neighbour is the weakness
of that part of it which sets aside the Divine Disposer of
events, and puts an arbitrary classification in place of the
na.tural order of the world. I hope I have not mis-
represented the principles of Comtism ; T know, however,
that this fairly represents my husband's interpretation of
them.

Our third son, Edward, was born about Midsummer in
this year. His father gave him his second name, Lindsey, to
perpetuate that of my mother's uncle, Theophilus Lindsey,
a good man, and one of the earliest English Unitarians who,
like my father, seceded from the Church, and who gave
up the lucrative living of Catterick, in Yorkshire, where
he was much beloved, because he could not conscientiously
carry on the duty in accordance with prescribed doctrines.
Such secessions, united with such strong religious belief,
do not often happen in these days; but we cannot judge
of the motives of those who do not feel them to be neces-
sary for conscience' sake. Many distinguished clergymen
who hold the doctrines of Christianity far more loosely,

find their proper places, there will be an end to these confusions,
which result from the various ways in which the great subject is
looked at by speculators whose mental eyes are differently placed in
relation to it. This is only saying that the true knowledge of words
will be the true knowledge of things.

FRANCIS BAILY'S DEATH. 117

and give a far less literal assent to the New Testament
narrative than either my great-uncle, my father, or my
husband, remain in the Church with a belief that their
moral influence will be of greater use than their intel-
lectual scruples. In this case the possibility of the Church
becoming too broad to hold together is not felt to be an
evil, as even should it through this cause die a natural
death, its work will have been well done. Mr. De Morgan
felt that the profession of belief of every clergyman im-
plies so absolute and entire an adhesion of the whole
soul to the doctrine which he undertakes to preach, that
should that animus be altered, membership, in the sight of
God, has ceased with it; and the outward and visible sign
can really stand for nothing when its inward and spiritual
essence is gone. But he judged no one rigorously but
himself, though he was happy in knowing that he had
been connected with the memories of men of worth and
learning, who never hesitated when their choice lay be-
tween truth as it appeared to them and any other con-
sideration.

Shortly before Edward's birth we lost our old friend 1844-
Francis Baily. Early in this year his usually fine robust
health had given way, and a disease of the kidneys, pro-
bably the remote result of the shock given to the brain by
his accident, declared itself. He lingered some weeks,
always cheerful and hopeful, but perfectly ready for what-
ever turn his illness might take. His friends were less
prepared to lose him than he was to go. His death
occurred in June, and was a loss to Science l which could
not well at that time be filled up. Sir John Herschel
wrote that he was a man sui generis; and the letters

1 I have throughout this memoir used the word science in reference
to Mathematics and Logic, and those branches of knowledge in which
processes of reasoning are applied to subjects of observation. This is
the older meaning of the word. It is generally, though of course not
exclusively, used now to express knowledge gained by observation
alone. I remember the time when, in reference to Dalton's atomic
theory, it was said that chemistry had become a Science.

118 MEMOIR OF AUGUSTUS DE MORGAN.

1844. which passed among his friends contain a repetition of
this feeling, with an expressed determination to do by
their united effort what he had done for so many years.
This refers especially to the Astronomical Society, of
which he had long been President, and the members of
which found it difficult to appoint a successor. Mr. Airy,
Sir J. Herschel, Mr. Sheepshanks, and Mr. De Morgan
composed his epitaph. It was, I think, drawn up in the
first instance by Sir J. Herschel or Mr. De Morgan, and
carefully revised and altered by the others.1

standard Mr. Sheepshanks, who had accurate knowledge and

experience of scientific instruments, undertook to complete
the construction of the Standard of Length. In a letter
to my husband he says : —

I think Airy's paper on the supports of the standard scale
should be printed forthwith. . . . This naturally leads me to
the final clause, the inscription Regula mensurarum in perpetuum
Baily's definita. One would not (where Baily is concerned) even in a
Latin epitaph (and the language and mode of employment are
not mendacious) use exaggerations. When I undertook the
scale I hoped and believed a good deal was done ; but when I got
from Airy a precis of facts I found that it was chiefly of a nega-
tive character, viz., that our scale had changed its form, &c.,
and the only positive advance (beyond preparation) was, that

1 There is a bust of Francis Baily in the apartments of the Astro-
nomical Society in Burlington House. If the time should ever come
when observations of the form and size of the different parts of the
head and face are systematically made with a view to determine the
elements of character, any conclusion drawn from this bust would be
a great injustice to our dear old friend. It was taken from the por-
trait, which is weak and inadequate, and has exaggerated these
defects. While it was in progress. Mr. Baily the sculptor asked my
husband and myself to see the clay model at his studio. He invited
criticism, and at my suggestion added so much to the forehead that it
bore a strong likeness to the subject ; and Miss Baily when she saw
it burst into tears, exclaiming, ' It's himself.' But the sculptor after-
wards found that the penthouse brow and large forehead were not
* ideal ' enough. He said his work had been spoiled, removed all the
added clay, and left the weak and characterless head which professes
to be a likeness of Francis Baily.

CHANGE OF RESIDENCE. 119

two iron bars prepared by Colby had maintained their difference. 1844.
There were, indeed, some good measurements of expansion, but
these were by Simms and his nephew, and I intend repeating
them with, if possible, greater r.icety. If this subject is men-
tioned (and it should be), say that he was unhappily arrested in
the act of definitely fixing the national measures.

In the execution of his work, which was carried on in Richard

Sheep-

a cellar under the chambers of the Astronomical Society shauks's
in Somerset House, Mr. Sheepshanks recorded 89,500 observa-
micrometer observations. Only those who understand the i
nature and object of these can estimate the enormous
labour involved. He had to make frequent visits to
London for this purpose. We saw him often at the time,
but I have only my own memory for the statement that
much discussion on the experiments and observations
passed between him and my husband, and that when
difficulties occurred, Mr. De Morgan was often able to
assist in their solution.

We moved in July from Gower Street to Camden Camden
Street, Camden Town. My husband walked to the College
in time to be there every morning at 8.30, that he might
look over the pupils' papers before giving his lecture. He
could not come home, as before, in the middle of the day,
and on this account I was sorry for the change; but
in other respects it was far better, as the house was
roomy and convenient for a young family, and the air I
thought fresher than in Gower Street.

His readiness to serve his pupils and the College
had brought him some extra work, and some pleasure
in consequence. The Professor on whom the teaching of
Mathematical Physics devolved proved quite unequal to
his task. The pupils who came to him from the Mathe-
matical class were already much his superiors in know-
ledge, and in their strait they appealed to my husband.
With the approbation of the Council, he at once undertook
to meet the difficulty. He gave, during the remainder of
the session, e^tra.time and instruction to these young

120 MEMOIR OF AUGUSTUS DE MORGAN.

1844. men, who at the end of the session presented to him a
handsome copy of Wilkinson's Ancient Egyptians. The
letter accompanying the gift is signed with names of
Henry Robert Reynolds, Joseph Rees, Richard Holt
Hutton, and C. Howard.

In this year the Useful Knowledge Society came to an
end, having completed its work. Its farewell address has
been already mentioned. Mr. De Morgan's last under-
taking for it was a book entitled The Globes Celestial and
Terrestrial, written as a description of the Society's globes,
published in 1844.

Maiby's The Society, which had already brought out the c Maps

of the Stars,' had turned its attention to the want of accu-
rately made globes of the heavens and the earth. These
were constructed by Mr. Malby, under the direction of
several men of Science. The celestial globe needed most
revision and improvement. Up to the year 1823 the
21-inch globe by Gary and the 18-inch globe by Bardin
were the best in use ; and of these two, Gary's, ' having
annexed to every star its proper numerical or charac-
teristic valuation,' ! was judged to be the best. Both
were founded on Wollaston's Catalogue of 1789; and
Gary's globe contains the stars extracted from Flamsteed's
Catalogue by the two Herschels.

Mr. Baily had laid down, though not with the full
alteration which he thought necessary, the lines which
bound the constellations. Sir J. Herschel, being appealed
to by my husband on behalf of the nebulae, wrote :—

Why globe-makers will persist in laying down nebulae of
Classes II. and [II. is to me astonishing. There are but half
a dozen of Messier's and my father's 1st class which can be seen
with the naked eye, and the 2nd class ones are for the most part
invisible with a 3 inch object-glass. The per-centage of Dunlop's
nebulae which can be seen with the naked eye is still smaller.

1 Letter from Mr. J. W. Woollgar, of Lewes, to the Philosophical
Magazine.

MALBY'S GLOBES. 121

Indeed, with the 20-foot reflector, out of 629 l of which his cata- 1844.
logue consists, I have succeeded in observing only 207, and of
these I have great doubts of the identity of between twenty and
thirty. What sort of objects Mr. D. has set down as nebulae in
the other 422 cases I have no idea. All I can say is, that out of
1,700 more or less observed by myself at the Cape, the above
are all of Dnnlop's which have not proved coy. You. will judge
by this whether or not to recommend your globe-undertakers to
map down Dunlop's catalogue in its integrity.

As to double stars, I think Struve's great catalogue will go
far to saturate a 36-inch globe.

Let me know whether you are very much interested in Mr.
Malby's undertaking, as in that case I would send you the list
of those Nos. of Dunlop's nebulas which I either know certainly
to exist in or near his places, or have found nebulae which, by a
stretch of good-natured identification, I should be disposed to
admit as observed by myself.

Some large and showy globes had been made in 1823,
the trustworthiness of which was not guaranteed by the
name of any scientific authority. As Mr. Woollgar, in
writing of these, said, ' globes are oftener purchased as
articles of furniture than as philosophical instruments/
and these large globes fitted the purpose. Mr. Malby's
globes could not lie under this reproach, for even as
articles of furniture they were not showy enough to suit
the upholsterer, while their accuracy was beyond question.
But as a globe can never be even quite up to the amount
of astronomical or geographical knowledge at the time of
its completion, it must from time to time require additions,
if not corrections, and in course of discovery will at length
be superseded for practical use, as the globes made in
1844 may be at this time.

From their improved construction, great accuracy,
and careful measurements, questions concerning ancient
Astronomy, depending for the most part on the preces-
sion of the equinoxes, could be determined by these

1 The figures are slightly blotted in the letter, and I have not
Dunlop's Catalogue to ascertain the number.

122 MEMOIR OF AUGUSTUS DE MORGAN.

1844. globes. One who rejoiced greatly in them was Mr. John
Ta\?ur. Taylor, known for his inquiry into the authorship of
Junius, and for his speculations on the Great Pyramid.
He had made some suggestions on the formation of the
Astronomical globe, and wrote to my husband : ' I can
now call up all the phenomena recorded by Aratus or
Hipparchus, not to forget Homer, Hesiod, Virgil, Ovid,
and Columella, and I may even venture to correct the
great constructor Ptolemy, when he makes a slip in his
notations. Ulugh Bey, too, and Tycho, and old crusty
Flam steed, may come in their turn to the spherical ordeal.
All this I owe to you, for had it not been for your friendly
interference and sanction, I might never have seen my
attempt submitted fairly to the world.'

Mr. Taylor's large claim to original suggestions in
this work might not perhaps be fully acknowledged by
the Astronomers who helped to complete it. Notwith-
standing his practical and extensive dealings with the old
philosophers, and his satisfaction in correcting Ptolemy's
slips, he was himself far from sound in his scientific
knowledge, and subjected himself to a severe castigation
from Mr. Sheepshanks for meddling with the Liverpool
Observatory and its manager. He also set Astronomers
right about the comet of 1848, which he declared to be the
same as that of 1556. ' This,' Mr. Hind says in a letter
to Mr. De Morgan, 'is the last of Mr. John Taylor's
Astronomical extravagances.' The motion of the first
comet was direct, that of the one observed in 1848 retro-
grade. Mr. Taylor's announcement was made in the
Liverpool Mercury, and corrected, I think, by Mr. De
Morgan in the Athenceum. But his researches on the
Great Pyramid are of value. Mr. De Morgan said of
him : ' He is by temperament a discoverer of hidden
things, and has employed much ingenuity in discovering
what we may call two crack secrets, because they have
never been fairly cracked,' The other crack secret was
Junius.

ASTRONOMICAL TEACHING. 123

The moving picture of progress in any study has for 1845.
its background a series of ignorant guesses and foolish
conclusions. A specimen of what was taught as Astronomy
in the fourteenth century is not more grotesque and is
less simple than what was called teaching within our
own memory, and perhaps may still be so called in some
remote young ladies' school. Eeferring to the works of Astronomy
a class of authors who seem to think that the pretext
of writing for the especial instruction of young ladies is back-
more than a sufficient excuse for any amount of nonsense,
Mr. De Morgan adduces the following examples. The
book from which the extracts are made had reached its
fourteenth edition.

Among the questions on Sagittarius are the following : —
' To what sin were the Athenians addicted ? What reflection
does Dr. Doddridge make on the occasion ? ' Apropos of the
constellation of Ursa Major is this question : * Who drove stags
in his phaeton instead of horses ? ' and the answer is, * Lord
Orford, who died in 1791.' The concatenation is that bears
can be tamed, and that Prince Radzivil drove them in his
carriage at Warsaw. On Musca the questions are, ' What are
the distinguishing characteristics of flies ? In what manner,
demonstrating his propensity to cruelty, did Domitian treat
them ? Hence what sarcasm was passed upon him ? How has
Sterne represented the humanity of a feigned character to a
fly ? How did contrary behaviour in a female (according
to Darwin) break off an expected matrimonial connection?'

There were a few other books of a better sort pub-
lisher!, but they did not reach fourteen editions, and,
we may believe, seldom found their way into girls'
schools.

There had existed from the year 1817 a Mathematical Old Mathe-
Society, or club, which met in Crispin Street, Spitalfields. society.
It was originally composed of working men, many of them
silk weavers, and among the early members had been
some men of known name. The conditions of member-
ship were that each member should have his pipe, his pot,

124 MEMOIR OF AUGUSTUS DE MORGAN.

1845. and his problem. A short account of this society is given
in the ' Budget of Paradoxes.' It gradually declined as the
harder life of the working man deprived him of leisure time,
or perhaps as the pot took the place of the problem ; and
in this year 1845 a proposal was made to incorporate what
was left of it into the Astronomical Society. Only nine-
teen members remained, and they were not working men.
Those who were not already members of the Astronomical
were received without payment of fees, and it only re-
mained to convey the books and other property of the old
society to the rooms at Somerset House. Mr. De Morgan
undertook to look over and to superintend the removal of
the books, which now form a small portion of the library
of the Eoyal Astronomical Society.

Two or three years before this time, some gentlemen,
interested in the history of Science, had projected a
society to be called the ' Historical Society of Science.'
Mr. Pettigrew, Mr. Richard Taylor, the printer, and
Mr. De Morgan were among the first of these. Mr.
J. 0. Halliwell, the archaeologist, had taken a prominent
part in the scheme, and became the secretary. My hus-
band, who had looked forward to useful results from the
work of this society, found in this year that it was be-
coming extinct for want of attention in collecting sub-
scriptions, and from general neglect. He immediately
called the attention of the other members to this state of
affairs, and the society came to an end without undue
pressure on the Secretary, who was not in circumstances
to meet it, but who incurred some blame from one or two
of the persons concerned.

Rev. s. When my husband was a boy, living at Taunton, the

Maitland. j^ Samuel Maitland, not then in orders, was his mother's
friend and neighbour. He afterwards became a friend and
correspondent when the subjects of his works formed part
of those over which my husband's studies extended. ' His
series of essays " On the Dark Ages " was the most read
of all his works. He was one of a class of whose writings

REV. SAMUEL MAITLAND. 125

it must be said that wherever they take they bite. They 1845.
are imbued, but not in excess, with a kind of humour
which seems almost their own. It has more likeness to
the peculiar humour of Pascal than is seen in any writer
of our day.'1 Though Dr. Maitland was not a Mathema-
tician, the subjects of mutual interest were many, and
their correspondence touches upon all kinds of questions,
from those of Dr. Maitland's works which involve much
sound learning on the theology of the dark ages, to his
latest little volume, Superstition and Science, in which
the phenomena of spiritualism and the miracles of the
Catholic Church are considered in relation to Scientific
inquiry. The attention which Mr. De Morgan had Date of
given to the question of Easter was shared with Dr.
Maitland. My husband had contributed an article to
the Companion to the Almanac fur 1845, giving the
reasons why then, as in 1818, Easter Sunday had fallen
on, instead of after, the first full moon after the Vernal
Equinox. There had been much fruitless discussion on
this in 1818, and to avoid a repetition of it — for the
question was already agitated in Parliament — a full expla-
nation was given, in the above-mentioned article, of the
cause of deviation from the rule, and the relation of the
whole subject to the Christian and Jewish calendars. In
the next year, 1846, an article On the Earliest Printed
Almanacs gave further information, and his Book of
Almanacs, published in 1851, left no means of knowledge
wanting. Dr. Maitland's letters at this period showed
his interest in the Easter question. He was then librarian
to the Archbishop of Canterbury, and the library at
Lambeth Palace afforded him means of research in it,
and experience on another question, which was valuable a
few years later, when the British Museum Library Cata-
logue occupied the thoughts of scholars.

My husband's acquaintance with Lord Brougham,

1 From an obituary notice by Mr. De Morgan on the Royal
Society's Memoirs.

126 MEMOIR OF AUGUSTUS DE MORGAN.

1845. who never visited us, arose out of the business of the
Lord Useful Knowledge Society and of University College.
Brougham. The correspondence, which lasted from 1830 to Lord
Brougham's death, is chiefly on Scientific subjects, on
many of which the statesman consulted the Professor.1
One of these was the properties of curves in Optics, on
which Lord Brougham had experimented and written.
He was also the author of a life of Newton for the
Society. Mr. De Morgan had, in this year, brought out
a memoir of Newton (to be noticed further on), in Charles
Knight's British Worthies; and many of Lord Brougham's
letters refer to the claims of Newton as set forth by dif-
ferent writers.

When, shortly after this time, the injuries inflicted
on Guglielmo Libri by an unjust accusation of the
French Government aroused the indignation of most
English men of Science, Lord Brougham expressed his
sympathy, and tried to help M. Libri's cause by commu-
nicating with his own friends having influence in France
as well in politics as in Science. He, like others, found
and acknowledged the unjust bias of M. Arago wherever his
national prepossession could come in. This showed itself
in political antagonism (supposed, in M. Libri's case, to
arise from his Italian birth and proclivities), as well in
scientific questions as in the case of the simultaneous
discovery of the planet Neptune by Adams and Lever -
rier.

Discovery The year 1846 was made famous by the announce-
ment to the world of this discovery. From every point
of view its history is an interesting one, but it is so
familiar to most readers that I must ask pardon for
reverting to its principal points, that the part taken by

1 I regret that I have none of Mr. De Morgan's letters to Lord
Brougham on the subject of Newton, or on any question of general
interest. I am greatly indebted to the present Lord Brougham for
his kindness in sending me a few letters, but the mass of documents
is, I understand, so great at Brougham Castle as to render a thorough
search exceedingly difficult.

DISCOVERY OF NEPTUNE. 127

my husband on the reception of the news by Astronomers 1846.
may be understood.

This discovery was an instance of that law of progress
by which we find that a truth, when the time has come
for its reception, is seldom the prize of one mind only : it
may be that some far-seeing solitary minds have early
anticipated the knowledge for which the world is not pre-
pared, but in its full advent a new truth has more than
one recipient. It was so in the case of Neptune. In
observing the place of Uranus early in this century, Aberra-
Astronomers had found that the observable course of the Uranus,
newly discovered planet did not coincide with that given
by mathematical calculation. This appeared from M.
Bouvard's tables of Uranus from 1781 to 1821. Other
irregularities were found, but the idea of a large dis-
turbing body wa,s not generally entertained ; and M.
Poinsot, who had called the attention of the French
Institute to the observation of a star, supposed to be
a new planet, by Messrs. Wartmann and Cacciatore,
was laughed at. It is true that in 1834 Dr. Hussey
wrote to Mr. Airy that he had conjectured the possibility
of some disturbing body near Uranus, and that he had
found that MM. Bouvard and Haussen had corresponded
on the subject. Mr. Airy, however, was doubtful of the
possibility of determining the place of the planet until
the nature of the irregularity should be better known.
Eight years before the actual discovery Bessel gave it as
his opinion to Sir John Herschel that the disturbances in
question could be due only to the action of a large body
beyond the orbit of Uranus. The direction of investi-
gation was thus to a certain extent pointed out ; it was no
less, when attained, f the greatest triumph of inductive
Science which Astronomy has yet to record.' This great-
ness consisted in the fact that the exact place of the planet
was obtained not by actual observation, but by mathema-
tical calculation, founded upon the elements furnished by
the action of the disturbing forces. ' Two Mathematicians

128 MEMOIR OF AUGUSTUS DE MORGAN.

1846. had worked out the problem, the English Astronomer
communicating his results in November 1845 to the
highest authorities in the astronomical world, by whom
they were reserved for further confirmation ; the French
Astronomer, with more confidence in his work, making it
known to the world at once. Mr. Adams' calculations
antedated M. Leverrier's by eight months, but M.
Leverrier's promptitude of publication secured for him
the honour of the discovery.' 'Mr. Adams,' adds Mr. De
Morgan, ' furnished Mr. Challis with the means of actually
securing two observations of the planet previously to any
announcement by M. Leverrier.'

M. Leverrier's communication was followed immedi-
ately by recorded observations of Neptune by M. Galle,
the Berlin Astronomer, who wrote in September that the
planet had been seen by him as a star of the 8th magni-
tude not marked upon any chart.

There could be 110 question of M. Leverrier's discovery;
it remained to be seen why, when the English discoverer
was so nearly the first known to be such, he had been
anticipated by the French Astronomer. Mr. Airy explained
that in answer to the letter in which Mr. Adams had
announced it to him, he had requested Mr. Adams to give
him some further explanation. This letter of inquiry had
not been answered till long after ; hence the delay, deeply
regretted by all. On these facts, and on the discussion
which followed in the Astronomical Society, Mr. De
Morgan wrote : —

No blame need be attributed to any one ; but I think it
will turn out that the Mathematicians of this country had not
faith enough in their own Science. And, most assuredly, we
may look forward to seeing the wise men who never believe
until the thing is done — the sober men to whom everything that
is to be is a figment in the brain of a visionary — the practical
men who are not sure that there is a future until it comes to
them in the shape of time present, all loud in their outcry, some
against one, some against another, for not having done that

ADAMS AND LEVERRIER. 129

which, six months ago, they would have been the first to have 1846.
laughed at them for doing.1 . . . The planet

That M. Leverrier is to all intents and purposes the dis-
coverer of the new planet is beyond a doubt. No evidence in
his favour could be stronger than that of Messrs. Adams, Challis,
and Airy. It is quite within probability that it might have been
discovered in November 1845, from the true elements given by
Mr. Adams in October, as stated by Mr. Airy. That it was on Mr.
Challis's papers before it had been seen abroad is certain. Why,
then, is this remarkable discovery French, and not English?
Simply because there is not sufficient faith in Mathematics
among the Mathematicians of this country. I should not say
this upon one instance involving only three men; I know it
otherwise. Our men of science too often think it wise and
practical to doubt results of pure Mathematics, and the French
who run into the other extreme have a decided triumph in this
instance. The results will do much good among us. Few of
our philosophers are deep Mathematicians, and those who aspire
to the character without laying the foundations of exact science,
are apt to take a tone with respect to it to which its culti-
vators have deferred until their deference has acted on their own
minds, and affected the rising generation. In one sense, we may
rejoice at the check which this spirit has received. For a long
time to come, in every instance in which it shall show itself, it
will be put down by the magic word Leverrier.

Sir John Herschel, who declared at the British Association
that the movement of the planet had been felt (on paper, mind)
with a certainty hardly inferior to ocular demonstration, is
precisely the person who thirteen years ago (Cabinet Cijclo-
2)cedia, ' Astronomy,' p. 5) published what there can be no doubt
was meant for a rebuke to this want of faith, and also to the con-
fidence of those who made themselves judges of what they could
not possibly understand.

The history of this discovery, and of the way in which
it was received, is a notable illustration of national cha-
racter.

At first, on hearing how nearly Mr. Adams had anti-
cipated him, M. Leverrier felt some apprehension that liis

1 Athenaeum. I have changed the editorial we in one or two places;
he never allowed these articles to ba altered by the editor.

K

130 MEMOIR OF AUGUSTUS DE MORGAN.

1846. glory might be taken by another. These apprehensions
were soon quieted by the generous and graceful statements
of the three persons most concerned — Mr. Adams, the
Astronomer Eoyal, and the Cambridge Astronomer. But
there appeared violent articles in some of the French
newspapers, which, however, were disclaimed by MM.
Arago, Leverrier, and others. There was, nevertheless,
some amount of irritability displayed on the first an-
nouncement to the Institute, though the more forbearing
majority concurred with M. Libri, who said : ' En atten-
dant, il est essential de proceder avec la plus grande
calrne a 1'examen de cette affaire. Plus on y mettra de
reserve et d'urbanite, plus nous en avons 1'assurance
Peffet sera favorable aux Astronomes Fra^ais.'

The Academy itself suppressed any feeling of jealousy,
and showed itself perfectly ready to discuss the question
of the relative merits of the discoverers with fairness. But
M. Arago refused to allow the Englishman's claim, saying
that Mr. Adams c was not entitled to the slightest
allusion in the history of the discovery.' In reference to
this access of national feeling, which was afterwards
carried out by M. Arago's persistent effort to have the
planet named Leverrier, Mr. De Morgan wrote : —

Arago. Let M. Arago refrain. There will be one part of this matter

the less subjected to his distorting mirror of national bias, in
which the distortion is rendered less perceptible by brightness of
style and clearness of illustration. We should be the last to
deny the varied talents, deep knowledge of present science, ad-
mirable enthusiasm, a*nd concentrated power of producing effect,
which the distinguished Secretary of the Institute brings to his
part. But as an historian of science, he may be held to be the
Bailli of the day, his mania, however, being French and not
Hindoo. And wre may be satisfied that among the French them-
selves this Bailli will some day find his Delambre. His ideas
are so confused by the state in which the fear of an English
claim 1 as put him, that he styles his own determination to call
the new planet by no name but that of Leverrier, an undeniable
proof of his own love of the sciences, and an adherence to a
legitimate sentiment of nationality.

ADAMS AND LEVERRIER. 131

But on this feeling of nationality there were other 1846.
voices raised. Mr. De Morgan himself says : — NeCumne

All the elements of M. Leverrier's discovery were laid else-
where, as well as in France ; let it be enough for his satisfaction,
as it is for his fame, that he worked out the problem first. We
may wish that the complete honour of this great fact had fallen
upon the English philosopher, but far beyond any such merely
national feeling is our desire that philosophers should recognise
no such distinction among themselves. The petty jealousies of
earth are things too poor and mean to carry up amongst the
stars. Light and unmeaning as they are, they would be found
heavy incumbrances on a voyage so long as that to Uranus.

M. Biot, writing of the address in which Mr. Airy M. Blot,
narrated the facts, says :—

Thus, in the first week of October, 1845, precisely eight
months before M. Leverrier's first announcement, the new planet
was predicted by Air. Adams, and he alone was in the secret of
its position. . . .

I do not speak here in accordance with the narrow sentiments
of geographical egotism, improperly called patriotism. Miuds
devoted to the culture of science have, in my opinion, a common
intellectual country embracing every kind of polar elevation.

Professor Striive threw in his vote of equal justice : —

Far be it from me to have any intention of withholding our Professor
entire admiration from the eminent merit of M. Leverrier. Bat striive«
impartial history will in the future make honourable mention of
the name of Mr. Adams, and recognise two individuals as having,
independently of one another, discovered the planet beyond
Uranus. In the same way it attributes the discovery of the
Infinitesimal Calculus at once to Newton and to Leibnitz. . . .
In Mr. Airy's report we see that, in September 1845, Mr. Adams
arrived at a result, and in October he transmitted to Mr. Airy a
paper containing the elements of the present planet, so nearly
approximating that it might have been found in the heavens ten
months before it really was.

Mr. De Morgan's belief that the failure — which is
almost too strong a word— on the English side was due to

K 2

132 MEMOIR OF AUGUSTUS DE MORGAN.

1846. the want of confidence in their science among Mathema-
ticians, received confirmation from the report, by Mr.
Challis, of observations at the Cambridge Observatory,
founded on Mr. Adams's calculations. The statement was
laid before the Senate in December, and in it was men-
tioned a memorandum made in 1841, and shown by Mr.
Adams to Mr. Challis, recording the writer's intention to
solve the problem as soon as he had taken his degree
of B.A.

The unusual character of the question is adverted to
in this first statement of Mr. Challis : —

Mr. The usual character of perturbations is to find the disturbing

observa-8 action of one body on another by knowing the positions of both,
tions. In the case of Uranus, Mr. Adams's problem was the inverse one ;

from known disturbances of a planet in a known position, to find
the place of the disturbing body at a given time. ... It will
appear by the above account that my success might have been
more complete if I had trusted more implicitly to the indications
of the theory. It must, however, be remembered that I was
quite in a novel position; the history of Astronomy does not
afford a parallel instance of observation undertaken entirely in
reliance upon deductions from theoretical calculations, and those,
too, of a kind before untried. . . . We may certainly assert to
be fact for which there is documentary evidence, that the problem
of determining from perturbations the place of the disturbing
body was first solved here ; that the planet was here first sought
for; that places of it were here first recorded, and that approxi-
mate elements of its orbit were here first deduced from observa-
tion. And that all this, it may be said, is entirely due to the talents
and labours of one individual among us, who has at once done
honour to the University and maintained the scientific reputa-
tion of the country.

Both discoverers in due course received every possible
distinction at home and abroad. M. Leverrier, besides
other honours given to him, was elected an Associate of
the Royal Astronomical Society, and, immediately after the
discovery, proposed for the medal. And here a difficulty
arose. It was usual to give only one gold medal at any

ADAMS AND LEVERRIER. 133

time, and in order to secure the certainty of merit in the 1847.
candidate, this could not be adjudged by a smaller ma-

jority than three to one on the Council. On the present The Astro-
occasion the Council, which for the adjudication of the Society's
medal met always in January, was so divided in opinion
on the question that the requisite majority was not ob-
tained. It was felt that although M. Leverrier's claim
was unquestionable, the acknowledgment of it in this form
would be a manifest injustice to Mr. Adams, whose claim
in one way was possibly greater, though it failed in the
requisite element of success — that of its being publicly
made known. On this arose a great difference of opinion
among members as to the right steps to be taken. All
were anxious that full justice should be done to both dis-
coverers, and all were naturally desirous that the Astro-
nomical Society should not be behindhand in its acknow-
ledgment of the great gain to Science of the discovery,
made, as it had been, by Mathematical calculation.

No decision was come to, though the discussion had
been long and anxiously carried on in the Council, and
the time for the award went by. But the great body of
the members could not readily submit to leave things as
they were without further explanation, and a special
general meeting was called to consider the propriety of
suspending the by-laws and of reconsidering the whole
question.

There were some members of the Society who took no
part in the usual work, but attended meetings on great
occasions, when it might be expected that their names
would give weight to their opinion. One of these was
Mr. Babbage, who was known to have a strong predilec-
tion for French science, and as strong a feeling against
that which had any connection with Cambridge. He also
attached much importance to the distinction of a medal,
and thus was led strongly to support the claim of M.
Leverrier, to the exclusion of that of Mr. Adams. Not
succeeding in his efforts to reverse the decision, or rather

134

MEMOIR OF AUGUSTUS DE MORGAN.

Mr. Sheep-

shanks's

opinion.

1846. no-decision of the Council by proposing a vote of regret
™e planet upon its measures, he wrote to the Times giving his own
views of the matter, and thus complicating the difficulties
of the position. The most active members of the Council
declared that they would not work on the possible con-
dition that a vote of c regret,' or, which was the same
thing, c censure/ should be passed upon their measures.

Mr. Sheepshanks, on the occasion of the South and
Troughton arbitration, had given offence to Mr. Babbage,
and his strong desire that justice should be done to Mr.
Adams only increased Mr. Babbage's displeasure at the
non-award of the medal. Mr. Sheepshanks was happily
more prudent in his expressions, and though amusingly
sarcastic in his letters, temperate in his public behaviour.
If he had not been so at this time, the concussion in the
Society might have ended in a complete disruption. He
was a fellow of Trinity, with a strong love for his own
University, and a desire that the glory so fairly earned by
one of its members should not be quite lost to Cambridge.
He says, in a letter to my husband dated November 20,
1846 :-

As to the medal, I will tell you my mezzo-termine. To give
the medal in due course to Leverrier, and, if the Council think
fit, after due deliberation, to grant, by means of a special meet-
ing, a medal to Adams, who did undoubtedly discover the planet
nine months before Leverrier, and it was by no fault of his that
we did not catch it first. His communication to the Astronomer
Royal and to the Plumian Professor on an astronomical subject
is surely a publication so far as Adams is concerned — according,
at least, to all rules hitherto recognised. He saves us, I think,
all real difficulty by waiving his claim to the discovery ; for if we
were called upon to decide by Waring's rule we should be
compelled to decide in his favour, at least, after verifying the
postmarks of the letter quoted by Airy.

Now, as he has not raised this very thorny point, it seems to
me that quiet and good-tempered and sensible people, who have
not committed themselves to a positive opinion before they had
heard all the story, may come to some conclusion satisfactory to
all parties except the ultra-French or the anti- Cambridge.

THE ASTRONOMICAL MEDAL. 135

On the part taken by his three friends, Mr. Adams, 1846.
Mr. Airy, and Mr. Challis, Mr. Sheepshanks says : c I am
far better pleased with the perfect candour and simple
gentlemanlike feeling of these men, than by anything I
have heard of for a long time.'

The writer conceded his opinion on the medals when
he found how utterly impossible it would be to bring all
parties to unanimity. He soon after wrote, e If we don't
get rid of the medal, it will capsize us.' And Mr. Airy,
who had expressed his feeling that if no medal was given
on this occasion the Society could never give one here-
after, also yielded to the present necessities of the case.
My husband, from having given close attention to the
whole question from the beginning, and seen its great
difficulties and complications, advised a course which was
taken. After the meeting, while the matter was pending,
he wrote : —

This question of medals is almost the only one that can Mr. De
come before the Council, into the discussion of which may
enter that question of right and wrong on which an honest man
never allows his opinions to be overruled by considerations
of expediency. On the knowledge of this, a wise by-law
was enacted, which requires a majority of three to one in favour
of the award of a medal. The consequence is, that when
opinion is much divided no decision can take place. It was an
unwise thing to force back upon the consideration of those who
had long and anxiously deliberated without coming to any con-
clusion, the discussion of a question involving so many disputed
points. It would have been better if the meeting had taken the
matter into its own hands, and called a special meeting, not to
enlarge the powers of the Council, but to do the thing itself.
The meeting, however, showed, on more points than one, a strong
feeling that so large a body, and so mixed, was not a proper
court for the hearing of such a case. It does not follow that the
special meeting when called need of necessity adopt the conclu-
sions of the general meeting which called it. No one Parliament,
though it may send business to its successor, can dictate how
that business shall be done. And if the Society will take a
little advice very respectfully offered, they will allow the matter

136 MEMOIR OF AUGUSTUS DE MORGAN.

1846. to rest where it is, and not compromise the working utility,
The planet perhaps the very existence, of their very useful body by persist-
i ep une. -^ ^ demanding a decision from those who have the best
possible reasons to know that they cannot agree.

And afterwards :—

The Society has given to both M. Leverrier and Mr. Adams
the full value of twenty medals, or rather, a prize of a higher
order than any medal. All the bases of the discussions take for
granted that both those gentlemen possess much more than the
ordinary share of merit to which, under usnal circumstance?,
medals are awarded. All the varieties of opinion are formed
upon this nucleus, and could not have existed without it. In all
but the mere gold which goes to the manufacture, the dis-
coverers have had their medals over and over again.

But, as was natural, the Astronomical Society could
not feel quite satisfied to do nothing, and though gold
medals were not given in the year to the two discoverers,
their merits were not long afterwards acknowledged by
Testimonials from the Society to each gentleman, £ For
his Researches in the Problem of Inverse Perturbations,
leading to the Discovery of the Planet Neptune.' l

I have said more of this discovery than may be thought
to belong to my husband's work in the Society. But all
that he said and wrote on the question was strongly
characteristic, expressing his high estimation for all the
intellectual and, I may add, moral qualities of the parties
concerned, and his exceeding disregard of distinctions.
But besides this I have heard that the way in whirh
many of the impediments were surmounted was due to his
counsel.

Other questions connected with the Astronomical
Society had arisen during the year 1846 in which Mr.
De Morgan was involved.

The old difficulty of organisation was strongly felt at

1 Testimonials were given in the same year to the Astronomer
Royal, Prof. Argelander, Mr. Bishop, Sir J. Herschel, Prof. Haussen,
Mr. Hencke, Mr. Hind, Sir J. Lubbcck, and Mr. Weisse.

PRESIDENCY OF ASTRONOMICAL SOCIETY. 137

this time, because the real working men had done their 1846.
parts so long and so thoroughly in the face of many em-
barrassments caused by the more officious but less prac-
tical members, that their time of rest was overdue.

My husband never slackened in his exertions. What °r^g[d^c
others could not do he undertook ; but when in this year to Mr. De
the place of President was vacant, and there were good
reasons outside of the working part of the Council and
one or two turbulent spirits within which made it neces-
sary that a useful President should be secured by those
who could work with him, my husband was entreated, as
he had been before, to take the chair. His reasons for
refusal will be found in his letters to Sir J. Herschel and
Mr. Sheepshanks. The latter, who had the organ of
firmness fully developed, but who considered himself
' anything but obstinate,' replied to the programme and
refusal thus : —

DEAR DE M., — One evening after supper John Hind of Sydney
addressed Whewell thus : — ' I don't quite hear what you say, but
I beg to differ entirely with you.' Now I have heard and do
understand all that you say, and more that yon would say, and
I differ with you. But I have given up trying to convince
people against their will, ' 'cos I never found no good come of it.'
So, just beholding your countenance as your wife painted it
(decidedly obstinate if wrong, which most people are who are re-
solute when right), I give up all hope that my first best mode
of combination will answer. I see and have seen for a long

time a little cloud or two rising. Poor S has risen and

pelted, and is, I suppose, now exhausted. We have excellent
men, who don't understand or make allowances for others (I ex-
cept self and you), and we have no sufficient bond of union.

If you and others can prevail on Herschel, well and good.
You certainly can do a good deal as Vice, though by no means
so much as if you were President. I shall look twice before I
consent to continue Secretary, not merely for the trouble which
this occasions to a man disliking all work (except such as he
takes a whim to do), living forty miles from town, but really
because a more methodical and resident person is actually re-
quired just to keep things in order.

138 MEMOIR OF AUGUSTUS DE MORGAN.

1846. A few days after the writer added some exhortation

and remonstrance to his former missive :—

* Omne ignotum ' — how can you fancy that a practical or
gazing Astronomer is wanted for our Pres. ? Airy and Main and
Challis and Johnson are the only members within reach who are
strictly practical Astronomers, though several have, each in our
way, practical knowledge. But I don't remember any instance
where this knowledge was required in a Pres., nor can I well
conceive a case wherein it would be required.

I say, as a nailer, how dare you report the proceedings of the
B. A. S., not having sufficient knowledge, as you say, for Presi-
dent? Answer me that, good man, 'and thou shalt be to me a
very stout Apollo.'

I may just ask here, with reference to my old friend's
allusion to my husband's Athenceum reports — did Mr.
Sheepshanks credit all the reporters of the learned So-
ciety's proceedings with knowledge which would qualify
them for the President's chair? But Mr. S. at length
gave in.

If Sir J. H. will take the Presidency, it being understood not
merely that he is not required, but really not wanted, except on
anniversaries and when he can make it convenient, it is the best
move we can make. Pearson would do very well if we coald be
sure he would never come at all. Lord Wrottesley is a capital
fellow, but, considering some of your arguments, is scarcely the
person you should choose. Airy will take it if necessary, but
I don't like to propose him for several reasons, one of which
is that I dislike tasking his time and health so severely.

Sir John Herschel terminated the embarrassment by
consenting to the wishes of his friends. Mr. De Morgan's
views of the subject will be found in his letters.

139

SECTION VI.

CORRESPONDENCE FROM 1836 TO 1846.

To his Mother.1

MY DEAR MOTHER, — I have read yonr letter carefully ; and the 1836.
papers, and as much of the book as was necessary to show that
it contained no argument, and was in fact addressed to those who
already believe all it contains. If I can make you see clearly
that our modes of arriving at what we believe to be true are so
totally different that an attempt to discuss the subject together
would be an impossibility, it is all I expect. If your knowledge
of the New Testament had been of your own getting, unwarped
by the devices of a Church of which it has always been the
avowed doctrine to use every means which the age will allow to
force men to agree to its own interpretations, I could go much
farther, and could show you that taking every book of the New
Testament to be an authority to that extent only in which it was
recognised as an authority in the first three centuries, and taking
the words in their most probable meaning, there is no ground of
fear for any honest man who uses the best means in his power to
come at truth.

But between us there is in this matter no common ground on
which to argue. Nothing is more easy than to be positive and
certain, or to affirm the perdition of all who cannot see any par-
ticular system of doctrines to be true : but before you declare
that you must be right and I must be wrong, consider the
following points, and ask yourself what part of the whole New
Testament has more right to a literal interpretation than this :
* In the measure which you measure with, you shall be measured/
I take the most literal translation, and not what your misleaders
are pleased to call their ' authorised version.'

1. You have a number of books bound up into one, which
you call the New Testament. You never meddled with the

1 See p. 86, ante.

140 MEMOIR OF AUGUSTUS DE MORGAN.

1836. question whether all these books are genuine, and were really
written by the persons whose names they bear. Still less with
the question whether being written by different persons, at
different times, to different persons, &c., they can be used in
interpreting each other in the same manner as the different parts
of a book written by the same person. I have been obliged to
consider this.

2. These books are written in a foreign language, and
more than that, in a dead language, of which every one knows
that it is utterly impossible to render any phrase exactly into
corresponding English. This question no way concerns you.
You dwell upon a single English word in the translation just as
much as if it were the original itself. To me your version is
useless, as I know that those who made it were utterly incom-
petent to take that view of the original language which the sub-
ject requires.

3. These books have come down to us in manuscripts which
differ from each other repeatedly, and in one or two instances, if
not in more, there is proof, which theologians of all parties
unite in admitting, that additions have been made to the writers'
text. You care nothing for this ; I doubt if yon knew the fact.
I have been obliged to know it.

4. Your expressions amount to the following : — If you do not
take it for granted that King James's translators chose the
right Greek, and turned it into the right English, and more than
that, drew all their inferences correctly, God Almighty will
punish you to all eternity.

5. Out of all that precedes you have got a complicated creed,
on implicit belief in which you insist. I recommend you to follow
the plan adopted by Locke, when he wanted to ascertain what
the Christian religion was. He looked carefully through the
Acts of the Apostles, and collected every single instance in which
a Christian was made by the Apostles ; for, he argued — and in so
doing he upset every church which has existed since A.D. 300 — if
I can become as much of a Christian as the first converts of the
Apostles, I shall certainly obtain the essentials of Christianity.
Do this yourself. Construct a creed out of all which the Apostles
required, without adding a single word, and compare it with your
own. For what else was so precise an account given of so many
admissions into the Church ? And this not with a view to
changing your own opinions, for if your creed gives you comfort
I would not change a letter of it ; but with a view to the follow-

CORRESPONDENCE, 1836-46. 141

ing question : Do yon believe that the God of truth has so mis- 1836.
led the world as to give it a religion the essential parts of which
cannot be gathered from the manner in which those who first
taught it admitted proselytes ? Certainly a newly baptised
Christian, if sincere, did not perish everlastingly if he died the
moment after his baptism. But your Church positively declares
he did unless he believed what they call the ' Catholic faith.'
Now ask of yourself in sincerity, where is it set down in such a
manner that a wayfaring man, though a fool, could not err, that
the Apostles taught this creed, or anything like it ?

Again, take another test. Certain of the Apostles wrote
accounts of the life and doctrines of Jesus Christ. Matthew
wrote in Hebrew, no doubt for the Jews ; Luke in Greek, for
the Gentiles. These books were never collected into one till
centuries after Christ, nor is there any proof that the earlier
Jews ever saw the Greek Gospel, or the Greeks the Jewish one.
It is most obvious that each of these accounts mnst contain the
essential parts of the Christian religion. It is also most obvious
that an epistle of Paul to a town in Greece must not be joined
with one written to Romans, both of which were never seen for
many years in Judea (so far as can be shown), to make up a doc-
trine essential for the salvation of Jews. Now try again. Make
np your creed out of any one of the Gospels, if you can. Surely
two fairer tests cannot be proposed to any person who knows
what reason is: and still more when it is merely a question
whether one person ought to be-ieve that another must suffer
eternal punishment because he will not treat as one book a
number of different books in a manner which would be laughed
at if applied to Livy and Tacitus. And yet they both wrote
Roman history at periods as near to each other as those at which
the books of the New Testament were written.

All this has no reference to the question whether the creed
could be got out of the whole New Testament together if per-
mitted. Before God I declare that I have examined closely the
history of the early Church, together with abundance of contro-
versy on both sides, not forgetting the books of the New Testa-
ment on which they are written, and can find nothing like the
creed of the Churches of Rome or England. The former does not
pretend to find what you call the essential doctrines of Christi-
anity in the New Testament, but appeals to tradition. It is easy
to rail at them, but to the best of my knowledge and belief,
derived from historical reading and actual observation, the

142 MEMOIR OF AUGUSTUS DE MORGAN.

1836. Church of Rome contains as much honesty as that of England,
and a vast deal more knowledge. It would not take one quarter
as much evidence to make me a Catholic as to make me a
Church of England man.

I should have no objection to be better acquainted with Mr.
Baptist Noel, but you are grievously mistaken if you think any
discussion with him could have any effect on me.

1. Because he has never studied either side of any contro-
versy, or at least of those on which such a discussion would
turn, as he himself avowed to me, though he must have been at
that very time meditating a controversial work, or one meant
for such, which he shortly afterwards published, and which took
the point in dispute for granted on his own side in the title-page.

2. Because he would be better employed in meditating how to
reply to the complete and conclusive reply which he received
from a Unitarian minister, whom I blame very much for replying
to so weak an attack. Your letter, my dear mother, was quite
as good logic as the Rev. B. Noel's book, and indeed would
make a pretty abstract of it. And yet you could see that you
did not profess to be able to argue the question ; but the Rev.
B. Noel was not able to see so much. He is, nevertheless, a
liberal and amiable man, but he mistook his ground altogether
when he thought he was a fit match for the head of a body so
learned (compared with Church of England clergy) in the
history of his own creed as the Unitarian ministers. If you
want an opponent for me, take some one, if you can find him,
who has studied both sides of the question. But even then I
should object to discuss with him —

1. Because I never saw or heard of any one who was made to
change his opinions by discussion. 2. Because such subjects are
best discussed between a man and himself in retirement, and
with the real original accounts before him. 3. Because I see in
all that is orthodox a lack of that charity which Paul considers
as more essential than everything else, coupled with what
virtually amounts to a claim of infallibility. 4. Because number-
less unanswered arguments lie before me, which the Established
clergy have left off attempting to answer. Instead of attempting
to drive me, an individual with little time on his hands, to go
through the oft-repeated job of cutting the flimsy web of an
Athanasian Christian, move your own clergy to print their
assertions, and leave those who have leisure for answering to
deal with what they ahall advance. I shall then be able with

CORRESPONDENCE, 1836-46. 143

little trouble to verify both sides ; and as what is called Christi- 1836.

anity by the Church of England has never failed to meet with

its answer, even when it was declared felony to answer it (for

suoh were the arguments used at one time), I have little doubt

any person who shows a respectable knowledge of the history of

the Church will meet with a speedy reply if he will venture into

the field.

Now with regard to these matters, you may surely, my
dearest mother, collect from what I have said, that there will be
little wisdom in attempting to revive this subject. Appeals to
my feeling?, whether from the bitter stroke we have lately had,
or from your distress that I cannot believe as you believe, are
trying to wound the wrong parts. It is impossible you can be in
earnest when you think that I who have been for the full half of
my animal, and the whole of intellectual life, accustomed to con-
sider doubtful things by help of reason alone, should be moved
to any opinion because any person alive believes it so strongly
that he or she is grieved that I do not believe it also. Such
appeals might be made to induce a person to examine that
opinion, but I have examined it, and I conscientiously believe
more than most of the clergy on whom you pin your faith.
Still more weak are your implied assertions that my late illness,
&c., are chastisements from God. How could you know this if
it were true ? or how can a very slight consequence of that want
of tendency to inflammation which it has pleased God should
preserve me from colds, fevers, cholera, &c., and which forms a
constituent part of my power to sit at work many hours without
headache or pain, be considered as a chastisement ? Believe me,
I see nothing in it but a very slight and easy composition for
the want of liability to many worse things. In the name of
common sense let the Almighty manage His own world. The
presumption with which modern Christians explain all that
happens, and point out the intention with which it all came, is
one of the strong marks by which the perversion of the system
may be known. If the tower of Siloam were to fall precisely
upon one hundred people, all Calvinists, it would never enter my
head to suppose that they were thereby declared to be objects of
God's particular displeasure. As long as my reason lasts I shall
never want a better argument than that.

I have looked over dear Eliza's papers with the interest with
which everything that concerns her affects me at this moment.
They relate to points which have now been in discutsion fifteen

144 MEMOIR OF AUGUSTUS DE MORGAN.

1836. hundred years, and on which she had to form her own opinion
with such means as she had ; as have you and myself. But such
matters are not with me matters of feeling, they are to be tried
by reason and evidence — that is by me, for I do not object to any
one who thinks he can find truth by another method trying what
he can do. You are to judge yourself, I myself, and^ it M is" im-
possible that any two people can usefully discuss any subject,
one of whom believes that a conviction of the truth of opinions
is an argument in their favour. Yours most affectionately,

A. D. M.

To Dean Peacock.

69 Gower Street, Nov. 13, 1838.

DEAR SIR, — I would not trouble you, generally speaking, to
notice an undergraduate just arrived, but I think my young friend
M., the bearer of this, has merit enough to be an exception. He
has gone through a good course of reading, and is something like
a low wrangler in his present attainments, or rather higher, with
very good chance of being made into a high one. He stood a
stiff examination for our Flaherty scholarship, as we call it, at
Univ. Coll., and though second came off with great honour.

I remember with great gratitude and pleasure the notice I
used to receive myself from those in high station, when I was an
undergraduate, having no other claims than of the same de-
scription as those which M. now has. I should have left him
to find his way in his own College, not doubting that his acquire-
ments and industry would soon make him marked ; but I find
he is almost entirely without acquaintance. If, then, you will
introduce him to one or two of your good men, as we used to call
them, his future competitors, you will do a service where it io
well deserved, and I shall feel very much obliged. I should like
him early to know some reading men out of his own College,
from whom he may learn that its system is not necessarily
that of the University.

I do not doubt you found a letter from me containing my
proposed test of convergency and divergency.

You are, of course, interested in all that concerns Dr. Young.
A publisher in London has bought or will buy the plates of the
Lectures. He proposes to republish them (catalogue excepted) in
parts, transferring the copper to lithograph. My colleague
Sylvester is to put notes, which with reading he will do very
well. I am now proposing it to the Soc. for tho Diff. of Useful

CORRESPONDENCE, 1836-46. 145

Knowledge. Do you think favourably of the plan ? My own 1838.
opinion is that Young's lectures are an unsearched mine of good
things, often very happily expressed. But two quarto volumes
frighten most people. It is of course a work which any one
would like to see republished, but should your opinion be as
strong as mine the expression of it would materially forward the
object. I remain, dear sir,

Yours faithfully,

A. DE MORGAN.
69 Gower Street, Nov. 13, 1838.

To Francis Baily.

MY DEAR SIR, — The word rapa or rapum means a turnip, or
any small white root. There is in Italian rapa, a turnip, and in
English the same word is seen in rape-seed..

Raparium and rapina (both words are used) mean a collection
of many rapoe, a turnip- store, or turnip-field. Consequently
your rapina must mean a cluster of stars.

What a capital new word for the starry heavens — a turnip-
field !

Yours truly,

A. DE MORGAN.

69 Gower Street, Monday Morning.

To 8ir John Herschel.

69 Gower Street, Nov. 22, 1842.

MY DEAR SIR JOHN, — Thanks for your letter and the compli-
ments— non omnis moriar — with that big book. I shall be the
tenant of some old book-stall a hundred years hence, and some
one, perhaps myself, Lethed and transmigrated, will give half a
crown for me — as I have done for others, or perhaps for myself
again in some pre-transmigration — and will put me down in a
bibliographical list, with a slight mistake of the name (non
omnis moriar), and of a hundred years or thereabouts in the
date.

As to Lardner's ' Cyclopaedia,' you must address direct to Long,
man, who is the real editor now. I think a second edition stuck
full of southern plums, with some nice nebulae, neat as imported,
would be a capital dish. When shall we begin to see the
southern heavens through your spectacles ?

L

146 MEMOIR OF AUGUSTUS DE MORGAN.

1842 ^ f°rg°fc my hieroglyphic of Uranus ; I told you, I think, that

the baronetage draws Mars instead of Uranus in your shield.

I pointed out the mistake of latitude to Charles Knight's
people to-day. They told me they were partly aware of it
already. What is meant by being partly aware of the pole-star
not being exactly on the pole ?

' In order to be sure that a general proposition is true we
must be sure that all its particular applications are true.' If * in
order ' means previously I deny the assertion. Certainly, to be
sure that a general proposition is true we must be sure that all
its particular cases are true, for a general proposition =2 (par-
ticular case).

I suppose it is meant that there is no surety without exami-
nation of all the particular cases ; this I admit too, but I suppose
it is farther meant that there is no surety without enumeration
of the particular cases : if so, this I deny.

For example, the angles at the base of an isosceles triangle
are equal. In the proof I have moral certainty that I examine
every isosceles triangle ; any one whatsoever is every one. Ab-
straction and rejection of all that distinguishes one particular
case from another is the mode of induction, if people like to call
it so, which general reasoning employs.

' Consequently it is reasoning in a circle to include the truth
of the particular from that of the general.' I deny the conse-
quence. If any one likes to say, on the preceding view, that
general reasoning is induction of particular cases, which I do not
in a certain sense deny, he must not say that I conclude or infer,
but only that I go to a drawer in which I have laid up all the
cases ready for use, for this must be the correlative meaning of
inference. But shall the very man who found out that I had
got my drawer full be the one to deny me liberty to take out
the contents, becanse the etymology of the words I use to
describe such out- taking rather seems to describe making the
goods, as wanted, by a machine, than taking them out ready
made from a receptacle ? No, if he goes and alters my words of
first process, he must allow me either to resist or to alter the
words of second process to match.

Again, how dares any one say, ' To be sure of the general, we
must be sure of all the particulars ' ? Epimenides said all the
Cretans are always liars. Now Epimenides was a Cretan him-
self; how could he establish his proposition ? If it were true, it
was therefore false.

CORRESPONDENCE, 1836-46. 147

* Has he examined all the particular cases of his proposition ? '
He either knows this a priori or he has examined (that is, if he
knows it to be true) ; if he knows it a priori, then he opens the
net, and out we jump; but I will answer for it he has not
examined all the possible cases.

Is there not a confused way of talking about truth ? When
we prove a truth, that is, give ourselves certain knowledge of its
being a truth, we talk as if we had made a truth. We say ' one
proposition is the consequence of another ; ' when it should be
' our knowledge of one proposition is the consequence of our
knowledge of another.'

He who said peace among men forbade Metaphysics. When
their cloudinesses the axioms of mental philosophy declare war
against l two straight lines can't enclose a space ' they remind me
of the Chinese trying to take an English battery.

Here are some undoubted truths : —

sin oo =0, cos oo =0 ;

tan oo = -h -v/ — i, cot co =H->/— 1.

As to sec oo and cosec oo I am doubtful. They are either 0
or oo . I suspect the former.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

69 Gower Street, Dec. 30, 1842.

MY DEAR SIR JOHN, — Many thanks for the reduction of
Schiller's observations to the latitude of London. I dare say
you have applied the correction —

+ (English — German)

very skilfully, but I am so ignorant of that language that I shall
not find you out if you were to err in the first place of gutturals.

When your missive arrived, I was engaged with a young
Turk whom I indoctrinate in differential equations and matters
arising thereout. I gave him your wafer as a sort of auto-
graph, whereupon the following dialogue took place : —

He. Oh, Sir John Herschel ! what is it he has done with the

L 2

148 MEMOIR OF AUGUSTUS PE MORGAN.

1842. Moon at. the Cape of Good Hope ? I have got his book, and „
have read it with the greatest delight.
J. It's a hoax.

He. A hoax ! Well, I was so delighted to think it was all
true. I told our Ambassador of it yesterday, all that had been
seen in the Moon, and his Excellency only laughed at me and
said it must be a hoax.

Depend upon it there are thousands in the condition of this
young man.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

Camden Street, Oct. 7, 1844.

1844 MY DEAR SIR JOHN, — A certain man, named Malby, who

makes and edits globes, has procured the copyright and plates
of certain 36-inch globes, on which he means to lay down
nebulae, to wit, —

Messier,

W. Herschel (1786, 1789, 1802),

Dtmlop (1828),

J. Herschel (1833) ;

also double stars, &c., &c. Now it strikes me that if by waiting
any reasonable fraction of a revolution of the equinoxes he would
have your southern patches to dig into his copper, it would be
wisdom in him to wait. Can you tell me within two or three
revolutions of the Moon's node when the world is likely to have
your work ?

To tough jobs long periods ought to be applied, both for
safety and solemnity. But if you are able to reply that you will
be ready in a jiffy, or a crack, or less than no time, or a brace
of shakes, or the twinkling of a bedpost, or before you can say
Jack Robinson, or even the sum of them, of course he must wait.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, October 1844.

MY DEAR SIR JOHN, — I take much interest in Malby's globes.
1. Because I am writing a * Use of the Globes ' for them, of
which I send you an old proof to destroy at your leisure.

CORRESPONDENCE, 1836-46. 149

2. Because Baily's last printed work is the set of revised 1844.
boundary lines for constellations which appears on them.

3. Because Malby is a very spirited fellow. A man proposed
a feasible way of mounting the globe so as to adjust it for any
era, giving in fact the pole of the equator a motion round the
pole of the ecliptic. Malby immediately set to work, got the
globe made with an additional contrivance for solar apogee, and I
have a specimen now in my hands. They are soon to be adver-
tised. If I were your mortal enemy I should like nothing better
than to dispute with you about heliacal risings, &c., of 3,000
years ago. How I should grin to think that you were at your
spherical trigonometry while I was getting within more accuracy
than an heliacal rising is good for, by two or three motions of the
hand, and a squint or two along wooden horizons and brazen
meridians !

Malby has also a very neat planisphere with one revolving
surface and one fixed, and on bringing the hour of the day
on the edge of the revolving surface to the day of the month
on the edge of the fixed, the hollow part of the revolving
surface shows the visible heavens for that hour and day.
These planispheres usually have three surfaces and two adjust-
ments.

But whether I shall in a month or two claim your kind offer
about Dunlop's nebulae depends upon Malby's decision about the
whole scheme. I shall recommend him to defer it altogether
till your work appears. What can Dunlop have been at ?
-Your optical power must have been incomparably greater than
his.

Are there any atmospheric minutiae which last long enough
for a careless observer, who never looks for a thing a second
time, to note as nebulae ?

Banquo. The air hath bubbles as the water hath,

And these are of them — whither are they vanished ?

Macbeth. Into the air, and what seemed nebula melted

As breath into the wind ; would they had stayed !

No more at present from

Yours very truly,

A. DE MORGAN.

150 MEMOIR OF AUGUSTUS DE MORGAN.

1845.

To Sir John Herschel.

7 Camden Street, May 19, 1845.

MY DEAR SIR JOHN, — As I gave you rather a bad impression
about the Mathematical Society from their old clay and pewter
days, I feel bound to tell you that Captain Smyth, Galloway,
and myself went down and examined their library and them-
selves, and saw a good many, and got the names and occupations
of all. We found an F.B.S., an F. Ant. S., an F. Linn. S., a
barrister, two silk manufacturers, a surgeon, a distiller, &c. ;
and we found that all had really paid attention to some branch
of Science. One Mr. Perrott is, I am told, a man of note as a
chemist. We certainly shall not lower the average knowledge
of our Fellows by accepting their proposition. I went down
rather against the scheme, but was perfectly changed by what
I saw and heard.

Their library is a good one. The matter will soon be dis-
cussed at a Council.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, May 28, 1845.

MY DEAR SIR JOHN, — No difficulty at all. Our by-laws
permit a general meeting, called by the Council, with a week's
notice, to destroy every by-law, and make a complete new set.
The Charter is liberty itself in this particular.

A general meeting will be called after the next ordinary
meeting. Of course, we could not depart a hair's-breadth from
the statutable mode of election without.

As to the Cambridge Transactions, I have not got them,
and know little of them as a whole. In addition to what you
name there are Murphy's -papers, which are remarkable, particu-
larly those on definite integrals ; but were I you, I should consult
Hopkins, the secretary, on the details.

The transactions generally may be described as having had a
tendency to bring forward discussions of principle among the
members of the University. There is, you may safely say,'
sufficient proof in them that the ordinary system of University
reading, which crams details of methods, put together in exami-
nation form, with fearful rapidity upon the young student, does

CORRESPONDENCE, 1886-46. 151

not destroy the power of reflecting upon the basis of mathe- 1845.
matical knowledge, or physical. Strongly objecting, as I do,
to that system in many points, I should admit the Cambridge
Transactions as a decisive fact against me if there were more of
it, so that the contents could be cited as a proof of the general
consequences of the system.

You should not forget the Cambridge ' Mathematical Journal.'
It is done by the younger men. Four octavo vols. are published.
It is full of very original communications. It is, as is natural
in the doings of young mathematicians, very full of symbols.
The late Dr. F. Gregory, whom you must notice most honour-
ably— I send you a mem. of him, which please to return — gave
his extensions of the Calculus of Operations what used to be
the separation of the symbols of operation and (quantity) in it.
He was the first editor. He was the most rising man among
the juniors.

Yours very truly,

A. DE MORGAN.

To the Master of Trinity.

7 Camden Street, June 9, 1845.

MY DEAR SIR, — I am much obliged to you for the misprint
and the supposed misprint.1

* Nineteenth century ' is a bad misprint ; and I ought to have
detected it by the absence of the words ' march of intellect ' in
the immediate neighbourhood, for how can the first phrase come
in without the second ?

As to the second, I may say with Fouchy, ' C'est pire qu'une
crime, c'est une faute.' For it was Rheticus who published it,
the work being Copernicus's. But I have phrased it as if
Rheticus wrote a work of his own with the title cited, whereas I
meant to say that he had published one of Copernicus's, who
was like Newton, and wanted a kind of half -godfather, half-mid-
wife, for all he published.

There is another misprint which vexed me more, because context
will not help. It is the old accusative decenniom for decennmm
in the title of the canon. This was the printer's doing, after
revise returned, I fully believe, for I know that I read the title
most carefully.

1 I have not found these misprints. I suppose them to be in one
of his Cambridge tracts. — ED.

152 MEMOIR OF AUGUSTUS DE MORGAN.

1845. I have not anything to retaliate upon the Hist. Math. Sc.

at present, but if you are preparing a new edition I will look at

it in the vacation quoad Mathematics and Mathematical Physics.

You duly acknowledged the receipt of my corrections about

Milbourne and Horrocks. I remain, dear sir,

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, July 21, 1845.

MY DEAR SIR JOHN, — I hope you have found rest agreeable
after your Cambridge labours.

I have had a book by me for years called ' An Original Theory
or New Hypothesis of the Universe,' by Thomas Wright of
Durham, London, 1750, 4to, 30 mezzotinto engravings. I had
always supposed it to be Ocular and Elizabethan,1 if you know
what that means, and so put it among my curiosities of that
kind. But overhauling my limbo to write an article about
quiddities I began to examine this book, and I find it is at great
length the true theory of the milky way as a resolvable nebula,
with distribution of the universe into patches of starlight.

It was a book published by subscription, and therefore not
much repandu. It was seeing Dr. Smith's (Harmonic Smith's)
name among the subscribers which first made me suspect it was
not a heaven-born genius who wrote it.

Yours very truly,

A. DE MORGAN.

To Captain Smyth.

7 Camden Street, Nov. 3, 1845.

MY DEAR CAPTAIN SMYTH, — I find there is a circumstance
about ' Poliphilus ' which Brunet does not mention. The
author's name is Francis Colonna; if the thirty-eight initial
letters of the thirty-eight chapters be written down, they make
Folium f rater Franciscus Columno, peramavit.

Yours truly,

A. DE MORGAN.

1 Those accustomed to the writer's expressions will see in this a
paraphrase of the slang, * My eye and Betty Martin.'

CORRESPONDENCE, 1836-46. 153

1845.
To Sir John Herschel.

7 Camden Street, Nov. 29, 1845.

MY DEAR SIR JOHN, — First as to things in general, that you
may have a piece to tear off about life insurance, if you like, and
send to the managers. I have undertaken the Annual Report
again. Have you any subjects to suggest ? Have you anything
to say about your own printing ? Have you actually put metal
to paper in anything more than a steel pen ? Do you know
anything more than mankind in general about Count Cassini,
who is gone, leaving you the sole hereditary Astronomer ?
Will the fourth Herschel start as he did, and go and be a
botanist ? Ask H' what he thinks H" will do.

I hope you are using proper means for your cold, and getting
rid of it accordingly ; w.heu it comes to loss of sleep and appetite
it must be dealt with sec. art. It is not true that a man of forty
is either a fool or a physician ; he may be both, or neither. But
according to that rule, I am '9854 of a physician l myself, and in
that capacity I beg you to take care of yourself. . . .

If you want a laugh read Sheepshanks's pamphlet, if you
have not read it already. A man who acknowledges his own
name to be an ugly one must be a hero of moral courage. If he
had lived in the Middle Ages he would have been vir clarissimus
eruditissimusque Ricardus de Ovium Cruribus, which would not
have sounded common at all. There was one Middle Age name
which I could not make out. I searched and searched, you can't
think how much. It was Jacobus Humus, Scotus Theagrius,
James Hume, a Scot — of what ? I tried every part of Scotland,
and endeavoured to Latinise it into Theagrius. At last I hap-
pened to mention it to a Scotchman (they all know all their
lairdships), and he said, 'Oh, of course, Hume of Godscroft, petty
estate.

1 I omit the correction for folly.

To Captain Smyth.

1846.
Nov. 26, 1846. Latter

Capt.

MY DEAR CAPTAIN SMYTH, — Sheepshanks has written to me on Smyth,
the same subject, and I have given him at length reasons why I will
not be President. I will vote for and tolerate no President but
a practical astronomer. Besides which, the chair would bring

154 MEMOIR OF AUGUSTUS DE MORGAN.

1846. me more in contact with certain parts of our glorious constitution
than I conld any way stand.

But I have offered either to do the work of a Vice-President,
if Herschel or some other good man will be President, or to
take every duty of Secretaryship except the editing of the
Monthly Notices and Memoirs. I sent Sheepshanks the following
programme, which I amend for your use : —

President : Herschel, absent. Quiet enough when present.

Acting Vice-President : Capt. W. H. Smyth — too fond of
cigars and black-puddings, but otherwise a capital quarter-
master.

Secretaries : Rutherford, for the Memoirs. A. De Morgan —
well enough in his way, but cranky — for all miscellaneous work,
from wax candles to Council minutes.

Foreign Secretary: Rev. R. Sheepshanks (composition
not wax by any means. A President overdue, but won't dub
up — ought to go through the court) for the Monthly Notices.

If Galloway would take Rutherford's place, who wants to get
off, we should be in capital force. And we look forward to Hind
being a famous man.

II n'y a que moi qui a toujours raison.

Think of the above, and see if it won't work. I will work,
but in my proper place. The President must be a man of brass
— a micrometer-monger, a telescope- twiddler, a star- stringer, a
planet-poker, and a nebula-nabber. If we give bail that we
won't let him do anything if he would, we shall be able to have
him,1 I hope. We must all give what is most wanted, and his
name is even more wanted than his services. We can do with-
out his services, not without loss, but without difficulty. I see
we shall not, without great difficulty, dispense with his name.
Kind regards all round.

Yours truly,

A. DE MORGAN.

To Sir John Herschel.

MY DEAR SIR JOHN, — We have just been making our arrange-
ments for the Society for the ensuing year, and one thing is
that you are not to be asked to do anything, or wished to do
anything, or wanted to do anything. But we want your namet

1 Herschel (understood).— S.E.De M.

CORRESPONDENCE, 1836-46. 155

and when you hear the precise state of things I hope you will 1846.
see that you can give it, and can see that you will give it.

Baily, as you know, was the fly-wheel of the Society ; there
was an inexhaustible fund of momentum in him, which he im-
parted as wanted, and to the amount wanted. Since his death
there is nobody of whom we can say that he is always good for
D — V ; D being the duties of any office, and Y the amount of
them which the holder happens to discharge. And we find it
necessary to put our shoulders to the wheel, and to bestir
ourselves.

Certain persons wanted to make me President, which I posi-
tively refused, holding that to appoint a person who has never
promoted astronomy otherwise than as promoting mathematics
is indirectly doing so (there wants a word more strong than
indirectly, and less strong than directly — say ^ directly and in-
directly)— would be ToVr (direct and indirect) confession of
weakness. But I have proposed a plan of administration which
I am sure of as to the working part, and which I hope you will
sanction as to the proemium. Seriously, it is a dignus vindice
nodus.

President: Sir J. Herschel. No duties. If he likes to
attend anniversary meetings all the better, but nobody expects
even this, except quite convenient. Work all parcelled out.
None left for him. Name the thing wanted.

Acting1 Vice- President : Captain Smyth. Will do it with
pleasure ; ascertained.

Secretaries : Galloway takes the printing of the Memoirs.
Consents if the plan holds. Has been Sec. some years.

De Morgan takes the routine management of the Society, all
but Memoirs and Monthly Notices. Has had eight years of
routine, Memoirs, and Notices, all three, and would not meddle
with it again except for the conviction that the Society would
go to pieces forthwith if something energetic were not done at
once. On condition that the President is a man of practical
astronomy.

Foreign Secretary : Sheepshanks. Takes the Monthly Notices.
Has had the Secship. for the last year.

Assistant Secretary: Williams. Seems a working man, but
new.

1 Includes making up a party for the cigar divan after every
dinner.

156 MEMOIR OF AUGUSTUS DE MORGAN.

184C On ^8 case I hope yon will consent to your part of our

Cabinet. The rest of the Council we fill up in the best way we
can — no great difficulty.

If you feel able to consent, I am tolerably sure that we are
safe for two years, during which time we must keep our eye
upon the future.

Trusting to the nascitur nonfit principle will give the Society
a fit of moritur. I remain,

Yours very truly,

A. DE MORGAN.
7 Camden Street, Nov. 29, 1846.

157

SECTION VII.
FROM 1846 TO 1855.

' IN the year 1846,' Mr. De Morgan wrote, { I had begun to 1846.
collect various matters which had suggested themselves at thtfsyi-
different times, connected with the theory of the Syllogism logism-
in Logic.' In the year 1847 the Formal Logic was published.

The memoirs On the Syllogism, Nos. I., II., III., IV.,
and V., are Mathematical workings of the principles
developed in the Formal Logic ; and the tracts On the
Structure of the Syllogism, and On the Application of the
Theory of Probabilities to Questions of Argument and
Authority, immediately preceded it.

The lirst chapter of Formal Logic consists, with a few
alterations, of the tract entitled First Notions of Logic
preparatory to the Study of Geometry ; London, 1839. The
work as a whole, and in its higher parts, is original, but
the author has been careful to distinguish between what
he claimed as exclusively his own and the work of others
by printing in italics, in the Table of Contents, the head-
ings of those articles which refer to his peculiar system.
A reference to this table will show how large and essential,
a portion was claimed as entirely new. After working
these points out in his own mind, the author found that
he was able to explain by their means passages of Aristotle
till then obscure to himself as well as to others. The
two principal features of his own system were the intro-
duction of contraries or contradictories, and the idea of
definite quantity, into the syllogism. Where all, none, or
some had been the utmost quantification employed before,

158 MEMOIR OF AUGUSTUS DE MORGAN.

1847. the ideas of more or less with their contradictories formed
Formal an essential part of the Formal Logic.

The tract On the Syllogism, &c., read at Cambridge in
November 1846, excited great interest in the minds of
those Logicians who were following out the application of
Mathematics to Logic. Dr. Whewell had wished the
writer to read it himself, and kindly begged him to visit
him at Trinity Lodge for the time. This he was not able
to do. I wish it had been practicable for him to mix
more freely and frequently with the friends who shared
his interests ; but on looking back to the great variety of
subjects he treated, and the work he was engaged in at
the time, it is evident that this would have been impos-
sible. The memoir On the Dispute between Keill and
Leibnitz was printed in this year. I hoped, on first con-
sidering in what way to mention the Logical works, to be
able to supply some of my own deficiencies by inserting
the letters which were addressed to him both on the re-
ception of the tract and the publication of the volume.
But they are too numerous to form a part of this work.
I am, however, very thankful to be able to insert here
some excellent strictures on that which I dare not myself
have attempted to describe — the relation of Psychology
and Mathematics in my husband's mind. These remarks
were kindly given to me by Mr. De Morgan's friend and
former pupil, Mr. Cecil Monro:—

Such attention to Logical method is not to be confounded
with mere accuracy and explicitness of statement and demon-
stration. These are vital qualities, indeed, of Mathematical
exposition, qualities which every one sees to be characteristic of
Mr. De Morgan's work ; which are, in fact, characteristic of it
in an extraordinary degree ; but it is in a more important sense
. than this that he was at least as great in Logic as in Mathematics.
Even in his most strictly Mathematical writings the examination
of mental processes is visibly an end in itself, as distinguished
from the exhibition of mental products. In its psychological
aspect his end is pursued through historical and even bibliogra-
phical inquiries, which, independently of their value as informa-

NEW QUANTIFICATION OF PREDICATE. 159

tion, are perhaps still more interesting as episodes in that pursuit. 1847.
Upon its Logical side the end may be said to have been attained, Letter of
and with a completeness upon which I believe high authorities
would not as yet be forward to pronounce, in a series of works
of which the well-known Formal Logic is but a part. If, as is
certainly true, his other works could only have been written by
a Logician, these last could only have been written by a Mathe-
matician. Everybody knows that Mathematics are an admirable
model of exactitude ; but not everybody knows that they also
furnish an admirable type of generalisation. Indeed, generality
is often confounded with vagueness, and therefore treated as
incompatible with exactitude.

The fact is known that, having very thoroughly worked at
the generalisations of Mathematics in theory and practice, Mr.
De Morgan was enabled to establish with perfect precision the
most highly generalised conception of Logic, perhaps, which it
is possible to entertain. It is no new doctrine that Logic deals
with the necessary laws of action of thought, and that Mathema-
tics apply these laws to necessary matter of thought ; but by
showing that these laws can and must be applied with equal
precision and equal necessity to all kinds of relations, and not
only to those which the Aristotelian theory takes account of, he
so enlarged the scope and intensified the power of Logic as an
instrument, that we may hope for coming generations, as be
must have hoped,1 another instalment of the kind of benefit
which history shows we ourselves owe to the Aristotelian theory,
not merely in the analysis of one mental operation, but in the
every- day practice of them. Mathematics are, meanwhile, and
perhaps will always remain, the completest and most accurate
example of the generalised Logic. At any rate, in the mind of
the author, Logic and Mathematics as ' the two great branches of
exact science, the study of the necessary laws of thought, the
study of the necessary matter of thought,2 were always viewed
in connection and antithesis.

C. J. MONRO.

Mr. De Morgan had written to Dr. Logan in Sep- Corrc-
tember 1846 that he was ' making a vigorous onslaught
on the Aristotelian syllogism, which,' he says, 'I find has

1 Syllabus, § 96, note.

2 On the Syllogism, No. v. &c. (Camb. Ph. S. vol. x., Part 11,
1863), the last page.

160 MEMOIR OF AUGUSTUS DE MORGAN.

1847. wanted the interference of a Mathematician very much.'

TT -I*

contro- He asked Dr. Logan to tell him of any place in which the
versy. history of the syllogism is given — anything about Barbara,
Celarent, &c., their birth, parentage, and education. He
also gave him some of the results of his recent inquiry
into the application of the Theory of Probabilities to ques-
tions of argument and authority. In reply to this, Dr.
Logan sent him a short note on the history of Logic.
On September 30 he wrote to Sir William Hamilton, the
Professor of Logic in the University of Edinburgh,
' inquiring about the history of the Aristotelian theory
of the syllogism.' 1 This was answered in a friendly
tone, Sir William Hamilton sending Mr. De Morgan
' a copy of the requisites for a prize essay,' given out to
the students at the close of last session, and offering
further information if required. But in all the state-
ments of what had been taught by the Edinburgh Pro-
fessor my husband did not find any reason for believing
that his own discoveries on the syllogism had been antici-
pated; and he was able to bring forward distinct proof
that, even on the quantification of the predicate, which
had been taught in a form less complete than his own
by Sir William Hamilton, he had himself never had the
opportunity of gaining a suggestion from the Edinburgh
lectures. However, after the Cambridge tract had been
in Dr. WhewelPs hands, and in answer to a letter on the
subject from Mr. De Morgan, Sir William says that he
(Mr. De Morgan) is wholly indebted to himself for infor-
mation on the subject; and in his own words, 'should
you, though recognising always my prior claim, give forth
that doctrine as a speculation of your own, you will be
guilty — pardon the plain speaking — both of an injurious
breach of confidence towards me and of false dealing
towards the public.'

To this the following reply was sent:—

1 I have always used, as far as possible, Sir William's own words
from his subsequent letters on the transaction.— S. E. De M.

FORMAL LOGIC. 161

DEAR SIR WILLIAM, — Your letter of the 13th inst., which I 1847.
have read with astonishment, shows me the propriety of abstain- Hamilton
ing from correspondence upon the subject in question. When
my paper appears, which 1 expect it will do in a few days, I
shall have the honour of requesting your acceptance of some
copies, that you may be able to put them into the hands of those
with whom you may think proper ta advise.

I will not further allude to the hasty manner in which you
have expressed your suspicions of an odious charge, except to
state that it does not diminish the sincere respect with which I
subscribe myself

Your most obedient servant,

A. DE MORGAN.

These few lines show the temper in which the contro-
versy began. I purposely refrain from attempting to
record in detail the arguments used on both sides. The
statement appended to the Formal Logic will give to
inquirers a full insight into my husband's reasons for
believing himself the originator of those Logical pro-
cesses which he claimed as his own. So far as the dis-
cussion assumed a personal character it is his biographer's
duty to record it; but the questions raised were of too
technical a nature to be dealt with in a work like the
present, even if I were competent to discuss them. Besides
the statement in the Formal Logic, Mr. De Morgan made
some mention of the controversy in iheBudget of Paradoxes.

Sir William returned, unread, the copy of the Formal
Logic which Mr, De Morgan presented to him ; but in
the year 1852 controversial warmth must have abated,
for books and courteous letters were then exchanged
between the Logicians.

I cannot deny that he rather enjoyed such encounters,
but no one ever engaged in them with less feeling of
personal animosity. It was like a game of chess — a pas-
sage of arms. But he did full justice to Sir William's
splendid metaphysical powers, and says, in reference to
the controversy, * of which I suppose that the celebrity of
my opponent, and the appearance of parts of it in a

M

162 MEMOIR OF AUGUSTUS DE MORGAN.

1847. journal so widely circulated as the Athenceum, has caused
Hamilton. many students of Logic to hear or read something.' He
himself was a mathematical Logician. Sir William's
philosophy might be called poetical. I have heard his
pupils speak of him as ( inspired ; ' and the clear mental
sight which enabled the one to develop the doctrine of
limits in the Differential Calculus was more at home in the
quantification of parts of the syllogism than the genius
which enabled the other to bring out his admirable
analysis of cause and effect. After Sir William's death
Mr. De Morgan wrote an obituary notice of him in the
Athenceum, in which his intellectual powers and great
research were set forth so luminously as to excite wonder
in persons not acquainted with the writer's character.1

1 Readers of Mr. Herbert Spencer's volume on Sociology may
have been puzzled by a passage (p. 412) in which the subject of this
memoir appears to be accused of a misquotation, in his own interest,
of some matter relating to priority of Logical discovery. It runs as
follows : —

One further point only will I name. Professor Baynes says : ' Professor De
Morgan's emphatic rejection of Mr. Bentham's claim after examining the relevant
chapters of his " outline " is in striking contrast to Mr. Herbert Spencer's easy-
going acceptance of it.' Now, though to many readers this will seem a telling
comparison, yet to those who know that Professor De Morgan was one of the
parties to the controversy, and had his own claims to establish, the comparison will
not seem so telling. To me, however, and to many who have remarked the
perversity of Professor De Morgan's judgments, his verdict on the matter, even
were he perfectly unconcerned, will go for but little. Whoever will take the
trouble to refer to the Athenaeum, November 5, 1864, p. 600, and after reading a
sentence which he there quotes, will look at either the title of the chapter it is
taken from or the sentence which succeeds it, will be amazed that such recklessness
of misrepresentation should be shown by a conscientious man, and will be there-
after but little inclined to abide by Professor De Morgan's authority in matters
like that here in question. v

The reader who * takes the trouble ' to search out the passage in
this Athenxum a quarter of a century old will not find a * matter like
that here in question.' But he will be enabled to form a juster estimate
of the above passage when he learns that the victim of Professor De
Morgan's inaccuracy or unconscientiousness was neither Bentham nor
Hamilton, but Mr. Herbert Spencer himself.

The quotation itself occurs in a brief notice of Mr. Spencer's
Principles of Biology, which I here reprint in full : —

This is one of two volumes, and the two but part of a larger work : we can

FORMAL LOGIC. 163

I have mentioned my husband's early interest in 1847.
Berkeley's philosophy, and Mr. J. S. Mill's opinion of the
manner in which some of Berkeley's arguments were
affected by Mr. De Morgan's enunciation of the principle

therefore but announce it. Biology means the Science of Life. As to what con-
stitutes life, we expected to have to remain in the dark. Schelling says it is ' the
tendency to individuation.' Richarand says, 'Life is a collection of phenomena
•which succeed each other during a limited time in an organised body : ' a very good
definition. But is champagne alive as long as it fizzes, and a top as long as it
spins ? De Blainville says, ' Life is the twofold internal movement of composition
and decomposition, at once general and continuous.' Mr. Spencer formerly defined
life as ' the co-ordination of actions.' Mr. Lewes says, ' Life is a series of definite
and successive changes, both of structure and composition, which take place
within an individual without destroying its identity.' Mr. Spencer ends with
' The definite combination of heterogeneous changes, both simultaneous and
successive.' We have heard other definitions. Time was when life, bon ton, and
the thing, were synonymous terms ; and, according to the City lady, it consisted

in-
Drinking tea. on summer afternoons,
At Bagnigge Wells, with china and gilt spoons.

All the definitions we have given apply to the life of organised material beings.
Thus restricted, our definition is, that life is that state of a material being in which
structure which performs functions is maintained by matter which the living being
has power to draw from without, and which, when a man and an Englishman, he
calls nutriment.

In a later edition of the Sociology Mr. Spencer has, in answer to
remonstrance, added a note of self -justification. This note is to the
purpose so far as that it will enable readers to discern the real
gravamen of Mr. De Morgan's offence. Whether Mr. Spencer had
just cause for annoyance in his reviewer's evident want of respect
for the science of Biology (that is, so far as it undertakes to define the
nature of life) may be an open question. But with respect to the
misquotation, a reading of Mr. Spencer's chapter containing his defini-
tion will show that it was the result of a simple oversight. It appears
that the quotation should have stood ' the definite combination of
heterogeneous changes, both simultaneous and successive, in corre-
spondence with external co-existences and sequences.' I do not pre-
sume to enter here into any discussion of the definition, and therefore
only cite it that those who understand it (which I do not profess
to do distinctly) may know the nature and extent of the injustice
done to it in the review. I abstain from expressing an opinion as to
the propriety of Mr. Spencer's mode of presenting his case, preferring
to leave the decision to my readers.

It is proper to add that Mr. Spencer has in private correspondence
disclaimed all intention of imputing unconscientiousness. All that
can be said of this is, that better ways of not imputing unconscien-
tiousness might be suggested.

M 2

164 MEMOIR OF AUGUSTUS DE MORGAN.

1847. of limits in the Differential Calculus. But his views of
Berkeley's the psychology of Berkeley as compared with his own are

philosophy. v J 5r . j i.

more generally interesting.

In the chapter On Objects, Ideas, and Names in the
Formal Logic, the writer says : —

That our minds, souls, or thinking powers, use what name
we may, exist, is the thing of which of all others we are most
certain, each for himself. Next to this nothing can be more
certain to us — each for himself — than that other things also exist ;
other minds, our own bodies, the whole world of matter. But
between the character of these two certainties there is a vast
difference. Any one who should deny his own existence would,
if serious, be held beneath argument ; he does not know the
meaning of his words, or he is false or mad. But if the same
man should deny that anything exists except himself — that is, if
he should affirm the whole creation to be a dream of his own
mind — he would be absolutely unanswerable. If I (who know
he is wrong, for I am certain of my own existence) argue with
him, and reduce him to silence, it is no more than might happen
in his dream. . . .

A celebrated metaphysician, Berkeley, maintained that with
regard to matter the above is the state of the case ; that our
impressions of matter are only impressions communicated by the
Creator without any intervening cause of communication.

Our most convincing communicable proof of the existence of
other things is, not the appearance of objects, but the necessity
of admitting that there are other minds beside our own. The
external inanimate objects might be creations of our own
thought, or thinking and perceptive functions. They are so
sometimes in the case of insanity, in which the mind has fre-
quently the appearance of making the whole or part of its own
external world. But when we see other beings performing
similar functions to those which we ourselves perform, we come so
irresistibly to the conclusion that there must be other sentients
like ourselves, that we should rather compare a person who
doubted it to one who denied his own existence, than to one
who really denied the external existence of the material world.

In his interleaved copy of Formal Logic is a pencil
note alongside of the foregoing : —

To read Berkeley so as to give him a fair chance, some one

GEORGE BOOLE. 165

else should turn the page over ; for, unphilosophical as it may 1847.
be, the touch of the paper periodically intervening is a snake in Berkeley's
the grass — an unphilosophical snake. It is hard to make philo- p L
sophers of the fingers.

No doubt it would favour Berkeley's scheme if no
appeal to the external, through the senses, were possible
to his reader. But surely this would be giving him more
than a fair chance. Another interleaved note : —

Personal identity is what every one has a clear conception of
until he reads physiology and metaphysics. In that process he
learns that the knife sometimes (gradually) gets a new handle,
and sometimes a new blade, and all his notions of identity
vanish, with nothing but memory left to puzzle him. ' Mais
quand je rne tate, et quand je me rappelle, il me semble que je
suis moi.'

If physiology teaches that we are automatic, it ought
to find a new name for the nightingale and chess-player,
which can be wound up when they have run down.

Dr. George Boole,1 author of The Laws of Thought, had
introduced himself in the year 1842 to Mr. De Morgan by
a letter on the Differential and Integral Calculus, then
recently published. His character and pursuits were in
many points like those of the author, who found great
pleasure in his correspondence and friendship. He was a
Mathematician as well as a profound and original student
of Logic and Metaphysics. In 1839, the same year in
which the First Notions of Logic appeared, he had sent his
Mathematical paper, Researches into the Theory of Ana-
lytical Transfer, to the Cambridge Philosophical Journal,
and in 1844 received the gold medal of the Royal Society
for a paper On a General Method in Analysis. In the
course of these speculations he was led to consider the
possibility of constructing a calculus of deductive reason-
ing; and he found that logical symbols conform to the
same fundamental laws which govern algebraical symbols,
while they are subject also to a special law. * Mental

1 Professor of Mathematics in Cork College.

16G MEMOIR OF AUGUSTUS DE MORGAN.

1 847. science,' says his biographer, ' then became his study,
Dr. Boole. Mathematics his recreation ; yet it is a remarkable fact
that his more important and valuable Mathematical works
were produced after he had commenced his Psychological
investigations.' l In 1847, his attention having been
drawn to the subject by the publication of Mr. De
Morgan's Formal Logic, he published the Mathematical
Analysis of Logic, and in the following year communicated
to the Cambridge and Dublin MathematicalJournal a paper
on the Calculus of Logic. His great work, An Investigation
into the Laws of Thought, on which are founded the Mathe-
matical Theories of Logic and Probabilities, was a develop-
ment of the principle laid down in the Calculus, its design
being ' to investigate the fundamental laws of those opera-
tions of the mind by which reasoning is performed ; to
give expression to them in the symbolical language of a
calculus, and upon this foundation to establish the Science
of Logic and construct its method ; to make that method
itself the basis of a general method for the application of
the Mathematical doctrine of probabilities ; and, finally,
to collect from the various elements of truth, brought to
view in the course of these inquiries, some probable inti-
mations concerning the nature and constitution of the
human mind.'

I have given Dr. Boole's own statement of the design
of his work at length because it conveys in few words, not
only some idea of the aim of his investigations, but of the
relations between the three sciences of Psychology, Mathe-
matics, and Logic. An estimate of his mental work and
its value to science was given in a few words, after his
death in 1864, by my husband : —

' His first paper in the Cambridge Mathematical
Journal contains remarkable speculations which can here
be described only in general terms, as extensions of the
power of algebraic language. These papers helped to

1 Taken substantially from a notice of Dr. Boole in the Obituary
Notices of the Royal Society, by the Rev. R. Harley.

GEORGE BOOLE. 167

give that remarkable impulse which algebraic language 1847.
has received in the interval from that time to the present.
. . . That peculiar turn for increasing the power of
mathematical language, which is the most characteristic
point of Dr. Boole's genius, was shown in a remarkable
way in his writings on Logic. Of late years, the two great
branches of exact science, Mathematics and Logic, which
had long been completely separated, have found a few
common cultivators. Of these Dr. Boole has produced
far the most striking results. In alluding to them we
do not say that the time is come in which they can even
be generally appreciated, far less extensively used. But
if the public acknowledgment of progress and of genius
be delayed until the whole world feels the results, the last
century, which had the lunar method for finding longi-
tude, ought to have sought for the descendants of Apollo-
nius to reward them for his work on the Conic Sections.'

* Dr. Boole's system of logic shows that the symbols
of algebra, used only to represent numbers, magnitudes,
and their relations, are competent to express all the
transformations and deductions which take place in
inference, be the subject what it may. What he has
added may be likened to a new dictionary, by consultation
of which sentences written in the old grammar and syn-
tax of a system take each a new and true meaning. No
one is ignorant that the common assertion, " Nothing is
both new and true," is a perfect equivalent of " Everything
is either old or false, or both." Dr. Boole showed that
a schoolboy who works a certain transformation, such as
occurs in many a simple equation, has the form, though
applied to very different matter, of this logical passage
from one of two equivalents to the other. Taken alone,
this is a pretty conundrum, if any one so please. But when
looked at in the system of which it is a part, and when
further considered as the produce of a mind which
applied the same power of thought with rare success over
the whole of the higher Mathematics, those who so look,

168 MEMOIR OF AUGUSTUS DE MORGAN.

1847. and so consider, are justified in presenting it as a type of

Booiege genius, and as a specimen which may give those who are

not mathematicians a faint notion of an originality of

speculation which, applied to the progress of science, has

attained most useful results, and made a lasting name.' l

My husband's regard for Dr. Boole was founded
not only on admiration of his originality and power,
but on sympathy with the moral and religious basis of
his psychology ; for Dr. Boole, like Mr. De Morgan,
believed that every system which rejected the existence of
God as a constantly sustaining cause of all mental as well
as physical phenomena, was like a consideration of the
nature and growth of a tree without reference to the root.
They did not often meet, for Dr. Boole's life was passed
in Ireland after his appointment to the Mathematical
chair in Cork ; but when his visits did occur, they were a
real enjoyment to both — I believe I may say to all, for I
shared in the pleasure of his conversation, ranging as it
did over a wide field of thought, and touching poetry
and metaphysical as well as mathematical science. My
husband was, I believe, instrumental in some degree in
obtaining the appointment at Cork, where Sir Robert
Kane, who had married our friend Mr. Baily's niece, was
Principal.
Sir My husband's friendship with Sir Frederick Pollock,

Frederick

Pollock. then Lord Chief Baron, had begun some time before this.
Sir Frederick, who had been Senior Wrangler of his year,
kept up his mathematics in the midst of his legal avoca-
tions. He was a good Mathematician, among other
matters interested in the properties of triangles and in
magic squares, and, I believe, made some original dis-
coveries. He often communicated these to Mr. De Morgan,
who occasionally gave him a lift when any stumbling-
block came in his way — at least, so he told me. He was
a most agreeable companion, full of interest in all sub-
jects of thought, and of all men I ever knew he seemed to
1 From a MS. unpublished paper, drawn up by Mr. De Morgan.

COMPETITIVE EXAMINATION. 169

me to have highest value for talent of all kinds ; and of 1847.
all well-read persons no one was so ready with an illus-
tration or a quotation, either in prose or poetry, suited to
the occasion.

The Introductory Lecture given by the Mathematical 1848.
Professor on the opening of all the classes in University tory
College at the session of 1848, was on a question in ecL
education on which he had thought much, and on which
his opinion had strengthened as his experience in teaching
increased. He considered competition — the striving one
against another for the highest place among boys or young
men — to be among the crudities of an imperfect system,
and to be as ineffectual in gaining the end either of making
the best scholar or showing the best scholar, as its moral
tendency is bad.

It is quite true, as he himself has said to me in talking
of this subject, that the boys are generous and sharp enough
to see who deserves the prize, and very little ill-will or
jealousy ever comes into the competition; but they do
not know, any more than their teachers, how much easier
the work is for some than for others ; and as the teacher
cannot take this into account, injustice in one way can
hardly be avoided. Hence his objection to marks in look-
ing over examination papers. He said he could judge of
the merits of the competitor from the whole work, but he
could not reckon it up by marks, and he always refused
to examine in this way. But he also felt and often ex-
pressed his opinion of the terrible mischief to health done
by urging a young man to go a little beyond what he
could accomplish with interest and success if no undue
pressure were put upon him, and by the 'cramming' to
answer questions set at the pleasure of the examiners, in
place of the natural and well-directed effort to learn the
subject which an enlightened teacher can always evoke
in an intelligent pupil. He himself, a most successful
teacher, to whose instructions his pupils always looked
back with the consciousness that to him they owed the

170 MEMOIR OF AUGUSTUS DE MORGAN.

1848. habits of sound thought and correct reasoning which were
Education, among their best mental possessions, believed and said
that it is owing to the imperfection of the teacher, not to
the want of effort in the pupil, that the boy or young man
fails to make progress. There are doubtless cases in
which the capabilities are naturally wanting, and when a
strain to do what cannot be done is useless ; but this only
shows the necessity of discernment. Some of his friends,
who greatly liked the lecture of this year, saying that
• all his arguments were unanswerable, still hesitated to
give in to all his conclusions. His old friend and fellow-
collegian, the Eev. Arthur Neate, among others, asked, if
the stimulus of competition were taken away, what would
be put in its place. I do not know what he replied to
Mr. Neate, but I know what he said to me at the time.
' With such young men as those who struggle to be
highest, and who suffer in the struggle, no stimulus
is needed beyond their own pleasure in learning ; and if a
teacher cannot make them feel this, he does not deserve
the name of teacher.'

Rev. Baden Among those who fully concurred with him was our
competitive friend the Eev. Baden Powell. His thoughts on the
subject were suggestive. He wrote : — ' Accept my thanks
for a copy of your admirable Introductory Lecture. I
wish it could be more widely circulated among our
candidates here and at Cambridge. Perhaps there
was something in this respect better in the system of
our ancestors' Disputations, in lieu of examinations.
I have often wished there were something like making
a man read a dissertation on a subject of his own
choosing, and then cross-examining him on his own argu-
ment. Many would be plucked from not understanding
their own meaning.' And Sir John Herschel wrote, ' I was
greatly delighted with your protest against the cramming
system in your opening lecture.' So also Dr. Whewell :
* I see you have been kicking against examination read-
ing. So far good. But is your College going to do

COMPETITIVE EXAMINATION. 171

anything which will really diminish it ? I should like to 1848.
hear how any attempt of this kind prospers. I think the **Y- Dr-
object an excellent one, and have some notions of my own
as to the way in which it may be forwarded.' Such
declarations of opinion from such men ought to have
weight with their successors.

Mr. De Morgan, while fully agreeing with Mr. Baden
Powell on the wisdom of letting the student show what
he can do by his original work, did not disapprove of
examinations, not competitive ones, to test the amount of
knowledge really gained. At that time his arguments
were unheeded. The torrent of competition carried all
before it, and not seldom swept down its victims to de-
struction. Wiser notions are coming into men's minds,
and the evil is acknowledged, though, from what I hear
of the state of things at Cambridge, better methods are
not yet found. Educators have to learn that the aim of
education is to develop power, not to cram knowledge;
and also, what is now never thought of, that mental and
moral faculties come into activity at different times in
different individuals, and that a talent which is inert or
unnoticed in a boy of twelve, may be a brilliant element
of the mind at twenty, if not forced up or crushed out by
mismanagement.

The Astronomical Society's difficulties in obtaining Astrono-
good and efficient chief officers were not over. It is so
long ago that I can betray no confidence by telling of
these embarrassments in Captain Smyth's language : —

SIR AND SEC., — I am but a temporary V.P., it is true, and
therefore have little authority to shove my oar into others' row-
locks, but the Stilus Reipublicce shakes me to the centre. . . .

The anniversary approaches, and so do our difficulties. The
last time I saw friend Galloway he swore like a Flanders soldier
that he would not serve another year ! This oath fills me with
consternation, and my eloquence having failed, will you exert
yours ?

Then, again, there's the Council ! Did you ever ? Pray

172 MEMOIR OF AUGUSTUS DE MORGAN.

1 848. think of these things, exert your energies, and preserve us. So
shall you deserve well of your contemporaries, of posterity, and
of yours very truly, — W. H. SMYTH.

The writer had filled the President's chair after Sir
John Herschel and since the last difficulty, but it was
again vacant, and Mr. De Morgan was very earnestly
begged to take it. But he refused, for, while working
harder than ever, if possible, to keep up the character
and usefulness of the Society, his old reasons were still in
force. He always feared the love of rank and money
finding its way among the honest, useful workers who
had hitherto composed it. He held up the example of
the Royal Society as one in some ways to be avoided, and
resisted every measure that would tend to bring in the
sort of influence which had fettered its scientific work
during the last century. His commentary on the Royal
Society's history in times past will be found in the Budget
of Paradoxes, as well as some allusion to the fact of
his never having sought for membership. Touching the
charge against Sir John Hill, that his animus towards
the Society was occasioned by his failure to obtain admis-
sion to its ranks, he says, £ Whether I could have been a
Fellow, I cannot know ; as the gentleman said when asked
whether he could play the violin, " I never tried." On
the last point, however, Admiral Smyth gave evidence :—

Know that I dined yesterday with the Philosophical Club,
where was an ominous growl about your not being in the Royal
Society, and, on the entreaties of several warm friends, I under-
took to state the same to you. My own regret you are fully
aware of. Pray, therefore, reconsider the case, for it is declared
to be no favour at all to you, but a signal one to the Society,
to allow your name to be hung up. Pray grant this, and your
Petitioner will ever pray, &c.

At this time a good many friends used to meet peri-
odically at our house, and my husband enjoyed the
opportunity they gave him of seeing them in an informal

VARIOUS FRIENDS. 173

way. Besides several of those I have named, many of the 1848.
Professors of University College and their families of
course visited us. At this time the Rev. Alexander Scott,
afterwards Principal of Owen's College, Manchester, filled
a chair in University College. Mr. Arthur Hugh Clough
was Principal of University Hall. M. Libri and his wife,
Dr. Westland Marston, Miss Mulock, now Mrs. George
Craik, Mrs. Follen, the abolitionist, and Mrs. Catherine
Crowe, of ghostly renown, were among our guests. As
my husband was connected with the Athenceum, his vic-
tims and co-reviewers were a lively element in these
mixed assemblies, and we found in the meeting of persons
of very opposite pursuits, that some who seemed the
farthest removed from each other would often rejoice to
meet, and were found in unexpected connection. Several
friends addicted to what are called mystical studies,
found their way to us, drawn partly by my own love of
trying to unveil mysteries, partly by the sounder know-
ledge which my husband, who did not quite despise
the obscure sides of early science and mediaeval philo-
sophy, could bring to the subject. Of these, I think
the Rev. Jas. Smith, author of 'The Divine Drama
of History,' was the most learned and the least appreci-
ated by the world at large ; for his estimate of Sweden-
borg as an authority on spiritual questions, and his
admiration for Joanna Southcote as a ' typical woman/
were thought to throw discredit on his good sense.
Swedenborg is not held utterly contemptible now — though,
as Mr. Smith said then, he is least understood by his own
followers.

A not infrequent visitor on these evenings was Mrs. The Ladies
Elizabeth Reid, a widow lady of property, whose father Bedf?rdm
had been an influential Nonconformist, and who had long S(iuare-
sought for coadjutors in her design of establishing a
model ladies' College. She had written to Lady Byron
and to me of it fifteen years before, but her plans were
not as practical as her intentions were good, and it was

174

MEMOIR OF AUGUSTUS DE MORGAN.

1849.

Ladies'
College in
Bedford
Square.

not until she found herself among a number of sound-
thinking liberal men that she gained help and advice to
carry her wishes into effect. Some of the Professors of
King's College — among them the Rev. F. D. Maurice and
the Rev. W. Mcolay — gave her the best advice and
encouragement, and when the plan was matured, their
experience drawn from the Queen's College in all techni-
calities respecting the arrangement of classes. Mrs.
Reid took the house in Bedford Square, paid the rent
and much of the expense during the first years, and
otherwise endowed the Institution. She was among our
friends, and we were able to interest many friends of
education in the undertaking. Prof. Scott kindly promised
his aid as Professor of English, Mr. Francis Newman took
the Professorship of Latin, and my husband gave lectures
or lessons on arithmetic and algebra for one year, to give
as good a start as possible to the new college, which
opened at the end of 1848. Of my own work in the
formation of the Ladies' College I will only say that it was
the means of ensuring his interest, and thus obtaining
for the place an advantage which it could not otherwise
have had.

For some years there had been a growing desire that
the education of girls should be brought out of the state
of absolute inanity in which it existed in ladies' schools.
A specimen of the instruction has been given at p. 123,
and from the Astronomy we may have an idea of the
other branches of science, and form a guess at the History
and Language. It was seen that something a little more
efficient was wanted — some system which, if not ap-
proaching in extent, should yet be equal in soundness to
the teaching given to boys and young men. To meet this
want a few enlightened clergymen and others had some
time before established the Queen's College in Harley
Street. The orthodox King's College had grown up
shortly after the establishment of the heterodox Uni-
versity College — as some persons thought, in rivalry and

FEMALE EDUCATION.

175

hostility to it — as wiser ones saw, another step in the 1849.
right direction under different conditions. The Queen's
College for ladies, which owed its origin and success to
some of the Professors of King's College, was based on
the same principles, but as being designed at first for
members of the Church of England, was objected to by
parents who did not wish their daughters either to join
the prayers and Bible teaching, or to feel excluded from
what their fellow-learners partook of. The growing num-
ber of this class showed that there was yet room for
another College, founded, like University College, on
principles of absolute neutrality as to doctrinal teaching.

These high-class day schools l have increased in num- Overwork.
ber from that time; but I am told that those of the
present day share the faults of their predecessors, for each
teacher or Professor sets what task he likes irrespective
of those imposed by his colleagues. The amount of out-
of-school work was formerly excessive, and young girls
suffered in proportion. I have known cases of illness for
life, insanity, and even death from this cause, and as the
finances of the school depended on the number of classes
entered by pupils, young girls were often recommended
to take ten, twelve, fourteen, or fifteen ; and their parents,
knowing no better, consented. I have heard entreaties
on the poor girls' part to have their lessons at home
shortened met by the answer, ' You have so many hours
here and so many at home, there is time for all.' Strength
for all was not thought of, and time to think over and
assimilate what had been learned still less. Many hard-
working girls became ill, many heedless ones quite in-
different, but, as a remedy for either evil, the idea of
fitting the kind and amount of work to the kind and
amount of power never entered the teachers' heads. It is
too ' advanced ' a notion, but when we have overtaken it
the ' schoolmaster abroad ' will be a beneficent genius,

1 Colleges, such as Newnham or Girton, are of course not included
in these remarks. I believe they are more wisely managed.

176 MEMOIR OF AUGUSTUS DE MORGAN.

1849. scattering blessings in his path, instead of, what he has
been made by over-driving, a rampant lion, seeking what
he may devour.1

Although not among our frequent visitors, Sir Rowland
Hill was an old acquaintance of my husband's. Before
the time of which I am writing he had brought his
great scheme of penny postage into operation, having
grappled with and overcome gigantic obstacles. Mr. De
Morgan had corresponded with him on this work, and in
1848 made many suggestions for the postage of books and
MSS. Sir R,. Hill, after stating the conditions of posting,
and the amount of writing allowed in the address, requests
him not to refer in writing to the source of his informa-
tion, saying, * You will perhaps think all this ridiculous,
but there are real as well as imaginary difficulties in doing
more — at present, at least.' My husband gave a good deal
of help anonymously to this great reform, and, I think,
suggested the book postage.

At this time he was actively interested in the
questions raised by the proposed compilation of a com-
plete catalogue of the British Museum Library. I
need not enter into the discussion which this subject
excited, further than to note that some expressions made
use of by Mr. T. K. Hervey, then editor of the Athenceum,
led to Mr. De Morgan's discontinuing his contributions to
that journal for some years.

Gusiieimo During the agitation of the catalogue question he
often visited the British Museum, and on one occasion
met Count, or Professor,2 Guglielmo Libri, who had come
to England in a state of utter despair, owing to the
charges of theft made against him by the French
Government. Mr. De Morgan was at once favourably

1 January, 1878. Only yesterday a friend told me that while
walking in the street, violent and frightful screams startled her, and
on inquiring at the house from whence they came, she was told that
a young lady was dangerously ill of brain fever, having just passed a
College examination.

* He preferred the latter title,

GUGLIELMO LIBRI. 177

impressed by M. Libri, but from his agony of mind and
imperfect knowledge of English, it was a difficult matter M. Libri
to get at particulars of his case. Gradually facts were French Go-
brought forward and documents produced. The one most verument-
patent fact, attested by M. Guizot, then Prime Minister,
that M. Libri had offered all his books and manuscripts to
the French nation, on condition that they should be kept
together and called by his name, was a sufficient pre-
sumption of his innocence to lead to the belief that
further proof would be forthcoming ; for no one would
believe that books, stolen from a public library, would be
openly placed there by the very man who had abstracted
them. M. Libri became our attached and valued friend,
always recognising a firm and able defender in my
husband, whose articles in the Athenceum and elsewhere
were the means of establishing a belief in his innocence in
England. Some reference to the political relations of
France and Italy will throw light upon the persecution
he, an Italian, experienced from the French Government;
but the political condition of France, on which he expressed
himself very openly, helped to determine the events of
his life.

He was born in 1800, of a noble Tuscan family, and
was made Professor of Mathematics in the University of
Pisa when twenty years old. Being looked upon as a
Liberal by the Government, he was forbidden to remain
in Italy, which he had left on a visit to Paris in 1830.
He returned to Paris, where he was naturalised, and in
1833 was made a member of the Institute, holding
among other appointments that of Inspector of the
"Royal Libraries and Mathematical Professor in the
Sorbonne. His History of the Mathematical Sciences in
Italy, in four volumes, is spoken of by Mr. De Morgan
as a great work. But he did not confine himself to
scientific work; he helped the cause of Louis Philippe
by his writings, opposed the Jesuits both in their
French and Italian schemes, and gained the enmity of

R

178 MEMOIR OF AUGUSTUS DE MORGAN.

1849. the opposite party, by whom he was denounced as a
Gugiielmo monarchist, and as an Austrian traitor to the cause

.Libri.

Italy. Whether he was right or wrong in his politics is
matter of opinion. He had expressed his own very freely,
and thus had become an object of suspicion to the Govern-
ment of the time. But there was another reason for his
unpopularity in France. ' In science he would not be a
Frenchman, but remained an Italian. One of his great
objects was to place Italian discovery, which the French
historians had not treated fairly, in its proper rank. This
brought him into perpetual collision with M. Arago at
the Institute, and personal enmity was the consequence.
Those who know French science, and how little it attends
to history and to the learning which aids history, will
guess what a nuisance must have been the presence of an
able scholar and a profound Mathematician, with every-
thing that the French ignore at his fingers' ends, carrying
the fire of reason and the sword of reference into their
most sacred haunts; and worse still, the small shot of
ridicule, against which few Frenchmen have any armour.
When they were establishing showers of toads by second-
hand citations from old authors, M. Libri went to the
originals and got them a shower of oxen upon the same
evidence ; maudit Italien. At the same time we must do
the French savans the justice to say that M. Libri is a
warm nationalist, and that we will by no means guarantee
his having been always in the right. Neither can the
insinuation about stealing books be traced to the Institute.
We suspect that political animosity generated this slander,
and a real belief in the minds of bad men that collectors
always steal, and that the charge was therefore sure to be
true.'

'Every one who becomes acquainted with M. Libri
soon learns that the restoration of Italian fame is always
in his thoughts, and, though learned in the history of
other sciences, his interest in collecting is that of a propa-
gandist, who would gladly, if he could, furnish every

GUGLIELMO LIBRI. 179

library with the means of verifying Italian history. ., . . 1849.
He specially collected Italian books, and the thefts 9ffer of his
charged are mostly of that kind of literature. He offered the French
his whole collection, books and manuscripts, as a present ment.m
to the French nation on condition that they should be
kept together and called by his name, which was refused.
The offer was made to M. Naudet, of the Royal Library.
When difficulties arose as to the stipulation, M. Libri
complained to M. Guizot, the most influential of the
Ministry in literature, always his firm friend, and a firm
believer in his innocence. M. Guizot certified this fact to
the editor of an English journal in 1849, and gave it in
evidence to a commission sent from Paris to examine
him, as we learn from his handwriting. This shows the
state of things in Paris with respect to M. Libri at the
time of his escape to England in the year 1848. It had
been rumoured that he, who was well known as having
bought rare books and as having sold a large collection,
had robbed the public libraries of a number of books to
the amount of several hundred thousand francs, and a
note was one day put into his hands at the Institute by
the editor of the National, threatening him with popular
vengeance, and advising him to disappear if he hoped to
escape. A report was drawn up by M. Boucly, the Pro-
cureur du Roi, founded upon anonymous accusations, and
soon after M. Libri's escape to England — a step recom-
mended at once by his friends in France — this report was
published in the Moniteur. To it he replied, so com-
pletely proving his innocence, that 110 more was heard of
the document. In a letter to M. Falloux he continued
his defence, which produced no effect. His books and
furniture were seized, and a commission was appointed to
examine them. This commission made its report in
1850, and in 1852 the Acte d* Accusation was passed.'

During the time he had been in England he had
gained some steady, energetic friends, many of whom
gave him sympathy and assistance. Scholars and biblio-

N 2

ISO MEMOIR OF AUGUSTUS DE MORGAN.

1849.

Gugiieimo graphers were convinced of his innocence, but no defence
of him in France was permitted, where he had lost all
property and position. But the facts of the case became
evident to all who chose to examine them. M. Guizot, Lord
Brougham, Mr. De Morgan, and other judicious friends
found from careful inquiry in Paris that the Acte d? Accu-
sation in this case implied summary conviction. They
recommended him not to return to Paris for trial, and
judgment went by default, though after some years the
accusation was withdrawn. Mr. De Morgan said of the ac-
cusation that it involved a new form of syllogism : ' Jack
lost a dog ; Tom sold a cat : therefore Tom stole Jack's
dog.' And it was discovered, after all, that in several
cases the editions sold by M. Libri were not those which
the library was reported to have lost. In several cases
the library had not lost the book at all. In several cases
the lost book had been found elsewhere, and in no one
case was it proved that a book once belonging to a public
library was found in M. Libri's possession without proof
of having been honestly come by.

M. Libri had every social quality to secure regard and
friendship. He was a fine classical scholar and an original
thinker, having the sparkling merry humour of his
countrymen, and, like an Italian, was simple and affec-
tionate, but hasty and irascible. He had been in youth
exceedingly handsome, and at this time, when of middle
age, was one of the noblest-looking men I ever saw. In
1850 he married Madame Melanie Colin, a generous,
self-devoted woman, who made great efforts to procure
justice for her husband. She went to Paris, consulted
with his friends, and appealed to his enemies, but the
anxiety and exertion were more than her strength could
bear, and it was thought that her subsequent illness and
death were caused by the strain upon her powers.
1850. The death of our friend Mr. Galloway, who had been

Galloway, living in Torrington Square, occurred in the following
year. It was preceded by some months' illness from spasms

DEATH OF THOMAS GALLOWAY. 181

of the heart, which he bore with calmness and patience.
Mr. De Morgan, who had a warm regard for him, spent what
time he could gain in the intervals of his lectures in his
friend's sick room, and his visits were looked for as afford-
ing some alleviation in a difficult nursing, not only as to
such difficulties as arose in Mr. Galloway's absence from
business, but, I believe, with the patient himself, who was
sometimes induced by his quiet persuasion to take a
remedy for which he felt disinclined. ' I can never,' Mrs.
Galloway writes, ( cease to remember with love and grati-
tude how tenderly your beloved husband watched his
downward progress, sitting day by day by his bedside,
and talking to me in a low tone in the hope that it might
induce sleep, and anxiously trying to get him to take
food, on the amount of which the doctors said his life
depended.'

Mr. Galloway had been more than once my husband's
colleague as secretary of the Royal Astronomical Society,
and had in many ways done service to Science. He would
in all probability have been Professor of Natural Philo-
sophy in the University of Edinburgh if he had not been
elected registrar or actuary of the Amicable I <ife Assurance
Office in 1833, as before mentioned. He had in early life
intended to enter the Church, but, like Mr. De Morgan,
found the teaching of Mathematics a more congenial em-
ployment than preaching, and held for a few years the
appointment of Mathematical teacher at Sandhurst. His
interest in the welfare of the Astronomical Society was
strong and lasting, but he was very unassuming in his
estimate of the work he had given to it, and begged my
husband during the last days of his life to prevent any-
thing like eulogium on his service. This arose partly,
no doubt, from his own simplicity and humility of cha-
racter, partly from the consciousness that Mr. De Morgan
was always anxious to do full justice to all his friends.
In the little memoir written by Mr. De Morgan for the
Royal Society this wish is recorded, but the biographer

182 MEMOIR OF AUGUSTUS DE MORGAN.

1850. adds that it was scarcely possible to comply with it, for a
true account of Mr. Galloway's services to Science was in
itself a eulogium.

1851. Those of us who can look back more than thirty years

slaver' w^ remember the feelings excited in England on negro
slavery by 'Uncle Tom's Cabin' — how it brought to a
climax the sympathies and efforts of those who had long
worked in the same cause, and how it stimulated those
who had been inactive, because ignorant of what was
going on, to consider how she or he could contribute
towards diminishing the sufferings of the negroes. My
husband felt intense interest in this question, and pity
for the sufferers on both sides. I remember his sitting
up the greater part of one night reading f Uncle Tom's
Cabin,' and it was evident that the subject pressed
heavily on his mind. We found several friends, among
them some active abolitionists from the United States,
who liked our idea of a National Address from Great
Britain to the United States of America, to be signed by
ever}- one who could think and feel upon the subject. Mr.
De Morgan drew up an address such as appeared to these
friends calculated to encourage a wise effort at gradual
but certain emancipation. It claimed for us, the writers,
a right to offer sympathy and assistance, inasmuch as our
countrymen and women had, until very lately, been accom-
plices in the enslavement of the negro. It invited mutual
consultation and counsel, and promised what help could
be afforded by one nation to another in the tremendous
work of getting rid of the burthen of slavery with as little
injury as possible to slave-owners and slaves. One or two
friends, men of worth and learning, gave some suggestions
in the writing of this document, of which I have not now
a copy. Had it been sent in its original form, and ac-
cording to the wishes of its promoters, its influence would
have been hardly a drop in the ocean ; and, as it after-
wards proved, the time for remonstrance and argument
was nearly over. But our design was not carried into

COMPETITIVE EXAMINATION. 183

effect as we intended. Before it could take form other
influential opponents of slavery heard of it, and drew up ^fver\% °n
an exhortatory address from the women of England to
their sisters in America. This address was in the main
moderate and good ; the feeling it expressed was unexcep-
tionable, but it was couched in slightly religious terms,
which gave it the appearance, as we thought, of an
assumption of spiritual superiority over those addressed;
and we, who had hoped for the concurrence of thoughtful
and influential men, felt that our effort lost strength by
being made exclusively a woman's movement. Accord-
ingly the original promoters of the plan withdrew. I do
not think the Address of the Women of England, which
was well introduced and signed, did either good or harm
in America. Our abolitionist friends lamented our failure,
but beyond causing some slight irritation among the
American ladies, who did not like its tone, and did not
see in it the good feeling of the writers, it had no effect
at all.

In the Introductory Lecture on the opening of the 1853.
session of 1848 my husband had distinctly stated some ^iTnlon
of his strong objections to competitive examinations, and examina-
their preparatory cram, with other parts of the educa-
tional system as it was (I wish I could add, and is no
longer) carried on.

He had strongly expressed his disapproval of the
course proposed by the University of London on its first
establishment, and refused to take part in the examina-
tions.

At that time the enormous variety of subjects on
which a young man was required to answer questions,
without reference to any special ability, was stultifying
and confusing even to the brain which could receive them
all without damage to physical health. Apropos of this
reckless and fruitless waste of mental effort, my husband
wrote an illustrative ' Cambridge examination : ' —

184 MEMOIR OF AUGUSTUS DE MORGAN.

1853. Q. What is knowledge?

University A. A thing to be examined in.

of London

examina- Q. What is the instrument of knowledge ?

A. A good grinding tutor.
Q. What is the end of knowledge ?
A. A place in the civil service, the army, the navy,
&c. (as the case may be).

Q. What must those do who would show knowledge?

A. Get up subjects and write them out.

Q. What is getting up a subject ?

A. Learning to write it out.

Q. What is writing out a subject ?

A. Showing that you have got it up.

His objection to the methods pursued by the Univer-
sity of London will be found in his letter (p. 222) written
in answer to a request.

In his strictures on the teaching of Physiology he
had evidently not contemplated the possibility of the
dissection of living animals for demonstration, now hap-
pily forbidden by Act of Parliament. Had the question
of its expediency for the sake of Science been put to
him he would have said, as he always did on such occa-
sions, that no imaginary end could justify means which
were opposed to a positive law of humanity.

And his own words on the subject of vivisection show
what he thought of it. A surgeon had been describing
to us some of Majendie's atrocities (since equalled by those
of English and Scotch physiologists), and after our friend
was gone I referred with horror to what he had said. My
husband, who had been silent some time, said, ' Don't talk
of it;' then, in a minute or two, pausing between the
sentences, he added, f They will learn nothing by it. It's
all of a piece. There is no God in their philosophy.'

Some few years after this time he came home one day
from the College evidently amazed, and told me that some
pupils had applied to him to interfere in the following

UNIVERSITY COLLEGE. 185

circumstances. A cat had been poisoned ' for Scientific 1853.
purposes ' before one of the classes. I asked him whether
a repetition of this could not be prevented. He said,
6 Certainly : it must not happen again. It was too bad.
I shall speak to - — ,' another Professor on the medical
side, c and he will see to it.' Accordingly he spoke to — • — ,
who satisfied him somehow that the thing would not
recur. He had little notion that the Professor appealed
to was and had been performing experiments before his
pupils OQ living dogs and cats. These were of so cruel a
nature that I will not describe them. They were detailed
to me by a highly respectable surgeon, who had been a
student of the class referred to.

In November a circumstance which showed an un- Dr- Peeue'a

egacy.

certain interpretation on the part of the College Council
of the main principles of the foundation, made my
husband look forward with abated confidence to the
future of his Professorship.

During the first years of University College, its prin-
ciple of non-interference with religion had been well
adhered to ; indeed, we received so many assurances on
the subject at distribution speeches, opening lectures, and
in many other ways, that no fear was felt, and my husband
worked on in the happy conviction that he was aiding the
great cause which he had most at heart. But for some
little time before this he observed indications that the
monetary success of the classes would be held a stronger
motive in deciding questions connected with the working
of the College, than its fulfilment of the pledges given of
thoroughness in instruction and adherence to principle.
He told me of these things with some anxiety. He saw,
or thought he saw, a more decided tendency to temporise
to secure the monetary success of the Institution in other
directions ; and in the year 1853 an occurrence fraught
with danger, to the principle on which it had been esta-
blished proved that his fears were well founded.

186 MEMOIR OF AUGUSTUS DE MORGAN.

1853. Dr. William Gurdon Peene, of Maidstone, left seven-

legacy?11 * teen hundred pounds for the purchase of books for the
library of University College. These books were to be
works on foreign literature and science, and the choice of
them was to be entrusted to the Professors of Greek,
Latin, and Mathematics, provided these three were
members of the Church of England ; ' Otherwise ' (as
expressed in the will), ( one or more shall complete their
number by choosing qualified persons from the other Professors,
private teachers, or quondam alumni resident in London. If
none of the three named be members of the Church of Eng-
land, I beg the Council to appoint.9

On hearing of this bequest, and learning that some
members of Council were inclined to accept it with the
prescribed conditions, Mr. De Morgan wrote to the chair-
man of the Council as follows :—

University College, Nov. 5, 1853.

SIR, — A proposal now before the Council, and to be discussed
this day, involves the application of a religious test to certain
Professors, with a view to their exclusion from a certain office to
be founded, in the event of their opinions not being of a certain
class.

I beg you will draw the attention of the Council to the
following personal statement. The matter in question may
never come before the Senate; and if it did, I could not expect
the Senate to convey to the Council remarks which refer entirely
to my own personal position. If, when I first sought the honour of
a chair in this College, I had asked what security existed for my
never being excluded from anything on account of my opinions, I
should have been told, and with reason, that if so many public
declarations as had been made, both printed and oral, uttered
with every mark of sincerity and received with every appearance
of enthusiasm, were not sufficient guarantees, I should do well
to reconsider my intention of acting under those whom it was
clear, by my question, that I mistrusted.

Again, admitting that the College, corporately, would never
institute a test or create a disqualification, if I had asked
whether it would allow any one else to do so within its walls, or
if, giving credit for the full determination to maintain a perfect

PEENE LEGACY. 187

religious equality among the students, I had asked whether it was 1853.
possible a Professor might be placed under disqualification, I Lettertothe
should have been told, and with reason again, that if the length Council«
and breadth of the declarations I have alluded to were not
sufficient to contain these and any other possible cases, all the
lawyers who ever varied the counts of an indictment, or reckoned
up the rights which pass with a freehold, would not be able to
frame anything which would satisfy so suspicious a person.

I joined the College in the full conviction that the plain
English of scores of declarations would have warranted the pre-
ceding replies. To my utter surprise, on the very first occasion
on which money is offered on the condition of establishing a
religious test, all I hear seems to indicate that it is far from
certain that the offer will be rejected. What the Council has
ever done to warrant such a want of certainty I cannot imagine;
for if ever any Institution in this world honoured its faith and
practised its professions, University College has done so, up to
this moment, in the matter of religious equality. I myself should
never have imagined the necessity of stating that my connection
with this College was the consequence of the good and sound
and religious principle shown in its leading maxim, but for the
doubt to which I have referred. No one is so humble that faith
need not be kept with him. In the name of all the declarations
which the College has put forth from its first institution, I claim
the performance of the obligation therein undertaken to maintain
every student, every Professor, every officer in perfect religious
equality with the rest, from the President of the Council down
to the sweeper of the floor.

This I claim with the most perfect respect for the Council,
which, among many other reasons, I feel because the principle
of the College has always been maintained, and, I fully believe,
will still be maintained. But I think it possible that the strength
of the individual claim of those who have trusted the College,
and have spent the best years of their lives in its service, may be
overlooked, and for this reason only I trouble you with these
remarks. — I am, sir, your most obedient servant,

A. DE MORGAN.

P.S. — The only precedent which bears on the matter, within
my recollection is as follows : At the opening of the College,
each student was desired to state whether he was Churchman or
Dissenter, and the answer was affixed to his name in the list.
The motive was the most innocent in the world ; it was the

188 MEMOIR OF AUGUSTUS DE MORGAN.

1853. statistical one. Great objection was raised. It was affirmed

Peene that the College on its principle could have neither need to

know nor right to inquire the religious status of any student.

In deference to this objection, the force of which could not be

denied, the practice was discontinued.

This letter was laid before the Council. In reply to
it a copy of the resolutions passed in the following month
was received. My reason for giving them here will be
found in the first resolution, which contains a full ac-
knowledgment of the principle of religious equality.

Copy of Resolutions passed by the Council on December 10, 1853.

1st. That the Council cannot but regret that the late Dr.
Peene should have accompanied his valuable legacy by a direc-
tion with regard to the function of choosing the books, which
can, by any construction, be supposed to infringe that principle
of religious equality to which the present Council and their pre-
decessors have invariably adhered, as well in the appointment of
Professors,1 the admission of students, and the award of honours,
as in the general administration of the affairs of the College.

Considering, however, that the function in question is totally
unconnected with the ordinary duties of the Professors, and
might have been assigned by the testator to persons unconnected
with the Institution, and that it is to be regarded as a trust
under Dr. Peene's will, and not as a duty imposed by the
authorities of the College ;

Considering, also, that any Professor will have the power of
declining the trust altogether if he should for any reason think
proper so to do, without being required to make any profession
of his religious opinions ;

And, lastly, considering that the value and utility of the
proposed annual addition to the library are not likely to be in
any degree impaired by the terms of the bequest —

The Council have determined to accept Dr. Peene's legacy,
being of opinion that in so doing they do not violate that prin-
ciple uf religious equality on which the College was founded.1

2nd. That, as some difference of opinion has existed on this
question, the Council, being anxious to prevent any misappre-

1 The italics are mine.— S. E. DE M.

PEENE LEGACY. 189

hension as to the grounds of their decision, have thought it 1853.

right to record their reasons in the foregoing resolution. The prin-

3rd. That the Secretary be directed to communicate the fore- universit

going resolutions, together with a copy of the extract from Dr. College.
Peene's will, to the three Professors named in the will.

It will be seen by this that the principle of religious
equality was still fully recognised twenty-six years after
the foundation of the College, as having been that ' on
which the College was founded,' and as having been ' in-
variably adhered to by the present Council and their
predecessors, as well in the appointment of Professors,
the admission of students, and the award of honours, as
as in the general administration of the affairs of the
College.'

F wish I could find, for the reason advanced for passing
by a principle so distinctly acknowledged, any other word
than that which my husband applied to it — ' a shuffle.' The
determination to accept the books on the prescribed terms
confirmed his fears, and on hearing of it his first impulse
was to resign his chair. He was induced to remain by
the consideration that the classes were not numerous,
and that he wished to see the College in a more pros-
perous state before quitting it altogether. I did not, for
my part, endeavour to influence him in this matter.
Indeed, at this time my whole thoughts were filled most
painfully by the illness of our eldest child, whose danger
was not at first realised by her father. I think that when
he spoke to me of the condition of affairs at the College,
I did not strongly urge his leaving it, for I knew that his
doing so would be a trial, and that he was then unpre-
pared for the one already hanging over us. But, with
reference to the resolutions, he said, ' They have got in
the thin end of the wedge ; the next move will be a
stronger one.' And so it proved.

The end of this year was the beginning of a long
period of sorrow and suffering to us. Our eldest dear child,
Alice, who had caught cold after a severe attack of

190 MEMOIR OF AUGUSTUS DE MORGAN.

1853. measles, died before Christmas. I had feared the termi-
Death of nation of the great weakness and delicacy which I had
daughter, vainly tried to prevent. Her father did not realise the

degree of illness till the end was near, and the blow fell
heavily upon him. He was not then so used to death and
sorrow as we afterwards became, and his want of sight
and natural hopefulness of disposition made him unaware
of the degree of danger in this and in other cases. This
hopefulness left him after repeated sorrows. He always
dwelt on the belief that those whom God loves are the
early taken, but after we lost Alice his cheerfulness
diminished, and I do not think he ever laughed so heartily,
or was heard whistling and singing merry snatches of
songs as he used to do when all our children were with
us. I cannot write of these events. A few references to
them will be found in his letters.

1854. The next year passed with scarcely any incident
worthy of recording. After our loss my husband re-
mained very much at home, seeing scarcely any one but his
fellow-Professors in his daily visits to University College.

An application was made to him to examine and give
certificates in the City of London School, but this he de-
clined on grounds connected with the methods and subjects
of examination.

In July he gave a lecture to the Society of Arts on a
kindred subject, namely, On the Relation of Logic and
Mathematics to other Branches of Science. This lecture,
which was rich in argument and illustration, was only
reported in abstract in the Society's Journal. One of its
strongest positions was the insufficiency of Mathematics
as a mental discipline for inducing logical habits of
thought, unless in conjunction with some amount of
direct Logical teaching.

1855.

Mr. Sheep- jn fae autumn of 1855 our dear old friend Mr.

shanks &

death Sheepshanks died at Beading. For the last few years

DEATH OF RICHARD SHEEPSHANKS. 191

we had seen him but seldom, for he came to London only 1855.
for the Eoyal Astronomical Society's meetings after the
work on the Standard Scale was completed. This work
had been very severe, and probably reduced his strength,
which was never great. His death was a blow to many
friends, to none more than to my husband, who went to
Reading to the funeral — a painful duty, made less pain-
ful by his habitual manner of looking at death. He
wrote afterwards to me (for I was with the children at
Eastbourne), —

I returned tliis evening. I saw the body of my good old
friend safely into a bricked vault, specially made for him and
his sister, in the cemetery a mile out of the town. There
were Airy, Johnson, Simms, myself, and some others. I saw-
Miss Sheepshanks for a few moments. . . . S. has, of course,
made her his sole heiress and executrix. She intends to give
all his books and instruments where they may be most useful
— perhaps to the Astronomical Society. The house is a very
nice one, with a garden so full of rich coloured flowers as to
make me almost admire it, with greenhouses, which I did not go
into, and a little observatory.

Miss Ann Sheepshanks, who had lived with her
brother since the time he left Cambridge, lost with him
her great interest in life. She devoted all the energy of
a vigorous and self-sacrificing nature to the perpetuation
of his name and memory, and the honour due to his
unostentatious but most useful efforts to promote Astro-
nomical knowledge. There was much self-denial as well
as exertion in her efforts to attain her end. She gave
10,0002. to the University of Cambridge for an Astro-
nomical scholarship, to be called by his name. She pre-
sented his instruments and books to the Astronomical
Society, being in return elected to an honorary fellowship,
and she collected materials for a memoir, which was
drawn up by Mr. De Morgan.

At this time the phenomena to which I have before
slightly referred began to attract general notice, chiefly
under the form of table-turning ; and natural philosophers,

192 MEMOIR OF AUGUSTUS DE MORGAN.

to whose experience this and all its kindred manifestations
were so completely opposed, sought for explanation in the
credulity and inability to observe of the believers. Mr.
Faraday combated the influx of superstition in a lecture
On Mental Training, given in the spring of 1 854, at the
Royal Institution. In this lecture he affirmed a principle,
which Mr. De Morgan commented on two years after in a
review of the printed lecture in the Athenaeum. Wilt
the time ever come when the reviewer's caution will be
needless ?

The lecturer has laid down in the strongest and plainest
terms the principle of Physics, which was the bane of what is
known as the Philosophy of the Schoolmen. It. occurs in a
lecture On Mental Training, delivered May 6, 1854, at the Royal
Institution. These are his own words : —

4 The laws of nature as we understand them are the founda-
tions of our knowledge of natural things. Before we proceed to
consider any questions involving physical principles we should
set out with clear ideas of the naturally possible and impossible.9

We stared when we read this, — ' set out in physical investiga-
tions with a clear idea of the naturally possible and impossible ' '
We thought the world had struggled forward to the knowledge
that a clear idea of this was the last acquisition of study and
reflection combined with observation, not the possession of our
intellect at starting. We thought that mature minds were
rather inclined to believe that a knowledge of the limits of
possibility and impossibility was only the mirage which constantly
recedes as we approach it. We remembered the Platonic idea, as
clear as the crystalline orbs it led to, that the planetary motions
must be circular, or compounded of circular motion, and that
aught else was impossible. We remembered with how clear an
idea of the impossibility of the earth's motion the first opponents
of Galileo started these maxims into the dispute. We doubt if in
any mediaeval writer the principle on which they acted has been
so broadly laid down as by our author in the phrases above
quoted. The schoolmen did indeed make laws of nature the
foundation of their knowledge, and clear ideas of possibility and
impossibility helped them in the structure. But they rather did
it than professed it. — Athenaeum, March 1855.

Mr. Faraday believed that a full explanation of the

SCIENCE AND SUPERSTITION. 193

movement of tables might be found in the unconscious 1855.
action of the muscles of those present, and devised an
instrument which he believed adequate to detect it, and
to bring to the involuntary operators the conviction that
the phenomena, imagined spiritual, had been caused by
themselves. I remember hearing him at an evening
party at Sir John HerscheFs explain the action of this
instrument, the indicator. A number of ladies and gentle-
men listened with interest and attention ; the explanation
seemed satisfactory, and was received with the respect
due to the great fame of its author. Mr. De Morgan, who
was known to be one of those whose credulity required
a check, stood by with some amusement on his face. I
almost wished him to tell some of those things which
he had seen which made him doubt the sufficiency of
the explanation. But he said it would be useless.

This occurred before the lecture was printed, but it
had, I think, been delivered.

194 MEMOIR OF AUGUSTUS DE MORGAN.

SECTION VII.
CORRESPONDENCE 1846-55,

To Rev. Dr. Whewell.

Camden Street, Oct. 21, 1846.
1846. MY DEAR SIR, — First, I arn very much obliged by your kind

invitation, but my lectures are imperative, and I cannot leave

town in November.

Next, as to Athenceum police report, you Lave made worse

guesses, unless indeed you never were mistaken in your life.1

Now as to the papers. The only wish I have for them to
• appear in one is that I may get my copies all at one time, and

get them disposed of with one trouble. Whether, this condition
being fulfilled, they are printed in the form of two papers or one
does not matter, and I agree with you that they are distinct
enough to be two, and might better be so.

I am going to publish a work on Logic, which, as I told you,
will appear soon after the paper. This is sufficient reason for
not developing in the paper. Indeed, the Society must know
that fact, and take it into consideration in deciding on the
printing. There is of course an advantage in new things going
first through the usual channels in which scientific matters are
propagated, and so I should like the Transactions to have them.
But, Ma re perspecta, the Society may think otherwise, par-
ticularly if there is heavy matter, typographically speaking, on
hand already. Your suggestion about taking a subject I will
think of, but what subjects run very thickly in syllogisms ?
They are mostly full of proof of a very few. Some of Butler's
Analogy or a chapter of Chillingworth would perhaps be
promising. The syllogistic examples in books of Logic are
literally nothing more than terms of one word or so substituted
in the formal syllogism — I gave some examples (one of each
mood) in the Penny Cyclopaedia, article Syllogism —which (a few

1 The ' A thenxum police report' was a humorous skit upon the
discovery of the planet Neptune.

CORRESPONDENCE, 1846-55. 195

at least of them) are more like ordinary sentences involving a 1846.
syllogism.

As to subjective and objective (I shall say ideal and objective,
as subject-ive will not do for logic) I see your difficulty, and must
consider whether I have not shown that I see it when the proof
sheet comes. I have a great fear of not using the word in the
sense of anybody else. The object itself, as far as we can think
of it, is the idea of an object. The first step I make is the exist-
ence of my own mind ; the next, that of other minds. If every-
thing in existence be a dream of my mind, a thing of which I
have ideal possibility, there are no objects. If you attempt to
argue me into belief of your existence and beat me (not argue
by beating me, which is the sort of argument by which Berkeley
has been answered before now), I may not be able to answer
you ; but all that is no more than might happen in my dream.
I might sleep, as it is, and dream that I was arguing with some-
body who proved to me most satisfactorily that I was awake.
But getting by the argument of analogy the existence of other
minds, I then begin to know objects — other minds get the same
as I get, from somewhere. A source of ideas to more minds
than one, or to all minds under the same circumstances, would
be what I should call my definition of an external object, if,
unfortunately, an external object under the same circumstances did
not imply objects already. Call it then a test of objects ; material
or not, is of no consequence. Hence the idea of external objects.

By the idea I merely mean that which is in the mind. I
should distinguish a horse in the mind from that which is in the
mind about from whence a horse comes into the mind-, idea of
mental state produced, and idea of producing external cause ;
idea of idea, and idea of object. When I speak objectively, I refer
to my idea of the object ; when ideally, to my idea of the idea.

But should not objects be divided into external and internal ?
What am I to call an idea, looked at as presenting me with the
idea of itself ? I talked of the idea of a horse ; I spoke then of
my mind in the state of looking at itself picturing a horse ;
another mind would have done.

All this, I believe, is common enough. I have put it down
that you may see how far our language agrees. Now as to my
paper, pray observe that my notion, if such must be inferred
of the case of the words subjective and objective, refers to the
case in which all they have to do with formal Logic is stated.
And my paper is wholly on formal Logic. The writers on this

o 2

196 MEMOIR OF AUGUSTUS DE MORGAN.

1846. subject, so far as their confusion on this point entitles one to say
they speak one way or the other, speak ideally, and not objectively.
Nay, more, they even admit contradictory propositions as ideally
enunciable, and subject to contradiction like others. Thus,
4 every collection of two and two is five ' is properly convertible
into ' some fives are collections of two and two.' Accordingly
they give and take no denial except contradiction ; nothing with
them overturns ' every A is B,' except ' some A's are not B's/
But when we come to apply Logic to the working wants of the
mind we find another kind of denial, namely, denial by non-
existence ; necessary non-existence, or contingent, as the case
may be. When we speak objectively, there may be denial by
contingent non-existence perfectly distinct from denial by con-
tradiction. Thus objectively I deny that 'all unicorns are
animals/ not by saying that there are unicorns which are not
animals, but by saying that there are no such objects as uni-
corns ; and so far as a unicorn is not, so far it cannot be animal,
or anything else. Ideally, I admit, unicorns are animals ; my
notion is the notion of animal.

I distinguish, then, denial of the terms from denial of the
copula.

A is B ideally, objectively, or (say) x-itively.
No ! for A has no x-itive existence.
No ! for B has no x-itive existence.

No ! for the x-itive existence of A and B belongs to is not,
not to is.

Formal Logic usually is made only to treat of the copula. To
be strictly formal I need not introduce ideal and objective, more
than English and French, black and white, x and y. Two species
ot existence implied as belonging to the terms brought forward
would do as well. But ideal and objective is the important dis-
tinction in practice, and as to assertion or denial, so far as I
want it, is easy.

I should now ask you to consider some phraseology.

There are seven definite relations of term and term. I do not
call x ) y definite, for it consists equally well with y ) x and
y: x.

1, 2. Start with identical and contrary, complete co-existence
or complete mutual exclusion containing all things between them.
As (man being the universe) North Briton and Scotsman, or
Briton and alien.

CORRESPONDENCE, 1846-55. 197

3, 4. Sub-identical and super-identical, complete content or 1846.
complete containing. Thus Londoner is a sub-identical of man,
man a super-identical of Londoner (man being itself a sub-
identical). The case in which the super-identical is the universe
may give rise to the extreme super-identical and its extreme case
of extreme identity.

5, 6. Sub-contrary and super-contrary. The first complete
exclusion of one term from the other, both terms not filling up
the universe as (man being the universe) Englishman and
Frenchman. The second contrary overlapping, or where every-
thing in the universe is either one or the other, and some things
are both. As (terrestrial object being the universe) man and
irrational being, if madness and idiocy be included under irra-
tional.

7. Mixed (what ought to be the name ?), where each term
has part in common with the other part not in common, and
both terms do not fill up the universe. The usual form^of asser-
tion, as : — Some animals are dark-coloured. I want the word
for mixed, and better ones for the others, if any. Mixed is : —
Both have part in, part out, and there are which are neither.
There is no hope of a word for all this. Some word formed
to contain the idea of common part must do, and it should be
Latin like the rest.

I tried an experiment yesterday with my daughter of 8J years
old as to the ideas of necessity, and there was a dialogue as
follows : —

Q. If you let a stone go, what will happen ?

A. It will fall, to be sure.

Q. Always?

A. Always.

Q. How do you know ?

A. I'm sure of it.

Q. How are you sure of it ? Would it be true at the North
Pole, where nobody has been ?

A. Oh yes, people have been to the North Pole, else how
could they know about the people who live there, and their
kissing with their noses ?

Q. That's only near the North Pole. Nobody has ever been
at the Pole.

A. Well, but there's the same ground there and the same air-
Hotter or colder can't make the air heavier so as to make it keep

198 MEMOIR OF AUGUSTUS DE MOEGAX.

1846. np the stones. Besides, I've read in the Evenings at Home that
there is something in the ground which draws the stones. I am
quite sure they would fall. Now, is there anything else you
want to be a little more convinced of ?

Q. How many do 7 and 3 make ?

A. Why, 10, to be sure.

Q. At the North Pole as well as here ?

A. Yes, of course.

Q. Which are you most sure of, that the pebbles fall to the
ground at the North Pole, or that 7 and 3 make 10 ?

A. I am quite as sure of both.

Q. Can you imagine a pebble falling upwards ?

A. No, it's impossible. Perhaps the birds might take them
up in their beaks, but even then they wouldn't go up of them-
selves. They would be held up.

Q. Well, but can't you think of their falling up ?

A. Oh yes, I can fancy three thousand of them going up if
you like, and talking to each other too, but it's an impossible
thing, I know.

Q. Can you imagine 7 and 3 making 12 at the Pole ?

A. (Decided hesitation.) No, I don't think I can. No, it
can't be ; there aren't enough.

Here her mother came into the room. As long as the ques-
tions were challenges from me it was all defiance and certainty,
but the moment Mrs. De M. appeared she ran up to her and
said, * What do you think papa has been saying ? He says the
stones at the North Pole don't fall to the ground. Now isn't ifc
very likely they fall just as they do here and everywhere ? ' But
she did not mention the 7 and 3=12 question, nor appeal to her
mother about it. I remain, dear sir,

Yours very truly,

A. DE MORGAN.

To Rev. Dr. Whewell.

Camden Street, Camden Town,

Oct. 26, 1840.

MY DEAR SIR, — I have intended for some days to be at you
once more in enunciation, on the remaining point of your letter.
But I have been hindered by the necessity of looking sharply at
the proofs of an account of Newton, which will appear shortly.
In this matter I am the avvocato del diavolo, as he is called, who
is the ex-officio opponent at Rome of canonisation. There is

CORRESPONDENCE, 184(3-55. 199

only one matter in which the facts, in the most objective sense, 1846.
come out differently with me from other people. The Biog.
Brit, says (copied by Brewster) that Whistori says that Newton
was so offended by being represented as an Arian, that he
therefore refused W. admission into the Royal Society. Refer-
ence is made to the edition of W.'s memoirs of 1753, which
bibliographers know to contain additions. This edition is scarce,
but on consulting it, I find that the representation is an absolute
falsification; for W. gives the same reason as in the edition of
1749, which has nothing to do with any ism at all, or arian either.
Sir D. Brewster has had a lucky escape. It was by mere
accident I looked at the Biog. Brit., a work which I never trust
in the life of Newton. He gives the same account, with the
same reference, without saying he has taken it from anywhere
else. Had I not happened to have found his source, I should
have left him to clear himself by confessing copying without
verification, or otherwise at his discretion. This failing of copy-
ing references without acknowledgment has cost me hundreds
of hours uselessly employed.

Now to enunciation. We must define. If I carry a mes-
sage out of my mind into yours, and you receive it, and know
that I meant to send it, and if, moreover, I did mean to send it —
I certainly enunciate, if the etymology be to give the meaning.
But if logical enunciation in pure form be required, there
must be subject, predicate, and copula (is or is not), all duly
announced.

According to Aristotle there must be in enunciation either
truth or falsehood. Thus prayer, he says, is not enunciation.
I say there is truth or falsehood, may be either.

Are we on a question of definition of words, or on one of
separation of things ? If I shut up my window, meaning to
have you believe I am out, I enunciate ' A. De Morgan is not at
home ; ' not verbally, if by enunciation is meant what I call
verbal enunciation. So if I know you to be searching for, say
your hat, and I point to the chair on which it lies, I do not say,
1 Your hat is on that chair,' but I convey, or mean to convey,
the message to your mind. If I were to chalk an X on the
great gate at Trinity, meaning to charge the management
with peculation, and if others so understood it, the Judge would
leave it to the jury to say whether both facts were proved,
my intention and others' reception. If they were satisfied on

200 MEMOIR OF AUGUSTUS DE MORGAN.

1846. these points, he would instruct them that the X was a libel, and
would leave them to find damages accordingly.

There is no doubt that in law the enunciation of a libel is
wholly independent of the symbols used. The rule of law is
very distinct ; writing, signs, pictures, &c., are equally libels,
when intention is proved ; and in the civil matter the law
decides, not the jury, whether the matter is libellous.

The message intended, and received as intended, constitute
with me enunciation. If others object to the word, I must
choose another word ; bub this is the thing I mean. Provided
always that there is in reality subject, predicate, and copula.
Whether message intended but not received is enunciation, that
is, whether the difference should not have been a distinctive
term, is matter of convenience. If I understood Arabic, to make
what the French call a fiere supposition, and thinking you did,

wrote you t ^ t^/r^J' or w^atever ^ might be (if more dots

are wanted pray stick 'em in), and if you did not understand it,
there might well be a word to denote this imperfect message.

If I were only to raise an image or single idea, not affirma-
tion of agreement or disagreement — as, if I were merely to call
your attention by uttering the single word book, apropos of
nothing, I could not be said to enunciate. If you took it as my
saying, 'It is my pleasure to say a word, viz. book,' you take
an enunciation. If that were what I meant, the enunciation
is perfect. But if I meant nothing but to set you wondering-
what I meant, there would be nothing going between us. This
mere utterance would, I suppose, be the Xoyos O-^/ACU/TI/COS of Aris-
totle, as distinguished from the a7ro<£avri/cos. What I contend
for is, that that which is absolutely considered semantic may be
apophantic by the understanding of the parties.

I do not see how ' A is B ' is in any other way more apo-
phantic than * ~" which is no enunciation to you, but for
what you know may be to another. This is enunciation to me —

and to all who understand Mavor's short-hand. If prayer be
not enunciation, as Aristotle Rays it is not, how does the other
party know it is prayer ? Does not the pray-er say — I pray
this?

I have got some further development of my Logic in definite
syllogisms, derived from the classification in my last ; with some
curious entrance of a principle corresponding to that of like

CORRESPONDENCE, 1846-55. 201

signs give plus, unlike minus. Common a fortiori reasoning will 1840.
take its place in a class of distinct syllogisms,
I remain, dear sir,

Yours very truly,

A. DE MORGAN.

To Sir Rowland Hill.

Camden Street, Camden Town,

May 5, 1848.

MY DEAR SIR, — I am much obliged to you for the notice. 1848.
I believe you when you say there are difficulties, because you
get over them. Still, to my untutored mind, it is wonderful the
Post Office should imagine that anybody would write in a book
at 6d. a pound to save postage.

I hope that the end of it will be that anybody may write
anything, and I have reason as follows : —

There is an old book I want ; for example, the first edition
of Wingate's Arithmetic, 1630. If one of my country friends
finds it, what will be in the inside of an old Arithmetic ? A
hundred to one, something like —

Ann Price, her booke,

God give her grace therein to looke,1

scrawled over the inside of the cover and the fly-leaf — that is,
over more than one page. Now it does not consist with the fit-
ness of things that Ann Price's aspirations after Arithmetic in
the seventeenth century should prevent a professor of Mathematics
in the nineteenth from ascertaining the exact share of Wingate
in the invention of decimal fractions.

You stop the circulation of old books. However, as I said,
if you say it can't be, I will believe you, provided the impossi-
bility may be interpreted as temporary.

But for the love of order, and the Constitution, and the other
things that were dusted on the 10th ult., don't compel all the
old-book people to stand up for equal rights and against class
privileges. You'll make Chartists of Sir H. Ellis, and Hallam,
&c., &c., to say nothing of,

Yours truly,

A. DE MORGAN.

1 Ann Price's (probable) handwriting imitated. — S. E. DEM,

202 MEMOIR OF AUGUSTUS DE MORGAN.

To Dean Peacock on his Marriage.

7 Camden Street, Oct. 21, 1847.

1847. MY DEAR SIR, — This morning I found two cards for me at

the College, which informed me of your marriage, of which I had
heard nothing. In fact, for any thing I knew, you might have
been as confirmed a Benedict as any Pope of that name. But
owing to the practice which ladies have of not putting the name
they leave as well as the one they take, I had no guess who Mrs.
Peacock had been ; and the theory of probabilities does nothing
in the way of inferring the probable name which a bride quits,
having given that which she takes. So I resolved on writing
hearty congratulations and warm good wishes on the existing
a priori (or if you will have it that priors are out of question by
their vows, say a diaconiori) presumption that you were well able
to know what was good for yourself. But it so happened that
an Ely man saw the cards in my hand, and, as the phrase
goes, told me all about it ; and I was enabled to conclude from
other evidence that I might just keep my good wishes, and put
good prophecies in their place. Take them both, however. As
to this practice of putting only one value of the variable on
wedding cards, I object to it altogether ; in fact, I denounce it,
and will prove my objection good. I suppose no one will deny
that the cards represent the instant of the ceremony at which
the contract becomes indissoluble ; for before that moment the
announcement would be presumptuous, and to suppose that any
time elapses after it would be to suppose that a man takes that
time to consider whether he will acknowledge his marriage,
which is absurd. This being granted, let A B represent the
duration of the lady's life, and let M be that moment of the

ceremony at which the contract becomes indissoluble. Let the
lady's name during A M be Sclwyn, and during M B Peacock;
then, because by common courtesy a lady is not a discontinuous
fraction, it follows that what is true up to the limit is irnoat
the limit, therefore at the moment M her name is Selwyn. But
for a similar reason her name at the same moment is nlso
Peacock ; therefore at the instant M she has both names, whence
both ought to appear on the wedding cards. Q.E D.

I have your books on arithmetic in safety and memory, and
am only waiting to return them till I have put a copy of my

CORRESPONDENCE, 1846-55. 203

Logic into the parcel, which I hope to do in about a fortnight. 1847.
As matters are, I feel no compunction at having kept them so
long. I beg to offer my best compliments to Mrs. Peacock, and
my apologies for introducing myself by inserting her name into
a demonstration. But first principles must be carried to their
full extent ; and I remain, my dear sir,

Yours most sincerely,

A. DE MORGAN.

To T. K. Hervey, Esq.

Dec. 1848.

DEAR HERVEY, — .... A man named Lacroix, a French 1848,
bibliomaniac, has been over here. He came over with strong
prevention against Libri, but examined his case here, and is gone
back very angry with his accusers. He is preparing a pamphlet
de son chef in defence of Libri, of which the latter promises me
an early copy, or proofs if he can get them. So far good. But
if you could light on any information about Lacroix (nicknamed
Jacob Bibliophile in his own country), or any one of his biblio-
graphical publications, so much the better; for this Lacroix
must be looked after. Panizzi and Libri unite in declaring that
of upwards of 1,700 manuscripts, sold by Libri to Lord Ash-
burnham some years ago, Lacroix named them all, with a few
exceptions, and described where they originally came from,
merely from his knowledge of existing manuscripts and their
localities, thus negativing from his own personal knowledge the
charge of theft as to very nearly the whole lot. This story is
so extraordinary that, if true, as I cannot doubt it must be in
the main, this same Lacroix should be brought forward in Eng-
land and his works noticed. I can believe such a story, for I
have heard such things well attested of people who pass their
lives in studying the physics of books and MSS.

Yours truly,

A. DE MORGAN.

To T. K. Hervey, Esq.

Dec. 1848.
' And serve it with Hervey's sauce.'

JERDAN.

DEAR HERVEY, — That unconquerable mania which you have
for thinking your puns as good as mine (you say better, but I
don't believe you think that — the most singular fancies are

204 MEMOIR OF AUGUSTUS DE MORGAN.

1848. sometimes carried further than they go, out of mere bravado)
is a study for the psychologist. I shall forward a statement to
Sir W. Hamilton.

Pray when within two years have yon mentioned Lacroix ?

However, since you know him. which I didn't, yon now know
that he has a memory.

And what makes you say that I never read any papers but
those of a mathematician ? Mathematica ! quoth he — are you a
mathematician ? and did I not read all the we-should-gladly-
forget-them-if-you-woiild-let-Tis articles, which procured you the
memorable rebuke (which you will never get over) with which
I have headed this letter ?

And as to preventions, was I not talking of a Frenchman ?
and if he had described himself, would he not have used the
word ? And did I not get the word from Panizzi, and was I not
assured of an Italian borrowing a Frenchman's phrase — who
deniges of it ? Yours truly,

A. DE MORGAN.

To Capt. Smyth.

7 Camden Street, Dec. 19, 1848.

MY DEAR CAPTAIN SMYTH, — Pray what is the matter with
yon ? Pray write and say yon are quite well ; but mind, I
detest lying of all things, so be sure you speak the truth.

I took a solitary glass of porter yesterday to your recovery,
for I did not choose to admit any of the profane dogs about me
to the ordinance, which is quite above their appreciation.

Airy gave us a very good telegraph lecture. I mean on
telegraph, not by telegraph. But time may come when we
shall sit down in our own room and hear him lecture from
Greenwich.1

Seriously, let me know how you are. With kind regards to
all, I am yours truly,

A. DE MORGAN.

To Sir John Herschel.

March 18, 1849.

1849. MY DEAR SIR JOHN, — Sir H. N. is as correct as his authori-

ties. Censorinus, who gives the most distinct account, says that

1 I do not suppose the writer had the smallest conception of the
wonderful literalness with which his prediction would be fulfilled. It
must be remembered that the telephone was not even dreamed of
thirty-three years ago.— S. E. DE M.

CORRESPONDENCE, 1846-55. 205

there was leap-year every fourth year, bat does not say from 1849.
whence the years were reckoned.

We have no authority for saying which particular years
were leap-years — either in the pre- Augustan piece of the Julian
Calendar, or at the start made after the Augustan reformation.

Nevertheless, I think a little train of reasoning will bring us
to the following theorem.

The Julian Calendar starts with what, by reckoning back, we
should call January 1 of the year —45, on the supposition that 0
does not exist, but that we pass from +1 to —1 consecutively,
on the supposition that every fourth year is leap-year.

There is much reason to suppose that Caesar began his year
on January 1 because there was a new moon on this day. Other-
wise it is likely he would have commenced it on the shortest day
preceding. He is thought to have gratified the feelings of the
Romans by making his start on a new moon day, and Macrobius,
in the words * Annum civilem Caesar habitis ad unam dimensi-
onibus constitutum, edicto palam proposito publicavit,' is held
to have alluded to this. Now the fact is that January 1, —45,
back-reckoned as before noted, is found to have been a day
of new moon. Dr. Smith's Dictionary of Greek and Roman
Antiquities (a book you ought to have — there is a good article
on the Calendar) says it was at 6h. 16m. P.M. My rough
calculation gives lOh. 55m., which I take to be within a quarter
of an hour.

Now, as our tables reckon back (old style) upon the suppo-
sition of uninterrupted leap-year every four years, I take it that,
as to the interval, we may depend upon knowing the exact
number of days that have elapsed.

Bat how are we to explain the dropping into leap-year
at +4?

Diagram I. shows us —

J. Julian leap-year.
P. Priests' mistaken leap-years.
A. Augustan leap-year after the suspension.
At the end of the year 4, the priests' leap-years and one
Augustan make 13, just what there ought to have been by our
back- reckoning. If, then, +4 was Augustan leap-year, we are
all right. I assume that the first year of the reckoning was cer-
tainly not a corrected year. Accordingly the first priests' leap-
year was —42 J., showing the Julian intention was never carried
into effect.

206 MEMOIR OF AUGUSTUS DE MORGAN.

1849. Diagram II. shows how, according to the well-known Roman

mode of counting, the edict of Augustus in —8, there shall be no
leap-year for twelve years, would be accounted to make +4 leap-
year. If a man had been sentenced on Monday evening to six
days' imprisonment, he would have been let out on Saturday
morning. This seems to me to explain how we may reckon
intervals from our January 1 —45, but from thence to + 4 inter-
vals must be corrected, though not after. The dates —45 and

— 8 are well fixed by the consuls being named

The general impression is that the first of Caesar's years,

— 45, itself was his bissextile. This seems to me absurd.
Caesar did not care about equinoxes. All he wanted was to
keep an average of 365^, and correcting before the error bad
accrued would surely never have struck him or Sosigeues.

Moreover, the preceding theory accounts for 4<n, and shows
Low the new moon may be made to fall where we know it did.

Yours truly,

A. DE MORGAN.

To the Rev. Wm. Heald.

DEAR HEALD, — .... Talking of curious powers, tell me
what you think of the following story. It quite beats me.

I have seen a good deal of mesmerism, and have tried it my-
self on -• for the removal of ailments which required much

medicine, but which mesmerism met without medicine from the
time it was employed. Of the curative powers of this agent I
have no more doubt than one has of things which he has con-
stantly seen for years. But this is not the point. I had fre-
quently heard of the thing they call clairvoyance, and had been
assured of the occurrence of it in my own house, but always
considered it as a thing of which I had no evidence direct or
personal, and which I could not admit till such evidence came.

One evening I dined at a house about a mile from my own
— a house in which my wife had never been at that time. I left
it at half-past ten, and was in my own house at a quarter to
eleven. At my entrance my wife said to me, * We have been after
you,' and told me that a little girl whom she mesmerised for
epileptic fits (and who left her cured), and of whose clairvoyance
she had told me other instances, had been desired in the mes-
meric state to follow me to — — Street, to 'a house. The

thing took place at a few minutes after ten. On hearing the
name of the street the girl's mother said, —

CORRESPONDENCE, 1846-55. 207

1849.
* She will never find her way there. She has never been so

far away from Camden Town.'

The girl in a moment got there. ' Knock at the door,' said
my wife. 'I cannot,' said the girl ; ' we must go in at the gate.'
(The house, a most unusual thing in London, stands in a garden ;
this my wife knew nothing of.) Having made the girl go in and
knock at the door, or simulate it, or whatever the people do, the
girl said she heard voices upstairs, and being told to go up,
exclaimed, ' What a comical house ! there are three doors,' de-
scribing them thus.1 (This was true, and is not usual in any
but large houses.) On being told to go into the room from
whence voices came, she said, * Now I see Mr. De Morgan, but
he has a nice coat on, and not the long coat he wears here;
and he is talking to an old gentleman, and there is another old
gentleman, and there are ladies.' This was a true description
of the party, except that the other gentleman was not old. ' And
now/ she said, 'there is a lady come to them, and is beginning
to talk to Mr. De Morgan and the old gentleman, and Mr. De
Morgan is pointing at you and the old gentleman is looking at
me.' About the time indicated I happened to be talking with
my host 011 the subject of mesmerism, and having mentioned
what my wife was doing, or said she was doing, with the little
girl, he said, * Oh, my wife must hear this,' and called her,
and she came up and joined us in the manner described. The
girl then proceeded to describe the room ; stated that there
were two pianos in it. There was one, and an ornamental side-
board not much unlike a pianoforte to the daughter of a poor
charwoman. That there were two kinds of curtains, white and
red, and curiously looped up (all true to the letter), and that
there were wine and water and biscuits on the table. Now my
wife, knowing that we had dined at half-past six, and thinking
it impossible that anything but coffee could be on the table, said,
' You must mean coffee.' The girl persisted, ' Wine, water, and
biscuits.' My wife, still persuaded that it must be coffee, tried
in every way to lead her witness, and make her say coffee. But
still the girl persisted, ' wine, water, and biscuits,' which was
literally true, it not being what people talk of under the name
of a glass of wine and a biscuit, which means sandwiches, cake,
&c., but strictly wine, water, and biscuits.

1 A little diagram is given of these doors (she counted three, but
indicated more) in the letter. — S. E. DE M.

208 MEMOIR OF AUGUSTUS DE MORGAN.

1849. Now all this taking place at twenty minutes after ten, was

told to me at a quarter to eleven. When I heard that I was to
have such an account given, I only said, ' Tell me all of it, and I
will not say one word ; ' and I assure you that during the narration
I took the most especial care not to utter one syllable. For
instance, when the wine and water and biscuits came up, my
•wife, perfectly satisfied that it must have been coffee, told me how
the girl persisted, and enlarged on it as a failure, giving parallel
instances of cases in which the clairvoyants had been right in all
things bat one. All this I heard without any interruption. Now
that the things happened to me as I have described at twenty
minutes after ten, and were described to me as above at a
quarter to eleven, I could make oath. The curtains I ascertained
next day, for I had not noticed them. When my wife came to
see the room, she instantly recognised a door, which she had
forgotten in her narration.

All this is no secret. You may tell whom you like, and give
my name. What do you make of it ? Will the never-failing
doctrine of coincidence explain it ?

I find that there are people who think that the house in the
garden, the number of doors on the landing, the two gentlemen
beside myself, and ladies, the red and white curtains, the
singularity of the loops, the two so-called pianos, the lady joining
myself and one old gentleman apart from the rest, the wine, water,
and biscuits, the truth of the whole and the absence of any-
thing false, are all things that may reasonably enough arise
by coincidence, when the daughter of a poor charwoman
(twelve years old1) undertakes to tell a lady all about where
her husband is dining, in a house where neither has ever
been.

I have seen other things since, and heard many more ; but
this is my chief personal knowledge of the subject.

Yours very sincerely,

A. DE MORGAN.2

1 She was turned eleven — in her twelfth year.

a I heard all about the house and furniture, &c. , before the girl
told me what was going on. Mr. De Morgan has represented it to
Mr. Heald as occurring after, and it is quite possible that I told
him in this order. But I never heard of this letter till after his death.

—S.E.DEM.

CORRESPONDENCE, 1846-55. 209

To Sir John Herschel.

41 Chalcot Villas, March 26, 1850.

MY DEAR SIR JOHN, — I never heard the polar axis approxima- 1850.
tion. Pray throw it out in type, for it is quite a funny thing
that we beat the French after all. And the polar axis is the
only sensible diameter the earth has got. He keeps snug and
quiet, and lets all the others spin about him. I think a dialogue
might be written between the polar axis and an equatorial
diameter — quiescence against restlessness.

And so Logical systems are bothersome. I have got sixty-
four more syllogisms symbolised, in which terms take quantity
from others. As —

For every Z there is an X, which is not Y.
Some Y's are Z's.

Required the inference.

Symbol ('(().
Inference (. ( .
Some X's are not Z's.

These are really hard. To give an instance.

' To say nothing of those who succeeded by effort, there were
some who owed all to fortune, for they gained the end without
any attempt whatever, if indeed it be not more correct to say
that the end gained them. But for every one who was successful
with or without effort, at least one could be pointed out who
began, but abandoned the trial before the result was declared.
And yet so strangely is desert rewarded in this world, there was
not one of these faint-hearted men but was as fortunate as any
of those who used their best endeavours.'

I will answer for it that if this were presented to any writer
on logic without warning, he would pass it over as not self-
contradictory at least. But for all that, it contains the same
error as the following : — ' All men are animals, and some are
not.'

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Whewell.

7 Camden Street, May 25, 1850.

MY DEAR SIR, — I am much obliged to you for the continuation
of the chain of events. I see you are propagating an undulation

P

210 MEMOIR OF AUGUSTUS I>E MORGAN.

1850. through the College — a very elastic medium. I hope the matter
will not lead to a gown and town dispute — a nominalist and
realist discussion ; the gown being nominalist, or dealing in
words, while the town is realist, or, as the French say, proceeds
par voie du fait. I mean to approfound the matter when I get
an evening clear, as far as I can. I am loth to believe the text
of Aristotle to be unimportant anywhere. I suspect that he
shares the fate of Euclid in modem times — to wit, that every-
body believed him to be so near perfection as to be willing to
give him the finishing touch — to bring him quite up to it.
Ptolemy has escaped this fate ; but then Ptolemy, the real
original, was comparatively little read — his explainers traded on
their own bottoms. Compare the number of editions of Ptolemy
with those of Euclid and Aristotle.

I am sorry you are all against the Hoyal Commission. I
think that such a Commission as would certainly be appointed —
properly supported by the Universities — would much tend to
open the public eye to what the Universities really do. So very
little is known about them that something of the kind is much
wanted. If it had been a Parliamentary Commission, it would

have been another thing. You might have said ' ,l We

do our work better than you do yours, at any rate.'

Listen to my last brand-new definition of metaphysics : —
' The science to which ignorance goes to learn its knowledge,
and knowledge to learn its ignorance. On which all men agree
that it is the key, but no two upon how it is to be put into the
lock.'

Yours very truly,

A. DE MORGAN.

1 Fill up with the rpias rer/>aypa/M/zara>i/, which it would not be
canonical to write.

To T. K. Hervey, Esq.

July 3, 1850.

DEAR HERVEY, — If you read again the articles2 which have
appeared in the Athenceum, you will see that it is not merely that
as long as no proof is offered the presumptions are in favour of
M. Libri, but that he, M. Libri, has actually overturned by
documentary evidence — which you, speaking editorially, saw —
every specific accusation mentioned as capable of being brought

3 The writer's own articles in defence of M. Libri.— S. E. DE M.

CORRESPONDENCE, 1846-55. 211

against him. As far as I understand the matter— I mean the 1850.
recent matter — it is this. M. Libri not appearing is declared
guilty, par contumace. No evidence is offered in such a case ;
an indictment only, making allegations, is enough. He can still
return and stand his trial, if he should be mad enough to trust
himself in a country in which his witnesses would be prevented
from appearing by intimidation.

This is the reason why yom saw no evidence in the Gazette
des Tribunaux — because none was offered, or could be. All this
you will find on inquiring into the French law ; and you will
find that the trial and sentence par contumace are provisional. I
believe the appeal would be the real trial if he went to France.
I have never communicated with you on this matter (though I
confess I rather longed to do so), because I did not feel at liberty
to try to make use of the Athenceum in a matter in which I felt
personally interested, when I had, for reasons discussed between
us, felt obliged to withdraw from general contribution. This
would have been making a convenience of you, as J should have
thought, even if you did not.

You will remember that I was neither friend nor acquaintance
of Libri, but strongly prepossessed against him, when, as I was
going to treat the subject in the Athenceum, I demanded of Panizzi
the proof-sheets of his forthcoming defence against the allegations
of M. Boucly's report, and access, which I got, to the original
documents on which he founded his refutation. Being fully
satisfied as to his innocence, I cultivated his acquaintance ; and
since that time much collateral evidence has reached me, not only
as to his innocence, but as to his being in truth a high-minded
and earnest employer of first-rate talents and learning in first-
rate pursuits — far above what the time-serving French savans l
can imagine or appreciate. As being now proud to call myself
a personal friend of his, I am hardly so well qualified to treat
his case in a public journal as I was when my only knowledge of
him (as to his character) referred to his means of meeting the
allegations made against him.

If he should entertain the idea of demanding his trial in
France, I will do all J can to hinder such a piece of insanity.

The idea that there has been discussion of evidence in this
proceeding and conviction par contumace is very common, I find.
I have no doubt that M. Libri will take some public steps to

1 I mean those of them (a majority, not all) who are time-serving.

p 2

212 MEMOIR OF AUGUSTUS DE MORGAN.

1850. inform the English public how the matter stands. All this is
written without communication with him.

You will, of course, take care to be well informed as to the
nature of the above proceeding. That being the case, I think
you will probably find that the matter stands, to any reasonable
mind, just where it did. If you * state the position in which
the case stands,' I think it most likely that you will do nothing
which any friend of M. Libri can regret.

On casting my eye over your note, I marked the words, which
I missed at first, ' That proof has been given in a court of law ;
on what amount of valid evidence I cannot say.' Now I say that
you will be able to ascertain that there has been neither proof
nor evidence — only indictment — allegation and judgment by
default of appearance. Of course, a tender of evidence is implied
in the indictment, and, for aught I know, in the recital.

Yours truly,

A. DE MORGAN.

To the Rev. Dr. Whewell.

July 12, 1850.

MY DEAR SIR, — I have got my paper on logic out of hand,
and have begged the Pitt Press to retain one of my copies for
you, and to send it to you ; which if they neglect, I shall be much
obliged by your reclaiming, as the French say.

I have to-day got Sir W. Hamilton's system for the first time
in a full and acknowledged form. His pupil, Spencer Baynes,
has published the essay on it which got the prize in 1846 ; the
very essay, the requisites for which, sent to me, made the founda-
tion of Sir W. H.'s charge of theft. It has appendices and
a note by the arch-syllogist himself. I and Boole come in,
without being named, for a lecture against meddling with logic
by help of mathematics. Pray get this work and read it care-
fully.

My next thoughts about the subject will be on the relation
between the laws of enunciation and the laws of thought, and
particularly with reference to certain invasions of each other's
province which I imagine to exist.

I shall return to an objection of yours to my assertion that
prayer enunciates. (You may have forgotten it, but I have all
my logic correspondence together, and have been looking over
it.) You say that under such an extension a man who shuts up
his window enunciates that he is not at home. I dispute your

CORRESPONDENCE, 1846-55. 213

example as to matter, though not as to form, if you choose a 1850.
better one. Closed windows may denote death or absence, &c.
But change it thus. A man who ties a white glove on his knocker
enunciates that a child is born in the house. I believe there is
no ambiguity of meaning here. I hold that he does enunciate.
However, this is all for consideration. I remain, dear sir,

Yours truly,

A. DE MORGAN.

To Sir John Herschel.

Oct. 15, 1850.

DEAR SIR JOHN,— ....

I always advance the following as the infinitely small quan-
tity which is the most puzzling of all. All others are mental
creations, but this one seems different.

Let ib be granted that a target which must be hit can be con-
ceived. It may be the whole enceinte of the room, ceiling, floor,
walls, &c.

Let it granted that the fixing of an arrow with a mathemati-
cal point can be distinctly conceived. I don't ask for workman-
ship.

Let Abe & point in the target. Since some point must be hit,
and all are equally likely, there is some chance of hitting A — that
is, it is not impossible to hit A, which is synonymous.

But the chance of hitting a given point is certainly less than
any that can be assigned.

Therefore there does exist in the mind an idea of a quan-
tity which, not being nothing, is less than any that can be

In geometry we do not meet the same difficulty, because we
learn (how correctly I give no opinion on) to know the point, line,
surface, and solids as different species of magnitude, but belief
cannot be subdivided into different species. Is not an expecta-
tion of hitting A homogeneous with that of hitting some point
within a given area ?

I do not know whether you have returned. I hope all your
clan are well, and you yourself not disposed to give any hints
about your scientific life being terminated, as you did a while ago.

Yours very truly,

A. DE MORGAN.

From my examination room, where I shall sit two hours and
a half more, without anything to do except just what I please,

214 MEMOIR OF AUGUSTUS DE MORGAN.

1850. so don't say I write in a hurry. University College, London,
October 5, 9h. 30ra. A.M. + the error of my watch, 1850, the last
year of the first half of the nineteenth century, let who will call
it the first year of the second half.

To Rev. W. Heald.

7 Camden Street, Aug. 18, 1851.

1851. DEAR HEALD, — It has become quite the regular thing for the
depth of vacation to remind me — not of you, for anything that
carries my thoughts back to Cambridge does that, — but of in-
quiring how you are getting on, of which please write speedy word,
according to custom, once a year. For myself I have nothing
particular to report. My wife and seven children are all at
Broadstairs— as they were when I last wrote — so that the in-
formation is that they really came back in the interval. I pre-
sume you really have not come to town to see the Exhibition,
supposing that you would surely have let me know. Are you
not coming ? Whether I with my short sight should know you
again after a quarter of a century, plus a quarter of a year, is
a problem I should very much like to solve. But you seem
determined not to furnish the data.

It seems to me that I must have written to you just before
the Pope made his onslaught, which has occupied people ever
since. I remember, soon after the Catholic Emancipation Bill
was carried, reminding a friend of mine, a Catholic barrister,
that that Bill was an experiment — a very proper experiment —
one it was disgraceful not to have tried before ; but still an
experiment, in trial of whether it really was practically possible
that people with any foreign allegiance, call it spiritual or any-
thing else, could permanently exercise the rights of citizenship
here. The occasion was his speaking very seriously and earnestly
of it being a matter of discussion among the Roman Catholic body
whether they had not in right of the E. Bill a right to proceed
in Chancery against the Colleges at Oxford and Cambridge, which
were founded on condition of praying for the souls of the
founders, to make them either so pray or give place to those who
would. It gave me at the time (the man being neither a san-
guine man nor a fool) a fixed idea that from the very time of the
Emancipation Bill passing there was a settled purpose of legal
invasion. And I have never since faltered in the opinion that,
be it settled how it might, the time would come when, on poli-
tical grounds, the question would be reopened ; and I prophesy it

CORRESPONDENCE, 1846-55. 215

now within a few years — that is, I foretell a discussion whether 1851,
the mere circumstance of owning a foreign power in any sense
and manner whatever is or is not to be an absolute disqualifica-
tion from even voting for a member of Parliament.

I have just heard from Arthur Neate, who with a wife and two
children is doing near Alvescot what you are doing at Leeds,
saving that his two parishes put together would not soul a tenth
part of the bodies in your one. His father and mother are still both
alive, though both very old and failing. Of other people I know
nothing, I mean of your and my contemporaries. It is long since
I have seen any one. I met Farish the other day, old and deaf.
I am not sure I do not remember his father looking younger.
I dare say you, like myself, look not very old of your age, for we
both looked older than we were at Cambridge, so that if you have
a provincial synod, you will hardly look ancient enough to be
one of the patres conscripti. But you have not a Bishop, I am
afraid, who will bring your part of the world abreast of H. Exon.
Peace be with him, I was going to say, but I know she won't.

Resolve me this. If our old friend P were alive, would

he be Puseyite or not ? The only one Cambridge man that I ever
annoyed by taking it for granted that he was not Puseyite when
he really was a strong one, was a man of whom I could tell the
following story, but I won't (that is to say, you are not to repeat
it, for it might get round).

I knew him at Cambridge when he was a great friend of

B , whom you perhaps have met at Neate's. A few days after

he was ordained he came to see me, and being fresh off the anvil
he could not but talk a little theology. So as he got over the
ground he came at last to the following sentence, which brought
him up all standing, as they say at sea — you are to imagine a
sudden start of recollection at the *, I having stared at f : —
' But you see those Catholics made a sacrament of baptism
f *. Oh, by-the-bye, so do we.' Fact, upon my honour; no
exaggeration. But he is now with the Bishop of Exeter on the
point.

I wish you would do this : run your eye over any part of those
of St. Paul's Epistles which begin with IlavAos — the Greek, I mean
— and without paying any attention to the meaning. Then do
the same with the Epistle to the Hebrews, and try to balance in
your own mind the question whether the latter does not deal in
longer words than the former. It has always ruu in my head

216 MEMOIR OF AUGUSTUS DE MORGAN.

1851. that a little expenditure of money would settle questions of
authorship in this way. The best mode of explaining what I
would try will be to put down the results I should expect as if I
had tried them.

Count a large number of words in Herodotus — say all the
first book — and count all the letters ; divide the second numbers
by the first, giving the average number of letters to a word in
that book.

Do the same with the second book. I should expect a very
close approximation. If Book I. gave 5-624 letters per word, it
would not surprise me if Book II. gave 5'619. I judge by other
things.

But I should not wonder if the same result applied to two
books of Thucydides gave, say 5713 and 5728. That is to say,
I should expect the slight differences between one writer and
another to be well maintained against each other, and very well
agreeing with themselves. If this fact were established there, if
St. Paul's Epistles which begin with IlavXos gave 5*428 and the
Hebrews gave 5*516, for instance, I should feel quite sure that the
Greek of the Hebrews (passing no verdict on whether Paul wrote
in Hebrew and another translated) was not from the pen of
Paul.

If scholars knew the law of averages as well as mathema-
ticians, it would be easy to raise a few hundred pounds to try
this experiment on a grand scale. I would have Greek, Latin,
and English tried, and I should expect to find that one man
writing on two different subjects agrees more nearly with himself
than two different men writing on the same subject. Some of
these days spurious writings will be detected by this test. Mind,
I told you so. With kind regards to all your family, I remain,
dear Heald,

Yours sincerely,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, Aug. 29, 1852.

1852 -M-Y DEAR SIR JOHN, — . . . Induction seems to lead to the

conclusion that an astronomer who is Master of the Mint gets
some odd mode of chronology. The first cut a great piece off
the beginning, the second will cut a great piece off the end, and
doom us all to be squabashed in 1865. The next, I suppose,
will cut a great piece out of the middle, which will be the most

CORRESPONDENCE, 1846-55. 217

singular job of the three. What if he should say that the 8th, 1852.
9th, and 10th centuries never existed ? I wish they hadn't.

When De Gasparis gets his next planet, he and Hind will be
six of one and half a dozen of the other. Do you mean to say that
just as we have got the place snug, drained, lighted, and electro-
wired and railed, that as soon as we shall jnst have learnt to have
an idea of behaving to each other like people whose posterity
may in time be Christians, we shall have to become fossils, and
megatheriums, and such like, for smarter chaps than ourselves
to write books upon ? I will never believe it till I see it, and
then only half. Why, it is only just four hundred years since
printing was invented. A book, with ordinary care, will last a
thousand years. It is astonishing what good condition those of
1480 are in, even after a course of bookstalls. Surely the
nature of things is to live their lives out. . . .

Yours truly,

A. DE MORGAN.

To Dean Peacock.

7 Camden Street, Aug. 30, 1852.

MY DEAR SIR, — . . . All I know about Young personally is,
that one evening in 1828, when I first pushed my nose into the
scientific world, I was presented to Young, Davies Gilbert, and
Wollaston.

Wollaston said, when I was introduced as Professor of
Mathematics in the University of London, ' Are they to have
a Professor of Mathematics ? ' I told him they had one, and
that I was he. Nothing more passed. Young lifted his eye-
glass, and made his bow serve the double purpose of acknow-
ledging the introduction, and bringing his eyes to the lenses.
He made me certain that he saw me, and impressed me with an
idea from his manner that he was fine. Perhaps he was only shy
— shyness takes every other form to avoid its own.

Davies Gilbert was the only one of the three who had the
manners of a man of the world. I believe I never saw the two
first again.

I never knew till many years afterwards that I was well
acquainted with some members of Young's family. His brother,
Robert Young, was a Quaker, who married, as I was told when
a boy, a lady, who was not a Quakeress, and was disowned
by the sect. This lady was a most intimate friend of my
mother, and Robert Young is one of the earliest persons I can

218 MEMOIR OF AUGUSTUS DE MORGAN.

1852. remember. He was a banker, and something else, I think, at
Taunton ; he afterwards went to Bristol, and was in some
business. When I was sent to school near Bristol in 1820, 1 was
consigned to R. Y., who especially warned me not to walk
in my sleep, as there were no leads outside the window — they
had been removed. The consequence was that, though I never
walked in my sleep before or since that I remember, I was
awakened by the wind blowing on me, and found myself before
the open window, with my knee on the lower ledge. I crept
back to bed, leaving the window open, and the family, being
alarmed by the noise, came into my room, found me asleep and
the window open ; so that as their fenestral logic did not reason
both ways, they forgot that the leads were not there, and
searched the whole house for thieves. Long afterwards I met
R. Y. in Stratford's room, negotiating about some papers of Young
referring to the R. A., and there 1 learnt whose brother he was.
John Young, I am pretty sure, was a brother, if not a cousin.

You will remember that it has been said that Somersetshire
has been very deficient in great men ; and the exceptiones fir-
mantes regulam have been Roger Bacon and John Locke. It is
time that Young should make a third.

I do not know whether you have all your information about
Young's family. If you want any inquiries, I have some old
friends still at Taunton, and will ascertain what you want.
Milverton, Young's birthplace, is a few miles from Taunton.

I hope you will not overwork yourself; and remain, dear
sir,

Yours sincerely, &c., &c.

To Rev. W. Heald.

7 Camden Street, Sept. 11, 1852.

DEAR HEALD, — I make my annual renewal of correspondence,
which I have got into a habit of doing when my wife and chil-
dren leave town. They have gone this year to Herne Bay — not
so far from London as last year, when they were at Broadstairs.
By the way, a scientific friend of mine directed to me at Broad-
stairs, near London, when near Ramsgate would have been
nearer the mark. On my asking him what he meant, he said he
remembered some very broad stairs down to the river just below
London Bridge, and he had a vague idea that they were the
Broadstairs. Doubtless there are very broad stairs there-
abouts. This put me on asking the etymology of Broadstairs,

CORRESPONDENCE, 1846-55. 219

and I find that by stairs are meant passes down the cliff — 1852.
natural passes. What are you and yours doing ? Do not fail
to tell me all about yourself, without my drawing it all out of
you by specific questions. By the way, is the Mr. Prickett I see
in the papers on whom somebody has been forging, any relation
of our old friend ? Of myself and family, nothing particular.
We're all about a year older since I last wrote to you. I have
been looking over and sorting correspondence of more than
twenty years, and I do not see any particular marks of growing
old in your handwriting. Are yon not seriously contemplating
the necessity of calling yourself 50 years old if things go on as
they have been doing ? By my estimate of your age, you will
be saying 49 next birthday. I am 46 past, but, between our-
selves, 1 have two of my wise teeth still to cut.

I looked out in the papers to see if you were moving or
seconding anybody into Convocation, or being done the same to
yourself. What do you think about the revival of Convo-
cation ? Did it ever happen to you to study any of their old pro-
ceedings ? Where are they all ? I remember that, a propos of
the Easter Question, I wanted the acts of the Convocation
which met next after the Restoration ; but, though Maitland
did all he could for me in the Archbishop's library, the return
was non est inventus. Maitland is now settled at Gloucester
again ; what doing I don't know. He is now well stricken in
years : thirty-five years ago he had completed Cambridge, had
been educated for the bar and practised, had got sick of it, had
retired, had married, and sat himself down comfortably at
Taunton, next door but one to his father, my mother being the
intermediate. I doubt his being less than thirty-five then, so that
he must be seventy, I should say, at least — and he looks it. At
Taunton he used to collect books and play the fiddle, and my first
acquaintance with Haydn's twelve was made through him and
his sister-in-law. He also bound his books himself, and he bound
the upright of his bookshelves, and lettered them ' Maitland's
Works,' at which his friends used to pull with great curiosity to
know what he had written ; and those who did not pull thought
it very odd that he should write so many thin volumes on
equidistant subjects.

I wrote you a note to see if you knew who A. E. B. of Leeds
was. I suppose you do not. He shines in a publication called
Notes and Queries, which I take in, and find a great deal of mis-
cellaneous in it. Did you know James Parker, the vice-chan-

220 MEMOIR OF AUGUSTUS DE MORGAN.

1852. cellor, who is jnst dead ? He was a great friend of Farish's. Of
our old friends I know but little. Neate is thriving. His father
and mother are still living, which few men of forty-five or
thereabouts can say. He vegetates, I am afraid ; his parishes are
not very populous, and though he does everything in the way of
looking after them, his grasp is not full. For aught I know
your parish would make fifty of his in number of souls.

August 31. — I see to-day that Maitland has published a new
ittle book, combining several tracts with mediaeval pictures.

I bought an auctioneer's lot the other day for one book, and
found, among the rest, Hone's Trials, which I had never read
through, though, when I was a boy, I had my curiosity greatly
whetted by the sharp way in which they were kept out of my
sight, while I was admiring the presence of mind of the defend-
ant, and the circumstance of a man not regularly educated sticking
logically to one point (a great rarity), namely, that the non-pro-
secution of parodies in favour of ministers proved that the ani-
mns was political, and that religion was a pretext. There came
into my head a long- for gotten story told me by Place, the cele-
brated political tailor, more than twenty years ago, which shows
that Cobbett, with all his pen-assurance, had not the nerve of poor
Hone. When Place and some friends went to consult with
Cobbett about his defence to the action for seditious libel which
was coming on (on which he was convicted and imprisoned),
Place told him that if he wanted to escape conviction he had
only to produce the letters which public functionaries had written
to him on points of his paper —bar, judges, the Speaker of the
H. of C., &c. ; that if he did this he would prove that be was not
considered a common libeller even by the friends of Government ;
and that having thus made a locus standi he could deal with the
specific charge as a fair political comment, and compare it with
others. Cobbett was hardly able to speak of this plan, so great
was his agitation at the boldness of producing these letters, which
would have made a great sensation, for there were very curious
private applications for his good word. He did not dare to do it,
was regularly browbeat by the judge, even in what he did ven-
ture, and was convicted. Such is the difference between ^en-
courage and tongue -courage.

Pray present my best compliments to Mrs. Heald. I am sorry
I cannot say remembrances. There ought to be a prospective mode
of address. It would sound very odd to say, in the case of a
person whom the writer had not seen, * Present my most san-

CORRESPONDENCE, 1846-55. 221

guine anticipations;' but what would be so odd as 'compli- 1852.
ments ' if used for the first time ?

Surely the time must come when the vortex of London will
suck you in for a few days. In the meantime let us speculate
on the question whether we should know each other if we met
in the street after twenty-seven years of non-visual intercourse.

Yours most sincerely,

A. DE MORGAN.

To Rev. W. Heald.

7 Camden Street, July 1853.
* * .* * * *

I remember giving you my experience in regard to clairvoy- 1853
ance. I will now tell you some of my experience in reference
to table-turning, spirit-rapping, and so on.

Mrs. Hayden, the American medium, came to my house, and
we had a sitting of more than two hours. She had not been
there many minutes J before some slight ticking raps were heard
in the table apparently. The raps answered by the alphabet
(pointing to the letters on a card), one after the other (a rap or
two coming at the letter), to the name of a sister of my wife,
who died seventeen years ago. After some questioning, she
(I speak the spirit hypotheses, though I have no theory on the
subject) was asked whether I might ask a question. ' Yes,'
affirmative rap. I said, ' May I ask it mentally ? ' * Yes.' ' May
Mrs. Hayden hold up both her hands while I do it ? ' ' Yes.'
Mrs. H. did so, and in my mind, without speaking, I put a
question, and suggested that the answer should be in one word,
which I thought of. I then took the card, and got that word
letter by letter — C HESS. The question was whether she
remembered a letter she once wrote to me, and what was the
subject? Presently came my father (o&. 1816), and after some
conversation I went on as follows : —

4 Do you remember a periodical I have in my head ? ' ' Yes.'
' Do you remember the epithets therein applied to yourself ? '
* Yes.' ' Will you give me the initials of them by the card ? '

1 This is true. About ten or fifteen minutes elapsed after we sat
down before the raps came ; but Mr. De Morgan has not mentioned in
this letter that for a few, perhaps five minutes, we sat waiting for them.
On his leaving the room they were heard at once, and went on when
he returned.— S. E. DE M.

222

MEMOIR OF AUGUSTUS DE MORGAN.

1853. * Yes.' I then began pointing to the alphabet, with a book to
conceal the card, Mrs. H. being at the opposite side of a
round table (large), and a bright lamp between us. I pointed
letter by letter till I came to F, which I thought should be the
first initial. No rapping. The people round me said, 'You
have passed it ; there was a rapping at the beginning.' I went
back and heard the rapping distinctly at C. This puzzled me,
but in a moment I saw what it was. The sentence was begun
by the rapping agency earlier than I intended. I allowed C to
pass, and then got I) T F O C, being the initials of the con-
secutive words which I remembered to have been applied to my
father in an old review published in 1817, which no one in the
room had ever heard of but myself. C D T F O C was all right,
and when I got so far I gave it up, perfectly satisfied that some-
thing, or somebody, or some spirit, was reading my thoughts.
This and the like went on for nearly three hours, during a great
part of which Mrs. H. was busy reading the ' Key to Uncle Tom's
Cabin,' which she had never seen before, and I assure you she
set to it, with just as much avidity as you may suppose an
American lady would who saw it for the first time, while we
were amusing ourselves with the raps in our own way. All this
I declare to be literally true. Since that time I have seen it
in my house frequently, various persons presenting themselves.
The answers are given mostly by the table, on which a hand or
two is gently placed, tilting up at the letters. There is much
which is confused in the answers, but every now and then comes
something which surprises us. I have no theory about it, but
in a year or two something curious may turn up. I am, how-
ever, satisfied of the reality of the phenomenon. A great many
other persons are as cognizant of these phenomena in their own
houses as myself. Make what you can of it if you are a philoso-
pher.

Now I must shut up. Give my best regards, &c.

Yours very sincerely,

A. DE MORGAN.

To Professor Michael Foster.

November 15, 1853.

University DEAR SIR, — You have asked me for a sketch of my chief

Examina- objections to the system pursued in the University of London.

lions. This is a matter into which I have not time to enter in great

detail ; nor would it be necessary. I have always looked forward

CORRESPONDENCE, 1846-55, 223

to the time when the graduates of the University would them- 1853.
selves feel that their Alma Mater will not take its proper place
among the Academies of Europe until its requisitions are based
upon higher views of education than appear to have prevailed at
its foundation. I say at its foundation, not among its founders ;
for the first institution preceded by several years that revival of
serious thought upon mental subjects in which we now live, and
which is far from having attained its full development.

With great respect for many who have been and are mem-
bers of the Senate, I do not feel the slightest diffidence in
opposing my opinion to the results of their collective delibera-
tions. No man who has thought on a subject for a quarter of a
century, with daily power of testing his opinions, need fear to
oppose himself to a system which has not emanated from one
mind. Solomon said that in the multitude of councillors there
was safety ; safety, not wisdom. A numerous body always
compromises, and never works out a sound principle without
limiting its application by considerations drawn from the ex-
pediency of the moment ; practicability is the word, freedom
from present difficulty is the thing.

The plan of the Universities of the Middle Ages, to which in
a great degree we owe both the thought and the operative ability
of the last two centuries, rested on a simple principle, which
stood ready for any amount of development which its own good
consequences might make possible. All existing knowledge, the
pursuit of which could discipline the mind for thought and
action, was collected into one system, and declared to be avail-
able for the purpose of a University. And in this manner reason,
language, and observation were cultivated together, Every
means was employed for forming the future man in his relation
to himself, to other men, and to the external world. The worst
thing, if not the only thing, that can be said against them is,
that at some periods they thrashed the chaff after the corn had
been beaten out. The worst thing that can be said against their
successors in England is that they have not sufficiently allowed
the development of the old principle in reference to branches of
knowledge which progress has converted into disciplines, and
that, each in its own way, they have given undue prominence to
one of the ancient disciplines.

The sciences of observation occupied rather a subordinate
place, because in the disciplinatory sense they had attained but
little efficacy. To which it is to be added, that the very wants

224 MEMOIR OF AUGUSTUS DE MORGAN.

18-53. of daily life, in a rude state of co-operative power, made daily
life itself snch a discipline of observation as we have now no
idea of. Every savage has all the knowledge of his tribe in
matters to be drawn from observation and applied in practice.
The man of the fifteenth century, much nearer to the savage
than ourselves, had a considerable share of it. The man of our
day has just as little as he pleases, and no more than his indi-
vidual temperament and opportunities may lead him to acquire ;
the temperament not being fostered by education, and the oppor-
tunities being mostly subsequent to it.

The great point, then, in which the old -Universities ended by
ignoring the progress of the world around them, the great point
on which it might have been the privilege of a new one to show
them that the world could teach them something even on the
fundamentals of education, was the neglect of the discipline of
observation, of language as connected with it, and of inference
as immediately derived from it. And how has the University
of London fulfilled its especial mission ? It has granted the
existence of the deficiency, proclaimed its own intention to
provide a remedy, and set its alumni diligently to work to read
words and to look at diagrams about the way in which other
people have used their eyes and their bands. This is no ex-
aggeration. Because observation of phenomena had been neg-
lected, and ought to have been a part of all sound discipline,
the University of London demanded of its candidates a knowledge
of the manner in which those who have seen things for them-
selves describe them to others.

For example, a candidate for the B. A. degree is required,
in addition to matters which enter the ancient disciplines,
to be examined in animal physiology. And he may pass this
examination without knowing more from his own observation
of what is under the skin of any animal, than he learns from
the words of a book or the lines of a drawing, which no one
can understand except he be familiar with the original object.
I will venture to say that a large majority of those who
have passed the examination in physiology know nothing about
the interior of the body from their own observation except that
blood follows a cut in the finger. I appeal to the examiners
whether it be not as I say, and whether the answers given do
not clearly show it.

Thus, for the first time in the annals of liberal education, a
University has proclaimed that more words, as words, with no

CORRESPONDENCE, 1846-55. 225

meaning attached, are a worthy discipline. In learning languages 1853.
words are things ; they are the things to be studied, and the
student compares the unknown with the known, the strange
language with that which he has spoken all his life. In the
exact sciences the notions treated of are present and living
realities. In the common branches of physics the student has a
daily knowledge of the species of phenomena which he is to
study in their systematic relations ; he knows air and water, and
his stick is a lever. But in the physiology of the University of
London he has only words descriptive of what he neither knows
nor can know by words alone ; if there be any shadow of ad-
vantage to be gained, it is that species of advantage which he
gains to better purpose from ordinary physics. The great thing
wanted, the training of the faculty of observation in connection
with language and reason, is wholly left out of sight.

Will it be replied that students cannot dissect ? that they have
no opportunities, that they have no skill ? that without such
teaching as they cannot get, and such time as they cannot
give, their researches into the textures would be of as much
avail as those which are made with a carving-knife upon the
roast or boiled joint ? I freely admit it all ; but I deny the con-
clusion that therefore the University of London should supplant
observation by reading. I say nothing is proved except that
physiology is a very unfit subject for the purpose, as seems to
me clearly proved on other grounds.

The proposal for reform which I should submit is that actual
examination upon natural objects should be a part of the trial
for the B.A. degree ; and that the objects should be of the vege-
table world. These are accessible to all ; and the matter to be
tried should be, not whether the student has this or that amount
of acquirement, but whether he has gained the powers of
observing for himself, and stating and reasoning of the results.
There are various reasons why vegetable structure is better fitted
than animal for the commencing observer ; but it is enough that
the newly gathered plant is always within his reach, and that
the newly killed animal is not.

The next point I will mention is that of the examinations for
honours. There are two systems in this country, — that of
Oxford, in which the candidate for classical honours is examined
against his subject ; that of Cambridge, in which the candidate
for mathematical honours is examined against his competitors.
At Oxford, his class determines his qualification ; at Cambridge,

Q

226 MEMOIR OF AUGUSTUS DE MORGAN.

1853. his place determines whether he is above or below any given
competitor. A.t Oxford his mind may, though not without
certain wholesome restraint, develop itself in reading and
thought dictated by its natural bent. At Cambridge the exami-
nation realises the bed of Procrustes. The Oxford system has a
tendency to develop the useful differences between the varied types
of human character. The Cambridge system is an unconscious
effort to destroy them. I shall not be suspected of any original
bias against the Cambridge system. I once thought that the
race for the place in the list was a valuable part of that system,
but I have slowly arrived at the full conviction that the Oxford
plan is greatly superior. The system of private tutors, the drill
in writing out, and the mode in which so many of the elementary
books are got up, are well worthy the attention of all who are
interested in the subject of this letter. They are the natural
consequences of the personal competition for honours ; and if
ever the number of candidates in the University of London
should bear any considerable proportion to that in the University
of Cambridge, the same cause will produce the same effect. I
hope this subject will receive some attention. Why, because
political tendencies have thrown the University of London
almost entirely into Cambridge hands at the outset, should all
that is from Cambridge be received as of course, and without a
discussion of what is to be found at Oxford ?

Probably it will be objected that the medals and honours
cannot be awarded without a competitive examination. To this
I answer that the existence of medals and scholarships is of
very small importance compared with that of the evils I have
alluded to. If I am right, they had better be abolished than
allowed to introduce the evils of competition into the main
examinations for honours. And the natural consequence would
be that they should be given, not for general proficiency, but on
special grounds, to be tried some time after the elementary
career has closed.

My view of the advantages of a liberal education is most
assuredly not peculiar to myself. Let it be supposed that the
former student has forgotten everything, that not a word of
Latin is left, and not a proposition of Euclid. What remains to
him ? If little or nothing, then his education has not deserved
its name. But if, in spite of the loss of all that acquirement
which he has had no daily need to recall, he be a man of trained
mind, able to apply vigorously, to think justly, to doubt dis-

CORRESPONDENCE, 1846-55. 227

creetly, and to decide wisely, he has been well educated, and the 1853.

loss of the positive knowledge which I suppose him to have lost

is comparatively a small matter. I do not underrate knowledge ;

I would educate for it, even if it gave no powers ; but I am sure

that if we take care of the habits, the acquirements will take

care of themselves.

Throughout the whole of the requisitions runs a tone which
would give any one the notion that the study demanded is sought
only for its results, and that it will be tested only by the know-
ledge of results shown. I look at the programme of the mathe-
matical propositions required, and I find the implication that as
long as a certain list of truths is known, it matters not how. I
admit that the examiners by setting this list at defiance, by pro-
posing questions which try the knowledge of principles, and
which necessarily require them to travel out of the list, have done
much to neutralise its evil tendency. But I cannot suppose the
necessity for a complete alteration is thereby done away. We
are informed that the principal properties of triangles, squares,
and parallelograms (when did the square cease to be a paral-
lelogram ?) are to be treated geometrically. Among the principal
properties of parallelograms are those of similar parallelograms ;
their study involves a doctrine of proportion. But only the first
of the six books of Euclid are demanded. Must similar paral-
lelograms be treated by what is called a geometrical theory of
proportion? If not, how are the principal properties of
parallelograms to be treated geometrically, as demanded? If
yes, what is that geometrical theory of proportion, other than
Euclid's, so well known that it may be trusted to implication ?
The only proportion alluded to in any part of the list is alge-
braical proportion, which, as usually understood, is the doctrine
of the ratios of commensurable quantities, expressed by letters,
with either every possible amount of gratuitous assumption
about incommensurable quantities, or else a total refusal to
consider them.

Might not what we may well hope, and what I am inclined
to believe, will be the greatest University founded in the nine-
teenth century dare to promulgate definite views on the mode
in which study should be conducted, its ends, its uses, and the
proofs of its efficiency ? Is it not the duty of that University to
make it apparent that she receives and cherishes the sound
principle so long maintained by her predecessors without pledg-
ing herself to the abuses which time and negligence have allowed

228 MEMOIR OF AUGUSTUS DE MORGAN.

1853. to creep in ? I hope the graduates will show that their colleges
have trained them to ask these questions. If they be not asked,
and asked to good purpose, the University may gain a parlia-
mentary voice, but it will not gain the respect of that highly
educated world to which the common sense of common people
teaches them to look up for opinions on the higher education.
And the old institutions which are rousing themselves into
activity will have it delegated to them, a century hence, to teach
the University of London what it was hoped by some the
University of London would teach them.

I am, dear sir,

Yours truly,

A. DE MORGAN.

To Admiral Smyth.

7 Camden Street, January 5, 1854.

1854. MY DEAR ADMIRAL, — You probably know why your note has

remained unanswered. I and Mrs. De Morgan are just beginning
to recover the shock it has given us. Your sheets may come as
usual if you have any to send.

I congratulate you on the news you conveyed to me, though,
having mislaid your note, I cannot remember the name. You
have twice had to bear a loss similar to mine, and I hope you
will depart yourself in the course of nature before the distant
time comes when you would have to face it a third time.

If you have anything to contribute or to suggest for the
Annual Report, now is the time. Our kind regards to Mrs.
Smyth and the young ladies.

Yours sincerely,

A. DE MORGAN.

To the Rev. Dr. Whewell.

January 24, 1854.

My DEAR SIR, — Your book on the ' Plurality of Worlds '
reached me at a time when I could only throw it by for better
days, and I believe it would have remained on one side as an
anonymous attempt to prove what every one believed — without
knowing anything about the matter — if I had not been told,
casually, that you were the author, and that the title ought to
have been ' On the Singularity of the World.' Accordingly,
knowing whom to thank, I thank him ; and learning that the
argument is singular, I read the book.

CORRESPONDENCE, 1840-55. 229

I have always held that when the phrase ' there is a good ] 354.
deal to be said on both sides ' applies, it means that we do not
know much about the matter. Your book is a converse instance ;
that when we do not know much about the matter there is
always a good deal to be said on both sides. Not that I mean
to give up the poor dear lungless lunarians, or the jovial cinder-
sifters, altogether, quite yet. I admit the argument from time
to space ; but, granting that the human world is only d t out of
t of the whole of time existence, we may grant it to be d s out of
s, of space existence ; and all the stars and planets may be in
their several progresses from — oo to +00, and every one at a
different part of it, with at least the chance of two given ones
being within m of each other, only m =ao — ( — oo). And this
on the supposition that there is but one kind of progression ; it
being more likely, however, that this progression is infinitely
varied in space, so that, instead of diminishing the immensity
of creation — as usually taken — namely, for one time, the idea of
one mode of existence infinitely varied in space, you have made
prominent a system of triple entry, time, space, law of pro-
gression.

I find in your book the germ, or more, of a notion which I
have had for twenty years — and which may have occurred to
many others, and probably has. I have been laughing all that
time in the sleeve at the clergy, for not seeing that the infidel
geology, as they call it, is in truth the most unanswerable proof
of supernaturalism that ever was propounded. Between an un-
intelligibly self-existent Creator, and an unintelligibly self-
existent order of things — self-reproductive natura rerum, — my
reason never saw a priori choice ; not having the slightest idea
which of two wholly inconceivable things was most conceivable.
But the straightforward impossibility of human existence at
some calculable time brings us to the alternative of an absolute
creation — or the growth of some lizards or fishes into men —
through various stages. I do not read controversies about the
pros and cons, of the Book of Genesis, and this argument may for
aught I know be common ; but it never oozed into any conversa-
tion in my hearing, though I have frequently looked out for it
when I heard the orthodox and the heterodox fighting about the
matter.

Yours very truly,

A. DE MORGAN.

230 MEMOIR OF AUGUSTUS DE MORGAN.

To Rev. Dr. Whewell.

May 21, 1854.

1854. MY DEAR SIR, — I have to thank you for the dialogue. If

you deny a plurality of worlds I presume you admit a plurality
of opponents — to judge by the letters.

You seem to be expressing your anti-pluralism more posi-
tively than before. Your work seemed to say — don't be so sure ;
your dialogue seems to maintain something more like a leaning
to the other positive conclusion. I suppose you will not object
to the conclusion that the stars either are inhabited, or that they
are not. This is mine, with a leaning to the affirmative of this
kind : — Let it be granted that each planet has upon it, or in it, or
around it, some things which have a destiny of their own, for
which they might be conceived to exist independently of the
other planets or stars. These things I should call inhabitants of
that planet, but whether conscious or unconscious, intelligent or
•unintelligent, &c., &c., I could have no opinion. But I cannot
divest myself of the idea that they have uses independent of us —
and these uses are inhabitants. I strongly suspect that, to use
law phrases, these uses are also trusts, and therefore suppose
responsibilities.

Yours very truly,

A. DE MORGAN.

To Admiral Smyth.

7 Camden Street, July 16, 1854.

MY DEAR ADMIRAL, — Here you see the balance of blue queen's
heads forwarded to me on a special service. I hope a larger
proportion of Napier's blues will find their way home again from
the Baltic.

All is going on well as to the Government proceedings.1 We
shall not be stirred these ten years, I augur. You know the
story of the birds in the nest listening to the farmer plotting
how to cut the corn. Now Government is a man who cannot
work for himself. He acts through people who report. Deep
calleth unto deep — that is, one office reports to another, and the
other refers back, and then they consider, and red tape becomes
grey before they have settled how to proceed. And if you then
give them six months' start, and set a snail after them, the

1 Referring to a proposed removal of the Astronomical Society from
their rooms at Somerset House.

CORRESPONDENCE, 1846-55. 231

snail beats them by a thousand lengths ; and then there is a 1854.
change of ministry and a new report to 'my lords,' and 'my
lords ' make a minute which means in time a year, and so on
ad infinitum.

Kind regards all round.

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Whewell.

October 27, 1855.

MY DEAR SIR, — M. Biot presses for the meaning of Newton 1855.
buying a supersedeas. He wants to give it in a forthcoming
article. (Brewster, vol. i. p. 18.) Could you ask any one in
college to see what it may have meant ? I am pretty sure no
such thing was for sale in college in my time, for freshmen or
any other.

Excuse my troubling you again. The world has so passed by
that I am not sure I know the name of any office-bearer in
college. I have only an indistinct remembrance that Prof.
Sedgwick is Vice-Master.

I told Biot that China ale was tea, and reinforced it by tell-
ing him that water was often called Adam's ale in England.
This, he says, has amused the French philologers very much.

Pray come to the rescue of a Frenchman in a fix about a
college phrase. I must send the French philologers the phrase
Henry Soph.

Yours very truly,

A. DE MORGAN.

To Sir J. Herschel.

November 10, 1855.

MY DEAR SIR JOHN, — I am glad to see your signature, failing
more, and also that you are in pretty good spirits. We shall see
you come out in chemistry yet, with the discovery of a new prin-
ciple, Uncommonly-impossible-to-get-ine, obtained by treating the
singular Takes- a- week's- cooJcingic Acid with all the salts in suc-
cession of your new metal Describa~ble-in-six-foliopagesium.

I shall not bother you with the proofs of your memoir.1 I
shall respect the text as if it were Horace — and there are no

1 Memoir of Francis Baily.

232 MEMOIR OF AUGUSTUS DE MORGAN.

1855. lections that I am aware of — and I shall add a few editorial n oes ;
one must notice the new moon-bobbery which has upset the
eclipse of Agathocles and every other, and perhaps some other
little matters. I made a few additions to the biography in a
subsequent Annual Report, which I shall append, but not incorpo-
rate. You shall have revises — not to correct, but to protest
against, pro re nata, and your protests shall meet with more
attention than such things usually meet with.

The Sheepshanks inscription is now in Whewell's hands.

Tours very truly,

A. DE MORGAN.

233

SECTION VIII.

1856-65.

MY mother-in-law died after a long illness this year, to 1856.
the great sorrow of her three sons. Though there was Mr. De°
great difference of opinion, chiefly on doctrinal matters, Bother! S
between rny husband and herself, there was strong mutual
affection, and some resemblances of character. He shared
with her the quality which he used to find troublesome
when he lived in her house ; namely, anxiety to a morbid
degree about those she loved when they were out of her
sight. If he came home an hour later in the evening
than she expected, she conjured up all kinds of terrible
accidents which he might have met with. One reason
of this, on Augustus's account, was his want of sight on
the right-hand side. He was very like her in this morbid
anxiety, so that those who left the house in the evening
had to be punctual in the time of their return if they
wished him to be easy. From his mother he inherited his
musical talent, and most probably his mathematical
power, for she was the granddaughter of James Dodson,
the author of the Mathematical Canon, a distinguished
Mathematician, the friend of Demoivre, and of most other
men of science of his time, and an early F.R.S. But he
was Mathematical master at Christ's Hospital, and some
of his descendants seem to have thought this a blot on
the scutcheon, for his great-grandson has left on record
the impression he had of his ancestor. When quite a boy
he asked one of his aunts * who James Dodson was ; ' and
received for answer, ' We never cry stinking fish.' So he
was afraid to ask any more questions, but settled that

234 MEMOIR OF AUGUSTUS DE MORGAN.

1856. somehow or other James Dodson was the ( stinking fish '
of his family ; and he had to wait a few years to find out
that his great-grandfather was the only one of his
ancestors whose name would be held deserving of record.
My husband also inherited his love of a city life from
his mother, who declared that a night in a country house,
with 'the dreary trees moaning all round,' made her
sleepless.

Mrs. De Morgan's death occurred while she was living
in the house of her second son, Mr. George De Morgan,
the barrister and conveyancer. My husband, of course,
visited her almost daily, and was struck with the reality
of her conviction, constantly asserted, of the presence of
Jesus Christ. He spoke to me of the frequency of this
appearance, or supposed appearance, to the dying, and
wished that the instances should be always carefully
recorded.

Mrs. De Morgan was one of eleven children and nine
daughters of Mr. John Dodson, of the Custom House.
Eight of the daughters married officers of either the
Military or Civil service in India. At the time of her
death there was living, besides her sons Augustus and
George, Campbell Greig De Morgan, who was Senior
Surgeon to the Middlesex Hospital — a man much beloved
and highly distinguished in his profession. He survived
his brother Augustus four vears, dying in 1875.

Dislocated A few days before our return from Eastbourne in the

autumn, I was startled by receiving a long letter from my
husband, written in pencil and in the middle of each page.
He always wrote every day, but it was often not more
than to ask after me and the children, and to tell me
whom he had seen, with occasional information about the
cat or the canaries. This pencil letter was a dramatic
description of how he had the day before fallen off the
ladder in his library and dislocated his shoulder; how
the doctor had been fetched and had replaced the

DECIMAL COINAGE. 235

shoulder in the socket, which the patient said had given 1856,
him no pain. His account would have amused me if it
had not frightened me so much. On hurrying to London I
found him reading comfortably in his arm-chair. Happily
he neither suffered from pain nor fever, and the weakness
in the arm caused by the accident did not last long.

As early as the year 1824 Sir John Wrottesley, father Decimal
of the first Lord Wrottesley, had introduced the question of jiTstofv 'of
Decimal Coinage in the House of Commons.1 His pro-
posal was to retain the pound as the unit, dividing it by
tens until it reached 1,000 farthings. The motion was
not pressed to a division.

In 1832 Mr. Babbage's work On the Economy of Manu-
factures was brought out. In this the plan of a decimal
system was advocated, and lesser attempts b}r other
writers followed. In 1833 the first number of the Penny
Cyclopcedia was published, and Mr. De Morgan in the
article Abacus gave a good summary of the advantages of
the proposed change.

It [the abacus] never can be much used in this country
owing to our various divisions of money, weights, and measures.

1 A very early suggestion on this subject is to be found in a little
book of my father's, long out of print. Speaking of the abacus, the
use of which he had described, he says, ' The Chinese use this toy
in the common concerns of life ; and they can do it with great ease,
since in their nation the decimal arithmetic is preserved in the
weights, measures, and money. The French and Americans have
returned to their ancient and best mode of counting ; but it will be
difficult to establish it in this country on two accounts : first, it
would be considered an innovation, and it is almost incredible how
great is the number of persons who prefer their father's mumpsimus
to a modern sumpsimus. Secondly, it is a question of mere public
benefit, without reference to party politics ; and it must be a fortunate
concurrence of circumstances to produce an individual resolute enough
to bring forward a motion that would get rid of our troublesome
modes of numbering, and introduce that which is the simplest, the
best, and the most ancient.' (Tangible Arithmetic, by W. Frend,
1806.)

236

MEMOIR OF AUGUSTUS DE MORGAN.

1850.

First Com-
mission on
weights
and mea-
sures.

We should need one abacus for pounds, shillings, and pence,
another for avoirdupois weight, a third for troy weight, and so
on. In China, however, where the whole system is decimal —
that is where every measure, weight, &c., is the tenth part of the
next greater one — this instrument, called in Chinese schwanpan,
is very much used and with astonishing rapidity. It is said
that while one man reads over rapidly a number of sums of
money, another can add them so as to give the total as soon as
the first has done reading.

General Pasley tried to bring forward the question in
1834 in a volume On Coinage, Weights, and Measures, and
on the Advantages of a Decimal System. Four years after,
Mr. Spring Eice, then Chancellor of the Exchequer,
obtained the appointment of a Eoyal Commission on
weights and measures. In the Companion to the Almanac
for the year 1841, Mr. De Morgan showed the advantages
that would arise from the adoption of a decimal coinage.1
He insisted on the introduction of an entirely decimal
system of accounts, in combination with such change in
the coinage as should be best adapted to, and be the
means of introducing such a system of accounts. He
showed how easily our present system might be changed
to a decimal one by retaining the pound sterling, and
dividing it into 1,000 parts ; and recommended the reten-
tion of as many of our coins as bore a relation to the
pound, and the very small alteration in the value of six-
pences and shillings needed to bring them into the new
system. The plan of the proposed change is explained,
and names of coins suggested. He strongly advised that
the change be made first in the coinage, believing that
the complications which would arise from carrying it into
weights and measures would throw everything into con-
fusion. He saw that the minds of the mercantile and
working classes must be made familiar with the decimal

1 * On the Use of Small Tables of Logarithms in Commercial Calcu-
lations, and on the Practicability of a Decimal Coinage.' Companion to
the Almanac, 1841.

DECIMAL COINAGE. 237

reckoning in money in the first instance. 'Education,5 1856.
he said, ' must promote the demand for a complete decimal
system, but the application of the principle to coinage
only must first promote education.' In answer to the
question, 6 how much of the time spent in education in
Great Britain and Ireland is spent in overcoming the
disadvantage of our present system of coinage ? ' he said,
' I believe that five per cent, is under the mark, taking
in all classes ; that in purely commercial schools it is a
great deal more ; but that in all together, from. Oxford
and Cambridge down to the lowest village school, more
than one-twentieth of the whole time passed in every kind
of learning and practising is lost, by the having two
systems of Arithmetic to learn, the common decimal, and
the monetary.'

At the end of the year 1841 the Report of the Commis- Report of
sion of 1838 was made. In it the Commission strongly Si0™
recommended the adoption of a decimal scale of weights
and measures preparatory to a change in the money ; than
which, the Report says, ' no single change which it is in
the power of our Government to effect would be felt
as equally beneficial when the temporary inconvenience
attending it had passed away.' The details of the change
recommended are those set forth by Mr. De Morgan in
the Companion to the Almanac.

In the year 1842 he gave more extensive information
on the subject in the same work, and in the next year
(1843) another Commission to inquire into weights and (
measures was appointed. It consisted of the Astronomer j ^* £****<
Royal, Lord Wrottesley, the Dean of Ely, the Speaker, Sir j
John Herschel, Sir J. W. Lubbock, Rev. R. Sheepshanks, l&p1
and Professor Miller.

The next step was taken in 1847 by Dr. Bo wring,
afterwards Sir John Bowring, who brought forward the
subject in the House of Commons. The florin, or one-
tenth of a pound, now in circulation, was in consequence
issued by Government, but no further attempt was made 1

238 MEMOIR OF AUGUSTUS DE MORGAN.

1856. to decimalise the money, and Sir John Bowring soon
after went to China.

There is an article in the Companion to the Almanac
for 1848 by Mr. De Morgan.1 He describes the state of
feeling at that time on the question as compared with
what it had been when it was first agitated. Referring
to the debate on Sir John Bowring's motion, which re-
sulted in the introduction of florins, he says ' the Chancel-
lor of the Exchequer, in yielding the first step, rested his
non-acquiescence in the whole extent of the motion on
the want of public interest in favour of the question, and
the slow growth of belief adverse to existing usages. He
said, as plain as a Chancellor of the Exchequer could
speak, " Force me, and here I am ready to be forced." :

Since issuing the florin Government had taken no
further steps towards the complete decimalisation of the
coinage, but Sir John Bowring, who was in England in
1853, was still hopeful for more, and many of the most
enlightened friends to the measure, both mercantile and
scientific, were anxious that the efforts already made
should not be lost. In 1852 Mr. William Brown called
the attention of the Liverpool Chamber of Commerce to
the importance of the question as regarded currency and
accounts, and a memorial was presented by the Chamber
in favour of the proposal already made. About the same
time the Royal Commission last appointed made its re-
port, which confirmed all the recommendations that had
been made by the Commission of 1838. The Com-
missioners expressed their hope that no new coins should
be issued except such as should be expressible by one
figure in the decimal scale, descending from the pound
sterling, and that every new coin should have marked
upon it its value with reference to the pound sterling.

Early in the year 1853, Mr. (afterwards Sir) William

1 In this article the Commission of 1838 is spoken of as the luxt
Commission on the subject, but it must be remembered that that of
1843 was still sitting, and did not report till 1853.

DECIMAL COINAGE. 239

Brown, M.P., as representative of the Liverpool Chamber 1856.
of Commerce, had interviews with the Chancellor of the 0f°Houseee
Exchequer and the President of the Board of Trade, to Commons-
suggest the appointment of a Committee of the House of
Commons to consider the whole subject of decimalising the
money, weights, and measures. Mr. Gladstone saw, with
the most practical of those who had dealt with the
question, that to include the subject of weights and
measures at that time would throw needless difficulty in
the way. Taking up one subject at a time, it would be
more easily understood ; and when the plan should be
adopted and its advantages felt, the difficulty of securing
a uniform system throughout would be removed. This
Committee was appointed, with Mr. William Brown for
Chairman.

My husband's correspondence at this time shows how
large a share he had in the uphill work in which he was
at once expounder, adviser, and referee. He was applied
to for information on every part of the question — on
weights and measures, on foreign money, on the history
of the change to a decimal coinage in other countries,
and on the changes that would be required to decimalise
our accounts and coinage in such a way as to cause least
difficulty in our money transactions both at home and
with our neighbours abroad ; for references to books of
authority ; — in short, for every sort of information that
would enable the advocates of the reform to support their
cause. All this he gave freely and readily, more perhaps
in answer to private inquiries even than in print ; and the
amount of work done by him in this way — all extraneous
to his lectures and other occupations — can only be guessed
at by those who were with him at the time, or who have
seen his correspondence since.

Here is an instance. Sir John Herschel asks —

What book, report, or resume contains what yon would refer
any one to, who wanted to get a clear view, in a short time, of
the history of the change to a decimal system of currency in

240

MEMOIR OF AUGUSTUS DE MORGAN.

1856.

Interna-
tional
Associa-
tion.

France, and more especially in the United States ? I should
like to have a reference to some authentic report as to the latter,
and indeed to anything official as regards the former ; but what
I chiefly want to be able to point out is an historical view of the
origin of the thing, the order of procedure, the course of action
of the Governments, the way it was met on the part of the
countries, and the steps by which it ultimately rooted itself.
I know you are as full of information as an egg is of meat.

On receiving the answer:—

1 am really sorry I have plagued you about it, but I thought
you would very likely have been able at once to name a work
which, referred to, would do the needful. Such a work I now
perceive is yet to be written, unless Dr. Bowring's now forth-
coming one be that work.

He has called twice on me about it. What an ardent
creature he is ! He seems to me as if he lived on live birds.

Many people who had pet schemes of their own as to
the proposed coinage brought them to my husband, and
several of these had influence enough to get their plans
considered by statesmen. These formed impediments in
the way. The various views on the change of coinage
were numerous, and I shall only refer further on to that
which, though well meant, formed the greatest obstacle
— the International Association for a Decimal System in
Weights, Measures, and Coins.

In the year 1854 the Parliamentary Committee
reported in favour of the decimal plan which had been
proposed by scientific men, and, on the issue of this
report, the Decimal Association was formed. Its first
meeting was held in July 1854. Sixteen members of
Council were chosen, all influential in Parliament or
commerce. Their number was afterwards increased by
seven, one of whom was Mr. De Morgan.

The Association recommended the adoption, or reten-
tion, of the pound as the unit of account ; the only new
coins which would be required to complete the scale bcin^
the cent, a silver coin ten to the florin, and the mil, a copper

DECIMAL COINAGE. 241

coin ten to the cent : the decimalisation of weights and 1856.
measures to be afterwards considered.

A deputation from this body (among whom were Lord Deputation
Mont eagle, Mr. Cobden, Mr. Bright, General Pasley, Gladstone.
and others) waited on Mr. Gladstone, the object being to
urge the coinage of a sufficient number of cents and mils
to circulate with the present money, of which the coins
which did not come under the system should be gradually
withdrawn.

Mr. Gladstone ( saw in the deputation a great deal of
power, as well as of intelligence, represented,' but hesitated
as to the adoption of the pound as the unit of account,
and believed the nation was hardly ready for the change.
Mr. William Brown, who was the commercial leader of
the movement, wrote to Mr. Gladstone, showing how all
the various objections had been met.

1. As to the adjustment of railway fares, by the fact
that several directors of leading lines were members of
the Association.

2. As to the Post Office, by Mr. Eowland Hill, who
was an advocate of the measure.

3. As to the turnpike tolls, by Professor Airy.

4. As to the Customs and Excise duties, which had
been supposed to be a great difficulty. Mr. Brown pointed
out that nowhere would the convenience of the change
be more rapidly felt, both in saving labour and securing
accuracy, than in the accounts and returns of the national
income and expenditure.

5. In the wages of working men, wherein the difficulty
was shown to be imaginary.

But Mr. Gladstone still thought the time not ripe for
the change.

Another deputation waited on the President of the
Board of Trade. It consisted of men who represented
every phase of the subject, each one taking his own
special part in the discussion. The recommendation in
which all concurred was that the sovereign should be re-
ft

242 MEMOIR OF AUGUSTUS DE MORGAN.

1856. tained as the unit, the florin one-tenth of the sovereign,
the cent, a new silver coin, one-tenth of the florin, and
the mil, or old farthing, one-tenth of the cent. There
would be no difficulty as to the change of value of the
farthing, for, as the copper coin is circulated at a nominal
value far beyond its intrinsic worth, its current value
might be declared each time by proclamation.

Among other things it was said that ' men with the
rare facility of explanation possessed by Professor De
Morgan might fix the attention of meetings of the work-
ing classes upon the value of the easy road that would be
opened to a knowledge of Arithmetic by the proposed
change ; but by those who had to legislate for the people
the fact was known, and there was no need to withhold
the advantage until the masses, becoming informed of its
value, should seek it for themselves ; it was, on the con-
trary, precisely a case in which the Government, supported
by those best informed, should take upon itself the
responsibility of conferring a practical boon upon the
people in advance of their knowledge.'

These proceedings of the Decimal Association, of
which I have only made a slight mention, were printed
with an introduction by Mr. De Morgan, which touches
all the most important points of the subject. It concludes
with these words : —

' The Chancellor of the Exchequer says that Govern-
ment holds an impartial position, and is ready to be guided
by the decision of the public. Every one knows that, in his
own circle, the opinion in favour of a decimal coinage,
based on the pound sterling, is that of a very large
majority of all who know what it means. What, then, is
left ? Nothing, but that the public should let the Chancellor
of the Exchequer know that it has decided, and what the de-
cision is.9

The writer was over-sanguine as to the adoption of the
measure. Delays, unfounded objections, and, more than
all, the obstacles created by injudicious reformers of the

DECIMAL COINAGE. 243

whole, put a stop to the work, and rendered all the efforts 1856.
which had been spent on it of no avail.

After more meetings and much correspondence it was Renewed
agreed to bring the question again before Parliament.
This was done on June 12, 1855, by Mr. Win. Brown, who ment
moved, after referring to the recommendations of the
Commission of 1838 for restoring the standards, to those
of the subsequent Royal Commission, and the Committee
of the House of Commons, that an address be presented
to her Majesty, praying her to complete the decimal
scale (already existing in the pound and the florin) by
authorising the issue of silver coins to the value of 1-1 00th
of a pound, and copper coins to represent 1-1 000th part of
a pound, to be called respectively cents and mils, or such
other names as to her Majesty should seem advisable.

The motion was seconded by Lord Stanley, now Earl
Derby, who cited the authorities of Babbage, De Morgan,
Pasley, and Huskisson, on the practicability and advantage
of the change. After showing the defects of several plans
proposed, he advocated that supported by the Decimal
Association, and introduced to the House by Mr. William
Brown.

Mr. J. B. Smith moved an amendment that a humble
address be presented to her Majesty, praying that she
would be pleased to invite a congress of all nations in
some convenient place, with the view of considering the
practicability of adopting a common standard of money,
weights, and measures.

Mr. Lowe (then M.P. for Kidderminster) made a very
amusing speech, to show, first, that the present system of
coinage did very well, and that the mischief of a change
would be greater than any good which could result from
it. Secondly, that the method proposed of decimalising
by division and not by multiplication was fallacious. He
would have a low unit, and multiply by tens. He
made humorous illustrations and allusions, and caused
much laughter. The then Chancellor of the Exchequer,

B 2

244 MEMOIR OF AUGUSTUS DE MORGAN.

1856. Sir G. C. Lewis, expressed his belief that the time was not
come for the change, and recapitulated other plans as
possibly preferable to the one before the House. He spoke
of the opinion, already reported, of Sir J. Herschel, the
Master the Mint, as involving great difficulties.

Finally two resolutions were carried : —

' That in the opinion of this House the initiation of the
decimal system by the issue of the florin has been eminently
successful and satisfactory.'

And-

' That a further extension of such system will be of great
public advantage.9

But the practical resolution for an address to her
Majesty, praying for the completion of the scale by the
issuing of cents and mils, was withdrawn. The question
was therefore left by the House of Commons much as
it had been before, with the exception of the greater
publicity given to the arguments on both sides by the
debate. But a Commission was appointed to investigate
the whole subject of weights, measures, and coinage.

In an article in the Westminster Review, in which a sum-
mary of the question was given, Mr. De Morgan, writing
of the Chancellor of the Exchequer, 'the chief of our
financial Arithmetic/ says, —

The right honourable gentleman , after saying that 'there
are differences of opinion,' proceeds to give * some of the
plans ' which have come under his observation. One is
the tenpenny plan; others are as follows: — 1st. 10 farthings
or mils, one cent ; 10 cents one dime ; 10 dimes one prime.
2nd. 10 farthings or mils one coin unnamed ; 10 of these a
florin ; 10 florins a Victoria. 3rd. 10 farthings or cash two-
pence; 300 cash a cent; 10 cents a mil. 4th» 10 farthings a
lion ; 10 lions a florin ; 10 florins a queen. To these four
'plans' we beg permission to add two of our own invention,
as distinct from the above as the above are from one another.
Our first plan is 10 farthings a what's-his-name ; 10 what's-his-
names a how-d've-call-it ; 10 how-d'ye-call-its a thingembob.
Our second plan is 10 farthings a George ; 10 Georges a Corne-
wall ; 10 Cornewalls a Lewis.

DECIMAL COINAGE.

245

All the old arguments were considered, and the
answers to them repeated and enlarged. As to the
witticisms of Mr. Lowe, they had been answered by Mr.
De Morgan in a paper published by the Decimal Associa-
tion, Reply to the Facetice of the Member for Kidderminster.
' Mr. Lowe is of opinion,' the Westminster Review says,
' that if a poor man owed another a penny, for which four
mils is too little, and five mils too much, this mil between
them would lead to a mill between them ; and some of the
conscript fathers cheered him.' In the 'Beply,' a
dialogue between an orange boy and the member for
Kidderminster shows, in the method of the latter, how the
supposed difficulties in a money transaction with an old
apple woman might be overcome.

The Review takes in the substance of the two Eeports
of Commissioners, 1841 and 1853; the Report of the
Committee of the House of Commons, 1854; the debate
of June 12, 1855 ; the publications of the Decimal
Association, and the Journal of the Society of Arts, with
a list of about one hundred publications on the subject in
1853, 1854, and 1855. At the end of this year 1855 he wrote
for the Companion to the Almanac of 1856, Notes on the
History of the English Coinage, giving many particulars of
the history and origin of money in England and other
countries, both as to coins and accounts. Speaking of
the ruined and confused state which the coinage had
reached at the time of the Restoration, he describes the
reform projected by Montague, afterwards Lord Halifax,
and carried into effect during his administration -by Sir I.
Newton, who only added to the pieces already in circula-
tion the quarter- guinea, which was found too small for
use. A note in the author's handwriting states, 'The
next Scientific Master of the Mint coined a quarter-
sovereign, which was never circulated.' Sir John Herschel
gave my husband one of these pretty little gold coins,
which he valued greatly. It was lost, in moving, after
his death.

1850.

woman
argument.

246 MEMOIR OF AUGUSTUS DE MORGAN.

1856. Many sanguine persons had been withheld from join-

ing the Decimal Association, in the hope of establishing
• an International Currency; ca proposal which/ Mr. De
. Morgan said, ' unites the millennial and decimal systems.'
They also contemplated the universal decimalisation of
weights and measures. Mr. J. B. Smith's resolution for
an Address to the Queen, praying her to invite a congress
of all nations for this purpose, had not been carried, but
shortly after, in the autumn, the Paris Exhibition took
place, and the difficulty of harmonising the various
weights, measures, quantities, and prices of the articles
brought by contributors from twenty-two different states
or countries, led to the consideration of the possibility of
making a uniform system throughout the world. The
advantages of such uniformity would be felt both morally
arid socially, in making free trade more easy, and war
between nations more difficult. All these, as well as the
benefits to commerce and merchandise, were fully acknow-
ledged by all the advocates of decimal coinage. The only
question was as to the first step. The mutual advances
made by the French and Americans by interchange of
specimens of weights and measures were followed by
memorials and petitions to their respective governments
in favour of a congress of delegates from the leading
nations of the world. In Tract No. 12 of the Liverpool
Financial Reform Association, all the evils of the present
confused state of the means of effecting commercial ex-
changes were shown, and all the arguments for a complete
decimal system throughout brought forward. Shortly
after the Paris Exhibition an ( International Association '
was formed, ' for obtaining a uniform decimal system of
weights, measures, and coin throughout the world.' The
proposals and arguments of this Association caused a
great deal of extra work to the active members of the
Decimal Association. Among my husband's letters are
several like this from the secretary — it enclosed some new
tract or report of speech : —

DECIMAL COINAGE.

247

Pray take charge of the ' International,' &c., &c., &c., Asso- 1856.
ciation, and blaze away from time to time, rifle-shot being better
than 60-pounders in such a cause.

The 60-pounders and small shot were cast and fired with-
out thought of time and labour, by one who, besides his
expenditure of both in daily lectures, &c., at University
College, did more work than would have filled the time of
an ordinary man.

His next public effort was the delivery of a lecture in
the large room of the Society of Arts, at a meeting, to of Arts.
which the advocates of the various plans were invited, of
the Decimal Association. The lecture was On the Ap-
proaching Simplification of the Coinage. We move very
slowly in good and useful directions. The ' approach '
of twenty-seven years ago remains in 1882 just where it
was. The lecturer said : —

The various systems1 which had been proposed had all sunk
out of notice but two — the pound-and-mil system, and the ten-
penny system. These terms were used sarcastically, which was
no disadvantage, but then they must be correctly given. Some
opponents on the tenpenny side had called themselves ' Little-
endians,' and the pound-aud-mil people ' Big-endians.' These
had got hold of the poker by the wrong end. Samuel Gulliver,
on whom all relied except the Irish bishop, who, when the
voyage to Lilliput appeared, declared he did not believe half of
it, stated that the Endian dispute arose out of the following
dogma : — ' True believers break their eggs at the convenient
end.' Now, the pound-aiid-mil people believe that the small end
was that at which the coinage ought to be broken, and a small
crack of 4 per cent, in the copper served their purpose. But
the real Big-endians, the tenpenny people, smashed the sovereign
into tenpenny bits, making such a hole as let out all the meat
in getting rid of the pound and shilling.

The lecturer showed how very small a change in the
present coinage need be made to introduce the new system.
He had been supposed to look at the matter from a
scientific rather than a practical point of view, and many

1 Referring only to coinage.

248 MEMOIR OF AUGUSTUS DE MORGAN.

1056. writers had objected to his having a voice in the question.
But these writers did not know or had forgotten that he
was an actuary of twenty-five years' standing, besides
being a teacher of monetary Arithmetic. He had also
a position which made him better able to judge than he
would have been either as a Mathematician or as an
actuary. He had been for twelve years 1 a manager of a
savings bank, and in that capacity had had, scores upon
scores of times, to receive and pay out from two to
three hundred pounds in a couple of hours, and in all
kinds of coins, from a shilling and some halfpence up-
wards. When he looked at the banker's clerk, with his
luxurious table and his convenient scoop, and all his other
paraphernalia, he at the pay-table of the savings bank
looked upon that same clerk as an aristocrat, who knew
little of the difficulties of humble life.

The lecture was followed by a discussion, Mr. De
Morgan in the chair, which lasted two evenings, and in
which the members of the International Decimal Asso-
ciation, who wished to adopt the French system entire,
and the £ tenpenny people ' defended their respective
plans. The sense of the meeting was ultimately taken,
when, with one exception only, the opinions were declared
to be in favour of the pound-and-mil system. At this
time some articles by Mr. De Morgan On the Approach-
ing Simplification of the Coinage, intended to make the
subject clear to all classes, were published in the Metro-
politan.

In the spring of 1857 Lord Overstone, one of the
Commissioners for inquiring into the subject of decimal
coinage, communicated sixty-five questions to the Decimal
Association. Those questions were answered by Mr. De
Morgan, Sir J. F. W. Herschel, the Dean of Ely, the
Astronomer Royal, Professor Miller, Mr. W. Miller,
Mr. J. B. Franklin, and others. Those which were

1 During our residence in Camden Street. He thought this the
best way in which he could be useful to his poorer neighbours.

DECIMAL COINAGE.

249

given by the above members in October were printed by 1856.
the Decimal Association in November 1857.

Answer * No. 1 (Mr. De Morgan's) is preceded by some
remarks by himself. He says, —

These questions are the first attempts I have seen to bring the Lord^Over-
advocates of the pound-and-mil system to a close hand-to-hand questions,
controversy with the existing system. In such a trial of strength
the weak points of both systems may appear, but the weak
point of the assailant's system is sure to be discoverable from his
mode of attack.

After pointing out some of the weak points (those
implying statements or opinions held by him to be
essentially unsound), he says : —

It must be conceded that the questions are wholly free from
some absurdities very common among opponents of the pound-
and-mil scheme. They do not bring forward the usual dirge upon
the fraction of a farthing which the possessor of some copper
pieces must lose, for once, on the day when the change takes
place. The only question asked on this point is a sensible one,
fully deserving of consideration and answer. They do not
enable us to amuse ourselves with the supposition that we mean 2
apple women to transact business by help of '0041666666666 ad
infinitum.

The c Answer ' runs through forty-one pages of small
print, a portion being taken up by repetition of the
questions. They are amusing and instructive even in
subjects only indirectly related to coinage. The questions
included references to authorities believed to be un-
answerable. These were easily dealt with. Here is a
specimen slightly abridged : —

9. In an old treatise on coin and coinage (Vaughan,
1675) this passage occurs : —

Of all the numbers, twelve is the most proper for money,
being the most clear from fractions and confusion of accompt, . .

1 I give them in the order in which they are printed.

2 Referring to Mr. Lowe's ideal apple woman.

250 MEMOIR OF AUGUSTUS DE MORGAN.

1856. by reason that of all the other numbers it is most divisible, being
divisible into units, as all numbers are ; into two parts, as no odd
number is ; into three parts, as no even number is but six, and
the numbers that consist of sixes ; into fourths, into which six is
not divisible ; and into sixths.

In the memoir dictated by Napoleon at St. Helena is
this passage : —

On avait prefere le diviseur 12 au diviseur 10 parceque 10 n'a
qoe deux facteurs, 2 et 5, et que 12 en a quatre, savoir 2, 3, 4, et
6. II est vrai que la numeration decimale . . donne des
facilites aux astronomes et aux calculateurs ; mais ces avantages
sont loin de compenser 1'inconvenient de rendre la pensee plus
difficile. Le premier caractere de toute methode doit etre
d'aider la conception et 1'imagination, faciliter la memoire, et
donner plus de force a la pensee.

To the quotations from Vaughan and the Emperor
Napoleon this answer is given : —

When an old writer is stript of his conceits, translated into
correctness, and under those changes presented as a sage of
antiquity, the only way to meet his authority is to restore his
true form, and to allow his whole character to be judged.
Whether the divisors of 12 gain anything by Mr. Vaughan's
advocacy may be ascertained by reading the whole passage. . .
The punctuation may be excused, since the work was printed
after the author's death by his crotchety brother, Henry
Vaughan, the Silurist. He is speaking of the proportion of gold
to silver in value, which he would have 12 to 1, because 12 has
many divisors. — (Pp. 73, 74.)

* But the most, and the most judicious propositions that I
have seen, both at home and in other parts, do agree upon twelve
for one as the most equal proportion ; and it agrees with the
proportion of Spain, upon which in this subject we ought prin-
cipally to have our eye fixed ; and for my part I do the rather
incline to this proportion, because 12 of all the numbers is the
most proper for money, being most clear from all fractions and
confusion of an accompt, by reason that [here the divisors
enumerated as in the question]. And to the sixth this proportion
seems like to square with the conceit of the alchemist, who
called gold Sol, and silver Luna, whose motions do come near upon
the point of 12 for 1.'

DECIMAL COINAGE. 251

Lord Overstone had wisely left Yaughan's Sun and 1856.
Moon out of his question. The answer goes on : — stone'?™1

questions.

Yaughan was a clever attorney, who had read more out of
law than he was able to digest. Sir William Petty will be
allowed to have a much better judgment by all who have read
in both. In his Quantulum-cunque, reprinted in 1856 by the
Political Economy Club, it has been pointed out to me that he
speaks as follows : —

' The use of farthings is but to make up payments in silver '
(N.B. Copper farthings and silver pence were then in circula-
tion), ' and to adjust accompts, to which end of adjusting accompts
let me add that if your old defective farthings were cryed down
to five a penny you might keep all accompts in a way of decimal
arithmetic which hath been long desired for the ease and
certainty of accompts.'

Decimals were not well understood in Petty 's time. His
system would give 1,200 farthings to the pound. But his main
point evidently was that the multiplier 5, by its relation to 10,
is an easier multiplier than 4.

Mr. Yaughan lived at a time when decimal fractions were
not familiar to the mass of arithmeticians. It would be easy to
show that, up to the year 1700 at least, the mastery over decimal
fractions which is common in our day was almost confined to
high mathematicians. Mr. Yaughan's statement merely amounts
to this, that 12 is better than 10, because it has more divisors.
The answer is that 10 is better than 12 because it is the radix
of our present system of counting. Mr. Yaughan's objections
would be exceedingly valuable if a new system of numeration
were to be under contemplation.

Napoleon at St. Helena is no authority. He had never been
a shopkeeper or a money calculator; and if he had been, his
position at St. Helena was not favourable to sense or candour.
He was grumbling at all creation ; nobody knew his own
business, not even the General who commanded against him at
Waterloo. He is very unfortunate in his expression. He
adopts the erroneous supposition that the decimal system is only
useful to scientific calculators, and styles them astronomes et cal~
culateurs. Now the Astronomer is the only scientific calculator
to whom, as such, decimalisation is impracticable. He is in.
such continued connection with the records of his science that
he cannot afford to decimalise angular measure. He is a

252 MEMOIR OF AUGUSTUS DE MORGAN.

1856. merchant who wants all his ledger for 2,000 years past. The
French tried it and failed ; it is the only part of the metrical
system which is not in nse at this day, except indeed the tenth
day of rest, which, being an attack on religion, disappeared with
the return of Christianity. Scientific calculators in general use
decimals, and they want the world at large to have the advan-
tage which they feel every day of their lives. — (P. 7.)

These appeals to the authority of Vaughan and the
French Emperor were answered by some of the other
members of the Association. The Astronomer Royal's
reply is much to the point:1—

Napoleon's infantry, cavalry, guns, rations for troops, re-
quisitions in francs for their support, were all expressed on a
decimal scale ; and he never failed in ' distinctness of conception,'
* facility of recollection,' 'readiness and ease in mental calculations,'
or in * making fractional parts,' in dividing an army, from these
circumstances. So far as I see, the same applies to smaller
numbers.

Sir J. Herschel's answer to Lord Overstone's questions
filled thirty-seven pages. Those of the Astronomer Royal,
the Dean of Ely, Professor Miller, Mr. Miller (Cashier of
the Bank of England), and Mr. J. B. Franklin, being
much shorter than the other two, were collected in one
pamphlet of fifty-five pages. The preliminary Report of
the Commission of 1855 was published about the same
time (1857). It contains, besides the answers given by
advocates of various schemes to Lord Overstone's questions,
a great deal of evidence obtained from well-informed
witnesses, of the operation of the decimal system in other
countries. It is a very large blue-book. The Govern-
ment was now in full possession of all the information
that could be gained upon the question.

Much discussion was naturally excited at this time,

1 It will be apparent that the work of other friends to the decimal
cause is not made so prominent in this memoir as that of Mr. De
Morgan. Space would not allow of my mentioning it at any length,
even if my husband's share were not that with which I am concerned.
But I believe that his share was the largest.

;

DECIMAL COINAGE, 253

and the clear-headed advocates of the measure, and those 1857.
who ' darkened counsel,' all contributed their share. In
a long article in the Literarium of October 7, 1857, Mr. \
De Morgan sums up the history. He says, e the Decimal
Coinage discussion is now in its third phase.' After nar-
rating what had been done up to the year 1855, he
adverts to the penny scheme, the plan of counting by tens
and hundreds of pence, leaving the shillings and sovereigns
in which the pence were to be paid, to take care of them-
selves. After the debate of 1855 had been followed by
the Royal Commission, the penny scheme came fairly into
discussion, 'for such, in a manner, is evidence with cross-
examination. The preliminary Report of the Royal Com-
missioners shows the result. One of the chief advocates
for the penny fairly bolted out of the course, and declared
himself for remaining as we are ; another did nearly the
same thing. This was the end of the second phase.
Lord Overstone completed the downfall of the penny
scheme by proposing sixty-five questions, mostly in
advocacy of the plan of remaining as we are, and led the
way to the third phase of the discussion, thereby doing
the best possible service to the cause.' At this time the
dispute turned upon the question whether it would be
best to adopt the pound-and-mil system, or to remain as
we are.

Mr. De Morgan again set forth the nature of the
change in the currency which would be necessary on the
adoption of the pound-and-mil system.

It would be embarrassing to have two sets of coins not fairly
interchangeable. No such thing is proposed. The penny, even
if still called a penny, would be lowered four per cent., and
would become 4 mils ; the halfpenny would become two mils.
The cent, 2^ of old and extinct money, would be five halfpence,
and ten farthings, if the mils were called farthings. The poor
would know it as 2^d. from the outset, for they would never
know the difference between a penny and 4 mils.

The paper concludes, speaking of those who had

254 MEMOIR OF AUGUSTUS DE MORGAN.

]856. believed our present system to be better than a decimal
one: —

If this school be a logical one, it ought to be prepared to
maintain that a country with a decimal system already established
ought to abandon its coinage, and to introduce the succession of
4, 12, 20. This is a conclusion at which all parties would have
laughed three years ago, and at which those who are to come
after us will well laugh when the objections to this salutary
reform are written down in histories after the happy, and we
hope speedy completion of the change.

It is now 1882, and our reckonings and payments are
still made in pounds, shillings, pence, and farthings.

Let me add one argument, which I have never seen
used, in favour of decimals. It touches the morality
of the question. Small shopkeepers, especially haber-
dashers, find the full benefit of the present system by the
use they make of farthings, and the difficulty of bringing
them fairly into the calculation. At this time articles in
small retail shops are often priced %d. less than an even
sum of pence. The result is that to persons unaccus-
tomed to reckoning they appear cheap, while in reality
the impossibility of halving and quartering farthings in
accounts where farthings are of frequent occurrence gives
a gain over the professed prices of some halfpence on every
bill. The shopman cannot be expected to do a difficult
sum in small fractions for every customer, and each cus-
tomer loses very little, but where these customers in each
day count by hundreds, as in many of the large retail
ready-money shops, the gains in this way must be con-
siderable, as those who understand business well know.

The Commission sat through the years 1857, 1858,
and 1859. From resolutions passed on March 1, 1859, it
appears that nothing had been ascertained which ren-
dered the change desirable ; that while the weights and
measures remain as at present the coin could not be
touched ; and as the weights and measures could not be
interfered with, the coin must be left alone. These, in

DECIMAL COINAGE. 255

few words, were the substance of the decisions of Par- 1856.
liament.

The energetic promoters of what would have been
both morally and socially a most useful measure were
naturally disappointed. Their efforts did not entirely
cease at the time, and Mr. William Brown, Mr. De
Morgan, and others, still did their utmost to keep the public
interest alive on the whole question. Mr. Brown, whose
philanthropy showed itself in many ways, died in 1864.
Of him my husband says, —

6 The agitation for a decimal coinage was put to rest
by the illness and retirement of Sir Wm. Brown, whose
recent death has revived the memory of his splendid
benefaction (a fine library) to the town of Liverpool. A
parliamentary leader of weight and energy is absolutely
necessary to the success of any public measure ; and as
soon as the man shall be found who combines with
William Brown's great energy his interest in the subject,
the agitation will be revived. All the work that has been
done is good material for a new attempt, and a new
beginning will be made under great advantages. All the
discussion about the metrical system works to the same
end. We may be well assured that our system of calcula-
tion will not always be cramped by counting in one way
and measuring in another. And our firm belief is that
the way to work the change will be by beginning with
the coinage, in which decimals are most wanted and
most easily obtained.' l

We have now to help us in this work the aid of the
Board schools. There is no reason why the strong efforts
of the Decimal Association should be lost ; and in the hope
that the revival to which my husband looked forward
may not be far off, I have given this history. All his
writings on the subject are instructive, and the series of
articles in the Penny Cyclopedia on Weights, Measures,

1 Athenxum, review of ' Battle of the Standards,' April 9, 1864. t X*

256 MEMOIR OF AUGUSTUS DE MORGAN.

1856. and Coins, would form a large volume, containing infor-
mation on every part of the question in all its relations.1

Sir Isaac The memoir of Newton by Mr. De Morgan, which

appeared in 1846 (Knight's British Worthies), was, after
Baily's Life of Flamsteed, the first English work in which
the weak side of Newton's character was made known.
Justice to Leibnitz, to Flamsteed, even to Whiston, called
for this exposure ; and the belief that it was necessary did
not lower the biographer's estimate of Newton's scientific
greatness, and of the simplicity and purity of his moral
character. Francis Baily's discovery of the correspond-
ence between the Rev. John Flamsteed, the first, Astro-
nomer Royal, and Abraham Sharp, as well as between
Newton, Haliey, and Flamsteed, on the publication of
Flam steed's catalogue of stars, had thrown a new light on
the character of Newton. It appeared that the practical
astronomer had been treated ungenerously by Newton,
who failed to observe the conditions of publication agreed
to by all parties; and afterwards when remonstrated with
omitted the name of Flamsteed in places where it had
formerly stood in the earlier editions of the Principia.

My husband entered into the inquiry with keen in-
terest, and with a power of research possible only to one
who was fully master of the history of Mathematical disco-
very.2 With reference to Newton's character he says : — 'We

1 I am told that a movement in this direction is now thought of.
Whatever documents on this subject were left by my husband are still
in existence.

2 Several of the works in which the questions relating to Newton's
Mathematical discoveries were treated are as follows : —

1. 'Memoir on Newton/ by J. B. Biot. Biographe Universelle,
1794.

2. * Life of Newton,' by Sir D. Brewster. Family Library, No.
24, 1831.

3. Life of Flamsteed, by F. Baily, 1835. Article in Quarterly
Review by Barrow, No. 109. Remarks on the same by Dr. Whewell.
Article in Edinburgh Review by Mr. Galloway.

4. 'Life of Newton,' by Lord Brougham. Library of Useful
Knowledge.

STR ISAAC NEWTON. 257

must differ in some degree from our guide,1 as well as from 1857.
all those (no small number) whose well-founded veneration moral011
for the greatest of philosophical inquirers has led them peculiarity
to regard him as an exhibition of goodness all but perfect,
and judgment unimpeachable. That we can follow them
a long way will sufficiently appear in the course of this
sketch.' Later on he says, f The great fault, or rather mis-
fortune, of Newton's life was one of temperament ; 2 a
morbid fear of opposition from others ruled his whole life.
When, as a young man, proposing new views in opposition
to the justly honoured authority of Descartes and lesser
names, he had reasons to look for opposition, we find him
disgusted by the want of an immediate and universal
assent, and representing, as he afterwards said, that
Philosophy was so litigious a lady, that a man might
as well be engaged in lawsuits as have to do with her.

5. (Art.) 'Newton,' by A. De Morgan. Penny Cyclopaedia, 1840.

6. ' Life of Newton,' by A. De Morgan. Knight's Cabinet Portrait
Gallery (British Worthies), 1846.

7. Tract upon Keil and Leibnitz, by A. De Morgan. Cambr.
Phil Trans., 1846.

8. * A Short Account of Recent Discoveries in England and Ger-
many relating to the Controversy on the Invention of Fluxions,' by
A. De Morgan. Comp. to the Almanac, 1852.

9. 'On the Authorship of the "Account of the Commercium
Epistolicum,"' by A. De Morgan. Phil. Magazine, June 1852.

10. ' On the Early History of Infinitesimals in England,' by A. De
1 organ. Phil. Magazine, November 1852.

11. Life of Newton, by Sir D. Brewster, 1855.

12. Review of Brewster's Life of Newton, by A. De Morgan.
North British Revieiv, 1855.

13. Articles in Notes and Queries by A. De Morgan, 1853 and 1856.

14. Correspondence of 8ir Isaac Newton and Prof. Cotes, by
J. Edleston, Fellow of Trin. Coll., Camb. 8vo., London, 1850.

15. Historical Essay on the First Publication of Sir Isaac Newton's
« Principia,' by Prof. S. P. Rigaud. 8vo., Oxford, 1838.

16. Gentleman'' s Magazine, Ixxxiv., p. 3.

17. Weld's History of the Royal Society. 2 vols. 8vo., London.

1 Sir D. Brewster, from whose ' Life of Newton ' in the Family
Library the facts are taken.

2 My husband always used this word for what I should call ori-
ginal character or inborn disposition.

258 MEMOIR OF AUGUSTUS DE MORGAN.

1857. How could it be otherwise? What is scientific investiga-
tion except filing a bill of discovery against nature, with
liberty to any one to be made a party to the suit ? Newton
did not feel this, and, not content with the ready accept-
ance of his views by the Koyal Society, a little opposition
made him declare his intention of retiring from the field .
He had the choice of leaving his opponents unanswered,
and pursuing his researches, committing it to time to
show the soundness of his views. That this plan did not
suit his temper shows that it was not the necessity of
answering, but the fact of being opposed, which destroyed
his peace. And he steadily adhered, after his first
attempt, to his resolution of never again willingly appear-
ing before the world. His several works were extorted
from him ; and, as far as we can judge, his great views on
universal gravitation would have remained his own secret
if Halley and the Eoyal Society had not used the utmost
force they could command. A discovery of Newton was
of a twofold character — he made it, and then others had
to find out that he had made it. To say that he had a
right to do this is allowable ; that is, in the same sense in
which we and our readers have a right to refuse him any
portion of that praise which his biographers claim for
him. In the higher and better sense of the word he had
no right to claim the option of keeping from the world
what it was essential to its progress that the world should
know, any more than we should have a right to declare
ourselves under no obligation to his memory for the ser-
vices he rendered. To excuse him, and at the same time
to blame those who will not excuse him, is to try the first
question in one court and the second in another. A man
who could write the Principia, and who owed his bread
to a foundation instituted for the promotion of knowledge,
was as much bound to write it as we are to thank him for
it when written.'

The principle here expressed governed the writer's
own life. What he knew belonged to the world, if by the

SIR ISAAC NEWTON. 259

knowledge the world could benefit; and no sooner had it 1857.
become his own than he felt as much bound to give it to
whomsoever could receive it, as he did to repay to the
uttermost farthing, and with interest, a debt that he
believed himself to have incurred.

Newton went to Cambridge as a sizar — ' a student Newton as
whose poverty compels him to seek to maintain himself in graduate"
whole or in part by the performance of some duties which
were originally of a menial character. By this means a
youth could live by the work of his hands while he pursued
his studies. In our days there is little distinction between
the sizars and those above them; except in college
charges, none at all. Those who look upon Universities
as institutions for gentlemen only — that is, for persons who
can pay their way according to a certain conventional
standard — praise the liberality with which poorer gentle-
men than others have gradually been emancipated from
what seems to them a mere badge of poverty. But those
who know the old constitution of the Universities see
nothing in it except the loss to the labouring man and the
destitute man of his inheritance in those splendid founda-
tions. If sizarships with paid personal services had not
existed, Newton could not have gone to Cambridge, and
the Principia might never have been written. Let it be
remembered, then, that so far as we owe this immortal
work and its immortal work to the University of Cam-
bridge, we owe it to the institution which no longer exists,
by which education and advancement were as much open
to honest poverty seeking a maintenance by labour as to
wealth and rank. Let the juries, who find on their oaths
that scores of pounds9 worth of cigars are reasonable neces-
saries for young students, think of this, if they can
think? l

Proofs of all the writer's assertions on the jealousy
and even vanity of the man whose intellectual work he

1 Note to Memoir of Newton. The italics are mine,
s 2

260 MEMOIR OF AUGUSTUS DE MORGAN.

1857. prized so highly had been brought forward in the memoir
with a distinctness that left no room for doubt, though
the question was not entirely set at rest at that time.

Another question, that of Newton's religious belief, is
discussed in the Life ; * not,' the writer says, f from any
particular interest in it, for there are too many great
minds on both sides of the controversy to make one more
or less a matter of any consequence to either ; but because
we have a curious matter of evidence, and an instructive
view of party methods of discussion.' Notwithstanding
this disclaimer I believe my husband felt more interest in
the question, from its own nature, than he was himself
aware of. Whether I am mistaken in this may be sur-
mised by those who have read his own letter to his mother
in this volume. He says, ' Whatever Newton's opinions
were, they were the result of a love of truth, and of a
cautious and deliberate search after it.'

That Newton was a firm believer in Christianity as a
revelation from God is very certain, but whether he held
the opinions of the majority of Christians on the points
which distinguish Trinitarians from Arians, Socinians,
and Humanitarians, is the question of controversy.

The generic name Unitarian, with the specific names
Arian, Socinian, and Humanitarian, are ' bandied about
in interpretative discussion until they are so misused
that the chances are many readers will need explana-
tion of them. An Arian believes in the finite pre-exist-
ence of Jesus Christ before His appearance on earth;
a Socinian believes him to be a man who did not exist
before His appearance on earth, but who was a proper
object of prayer ; a Humanitarian, with all others who come
under the general name Unitarian (the personal unity of
the Deity being a common tenet of all), believes him to be
a man, and not an object of prayer.' Having given the
arguments on all sides, and taken into consideration
Newton's great fear of discussion and of opposition, the
biographer shows that the weight of evidence goes to

SIR ISAAC NEWTON. 261

prove that Newton, the devout Christian believer, was an 1857.
Arian at the least. Besides this evidence, he was the
friend of Locke, Clarke, and Whiston, all distinctly
Antitrinitarians.

It is to be remembered that during the whole of New- Newton's
ton's life the denial of the doctrine of the Trinity was beiitf°U6
illegal, the statute of King William III. (which relaxed
the existing law) making the offender ineligible for any
position of trust for the first offence, and liable to three
years' imprisonment with other penalties for the second.
In these days, when few men of science do more than
tolerate the idea of the existence of God, we may dwell
with satisfaction on the fact that the world, if not
wiser, is better. For whereas in 1696 a man was hanged
for denying the Trinity, in 1881 men deny their Father
in Heaven, and their fellow-men, instead of hanging
them, are content to leave the opinion of each to find
its own place in philosophy. If our intellectual con-
clusions are chaotic, our moral sense, in this respect at
least, is clearer than it was 200 years ago.

The c Life of Newton ' concludes with these words in
reference to the failings which truth compelled the
writer to disclose : — ' Surely it is enough that Newton is
the greatest of philosophers and one of the best of men;
that all his errors are to be traced to a disposition which
seems to have been born with him ; that, admitting them
in their fullest extent, he remains an object of unqualified
wonder, and all but unqualified respect.'

In the year 1855, three years after the appearance of Brewster's
Mr. De Morgan's tracts on the Fluxional Controversy,
Sir David Brewster's Life of Newton was published. Some
of the statements of the biographer in the British
Worthies were controverted, though not strongly; some
were softened, and some ignored. Sir David, in his great
veneration for his subject, had fallen into hero-worship,
and my husband's critique of his Life of Newton in the
North British Review, No. 46, 1855, shows this very clearly.

262 MEMOIR OF AUGUSTUS DE MORGAN.

1857. In this review l Brewster's objections and omissions were
refuted and supplied. The faults of Newton in the matter
of Flamsteed and Leibnitz are proved, and in relation to
the order of the discovery of Fluxions the character of
Leibnitz received its due testimony:—

6 We shall not stop to investigate the various forms in
which Sir D. Brewster tries to make him out tricking and
paltry. We have gone through all the stages which a
reader of English works can go through. We were
taught, even in boyhood, that the Royal Society had made
it clear that Leibnitz stole his method from Newton. By
our own unassisted research into original documents we
have arrived at the conclusion that he was honest, candid,
unsuspecting, and benevolent. His life was passed in law,
diplomacy, and public business ; his leisure was occupied
mostly by psychology, and in a less degree by mathe-
matics. Into this last science he made some incursions,
produced one of the greatest of its inventions almost
simultaneously with one of its greatest names, and made
himself what Sir D. Brewster calls the " great rival "
of Newton in Newton's most remarkable mathematical
achievement.'

The reviewer speaks of the pleasure he derived as a
boy from Brewster's invention, the kaleidoscope :—

' The two deans of optical science in Britain and in
France, Sir David Brewster and M. Biot, are both bio-
graphers of Newton, and take rather different sides 011
disputed points. Sir D. Brewster was the first writer on
optics in whose works we took an interest ; but we do
not mean printed works. We, plural as we are, remember
well the afternoon, we should say the half-holiday, when

1 Speaking of the titles of all the parties concerned, Mr. De Morgan
says, * Sir David never neglects the knighthood of Newton. . . . Should
we survive Sir David, we shall Brewster him. We hold that those
who are gone, when of a certain note, are entitled to the compliment
of the simplest nomenclature.' In the tracts on the Commercium Epis-
tolicum he reverses the usual phrase, saying, " Inasmuch as knighthood
was not honoured with Newton until," &c.'

SIR ISAAC NEWTON. 263

the kaleidoscope, which our ludi-magister (most aptly 1857.
named for that turn) had just received from London, was North *
confided to our care. We remember the committee of
conservation, and the regulation that each boy should, at
the first round, have the uninterrupted enjoyment of the
treasure for three minutes ; and we remember, further, that
we never could have believed it took so very short a time
to boil an egg. A fig for Jupiter and his satellites, and
their inhabitants too, if any ! What should we have
thought of Galileo when placed by the side of the in-
ventor of this wonder of wonders, who had not only made
his own telescope, but his own starry firmament? ' . . . .

' Since his own scientific sensibilities are keen, . . .
we hope they will make him fully feel that he has linked
his own name to that of his first object of human rever-
ence for as long as our century shall retain a place
in literary history. This will be conceded by all, how
much soever they may differ from the author in opinions
or conclusions; and though we shall proceed to attack
several of Sir D. Brewster's positions, and though we
have no hesitation in affirming that he is too much of a
biographer and too little of an historian, we admire his
earnest enthusiasm, and feel as strongly as any one of his
assentients the service he has rendered to our literature.'

The two biographers had differed in their estimate of
Newton's religious belief, Sir David Brewster, in the first
instance, maintaining his orthodoxy, ' by which,' Mr. De
Morgan says in his Review, ( we mean a belief of as much
as the Churches of England and Scotland hold in common.'
He himself believed Newton to be an Arian, and the MS.
creed of Newton found in the Portsmouth papers showed
that he was right. M. Biot, who had been a worshipper of
Newton early in the century, wrote to Mr. De Morgan at
the time, expressing his satisfaction and concurrence in
the statements of the North British Review. He received
from my husband a copy of the memoir, with which he
was greatly pleased. The author and M. Biot had met

264 MEMOIR OF AUGUSTUS DE MORGAN.

1857. in Paris twenty-five years before, but this M. Biot, now in
his eighty-second year, had forgotten.

In the course of the inquiry a question had arisen,
which my husband felt to be an important one, nearly
concerning Newton's moral rectitude. Catherine Barton,
the niece of the philosopher, was known to have kept the
house of his friend Lord Halifax. It was, however, never
publicly known whether they were or were not privately
married. From all that Mr. De Morgan could gather on
this subject, which amounted to a great deal of presump-
tive if not quite conclusive evidence, he was convinced
that, except as a wife, Newton would not have counte-
nanced his niece's connection with the Prime Minister.
This conviction was strengthened by the production of a
MS. letter of Newton's bought by our friend M. Libri at
a sale, in October 1856. But the opinions of scientific and
literary men were not unanimous.

All the facts and arguments connected with this ques-
tion were carefully embodied in an article for the Com-
panion to the Almanac for 1858. This article was objected
to by the publisher, Mr. C. Knight, on the ground of its
not dealing with a subject of general interest. It was
suggested to Mr. De Morgan to alter, or curtail his
writing, or to furnish another article, and he refused to do
either. This was the cause of his discontinuing his con-
tributions to the Companion to the Almanac. His reasons
will be found in the correspondence.

1858. My husband's time was too thoroughly filled to allow of

his taking an active part in many public movements,
but he was always glad to give what help he could to
benevolent schemes. He has mentioned, a propos of de-
cimal coinage, his work at the Savings Bank. Another
design which he much wished to see carried into execution
was the opening of playgrounds for poor children. Our
friend the Rev. David Laing, well remembered in his
parish of Trinity, St. Pancras, N.W., for incessant efforts

REV. DAVID LAING. 265

to improve and assist his parishioners ' in mind, body, 1 858.
and estate,' devised a plan for opening playgrounds ground3
wherever land could be obtained in London, in which poor movement-
children might play harmlessly and happily, uncontami-
nated by street influences. Mr. Laing asked me to join
his committee, and my husband fully shared the interest
felt in the scheme. We had a dinner at the Freemasons'
Tavern, at which Mr. Charles Dickens presided, and
spoke as warmly as he was known to feel for the little
vagrants, who, like the dweller in Tom All-alone' s, were
always being ( chivied ' away. A meeting, too, was held
for the same object, when Lord Shaftesbury was in the
chair, supported by Lord Ebury and Mr. De Morgan, who
both spoke warmly in our favour.1 Our object was not
attained, partly from the difficulty of exciting general
interest, partly from the want of workers on the committee,
for Mr. Laing's health gave way, and the society ceased
to exist. The want is now in some measure but not
entirely supplied by the playgrounds of the Board schools.
It was a few years before this time that Mr. Dickens
and Mr. De Morgan had met at the house of Mr. Charles
Knight at Broadstairs. I heard that the meeting gave
pleasure to both, but I was not myself of the party. It
was in the autumn, on one day of which the forty drowned
bodies of cattle were heaped on the little pier, as described
in the volume of letters recently published.2 I well re-

1 I wrote in Household Words 'A Plea for Playgrounds,' and a
longer article in Good Words some time after for Miss Octavia Hill's
playground.

2 Some little time ago I came upon a letter from Mr. Dickens to us
both, dated 1840. A difference of opinion had arisen between my hus-
band and myself on the meaning of one of the illustrations in Nicholas
Nickleby, that in which Mrs. Kenwigs, her four daughters, with Miss
Petowker the fireman's daughter, and the reciter of the Blood-
drinker's Burial, appear. Mr. De Morgan believed that the stout
lady was the fireman's daughter, and the thin lady the mother of the
little girls who were ' too beautiful to live.' The dispute ran so high
that it could only be settled by an appeal to head-quarters. Accord-
ingly Mr. De Morgan sent a letter to the author from ' a lady and

266 MEMOIR OF AUGUSTUS DE MORGAN.

1858. member Mr. Diekens's active interest in the scene, and I
heard the proposal to make the dead cattle into sausage
meat, which probably was carried into effect ' unbeknown,'
for several of the carcasses were bought by butchers. I
was strictly enjoined not to let ' sassingers ' come into the
house.

1859. Our three youngest daughters had been born in
Camden Street, and there were many associations with
the house which were, with the sad exception of our
eldest child's death, pleasant to my husband and myself.
But we wanted a more roomy house, and it was thought
that my severe illnesses might be averted by a better
air.

After we were settled at No. 41 Chalcot Villas, Adelaide
Eoad (at that time nearly surrounded by fields, and
fully two miles from the College), he left the house
always before eight o'clock in the morning, and met the
omnibus in the Hampstead Road, which took him to
Graf ton Street a short time before the lecture began. He
returned to dinner at five o'clock ; and as he only gave
himself about half an hour's rest after dinner before going
to his library, where he wrote or read for four or five hours,

gentleman who, being husband and wife, seldom agreed about anything,
though they were in one mind in admiration of the novel,' entreating
the author to adjudicate the question. We received the following
reply :—

4 1 Devonshire Terrace, York Gate, April 12, 1840.

4 Mr. Charles Dickens sends his compliments both to the gentle-
man and the lady who do him the honour to differ upon an illustrated
point in Nicholas Nickkby, and begs to inform them that the lady sitting
down is intended for Mrs. Kenwigs, and the lady standing up for the
designing Miss Petowker. But Mr. Dickens begs the gentleman and
lady unknown to take especial notice that neither of their portraitures
is quite correct, Mrs. Kenwigs being constitutionally slim and
delicate and of a slight figure (quite unimpaired by her frequent
confinements), and Miss Petowker a young female of some personal
attractions, set off by various stage effects and professional captiva-
tions.'

This was according to my husband's impression, so he was trium-
phant and I crestfallen.

DRINKWATER BETHUNE. 267

he seldom gave up an evening to friends without feeling 1859.
that his work for the next day had accumulated. When
he had nowhere to go to between the lectures he spent an
hour or two in the Professors' room with some of his
colleagues in the middle of the day, and this was his chief
rest and recreation. I cannot record any of the conver-
sation held there, but I know that for many years it was
very pleasant and sociable, and ma,ny a good anecdote
and riddle (generally traceable to Dr. Sharpey) have come
to me from that little conclave.

One day my husband told me that he had only been
in the Professors' room for a few minutes for two days,
for that a poor man driving a cab had been thrown from
his seat just as he was himself crossing the road. ' They
picked him up,' he said, 6 quite insensible, but he recovered
when we got him home. I saw him comfortably in bed,
and that he did not want anything. Yesterday he was
much better.' I found that the injured man's home was
more than a mile from the College.

Mr. De Morgan's friend Mr. Drinkwater Bethune held Essay on
a high Government appointment in India. Besides being t/.° '
a statesman and a distinguished scholar, he was a philan-
thropist, and was active in promoting the education of
Hindoos and Mahomedans. The lives of Galileo and Kepler
in the Library of Useful Knowledge were by him, as was also
an essay On Probability, which he wrote in conjunction
with Sir J. Lubbock. On the back of this little book the
binder had by mistake printed Mr. De Morgan's name,
and the attribution to himself of a work to which he had
no claim troubled the reputed writer, who, of course, was
uneasy till he had thoroughly disowned it. On the cover
of his own copy he substituted for his name those of the
real authors, adding after the printed words * by Augustus
De Morgan ' the comment, c the last named is liomo
trium literarum.' 1

1 F. U. R.

268 MEMOIR OF AUGUSTUS DE MOEGAN.

1859. In 1850, shortly before Mr. Drinkwater Bethune's

dra™0 death, he had sent to England some copies of a work by
Ramchundra, a native teacher, and head master of Science
in the school at Delhi. A copy was presented to Mr. De
Morgan, who saw in this treatise on problems of Maxima
and Minima f not only merit worthy of encouragement, but
merit of a very peculiar kind, the encouragement of which
. . . was likely to promote native effort towards the restora-
tion of the native mind in India.' With his lively interest
in all that belonged to India, the land of his birth, and with
his still wider interest in every effort of original thought,
especially where, as bearing the impress of national charac-
ter, it had place in the history of mental progress, he called
the attention of the Court of Directors to the work of the
Hindoo teacher, suggesting that Ramchundra should
receive a reward for his work, and that the work itself
should be brought under the notice of Mathematicians in
Europe. After some correspondence with the authorities
and with Rainchundra himself, the Court expressing
entire concurrence in his views, his offer to superintend
the reprint of Ramchundra's work was accepted. It
was a work of some labour, because it was done so
thoroughly. His preface, consisting of twenty-three
closely printed pages, gives a short but scientific history
of the rise and progress of Mathematical science in
Greece and India, and an analysis of the mental character
of the two nations in their respective leanings to geo-
metrical and algebraic thought, with the causes of the
entire extinction of Mathematical speculation in India,
while it remained to some extent active in Greece as long
as that country existed as a nation. The extinction of
active speculation, and its replacement by a taste for
routine, ' to which,' he says, ' inaccurate thinkers give
the name of practical,' he shows to be coeval with the
death of Science in a nation. This was the fate of Hindoo
philosophy, and how to revive active thought in the land
of his birth was to him a question of deep interest. His

HINDOO ALGEBRA. 269

counsel may still be valuable. ' Some friends of education,'
he says, * have advised that the Hindoos should be fully Ramchun-
instructed in English ideas and methods, and made the
media through which the mass of their countrymen
should receive ideas in their own language.' This plan
has not succeeded, and a deeper knowledge of the psycho-
logical aspects of national character might have predicted
the result. c My conviction,' my husband says, ' is that
the Hindoo mind must work out its own problem, and
that all we can do is to set it to work — that is, to pro-
mote independent speculation on all subjects by previous
encouragement and subsequent reward.' Eamchundra
had a stronger leaning to geometry than could have been
expected by a person whose sole knowledge of the native
mind was derived from the Vija Granita, but he had not
the power in geometry which he had in algebra. ' Should
this preface,' the writer says, ' fall into the hands of some
young Hindoos who are systematic students of Mathe-
matics, I beg of them to consider well my assertion that
their weak point must be strengthened by the cultivation
of pure geometry. Euclid must be to them what Bhascara
or some other algebraist has been to Europe.' It may be
that the prevalence of algebraic thought among the
Hindoos naturally accompanies their power of compu-
tation, and their love of symbolism (without beauty
of external form) shown in the mythology and astro-
nomy ; while the mathematical reasoning of the Greeks
fell, as might naturally be expected from their love of
symmetry and proportion in form, into a geometrical
method.

At this time, Lord Brougham being Lord Rector of Offer of
the University of Edinburgh, the degree of LL.D. was Edinburgh
offered to my husband. He appreciated the honour, but
declined it with thanks, saying to me that it did not suit
him : he ' did not feel like an LL.D.'

The International Statistical Congress was held in
London in 1860, and he joined a Committee for the

270 MEMOIR OF AUGUSTUS DE MORGAN.

1859.

Inspection, I think, of Scientific Instruments, but he did
not give much work to this.

1861. An uncompromising character like my husband's must,

Astronomi- while the world is what it is, sometimes make its owner

cai Society, appear combative. And indeed it always needs some

kindness and geniality in a dissentient to produce the

conviction that he is not actuated by love of opposition in

the part he takes.

Mr. De Morgan's fellow- workers in any cause soon
knew him well enough to feel sure what part he would
take in any occasion of difficulty involving self-sacrifice
for principle. An occasion of this sort occurred in 1861,
when he left the Council of the Royal Astronomical
Society.

The following list will show the offices he had held
since he joined it in 1828 : —

Feb. 1830. He was elected a member of the Council.

1831. Secretary with Hon. Mr. Wrottesley.

1832-38. Secretary with change of colleague.

1839-40. One of the Vice-Presidents.

1841-42. Member of Council.

1843-44. One of the Yice-Presidents.

1845-47. Member of Council.

1848-54. Secretary with Admiral Manners.

1855-56. One of the Vice-Presidents.

1857. Member of Council.

1858. Vice-President.

1859. Member of Council.

1860. Vice-President.

1861. Elected a Vice-President; declined to act.
From this list, taken from the Monthly Notices, it

appears that he held the place of Secretary for fifteen
years. By his own statement in the letter given farther
on, he filled it for eighteen years.

In 1860 he retired from the Club.1 After our removal

1 This consisted of the most influential members of the Society,

ROYAL ASTRONOMICAL SOCIETY. 271

in 1859, from Camden Street to Adelaide Road, the 1861.
distance made it difficult for him to be in London late
at night, on account of the necessity before mentioned
of his leaving home early in the morning. His resigna-
tion was received with regret. The meetings of this
friendly Club had been a great pleasure to him, but
he had latterly been unable to join them. His friend
Mr. De la Eue, then treasurer and secretary, wrote : —
6 Regret was universally expressed at the announcement
of your retiring, and also because it recalled to mind
how little you had been with us of late. The members
could not reconcile themselves to the withdrawal of a
name so intimately connected with the Club for the
last thirty years, and you were immediately proposed
as an honorary life member. I have to announce to
you that you were elected by acclamation, and that the
Club hope that you will dine with them whenever your
leisure and inclination permit of your doing so ; and this
wish I endorse on my own account most heartily.' I do
not think he ever found leisure, however much he might
have had inclination, to dine with his old friends again.

During this and the following year occurrences took Election of
place which affected his happy relations with the Society, president!
though not with the friends who continued to belong
to it. In the year 1861, six members of the Council
determined to place Dr. Lee, of Hartwell House, in the
President's chair. Dr. Lee was a respectable and esti-
mable man, who, by the maintenance of a private observa-
tory, had shown great interest in Astronomy ; but he was
himself more of an antiquarian than a scientific man,
and, but for his wealth, would not have been eligible as
President. It was the manner of proposing the candidate
at a packed meeting, and the canvass for his election by
his supporters, in place of the open election by which,

who assembled after the meeting. Their entertainment consisted of
coffee, cigars, sometimes a bowl of punch, and always much friendly
talk.

272 MEMOIR OF AUGUSTUS DE MORGAN.

1861. in compliance with the recommendation of the Council,
a President had hitherto been chosen, that constituted a
departure from the course hitherto followed. It was no
longer ' our little honest Society,' as my husband had
called it in writing to Admiral Smyth ; and all its oldest
friends — those who had made it what it was — declared
against the innovation. The other party prevailed, and
on the election of Yice-Presidents after the President's
election, Mr. De Morgan was informed that his name was
on the list. His friends, when his intention to leave the
Council was made known, entreated him to remain, seve-
ral of them urging that his was the name which could be
least spared. But he believed that his resignation would
cause the smallest possible shock to the Society, while it
would be a protest against the unconstitutional tendencies
which he wished to arrest. In answer to the official an-
nouncement of his election as one of the Vice-Presidents,
he sent the following letter :—

41 Chalcot Villas, Adelaide Road, March 1, 1861.

Letter on GENTLEMEN, — I have received from Mr. Williams a notifica-

Coundh tion that I was elected a Vice-President of the Society at the
General Meeting of the 8th nit. This election, legally valid, is
morally defective in one essential particular. The appointment
of a voluntary officer must be a result of concert between the
choosers and the chosen. It is a matter of prudence, when a
new system is established by a contested election, that the first
should inquire of the second whether he will be willing to take
the office on the terms which the altered circumstances of the
case expressly or implicitly lay down. Failing such inquiry,
any election, however good in law, is but an offer ; and to the
offer I reply, in all good humour, first by thanks, secondly by
non-acceptance.

Here I might close this communication ; but the regard]!
feel for the Society, in whose affairs T have taken part from
early manhood up to a time when old age is within signal
distance, impels me to explain myself farther. In placing before
you. the ground of my retirement, I am fully satisfied that the
retirement itself, accompanied by reasons, will do the cause more
good than any services of mine have ever done yet, and vastly

ASTRONOMICAL SOCIETY. 273

more than my continuance on the Council could do. Were I 186L
not so well assured of this, that the course I take becomes im- Letter on
perative, I should content myself with silent acquiescence, and
should defer my secession until the actual arrival of the state of
things which I fear is on its way.

Before I enter on the subject I will premise — first, that
there is nothing in my refusal to serve which has reference to
the new President, for whom I entertain, as always, high
esteem and regard. Had Mr. Airy been preferred to Dr. Lee in
the manner in which Dr. Lee has been preferred to Mr. Airyr
my course and my reasons would still have been what they are.
Secondly, I fully admit, should any one suppose I question it,
that the Society has not exceeded its rights a bit more than I
shall have exceeded my own rights in sending this letter.
Thirdly, I have not acted in concert with any former colleague,
and have not even given a hint of my resolution to any Fellow
of the Society.

The Astronomical Society has gained a high position by
sheer hard work. It is the plainest of all the scientific associa-
tions, and the one which least glitters by the show of rank and
wealth. Its sole thought has been the promotion of Astronomy,
And undivided attention to its real business has been rendered
easy by such harmony as is very rarely found in public bodies,
Nevertheless, during the last two or three years there has not
been that entire unity between the Council and the Fellows
which had always existed in time past. I believe that such
interruption of the usual concord as has taken place was the
consequence of adverse feeling in a very small number of the
Fellows ; how generated I do not know. Perhaps that bias
towards initiation of political action by which Englishmen spoil
so many of their extra-political associations may have taken
hold of some minds, I thought I saw symptoms of the Council
being a corrupt aristocracy, who made pocket boroughs of the
planets, and deprived the moon of her due share of the franchise.
I will make no further allusions to the manifestations, which satis-
fied me, independently of all I knew besides, that the side they
came from was the wrong side.

The feelings I have mentioned soon took the form of a desire
to facilitate combined opposition to the list of officers which each
retiring Council had always recommended to be their successors.
The existing Council met the expression of this [desire by the
proposal of those by-laws on the subject which now govern the

T

274 MEMOIR OF AUGUSTUS DE MORGAN.

1861. Society. That I was not against the change may be inferred
from my being the acting Secretary of the Committee of Conncil
which drew up the new by-laws, and the mover of their adop-
tion at the general meeting which passed them. My assigned
reason was that nothing could be too democratic for a scientific
society. I think so still. But I saw in silence, though with
great satisfaction, that the changes would speedily bring to issue
and to settlement questions, on the right and speedy settlement
of which the prosperity of the Society depends. And this is a
much better way than could be opened by the results of a period
of smouldering discontent. I saw that the good sense of the
whole body would soon be turned to reflection upon the question
whether the Society could exist in honour and in usefulness upon
any other basis than that of peaceful government by a Council :
not this Council, nor that Council, but a Council. That is to say,
government by one Council, under the statutory changes of its
details, until that Council ceases to be in harmony with its con-
stituents, and then government by another Council, composed, in
strong part at least, of different men.

I did not suspect that the Society would be so fortunate as
that reflection on this point should first be promoted by so slight
a pair of matters as the substitution of one President for another,
and the retirement of so dispensable a member of the Council
as myself. It is just as I could have wished. My own secession
will not — whatever it might have done twenty years ago — im-
pede the action of the Society, while the retirement of a person
who has known it so thoroughly as I have done for thirty years,
during eighteen of which he has officiated as Secretary, will
certainly lead to that reflection which I desire to promote.

The circumstances under which I retire are, in my view, as
follows. Half-a-dozen of the Fellows, desiring to pay a compliment
to a highly respected member of the Conncil, proposed him as
President, in opposition to another Fellow proposed by the Council.
That this, and no more than this, was their first intention, I feel well
assured. But, as they grew warm in the business, they availed
themselves of the usual resources of opposition — the personal
canvass, the newspaper article, and the invention of a principle to
justify a course which, in the first instance, had no reason except
the innocent one which I have stated. They lay it down that
A B having been President three times, and C D not at all, it is
now, as it were, C D's turn. That is to say, they propound a
law of rotation, independently of any reason which the Council

ASTKONOMICAL SOCIETY. 275

might have had for their recommendation. Should I have mis- 1861.
represented, or rather under-represented, the Fellows to whom I Letter on
allude, the misrepresentation comes of their own fault. They
had the power of stating the principles on which they acted to
the general meeting ; it pleased them to prefer the partial and
private canvass for their only mode of action, the paragraph
and its reason for their only statement of view.

They succeeded, and I am convinced that one element of
their success was that modicum of adverse feeling towards the
Council, of the existence of which I had seen proofs. Their suc-
cess transfers the responsibility of their course of action to the
Society as a whole ; and thus, and thus only, does that course of
action become a legitimate object of my criticism. I maintain
and uphold the itidividual Fellow in his claim to propose a Presi-
dent on any criterion of superior fitness which he pleases. I will
support him, acting for himself, in the assertion of his right to
use the canvass, the newspaper, or anything which a civilised
man can have recourse to, in preference to placing his views
before the assembled Society. But when the Society adopts a
proposal, the result then becomes my affair, with its reasons, if
any be assigned ; or, failing such assignment, with the reasons
deduced by myself from circumstances.

The power of organising opposition, recently and most
properly conceded by the Society to individuals, is one, the
corporate assent to any use of which should both be governed
and defended by reason. It was intended, as the Society itself
was intended, for the encouragement and promotion of Astronomy.
When employed and privately argued against a deliberate re-
commendation of the Council, it should not be sanctioned by
the collective Society except upon avowed grounds. I speak
of concerted plans, not of votes of individual Fellows, each
acting on his own judgment. If the existing system of ad-
ministration be not in harmony with the corporate feeling to an
extent which requires united action, it is expedient that the
Council should know the how and the why. This is reasonable,
because it will discourage and retard Astronomy, so far as the
Society can do it — and it can do something — if the Council and
the Society should take to working against each other in the
dark. Should the system continue, it is my fixed opinion that
the harmonious and useful body to which I have so long been
attached will go through a series of faction fights, compared to
which the recent matter is hardly worthy to be called a contest ;

T 2

276 MEMOIR OF AUGUSTUS DE MORGAN.

1861. and will emerge, if indeed it emerge at all, with crippled utility,
diminished honour, and wasted resources. This is my opinion.
I desire no one else to assent unless his own experience of col-
lective action should make him see the danger as I do, after that
reflection which I know my proceeding will excite. I do not
affirm that the substitution of one President for another is in
itself a dangerous act. I look at the whole history of the
Society for some years past, and on that whole I am irresistibly
impelled to form a very strong opinion.

I will add something which may tend to prevent a greater
calamity than my own refusal to act. It ought to have been
evident to the promoters of the recent division that the new by-
laws have the effect of making what is called the balloting list
into two or more, whenever two sets of nominators are therein
exhibited. Usually when parties contest such a question each
gives the whole of its own list, and any two lists are not the less
two because there may happen to be many names common to
both. It is most expedient that those who originate a second
list should take care to ascertain that those whose names they
take from the other list are willing to serve in either event. For
two lists which differ by one name only, especially when the
name is that of the proposed President, may symbolise two very
different principles. It might easily happen that many of the
common names might decline to give such assent to the principle
of one of the lists, as would be inferred from their accepting
office at the hands of a majority. It cannot reasonably be
expected that any nominee should rise at the meeting, and
declare his intention of not serving except on one contingency.
I duly considered the propriety of such course, and rejected it
for three reasons. First, it wonld have had such an appearance
of disrespect to an old friend as it would have been impossible
to neutralise, save by such explanations as would have brought
on a discussion which it was not for me to originate. Secondly,
because such a declaration — a dictation, as it would have been
called — would have been a firebrand thrown into the meeting by
way of commencing the discussion. Thirdly, because the
course announced would have caused difference of opinion among
those who thought as I did concerning the policy of the oppo-
sition to the Council.

The true way of secur'^g a working Council would be for
those who differ to take care, each side for itself, to present a
list of those whom they have reason to know to be willing to

ASTRONOMICAL SOCIETY. 277

serve upon the views which the nominating party has put for- 18G1.
ward. In the present case it has been proposed to me, by the Letter on
mere fact of election, and in no other way, to act as Vice-
President on the principle of filling offices only to pay compli-
ments, or else upon a principle of rotation, the compliment and
the system of rotation being settled by private canvass. Or if not
one of these, then upon the principle that the deliberate recom-
mendation of the Council may be set aside on no reason, either
assigned or discoverable. I disapprove equally of the compliment
reason, the rotation reason, and the nullity reason. I consider
them all as fraught with danger when applied without delibera-
tion. I am not prepared to say that, on due consideration of all
circumstances, the case might not arise in which any one of these
reasons might be sufficient. But I feel compelled to decline
action on either reason on no better support than the pro ratione
voluntas of the balloting-box. If, indeed, the promoters of the
change had come forward and had justified their course in public
meeting, I might possibly, though not concurring in their
reasons, have been able to accept the deliberate conclusion of the
Society, in lieu of the deliberate conclusion of the Council. I
have much respect for the result of argument, even when I do
not feel convinced by the argument itself. But I will not act in
the affairs of a Society which rejects the recommendation of its
best advisers on grounds which those who promote the rejection
do not submit to discussion ; and, were I not satisfied that the
successful majority do not comprehend the character of their
own proceeding, I should look upon them as almost wanting in
courtesy for not taking the pains to ascertain whether I could
meet their views, or whether they would have to substitute for
my name that of one of the gentlemen whose advice they were
disposed to prefer to mine. As it is, however, I can thank them
without reservation for the honour which I decline.

I cannot help saying that it will give me much satisfaction
to hear that no one but myself, however much he may be con-
vinced that a new and perilous period in the history of the Society
has commenced, judges it necessary to carry matters so far as I
have done. And with this, coupled with the expression of the
deep regret with which I separate myself from those with whom
I have so long acted in the most friendly concert, I remain,
gentlemen,

Yours sincerely,

A. DE MORGAN,

278 MEMOIR OF AUGUSTUS DE MORGAN.

1861. P.S. — It will be seen that I write as if I were addressing the
Fellows at large. This means that I expect that my letter will
be entered on the minutes of the Council, which are by express
by-laws accessible to the Fellows at their meetings.

These suggestions on government might apply to
larger bodies than the one addressed. They give an idea
of his political principles, which demanded the utmost
possible freedom for the individual, subject to a conserva-
tive respect for law. I have been told that the Astro-
nomical Society suffered at this time from the causes
which led him to leave it. But these things occurred
twenty years ago, and their effects have, no doubt, long
passed away.

1862. His correspondence with M. Biot had been chiefly on
the Life of Newton. In this year M. Biot died, and Mr.
De Morgan received from his son-in-law, M. Lefort, some
particulars of his early life as material for a biographical
notice.

introduc- An introductory lecture, the last he ever gave at

at Univer- University College, on the opening of this session, was
iS C° never printed. How greatly this was regretted by many
of his hearers I am unable to say. Seldom was an
address listened to within those walls with a more lively
interest, or received with such mirth and hearty acclama-
tions. The subject was a branch of his favourite one —
* Education,' and that branch was the method of exa-
mining at Cambridge. The attacks on the system were
made with so much humour, and so much good humour,
that the attacked could hardly have resented what they must
feel was so well deserved. Great amusement was caused
by the description of the self-satisfaction of an examiner
after he had set a question well fitted to show off his own
ingenuity and cleverness, but unfitted to elicit the thought
or power of the student. The illustrations which half
filled the lecture were taken from common sayings, old
ballads, and nursery rhymes ; and if the grave body in
the centre of the theatre, a few of whom could appreciate

LIFE ASSURANCE. 279

the force and humour of the quotations, felt their dignity 1862
at stake, the indisputable truth of every sentence justified
the utterance. Many of the students who felt the im-
portance of all that had been brought forward in this
playful guise signed a request that he would print the
lecture. A similar request was also sent privately from
Cambridge. He meant to rearrange and add to it before
publication, but he never had time for this, and the
slightest notes only are left.

I ought not to leave out his work in Life Assurance,
but of this I can say very little. I have heard it said
that his attention was drawn to this subject by my father,
who, from his own pursuits, was supposed to be interested
in it. This was not so, however. The two had always
mutual subjects of more interest to discuss, and, as far
as I recollect, it was scarcely mentioned between them till
Mr. De Morgan, who had been consulted on some Com-
pany's business, referred to my father for information as
to their way of doing it, a subject on which he had been
consulted before. My husband frequently gave opinions
on insurance questions. He was a contributor to the
Insurance Record, and gave many valuable papers to it
and to the magazine of the Institute of Actuaries. One
of the longest articles in this was a severe criticism and
exposure of Mr. T. E. Edmonds, who had given to the
world as his own a discovery which was made by Mr.
Benjamin Gompertz. The latter was distantly related by
marriage to Mr. De Morgan's family.

The last paper in the Insurance Record to which his
name is appended relates to the Albert Life Assurance Office.
Company. In 1861 he had made the valuation according to
the data furnished to him, and in 1862 gave his opinion
that the Society was in a condition to give a bonus.
When, eight years after, the Society was declared bank-
rupt, under circumstances which were far from creditable
to the management, his name and opinion were brought
forward as a justification of their proceedings. This was

280 MEMOIR OF AUGUSTUS DE MORGAN.

1862. first known to him by paragraphs extracted in our news-
Failure of papers from the Bengal Hurka,™ and other Indian papers,

Albert Life * L. ., _ . * . , _ 0 . *7\ '

Office. and afterwards by the Overland Summary, by which it
appeared that severe censure had been passed upon him
for the part he had taken in the monetary affairs of the
Albert. The question was not unimportant, because much
ruin had been caused by the failure of the office ; and
though this could not be traceable to his advice, his name
had been used as a screen by those whose mismanage-
ment, if nothing worse, had caused the calamity. As
was said, he had but to fight shadows, but this might be
worth while when the shadows rest upon a good name.
When all this came to his knowledge in 1870, he was too
weak and ill to care much about erroneous statements
respecting himself, but his friends prevailed on him to
write an explanation of the case, which was simple enough.
He had, he said, given an opinion upon the data laid
before him. He had not been required to investigate the
affairs of the office. Had this been asked, he would have
perceived that the managers were counting as realised
capital large sums which they believed would be paid to
them from various quarters, an error against which he
had strongly cautioned them, and into which he after-
wards suspected they had fallen. His letter, the last he
wrote upon public business, contains a little touch of his
old humour.

When a scientific opinion is given, it is intended that ' it '-
the whole opinion, remember — may be used in any way the
receiver pleases. Let him give ' it ' as it was given, without
alteration or suppression, and he may speak of it as he pleases,
may call it what he pleases, and may infer from it what he
pleases. He may call my life office valuation a receipt for mince
pies — which I certainly never intended it to be — but he must
not mix up with it anything out of Mrs. Rundell or Mrs. Glasse.
Let him give it but fairly, and I am content, if he will do the
— same, to take all the consequences of his change of description.

Mathemati- The last occurrence connected with Science which gave
16 y' him pleasure was the formation of the Mathematical

MATHEMATICAL SOCIETY. 281

Society. Our second son, George Campbell, had gained 1863.
the highest prizes for Mathematics and Natural Philosophy
in University College, though his father's scruples were
strong as to adjudging the first prize in his own class to
his own son. My husband told me that the papers, which
he knew to be George's, were much ahead of the other
competitors. ( But,' he said, ' I don't see how I can give
him my prize.' I reminded him that the sons of other
Professors had frequently taken their fathers' prizes, and
that justice to George required it. He said that was
true, and he would show the papers to another Professor,
who was enough of a Mathematician to judge. The
arbitrator, who did not know the writing, adjudged
the prize to our son, as his father had done, without
the slightest hesitation. George afterwards took his
degree in the University of London, and obtained the
gold medal for Mathematics and Natural Philosophy.
He likewise took the Andrews Scholarship in Uni-
versity College, but the work required, especially that
for his degree, was too much for a delicate frame, and
a severe cold caught about this time was the forerunner
of his last illness. The last three years of his life were
alternations of illness and partial recovery, though a winter
at the sea-side and a subsequent voyage to the West
Indies with his brother Edward gave him strength for a
time, and we hoped he might have outgrown his delicacy
of constitution ; but this was not to be.

It was in the year 1864 that Mr. Arthur Cowper Origin of
Eanyard and George were discussing mathematical pro-
blems during a walk in the streets, when it struck them
that l ' it would be very nice to have a Society to which
all discoveries in Mathematics could be brought, and
where things could be discussed, like the Astronomical.'
It was agreed between the young men that this should
be proposed, and that George should ask his father to
take the chair at the first meeting. I have a list in his
1 The words in which he told me of the occurrence.

282 MEMOIR OF AUGUSTUS DE MORGAN.

1864. handwriting of those Mathematicians who were invited
to join, with the names marked of the gentlemen who
accepted the invitations. Among these were many of the
first Mathematicians in England, and their number rapidly
increased.

One of the first documents relating to this Society —
it may have a value in its future history — is the following,
lithographed from George's writing :—

University College, Gower Street, Oct. 10, 1864.
SIR, — We beg leave to request the honour of your attendance
at the first meeting of the ' University College Mathematical
Society,' which will be held at the College in the Botanical
Theatre on the evening of the 7th of November, at eight o'clock
precisely.

Professor De Morgan has promised to take the chair, and
will give an introductory address, and the general objects and
plans of the Society may then be discussed.

It is proposed that the ordinary meetings of the Society
should take place once a month, and that the papers then read
should be lithographed and circulated among the members.
The annual subscription will not exceed half a guinea.
We have the honour, &c.,

G. C. DE MORGAN,
ARTHUR C. RANYARD,

Hon. Sees, pro tern.

1865. The first meeting was held January 16, 1865. My
husband was the first President, and his inaugural speech
contains so many of his own leading thoughts, that I
may give a few sentences. The first conveys his old
opinion, formed early in life, upon the constitution of
public bodies, and the inexpediency of crippling their
future action by legislation at the outset.

There is much discussion about what our Society should be.
But this cannot be settled and marked out ; it must be deter-
mined by the disposition of its members. All scientific societies
are in danger of getting into a groove, and settling into a
routine which possesses small interest to the great body of their
members. . . . On the other side, there is always the danger of

MATHEMATICAL SOCIETY. 283

guiding the Society off the rail, as it were, and getting it out 1865.
of the way in which the momentum of its members can be Inaugural
applied to move it. ... address.

Our great aim is the cultivation of pure Mathematics, and
their most immediate applications. If we look at what takes
place around us, we shall find that we have no Mathematical
Society to look to as our guide. The Royal Society, it is true,
receives mathematical papers, but it cannot be called a Mathe-
matical Society. The Cambridge Philosophical Society seems
to fulfil more nearly the functions of a Mathematical Society, but
it is in an exceptional position. It is the Society of the place
which may be regarded as the centre of the Mathematical world ;
it is a Society in which almost all the members are able to relish
its highest discussions. But in London we have no Mathema-
tical Society at all.

He had a few words for his old object of attack — the
Cambridge examinations : —

The Cambridge examination is nothing but a hard trial of
what we must call problems — since they call them so — of the
Senior Wrangler that is to be of this present January, and the
Senior Wranglers of some three or four years ago. The whole
object seems to be to produce problems, or, as I should prefer to
call them, hard ten-minute conundrums. These problems, as
they are called, are necessarily obliged to be things of ten
minutes or a quarter of an hour. It is impossible in such an
examination to propose a matter that would take a competent
Mathematician two or three hours to solve, and for the con-
sideration of which it would be necessary for him to draw his
materials from different quarters, and see how he can put together
his previous knowledge so as to bring it to bear most effectually
on this particular subject. It is, I say, impossible that such a
problem as this should be set in these examinations.

It must be one of our objects to introduce into our dis-
cussions something more like problems properly so called, and,
if possible, to keep ourselves from entertaining an undue n am-
ber of the questions just described. In some quarters the Mathe-
matics are looked at, I may say, almost entirely with reference
to their applications. These applications are not only physical
applications or commercial applications, which may be termed
external, but there are also what may be termed internal appli-
cations. Those very questions to which I have alluded already,

284 MEMOIR OF AUGUSTUS DE MOItGAN.

1865. respecting curves of the second order, are applications of the
principles of pure Mathematics. They form, in fact, a particular
Inaugural branch of the application of first principles. . . .

We must not mistake and misapprehend these internal appli-
cations ; we must not regard them as constituting entirely what
we are to turn our attention to. We have several things before
us besides these, which are very little attended to. One of these
is what may be called Logical Mathematics. We want a great
deal of study of the connection of Logic and Mathematics.
Where is any consideration of this question to be found ? If I
may be allowed to say more on a subject to which I have
devoted a good deal of time and thought, I would make a few
observations on this very important and yet very much neglected
one.

There is exact Science in two branches : the Analysis of the
necessary Laws of Thought, and the Analysis of the necessary
Matter of Thought. The necessary Matter of Thought, that
without which we cannot think, consists of Space and Time.
These exist everywhere, and we can imagine no thought without
them. Space and Time are the only necessary Matter of Thought.
These form the subject-matter of the Mathematics. The con-
sideration of the necessary Laws of Thought, on the other hand,
constitutes Logic. These latter have been little studied hitherto,
even apart from the study of the necessary matter of thought.

We mathematicians may very easily improve our reasoning
from the very beginning. For, though the Logic that Euclid
used is very accurate, there has been no inquiry made with
regard to it ; and the consequence is that for two thousand years
we have been proving, as we go through the Elements of Geometry,
that a thing is itself. That is to say, we have been proving, in
the Elements of Geometry, by help of a syllogism, a thing which
must be admitted before syllogism itself can be allowed to be
valid. Thus, does Euclid not prove that, when there is but one
A and but one B, if the A be the B, then the B is the A ? He
would not take such a thing as that without appearance of proof.
* A thing is itself; ' that is the assertion, that is what Euclid
would not take without proof !

To take an example. Let us suppose that there is a village
which contains but one grocer and but one Post-Office. Then,
if the grocer's be the Post-Office, the Post-Office is the grocer's.
For, if it be possible, let the Post-Office be somewhere else, say
at the chandler's. Then, because the Post-Office is the chandler's

MATHEMATICAL SOCIETY. 285

and the grocer's is the Post-Office, it follows that the grocer's is 1865.
the chandler's, another place, by hypothesis ; which is absurd ; Inaugural
and so with every other place except the grocer's. Therefore
the Post- Office is at the grocer's.

Is not this mode of proof in the third book of Euclid, being
the way in which proposition 19 is deduced from proposition 18 ?
Yet any body who should use it out of geometry would be laughed
at, though Euclid used it, and all those who have studied his
Elements have been proving things in this manner for two thou-
sand years.

There is no doubt about the matter, I say — and it will appear
more distinctly on further thought — that you are proving by
help of a syllogism what must be admitted before syllogism
itself is valid.

As to the chances of the Society finding for itself
lines of original work, he says : —

The higher Mathematics may be carried on with much greater
effect by elementary students if they will but study points of
Logic, History, Language, and perception of propositions by
simple common sense. Mathematics is becoming too much of
a machinery, and this is especially the case with reference to the
elementary students. They put the data of the problems into a
mill, and expect them to come out ground at the other end —
an operation which bears a close resemblance to putting in hemp-
seed at one end of a machine, and taking out ruffled shirts ready
for use at the other end. This mode is, no doubt, exceedingly
effective in producing results, but it is certainly not so in teach-
ing the mind and in exercising thought. If it should chance
that we find a disposition among the members of this Society to
leave the beaten track and cut out fresh paths, or mend the old
ones, we make this Society exceedingly useful. But if not, if it
be our fate only to become problem makers and problem solvers,
there is no harm done ; we shall but add one more association to
the list of journals, colleges, &c., devoted to this object. The
only objection is that this branch of the subject is sufficiently
well appreciated and more than sufficiently well practised
already.

Original papers by both its first President and Secre-
taries appear in the first pages of its earliest reports, and

286 MEMOIR OF AUGUSTUS DE MORGAN.

1865. some brilliant mathematical discoveries by Professor
Sylvester were communicated to it soon after its founda-
tion.

In 1866 George was teacher of Mathematics in Uni-
versity College School, and in January 1867, the last year
of his life, the Tract On the Proof of any Function, and on
Neutral Series, read before the Cambridge Philosophical
Society the year before, has this note appended to it :
4 My son Mr. G. C. De Morgan recently showed me this
case of failure of development.' The algebraic operation
is given.

His father had a high opinion of the power of George's
mind, which in some ways resembled his own. Our friend
M. Libri called him Daniel Bernouilli, in reference to the
two Bernouilli s, father and son. It gave his father plea-
sure to think that although he died so young, his son's
name should have been associated with his own.

287

SECTION IX.

CORRESPONDENCE, 1856-66.

To Sir John Herschel.

Camden Street, June 8, 1856.

MY DEAR Sm JOHN, — I have long had the idea of a piano- 1856.
forte in which each set of strings belonging to one note is to
communicate with a pipe for resonance ; and sometimes I have
thought that a spring at the mouth of a pipe struck by a
hammer would make a good instrument. In this case we might
have various pedals opening and closing the upper end of the
pipe. But I never imagined anything so grand as the intro-
duction of a vast force by means of electro-magnetism. I should
propose to call your instrument the electro-magnetic whack-row-
de-dow.

What is the reason why thirds and sixths, major or minor,
are more pleasant to the ear than fourths and fifths, which are
consonances of simpler ratio of vibration ? Fifths, by them-
selves, have a certain something which the ear does not like
much of, and consecutive fifths we all know are forbidden. But
thirds and sixths are very pleasant. If Dr. Smith's theory of
beats be true, I almost suspect I spy a way to explain this. But
I must get hold of an organ tuner, and learn whether they are
actually effective.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, August 15, 1856.

MY DEAR SIR JOHN, — What can you say for yourself? Your
last note was written in a good strong hand. This is hot
weather. When I was a boy I read how Cato the Censor used
to allow himself a little vinegar in his water when the heat was

288 MEMOIR OF AUGUSTUS DE MORGAN.

1856. great, and when a young man I used to imitate him. A few
drops of vinegar, half or a whole teaspoonful to the tumbler,
I found the most refreshing addition possible to a tumbler of
water, and I have revived the habit. Try it. Raspberry vine-
gar is a great deterioration of the principle. Cato would have
censored it prodigiously.

I have got a clincher about Cath. Barton and Lord Halifax.
Last Sunday Libri showed me a letter of Newton which he had
bought. The handwriting is indisputable. It came out of some
Newton papers which Rodd picked up in 1847. It is written
four days after the death of Halifax to a Sir John of Lincoln-
shire (probably Sir J. Newton of Westby, Newton's distant
cousin). It excuses him (J. N.) from paying a visit for these
reasons : —

' The concern I am in for the loss of my Lord Halifax, and the
circumstances in which I stand related to his family, will not suffer
me to go abroad till his funeral is over.'

Not a scrap of evidence exists that Newton was ever ac-
quainted with the other Montagues, though of course it is very
likely he knew them ; but relation of any kind, whether rapport
or parente, is utterly unknown, much as Newton has been poked
into. Newton was not an executor of Halifax. Qucere whether
Halifax's family means family in the usual primary sense of wife
and children ? Did Halifax leave a widow ? Was that widow
Newton's niece ? If so, a very natural reason for keeping the
house occurs. Macaulay, who used to battle the point, and fought
for the Platonics, now says he does not entirely reject my hypothesis.
Brewster has never written to me since I reviewed his book, so
I cannot send it to him. Lord Brougham is brought up by it ;
says it is very curious, and he must think about it. I believe
this letter will be Cath. Barton's marriage certificate.

Here is another letter which I picked up in sorting my
letters to-day : —

' SIB, — Please give me information on the following points: —

'1. A course of mathematical study by which an accurate and
comprehensive knowledge of the abstract principles of the science
shall be gained, and at tho same time such a course as will prove
an efficient instrument in the study of physical science.

1 2. The best works — Continental, classical, and English — on
the several branches of mathematics, and where I can get com-
plete lists of books.

* Yours , .'

CORRESPONDENCE, 1850-66. 289

I never heard of the man in my life. I made the following note 1856.
on the letter, and did not send it : —

* Est modus in rebus, sunt certi deniqiie fines.
How could I answer this letter in less than five sheets full of
lines ? '

Yours truly,

A. DE MORGAN.

To Sir John HerscheL

7 Camden Street, Sept. 10, 1856.

MY DEAR SIR JOHN, — This letter is not written to be framed
and glazed, but because, quoad the form, I must have a line no
longer than the sway of the wrist, because the arm is in a sling;
because on Friday last I put out the shoulder, because I and
my book. ladder slid down together, because the angle at which
said ladder may be trusted on a beaten and tightly nailed carpet
is very different from the same when the carpet is dusty and
what seamen call loose in stays, because the coefficient of friction
is vastly altered. However, I am thriving apace, and my wife,
who would not believe my report of exceeding good health
written with a pencil an hour after the replacement of the
shoulder, but ran up to see how things were, went back to the
children satisfied that I was a convalescent. . . .

Now mark, dislocations are among the minor evils which step
in to shut the door in the face of greater ones. If the bone had
been invincible, and all the wrench withstood by the muscles, I
should have had a long fainting fit or fever, a sprain of six
months, and it would have been a question whether I should
have used the arm again ; whereas, after a flash of fire and a
bump, cogito ergo sum began to act, and I got up as much as
ever alive to all things, and especially to the necessity of sending
for a doctor. However, all this is merely as to the form of the
writing.

Do you remember Sir H. Davy's habits ? Was he in the
habit of rubbing his hands together in any peculiar way and
frequently ? I want to know, because verification of a story
too long to write now depends on it.

I shall hope to hear a good account of yourself. With kind
regards to all around you, believe me,

Yours very truly,

A. DE MORGAN.

290 MEMOIR OF AUGUSTUS DE MORGAN.

To Rev. Dr.. Whewell.

Sept. 16, 1856.

1856. MY DEAR SIR, — I have been prevented from answering your

note by an effect of gravity which brought me and my book-
ladder to the ground together, and dislocated my right shoulder.
However, it is getting right now, and the whole thing is not so
bad as it is called. As to Galileo, I have inquired of Libri,
who is up to that case above all men, and he says that though
various statements have been made, he never could find the least
ground for supposing that any Pope had done anything in the
matter. And this was my impression also. I feel confident
that all the rumour is a mere sham.

The following (not to be used) may confirm you. The nar-
rator is Biot, to Libri, long ago.

A little before 1830 Biot was at Rome, conversing with the
chief Inquisitor, who said, * You men of science think that the
Inquisition is opposed to scientific statements, which is quite
untrue.' 'Then,' said Biot, 'I suppose the Professor at the
Sapienza College may teach the motion of the earth ? ' The
Inquisitor shook his head and said, 'No, that could not be
allowed.' Depend on it, if anything had been done, it would
have been widely promulgated.

Yours very truly, however illegibly,

A. DE MORGAN.

To Rev. Dr. Whewell.

7 Camden Street, Nov. 7, 1856.

MY DEAR SIR, — For your thin volume of additions just
received many thanks. These little supplements are like giblet
pie — a collection of all that is most racy : only, mind, I don't
mean to say they are goose giblets ; on the contrary, they shall
be owl giblets if the owl is still to be the bird of Minerva.

Now for notes and remarks. Who can unlatinise in our day ?
Who answers for Nicholas Cusa or Adam Marshman ? } He
might be Adam Marsh, or Fen, for aught we know. Have not
the French made Viete of M. de Viette, who would have been
horrified at his prefix of gentility being abolished ? We happen
to have plenty of evidence to De Viette.

1 Adam de Marisco de-latinised.

CORRESPONDENCE, 1856-66. 291

Smyth is rather slapdash sometimes. He killed Mezzofanti 1856.
in the R.A.S. Annual Report long before that polyglot bipes
implumis set off to leave his card on all the builders of Babel to
see if he could manage to pick up a stray dialect or two more
than he carried with him. I feel sure that if there had been any
revocation of the decree — above all in 1818 — Libri must have
known it. But I will get something yet. The Catholics are
evasive on the point. Smyth heard it, no doubt, so have I ; and
there is a disposition to have it believed among the R. C.

Page 51. In p. 19 of my notes on the Antegalileans I have
given a better account of Digges, and especially of the edition
of 1594, which you seem not to mention. I have it. It has an
actual defence of Copernicanism (physical).

P. 33. I have never seen the perspective of Bacon separately,
and so say nothing. But I am not without a silent suspicion
that the work published separately is by John Peccam, after-
wards Archbishop of Canterbury, a pupil probably of R. Bacon.

P. 47. The acceptance of the motion of light is not pro re
natd ; the motion of light is first proved by Jupiter's satellites,
which establish geometrically a motion of the effect called light ;
and then, with the velocity inferred of the effect, the aberration
is explained in quantity and quality both. There is not even
the assumption that light is material. Measured motion is
geometry, not physics. . . .

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, Nov. 13, 1856.

MY DEAR SIR JOHN, — I am glad to hear you are getting on.
I think you should not do too much in the way of being a free
body in the morning. The evening phenomena are fatigue.

I doubt your prognostic about the coinage. I think you may
be eatable by the time it comes. It is getting into country schools
and colleges, and I think people are learning it. The House of
Commons will probably be tried again next session.

As to how you might cook next century, you remind me of
an experiment I have often thought of — mummy soup. The
muscular fibre which remains must be partially soluble in water,
I should think. I should like to catch some of the Fee-Jee
Islanders — if that be the way to spell it — and feed them on the

u2

292 MEMOIR OF AUGUSTUS DE MORGAX.

1856. strongest mummy soup made in a Papin's digester. They
are cannibals, and would enjoy the idea. Fancy the souls of the
poor Egyptians, who preserved their bodies with such care for a
future resuscitation, seeing their remains devoured by ferocious
savages, and incorporated literally into the bodies of the same !

I have been looking at a 10-inch bar of aluminium which
Graham has lent me. Queer stuff. Costs at present its bulk of
silver, being £ of the weight. Smells a little, and rings like
Scyllaand Charybdis — I mean the Sirens. It makes a very pretty
noise. They are making it at Paris in earnest. They put 40 Ibs.
of sodium into some preparation at one go, I am told, during
the manufacture of a lot.

Our kind regards to all the ladies.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, Nov. 8, 1856.

MY DEAR SIR JOHN, — Are you doing well and getting on ?
I am going on with my shoulder famously, chalking on the
board ; l but I can't do everything yet. I have learnt that
whoso putteth out his shoulder, him shall his shoulder put out.

I think that if you were to give me an answer before Friday,
I might talk of you at the Astronomical, where people ask after
you. Next, how are all your party ? — no small one.

I saw Warburton a week ago at his own house, working
away at An Om, in utter falsification of the maxim that out of
nothing can come nothing.

I have nothing in the world to say about mathematics except,
musing idly, I found that Euclid has not demonstrated the way
to bisect angles.

I send you a lecture on decimal coinage. It is a slow-moving
subject, but it must be carried sooner or later, in spite of
ministers. They might have mentioned it at Paris, while they
were talking about everything. I mean the Plenipotentiaries.

Yours very truly,

A. DE MORGAN.

1 In his lecture-room. — ED.

CORRESPONDENCE, 1856-66. 293

To Sir John Herschel.

7 Camden Street, Oct. 9, 1857.

MY DEAR SIR JOHN, — . . . I am very glad to hear your son is 1857.
safe. You say nothing about yourself, so I hope there is nothing
to say. Subdivide yourself into any number of egos or ichs, but
take care you don't get the double identity, which sometimes
happens, in which a person is one person for a time and then
another. Did you ever read a novel called The Devil's Elixir ? If
not, try for it afc the circulating library. This Elixir has the effect
that if two persons drink thereof their identities get mixed up
in a very odd way. Each one becomes the other to a consider-
able extent.

By the way, you and I may be cousins all this time without
knowing it. One of my mother's ancestors — her mother's
mother, I think — was a Pitt, belonging to a family which con-
sidered itself an elder branch of the Chatham family ; and I
think I remember some expressions of hers being quoted which
seemed to savour of thinking it very presumptuous in the
younger line to come out as prime ministers, &c.

Multa renascentur quce jam accidere. Among them is a fact
which I discovered a few days ago — that I, A. De M.,have sailed
under our friend Beaufort's orders. He commanded the convoy
in which my father and mother brought me home to England in
1806, he being in the Woolwich frigate. I was then four months
old. So you see I was at the Cape long before you.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, Feb. 7, 1858.

MY DEAR SIR JOHN, — King Cole (2nd edition) is nearly per- 1858.
feet. Carmina cumfumo is not idiomatic, and that is all.1

When did 1858 begin ? on what meridian ? An insidious
question, demanded in the interests of equinoctial time. Why,
1858 had as many beginnings as there are meridians. When did
Wednesday begin ?

1 Speaking of a Latin translation of King Cole, which Sir John had
sent him. — ED.

294 MEMOIR OF AUGUSTUS DE MORGAN.

1858. If a year begin with a day there must be as many beginnings

of years as there are beginnings of days. Now I ask another
question. From 0° to 360° of terrestrial longitude, how many
meridians are there ? The political world will be content with
defining the year by the place. The astronomer, when he names
time, always names a place. If you like to begin the year with
the centre of the mean sun, in the mean equinox, it can be done,
but the poor almanac makers must not be puzzled, and I protest
against any more 185f , or the like.

I returned to the Royal Society the other day a book which was
given to them in 1728, and had probably wandered the world for
more than a century. That book and others satisfy me that about
the years 1734-40 the R. S. library was expurgated — purged
of all anti-Newtonian and infinitesimal books. This is curious,
but they were curious people in curious days.

There is a very marked absence of all materials for studying
the Newton and Leibnitz controversy in the R. S. library.

Yours truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, Feb. 11, 1858.

MY DEAR SIR JOHN, — I see your drift. But that year question
set me off on equinoctial time. Why, the question is an ethno-
logical, not an astronomical one. When the Portuguese and
Spaniards met in the Philippines — via India the Portuguese,
via S. America the Spaniards — they differed a day in their
reckoning, kept their Sundays on different days, and cursed each
other as only real Christians can curse. I never could learn how
the Pope settled it.

Taking Christendom as a point of departure from whence all
have gone whom we are concerned with, we shall find the
Americans beginning their Sunday after us, and the Anglo-
Indians before us ; the New Zealanders after us, the Australians
before us, owing to the way they go. But when New Zealand
goes to Australia there is a change of day for them, and vice
versa.

Rule. — Do at Rome as they do at Rome. And what they do
at Rome depends on the direction of travel by which they got to
Rome. If there were a constant meeting at the meridians oppo-
site Christendom by people of different modes of coming there,

CORRESPONDENCE, 1856-66. 295

there mnst be an arrangement made somehow. By a wise 1858.
arrangement of things it will be long before the opposite part of
the world is fighting the question. I don't see how there could
be three days current at once, unless some chaps had gone
twice round the world and never made a correction.

Did I ever explain to you how it is that the opposite hemi-
sphere to the one which has London for pole is nearly all water ?
You might go ahead in science many a day before you would
find the true reason. Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

7 Camden Street, May 25, 1858.

MY DEAR SIR JOHN, — When your excessively rare animalcules
had been duly studied, it struck me that all creation is full of
life ; and though I have neither pond, tank, nor aquarium, yet I
have access to divers atramentaria which in common life are
called inkstands. Out of these I soon fished some specimens,1
which I send you greatly magnified. I begin to have a suspicion
that the style of writing depends somewhat upon the monsters
which live in the ink, and that people would do well to examine
the fluid before committing articles. Most of the specimens are
difficult to make head or tail of — which is very frequently the
character of other products of the inkstands. Care, however,
must be taken how such things are published, for the world is
very incredulous. And Fabricius, in his Philosophical Entomo-
logy, says, ' Damnanda vero memoria Johannes Hill et Ludovici
Renard qui insecta ficta proposuere.'

As to the algebra, you are proving that you won't look at
symbols. What ! ! ! When nk is the number of vibrations in
one second, and ma the time of each vibration, you pretend to
tell me that you don't see —

ma x nk=z~L ;
or do you dispute —

ma x nk=mnJca ?

You will not easily make me believe that you were doing
anything but laying a trap for me to make a pun that you

1 Figures made by scribbling, and then folding the paper in half, by
which both sides are made alike and resemble strange insects.

296 MEMOIR OF AUGUSTUS DE MORGAN.

1858. might be down upon me if I missed it. But I see through
you — you were pretending to labour under a maiik d' intelligence.
As to the little dees — De Mogorgon — it is not the first time.
My old friend Farish (the professor's son) could not call me any-
thing else ; it went against his conscience up to the day of his
death. 'But why is the gentleman not called De Mogorgon?'
I am constantly tempted to make a mistake in one Greek name,
because in the second-hand booklists it always comes after mine.
Look into any book list of a miscellaneous character, and you
will see the succession following : —

De Moivre
De Morgan
De Mosthenes.

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Whewell.

Oct. 10, 1858.

MY DEAR SIR, — Many thanks for the Bacon which you found
in the Barrow. It all amounts to wondrous little, if, as you say,
Bacon was known to the Cambridge men generally. How could
Bacon be so little quoted ? The conceits of which that age was
fond were taken out of puerility by him, and made into wit and
covered with taste. And yet they knew nothing of him to speak
of. Newton's silence is emphatic. When I have time and
opportunity I intend to work out the thesis, ' That Newton was
more indebted to the Schoolmen than to Bacon, and probably
better acquainted with them.'

The question whether I wrote the two articles in the Atlie-
nceum is entirely the question whether personal identity lasts
through time.

Cowley I had forgotten. I have looked him up again, and
see that he merits Harvey's satire. Gassendi I knew of. He is
a Baconian prononce. I dare say you have received Mansel's
vol. of Bampton Lectures. I tell him by this post that it is the
best argument I have seen against subscription at matriculation,
Can you detect that the printer has punctuated Bampton's will
into full Priestleian heterodoxy ? . . .

Yours very truly,

A. DE MORGAN.

CORRESPONDENCE, 1856-66. 297

To Sir John Herschel.

Oct. 15, 1858.

MY DEAR SIB JOHN, — It's all very well for people to be clever, 1858.
and go to the British Association, and talk philosophy and
chemistry and — confound the hard words ! — transcendity, which
transcends all entity whatever, and is next of kin to the two
German equations —

E very thin g= God.
God =0.

This, I say, is all well as far as it goes. But can your philosophy
answer me this ? — Suppose the Northern Hemisphere to be all ,

land, the Southern Hemisphere all water : is the Northern Hemi-
sphere an island, or the Southern Hemisphere a lake ? Crack
that.1

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

Camden Street, Nov. 15, 1858.

MY DEAR SIR JOHN, — I have as much chance of meaning to
try for the Lowndean as I should have of getting it if I tried
(=0). Knew you not that I am a heretic who is B.A. of thirty-
one years' standing by reason of subscriptions being unsub-
scribable ? Moreover, I have other fish to fry. Cayley is a
capital man for it.

I hope you have been asked to do a memoir of Peacock for
the R.S. anniversary. He is lost at the time when he is moat
wanted.

I heard of your frisking about the country like a young

1 The geographical question was answered with another by Sir
John Herschel.

' Suppose all was water except a patch of land of an insular form
round the North Pole, N° in radius (N = 3), would that be an island ?
I should say yes, because it is land. Next, let N=4, same question.
Next, N = 5, N = 6, 20, 30, 90°.

' At what value of N does it cease to be an island ?

'Then N = 95, 100 ... 179° 59' 59". At what value does the sea
cease to be an ocean, a lake, a pool, a pond, or a puddle ? I pause for
a reply.' — Collingwood, Oct. 18.

298 MEMOIR OF AUGUSTUS DE MORGAN.

1858. gentleman, and was very glad to hear of it. You are now
c discharged cured,' and are, I hope, meditating some proof of
violent health. A new edition of the Differences would be a very
pretty step in the proof.

Did I send you this riddle ? — the answer is in itself a riddle.
If a comet were to take a much more elongated orbit, and the
King of Naples were to prohibit the importation of malt liquor
into his capital, in what particulars would two empty heads
differ ? Answer overleaf.

Kind regards to all your circle.

Yours very truly,

A. DE MORGAN.

Answer : The comet would have double eccentricity, and the
King of Naples would not.
What can it mean ?

To Sir John HerscheL

7 Camden Street, N.W., Jan. 1, 1859.

1859. MY DEAR SIR JOHN, — Many thanks for your dates. I want
one more thing — Who was Peacock's father? I have before
me a book by a clergyman of the name, whom I suspect to be
the one — Rev. Thos. Peacock, author of The Practical Measurer
and of Walking ame's Arithmetic Modernised.

I am very completely set up by your dates. The Prolocutor
of Convocation is, in fact, the speaker of the Lower House ; for the
clergy have their higher House, made of bishops, and their
lower House, made of dignitaries and proctors, so called, elected
by the lower clergy ; and they all have a hankering to be what
they once were, when they persecuted books as heretical, and
excommunicated the writers, and kept the pot boiling to the
wonderment and amusement of men and angels. And this was
called synodical action, but at last the State voted it torn-nodical,
and put it down. In our own day it has been revived to the
extent of allowing a day or two of talk, and appointment of com-
mittees to crganise talk for next time; but no measures have
been allowed to pass. And Peacock, as prolocutor, was, I
understand, very useful as a king of order and a stifler of pranks,
he being himself favourable to the revival of synodical action on
the principle of all the clergy being as discreet as himself, a
theory which beats out of the field Homoeopathy, Mesmerism,
Table-turning, Parliamentary Keform, and Perpetual Motion.

CORRESPONDENCE, 1856-66. 299

What they want is that Parliament shall not legislate for the 1859.
Church without consent of Convocation, and this Parliament
will never agree to. In the meanwhile they are allowed to use
logarithms, not Napier's, but of the sort which Sophocles men-
tions, A.dy<Dv a/oi0/xos, which is translated a set of words.

Now you may guess what the Prolocutor of Convocation is .
Until very lately, and from George I. or thereabouts, they did
nothing but walk in procession, at the meeting in Parliament,
to St. Paul's or the Abbey, where they heard a sermon, and were
prorogued. A happy New Year to all.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

Camden Street, May 2, 1859.

MY DEAR SIR JOHN, — Did your Southern dealings ever bring
you in contact with the history of the formation of the south
polar constellations ? Do you know any work which treats that
subject especially ? Did you ever come in contact with the
doings of Frederic Houtmann, the real framer of these constella-
tions, as far as giving their star materials is concerned ? Next,
answer the question Come sta, curiously Englished by How goes it,
with reference to yourself and selves. I suppose the Italian
phrase to be Ptolemaic, and the English to be Copernican.

What have I to do with Houtmann ? He adjoins himself
more slantendiculari to the question of a manuscript sold in
Libri's sale, as written by Galileo on the doctrine of the sphere.
Some question has arisen about the evidence, external and inter-
nal, and I have been looking up the points. The internal
evidence is to me very satisfactory ; and as to the handwriting,
there is a hitch about the letter r, which all the Galileos we
have to compare with make r} and the MS. makes i. In spite
of this I cannot help believing that the MS. is Galileo's. It
would be much better worth its money if it were not.

As to the state of things in general I have nothing to say. I
don't know whether the Austrians have forced a tete du pont
at Buffaloroary, or some such place, or not. I hope some bright
nebula or other is of a white heat, and is set apart for all who
make or instigate wars of ambition, I wish Lord Rosse could
find it out, and could show III. that I.1 has his spirit herme-

1 Meaning the first and third Napoleon. — ED,

300 MEMOIR OF AUGUSTUS DE MORGAN.

1859. tically sealed in a bottle, and heated up to a pressure of 100,000
atmospheres. It might make him behave himself, but perhaps
not. With kind regards to all,

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

Camden Street, May 18, 1859.

MY DEAE SIR JOHN,- Thanks for your pamphlet. I have not
had time to do more than glance at it, but will say what I think
when I have got through a heavy job of calculation — a job of
life and death, as one may say, for it is all about premiums and
claims and assurances, &c., &c.

Maurice de Biran, who died in 1824, aged about sixty, was a
philosophy who speculated and died, even as a silkworm spins
and dies. He will be a gaudy moth, I dare say. His cocoon
was published by Victor Cousin in 1841 in four volumes. He
was very much against Napoleon in 1814, which means, I sup-
pose, that he had been his parasite theretofore. He was a public
man of some kind. Probably his will was an impulse to better
his condition, or butter his condition. He passes for an acute
thinker in France, but I have never seen a line of his writing-.

I believe that so much of cause as is not mere notion of pre-
cedent and consequent is derived from our own consciousness
of power exercised at will. If we had been rational posts, in-
capable of motion, chewing the cud on what passed before our
eyes, and if with a will incapable of action, I do not see how we
should have had any real notion of cause. What the will is I have
not the least idea, or whether it ought to be called the shall or
not. Query, if it be really correct to call it the will, how is a per-
son whose will is undecided said to be shilly-shally ? Ought it not
to be willy-ivally ? Kind regards to the circle.

Yours very truly,

A. DE MORGAN.

To Miss Sheepshanks.

41 Chalcot Villas, Adelaide Road, N.W.,

August 24, 1859.

MY DEAR Miss SHEEPSHANKS, — I do not know what you have
done with my dear friend's books. There are one or two which
I should recommend to be given to Trinity College library, if

CORRESPONDENCE, 1856-66. 301

they can be detected. They contain handwriting of Horrocks, 1859.
the famous predecessor of Newton in the Lunar Theory. They
will no doubt have the book-plate of either Christopher or
Richard Towneley with these arms. . . -1

Such a book-plate in a book with handwriting in it is very
likely to be. Horrocks's, if astronomical. I found one of these
books at a sale, and gave it to Trinity College, and I remember
your brother having two at least. But the thing does not press.
A life of Horrocks just published reminds me of it.

August 27. — We are all pretty well, and I have got my books
into something which is not disorder. But two negatives do
not make one affirmative. . . .

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

41 Chalcot Villas, Sept. 9, 1859.

MY DEAR SIR JOHN, — You puzzle me. I always took it that
you and our friend Francis Baily foregathered at the Astro-
nomical Society, and then and there concocted a private friend-
ship, as many good men have done, and more by that same
token will do. But if Miss Baily was a friend of early boyhood,
you can hardly miss to have the same to say of Francis. She
must have been, I should say, ten years older than you : if Men
of the Time be correct in time, eight years. Explain this point,
T pray you. Where did you first make Francis B.'s acquaint-
ance ¥ As you have let out the name of the person who sold
you cakes, there is nothing that you can have any excuse for
being secret upon.

I am not clear in my memory about the names of any of my
purveyors till about fourteen years of age. I think I took their
names to be immaterial, and their sweetmeats the real thing.
But at the age I named I was introduced to Mother Fudge — her
real name — who could carry in her head the debts of any number
of boys, and no mistake. How she managed to remember the
several little accounts from 1 ^d. up to half-a-crown I never knew,
nor she either; but those who really wanted to do her, and those
who pretended to want it, found her utterly uncheatable. She
would run over their tradings for a week past with a confidence

1 The arms drawn appear to be — on a field argent, a bar sable sur-
mounted by three stars sable. — ED.

302 MEMOIR OF AUGUSTUS DE MORGAN.

1859. which was sure to get a verdict from the little mob ronnd her.
She could neither read nor write.

' Mother Fudge,' said a boy to her, ' can you make poetry ? '
* I, sir ? ' said she ; 'if I could make English-Poeters, do you think
I'd be here selling apples and pears ? ' * Now, Mrs. Fudge,' said
I, who had been reading Johnson's Lives, ' I could name you
three poets who did not get as much among them as you get by
this one school.' * Then I wouldn't give nothing apiece for
them,' said she ; ' they must have been regular bad ones.' I
think the copyright of ' Paradise Lost ' sold for about a year of
her profits from that school.

I have had a slight touch of gout — nothing to hinder my
walking, with a little pain, but just a straw to show which
way the wind is blowing. If you could have known of your
own consciousness how regularly the homoeopathic medicines
alleviated it when I stuck to them, and how it got back again
when I forgot them, as I often did in the moving, &c., you
would be satisfied that the post hoc of little globules was
propter hoc.

I have now got rid of my books ; that is, have shelved them.
And behold ! for the first time these two months I have walked
my fill without feeling lame.

Yours very truly,

A. DE MORGAN.

To Rev. Dr. Whewell.

41 Chalcot Villas, Adelaide Road, March 3, 1860.

1860. MY DEAR SIR, — I have received the copy of the History of
Discovery, for which many thanks ; also one from the Athenaeum
for review, which will go back uncut. I fully expect some one
will some day prove by instances that the Athenceum reviews
books without reading them, and the instances will be copies
which reviewers have not cut, preferring to take that trouble
upon their own copies.

I see you have at last admitted that Induction =Induction,
means Induction < > Induction. Whether you have gone as far
with lo(jic I have not yet found out.

And I see, with great satisfaction, that the name of Friar
Bacon begins to appear. Brother Roger has always been a great
favourite of mine since as long ago as B in the Penny Cyclopaedia,
and he ought to be allowed his share of the name of Bacon.

CORRESPONDENCE, 1856-66, 303

Bacon is a queer name ; but there seenas to be a providence 1860.
which watches over names, and makes the great men have bear-
able sounds. None of the hypotheses that, be the names what
they may, the exploits will sanctify them in time ! If Bacon and
Newton had been Wiggins and Figgins, would any time have
taken off the ridicule of the rhyme ? Could anybody with a
grave face have argued the question whether the immortal
Figgins was or was not indebted to the great Wiggins ?

I see a little theological philosophy. A rationalist Non-
conformist a few weeks ago opened one of his paragraphs thus : —
'Now, my brethren, let us proceed to make a logical incision
into the psychology of Grod.' This was making a subject of the
Deity. Subject is the sense in which the word was used in reply ^ <
to an argument of mine. I maintained that a good teacher must W*
have his heart in his subject, and his subject in his head. Not*c*-
if he teach anatomy, says Dr. Sharpey, for he could neither have
his heart in his subject, nor his subject in his head.

To Professor Kelland.1

41 Chalcot Villas, Adelaide Road, April 2, 1860.

MY DEAR SIR, — I have received your note announcing that
the Senate of the University of Edinburgh intend me the honour
of a degree of Doctor of Laws on the occasion of Lord
Brougham's installation as Chancellor.

I hope I shall give no offence by very respectfully declining
the honour. I mean the diploma. The honour lies in the good
opinion of the Senate, and that your communication gives me a
right to say I have already earned.

My reason for declining the degree is my own peculiar dis-
like of conventional titles, which are not what they seem to be.
If I had studied civil law I should be very glad to be styled fit
to teach it by any competent body ; but as I never have studied, I
object to call myself a teacher, and should object to others calling
me so, and I would not consent to accept a degree in law from
any University in the world. This is for myself, without im-
peachment of the conduct of others for adopting any conven-

1 In reply to an offer to confer on Mr. De Morgan the honorary
degree of LL.D. of the University of Edinburgh.

304 MEMOIR OF AUGUSTUS DE MORGAN.

1800. tional misnomer in which they may see good, or for which they
may find reason.

I am, dear sir,

Yours very truly,

A. DE MORGAN.

To a Friend.

41 Chalcot Villas, Jan. 19, 1861.

1861. MY DEAR , — Two days ago I heard from Miss Sheep-
shanks of the heavy blow which has fallen upon you and ,

a dreadful shock, and, I must suppose, wholly unlooked for.
With my strong and increasing disposition to congratulate those
who leave this world, I feel an increasing amount of sympathy
for those who are left behind ; and you and your wife's share of
this mournful event will command the sympathies of thousands
you know nothing of in addition to those of your friends.

I trust you both bear up, and try to balance what is left
against what is gone. That this is not easy I know. A few days
more than seven years have elapsed since it was my turn, and I
could not then feel that six left made any set-off against one
gone. I could only understand it. But time will do for you
what it has done for me.

My wife unites her sympathy and kind regards with mine.

Yours sincerely,

A. DE MORGAN.

To Rev. Dr. Whew ell.1

41 Chalcot Villas, Jan. 20, 1861.

MY DEAR SlR, — This very (Sun)day — how I do not know, but
I suppose the Parcels Company holds it a work of necessity and
mercy to distribute the parcels which have accumulated during
the frost ; most likely they have been obliged to suspend some
work by the state of the streets — I have received the volume of
Barrow, for which I have to return thanks either to you or the
College ; c'est egal, Vetat c'est moi ! I say nothing as yet, except
that it is exceedingly handy and time-saving to have these books

1 Wafered into a volume of tracts left by Dr. Whewell to Trin.
Coll. The succeeding letter refers to the memoir entitled ' On the
Syllogism, No. IV., and on the Logic of Relations,' in the Trans-
actions of the Cambridge Philosophical Society, vol. x.; partii., 1860.

CORRESPONDENCE, 1856-66. 305

in one volume. For B. is the man of all others, according to my 1861
experience, who is referred to by citation of one work for what
is in another. How could aught else happen to a cove who
called one of his writings Lectiones Mathematicce, and another
Lectiones Geometricce, and then treated what is considered as
exclusively Geometrical (as Euclid V. wrongly is) in his Mathe-
matical lectures, pp. 8, 9 (i.e. one word shared between them) ?
For metaphysical read psychological. I don't object to the word
a few lines higher up.

Do yon know the use of the word metaphysical, which is
growing up among the writers of the examination books which
have taken the place of all others ? — I mean at Cambridge. It
means requiring thought, and proceeding without symbolic calcu-
lation. When a proof of two pages of symbol drumming is
avoided by an act of reasoning, it is said to be ' too metaphysical.'
This is one of the consequences of the death and burial of
psychological thought in Cambridge. There seems to be a com-
plete acquiescence in the maxim that Oxford shall settle what
the world shall think, and Cambridge shall settle who is to be
Senior Wrangler. It is getting worse and worse from day to
day. Are any of the younger men alive to the facts ? With
best remembrances to Lady Affleck,

I am yours very truly,

A. DE MOKQAN.

To Rev. Dr. Whewell
41 Chalcot Villas, Adelaide Road, Jan. 20, 1861.

MY DEAR SIR, — There are some mistakes which are too small
to be of any consequence, and some which are too large. Ex-
tremes meet; — oo is curiously a comrade of +00. . . .l

The reason I call &3 — 2«— 5=0 a celebrated equation is
because it was the one on which Wallis chanced to exhibit
Newton's method when he first published it; in consequence
of which every numerical solver has felt bound in duty to make
it one of his examples. Invent a numerical method, neglect to
show how it works on this eqnation, and you are a pilgrim who
does not come in at the little wicket (vide J. Bunyan).

Newton was anything but illiterate. He knew Bacon. His
silence is most marked. How could he avoid every possible

1 Referring, I think, to some error in a figure in a former letter. —
S. E. DE M.

X

306 MEMOIR OF AUGUSTUS DE MORGAN.

1861. amount of mention of Bacon on every possible subject ? I never
said he did not know Bacon ; I only said he could not be proved
to have known of his existence. Nor can he. I think he has
taken such pains not to be known to know him as cannot be
attributed to accident.

I am glad to hear there are logicians at St. John's. It is a
college at which more pains are taken to make the men write ©
for ' circle ' in their writing out than to prevent their reasoning in
a circle. There is no attention given to writing in. Neverthe-
less, St. John's has preserved the shadow of a teacher of logic.
When I published my syllabus last year, I sent a copy to every
college in Cambridge, directed 'to the Tutor in Logic,' just to
make them stare. I got an answer from St. John's from Mr.
Mayor, who acknowledged the title. .

It is not examination that is wanted, but good teaching and
example. A paper of logic conundrums would be just as useful
as one of those fearful mathematical papers, to prepare for which
private tutors drill men in passing examinations. Thank Heaven
that I was at Cambridge in the interval between two systems,
when thought about both was the order of the day even among
undergraduates. There are pairs of men alive who did each
other more good by discussing x versus dx, and Newton versus
Laplace, than all the private tutors ever do. With kind re-
membrances to Lady Affleck,

I am yours very truly,

A. DE MORGAN.

From Professor Alexander Bain.1

University, Aberdeen, Feb. 7, 1861.

DEAR MR. DE MORGAN, — As two copies of your paper on the
' Logic of Relations ' have reached me, I beg to return you one of
them, and to thank you for the other. I am very much inte-
rested with this new subject which you have entered upon, being
convinced that the greatest omission both in logic and psychology
is the not seeing how far the principle of relativity goes. So far

1 This letter was given to me by Professor Alexander Bain. I have
departed from the general rule of not giving letters to my husbcind in
the correspondence, because in this instance the value of his own to
general readers is greatly enhanced by being accompanied by that to
which it is a reply. I wish it had always been possible to give both
sides of the correspondence, but this would have rendered it too volu-
minous. — S. E. DE M.

CORRESPONDENCE, 1856-66. 307

as I am able to judge, relation goes into everything ; no quality 1861,
existing except as related to some other, which we sometimes
call its negative, at other times its contrast, and again its cor-
relative. The straight line has no meaning without its contrast,
the bent line ; the occurrence of the two kinds is necessary to
our recognising either property. Every quality, every cognition
of the mind, implies an antithesis or couple. Hot — cold, up —
down, &c. If I say red, I mean to exclude all other members of
my * universe ' (to use your own well-chosen designation) ; and
if that be ' colour,' I exclude all other colours. The important
inferences deducible from the essential doubleness of all cognition
are, I am sure, very numerous, and I have no doubt you will con-
vince us of this if you continue the subject.

Yours faithfully,

ALEX. BAIN.

To Professor Alexander Bain.

41 Chalcot Villas, Adelaide Road, N.W.,

Feb. 9, 1861.

MY DEAR SIR, — I am sorry to have given you the trouble of
returning my second copy. I see I must have entered you as
of two Universities.

I quite coincide in your view as to a quality being unthink-
able except in company with its non. I forget where I said, long
ago, every name designates every object of thought as either in
the class or out ; but I did say it, and the equipollence of X and
non-X is the foundation of completeness even in common syllogism.
I hardly like to claim the word universe as mine, though I have
brought it down from its modern sense (the TO TTO.V) to the old
sense. Those who have derived the word from a mixture of
unum and diver sum (strange etymologists J) certainly very much
favour my plan of making it any aggregate of X and non-
X which is in hand. But the old universal was any name which
had plurality of things signified : of two only, the name turned
the two into one, in unum versa. I have made some people stare
by telling them that universality begins at two.

The combinations of relation are the ambiguities of language.
Looking on a little into compound relation, I come to such a
sentence as the following : —

' He is the father of a friend of every one of my children.'

Do I mean that one of his children is the friend of every one

x 2

308

MEMOIR OF AUGUSTUS BE MORGAN.

1861. of mine, or that every child of mine has a friend among his
children ?

Here is L(MN)' as distinguished from (LM)N/. This door
is a very little way open as yet.

Yours very truly,

A. DE MORGAN.

To Admiral Smyth*

41 Chalcot Villas, Adelaide Road, Feb. 19, 1862.

1862. MY DEAR SMYTH, — I am not very especially busy just now.

The obscure men are, as we know, precisely the men that
future necrologists will look out for. I find that the Biographic*
Obscurorum Virorum are very useful. I have an old Italian Glorie
degli Incogniti, which I find very useful for information about
men who are merely there to be shown up for non-notoriety.

Yours sincerely,

A. DE MORGAN.

To Sir J. Herschel.

MY DEAR SIR JOHN,

April 19, 18G2.

No news here ; not even a riddle. Here is a poem which
was given me : —

"AeiSc eiSvAAiov Sea,
Felis adest cum cithara,
Vacca lunam transivit,
Hoc jocoso motus visu
Rumpitur canellus risu
Cum cochleari lanx abit.

Which do you believe in, metal plates or guns ? I have just
received a pamphlet on the subject from Michael Scott. If this
be the great wizard, then we know how it was that —

When in Salamanca's cave

Him listed his magic wand to wave,

The bells would ring in Notre Dame.

The wand was a long match, and his range was so good

CORRESPONDENCE, 1856-66. 309

that he would hit the belfry at Notre Dame from as far off as f 1Q62
Salamanca. The end of it I have long foretold to be that the
different capitals of Europe will shell one another without the
trouble of sending out soldiers.

With kind regards to Lady Herschel and the juniors all,

I am, yours very truly,

A. DE MORGAN.

To Sir J. Herschel.

91 * Adelaide Road, April 29, 1862.

MY DEAR SIR JOHN, — Many thanks for the hexameters. They
are as good as they can be, but all the logic in the world does
not make me feel them, to be English metre, and they give
satisfaction only by reminding me of the Greek. Just as, mark
you, a flute-player — which I have been these forty-five years —
only plays Haydn and Mozart because he has the association of
the orchestral accompaniment, which arises in his head with the
melody.

The idea of the Scott ballad metre is not recent. When I
was at school, forty-two years ago, our ludi-magister read out
about 100 lines of Homer, which he said were versified by
Scott himself as a specimen. They were decidedly Scotfc, and
I thought not a little Homer.

The hexameter, it is clear, does not fix itself in the popular
mind. If it has done so proofs can be given, but I have not
met with them ; the popular mind knows neither quantity nor
accent, but that which is to last bites its own way in, without
any effort. Is the hexameter making any way ? Do people
quote any hexameters ?

It seems to me that the problem of a metre for translation of
the hexameter is not yet solved. The English hexameter is not
a better reminder of Homer than the usual metres of our
language.

I have discharged my conscience. Richard's visual organ.2

Yours very truly,

A. DE MORGAN.

1 The number of the house had been changed.

2 Dixi?— S. E. DE M.

310 MEMOIR OF AUGUSTUS DE MORGAN.

To Sir J. Herschel.

91 Adelaide Road, May 3, 1862.

1862. MY DEAR SIR JOHN, — A great many years ago you stood up

after dinner at our club, and gave strong hints that your time
was nearly up. But you brisked up, took the Mint, overworked
yourself, got an illness worth prophesying about, got over it,
and committed mathematical papers. Now here you are again,
talking about softening of the brain, and a knacker's yard, and
all kinds of incommensurables. If this mean that you are
going to be Chancellor of the Exchequer, why, take off the
income tax. If it be really melancholy foreboding, take on a
little quinine or brandy and water, and give up the hexameter
for six months. It is a mournful metre.

As to your catalogue of Greek ships and of nebulte, take care
you do not mix them accidentally, ' A catalogue of ships which
sailed against Troy, reduced to the year 1862,' by Sir J. H., &c.
People will stare to see how 2,500 years of precession turn a
trireme into a steamship. All our progress may be only pre-
cession of the equinoxes, motion backwards of the zero of
reckoning.

As to the hexameters, it is only now and then remembered
that verses among Greeks and Romans were not for recitation,
but recitative. An hexameter is a natural measure for a chant.
I dare say the rhapsodist in the streets of Athens gave it out
something like as a Puseyite parson gives out the Litany, only
with more taste. A famous hexameter might be made out of
the opening line of the hymn to the Virgin in * Masaniello,' but
our most natural measure is a foot too long, and the last spondee
is doubled.

Yours very truly,

A. DE MORGAN.

CORRESPONDENCE, 1856-66. 311

To Sir J. Herschel

91 Adelaide Road, N.W., May 30, 1862.

MT DEAR SIE JOHN, — I should not wonder if Sylvester and 1862.
you were at one without any intercommunication of your par-
ticles. I have had the same idea a long time. I have even
hinted at it through a glass darkly. In my third logic paper
there is the following passage : ' It is easy to frame hypotheses
which no one can of knowledge deny, under which attributes in
the brain should be as real as the sun in the heavens, or the
rocks on the earth, and this without a denying either the
existence of matter or the separate existence of mind.' If the
things of the universe be affections of the immovable primary
particles of space, the impresses on the brain may be veritable
copies, as real as the things themselves. A very pretty system
of pre-established harmony might be established. If all the
matter- universe be in motion of translation through the space-
universe or in transference, and if an individual in a certain part
of a certain nebula be to have a headache at a certain date, he
may at that date find the space particles, which are to keep up
his head, ready supplied with the adjunct affections — confound
them, whatever they are ! — which are essential to an ache of
predestined intensity. ' How charming is divine philosophy ! '

Of course all this means that I have received your letter and
book. I will look at the latter, and let you have it back soon.
I never heard of the dialogue between Hermogenes and Her-
mione. The puzzle about oo arises much, I think, from a want
of distinction between the subjective and objective infinity. But
before I fairly tackle the subject I have to superintend and, en
bloc, to calculate a valuation of about 30,000 life policies ; but
not 30,000 calculations — Heaven in its mercy forbid ! But I
must leave off. With kind regards,

Yours very truly,

A. DE MORGAN.

To Sir J. Herschel.

91 Adelaide Road, Aug. 9, 1862.

MY DEAR SIR JOHN, — I return you with thanks your MSS. on
algebra. There are little bits here and there that I wish had
been published. Did it chance to you that the first thing you

312 MEMOIR OF AUGUSTUS DE MORGAN.

1862. wrote never was published? It did so to me. The first thing
ever proposed to me was a treatise on mechanics for the U. K. S.
I wrote a few chapters, and, chancing to become a candidate for
what I now hold, I sent my MSS. in as a testimonial, and I
believe it greatly helped me. At any rate, I was picked oat of
fifty candidates, being known to be only twenty-one last birth-
day. I think Brougham and Warburton were the people who
dared a thing so bold, considering the danger of making any
ventures in an institution beginning under so many evil eyes as
the University of London. Olinthus Gregory was against it ;

S , who always had a wonderful faculty of getting something

against somebody, though he did not know me, and had never
seen me, either concocted or retailed to Stratford a story which
I never heard from elsewhere, namely, that my appointment was
the doing of Mr. Frend, then an acquaintance of mine of a few
months' standing, not on the Council, and at Cheltenham for
health all the time, and who learnt my candidateship and appoint-
ment from the newspapers at one and the same moment.

Who shall escape ? Mark the following. In some journal in
1851, M. Bertrand, in a paper on the convergence of series, is
charged with suppressing what I had done on the same sub-
ject. It is hinted that he had used what I had done. The facts
are —

1. M. Bertrand invented a set of rules before he had seen
mine, so he says, and I believe ; his method has all the marks of
independent thought. After he had observed the identity of his
rules and mine, in effect and each to each, it struck him to try
a hint of a M. Raube,*and he thereupon constructed a third
system. 2. He announced my rules in half a quarter-page of
translation from me, with inverted commas to every line, and
mentioned my name eleven times in his descriptions and com-
parisons. 3. He gave my book the date 1839 instead of 1842,
1839 being the date of the number in which the rules of con-
vergence appeared. 4. He sent me a copy of his paper as soon
as it appeared.

What could he have done more ? Nevertheless, he is un-
blushingly charged with unfair suppression by a man who knew
nothing of my book but what he himself had told him, for he
(the critic) gives the wrong date of 1839.

As to infinity, I hold J to be the infinite of infinites.

For 0 marks the change from + to — , which oo does not.

As we generally use oo, we admit oo1, which is not negative,

CORRESPONDENCE, 1856-66. 313

and oo3, &c. But quantity which changes sign through infinity 1862.
passes though ^. This will become a very important distinction.

The J of common algebra is high up above the — - of the differ-

dx

ential calculus.

I am rid of all fear about oo2. I believe in oo, oo2, oo3, &c., &c.;
and I intend to write a paper against the skim- milky, fast-and-
loosish mealy-mouthedness of the English mathematical world
on this point. My assertion is that the infinitely great and
small have subjective reality. They have objective impossibility
if you please ; or not, just as you please.

I have first to remove an ambiguity, which has played a large
part in causing confusion. To imagine is originally to form an
image in the mind. But it has been transformed into a synonym
of to conceive, to form a concept. The distance from here to the
sun is a concept. I have no image of it. But of six feet I have
both image and concept when I shut my eyes. Now many per-
sons, when they cannot image, speak as if they could not conceive,
and use the ambiguous word imagine. We cannot, they say,
imagine infinite space. I grant they can't image it, but I am sure
by their modes of denial that they have a conception of it. Locke
and others affirm that we arrive at the notion of infinity by finding
out that when, say, we add number to number, we find the
succession incapable of termination, and so fashion interminability
in our minds. I say the process is precisely the reverse. If it
were not for our conception of infinity we should not know the
interminability.

Who ever tried up to 10,000,000,000,000,000 ? It is certainly
not experience. If any one were to affirm that 1016 is only a
symbol, and that any one who should try would find himself
brought up by the nature of things, Locke has no answer,
unless, as would probably be the case, he should ask permission
to bring on the conception of infinity.

I therefore affirm the concept infinite as a subjective reality
of my consciousness of space and time, as real as my conscious-
ness of either, because inseparable from my consciousness of
either. When, therefore, I think of a finite space — say a cubic
foot — if I compare it with the totality of space, I say infinitely
small ; if I compare the totum with it I say infinitely great.

Now comes a postulate on which there may be a fight. Let
A and B be two magnitudes, any whatsoever, and C a third,
also any whatsoever. Let these magnitudes be concepts, imagin-

314 MEMOIR OF AUGUSTUS DE MORGAN.

1862. able or unimaginable. I take a right to affirm the conception of
D such that

A :B::C :D

The notion of ratio is a fundamental thing, not dependent on,
though only definitely expressible by number. A person who
cannot count, and who does not even know that language can
turn multitude into number, has the idea of ratio, relative mag-
nitude. He sees, feels, and knows that if A be the house, B is
too small for the chimney, and C too large.1 I claim the exist-
ence of D, so that A : B as C : D is a concept.

This being premised, then I have the infinitely small part of
any magnitude, and of that again, &c. For instance, if dx : x ::
a pint pot : all space, dx is an infinitely small part of x.

All this I mean to develop and fight for. So with kind
regards to Lady Herschel and the next generation,

Yours sincerely,

A. DE MORGAN.

To Sir J. Herschel.

91 Adelaide Road, Aug. 15, 1862.

MY DEAR SIR JOHN, — Many thanks for the dialogue.2 From
the parties to the dialogue I deduce the equation —

mogenes + mione_SL>hel

2

What a quantity of arguable propositions ! I cannot see how
you deduce your account of Descartes. As to at'ems — I spell
the name thus, considering it as a challenge to attack them, and
make your boast of it — I suspect that if you look back into the
world a thousand years hence you will find the remote posterity,
as we call it, fiddling away at the creatures, and knowing about
what we do.

I have often thought of the minimum of extension en-
dowed with attraction, &c., and adjusting his accounts with
.[ (io)». 000,000,000 1 (jo) 1.000,000,000 brethren instantaneously. It is
a wonderfully fine hypothesis for expressing what we see and

1 A rough sketch of a house, with a too small chimney on one side
and a too large one on the other.

2 Dialogue on Atoms, by Uermoyenes and Hermiow. Private
circulation.

CORRESPONDENCE, 1856-66. 315

know ; but for an actual objective truth, oh my ! And we 1862.
call them blind atoms ! Why, the fellows see faster and farther
than we do, by the above to 1, at least.

If a malevolent being could create one single atom more than
is in the plan, he would of course bring the whole thing to smash
at last. Query, in what time ?

I hope we shall know more about it next world. We can't
know much less than we do now, that's one comfort.

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Whewell.

91 Adelaide Road, April 1, 1863.

MY DEAR SIR, — I am not going to take the privilege of the 1863.
day, but it reminds me, though it is not the occasion of my
writing, that this very day ten years I made a sort of specula-
tion which I thought many would attribute to the influence of
the day. While I was chuckling at the idea of having quite suc-
ceeded in a new metaphysical insanity, arid before the pen was out
of my hand, there actually came in from a bookseller Heywood's
Analysis of Kant, 1844, and there I found the very same notion.
It occurred in a description of the ' paralogisms of reason,' as
they occurred in the first edition. You can tell me whether
there is any allusion to the subject in the later editions, and this
is my question.

I was considering a syllogism in which a term is a class of
which the individuals are the subject at different moments of its
existence. For instance, —

No black ball is ever a billiard ball ; this ball has always
been black ; this ball has never been a billiard ball.

The individuals of the class are the balls which we call one
ball at different times. Thereupon it struck me to think, how
is it that we call this ball the same ball all the time ? Whereas,
if we had a number of fac-simile balls in different places, we
should not say it is the same ball all the space. I suppose w e
borrow a notion from our personal identity, in which we feel
sameness. Consequently, if our presence had multipresence, if
the ego knew himself for himself in all the different parts of a
space without being able to say, I am one person here and
another there — any more than he can say, I am one person now

316 JfEMOIR OF AUGUSTUS DE MORGAN.

1863, and was another then — he would be very much inclined to
doubt the difference of balls, when the only difference is that of
place.

This supposes a faculty altogether beyond our comprehen-
sion— if, indeed, anything be within our comprehension on the
question of what is what — which ties spaces together, just as
memory ties times together.

All this I found in Kant (Hey wood, ut supra, p. 109). He
uses it to prove, as he thinks, that ego ' I think ' migh t be iden-
tical, though the thinking subject is variable. He will not
admit the space-string to constitute the nos of different places
one ego. I cannot find any of this in Hey wood's or Tissot's
translations, and I think it possible that he may have learnt
better in the interval of the editions. But you may be able to
refer me to some notice of it.

With this metaphysical reduction of omnipresence to depend
upon an incomprehensible something which has at least an
analogue in our own consciousness, I have looked for ten years
at various ontological writings about ' the unconditioned,' and
various religious works about ' the Almighty,' and I think I see
a very great tendency to confuse omnipresent personality with
infinite extent. At least there is a want of power to put the
distinction into language.

Are you aware of any Roman Catholic speculation on the
subject ? They must give mnltipresence to the saints whom
they invoke, and by whom they expect to be heard. And I
should suppose that some of their writers have touched on this
gift-

I am now writing on the subject of Infinity, trying to burn
the candle at both ends. I have found out for some years that I
am a full believer in the infinitely great and small, both . I mean
in the subjective reality of both notions.

I cleared off much obscurity by a distinction which I find
very faintly shadowed by the psychologists — that of a concept
which has image, and a concept which has none. I can image a
horse : I can't image the right to a horse, but I can conceive it.
I cannot image infinity, but I can conceive it — that is, 1 recog-
nise a notion with predicates. So that when a metaphysical
writer says, as some have said, that we cannot conceive space to
bo finite, and are equally unable to conceive it as infinite, I say
they ought to have said that we cannot conceive space to be
finite, nor image it as infinite. But neither can we image a

CORRESPONDENCE, 1856-66. 317

million of cubic miles, though we can conceive it, as proved by 1863.
our knowing truth and falsehood about it.

I am, yours very truly,

A. DE MORGAN.

To Eev. Dr. Whewell.

April 3, 1863.

MY DEAE SIR, — Did I provoke you to an ontological discus-
sion ? Did I chalk my hat and say, ' Now Fd like to see the
man who says that this is not silver lace ' ? That's what I call
provoking a discussion. I asked you, who are Kantescient,
whether you knew of a certain speculation in the later editions
of Kant ; and you say No. I am pretty sure you would have
remembered it at once if it had been there.

I am quite sure we shall never solve the problem which my
analogy went to suggest. But for all that, if we only envisage
a quality acting through space as memory acts through time, we
put multipresence upon a definite basis of unintelligibility —
there, I have managed to spell the word, and that is something
gained.

I value the analogies of space and time — the two indis-
missible extensions ; and I have before now made much profit of
the very remark you quote.

For aught I know, a body may act where it is not ; it may
leave consequences behind it. An annihilated star, which is seen
by light emitted during its existence, may be said, for aught we
can tell, to act where it is not, in as true a sense as matter, in
attracting distant matter, can be said to act where it is not.

But presence is a very ill-used notion. If a particle really do
attract all others, it is present throughout the universe. It is
present in one quality — in others, for aught we know. The
presence of matter is the presence of all its qualities — the only
things we know. Now who is to say that the spheres of the
qualities have the same diameters or even the same centres ?

Grant one centre to qualities of a particle, and there may be
millions of centres, all effective in spheres of different radii.
The sphere of attraction may be the biggest, or it may not.

Mansel, I detect partly by private, partly by public evidence,
is in the state of the old logicians about infinity. He cannot
separate the mathematical notion from the old mixture of infinite
in quality and in everything. Leibnitz had it to a considerable
extent, in spite of his power over the mathematical notion.

318 MEMOIR OF AUGUSTUS DE MORGAN.

1863. I bring the chief difficulties of quantitative infinity to some-

thing like this : —

When of A and B one and one only nmst be, when A is
visibly self-contradictory and B only incomprehensible, I vote
forB.

I shall be very glad to see anything of Ellis's. The thoughts
of his long illness would be valuable. He gained an enormous
power of thinking about mathematics without pen and paper.
I repeat my wish that his preface to Bacon could be separately
published. With kind regards to Lady Affleck,

I am, yours very truly,

A. DE MORGAN.

To Rev. Dr. Whewell.

April 7, 1863.

MY DEAR SIR, — Now I will provoke an opinion, not an
answer to a matter of fact ; and if anybody in College has ever
thought about the subject, I wish he would think about it again.

Aristotle has a chapter in the * Metaphysics ' about the
aTTctpov, translated ' the infinite.' The chapter opens with a
description of the meaning of the word, which has come down
without any strong objection that I can find. I give the sen-
tence itself, with a literal translation from MacMahon. I
hardly ever had to look closely at a sentence of Aristotle without
finding what reason might take either for a gross corruption or
an obvious interpolation. This chapter I suppose to have had
much sway in determining the logician's obstinate confusion
between the infinite, unlimited in qualities, powers, &c., and the
simple infinite of magnitude. Now from ' Metaphysics,' lib. x.
or xi., cap. 10 : —

To 8' OLTTClpOV 3} TO dSvVaTOl/ SicXOciV TO) jJLrj TTf<f>VK€Vai SuCPat, KO.6(i-

irep f) <£cov?7 doparo?, fj TO 8ic£oSov «xov CiTcXa/nyrov, rj o yw,oXi?, rj o
ITC<J>VKO<; ex€tv M *X€L Sie^ooW fj Trepas* ert Trpocr^cWt r/ ttyatpccrct, rj

' But the infinite is either that which it is impossible to pass
through in respect of its not being adapted by nature to be per-
meated, in the same way as the voice is invisible ; or it is that
which possesses a passage without an end, or that which is
scarcely so, or that which by nature is adapted to have, but has
not, a passage or termination. Further, a thing is infinite from
subsisting by addition or subtraction, or both.'

CORRESPONDENCE, 1856-66. 319

Here is a nice kettle of fish ! Now I try to put a sense npon it. 1863.

1. I take aTTctpov to mean rather without boundary than
without end ; indefinite. But the quantitative notion of having
no end does intrude and confuse that of having no determinate.1

To Rev. Dr. Whewell.

April 11, 1863.

MY DEAE SIR, — Many thanks for your letter. I feel helped
by the word Sucwu, because it is a very thoroughfaresome word.
As the lexicon says, it is used for going through a country, or for
running a man through the body, which is a process very
definitely suggestive of in at one side and out at the other.
It points very distinctly to the idea of bounded on all sides,
being that which aTretpov denies. And this, combined with an
a-rreipov gained by subtraction, confirm me in the notion that
Aristotle is treating of the indefinite — not necessarily, though
possibly, infinite in magnitude.

I agree with you that the adjective infinite without a sub-
stantive is like all other adjectives similarly situated.

On infinity — i.e., infinite quantity — a concept necessarily
connected in our minds as an attribute or predicate, with space
and time, I have come to the conclusion that we must treat it
as a concept without image. Throwing away the word imagine,
as spoiled by becoming a synonym of conceive, I distinguish the
concepts which we can image from those which we cannot. We
can put before the mind's eye, or the mind's mode of remembering
sensible things, an image or likeness ; a man, for example, as he
appears when alarmed. But alarm is a concept without image ;
it has predicates, it is the subject of true and false propositions,
but not as a thing having an image.

Now of quantity of space, and even of time — for succession
of things is among our sensible relations — we have images ; but
not when too small or too great. The infinitely small and the
infinitely great are below and above our imagining power, but
they are concepts with attributes. Those who reject both or
either because they cannot form an idea — by which they mean

an image — ought equally to reject those entia rationis, the

1 I much regret that I have lost the rest of this letter. But I
insert it as it stands, as the same subject is spoken of in the next. _
S. E. DE M,

320 MEMOIR OF AUGUSTUS DE MORGAN.

1863. of an inch and the length of 10100 miles. But these are subjects
of which we can predicate ; and so, I hold, is infinity.

I have made all manner of efforts to repudiate infinity of
quantity for forty years, in obedience to the dicta of people who
assured me I did not possess any idea of it, and I have failed.
And I have observed that no people seem so clearly to have the
idea as those who argue against it, while engaged in their task.
And I begin to lean towards the notion that the difficulties of
infinity of quantity arise from our having more knowledge of it
than of things, for which we depend on attributes — as mind or
matter.

The absolute, as you say, really has no predicates ; and it is a
very circular idea. Is not the being unconditioned, if per se
and necessarily, a condition ? Cannot is a word of limitation and
condition. Can the Creator commit suicide ? if not, he is, to
our thoughts, conditioned. I should like to know what Hamilton
would have said to this. Seeing that the Germans shine as
smokers and also as metaphysicians, and also that in the former
capacity they Now a cloud — which was the word for taking a
cigar in my day — it is worth while to think about transferring
the phrase, in a transcendental sense, to their other pursuit.

Yours truly,

A. DE MORGAN.

To Sir J. Herschel

91 Adelaide Road, May 10, 1863.

MY DEAR BARONET, — There's change for your 'Professor.'
Everybody attaches some ideas to a word derived from early
associations. The first ' learned Professor ' I read of under that
name was Olearius Schinderhausen, of Leyden, who disparted
with his cast-off suit biennially. I did not think I should live
to match him ; but as I never go out, and always work at home
in a dressing-gown, I also have but one coat in two years.

Seventy-one, eh ? Go on to eighty, and then apply to me
for further directions, if I should be in a condition to give them.
Addition of the same to a ratio of greater inequality diminishes
it. So says Jemmy Wood ; and the life of man confirms it.
When you were preparing sin ~lx, I was learning numeration
from my father on a zalileribreitstein — a pebble, of diameter and
flatness, picked up in the road. And I remember that when it
was lost I refused all arithmetic till another was found ; which,

CORRESPONDENCE, 1856-66. 321

considering that no one had told me the etymology of calculation, 1863.
showed a kind of natural philological acumen.

Yours very truly,

A. DE MORGAN.

To the Master of Trinity.'

91 Adelaide Road, October 21, 1863.

MY DEAR SIR, — .... If you read Notes and Queries, look
out for a few notes I have given on Robert Robinson. I shall
send down a cutting to paste into his ' History of Baptism,' or
any work the library of Trinity may chance to have.

I have been in communication with Mr. Wright about a book
he used out of that library. He was the most remarkable Cam-
bridge (town) man of the last century, I suppose; at least he
comes next after Maps and Jemmy Gordon.

I do not know whether you know Crabb Robinson (no rela-
tion), to whom I am indebted for anecdotes. He is eighty-six,
and pours out anecdotes about everything and everybody, espe-
cially his especial friends Goethe, Wordsworth, Southey, Cole-
ridge, Charles Lamb, et id genus omne. He tells me that
Wordsworth agreed with Samuel Parr that Dyer's ' Life of
Robert Robinson ' is one of the best biographies in the language.

Yours very truly,

A. DE MORGAN.

To Sir J. Herschel

91 Adelaide Road, November 19, 1863.

MY DEAR Sis JOHN, — Thanks for the paper on the standard.
Hurrah for anything which preserves our great units ! On that
condition I will accept the earth's axis or anything else. But I
stipulate for the foot, as for common usage. A yard is too long
to start from ; a foot I hold too long ; I should like better T^ of
2 yards.

Many years ago I demanded of my bootmakers the lengths
of foot of 100 adult men, taken as they came in his books. The
result was 10*26 inches as the average foot of man, English,
measured in Bedford Street, Bedford Place. This is rather
surprising, seeing that a bootmaker gives a little additional
rather than otherwise.

I hope the metrical people will continue to agitate. I do not

T

322 MEMOIR OF AUGUSTUS DE MORGAN.

1863. fear their metre, which will never go down; but they will do
good to the decimal principle. I think we shall get the decimal
coinage up again by their help.

I am dry of information of every kind.

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Husenbeth.

91 Adelaide Road, December 31, 1863.

MY DEAR SIR, — I am very much obliged for the excerpt.
But how do you manage with rubric letters on a dark morning
or by candlelight ? The first opening I made of the creed
showed me, by candlelight, 'ceque confondentes personas,'
which, said I, must be a misprint.

I am glad to be set right about the filioque. I was once —
but it dropt — puzzled to know how the Greeks could reject two
words of the Athanasian when they rejected the whole creed.
But like most (Western) others, I had but a cloudy notion of
the Greek Church. My Latin Prayer-book is certainly the old
Latin. A new Latin translation, the veritable original being
Latin, strikes me as would a Greek Homer translated from
Pope. . . .

I shall certainly attack reliable. One of the tale-writers in
All the Year Round has introduced it into a document purporting
to be of the early reign of George III. This is adding insult to
injury.

When I say a journal cannot refuse advertisements, I mean
that it cannot do so without danger to its prosperity. It is
found that any check to influx of business is bad policy.

If the Athenceum. of thirty years ago be examined, it will be
found that the reader's portion is increased relatively more than
the advertisement portion. It is astonishing how many persons
delight in running over columns of advertisements. . . .

Yours very truly,

A. DE MORGAN.

To the Rev. Dr. Husenbeth.

January 12, 1864.

1864. ^Y DEAR SIR, — Many thanks for the drama, which, not
knowing the original, I cannot divide between you and the

CORRESPONDENCE, 1856-66. 323

author of the second. I read it through, which is a point on 1864.
which most reviewers of books are apt to be evasive, and, as I
did so at one sitting, I need not say I liked it. As there are
only two Christians in it, or at most three if we connt Agellius,
there is no scope for a fault which I noticed in a book of the
Cardinal's, of which I forget the name, all about St, Pancras
(saint, not parish). That fault is that though the author can
draw characters, yet the moment he puts on the religion, it is a
domino of the same form and colour for all, which makes them
look just alike. I thought all the while of the great magician
who could make the Calvinism of David Deans and Jeanie as
distinct as their characters, sexes, and ages, without anything
that would bring either under the censure of the Presbytery.
Either Dr. Newman or yourself, or both, have managed three
tolerably different phases of religious character.

You may easily get far enough into my syllabus to see
the meaning of the symbols -)) )•( &c., which is all the book
was intended for — I mean the copy sent to you. In )) (•), for
instance, I see —

1. Premises.

2. Proof of validity.

3. Conclusion.

4. Quantities of all the terms.

Dr. Watts's book, which I call the English Port-Eoyal logic,
deals little in purely logical exercise. As to your reading it in
spite of what it says against the Pope, &c., I should have read it
all the more, for I enjoy being assaulted and batteried. But the
book is a good one. Had he been of the Parliamentary form of
religion, it would have been a great work, as great as any of
Paley, in the two Universities. ... I am, dear sir,

Yours truly,

A. DE MORGAN.

To Sir J. F. W. Herschel.

91 Adelaide Road, August 18, 1864.

MY DEAR SIR JOHN, — If you happen to recollect you were
Master of the Mint — I am sure you had reason enough to recol-
lect it— you cannot have forgotten that Newton was there before
you. His concessis, I find that N. and H. added each one coin
to the list ; N. the gold quarter-guinea, which was in circulation
until towards the end of the century ; H. the gold quarter-

Y2

324 MEMOIR OF AUGUSTUS DE MORGAN.

1864. sovereign, which was never circulated. Tell me, I pray, when
yon qnarter-sovereigned did you know that Newton had quarter-
gninead, or was it an accidental coincidence ?

Here I am, as usual in August, with one son in the house
and all the rest at Aldborough. My wife is mending, but has
been seriously ill. I hope I shall have a good account of your
section of the human race.

You know Tristram Shandy — who does not ? But you may
not know his views of proportion. He says his father was some-
times a gainer by a misfortune ; for if the pleasure of haranguing
about it was as ten, and the misfortune itself only as five, he
gained ' half in half,' and was as well off again as if the mis-
fortune had never happened. Cipher this out. I call it a
splendid bevue ; as good as the two last lines of the song about
the young man who poisoned his sweetheart in sheep's-h(
broth, and was frightened to death with —

Where's that young maid

What you did poison with my head ?

at his bedside.

Now all young men, both high and low,

Take warning by this dismal go !

For if he'd never done nobody no wrong,

He might have been here to have heard this song.

Babbage's Act has passed, and he is a public benefactor,
grinder went away from before my house at the first word. Tl
New Zealander shall sit on the remains of his doorstep to skei
the fragments of a broken barrel-organ. ' 0 si sic omnia ! '

Yours very truly,

A. DE MORGAN.

To Mrs. Smyth.

91 Adelaide Road, September 1, 1864.

MY DEAR MRS. SMYTH, — I see by the title-page that work is on
hand — when was it not ? It is thirty-seven years since I became
personally aware of the fact — that is, I have known the Admiral
nearly half his life, and yet there was a lot of it when I first
knew him ; he had retired from a life's work.

I wanted to see how you swallowed the Pyramid.1 I do not

1 Prof. Piazzi Smyth's work on the Pyramids, published just be-
fore this time. S. E. De M.

CORRESPONDENCE, 1856-66. 325

see any occasion to feel depressed abont it. The world is not 1864.
what it was when the Admiral and I were young. There are
strange break-downs of opinion and build-ups of system. I do
not know that it is more extraordinary than that I, of all persons,
should declare and publish my actual experience of phenomena
which so many will have to be actually the work of disembodied
spirits, which I can neither deny nor affirm. The Christian
world is actually tending towards the belief that a great many
mythologies and idolatries are really diseased revelations. Wait
a few years until it begins to be generally apprehended that
Juggernaut and Cham Chi Thaungee — if you happen to know
him — were originally divine, though a little altered by time and
priest, and it will then seem a very natural thing that the
measures in the Pyramid should have come from the same
quarter. I wish the reasoning had been a little more sound and
the mind less influenced by bias of system, but this is not peculiar
to primeval inspiration advocates. It is the beauty of these
extreme vagaries that they show off and illustrate the methods
which are most in vogue among savans who are quite in the
groove. But the moral courage which ventures upon a trip off
the line is not so common/

The work itself is part of an impulse which is doing strange
marvels, which will make Bishop Colenso die a heretic, and
which has made Robert Owen die a Christian; nay, which has
made a Christian of Dr. John Elliotson, the strongest materialist
almost that I ever heard of. If we go on in this way twenty
years longer, the name of God will be heard at a meeting of the
Royal Society, from which Dr. Camming will take occasion to
declare that the millennium has commenced.

There are educated persons by thousands not in the little
knot, who will look on Piazzi's book without much surprise as
to his mere conclusions. It is astonishing how little the world of
science knows about opinion outside.

Kind regards to the Admiral, who, I suppose, has his work
well-nigh done. What a beautiful feeling the proof of the title-
page gives !

Yours very sincerely,

A. DE MORGAN.

326 MEMOIR OF AUGUSTUS DE MORGAN.

To Sir J. F. W. Herschel.

91 Adelaide Road, September 20, 1864.

1864. MY DEAR SIR JOHN, — So honey-bees have stings as well as

wapses. So much the better. I do confess to a baker's dozen of
readings of your letter.1 Saving your presence, your usual mild-
ness and diffidence, and all those things of which I know no
more than my grandmother's torn cat knew of the differential
calculus, bring out the points with such strength that there is
no leaving off. It will do an abundant deal of good, and will
make the declaration a blessing. It is in good contrast with
Bowring, whose letter is capital in its way.

Truly you did express yourself wibh tolerable precision and
to much purpose in the old discourse. I have been pasting a
copy into that discourse, and it notes time well to find that the
copy wherein I paste it is one which poor Stratford gave my
wife long before she was even my sweetheart, and my eldest son
is twenty-five years old.

The inpasted copy is cut out of a reprint in the Bath
Chronicle, done for the special benefit of the Br. Ass.

"What is the collection of names they have got ? I suppose
they have handed out their best fifteen. ... I think I had as
good a right to be asked as . . . . ; 2 but possibly they took
me for too great a heretic. I dare not think they respect me
more than they do you ; but the temptation is great. How I
should strut !

They are now pledged to publish this declaration and the
names they have got. They might have dropt the thing after
Daubeny's letter.

I hope your bronchial state is better. To my last letter I
add that the little dust does not confine itself to your books ; it
gets into your throat.

Yours very truly,

A. DE MORGAN.

1 Many scientific men had been requested to sign a declaration of
their belief that science did not contradict revelation, &c. By the
' honey-bee's sting ' is meant Sir J. Herschel's answer, which con-
tained a trenchant reply to the arguments contained therein.

2 I think he was asked to sign perhaps rather later.

CORRESPONDENCE, 1856-66. 327

To the Rev. Wm. Heald.

September 27, 1864.

MY DEAR HEALD, — I suppose you and family are pretty well, 1864.
as you say so little about it.

In re Colenso, you can easily demolish him by assuming the
points. He has never told us what residue of the Xtian
religion he still believes ; why, whether the historical truth of
the O. T. is any part of the N. T. is just the point. If I remem-
ber right, he at one time could not use the ordination service ; but
he can now, I believe, after Lushington's decision in Williams's

The case about C. D. and A. B. stands thus. All the reviews,
&c., declare that A. B. is self, and C. D. wife. Neither of us
has contradicted it, which leads me to suspect that we cannot.
The style of A. B. is, I am assured by good judges, unmistak-
ably my own, and I certainly do see a strong likeness. All these
things put together cannot be got over. Were I you I should
assume the report to be true. I have not heard anything about
a second edition.

Yours sincerely,

A. DE MORGAN.

To J. 8. Mill, Esq.

91 Adelaide Road, October 10, 1864.

MY DEAR SIR, — Ten years ago I asked you whether certain
abridged dialogues of Plato were yours, to which you answered
in the affirmative. Have they been reprinted ? I very much
wish they were, if they are not. The presentation of Plato is
now frequent ; but there is nothing I know of in which a picture
of Plato is given, and remarks kept distinct.

I am reminded of this by a translation, of the Gorgias which
has just appeared, by Mr. Cope, Fellow of Trinity College, Cam-
bridge. A good translation, I dare say; but, to tell the truth,
I and many others like to have the pith of Plato extracted, and
find both Greek and full translations rather wearisome. Nostra
culpa, no doubt, but you must have thought such sinners not
quite below a missionary, or you would not have published your
abridgments. I suppose it is not given to man to relish both
Aristotle and Plato.

328 MEMOIR OF AUGUSTUS DE MORGAN.

1864. I often cut from a review and paste haphazard on to the fly-

leaf of a book. In your Plato articles I find, in this way, a
curious accidental paraphrase of the Trinity that may amuse
you. The Drnse system is described as historically identified
with the Caliph Hakem, the Persian Hamze, and the Turk
Davagi — Hakem the ' political founder,' Hamze the ' intellectual
(Xoyos) framer,' and Davagi the 'expositor and propagator.'—
(Athenceum, August 27, 1853.) I am, dear sir,

Yours truly,

A. DE MORGAN.

To J. S. Mill, Esq.

91 Adelaide Road, February 5, 1865.

1865. MY DEAR SIR, — The Algebra, which I am much pleased to

find you approve of, is to be divided between several. I have
no doubt I may claim to have first presented it complete, and
the connection of A00 1 with the rest is my own. But Warren,
Peacock, and others of those mentioned in my list at the
beginning of the work arc real predecessors. You are perhaps
aware that Peacock published two works on algebra. The first,
in one volume, is that which treats the subject most generally.
He is in full possession of all except what relates to the ex-
ponent, and here he is obliged to have recourse to interpretation,
that is, discovery of meaning from results.

With regard to the acceptance of the system, the time is not
yet come. The algebraists almost all make algebra obey their
preconceived notions. They have laws which algebra must obey.
Peacock had very nearly attained the idea of algebra as & formal
science, in which every result of the form is to have meaning.
His permanence of equivalent forms would have developed itself
into formal algebra capable of any number of material applica-
tions, if he had been a logician — I mean a student of logic. So
long as an algebraist has preconceptions which his science must
obey, so long is he incapable of true generalisation. Macaulay
said of Southey that what he called his opinions were his tastes,
and this is true of many persons, and of a great many algebraists.
Algebra must, a priori, be subject to this or that limitation, upon
what is really an acquired taste of the legislator. Pure logic is
in the same predicament.

1 I am not sure about this exponent. — ED.

CORRESPONDENCE, 1856-66. 329

For myself, it is my taste, if you please, that I will have a 1865*
formal algebra, in which, every form, every law of transformation
is universal. I admit that we have not yet arrived at it, but I
have entire faith in the future. I was in the spirit on the day of
Wellington's funeral, when, wife, children, and servants being
away to see the remains of the glorious old man carried upon
what was so justly called a cross between a locomotive and a
fire-engine, I was sole master of my house and myself. So I
sat down to eviscerate the following difficulty, and I believe I did
it. If the forms of algebra be universal, then %x=x gives

— =- or 2=1. I should not have been ashamed of myself if
x x

resolved on a formal algebra, I had invented a generalisation
of = to meet this case. But I had no occasion for any such
thing. I found that, by only taking permission to lay down as a
canon what mathematicians never scruple to do when they want
it, I was master of the field.

I have a paper now at Cambridge which explains my views,
so you see I have taken twelve years to think about it. In brief
as follows. Admitting in theory as full and free a use of infinites,
finites, and infinitesimals, as is made in practice, I say that —

1. The sign = is that of undistinguishability, say indistinction.
A=B means that A and B are not distinct. Equality is but a
case, though the most common one.

2. Distinction implies the use of a standard or metre.
Quantities infinitely great with respect to the standard, or
infinitely small, or unmeasurable by it, are undistinguishable. And .
this is the origin of Leibnitz's equation dx=dx -{-dx~2, the metre
having finite ratio to dx.

3. Whenever we divide or multiply both sides of an equation
by anything above or below the standard, the new equation takes
a different standard. When we multiply by an infinite we must
take a standard which was infinite, &c. Now 2% and x can only
be undistinguishable when x is infinitely small or infinitely
great. Let x be infinitely small. In passing from 2,u=aj to 2=1
we change our standard into an infinitely small quantity, and
2=1 is trae, that is 2 and 1 cannot be distinguished. The same
when x is infinitely great.

The difficulties which will suggest themselves are many and
obvious ; but I think that they are superable, and also that,
looking at actual algebra, they are not so great as the difficulties
which actually occur. For all these things I refer to the paper

330 MEMOIR OF AUGUSTUS DE MORGAN.

1865. when printed, to which so brief an account is more like a pre-
liminary objection than anything else.

Yours very truly,

A. DE MORGAN.

To J. S. Mill, Esq.

March 26, 1865.

MY DEAR SIR, — I thank you for the article on Comte received
a few days ago. It gives me a much more definite idea of Comte
than I ever had patience to get from himself. His writing
always had to me a smack of that unequalled prolixity which he
showed in his algebraic geometry, where he discourses in page
after page on the equation of a straight line, without a symbol.
I settled that he ivas not a psychologist. I make out from you
that he ivould not be, prepensely. I thought he was impatient of
the subject, but did not fathom all his guilt.

I am confirmed in my view that his philosophy is, so far as it
is distinctively his, negativism. For his positivism I find in all
thinkers, or nine out of ten ; his rejections, hardly anywhere.
Positive, because no more than positive. When understood thus,
he is a bearable companion, for one has a right to be as anti-
positive with his philosophy as he is positive with mind and
matter ; i.e., as he has taken part for the whole, I take his whole
for part.

I shall soon send you a paper in which I find I am a sort of
Positivist. There are those who reject all but phenomena ; there
are those who reject phenomena because they cannot have more.
Comte is the assailant of those who accept more because they
think they can get more. In the mathematical treatment of
infinity, small and great, most mathematicians reject the abso-
lute treatment because they cannot image, or treat as phe-
nomena, all the attributes of the notion. My notion is that oo7 and

— 7 have a subjective reality, of which various phenomena are

proper subjects of direct reasoning. The mathematicians have
virtually denied that A is B is a component of reasoning when
we know it to be true even though A and B should be porcu-
pines with difficulties for quills. In my paper in two parts, oo
is a porcupine, and = is a hedgehog.

I see you are in England again by your complimentary letter
to the Westminster electors. You pay them a higher compli-
ment than they pay you. I am always in doubt about the origin

CORRESPONDENCE, 1856-66. 331

of the word compliment. It looks like a formation from comply , 1865.
but I doubt it. I suspect that complement is the original, though
the present spelling and usage is as old as the Academy's
Dictionary. I suspect that old forms of civility were at last
described as complements, fillings up ; and that complimts, at the
end of a letter, meant that all usual forms are to be understood.
My theory receives a little support from comply not being a
French verb.

Yours very truly,

A. DE MORGAN.

I have as yet read your article for Comte only, for I really
wanted to know what he had been at. I must read it again for
criticism.

To J. 8. Mill, Esq.

91 Adelaide Road, April 27, 1865.

MY DEAR SIR, — I received the Examination to-day, and write
my thanks that I may not forget it, as I shall have no consecu-
tive reading for a week or two.

I hold, from observation, that a question is never fairly put
before a public meeting until it has been moved, seconded, and
opposed. A great many persons are really only half informed
by the mover and seconder what it is all about ; but the first
person who rises on the other side puts some light into it. It is
just the old law knowledge : the points at issue come out of the
pleadings on both sides. In like manner with controversies.
Hamilton has moved, Mansel has seconded, and now you rise to
take objections. And I also observe that the first opponent very
often puts his view of things into a much more attainable-in-a-
given-time form than if he had been the mover of a counter
measure. A dip into several unconnected pages makes me think
that may be the case here.

One of my dips is into 'All oxen ruminate.' I have shown
in my fifth paper on logic that Aristotle and all his real followers
never collected all the oxen. Their phrase was, ' Every ox r ami-
nates,' or, any ox ruminates. That the predicate is what I have
called in my third paper metaphysical I am satisfied. And I have
maintained that the common predicate of the world at large is
so. I say, ' man is born and educated a mathematician as to the
subject of his proposition, and a metaphysician as to the predi-
cate.'— Ex. gr. * Every man is biped,' i.e., is of biped quality or

332 MEMOIR OF AUGUSTUS DE MORGAN.

1865.^ attribute. I contend in that paper that the logician's form of
extensive reading stands or falls with the numerical syllogism,
which is the true genus.

Yours truly,

A. DE MORGAN.

To Chief Baron Pollock.

MY DEAR C. BARON, — First as to subjective and objective. Th e
thinking mind is the subject, id quod subjicitur. The external
thing, relation, &c., is the object, id quod objicitur. Or the acts
of the minds may themselves be objects ; i.e., one mind may b e
the object of another mind.

I see an apparition : is it subjective or objective ? If it be a
thing of my mind its existence is subjective.

This use and others are not very sound. But, generally,
objective has that relation to the thinking mind which subjective
has to the exciter of its thoughts.

When Kant makes space and time pure concepts of mind to
put things into, the things themselves being in some unin-
telligible sense external, he is said to make space and time purely
subjective*

As to your being old, you are the youngest I have lately heard
of. On Saturday, at University College distribution of prizes was
Lord Brougham, eighty-seven, much broken, but still himself,
and able to deliver himself as fluently as ever, and with that
powerful delivery of the one word which makes his sentences so
effective. And there was Crabb Robinson, ninety in May, and
quite alive to everything. And he will last for ever if he will
only take advice I heard given to him, i.e. not to talk more than
two hours at a time.

With your note came an acknowledgment from General
Perronet Thompson, B.A. of 1802, and Fellow of Queen's before
he was an ensign. And he works at acoustics as hard as ever
he did at the Corn Laws. I say nothing of boys of seventy who
are scattered about. Our kind regards to Lady Pollock and
the family.

Yours very truly,

A. DE MORGAN.

CORRESPONDENCE, 1856-66, 333

To Sir J. F. W. Herschel.

September 13, 1865.

MY DEAR SIE JOHN, — The world is changing round us very 1865.
fast. I have lost two very old friends on two successive Satur-
days— W. Rowan Hamilton and Smyth. Smyth went off very
quietly from mere exhaustion, without any long illness. He
had lost a great deal of strength in the preceding fortnight, but
had rallied a little, and was driven out on Friday, and went
calmly off on Saturday morning with effusion on the lungs.
Poor Mrs. Smyth is very calm ; it is the break of a tie of fifty
years.

W. R. Hamilton was an intimate friend whom I spoke to
once in my life — at Babbage's, about 1830 ; but for thirty years
we have corresponded. I saw him a second time at the dinner
you got at the Freemason's when you came from the Cape,
but I could not get near enough to speak.

They will take care that a full life shall be published. Of
forty members of the Nautical Almanac Committee of 1830,
there remain now, besides our two selves, Airy, Lord Shaftes-
bury, Babbage, Lee, Maclear, Robinson, South, Wrottesley — ten
in all ; this is fair vitality for thirty-five years.

I am, yours sincerely,

A. DE MOEGAN.

To Sir J. F. W. Herschel.

91 Adelaide Road, September 21, 1865.

MY DEAE SIE JOHN, — You must have been much in the way
of hearing all the rumours about George III. and his malady.
Do you remember hearing a story which I have heard from
boyhood, which I find numbers have heard, and which I believe
has been in print, but I do not know where ? It is stated that
one of the earliest indications of his complaint was a formal
announcement to those about him that he intended to begin his
speech from the throne with * My lords and peacocks.' To all
remonstrance he did nothing but persist, and they say that acci-
dental noises — as tumbling down books, &c. — were prepared to
drown the words. If the story be really true, I have no doubt
I have arrived at the meaning of his phrase — that is, at its
origin. But first, query, did it happen ? If it did, there was
method in his madness, With kind regards all round,

Yours very truly,

A. DE MOEGAN.

334 MEMOIR OF AUGUSTUS DE MORGAN,

To Sir J. F. W. Herschel.

91 Adelaide Road, September 27, 1865.

1865. ^Y DEAR SIR JOHN, — Then the story is a story, and has a

place in history. Now for its explanation. Old George III.
knew Shakespeare pretty well — much better than any other
literature. In 'Hamlet' there are several places in which
Hamlet seems on the very point either of disclosing his step-
father's villany or giving him some reproach, but breaks off
and substitutes something. In one case where ass is clearly
coming, he makes it peacock.

For thou dost know, 0 Damon dear,

This realm dismantled was
Of Jove himself ; and now reigns here

A very, very (ass) peacock.

Now George III. had old score recollections of the House of
Commons. I suspect that when his mind was in his wanderings
he determined to be revenged and to say, ' My Lords and Asses,'
and he remembered and imitated Hamlet's substitute.

I am, yours sincerely,

A. DE MORGAN.

To Lord Chief Baron Pollock.

91 Adelaide Road, December 22, 1865.

MY DEAR L. CHIEF BARON, — I don't believe in December 21
as the shortest day. Put on the twilight at both ends, and
calculate the shortest day. What care I for geometry ? It is
day as long as I can see to read, and even then the type must
be stated. There is Large Pica day, Small Pica day, Bour-
geois (pron. Burgice) day, etc. Diamond day is considerably
shorter than the geometrical day, in winter.

But now to your questions.1 'A^io? is an obsolete word = TI?.
IIws, the common word. 'A/xwo-ycTrws is a word of Plato and
Aristophanes (two people as opposite as L. C. B. Pollock and
L. C. B. Nicholson), meaning somehow or another. So it is, as
yon say, ' some unknown cause capable of producing.' We can-
not coin in English, I suppose, because it is the Queen's

1 As to the meaning of amo&gepotically in the preface to From
Matter to Spirit.

CORRESPONDENCE, 1856-66. 335

English, and 'uttering ' one's own coin is a felony. We cannot 1865.
say ' somehow or otherically.'

Yours sincerely,

A. DE MORGAN.

To Sir J. F. W. Herschel

91 Adelaide Road, September 27, 1866.

MY DEAR SIR JOHN, — I write without much purpose, unless a 1866.
funny fact be one. Ulugh Bey is the end of the chain. An
Arabic dictionary maker came to talk to me about getting his
names of the stars in Arabic ; thence came various Turks, thence
Turkish pupils he had had — whom I had had also ; thence
Ameen Bey, whose father was Hassein Effendi, who trisected
the angle, and who was taught by Ingliz Selim Effendi, who
translated ' Bonnycastle.' This Englishman who translated B.
must have been Richard Baily, Francis B.'s brother. He
certainly ran away and turned Turk, and both P. B. and
Miss B. told me that he translated Bonnycastle. Do you
happen to remember anything about him ? I remember that
Miss B. had his picture.

I hope you have fought the weather with needle-gun success.
By the way, where is it set forth that a leech is a famous
barometer, by indications to be seen in his behaviour in the
water ?

I have been looking at the writing of South about Babbage
and Davy. There is an exceeding patness of recollection about
him on this occasion as on former ones. Are we really to
believe that when he called on Sir H. Davy, and wrote a note
which he left in Davy's study, he took a copy of that note, so as
to be able to give it in complete form ? Or has he done what
Thucydides must be held to have done about the speeches of
his generals — made them as they might have been and ought to
have been ?

What is the real origin of the severance between South and
Babbage ? In all Babbage' s * Autobiography ' I cannot find a
hint of South's existence !

Do you possess Hyde's edition of Ulugh Bey's ' Catalogue '
(in Arabic and Latin) ? If so, I wish you would lend it to me.
I should not wonder if it were in your patrimony, though I
should hardly think you would have wanted it yourself.

With kind regards to Lady Herschel and all around you,

Yours sincerely,

A. DE MORGAN.

336 MEMOIR OF AUGUSTUS DE MORGAN.

SECTION X.

1866-1871,

1866. I COME now to the last important event of my hus-
band's life — the cessation of his connection with University
College. In recording this I wish to dwell as little as
possible on the fact, undoubted by all who were near him
at the time, that his last illness resulted from mental
trouble consequent upon it, in at least as great a degree
as from the losses which befell us later. But however
painful it is to write it, and however painful it may be to
read for the survivors among those who were indirectly
responsible for it, I have no choice but to state what was
the belief of all who had the means of forming a true
judgment.

He had joined University College in his early youth, in
opposition to the advice of some of his nearest friends,
who believed that his interests would not thereby be pro-
moted, and to the satisfaction only of those in whose
minds the upholding of a high principle was a more
weighty consideration than worldly success or affluence.
He was fully aware how much less lucrative a Professor-
ship in a new institution was likely to be than many
appointments which he might have obtained elsewhere.
The associations, too, inseparable from a perfectly new
institution were less congenial than those in which he
would have found himself at either of the two Universities,
where he would have worked under and with men whose
habits of thought (in some ways) would have been more
in harmony with his own.

He had worked in the new institution with untiring
energy for six-and-thirty years, because he trusted the

UNIVERSITY COLLEGE. 337

assertion of its founders and subsequent Governors that 1866.
the essence of its being was absolute and complete
religious equality in every portion of its organisation.
His anticipation that the pledge, so often and so emphatic-
ally given, would be fulfilled, was destined to a complete
and final disappointment.

The occasion arose on the appointment of a new Pro- Candi-
fessor of Mental Philosophy and Logic, in June 1866, in ofRey.Jas.
place of Dr. Hoppus, an Independent minister, who had
held the chair from the beginning. In accordance with
the laws of the College the testimonials of all candidates
were submitted to the Senate of Professors, who examined
and reported on them to the Council, in whose hands
rested the final appointment. From the first foundation
the Unitarians had been among the most powerful sup-
porters of the College, which could never have risen to its
then condition without their assistance in money and
effort. When it was first known that the Eev. James
Martineau, a Unitarian minister and a distinguished
scholar, was a candidate for the chair of Mental Philosophy
and Logic, a gossiping rumour came to the ears of my
husband and myself that the Unitarians on the Council
were working to bring in their own candidate. This was
merely foolish talk among a few persons, but I mention
it to show what my husband's feelings were on the subject
of the appointment. When he heard the report he declared
his disbelief in it, but said he would make inquiries, as
there must be no suspicion of the preponderance of any
one party in religion in that place. He inquired about
the rumour, and, as he expected, found it false. No
member of the Council at that time knew anything of the
relative merits of the candidates. It was evident, even if
any one who knew him well could have supposed it
possible, that friendship for Mr. Martineau, for whom he
had a sincere respect, did not influence his subsequent
conduct.1

1 I note this, as one of the newspapers spoke of my husband's

z

338 MEMOIR OF AUGUSTUS DE MORGAN.

1866. The report of the Senate, after enumerating Mr.

Martineau's qualifications for the appointment, as shown
by his writings, by his examination papers, and by the
testimony of his pupils, concludes with the words, 'All
these considerations evidently lead to the conclusion that
Mr. Martineau is the most eligible candidate. He appears
to be at least equal to the other candidates in ability and
learning, while he is superior to them both in reputation, and
in experience and success as a teacher.9 The question was,
however, raised at this early stage, whether Mr. Martineau's
position as a Unitarian minister would be injurious to the
class ; and of this doubt the Council, some of the influential
members of which were bent on appointing a Professor far
lower in the scale of orthodox belief than Mr. Martineau,
availed themselves. They postponed the appointment for
a time, and the Senate was called upon to make a second
report in consequence of new candidates having come into
the field, and some of the old candidates having sent in
additional testimonials. Their report of the second of the
candidates was given in these words : — ' Upon the strength
of this singularly strong testimony we have no hesitation in
concluding that Mr. Groom Robertson is exceedingly well
qualified to fill the vacant chair ; and that of the candidates
whose claims we have examined up to this point, he is the
ablest, and, as far as we can judge, the most learned, and
the most likely to rise to eminence, and to raise the repu-
tation of the College. But there yet remains upon the list
the name of Mr. James Martineau. As the Senate has
already recommended the appointment of Mr. Martineau,
and the Council has declined to appoint him, the Senate
does not think it necessary to present a second report con-
cerning him.'

In the hope and belief that the position of affairs was
not yet past remedy, fourteen Fellows of the College,
including some of its most distinguished alumni, sent a

* chivalrous advocacy of his friend's cause.' This conveyed an inexact
idea of the facts.

UNIVERSITY COLLEGE. 339

requisition to the Council asking that a special Court of 1866.
Proprietors might be summoned to consider the course taken

by the Council in deferring the appointment of the best Mr. Groom

J , ° . Robertson.

qualified candidate for special reasons to the vacant chair.
An objection to this on legal grounds was raised by the
Council ; they referred the question to the law officers of the
Crown, and before the opinion of these gentlemen (which
was in favour of the requisitionists) was announced, settled
it their own way by the appointment of Mr. Croom
Eobertson, who was a pupil of Prof. Alexander Bain, and
an adherent of the school of thought upheld by that
gentleman, and approved by the leading members of the
Council.

When Mr. De Morgan heard that the Council intended Resigna-

•mr • ir ' *• . n -n tionofPrO-

to reject Mr. Martineau for reasons connected with fessorshiy.

religious belief, he openly declared that should the Col-

lege make such a departure from the principle on which

it was founded, he should feel that his connection with it

was at an end. He waited with anxiety for their decision,

and when the news came that the acknowledged best

candidate was set aside on the ground of his Unitarianism,

and one below him appointed, he said that the College had

committed a suicidal act, and would never hold its old

place again. He did not hesitate as to his own course,

but at once sent in his resignation.

His letter to the Council, which follows, I know to
have been written without any intention of publication at
the time, or rather with a distinct intention of non-publi-
cation during his lifetime.

To the Chairman of the Council of University College.

91 Adelaide Road, November 10, 1866.

SIR, — I feel much sorrow in notifying to the Council
that my connection with the College must close at the
end of the current session.

For some years the returns of my chair have been so

z 2

340 MEMOIR OF AUGUSTUS DE MORGAN.

1866. small that, taking into account the time I give, my stay
Letter of has been an imprudence. I had nevertheless calculated

resigna-

tion. that I might, without too great an injustice to my family,

draw upon my capital, if I may use so grand a word, for
the means of retaining my post during this and the next
session, in the hope of the dawn of better days.1

The recent vote of the Council in the case of Mr.
Martineau renders it unnecessary for me to settle when I
shall leave the College ; it proves that the College has left
me. I am, as heretofore, strong in the determination not
to be overlooked, and not to be controlled in any matter
of religious thought, speech, or teaching. The Council
has decided that a certain amount of notoriety for advocacy
of an unpopular theology is a disqualification. Whether
a distinction was intended between the case of a candidate
and of an installed Professor I neither know nor care. I
assume that such a body as the Council would never enter-
tain this distinction. I concede that A is not B, but I
maintain that those who surrender to expediency point A
of principle are the men who will surrender point B when
the time comes, and who, until that time does come, will
be honestly shocked at the prophecy of their future con-
duct. Adherence to come is discounted to meet the con-
sequence of present departure. The principle of the College
has been partially surrendered to expediency ; no man can
say how much more will be given up, nor when. This I
said when the Peene legacy was accepted, and I was
laughed at. The acceptance of the conditions of that
legacy did not drive me from the College, because, after
much deliberation, and not a little help from what I now
see to be sophism, my love for the College and the life I
led in it barred the way with De minimis non cur at lex.

1 During the last years of his stay from various causes the proceeds
of his chair had fallen oft*. They had never been great, only one year
amounting to nearly 50CM. His continuing to hold it at a later period,
when the returns seldom exceeded 300L, and were becoming less, was
entirely due to his belief that the institution would fall still lower by
hia withdrawal.— S. E. DE M.

UNIVERSITY COLLEGE. 341

But I ought to have seen that minimum is the first step 1866.
from nihil to totum ; and when St. Denys, with his head
under his arm, had made that first step, I ought to have
foreseen the second.1 My self-complacency is comforted
by observing that there are even now men of experience
and thought who not only cannot foresee the third step,
but who affirm it will never be made.

Before proceeding to the most delicate part of the
subject I make two remarks.

First, in all that I say I am stating the decision of my
own court, by which my own course is determined. It is
for me alone to weigh evidence, and for me alone to de-
cide. This distinction is often forgotten ; such a letter as
the present is treated as appeal to those to whom it is
addressed, instead of recorded argument in a decided case.
Be it remembered that the first sentence of this letter
contains the needful ; all the rest is partly respect to the
body I am addressing, partly evidence of what is thought
by a person who has stood by the College for thirty years,
and who is likely to represent the opinions of many.

Secondly, I earnestly protest against being supposed
to impute to any one, in or out of the Council, the least
wilful or conscious impropriety of reasoning or conduct. I
mean to give the offence which, in our thin-skinned day,
is always taken at plain and uncompromising attack upon
alleged wrong proceedings ; but I am free of all intention
to be personally disrespectful to any of the promoters. I
can never forget the cordial co-operation of thirty years.

In the matter of Mr. Martineau, I am aware of the
existence of two cross currents. Since the first vote of the
Council I have weighed all that I heard, and have for
months been satisfied that there has been an objection to

1 St. Denys carried his head to Montmartre after his execution. I
take the allusion to mean that just as the miracle was complete as soon
as the Saint made the first step, so the alienation of the College from
its principle was effected at the very earliest departure therefrom. —
S. E. DE M.

342 MEMOIR OF AUGUSTUS DE MORGAN.

1866. his psychology as well as to his religion : the first is too far
J^i^f removed from atheism to please the philosopher, the
tiou. second too far removed from orthodoxy to please the

priest. No longer neutral between the disputes of
Christians, the College is to apply the abandoned principle
in another field. The frontier is to be rectified by putting
Theism in the place of Unitarianism, and making God an
open question, not to be the basis of any teaching on the
human mind. And so it is contrived that one and the
same victim, offered on the altar of the Janus Bifrons of
expediency, shall appease both the priest and the philo-
sopher, while each votary selects the particular head of
the deity to which his offering is made.

I proceed to show that (supposing me willing to re-
main) I am as worthy to be extruded as Mr. Martineau to
be excluded.

I have for thirty years, and in my class-room, acted on
the principle that positive theism may be made the basis
of psychological explanation without violation of any law
of the College. When in elucidating mathematical prin-
ciples it is necessary to speak of our mental organisation
as effect of a cause, I have always referred it to an
intelligent and disposing Creator. The nature of things,
the eternal laws of thought, and all the ways by which
that Creator is put in the dark corner, have been treated
by my silence as philosophical absurdities not worthy to
have their silly names intruded upon those who are to be
trained to think. Were I to remain under the new
system, I should hold it a sacred duty and — ah, poor
human nature ! — a malicious pleasure to extend ai
intensify all I have hitherto said on this subject.

Again, for more than thirty years I have been as
strong a Unitarian as Mr. Martineau. If I have not
raised my voice in this matter, and as strongly as Mr.
Martineau 1 has done, it is because I have been deeply

1 In writing the above (as will be evident to the reader) Mr. De
Morgan believed Mr. Martineau to be of the older Unitarian school,

UNIVERSITY COLLEGE. 343

engaged in other things, because I do not care what un- 1866.
reflecting people think they think, and because I have ^j^
found that the great bulk of reflecting men of all sects tion-
keep their Trinitarianism caged in a creed, and are, in
every practical application of religion except pelting
Unitarians, as truly Unitarian as Mr. Martineau himself.
Were I to continue in this College, under even the
ghost of a gag, I should soon be heard (without the walls)
on a subject to which I have paid long and close attention.1
I should soon bring the question to issue whether the
installed Professor is or is not a subject for such discus-
sion as has arisen about the candidate for admission.

I hope it will be clear that my absence is as desirable
as that of Mr. Martineau. But, for reasons given, I
deprecate the supposition of having sacrificed to principle.
I have only ceased to sacrifice because the temple has been
desecrated. My determination would not be altered by a
return to the old principle on the part of the Council.
I shall, therefore, not be suspected of any personal motive
when I urge the Council to reconsider their suicidal vote,
and to re-nail the old flag to the mast.

One point has perhaps been almost overlooked. A
teacher of psychology, if he do his duty, expounds all
systems of sufficient note, and puts forward the grounds
of each. Every one must have his own system, and if
one may therefore be suspected of bias, so must another.
Mr. Martineau has special reputation as an eclectic teacher.
He is noted for ability to prepare students for examina-
tions in which the examiners have no bias towards his
views. I have heard it remarked, before this discussion,
that he crams his pupils with different systems. Such a
man does not cram. It means that those of his students

which receives the New Testament records as literally true. I should
not be justified in referring to this mistaken impression if Mr.
Martineau's late writings, and his preference of the name of Theist,
were not well known.

1 These words, which may seem obscure, must be understood to
refer to his Unitarian belief. — S. E. DE M.

344 MEMOIR OF AUGUSTUS DE MORGAN.

1 866. who desire no better can cram different systems from his
Jr'£na-f lectures- There is more proof of his competency in this
tion. respect than in the case of any of the untried candidates.

Return to the old principle. If the College fall, it will
fall with honour. No concession of narrow minds, philo-
sophical or theological, will save it. The enemy will give
one sneer more, the friend nine cheers less. Thing'embigot,
who says that his son shall not enter the College if Mr.
Martineau teach there, never meant to send his son in
any case. The late vicar of St. Pancras, then a lessee
in Gower Street, found the noise of the playground
disagreeable, and sent word that if the nuisance were not
abated he should withdraw his patronage ; he had been
an inveterate opponent. He was left to subtract his
negative quantity if he pleased. Let Thing'embigot learn
the same rule of algebra.

On the other hand, the enemy of religious disqualifica-
tion, if the present course be persisted in, must decide
whether his son shall be educated under selection carried
up to its logical extent in the professed fear of God, or
exclusion nibbled at up to compulsion of circumstances in
the concealed fear of man as to religion, and another fear
of God as to philosophy. I should myself be puzzled to
make a choice, for if there be a tincture of atheism in the
second fear of God, there is a tincture of blasphemy in the
first. Of the two different ways of putting man in the
place of God, I think the world at large would prefer the
first.

My best wishes remain with the College which I leave,
but I wish to make myself clearly understood on the question
which has been opened. I trust that by return to and
future maintenance of the sound principle on which it was
founded, in which there is more religion than in all
exclusive systems put together, the College will rise into
prosperity under the protection, not of the Infinite, not of
the Absolute, not of the Unconditioned, not of the Nature
of things, not of the chapter of accidents, but of God, the

UNIVERSITY COLLEGE. 345

Creator and Father of all mankind.— I am, sir, with much 1866.
respect,

Your obedient, humble servant,

A. DE MORGAN.

The reading of this letter at the Council was (I was Reply of
told) followed by silence for a minute or two. The
minority who could understand its meaning and its motive
had already been outvoted. The majority could give no
answer, because they were determined not to give the
only one it called for, a return to principle. The secretary
was directed to inform the writer 'that your letter of
November 10, addressed to the Chairman of the Council,
was read at a session of the Council on Saturday last, and
that your resignation of the Professorship of Mathematics
from the close of the current session was accepted.'

The decision and its results gave great dissatisfaction
to the friends of religious liberty outside the College. The
newspapers, which represented different phases of thought,
expressed the variety of opinions held on the subject. By
those of the earnest and Liberal school the movement was
strongly condemned ; among other things it was said that
all real Liberals must ask whether it is wise to support a
College which, unsectarian in name, can yet be guilty of
such religious and philosophical bigotry. Here I may
remark upon the expression c real Liberals.' Every one
who has watched the progress of thought, especially during
the last half-century, must have seen that its tendency,
both in philosophy and in religion, is to the denial, or
what amounts to a denial, of God. I am not now attempt-
ing to condemn this tendency, but its prevalence has had
the effect of confusing formerly well-defined distinctions.
The ' Liberal ' has frequently gone from liberality to un-
belief ; and in the case of University College many pro-
fessed Liberals took the part of intolerance because they
preferred atheism to theism. The self-styled religious
party said that it was now clear that the profession of

346 MEMOIR OF AUGUSTUS DE MORGAN.

1866. desire to preserve the unsectarian character of the College
was so much dust thrown in the eyes of the public, ' and
that the College had declared itself truly a ' godless Col-
lege,' as it had long been called by the orthodox. Scoffers
laughed, and opined that ' the College ' could do without
its principles, but the principles could not do without their
College.

The next meeting of Proprietors was appointe d for

' February 2, 1867. But before the end of the current year,
and with reference to the requisition already referred to,
the Senate met again and supported the decision of the
Council, and in anticipation of the meeting addressed a
statement to the Proprietors. Though the real question,
which lies in a very few words, has been distinctly stated
in Mr. De Morgan's letter of resignation, I should be
thought to give an ex-parte account of the whole affair if
I were to omit the arguments on the other side. The
strongest of these may fairly be presumed to be embodied
in this statement of fifteen Professors, of whom more
than one had belonged to the institution from its found a-
tion. I feel it only right to give the document at length .

*•

Statement addressed to the Proprietors of University College.

A certain number of Fellows and Proprietors of University
College, London, have required the Council of the College to
convene a Special General Meeting of the Proprietors, 'to con-
sider a recent resolution of the Council declining to appoint
the Rev. James Martineau to the Professorship of Mental Philo-
sophy and Logic, after a Report of the Senate that he was the
best qualified candidate for the chair ; ' and a Special General
Meeting will be held, in consequence of this requisition, on
Saturday, February 2.

The subject which the meeting is convened to consider has
attracted much attention, and has been the occasion of many
articles in various daily and weekly papers ; and as is usually,
and indeed inevitably, the case when writers press forward to
instruct the public under the influence of a strong preconceived
opinion, and with an imperfect knowledge of the constitution

STATEMENT IN SUPPORT OF COUNCIL, 347

and history of the body which they criticise, and an imperfect 1866.
knowledge of the facts which they discuss, many circumstances
have been misrepresented. It is likely that these misrepresenta-
tions have influenced some even of the requisitionists ; and we
may assume without doubt that they have produced some effect,
more or less, on other proprietors who will attend the meeting.
We wish, therefore, to correct the more important of them, and
those especially which relate to the action of the Senate, or body
of Professors.

The gentlemen who have signed the requisition, and who
are indignant that Mr. Martineau was not appointed to the
vacant chair, have not thought it necessary to make themselves
acquainted with the evidence respecting the qualifications of the
other candidates. Most of them, in all probability, had no
means of knowing it. But as it would not have been seemly to
impugn the judgment of such a body as the Council of the
College, which had a full knowledge of the case in all its bearings,
and considered it very carefully, and which in fact made its
final decision after three months' deliberation, merely upon the
plea, that knowing only the reputation of one candidate, and
not having examined the claims of any other, they had a strong
opinion another way, they shelter themselves under the authority
of the Senate, and justify their very unusual attempt to pass a
censure upon the Council on the ground that the Senate reported
that Mr. Martineau was the best qualified candidate for the
chair.

The greater number of the requisitionists are Fellows of the
College, and were formerly distinguished students ; and probably
these gentlemen understand the constitutional relation of the
Senate to the Council. But in the articles on the subject which
have appeared in the public papers there have been expressions
as if the privileges of the Senate were invaded by the action of
the Council, or at least as if the two bodies were necessarily
placed in a position of antagonism by such a difference of opinion.
This is not the case. By the charter the power of appointing
Professors is given absolutely to the Council. Neither the
Senate nor a General Meeting can limit their discretion. But
it is wisely provided in our by-laws that, when a Professor-
ship is to be filled up, all the applications of candidates, and all
testimonials and other documents which they may present as
evidence of their qualifications, shall be submitted to the Senate,
and that the Senate shall report thereupon to the Council. But

348 MEMOIR OF AUGUSTUS DE MORGAN.

1866. a report so made is only an expression of opinion. The Council
retains perfect liberty of action. The choice of the Council is
usually in accordance with the opinion of the Senate. But
cases have occurred before in which the Council has exercised an
independent judgment, and departed from the recommendation
of the Senate, and the Senate has never felt itself aggrieved by
the exercise of such an indisputable right.

In this particular case there is especial reason why the Senate
should receive with respect the decision of the Council. On
subjects of professional learning, and in several departments of
science and literature, it is likely that there will be men amongst
the Professors better able to form a sound judgment than any
members of the Council. But on the question of Mental Philo-
sophy we believe honestly that the members of the Council
generally are as fully competent to form an opinion as the
members of the Senate.

Moreover, the relative strength of the recommendation of the
Senate has been misrepresented. It has been asserted that the
Senate ' reported to the Council that Mr. Martineau was incom-
parably the ablest candidate.' The first report of the Senate, in
which alone the qualifications of Mr. Martineau were discussed,
was not so unjust. The report examined the claims of Mr.
Martineau, as attested by his published writings, by the evidence
of his pupils, and by his Examination Papers, which he frankly
laid before the Council; and the conclusion was in these words: —
' All these considerations evidently lead to the conclusion that
Mr. Martineau is the most eligible candidate. He appears to be
at least equal to the other candidates in ability and learning ,
while he is superior to them both in reputation, and in experience
and success as a teacher.'

A still more flagrant injustice has been done to the other
candidates by the language of another writer, who chooses to
describe the Council as rejecting a first-rate man in order to look
about for *a safe man with indifferent qualifications as a teacher,'
one ' obscure enough to be inoffensive.' It is not necessary to
insist upon the qualifications of the candidates whose names are
not public, except to protest against the injustice of a writer who
knows nothing about the matter using such disparaging language :
but in the case of Mr. Rob3rtson, whom the Council have
appointed to the Professorship, it is rig lit to state tha conclusions
of the two reports of the Senate. The first report upon his
qualifications ended thus : — ' Mr. Robertson is only twenty-four

STATEMENT IN SUPPORT OF COUNCIL, 349

years of age. To judge from his testimonials, his philosophical 1866,
acquirements are already very uncommon ; nor ought we to
forget the great public service our College may render by giving
a man whose natural vocation, we are assured, is philosophy, an
opportunity of following his vocation.' The report then spoke
of the objection on the score of youth, and after alluding to
drawbacks in the case of certain other of the candidates, con-
cluded, ' But we are inclined to think that, of the disadvantages
under which they labour, Mr. Robertson's youth is the least
serious, as it is certainly the most remediable.' But the Senate
was called upon to make a second report in consequence of new
candidates having come into the field, and some of the old
candidates having sent in additional testimonials, after the
Council had extended the time for filling up the vacant chair.
When they drew up the second report, they had before them
additional evidence with respect to Mr. Robertson, which gave
assurance of the extent of his learning, and of the breadth and
impartiality of his views, and of his scrupulous fairness in
exhibiting fully contending theories. They expressed their con-
clusion in these words : — ' Upon the strength of this singularly
strong testimony we have no hesitation in concluding that
Mr. Robertson is exceedingly well qualified to fill the vacant
chair; and that, of the candidates whose claims we have ex-
amined up to this point, he is the ablest, and, as far as we can
judge, the most learned, and the most likely to rise to eminence,
and to raise the reputation of the College.' The report then
continued, ' But there yet remains upon the list of candidates
the name of the Rev. James Martineau. As the Senate has
already recommended the appointment of Mr. Martineau, and
the Council has declined to appoint him, the Senate does
not think it necessary to present a second report concerning
him.'

It would be almost ludicrous, if it were not rather lamentable
that parties in a controversy should be unable to conceive that
those who differ from them may differ honestly, to see how
little able the partisans of Mr. Martineau have been to take in
the notion that he may have been rejected upon his merits.
Various unworthy motives have been attributed to the Council ;
but it does not seem to have occurred to their assailants that
possibly they did not think Mr. Martineau the best Professor of
Philosophy that they could appoint. And yet a zealous advocate
of Mr. Martineau, in expatiating upon the soundness of his philo-

350 MEMOIE OF AUGUSTUS DE MORGAN.

1866. sophical views which ought to have recommended his appoint-
ment, points out triumphantly that they are opposed on various
points to the opinions of Hobbes, and Locke, and Hume, and
Paley, and Bentham, and Mill, and Austin, to say nothing of
Aristotle. Now it might have occurred to this writer upon his
own showing, that some thinkers might, whether rightly or
wrongly, at least honestly, think Mr. Martineau's philosophy
unsound ; and when it is considered from what class of thinkers
many of the original founders and many of the late supporters of
University College have proceeded, it becomes exceedingly pro-
bable that members of the present Council did sincerely and
honestly believe that his teaching would be at variance with
philosophical truth.

When this explanation of the strange phenomenon was
suggested, another argument was set up. We were told that
' the principle ' of considering the truth or falsehood of the
philosophical opinions of a teacher of philosophy * is monstrous,'
and is a kind of ' philosophical intolerance ' almost as bad as
religious intolerance. * The truth of a philosophical doctrine
cannot be settled with the same certainty as the truth of a pro-
position in Euclid Mental philosophy is at least as

valuable for the intellectual exercise it affords as for the conclu-
sions to which it leads ; and the duty of the Council is to choose
a particular teacher of the subject, not because he belongs to
one or other of the two great metaphysical schools, but because
he is the ablest candidate that can be got.' If it were acknow-
ledged on all hands that Mental Philosophy is a subject on which
no truth or certainty has yet been arrived at, it would be the
duty of the Council to appoint no teacher at all. It would be a
subject most worthy of the exertions of the trained student, who
still hoped against hope to arrive at truth ; but it would be no
study for a place of education. It continues to be a branch of
education because it is believed that truth and genuine know-
ledge are involved in it. The directors of a place of education
may be mistaken in their estimate of philosophical truth ; but
sorely they are not to be blamed for acting conscientiously on
their convictions.

But although it cannot reasonably be doubted that the decision
of the Council was determined, in the case at least of some of its
members, perhaps of many, by their estimate of Mr. Martineau's
philosophical merits, there is ground also for believing that it
was affected by a consideration of his position as a leading

STATEMENT IN SUPPORT OF COUNCIL. 351

minister of a religious sect : not, be it carefully observed, by any 1866.
consideration whether he belonged to this sect or to that, but by
the fact that he was a minister of religion, and a minister who
was placed in a prominent position. When it became known
that he was not appointed to the vacant Professorship, the first
outcry raised was that he was rejected because he was a Uni-
tarian, with the additional imputation that he was rejected, not
because the Council of University College objected to Unitarians
as such, but because they sacrificed their own professed principles
in timid and interested subservience to the prejudices and
bigotry of the outer world. This calumny was too gross to be
long maintained in face of the known characters of the gentlemen
who constitute the Council. But it did its work. It was the
origin of the agitation which was raised ; and probably it is still
believed by many persons. And not only was it the origin of
the agitation, but the agitators continue to agitate as if their
first assertions were true, although they know that the question
to be considered is a very different one.

On August 4 a motion was submitted to the Council in the
following terms : —

' That the Council consider it inconsistent with the complete
religious neutrality proclaimed and adopted by University
College to appoint to the Chair of Philosophy of the Mind and
Logic a candidate as minister and preacher of any one among
the various sects dividing the religious world.'

This motion was negatived ; so that no one has a right to
assign the principle here laid down as the ground of the subse-
quent action of the Council as a body ; although, no doubt, as
there was a minority who voted for the motion, it may be assumed
that those individual members acted upon this principle in their
subsequent votes ; and it is possible that other members, who
were not present in August, but were present in November, did
the same.

It is seldom expedient in any deliberative body to propound
a resolution in general terms, when the object is practical action
in a particular case ; and the Council probably judged wisely in
not affirming the general proposition in their minutes : but the
argument suggested is one which might be entertained and
applied in the particular case, without any departure from the
true principles of the College. It is important that the friends
of the College should know that such, at least, is the deliberate
opinion of the Senate. In the conclusion of their second report,

352 MEMOIR OF AUGUSTUS DE MORGAN,

1866. after stating that they did not think it necessary to report a
second time concerning Mr. Martineau, they added these
words : —

* We wish, however, to express our opinion upon a question
of principle which is supposed to be involved in the matter. If
it be thought by the Council that the characteristic principle of
the College, impartiality between religious sects,1 would be
violated or endangered by placing in the Chair of Mental Philo-
sophy a prominent theologian and a leader of one school of theo-
logical thought, even though the upright and honourable
character of the individual gave an assurance that he would not
consciously allow his theological opinions to affect his teaching
of philosophy, the Senate fully recognises the right of the
Council to entertain the objection ; and it is not disposed to
impugn the discretion of the Council, in whatever way the ques-
tion may be ultimately determined. In fact, the difficulty has
been felt in the Senate as well as in the Council.'

The report including this paragraph was carried, after an
adjourned debate, .by a majority of 14 to 2 ; so that it may be
fairly taken as expressing the deliberate opinion of the main
body of the Professors. It will be observed that the Senate
pronounced no opinion upon the case of Mr. Martineau. They
desired only to recognise and uphold the perfect right of the
Council to consider his ecclesiastical position before they appointed
him to the Chair of Mental Philosophy.

The reproach to which the Council is now subjected is of a
novel nature. It is something strange that gentlemen pro-
fessing liberal opinions should make it a reproach to other

1 This may be accepted as the semi-official declaration of the prin-
ciple of the College in 1866. It is evident that if it be the right one,
my husband's was wrong (see pp. 369-373).

It is also evident that if it were the full statement of that principle,
divines of all denominations alike might have been, by the Charter,
precluded from holding chairs in the College. Had this been announced
in the first instance, Mr. De Morgan might possibly have still held a
Professorship there, as in any other institution of moderate liberality ;
but he certainly would have made no sacrifices to retain it, in the idea
that he was supporting the sound principle of religious equality defined
by himself.

As a matter of fact, the reiteration of the statement that no reli-
gious qualification or disqualification could be tolerated in the College
had become almost tedious. — S. E. DE M.

STATEMENT IN SUPPORT OF COUNCIL. 353

liberals, that they are jealons of clerical influence in education.1 1866.
Such a jealousy is the usual concomitant of religious equality.
When the University of Sydney was founded, the authors of it
entrusted the selection of a Principal and Professors to a com-
mittee of gentlemen in England, informing them that, in conse-
quence of the equality of religious sects in the colony, they
would prefer that none of the Professors should be a minister of
any religious denomination. Their committee found it impossible
to discharge their trust to their satisfaction within this limita-
tion ; and as the instruction to them was not imperative, they
selected as Classical Professor and Principal the late Rev. Dr.
Woolley, who was a clergyman of the Church of England. The
appointment of Dr. Woolley was received at first with some
suspicion and dissatisfaction ; and it was not till the people of
Sydney became convinced by personal knowledge of the Tin-
sectarian character of his mind that they were thoroughly
reconciled to it. We by no means wish, nor would any judicious
friend of our College wish, to exclude all ministers of religion
from all Professorships ; but we mention this instance to show
that the advocacy of religious equality does not compel its
advocates in all cases simply to shut their eyes and ask no
questions as to the religious position of persons with whom they
have to do. In the last number of the Aihenc&um there is an
article upon the approaching Special Meeting of the Proprietors
of University College, in which the principles of the College are
thus described : — ' There was a universal belief created by every
kind of declaration on the part of the promoters, and fostered by
an unflinching adherence, that no disqualification on religious
grounds was to be tolerated, whether as to teacher or pupil.
The best Professors were to be chosen, independently of their
faith, and of their notoriety as followers of their faith.' This is
quite true as a general description, and we trust that it always
will be true. But the writer does not perceive that the two
clauses of his last sentence may be inconsistent ; and if he insists
upon the literal application of this rule in all conceivable cases,
he is a slave to the letter, and blind to the spirit of the principle
which he advocates. The College will appoint a Professor of
Anatomy, or a Professor of Latin, or a Professor of Natural

1 According to my recollection the reproach against the Council was
that they were sensitive only on the score of an unpopular clerical in-
fluence. It was not implied that they would as a body have shrunk
from the appointment of a liberal Churchman.— S. E. DE M.

A A

354 MEMOIR OF AUGUSTUS DE MORGAN.

1866. Philosophy, without any reference to their theological opinions
or their ecclesiastical denomination, because their theology or
their denomination will in no way affect their teaching of
anatomy, or Latin, or Natural Philosophy. But the College
may reasonably and consistently think twice before appointing a
professional theologian Professor of Mental Philosophy ; because
it is not only possible, but not unlikely, that his professional
theology will make him a worse teacher of mental philosophy.
We will borrow the language of one of the assailants of the
Council. * Such is the nature of speculative inquiry, that of
necessity it brings into view the truths of Revelation, and forces
up the question whether they agree with the principles which
the thinker has reached. If his mind have the logical grasp
requisite for the profoundest of all studies, he will not be content
with laying down certain doctrines regarding cognition, but will
follow their issues through the windings of thought, till they
come into contact with theology itself.' True : and if his
theology be really his own, good ; but if his theology be a fore-
gone conclusion — something which he has accepted independently
of philosophical investigation, — if he is trammelled by connexion
with a party or a denomination, if he has an ecclesiastical position
to maintain, or a theological reputation to lose, there is no small
chance that his philosophy will be, or has been, modified by con-
tact with his theology. We put the case generally ; but there is a
strong a priori probability that a layman will be a more unpre-
judiced, and therefore a better teacher of mental philosophy than
a minister of religion ; and, if so, it is no part of the duty of the
Council to ignore the distinction.

If the general principle be sound, there is no force in the
objection that our late Professor, Dr. Hoppus, was a minister of
religion. If the general rule be a safe one, the fact that no
harm followed from one departure from it 1 is no argument for
lightly departing from it a second time ; and still less is it an

1 The suggestion that the election of Dr. Hoppus was at the time
regarded as a departure from a general rule, shows that the writer of
this passage had not been connected with the College from its founda-
tion. The elections of two clergymen of the Church of England, among
the first appointed, were looked on rather as affirmations of a distinct
principle than as departures from an unexpressed * general rule.'

When Dr. Hoppus's name first appeared in the list of Professors, a
remark was made in my hearing on his being a minister of religion.
The reply, given by an influential member of the institution, was, * We
do not consider these things.' — S. E. DE M,

STATEMENT IN SUPPORT OF COUNCIL. 355

argument to debar the Council from their right to consider all 1866.
circumstances likely to affect a Professor's teaching.

We are assured on very good authority, that when the first
appointment to the Professorship of Mental Philosophy was to be
made in the College, there were two instances of eminent
ministers who thought of offering themselves as candidates for
the office, but were withheld by the conviction at which they
themselves arrived, after further consideration, that it would not
be consistent with the duty of the Council to appoint them.1

The preceding argument is perfectly general ; but in the
particular case of Mr. Martineau there is one point of another
kind which deserves consideration. No one will question that
the authorities of our College are bound by the strongest obliga-
tions to avoid carefully any act by which they wo aid induce our
students, or even put facilities in their way, to submit themselves
to one form of religious teaching rather than another. Mr.
Martineau is described as ' Professor of Mental, Moral, and Reli-
gious Philosophy ' in Manchester New College ; and we have every
reason to believe that he discharges faithfully, zealously, and
ably the duties of his office. In his letter of application for the
Professorship he stated that, if he were appointed, he should
transfer his lectures on logic and mental philosophy entirely to
University College. Moral philosophy is not included in the
duties of our Professorship. We may fairly conclude, therefore,
that, if Mr. Martineau had been appointed, he would have
lectured on logic and mental philosophy in University College,
and would have continued to lecture on moral and religious
philosophy in the institution called Manchester New College, all
the business of which is done in the building of University Hall,
which is immediately contiguous to the College. A very natural
consequence would have been, that students who were attracted
by his lectures in the College would have been led to attend the
further part of his course in the Hall. At present, if any
students seek the instruction of Mr. Martineau, they are at
perfect liberty to do so, but the College is in no way responsible.

The Council has been attacked for having proceeded to elect
Mr. Croom Robertson to the vacant chair at the same meeting
at which they received the requisition for a Special General
Meeting, without waiting for the answer to their consultation of

1 This statement would have had more force if substantiated by
particulars. According to my recollection these gentlemen had other
reasons for not coming forward. — S. E. DE M.

A A 2

356 MEMOIR OF AUGUSTUS DE MORGAN.

1866. the high law officers whether a meeting could legally be convened
for the purpose named in the requisition, and, if it could, without
waiting for the result of it. In the first place, the Council had a
perfect right to do this. By the very charter of the College the
power of appointing Professors is committed to the Council, and
not to a General Meeting : manifestly because the Council is a
body capable of judicial action, and a General Meeting is a
popular body, and not a fit instrument for such a purpose. The
Council is elected by the proprietors to discharge this and other
duties ; but they are not mere delegates of the proprietors, and
it has never been considered that they were bound to receive
instructions from them. No doubt the General Meeting may
express an opinion upon the acts of the Council ; but the duty of
the Council was to do what they thought best for the College,
and then to await the judgment of their constituents. If the
Council had delayed to act, for the purpose of deferring to a vote
of the meeting, they would have abdicated their proper function.
Our sole purpose is to uphold the legitimate authority of the
Council, and to vindicate their right (and, indeed, we might
insist upon it as their duty) to consider all circumstances which
make a candidate more or less fit to discharge the duties of the
office which he seeks. When the first report of the Senate was
drawn up, the Senate named Mr. Martineau as the best candidate ;
and although the objection presented by his ministerial position
was discussed, it was not insisted upon, and therefore it was not
mentioned in the report. When the second report was framed,
which was rendered necessary by the reception of additional
evidence, the relative position of Mr. Martineau and Mr. Robert-
son was certainly not left what it was before ; and, moreover,
the attacks upon the College made it incumbent upon us dis-
tinctly to recognise in the Council, and members of the Council,
the right to consider all points in the position of Mr. Martineau,
or any other candidate, which seemed to them likely to affect his
fitness for the Professorship. We learn now, on what we must
consider good authority (the Spectator of January 26), that
the issue to be submitted to the meeting is substantially the
same as the proposition of the writer in the Athenaeum, which
we have discussed above. The resolution announced runs thus :—
* That in the opinion of this meeting any candidate, who is other-
wise the most eligible for any chair or other office in this College
or the School, ought not to be regarded as in any manner dis-
qualified for such office because he is also eminent as a minister
or preacher of any religious church or sect.' The writer in the

MEETING OF PROPRIETORS. 357

Athenceum, and the framer of the resolution, under cover of a 1866,
specious general proposition, thrust out of sight the certain fact
that there are some departments of human knowledge, and
mental philosophy is eminently one of them, in which the pre-
possessions of a theologian and the habits of a theological teacher
may make him a worse qualified candidate than another man ;
and in such a case those who have to appoint the teacher are
bound to take cognisance of the fact, and it is very unwise to
fetter their discretion.

We pass no judgment on the particular case of Mr. Martineau.
We are quite ready to assent to the general proposition, that no
candidate ought to be regarded as ipso facto disqualified because
he is a minister or preacher. But we desire to maintain the
right of the Council to examine all the circumstances of every
case that comes before them ; and we earnestly entreat every true
friend of the College not to concur in any vote which would
seem to inflict a censure upon the Council for the legitimate
exercise of their discretion ; and, above all, not to concur in any
vote which would impose a restraint upon their freedom ot
judgment in future.

This was signed by fifteen Professors, of both Faculties.

On reading this document, -my husband said the
principal part of the question was left out altogether ;
for had he ever understood that the profession of religious
impartiality made by the founders of the College was only
to be understood ' as a general description,' his name
would never have been connected with it. He drew a
distinction between the part taken by the older Professors,
who, from their long connection with University College,
could not fail to know that its very life consisted in the
entire rejection of all religious distinctions, and that of
those more recently appointed, who, he thought, might
and probably did believe that the Council was not bound by
any condition except that of making the appointment
which might seem to them best for the worldly prosperity
of the institution. From this latter point of view, it is
not difficult to understand why a candidate believed to be
prominent in an unpopular sect should have met with dis-
favour in the eyes of the Council.

The special meeting of Proprietors was held early in

358 MEMOIR OF AUGUSTUS DE MORGAN.

1867. February 1867, and a few weeks later the annual meeting
took place. On both these occasions those who contended
for the old principle were beaten, and the College pro-
ceeded to work in its new character. Whether it is
held in higher estimation since then I have no means of
knowing. I only know that it is changed since I heard the
conversations of Lord Brougham, Thomas Campbell, and
my father at the time of its foundation.

My husband told me that during the session in which

he worked after his resignation was sent in he met his

colleagues as before in the Professors' room. Not one of

them ever spoke on the subject of his retirement, and he

left the place without one word of acknowledgment for

all he had done for it. Only once, after the end of the

session, he paid a visit to his old lecture-room. He went

to bring away the note-books and manuscripts which he

had used in his lectures. The visit was a painful one,

but was so cheerfully borne that I should hardly have

known all he felt if I had not said something to the

effect that I hoped he would not suffer for the trial. He

said, ' Oh, I shall do very well. I felt all the time to-day

that the College had left me, not I it. It was no longer

the old place. But then,' he added sorrowfully, c all my

thirty * years' work has been thrown away.' The answer

to this was of course easy. I said that no such efforts as

his could ever be without result ; that his teaching had

trained many strong and honest minds ; and that if the

College had done nothing more, its establishment might

have helped in the opening of the two Universities. He

acquiesced, but the blow was struck.

In the spring of 1867, after the efforts of many of the
best of his old pupils and friends to retrace the false step
had failed, some of these gentlemen, desirous that he
should not leave the scene of his work without taking

1 It will be observed that sometimes more than thirty years are
mentioned. He was Professor from 1828 to 1833, and again from
1836 to 1866— in all more than thirty-five years.

RETIREMENT FROM UNIVERSITY COLLEGE. 859

with him some memorial of their respect and friendship, 1867.
asked me whether I thought he would refuse a testimonial
in money.1 I answered without consulting him. He had
strongly objected to the system of testimonials, which of
late years had grown to such a height, and I was quite
certain that his answer would be in the negative. He
soon after received the following, enclosed in a letter
from our friend Mr. Jacob Waley : —

'May 7, 1867.

( DEAR SIR, — Many of your old pupils, at whose request Proposed
we address you, desire, upon your resignation of a chair bust.
which for upwards of thirty years you have filled with so
much distinction, to give some appropriate expression to
the high estimation in which they hold you.

' Our admiration for your philosophical views of edu-
cation, your skill in the art of instruction, and your
scientific attainments, as well as our cordial regard and
esteem for you as our old teacher and friend, render us
desirous of recording these feelings in some substantial
shape.

' We understand, however, that you feel you cannot
consistently accept any testimonial of intrinsic value. But
we hope that you may be persuaded to gratify your pupils
by sitting for a picture or bust to be placed in the library
of our old College. We remain, sir,

' Yours faithfully,

'JACOB WALEY. H. M. BOMPAS.

W. A. CASE. E. B. CLIFTON.

J. GL GREENWOOD. J. M. SOLOMON.

G. JESSEL. H. COZENS HARDY.

EICHARD HOLT HUTTON. THEODORE WATERHOUSE.'
WALTER BAGEHOT.

1 The year before his death several old pupils and friends kindly
obtained for him a pension of 100L from Government. On hearing of
this his first impulse was to decline it with thanks. I entreated him
to receive the kindness as it was meant.

360 MEMOIR OF AUGUSTUS DE MORGAN.

It gave a pain to my husband to refuse a request so
kindly and cordially made. His reply was as follows : —

' MY DEAR WALEY, — I acknowledge your kind letter of
the 7th with the cordial and gratifying inclosure, signed
by eleven old pupils, whose dates represent the time which
has elapsed since I rejoined the College in 1836.

' The inclosure is in itself a testimonial. It has all the
meaning and all the value. And to those who hold that
the mind of the teacher counts for something in the
making of the pupil, the string of names appended to it will
be no mean presumption that I have in some degree a
claim to the terms in which I am described.

6 1 am asked to sit for a bust or picture, to be placed in
what is described as " our old College." This location is
impossible; our old College no longer exists. It was
annihilated in November last.

' The old College to which I was so many years attached
by office, by principle, and by liking, had its being, lived,
and moved in the refusal of all religious disqualifications.
Life and soul are now extinct.

' I will avoid detail. I may be writing to some who
think that the recent transaction is a reparable dilapida-
tion, or even to some who approve of it. To me the
College is like a Rupert's drop with a little bit pinched off
the small end ; that is, a heap of dust.

c I can never forget that I have been usefully employed,
though I now wish iny life had been passed in any other
institution. I have worked under the conviction that I
was advancing a noble cause, until every letter in the
sentence " Augustus De Morgan, Professor of Mathematics
in University College, London," stands for 234 hours of
actual lecturing, independent of all study and preparation;
and all this under a banner which is now shown to have

A

been either shamfully raised or shamefully deserted.

< So much is necessary that my old pupils may under-
stand my mind, and the repugnance I feel towards any
proceeding which must record my connection with Uni-

KETIREMENT FROM UNIVERSITY COLLEGE. 361

versitj College. I am happy to say that the circumstances 1867.
have not created any personal bitterness of feeling ; indi-
viduals are to me what they were before. But if force of
will can succeed, the institution is to pass away from
before my mind, and to become as if it had never existed.

( You will see that I am altogether averse to lending
aid or countenance to any scheme which will tend to
remind others that I was a teacher in the College which
did homage to the evil it was created to oppose.

6 But I am even more sensible to my old pupils' remem-
brance than I should have been if I could have accepted
the result of their most acceptable good opinion. Such
remembrance would have been, in any case, a treasure.
It has now the additional value of a treasure saved out of
the fire.

6 You will, of course, communicate my answer, and
with my warmest thanks and most heartfelt regards,

* I am, my dear Waley,

'Yours sincerely,

'A. DE MORGAN.51

He often spoke with satisfaction of the uninterrupted
friendly relations which had for thirty years subsisted
between himself and his colleagues. From his declining
health and other circumstances he saw but little of them
latterly, but this was in no case due (on his part at least)
to personal feeling created by the question which had
caused his withdrawal.

One of his social pleasures during the last few years had Crabb
been in the acquaintance and friendship of Mr. H. Crabb
Eobinson, one of the first active promoters of the establish-
ment of University College. Through a life of nearly
ninety-one years Mr. Eobinson had been the steady friend of

1 This letter was printed after Mr. De Morgan's death for circula-
tion among friends who had been asked to join in an injudicious at-
tempt to found a scholarship under his name in University College.

362 MEMOIR OF AUGUSTUS DE MORGAN.

1867. freedom and progress, but his influence, which was con-
Mr.Crabb siderable, had been felt chiefly in his conversation and

Kobinson. *

social intercourse with other minds, for his writings were
few and comparatively unimportant. In December 1866
he had voted in the minority in the Council on the ques-
tion of Mr. Martineau's appointment, and on the next
meeting, when the cause was lost by a majority of one,
the chairman giving the casting vote, Mr. Kobinson was
absent from illness. This, and the adaptation of principle
which afterwards ensued, was a cause of great concern to
him. During the winter of 1865-66 Mr. De Morgan
helped him in the task of arranging and sorting his books,
a miscellaneous but very valuable collection. My hus-
band, who was interested in the work, said that it was a
very slow process, because every book or pamphlet looked
at gave occasion for some literary or historical anecdote,
and this sort of gossip was pleasant to his hearer, who
knew much of books and of men ; for Mr. Robinson had
been the contemporary of all — the friend of many — of the
eminent, political, and literary characters whose life and
work made the history of the end of the eighteenth
and much of the nineteenth centuries. He had been
the friend of Goethe, Wordsworth, and Coleridge. He
remembered and knew the political trials of Home Tooke
and his friends, and told me incidents connected with my
father's trial at Cambridge of which I had never heard.1
His Sunday morning breakfasts were, I suppose, occasions
of much pleasant intercourse among many intellectual
men of various opinions. At these my husband used to
meet the Rev. F. D. Maurice, the Rev. J. J. Tayler, the
Rev. J. Martineau, and many others ; and it was at these
parties of friends that his acquaintance with Mr. Mar-
tineau was chiefly formed.

Early in 1867, shortly after the trouble at the College,
the kind-hearted, consistent old man left this world. Mr.

1 I first saw Mr. C. Robinson at Mrs. Barbauld's. I was then
twelve years old.

FAILURE OF HEALTH. 363

De Morgan visited him daily, and saw the day before he died 1867.
that his end would be without pain. In the Diary and
Memoirs, published by Dr. Sadleir, a little sketch by Mr.
De Morgan gives a portrait of the subject, which shows
how actively his mind was still at work, and his interests
alive to the last.

The last work of any importance undertaken by my
husband was a large calculation, I think, for the Alliance
Assurance Company. But his health had begun to fail.
Every one who saw him observed the change which had
passed over him, and before the great sorrow which came
to us at the end of 1867 he was no longer the strong,
vigorous man, full of hope and activity, which he had
been before his alienation from the institution to which so
much of the work of his life had been devoted.

In October our dear son George was taken from us. George's
He had worked hard during the winter, and even late into
the spring, both in giving lessons and in examining the
papers for the degrees of the University of London. He
was at that time Vice- Principal of University Hall, Gordon
Square, but was almost every day with us in Adelaide
Road. His father, who only saw his cheerfulness and the
seeming improvement in his health when, after a short
time at Herne Bay, he parted from him to join us at
Bognor, did not realise his state, and hoped against hope
to the last. George went on with one of his sisters and
myself to Ventnor. He was still warmly interested in the
success of the Mathematical Society. As his name be-
longed to it as one of the secretaries, his father was
anxious that, if possible, the first diploma given should
have his signature. For this purpose parchment was
placed before him, and he evidently recognised its import,
passing his finger over the words Mathematical Society.
But he was too weak to hold the pen, and died two days
after. His father, already enfeebled in health, had been
at home with two of our daughters, and could not com e
in time to see him while he would have been recognised .

364 MEMOIR OF AUGUSTUS DE MORGAN.

1868. He bore the blow as bravely and firmly as he had borne
other trials, expressing his full confidence in the wisdom
which had removed from among us one who seemed in-
tended to tread in his own steps on earth. But another
trial awaited us in the illness of our third daughter. I had
to leave home with her for several weeks, and she recovered
so far as to remove much anxiety. In the year 1868 my
husband's own health, which had continued steadily to
decline, broke down entirely. A sharp attack of conges-
tion of the brain, the result of so much intense mental
suffeiing, left him so prostrated that it was evident he
never again would be equal to sustained effort.

We moved in the summer to 6 Merton Road, near
Primrose Hill, a house which he said was the most
comfortable he had been in since our marriage. We
dreaded this moving on account of his weak state, but
all was ready to receive him, and he did not suffer.

In his enfeebled condition the task of placing his books
was a heavy one. The room destined for them was much
smaller than the one he had had in Adelaide Road, which
he said was a palace. It was a work of time for him to
measure the walls, and to direct the placing of the new
shelves, but it was done, with intervals of rest. Alarge num-
ber of the books had been sold, but about 3,000 remained,
and I feared he could not get them all in, and of course
begged him to have help. He said, with his old spirit,
' They shall all go in, and I will put them all in myself ; '
and so he did. The work was done gradually, and I do
not think it hurt him. He always liked looking through
his treasures, and showing to any friend any special
rarity.

During the last few years of his life my husband occu-
pied himself a good deal in reading the Greek Testament,
and comparing the different versions and translations. I
regret much that many comments which he made on this
subject were not preserved, as he did not write them. He
also compiled a sort of history of his family and biography

LATEST INTERESTS. 365

of himself — not in a connected form — to be left as materials 1869.
for his Life, and from this book I have taken much of
the earlier part of this Memoir. He also rearranged and
.added to his Budget of Paradoxes, which, however, was
not published till after his death.

One of the last subjects which afforded him interest FreeChrig-

" tian Union.

was the proposed formation of a society to be called the
Free Christian Union. The idea, a beautiful and attractive
one, was the formation of a union for the promotion of good
in various directions of men of all religious beliefs and
opinions, on the common ground of the Fatherhood of God
and the brotherhood of man. But there was some inaccuracy
in the designation, for under the simple, universal principle,
professed Jews, Hindoos, and other Easterns were eligible as
members ; indeed, my husband said Christ himself and the
Apostles might belong to the society, which they could not
perhaps have done to many associations taking the name
of Christian. Either the designation or the conditions of
membership must be abandoned ; and on the former pro-
posal, several persons of well-defined orthodox opinions
left it. Mr. De Morgan hesitated before giving his name,
feeling that in the present uncertain and unsettled state
of opinion among the best meaning persons a union based
upon anything but absolute and simple theism was im-
possible. This would exclude the use of the word Christian,
leaving a common basis of belief so broad as not to satisfy
men of deep religious thought, while it would not admit
Comtists and others whose philanthropic views and de-
sires to benefit mankind were as wide and earnest as
those of the founders themselves.

He also desired to learn to what the designation
' Christian ' applied — what were the opinions of the
founders with reference to the work and mission of Christ.
The writings of some of these, friends whom he valued and
respected, had led him to suspect that in their view what
is called the supernatural element in the Gospels, the
account of the miracles and resurrection of Christ, were

366 MEMOIE OF AUGUSTUS DE MORGAN.

1869. due either to the exaggerations of Eastern fancy and
expression, or to the interpolations of superstitious times.
My husband, who believed fully in the account of the
resurrection of Christ as given in the Gospels, wished to
ascertain the views of those who held what are called
' advanced ' opinions on this head. He wrote and inquired,
but told me he could not make out what their ideas
were. I once said to him that I thought one element in
the question had been generally overlooked, the ' opening
of the (spiritual) eyes ' of the witnesses, as mentioned in
the Gospels on other occasions. This would give some
apparent subjectivity to the fact, but it is nowhere stated
that all present saw the rising of Christ. He said, ( Very
possibly, but there was a rising; the history is clearly
given and well attested, and the rejection of it would be
to cut away the root from the tree. And the accounts
given of this and the other miracles cannot be taken from
the history without throwing a discredit on the narrators*
character that would make all their statements worthless.
They say,' he said of the Rationalistic school of interpreters,
6 that it is the character of Christ that commands reverence,
and proves his mission from God. You cannot separate the
two. He himself claimed extra-natural powers, given by
the Father. If this was false He was false, and His cha-
racter would not have been what it was ; and the men
who could invent fictions about His works could not have
described the character as they did.' It was with reference
to this society that we spoke of public prayer. In his
letters on Christian union he speaks of a basis on which
people might meet and pray together. He had always said
to me that Jesus Christ had not enjoined public prayer ;
and though He had not forbidden it, the tenor of His
teaching was strongly in favour of privacy and seclusion
in this most internal and sacred communion. ' Enter into
thy closet, and when thou hast shut thy door, pray to thy
Father which is in secret,' &c. But though he felt this
strongly himself, he knew that all did not feel with him.

HIS DEATH. 367

He himself felt the happiness of prayer, but he said, ( I 1870.
regard it rather as a luxury than a duty.'

In reference to the vision of the apostles I may men-
tion that he had always been interested in cases of the
kind, especially those in which departing persons, while
fully conscious, assert the presence of those who have gone
before. Such instances, he said, were so common that one
could not believe them to be all illusion ; but whatever
they were, they should be recorded carefully.

In August 1870, seven months before his own release, £)eath
our daughter Christiana was taken. She had stayed at JjJL^,
Bournemouth on her return from Madeira, and died there. Christiana.
I came home the day after her death to find her father so
weak that he had that day fallen on the floor, and was
unable to rise without help.

From this time the decline in his health was very
apparent, but he did not seem to suffer, except from weak-
ness and sleeplessness. The physical state was a com-
plicated one, chiefly owing to nervous prostration, and
traceable in the first instance to the shock of the College
disappointment, and afterwards to anxiety and sorrow on
our children's account.

In March 1871 he became still weaker, and talked 1871.
very little. The only word I remember relating to his
own state was, after saying that any way all would be
right, £But I shall be glad when I have got it over.'
When I expressed a hope that he would not be taken yet,
he told me to ' leave it all in God's hands,' and he then
waited quietly for the end.

During the last two days of his life there were indica-
tions of his passing through the experience which he had
himself considered worthy of investigation and of record.
He seemed to recognise all those of his family whom he
had lost — his three children, his mother and sister, whom
he greeted, naming them in the reverse order to that in
which they left this world. No one seeing him at that
moment could doubt that what he seemed to perceive,

368 MEMOIR OF AUGUSTUS DE MORGAN.

1871. was, to him at least, visible and real. After this he said
very little, only on the last morning of his life asking me,
as he had been used to do, c if it was time to get up.' On
being told that it would soon be, he seemed to be carefully
dressing himself. Then he lay quite still till, just after
midnight, he breathed his last. The state of mind in
which he had lived, and in which he died, is shown by a
sentence in his will : —

I commend my future with hope and confidence to
Almighty God ; to God the Father of our Lord Jesus Christ,
whom I believe in my heart to be the Son of God, but whom
I have not confessed with my lips, because in my time such
confession has always been the way up in the world.

369

SECTION XI.

CORRESPONDENCE, 1867-70.

To Sir John Herschel.

91 Adelaide Road, March 25, 1867.

MY DEAR SIR JOHN, — ' How do you bear this trying weather ? ' 1867.
asked a friend during the l&iefroid d'enfer, as a Frenchman might
say. ' Trying weather ! ' said I ; ' convicting weather ! sen-
tencing weather ! penal servitude weather ! '

The question between me and the College is simple. I
entered that College on what all the world knows was its loudly
vaunted principle, that the creed of neither teacher nor student
was to be an element of his competence to teach or to learn.
After forty years of existence the College, for worldly reasons,
has decided that a teacher must not be too well known to be
heterodox : he must not be conspicuous as a Unitarian. Breach
of faith, surrender of principle, and D. I. O.

But this is not all. Between ourselves, the candidate who has
been refused the chair of Mental Philosophy because he is so very
wicked a Christian in religion, is also excluded because he is too
much of a theist in philosophy. He cannot help founding his
psychology on a moral Governor of the universe.

Now, I would not have objected to leaving the existence of
God and His action on the minds of men an open question for
the best qualified candidate to treat in his own way ; but the
interference of the College as a college, and a settlement of
that question officially, is a step in which it concerns me, with
my way of thinking, to take a part. The public knows nothing
about this view of the question, but the Council have been
roundly charged with it by one of themselves in debate, and by
me in my D. I. O. I have told them totidem verbis that they had
acted from fear of God in philosophy and fear of man in religion.
I am only here till the end of the current session. . . .

Yours sincerely,

A. DE MORGAN.

B B

370 MEMOIR OF AUGUSTUS DE MORGAN.

To J. S. Mill, Esq., M.P.

July 3, 1867.

1867. MY DEAR SIR, — A person described by you as a remarkable

working man, and your correspondent, is one whose case is
more than usually worth looking into. He had better write
to me direct, and state in some detail what he knows, and, as
well as he can, what he wants. I dare say I shall be able to
shorten his route. He must specify arithmetic, his knowledge
and habits, geometry, algebra, physics, if any. You need
not tell him that the glimpse I shall get of his mind is one of my
data. I hope you are lifelike in spite of Reform debates.
* Confound this rope ! ' said the Irishman who was hauling in the
slack, ' sure somebody has cut off" the other end of it ! ' Do you
not begin to suspect that somebody has stolen the third reading ?

Yours very truly,

A. DE MORGAN.

To J. S. Mill, Esq., M.P.

91 Adelaide Road, August 2, 1867.

MY DEAR SIR, — As touching your proposal to me to join the
committee of the National Society for Women's Suffrage, I
cannot accede. I never join political agitations, or associations
for procuring changes in the political machine. I remember
signing a petition which, as I understood it, was for franchise to
be granted to single women having the property qualification.
Your Society, as its title is worded, contemplates a full female
suffrage — e.g. a vote for a man and another for his wife. Sup-
posing me willing to join a political agitation, I should hardly be
ready for such a one as this. I should think better of two
votes given to the couple jointly — i.e. the two to agree upon the
two. I almost thought this was the meaning of the phrase
' compound householder,' when I first heard people mention it.1
I got as far as joining the Decimal Coinage, but this was for the ]

1 I cannot help thinking my husband wrote this for the sake of play-
ing on the expression * compound householder,' as he can scarcely have
missed seeing that the result of one vote to each of two people has the
exact effect of two votes to both if they agree, except only in the
of one of the two not voting at all. — S. E. DE M.

CORRESPONDENCE, 1867-70. 371

sake of education, and the furtherance of arithmetic among the 1867.
labouring classes.

Yours very truly,

A. DE MORGAN.

To Sir John Herschel.

91 Adelaide Road, August 8, 1867.

MY DEAR SIR JOHN, — Many thanks for the Latin original of
Schiller's poem.1 I always take the older language as being the
original. I see Spaziergang — in my dictionary it is Spatzier-
gang in the German- English and Spaziergang in the English-
German — means a walk. Now, I have not taken a walk for
many a year. Had I done so, I might have started off something
at this kind of pace : —

Good morning, Mr. Mountain, with the light upon your top,
Just the rubbing of Apollo's eyes before he opens shop ;
And you, you * daisy-spangled meads,' and you ' resounding grove,'
Where the feathered songsters make a row ; I'd feather 'em, by
Jove, &c.

But seniores priores : Schiller has the start. I hope your hexes
and pents show that you are in a good condition. I see you
don't care for the dissyllabic ending. No more did I when I
was at school ; and I was reprimanded, which I should not have
cared for ; but I was then remanded to set it right, and this was
a bore.

Of all the verses I made at school, I only remember one

couplet. The subject was poetic inspiration, and was very

classically intended. It pleased me to take it that dinner was

the thing, and I have always been inclined to support my thesis.

The pair of lines I remember is —

Gustat Virgilius — procul o procul este Camoense
Conclamat vates — hoc mihi nunien erit —

If you look into the Afhencewm of Saturday week, you may
chance to see a little account of the last mare's-nest at Paris — the
discovery that Pascal preceded Newton in the theory of gravita-
tion. The letters, if genuine, prove nothing. — - was guessed

to be the law before Newton or Pascal by Bouillaud. But the
funny point is that Pascal is made to talk of a tasse de cafe, years

1 A Latin translation from Schiller by Sir John.
B B 2

372 MEMOIR OF AUGUSTUS DE MORGAN.

1867. an(j years before coffee was known in Paris, so far as has been
stated. The first coffee- shop was really started nine years after
Blaise's death by a man named Pascal, and the first started in
England was in 1652 by Pasqua, a Greek. In England in 1657,
' Coffa — see Cawphe,' is in Phillips's dictionary, and of ' Cauphe '
it is said, ' it is much used in these parts.'

I have nothing to say about myself or my people. The world
wags as usual. I should like to hear of you. I have just found
out that Dr. Pearson began life as a junior partner in Sketchley
& Pearson, who kept a school at Fulham for boys from four to
ten. Here he had been for some years in 1800. I picked up a
sensibly written prospectus — they said plan then — of this esta-
blishment. He founded his great school at Sheen in 1811. I
make out that he was not a graduate of Oxford or Cambridge.
He was the undoubted projector of the Astronomical Society, and
his dinner there again set it going. Our kind regards to Lady
H, &c.

Yours sincerely,

A. DE MORGAN.

To Sir John Herschel.

91 Adelaide Road, August 15, 1867.

MY DEAR SIR JOHN, — A country clergyman (I think : how is
one to address where the party is a suspected clergyman ? May
one put down the probabilities as

Rev. [f] John Smith, Esq. ft] ? )

has written to me to know why, in the Runic almanacs, or very
many of them, the days of the week begin from Monday. I
could only suspect that their almanac makers had the notion I
had when a child. They told me the week had seven days, and
that the seventh day was to be kept holy ; and they kept Sun-
day holy, and called it Sabbath. So I thought Monday was the
first day, and I well remember taking it as of course that
day the women went to the sepulchre was Monday.

But this puzzled me more. They always made the ' Scrip-
tures,' when mentioned in the New Testament, mean Old and
New both. So when I saw (Acts) that the Bereans searched
the Scriptures, I thought they would find Bereans who searched,

CORRESPONDENCE, 1867-70, 373

and who found Bereans who searched, &c., and ad infinitum. 1867.
Query : Is this a convergent or a divergent series ?
Hard rain — great relief.

Yours sincerely,

A. DE MORGAN.

To Rev. Wm. Heald.

August 20, 1867.

MY DEAR HEALD, — My bit of news is my retirement from
University College, after two terms of service, 1828-31 and
1836-67. The world knows, or takes note of, only one side
of the cause. I was meditating retirement in a session or
two on account of the general decadence of the College, which
made the emoluments wholly out of reasonable proportion to the
time the duties took. In November last came a course of conduct
which made me glad to escape at the end of the current session.

University College, as you know, was founded on the prin-
ciple of giving secular education without reference to religion,
which was left to the parents. The best men who could be found
independently of creed, being of good fame and conduct, were to
teach all who were willing to be taught equally without reference
to creed. From this principle there was never a departure. At
the very outset, indeed, there was a circumstance of this kind.
Dr. Southwood Smith was proposed for a chair of mental
philosophy, with some mixture of moral philosophy. Zachary
Macaulay read extracts from a work of his, I think with the
name * On the Divine Government,' so heterodox that he, Z. M.,
declared he would take no further part if S. S. were chaired.
The Council gave way. But, for other reasons, I fancy, no one
ever complained of infraction of principle, and the case made no
noise.

The principle was put to a very severe test when Francis New-
man, then actually Professor of Latin, published his Phases of Faith
— an attack, it was said, on Christianity. No one proposed that
he should be called to account for a work the title of which did
not state his connection with the College. So it seemed pretty
certain that the College would always hold to its declared principle
of perfect indifference to the creed of a teacher.

The Professor of Logic and Mental Philosophy, Dr. Hoppus,
resigned in the spring of 1866. The best candidate beyond a
doubt to succeed him was Mr. James Martineau, a leading man
among the Unitarians, but not thoroughly in accordance with

374 MEMOIR OF AUGUSTUS DE MORGAN.

1867. the bulk of them. And thereby hangs a tale. The Unitarians
in general are highly intellectual, but have a practical dislike of
the spiritual. Mr. Marfcineau is a strong spiritualist, not merely
in religion, but in psychology. He neither can nor will teach
psychology, the structure and action of the mind, without a
distinct recognition not merely of a God, but of God and His
action upon the minds of men. This he teaches in his lectures
at University Hall — an unconnected appendage to University
College, in which Manchester New College is located, the students
of which attend lectures on secular subjects at University Col-
lege, and learn Theology at the Hall.

The Senate of University College (i.e. the Professors) re-
ported that Mr. Martineau was the best candidate. The Council
{which is composed of a small body of philosophical men, whose
creed no one knows; a larger body, perhaps one-third of the
whole, of Unitarians, and a fall half of the miscellaneous Church,
men, &c., whom one finds making up the mass of all public bodies)
rejected him on the ground that a very distinguished Theologian,
no matter of what sort, would injure the College, as giving an
appearance of breach of its neutrality. This influenced many,
but all the world knew that it was his sect being Unitarian that
was objected to, and fear of the unpopularity of the Unitarian
doctrine was of considerable effect. But it was very well known
in the College that the philosophical party was only making a
tool of the anti-Unitarian party. Their objection was to Mr.
M.'s theism in psychology. There is a school of philo-
sophers who cultivate what they call sensational philosophy.
They are driving at the doctrine that thought is a secretion of
matter, and they want to get rid of all but matter and its con-
sequences. . . . The fact then was, as I told the Council in my
letter of resignation, in these words, that Mr. M. was rejected
because he was too far from orthodoxy to please the priests, and
too far from atheism to please the philosophers ; that he was
offered up to the Janus Bifrons of expediency, each member
of the majority of the Council choosing the head of the idol to
which his offering was to be made .

To myself, who never will have anything to do either with
religious exclusion or with atheism, the proceeding was a call to
resign, which I immediately obeyed. I knew it to be an abandon-
ment of the principle of the College done in the worst way ; a
pretence of fearing heterodoxy, with the fear on the minds o f
the leaders of nothing but theism. Not a soul of the Council or

CORRESPONDENCE, 1867-70. 375

of the Professors has ventured to deny to me the truth of what 1867,

I told them. I did not publish my letter of resignation because

I did not wish to hurt my old friends in the College. If they

can get a mess of pottage for their birthright I should be very

glad they had it. I resigned in November, but remained until

the end of the session, of course. All that time not one of the

old hands among my colleagues made the slightest allusion to

the fact of my resignation, and I am sure they felt that they had

better let the subject alone. Two of the younger ones, indeed,

undertook to instruct me that I was wrong about the principle

of the College, which I had studied before they were born.

I believe, from observation, that both in colleges which pro-
fess exclusion, and in those which profess perfect neutrality,
there is a concealed under-current of, let us say, philosophy,
veiled under formalism in one case and toleration in another.
Get your smelling-salts ready, for I am going to tell you that
a certain section of your order are in earnest about nothing but
the endowments. These men see danger in all but formal
adherence to religion, and would rather have a world of con-
cealed philosophers than one of earnest believers in actual Pro-
vidence and guidance. This, I say, I glean from observation ;
there are easy means of verifying what I say. Of course, the
neutral places have their share of this. But a place like
University College — and not alone — has its share of the philo-
sophers who are really earnest about their system — religious
atheists — this phrase comes nearer than anything else ; men who
believe that the moral ends of the universe, so far as there are
any, are better answered by their concoction of reasoned right and
wrong than by any reliance on higher government. To one or
two perhaps of these men University College is indebted for its
rise or fall, whichever it shall turn out to be. I hope it will be a
rise, for they may as well have the profits of duplicity as others.

Perhaps I shall never write as much about University Col-
lege in all my life to come.

I am no way surprised at the money part of the business — I
mean the fear of diminution of pupils from a distinguished
Unitarian. Twelve years ago or more a Mr. Peene left about
1,500Z. to be a fund for buying books, and to be selected by
Professors of Latin and Mathematics, being members of the Estab-
lishment. To my surprise they caught at the money. But they
did not venture to acknowledge openly what they were doing .
They did not, as they ought to have done, write to me to know

376 MEMOIR OF AUGUSTUS DE MORGAN.

1867. if I could take the office. The secretary said (without applica-
tion to me) that he knew I would not take it. The other Pro-
fessors declined on principle, though they could have held it, and
some old students were appointed. But in time the other Pro-
fessors came into it quietly, without my being told. I smiled
and shut my eyes.

I have got over all the disgust of the matter, and am fast
losing the remembrance of the place. To my surprise I went to
my publisher's to-day, opposite the College, and was there half
an hour. When I had come away I remembered that I had
quite forgotten the College, and had not any recollection of
having seen it.

I suppose you have your share of the ritualism in Leeds. I
hear of it from my girls, who sometimes go to one of the show-
places. I read a book of essays about it a month or two ago.
There is the Roman system complete ; doctrine quite full on all
points ; a strong aspiration for the time when men will be pre-
vented from undermining the orthodoxy of their neighbours,
which can mean nothing but penalties for expression of heterodox
opinion in private life. We are getting on in every point, the
matter is coming to a crisis, and the hierarchy has no courage ;
one would suppose they back the winner.

Neate is with his family at Baden, or some such place. I have
hardly heard of Mason since he changed his living. I believe he
finds the change has done him much good. I have lately renewed
acquaintance with a man who was an infant when I last saw
him — Samuel S. Greathead, of Trinity College. He is the
nephew of S. Maitland, and is rector of Corringham, near Rom-
ford. He tells me that a large quantity of Maitland's papers
were destroyed by an ignorant executor.

Yours sincerely,

A. DE MORGAN.

To Sir John Herschel.

91 Adelaide Road, N.W., October 18, 1867.

MY DEAR SIR JOHN, — Be no way prepared to start when you
see no black border ; it is a thing which I never will use. Black
is not my colour of death. I followed to Kensal Green yesterday
the remains of my second son, George, who died of phthisis in
the throat on Monday at Ventnor, after three years of alarm as
to his lungs. A voyage to the West Indies two years ( + ) ago

CORRESPONDENCE, 1867-70. 377

appeared to restore the lungs, but the laryngeal affection came 1867.
on slowly, and ended this world for him without any great
suffering, he being perfectly satisfied until within forty-eight
hours — in fact, until he began to wander — that he was as strong
and well as need be — the phrase he used when he could not rise
in his bed.

I bear it well, and so does my wife. Many condoling friends
have found out that the great and special force of the blow is
that he was the son who was to follow in my footsteps, and had
made some beginning. To which I assent ; but, truth to speak,
I did not remember this until I was told, nor did it produce any
effect. I am peculiar, I suppose. I remember with satisfaction
that he and a young fellow-student were the projectors of the
Mathematical Society, which seems to have taken firm root ; but
this is only the general love of memorial which belongs to our
nature. Any other instance would do as well. A strong and
practical conviction of a better and higher existence does much
better for every purpose, and reduces the whole thing to emigra-
tion to a country from which there is no way back, and no mail
packets, with a certainty of following at a time to be arranged
in a better way than I could do it.

Our kind regards to Lady Herschel and the family. You
have been through the same Valley of the Shadow, and know all
about it.

Yours sincerely,

A. DE MORGAN.

To Miss Sheepshanks.

91 Adelaide Road, July 23, 1868.

MY DEAR Miss SHEEPSHANKS, — All are at Esher, and I have 1868.
sent your letter down there.

.... The Bishops of Oxford and Cape Town are a pair of
opposites : C. T. foolish, and believed to be sincere ; O. sharp,
and suspected of a sort of slyness. Colenso won my good opinion
before he became a heretic — when he would have got it of course —
by showing that he understood one part of the New Testament
which it is a rule to hide under the cushion. What did the Gentile
and Jewish converts do who had several wives ? Did they break
their contract with all but one ? There would have been a rule
laid down if they had, and a controversy. They kept their wives,
St. Paul ordaining that only the husband of one wife should be a

378 MEMOIR OF AUGUSTUS DE MORGAN.

1868. bishop or a deacon. This is the meaning of the regulation. Now
Colenso saw this, and did not require his converts to reduce
themselves to one wife. Not much noise was made about it, for
the divines at home did not like to raise the question.

Colenso is founding a church in Natal with success. He has
both a clerical and a lay body of followers. There will be
curious consequences, which will find their way home. One Pope
at Rome and an opposition Pope at Avignon did something
towards the sowing of Reformation seed. But which is Borne
and which is Avignon in this case seems not quite clear. When
Dr. Philpotts got up his diocesan synods against Gorham, he
declared very strongly that every diocese is a separate church,
with its own right to pronounce a doctrine. He was quite right ;
according to ante-papal Christianity nothing but a general
Council could override any one bishop and his synod. But he
did not see he played into the hands of the Independents. So
the synod was held, and it will not be the last.

The wind is getting up, and the day is cloudy and compara-
tively cool ; there is a synod of clouds.

Yours sincerely,

A. DE MORGAN.

To J. S. Mill, Esq., M.P.

91 Adelaide Road, September 3, 1868.

MY DEAR SIR, — You are, I suppose, in this interval, as likel y
as you will be to make a note about your Logic ; so I send a
couple of corrections (edit. 6, pp. 9, 71, vol. i.).

(P. 9.) You will be taken to mean — perhaps you meant —
that the phrase ars artium is due to Bacon. It was an old technical
definition of logic. Ludovicus Vives (in the only word of praise
he gives to a Schoolman, or nearly) commends Petrus Hispanus
(ob. 1277) for making it his definition, and corrects those who
think it only an hyperbole of praise, explaining it aH the art which
treats of arts.

(P. 71.) A wrong quotation may be defensible when it
enhances a joke ; at any rate, Sterne's recording angel would
erase the record with a grin, as he did Uncle Toby's oath with a
tear. But a defect of quotation which converts humour into
dry gravity is one over which the angel, if he shed a shower of
tears, would take care none of them should fall. In p. 71 you
say that a pedantic physician in Moliere accounts for the fact

CORRESPONDENCE, 1867-70. 379

that ' 1'opium endormit ' by the maxim ' parceqn'il a un vertu 1868.
soporifique.' From whom do yon get your quotation marks P
Not from Moliere. You know the original at the end of the
Malade Imaginaire : —

Mihi a docto doctore.

Domandatur causam et rationem quare

Opium facit dormire.

A quoi respondeo

Quia est in eo

Virtus dormitiva,

Cujus est natura

Sensus assoupire.

I never read this exquisite satire without wishing for a
Moliere to expose the school of thinkers of our day who invert
the process ; and having settled that opium has not and cannot
have a virtus dormitiva, will deny the sleep, or else declare that
it is only a coincidence. Eighteen years' experience has told me
that infinitesimal doses, so called, meet my symptoms as well as
the finite doses of the eighteen years preceding ; but the docti
doctores assure me that it cannot be, because there cannot be a
virtus curativa in doses so small. I think the Schoolmen were
the more rational of the two.

I cannot understand how you liken the virtus dormitiva to a
case of the ' scholastic doctrine of occult causes.' In fact, I have
never been able to arrive at such causes in the Schoolmen. I
know that these offenders are charged in our day, and since the
time of Bacon, with upholding certain things called occult causes,
but I cannot find any. Virtutes occultce and occult qualities I find
enough of. The following is my account of the matter.

The class of inquirers who cultivated magic, a large part of
which was mysterious physics, upheld the existence of many
qualities which do not show on the surface of things, and cannot
be inferred from the sensible qualities. Many of these were
fictions and many were truths. The sources of these things were
hidden in a sense in which they presumed more common
qualities were not. Thus Cornelius Agrippa (JDe Occulta Philo-
sopJiia) says that though heat in the stomach digests food, yet
the external heat from fire, for instance, will not do it. Accord-
ingly the stomach has a virtus qucedam occulta, quam ignoramus.
As the dead stomach will not do, we say it is an effect of vital
force, and laugh at the Schoolmen for their hidden cause.

380 MEMOIR OF AUGUSTUS DE MORGAN.

1868. The school of magicians has a great number of such occult

qualities, as plants which will produce certain dreams, or will
repel poison when worn next the skin, &c. They had also the
remarkable stone which attracts iron, and we have it too. Put
all these things together, make the school of magical writers
include all the Schoolmen, and you may attribute to their philo-
sophy the treatment of occult causes.

Their budget of facts was hampered with an immense number
of wonders handed down from the ancients. They were not
enough of our spirit to deny all they could not understand, so
they declared that the virtutes were of an occult character. Thus
the story, not rejected, of the Ark being still in existence on
Mount Ararat, made them pronounce that the glue which
fastened the timbers had an occult virtue; and if you and I
believed the fact, we should say the same. The great error of
the Schoolmen was too easy belief in antiquity ; the great crime
they are charged with is declaring that what they did not know
was hidden from them.

When Leibnitz attacked gravitation he called it an occult
quality , not cause. If you can put me on the scent of any
doctrine of occult causes, I will follow it up.

When Agrippa wrote De Vanitate Artium against all that
he had explained in the De Occulta Pkilosophia, and against every-
thing else, his chapters against logic and sophism have not a word
about the matter. Ludovicus Vives, who also satirised every-
thing, is equally free. I do not recollect any satire on the sub-
ject in any old writers, however fierce they may be against the
scholastic writers.

You say elsewhere that the following proposition is not
intelligible: 'Abracadabra is a second intention.' Literally,
* animal is a second intention ' may be held false, not un-
intelligible. For a second intention is a subjective use of a name .
Probably you mean that the proposition ' Abracadabra is a (name
of) second intention ' is unintelligible. But why more than
1 animal ' ? If you mean that Abracadabra is a mere sound, you
do less than due honour to the name of a medical instrument of
1,200 years' life. I suspect you are not aware that no less an
authority than Serenus Samonicus, in the Carmen de Medicina
(perhaps you don't care for his authority), lays it down that the
word thus treated —

CORRESPONDENCE, 1867-70, 381

1868.

a b

a b r

a b r i

brae
a b r a c
a b r a c a d
abracada
abracadab'
abracadabr
abracadabri

will cause fever gradually to abate if it be hung round the neck
of the patient. This was the Abracadabra, and it was a class of
objects, and could be a name of second intention.

This is a sextant (60°). Agrippa prefers the octant, —

a

a b

a b r

a b r a, &c.

I wish every voter in the country would hang one round his neck
until this election is over. Perhaps what would abate would
prevent.

I hope you are not thoroughly knocked up with heat and
politics.

Yours very truly,

A. DE MOEGAN.

(The following is from Mr. J. S. Mill's papers, witli the
above letter.)

Virtus Dormitiva.

In the article * Physique ' of the 'Diet, de Phil. Schol. of the
Abbe Migne's collection, after noting the virtutes and essentice as
scholastic faults, which is only true of their abuses, the author
proceeds thus : —

' Arnauld lui-meme, Arnauld le Cartesien, pratiquait les
vieux erremens de la scholastique, lorsqu'il disait a Malebranche,
" II est insense de se demander pourquoi Tame humaine pense a
1'infini et au necessaire. Elle y pense parce que c'est dans son
essence d'y penser."

' Aujourd'hui encore 1'ecole ecossaise et 1'ecole eclectique ex-
pliquent exclusivement les phenomenes psychologiques par des
facultes qu'on multiplie et qu'on distingue parfois avec une
ridicule subtilite ; et on s'imagine qu'en pla$ant ainsi sous les
faits intimes des facultes que la conscience n'a jamais percues
on a fait de la science.

382 MEMOIR OF AUGUSTUS DE MORGAN.

1868. * L'ecole rationaliste commet la meme erreur dans la question

de 1'origine du langage. L'homme parle parce qu'il a la
faculte, done il a pu inventer la parole.'

The Schoolmen never generalised a quality until they had at
least two instances. As long as there was only A which had a
certain virtus, they said nothing about it ; it was occult, i.e. un-
known. But when B was found to have the same they had such
knowledge as comes of classification, being almost all they had.

The moderns invented a name upon one instance, and made
it a cause. They said that magnetism was the explanation of the
magnet. The Schoolmen would have waited until the amber
showed its quality, and then the distinction of magnetism and
electricity would have been specific knowledge, the genus being
virtus attractiva. It is something to know two phenomena with
a generic agreement and a specific difference.

If the medical candidate had known the mind of those who
classed, he would have said, I do not know why except in that I
can refer the phenomenon to a class. We note agreements and
differences and arrange them. Arnauld, &c., might have a
similar answer made for them, but not for those who inferred
power of invention of languages from possession.

To J. S. Mill, Esq., M.P.

September 20, 1808.

MY DEAR Sm, — Seeing you at Avignon again reminds me of
a question I intended to ask long ago. If a mathematician were
asked what Avignon reminds him of, I do not know what he
would answer, except the Avignon edition of Gardiner' 's Logarithms.
Gardiner published a very celebrated folio of logarithms in 1742,
with a very solid subscription list of 120 persons, of whom two-
thirds are now known in the history of science — that is, to a
close inquirer. I greatly doubt that an old list could be found
except this of which the same proportion could be recovered.
Gardiner corrected all the errors with his own hand in all the
copies. My great-grandfather, James Dodson, who also in 1742
published his Anti-logarithmic Canon, with 1,100,000 computed
figures, did the same thing. I suspect there was some concert
as to this excellent plan between the two.

To proceed, in 1770 appeared at Avignon the reprint of
Gardiner, in folio, * Chez T. Aubert, Imprimeur, Libraire Rue de
I'Epicerie.' There is a printed Avis, signed T. Aubert, which

CORRESPONDENCE, 1867-70. 383

has a list of errata, and an announcement that the corrections 1868.
are all made in their proper places. But in my copy the cor-
rection is thus made. The correct figures are cut out and
pasted over the incorrect ones, with a written announcement
in English, signed G. Townsend, stating what has been done ;
he says it was done in the edition, but perhaps he only means
the copy. The editors have modestly concealed their names.
They were three industrious priests, Pezenas, Dumas, and
Blanchard, who would probably have remained unknown if
Lalande, who had been a pupil of Dumas, and who was in com-
munication with them, had not preserved their names in his
gossip.

If there should be any local science at Avignon I dare say
you will know some one who will be able to tell whether any
tradition of the three editors remains. Of course there will be
a copy in some public library, and it will be seen whether G.
Townsend's performance appears there. Pray do not trouble
yourself further than to make any local antiquary acquainted
with what is wanted. I suppose Avignon must now be what
people would call an out-of-the-way place ; but such places very
often have people who, like Captain Clutterbuck, spend their
whole time in illustrating their locality.

A nice job you will have made for the courts. Some ladies
have actually passed the revising barrister because there was
no opposition. The R. B. was right; he is not bound to know
that Jane Smith is a woman, nor could he raise the question. I
have a cousin whose wife is David. When the poll clerk sees a
female claimant, I suppose he will be bound to say, * Madam, you
cannot be the Jane Smith on the list, for the law says that voters
are all men. I must wait until some man comes forward and
declares he is the person described.' Then the poll clerk may
perhaps be subjected to an action. But if he should admit the
claim, there may be a scrutiny demanded, and perhaps a petition
against the return. The question will raise some logic. The
world of concepts being divided into man and non-man, if man
mean male person, and only man can vote, non-man equally
excludes Jane and her pussy and her pianoforte. They all come
under the contra-positive — All voters are men. All voters are
men, i.e. all non-men are non- voters. There is but one answer
to Jane, the cat, and the pianoforte, i.e. non-man. I hope you
will push the point and get rid of the bother ; it infests the
house. But, in justice, let no woman be placed on the register

384 MEMOIR OF AUGUSTUS DE MORGAN.

1868. except on her demand. To be a voter is sometimes dangerous.
A man ought to face the danger, but you have no right to enforce
it on women ; in principle you might as well enforce the militia
on them. Many women think exemption from politics is one of
their rights.

Yours very truly,

A, DE MORGAN.

To the Rev. J. J. Tayler.

91 Adelaide Road, N.W., April 9, 1869.

1869. MY DEAR SIR, — I have at last found head to complete the read-

ing of your two tracts, for which I am much obliged. I think I
also have to thank you for a copy of Mr. Martineau's tract, of
which we were speaking, and which I received within thirty-six
hours of our conversation. Your propositions for a free Christian
Union are brought to a point at which no opinion can be given
until more comes out. It seems clear that the freedom extends
to a rejection of all direct interference of Deity in old time, that
is by those who choose, with liberty to others to retain it, and to
dealing in the same manner with the actual existence of Jesus.
All that seems to be required is Mr. Martineau's triad (absit
Trinitas) of (p. 19) belief in God, piety, and charity. It seems
to be required that the morality of Jesus shall be acknowledged.
But whether because it finds a response in the human heart, or
because it is in some unexpressed way sanctioned by God, does
not appear. In fact, there are as yet many points which are only
seen through a glass darkly, but the one on which expectation
must now wait, which is in the field but without illumination,
is the question of worship. Is a joint worship contemplated ? I
cannot make out. The moment the plan is sketched out a hundred
points will arise. There are two classes of persons with whom I
should hold that neither you nor Mr. Martineau should refuse
communion : —

1. The old-fashioned Christian — the man who starts with
Peter.

2. Those who know no more whether there be a personal and
moral directing God than whether He have an Anointed. If
these men stipulate for another o, and adopt the creed of love of
go(o)d and love to man, they must either be admitted under
general agreement as to what is good — or a reason of inclusion

CORRESPONDENCE, 1867-70. 385

must be found in the assumed necessity of appeal to God to know 1869.
what is good. And if it come to that I wait for further infor-
mation as to how the appeal is made. If man be to settle morals
his own way, T would not bind myself to his law ; for though I do
not go quite the length and all the strength of St. Paul, I am
clearly of opinion that the heart of man is as deceitful as most
things, and is very much, not a little, wicked.

But further, supposing the intermediates could fraternise
with the extremes, could the extremes fraternise with one another ?
This is the old difficulty of compromise, under which many an
attempt at political and religious concentration has failed. We
know that if A and B coincide with C they coincide with one
another ; but if A and B should happen to be within x feet of C,
all we can positively affirm is that they are within 2x feet of one
another. And x may do where 2x will not. These are the first
things which strike an old thinker on the subject, who does not
feel equal to more than two sheets. There may be comfort in
the Scotch proverb that those who pluck at a gown of gold may
get a sleeve of it. In the meanwhile the name is too bold. ' Free '
' Christian ' ' Union ' ! Until you tell us how free and how
Christian you mean to be, no one can tell how united you will
become.

You have your sand, and you aspire to make rope. Michael
Scott's devils failed, but they did not know that a very easy pro-
cess would make their sand ropes into glass, which makes very
good thread. What have you got to mix with your sand ? That
is what I am curious to see. But the attempt is praiseworthy,
and must be most useful in any case of result.

Yours sincerely,

A. DE MORGAN.

To Sir Frederick Pollock.
[Not in his own handwriting.]

91 Adelaide Road, June 13, 1869.

MY DEAR SIR FREDERICK, — I should have said, till now, that
it would have been your business to receive me when I got to
the gate of the other world, but now I hold it not so sure. I
had an attack of congestion of the brain on Wednesday, which
kept me several hours in a condition of which I had after-
wards no recollection. I think I may put this against your
greater age, and consider myself as a candidate of equal preten-

C C

386 MEMOIR OF AUGUSTUS DE MORGAN.

1869. sions with yourself. It was not what they call the real apoplexy,
because it had no lasting effect on any organ ; but Mr. Weller,
senior, would have admitted it for a genuine appleplexy. I am
going on very well now, and if anything happens to the con-
trary, my wife will write.

Give our kind regards to Lady Pollock and all the family.

Yours sincerely,

A. DE MORGAN.

To Sir F. Pollock.
[Written in pencil.]

91 Adelaide Road, June 19, 1869.

MY DEAR SIR FREDERICK, — I enterprise a letter of my own
writing. I am glad to hear you have got hold of H. C. B.,1
whom I allow to be Herr Conversations Rath, though I cannot
answer for the German correctness of the title.

I suppose you will find a host of reminiscences — even I find a
large lot. The only thing I have done for many weeks is to
write — from the sheets — a little notice of his works for a
theological Review ; so I have picked it all through, and made
extracts. They say autobiography is always readable. Three
thick volumes, intermixed with letters, is a severe test, but I
think many will get through it. Certainly, it will be a repertory
of facts tending to literary history, in which the smallest bit of
personal biography is sometimes clinching.

As to myself, I progress. The medical men are agreed thj
nothing is apoplexy except what leaves injury to some pow<
or organ. The congestion, which they make out to be common, ic
voted no disorder at all. All which is very true, as to the
superiority of an attack which leaves no consequences over 01
which does leave them. But congestion is congestion, after all.
Our kind regards to Lady Pollock and all the family.

Yours sincerely,

A. DE MORGAN.

To Sir F. Pollock, Bart.

6 Merton Road, N.W., July 24, 1869.
MY DEAR SIR FREDERICK, — As we neither of us are strong on
the legs, and yet can use our fingers, I employ mine to beg you
1 Henry Crabb Robinson's Diary, &c.

CORRESPONDENCE, 1867-70. 387

will employ yours, at any leisure you like, in answering a 1869.
question.

I want a tolerably distinct account of the reading of a senior
wrangler of your day. How much had he read, and in what
books ? A very general view will do. Anything as to distinc-
tion between algebra and geometry will be valuable.

The people are all gone who could give any information.
With me it will be perpetuated in some shape.

I gain strength pretty fast, but am not without warning that
head-time is not come back yet. There are all kinds of legends
current about old reading. A trustworthy account would be of
historical value. With kind regards all round,

Yours sincerely,

A. DB MORGAN.

On looking at the list of seniors, I see that you are not only
the last left, but that yon come at the turn. In 1810 comes
Maule, who was in communication with Babbage about functional
equations, and all kinds of novelties. Maule would have been
conspicuous, among the moderns, with Herschel, Peacock, Bab-
bage, if he had held on. Had I not known you, I should, on
these circumstances, have applied to you, as the only chance left
for information essential to historical knowledge of Cambridge.

From Sir F. Pollock, Bart.

Hatton, Hounslow, July 29, 1869.

MY DEAK DE MORGAN, — I am glad to hear you ' gain strength
pretty fast.' I lose it slowly ; but I lose it. I shall write in
answer to your inquiry, all about my books, my studies, and my
degree, and leave you to settle all about the proprieties which
my letter may give rise to, as to egotism, modesty, &c. The only
books I read the first year were Wood's Algebra (as far as
quadratic equations), Bonny castle's ditto, and Euclid (Simpson's).
In the second year I read Wood (beyond quadratic equations),
and Wood and Vince, for what they called the branches. In the
third year I read the Jesuit's Newton and Vince's Fluxions ;
these were all the books, but there were certain MSS. floating
about which I copied — which belonged to Dealtry, second
wrangler in Kempthorne's year. I have no doubt that I had read
less and seen fewer books than any senior wrangler of about my
time, or any period since ; but what I knew I knew thoroughly,

c c 2

388 MEMOIR OF AUGUSTUS DE MORGAN.

1869. and it was completely at my fingers' ends. I consider that I was
the last geometrical and fluxional senior wrangler ; I was not up
to the differential calculus, and never acquired it. I went up to
college with a knowledge of Euclid and algebra to quadratic
equations, nothing more ; and I never read any second year's lore
during my first year, nor any third year's lore during my second ;
my forte was, that what I did know I could prodiice at any
moment with PERFECT accuracy. I could repeat the first book of
Euclid word by word and letter by letter. During my first year
I was not a ' reading ' man (so called) ; I had no expectation of
honours or a fellowship, and I attended all the lectures on all
subjects — Harwood's anatomical, Woollaston's chemical, and
Farish's mechanical lectures — but the examination at the end of
the first year revealed to me ray powers. I was not only in the
first class, but it was generally understood I was first in the first
class ; neither I nor any one for me expected I should get in at
all. Now, as I had taken no pains to prepare (taking, however,
marvellous pains while the examination was going on), I knew
better than any one else the value of my examination qualities
(great rapidity and perfect accuracy) ; and I said to myself, * If
you're not an ass, you'll be senior wrangler ; ' and I took to
1 reading ' accordingly, A curious circumstance occurred when
the Brackets came out in the Senate-house declaring the result
of the examination : I saw at the top the name of Walter
bracketed alone (as he was) ; in the bracket below were Fiott,
Hustler, Jephson. I looked down and could not find my own
name till I got to Bolland, when my pride took fire, and I said, ' I
must have beaten that man, so I will look up again ; ' and on look-
ing up carefully I found the nail had been passed through my
name, and I was at the top bracketed alone, even above Walter.
You may judge what my feelings were at this discovery ; it
the only instance of two such brackets, and it made my fortune
— that is, made me independent, and gave me an immense college
reputation. It was said I was more than half of the examination
before any one else. The two moderators were Hornbuckle, of
St. John's, and Brown (Saint Brown), of Trinity. The Johnian
congratulated me. I said perhaps I might be challenged ; ho
said, ' Well, if you are you're quite safe — you may sit down and
do nothing, and no one would get up to you in a whole day.'

This is confirmed by what the Bishop of Gloucester told me
Brown said at Lord Lonsdale's table at Lowther. The examina-
tion in the Senate-house became the subject of conversation,

CORRESPONDENCE, 1867-70. 389

Brown said no one answered any question that I did not also 1869.
answer, and letter.

I have no doubt Walter and Jephson had read more books
than I had, and knew (after a sort) more. Maule was a man of
great ability and immense acquirements ; he reminded me of
Porson more than anybody else did.

My experience has led me to doubt the value of competitive
examination. I believe the most valuable qualities for practical
life cannot be got at by any examination — such as steadiness and
perseverance. It may be well to make an examination part of the
mode of judging of a man's fitness ; but to put him into an office
with public duties to perform merely on his passing a good
examination is, I think, a bad mode of preventing mere patronage.
My brother is one of the best generals that ever commanded an
army, but the qualities that make him so are quite beyond the
reach of any examination. Latterly the Cambridge examinations
seem to turn upon very different matters from what prevailed in
my time. I think a Cambridge education has for its object to
make good members of society — not to extend science and make
profound mathematicians. The tripos questions in the Senate-
house ought not to go beyond certain limits, and geometry ought
to be cultivated and encouraged much more than it is.

Euclid and conic sections studied geometrically improve,
enlarge, and strengthen the mind ; studied analytically, I think
not. But I must have exhausted your patience — a virtue which
may be tried but not examined. My best regards to Mrs. De
Morgan and your family.

Ever sincerely yours,

FRED. POLLOCK.

P.S. — Looking over what I have written, I fear you will find
little that you want ; but I am still ready to answer any specific
questions.

To Sir F. Pollock.

6 Merton Road, Adelaide Road, N.W.,
August 1, 1869.

MY LEAR SIR FREDERICK, — Your letter has better Cambridge
history than any 100 pages of the Esq. Bedell — I forget his
name — who quoted Wm. Frend as saying that the market women
complained of being scotched a quarter of their wages, and quoted
the word three times in italics to call attention to it. Mr. Frend's

390 MEMOIR OF AUGUSTUS DE MORGAN.

1869. word was sconced — the old word for fined. If you can recall at
this rate, you will rival H. C. B.

Your letter suggests much, because it gives possibility of
answer. The branches of algebra of course mainly refer to the
second part of Wood, now called the theory of equations.

Waring was his guide. Turner — whom you must remember
as head of Pembroke, senior wrangler of 1767 — told a young
man in the hearing of my informant to be sure and attend to
quadratic equations. ' It was a quadratic,' said he, ' made me
senior wrangler.' It seems to mo that the Cambridge revivers
were Waring, Paley, Vince, Milner.

You had Dealtry's MSS. He afterwards published a very
good book on fluxions. He merged his mathematical fame in
that of a Claphamite Christian. It is something to know that
the tutor's MS. was in vogue in 1800-1806.

Now — how did you get your conic sections ?

How much of Newton did you read ?

From Newton direct, or from tutor's manuscript ?

Surely Fiott was our old friend Dr. Lee.1

I missed being a pupil of Hustler by a few weeks. He
retired just before I went up in February 1823.

The echo of Hornbuckle's answer to you about the challenge
has lighted on Whewell, who, it is said, wanted to challenge
Jacob, and was answered that he could not beat if he were to
write the whole day and the other wrote nothing.

I do not believe that Whewell would have listened to any
such dissuasion.

I doubt your being the last fluxional senior wrangler. So
far as I know, Gipps, Langdale, Alderson, Dicey, Neale, may
contest this point with you.

I go on fairly. With kind regards all round,

Yours sincerely,

A. DE MORGAN.

From Sir F. Pollock

Hatton, Hounslow, August 7, 18G9.

MY DEAR DE MORGAN, — You seem not to know the story of
Gunning's book (the Bedell you allude to). He really kept a sort

1 Much of this is not perfectly clear to me ; but I insert the letter
as it stands, as it may have interest for old Cambridge men. For the
same reason I have departed from my general rule, in inserting Sir
F. Pollock's letter in reply.— S. E. DE M.

CORRESPONDENCE, 1867-70. 391

of diary, in which he put all the scandal of every sort he met with 1869.
in Cambridge society — much about Porson ; Mansel's epigrams
and verses ; his contest with Sir Busick Harwood ; much of the
vulgar drollery of Jemmy Gordon, who did not survive till your
day : in short, a collection of very low and ribald stuff, mixed with
what was worth preserving (but Gunning could not distinguish
between the two). Some one persuaded him to burn it, and the
book he published was what he remembered when his memory
was gone and the real book burnt. His son Frederick was my
pupil, and did well as a barrister, from whom I had this. You
have put together as revivers five very different men. Woodhouse
was better than Waring, who could not prove Wilson's (Judge
of C. P.) guess about the property of prime numbers ; but Wood-
house (I think) did prove it, and a beautiful proof it is. Vince
was a bungler, and I think utterly insensible of mathematical
beauty. Milner was incomparable. The Claphamite Christians
are a class to be found in every form of religion ; and when they
are not too intolerant (which generally they are) they have
much of my sympathy, though I don't agree with them.

Now for your questions. I did not get my conic sections from
Vince. I copied a MS. of Dealtry's. I fell in love with the cone
and its sections, and everything about it. I have never forsaken
my favourite pursuit ; I delighted in such problems as two spheres
touching each other and also the inside of a hollow cone, &c. As
to Newton, I read a good deal (men now read nothing), but I
read much of the notes. I detected a blunder which nobody
seemed to be aware of. Tavel, tutor of Trinity, was not ; and
he augured very favourably of me in consequence. The applica-
tion of the Principia I got from MSS.

The blunder was this : in calculating the resistance of a globe
at the end of a cylinder oscillating in a resisting medium they
had forgotten to notice that there is a difference between the
resistance to a globe and a circle of the same diameter.

The story of Whewell and Jacob cannot be true. Whewell
was a very, very considerable man, I think not a great man. I
have no doubt Jacob beat him in accuracy, but the supposed
answer cannot be true ; it is a mere echo of what actually passed
between me and Hornbuckle on the day the Tripos came out —
for the truth of which I vouch. I think the examiners are
taking too practical a turn; it is a waste of time to calculate
actually a longitude by the help of logarithmic tables and lunar
observations. It would be a fault not to know how, but a

392 MEMOIR OF AUGUSTUS DE MORGAN.

1869. greater to be handy at it. Oh dear ! I longed to get among the
Fellows ; but when I did, I was utterly disgusted at the rubbish-
ing conversation that prevailed, and I then longed to get away.
You see I linger over Cambridge recollections ; but no par-
ticular time has been the happiest of my life, certainly not school.
Best regards to Mrs. De Morgan and your family.

Sincerely yours,

FREDERICK POLLOCK.

To the Rev. W. Mason.1

Adelaide Road, August 13, 1869.

DEAR MASON, — As touching myself I get stronger gradually.
I am slowly getting my books into order, which is a long job. I
have no more information of any very decided character than is
to be found in my wife's book, From Matter to Spirit. I retain
my suspense as to what the phenomena mean, but I am as fully
persuaded as ever of their reality.

The presence of the dead is a thing widely felt, but by cer-
tain temperaments. Bishop Jebb is an instance of no very
forcible kind, because the two worlds had been in constant con-
nection in his mind. I will give you a more curious one.

An actuary, a man of science and a keen searcher after old
printing, married a second cousin of mine. He was a cheerful
and kind-hearted man, but to all appearance as thoroughly un-
spiritual as a man could be. I never heard a word drop from
him which made it appear that another life was his familiar
thought. He was, though moderate in drinking, rather fond of
eating, and skilled in it. The ladies of his acquaintance who
had dinners to give would consult him on all details. His wife,
to whom he was devoted, died, and he himself fell into a weakly
state. I used to sit with him by the hour. A few weeks before his
death I found him debilitated by a long conference he had had
with a lady about a dinner she had to give : this merely to show
that his mind was not turned to the subject of death by anything

1 This was in answer to a letter in which Mr. Mason asks him, if
able, to give him * some information on the interesting subject to which
you alluded in your last.' 'I have long thought,' Mr. Mason says,
* that departed spirits are often with those they left at death. When
Bishop Jebb had been for some time under a paralytic seizure, he said,
on his recovery, that in the prospect of death he had felt that he slnmM
be as truly with his friends after death as he was then when speaking
to them.7— S. E. DE M.

CORRESPONDENCE, 1867-70. 393

external. He suddenly turned to me and said, * De Morgan, my 1869.
wife is often with me.' I was astonished, not at the phenomenon,
but at his being the recipient. ' Often ? ' said I. ' Every even-
ing,' said he, 'and oftener.' ' Do you see her? ' said I. * No,'
said he, ' but I feel her presence.' By these three words hangs
a long tale.

With kind regards to your family,

Yours sincerely,

A. DE MORGAN.

To Rev. W. Heald.

August 21, 1869.

MY DEAR HEALD, — I think I shall be able to keep up the
institution of a summer letter, though I may not be so long as
usual. It is the forty-fourth observance.

You think, one letter of yours says, that I am feeling the
effects of hard work ; in fact, that I have been working too hard.
Rid your mind of the idea. I have never been hard working,
but I have been very continuously at work. I have never sought
relaxation. And why ? Because it would have killed me. Amuse-
ment is real hard work to me. To relax is to forage about the
books with no particular object, and not bound to go on with
anything.

You remember that my amusement used to be Berkeley and
the like. Quite true. I did with Trinity College library what
I afterwards did with my own — I foraged for relaxation. I
used to shock you with my reading of Voltaire, who existed in
that library in about eighty quarto volumes. So you called me
an atheist vagabond, fancying that Voltaire was an atheist : he
was, in fact, theistic to bigotry, and anti-revolutionist to the same
extent.

I read an enormous deal of fiction — all I could get hold of —
so my amusement was not all philosophical. I have never worked
hard — never got so far as a headache. If I felt tired I left off. '

My illness is well enough explained by the following chain of
events.

1866. Discovery that University College was going to betray
its principles, and abandonment of the place in 1867.

1867. Long illness and death of my second son, with all the
anxiety occurring during the turmoil of the College affair. In
the meanwhile my third son had taken refuge from illness on
board ship, and was away for eighteen months in very fluctuating

394 MEMOIR OF AUGUSTUS DE MORGAN.

1869. health. One of my daughters was also labouring under the same
symptoms, and was four months with her mother at Hastings
after the death of my son. All this I could have borne. It
attacked the spirits, but I could have held on as I have always
done in sure reliance on the higher and wiser management which
* shapes our ends.' But the heats of 1868 broke down the phy-
sical force, and gave a cough and weakness which was followed
up by the consequences you know of. Does it, upon the pre-
ceding showing, require the hypothesis of thirty years of over-
work to explain an attack of diabetes which yielded to the first
remedies, or rather to diet alone, in a week, and a stroke of con-
gestion of the brain which left no result but weakness ? I have
heard of overwork on all sides, and have seen people stare at
their own omission of all the misfortunes — so called — which have
come upon me in the last two years.

I am now weak enough, but I gradually improve. I shall
soon get all the way upstairs foot over foot, that is, sans both feet
on one step at once, and without the banisters. At present it is,
after half is done, either a tug at the banister, or bring up the
second foot before you remove the first. Three weeks ago it
was this alternative the whole way. The stairs are a beautiful
dynamometer.

I am very anxious about Arthur Neate. He has an ugly
cancerous tumour on the lower side of the left cheek, which
opinion decides variously cancer or no cancer ; but those who
think it cancer think it a very serious case. He is not aware of
the dangerous opinions. If they be correct the matter will be
beyond doubt in a few months. As yet there is no serious
internal symptoms, and such things have sometimes passed off.
Neate is about sixty-four. I turned the grand climacteric (sixty-
three) in June last (27th).

August 30. — So much for delays and feelings of inability. I get
on fairly, head and arms, but the legs do not thrive in proportion.
I sawed a plank of wainscot (hard wood) ; and a man who can
do that ought to walk three miles, but I do not do more than one.

September 1. — My wife, who was at the sea with my second
daughter and a bronchial cough to be got rid of, came homo on
Saturday, and my daughter's cough nearly gone.

A man cannot have the sort of attack I had without some
amount of evidence of it. I had two well-marked consequences for
several days, an inability and a delusion. 1. I could not for a
week master the word congestion as the name of my own attack.

CORRESPONDENCE, 1867-70. 395

I had it at once for every other purpose. If I got hold of cow, 1869.
it was confusion, conglomeration — anything but congestion. If I
got hold of gestion, it was digestion, suggestion, &c. Several times,
and days after I had recovered my senses, I used to amuse myself
by trying, and was at last obliged to ask what had been the matter
with me.

2. When I woke to recollection of the universe, and for days
afterwards, I was possessed with the idea that before the
seizure I had received a letter from Ireland, written on the sup-
position that I was a clergyman, and offering me a great lot of
Irish preferment. If there be one political subject on which I
had never thought or cared, it is the Irish Church and its man-
agement.

My idea was that some poor patron, in a hurry to induct
some one into the benefices, by way of securing some vested
interest before the final disendowment, had taken it into his
head to select me as the holder of the profits for the rest of
their term. I was very anxious to set him right, not knowing
how much, consequence a day might be of. But as I got nearer
to the letter- writing state, the vision became fainter, and when
I at last looked, more to see what could have suggested it than
with any idea of finding, I could not get a trace of any such
letters. Besides these, I had not any consequences whatever of
the loss of consciousness.

I think this must go as it is. I hope your family are well,
and yourself. Do you know, or can you find, anything about H.
Parr Hamilton, the Dean of Salisbury ? Kind regards to Mrs.
Heald.

Yours sincerely,

A. DE MORGAN.

To Sir J. Herschel.

6 Merton Road, October 20, 1869.

MY DEAR SIR JOHN, — Surely I sent you my card, which you
will find within the envelope.1 This envelope arrived on Monday
with the pie of ITS which you see. But the Leverrier has not
come yet : no doubt it is hunting me all over N.W., with a

1 A card on which he had printed a small map of Merton Road and
the immediate neighbourhood as a guide to friends. Unless the ' pie
of TTS ' means the number of circles stamped by the Post Office on the
envelope, which appears to ^have travelled half over London before
reaching him, I cannot interpret it.— S. E. DE M.

396 MEMOIR OF AUGUSTUS DE MORGAN.

1869. change of air by a jaunt to Merton Road, S.W. In a few days
it will be time to look up the dead-letter office. I am afraid I
am not strong enough for this yet. Have you anybody you
could ask who goes near the P.O. often ?

I thrive — and the cold weather is bracing me up like a bundle
of asparagus, having been no better than a rope of onions. A
week's cold weather last winter would have kept me from striking
my flag. Two or three days of half-cold told me so, and then
took leave.

I shall be glad to see the Leverrier account. If it should
come, I will write at once. With kind regards all round your
circle,

Yours sincerely,

A. DE MORGAN.

To Sir J. Herschel

6 Merton Road, November 8, 1869.

. MY DEAR SIR JOHN, — The Queen used up so much of the fine
weather on Saturday, that the chief clerk of that office says he
can issue no more until he gets a further supply. So I am rain-
bound for to-day, and can clear off obligations. I, therefore,
retnrn your Leverrier with many thanks. What a miserable
mess has been made by Chasles, Lucas, and Co. ! I am obliged to
give up Chasles until he clears himself, which I have small hope
of his doing. The different accounts he has given at different
times are such as must be reconciled, or otherwise explained. If
there be no explanation except sub-human credulity, then
arises the question which is so important in lunacy inquiries,
When did this defect begin ? For Chasles has a lifetime of
memoirs full of references to MSS., many of them unseen as
yet except by himself. It will be unsafe to quote him — at
least to a letter-not extent.

I have lately lost my friend Libri, and of course, he being
removed, the accusations which he put down begin to revive. I
wrote a short article in the Athenaeum of the mortuary character,
and the Parisians, quite forgetting the beating they got, are
pleased to be excessively astonished at the revival of a defence
which silenced them fifteen years ago. There is a little knot of
subscribers in England who try to act privately on editors and
contributors. Ex. gr. : A person who described ....

(Nov. 11. — Sunshine came out, and drew me out also, and I
have not been able to resume until now. I walked 1J miles
yesterday I1 !* !* I catch up the unfinished sentence — X

CORRESPONDENCE, 1867-70. 397

.... himself as a known book-collector (N.B. — No less a person 1869.
than wax-chandler to the Queen, &c., very rich, and collects no
end of elegantly bound large paper ; all this I learnt afterwards)
came to me in a neat carriage and a heavy shower, and as he
was doing a wabbling preamble abont nothing, I cut him short
sternly with, ' Pray, sir, what is the upshot of all this ? ' He
answered that, seeing my article in the Athenceum- — which it was
very impertinent to assume was mine — he could prove in two
minutes that Libri was guilty of all that was imputed to him.

* What do you know of the matter ?'

' I have read all the pamphlets.'

' So have I,' said I, ' and some of them before they were
pamphlets.'

' Oh ! I thought perhaps you had not investigated.'

He then produced 'Vapereau,' a French biographical dic-
tionary of first-rate size and tenth-rate accuracy, and, opening at
Libri, said, ' Have you read that article ? ' 'I have,' said I,
' in former days, before I found out what a worthless affair
Vapereau was.' ' I assure you,' said he, * the people at Paris
are much astonished at your article.' ' No doubt,' said I :
4 they are the parties whom Libri's defence incriminates.' ' I
thought perhaps you were not aware of the facts, and that by
coming to you we might avoid a polemic* * Now,' said I, 'you
must go to the editor of the Atlienc&um, and polemic with him.
Do you really suppose you will prove to me that one of my
dearest friends was a robber by an extract from "Vapereau " and
Parisian opinion ? ' So he went away, and there has been no
polemic yet.

A matter of this kind brings out the hidden fun of the world.
So with kind regards all round,

Yours sincerely,

A. DE MORGAN.

To Rev. J. Martineau.

6 Merton Road, Adelaide Road, N.W.,
December 19, 1869.

DEAR SIR, — Many thanks — to you I suppose I am indebted —
for the reprints of the journal memoir of J. J. Tayler. He is
well recalled, which in his case is not very easy to do in writing.
It appeared to me that his treatment of controversy in conversa-
tion allowed the wave to pass over the reef without breakers. A
congregation of such men could have realised his plan of a

398 MEMOIR OF AUGUSTUS DE MORGAN.

1869. scheme of joint worship in which the party were agreed npon
everything except accurate definition of what they were agreed
about.

I have your two tracts — one of J. J. T., and the ' anniversary '
of 1869. If there be any more I should like to know of them.
For I am interested in the attempt, which, hopeless as it seems
to me to the extent proposed, may yet originate a sect in which
people may pray together without each man being fettered to
his neighbours.

But there must be some little definiteness of statement. I
tried hard to get from J. J. T. whether his Christianity had a
supernatural element. His final information was that he
thought it most likely the apostles had a supernatural element
which we do not understand.

I intend to keep watch on the attempt to couple super-
naturalists and anti-supernaturalists, for that is what is aimed
at. When I get something definite about its indefiniteness, I
intend to write about it.

Dubius sed non improbus. This is what Sheffield said of his
own religion, and the scholars (Dean Stanley included) make
him ' sceptical, but not wicked.'

Improbus means one who declares against the proof — one to
whom there cannot be proof. As when Pliny says that Hipparchus
counted the stars — rem Deo improbam — a thing unproved by the
gods ; and Virgil, Labor omnia vincit, improbus — toil yet unproved,
or untried, conquers all things.

Yours very truly,

A. DE MORGAN.

To Sedley Taylor, Esq.

6 Merton Road, December 26, 1869.

MY DEAR SEDLEY, — Many thanks for your pamphlet,1 which
I shall join on to some of Martineau's, &c., in one notice. I
think you will produce some effect on people who begin to have
a cranny through which the light comes. I saw Jas. Martineau
a day or two ago, and he tells me that his organisation is con-
templating the circulation of your pamphlet in aid of their view.
I wish their view were a little less of a dissolving view when

1 On Clerical Subscription. (M«ocmillan, 1869.) Mr. De Morgan
believed that this pamphlet hastened the disruption of the Free
Christian Union.

CORRESPONDENCE, 1867-70. 399

you come to look closely at it. I cannot make out whether they 1869.

have a super religion or not. I do not know how to fill up

the word. Now I tolerate everything except passing off one
thing under the name of another. There are people who can
detect in the foundation of Christianity a third alternative,

* Super or Imposture.' I cannot. I am content they should,

but I want them to be explicit. I am very much afraid they
want a common worship with the above question left open. No !
there is no objection to leaving it open if people will, but they do
not want it openly open, but secretly open, under a cloak of
some indefinite pretension of divine origin. I hope you will
follow up.

Yours sincerely,

A. DE MORGAN.

(The only letters to friends after this time that have
conie into my possession are two to Sir John Herschel, in
my husband's own handwriting, the first bearing date
June 25, 1870. In this he says, ' I am creeping along, and 1870.
shall get right about as soon as the blessed St. Alcuin's snail
got to dinner. It is one of the pleasant problems in the
works of that holy man that the sparrow asked the snail
to dinner at a league distance. Now the snail moved half
an inch a day. How long, the Saint asked, will it take him
to get to dinner ? ' The second is in an extremely feeble
hand, merely describing his own state. Sir John himself
died within the year. In his letter to me on receipt of
mine telling him of my husband's death, he wrote, CI
have been expecting as much. The last letter I received
showed me too clearly that the lamp was nickering in the
socket, and it is consoling to know that the end was so
peaceful and so painless, and so full of hope. Looking
back on our long friendship, I do not find a single point on
which we failed to sympathise ; and I recall many occa-
sions on which his sound judgment and excellent feeling
have sustained and encouraged me. Many and very
distinct indications tell me that I shall not be long after
him ; and I can only hope that my own end may be such

400 MEMOIR OF AUGUSTUS DE MORGAN.

1870. as you describe.' His last surviving correspondent was
the Rev. W. Heald, who died three years after him. All
his other old University friends had gone before.

I have, with respect to domestic matters and details,
done what I know my husband himself would have wished,
for he never liked making known what nearly concerned
his family. Moreover, those to whom he wrote at length
and on questions of general interest were friends with
whom he did not get frequent opportunities of conversa-
tion. Consequently, as we were almost always together,
his correspondence with myself and our sons and daughters
was fragmentary, and not suited for publication. I trust,
however, that the foregoing selections will not be thought
insufficient to show the character of one to whom letter-
writing was a pleasure and a relaxation, and among
whose leisure occupations it always held so prominent a
place.— S. E. DE M.)

LIST OF WETTINGS.

1828. Bourdon's Elements of Algebra, translation.

Elements of Arithmetic, 1st edition, 1831.

„ 2nd edition, 1832.

„ ,, 3rd edition, 1833.

16th 1,000, 1857.

ARTICLES IN QUARTERLY JOURNAL OF EDUCATION, PROM X831
TO 1835.

1831. (1) Account of the Polytechnic School of Paris, vol. i.

(2) Notice of Tables for facilitating Calculation, vol. i.

(3) Rev. of Pinnock's Catechism of Geometry, vol. i.

(4) On Mathematical Instruction, vol. i.

(5) Walker's Theory of Mechanics (rev.), vol. i.

(6) Barley's System of Popular Geometry (rev.), vol. ii.

(7) Bayley's Elements of Algebra (rev.), vol. ii.

1832. (H) A Plan for Conducting the Koyal Naval School,

vol. iii.
(9) Study of Natural Philosophy, vol. iii.

(10) A Preparation for Euclid, vol. iii.

(11) Barlow's Mathematical Tables, vol. iii.

(12) On some- Methods Employed for the Instruction of

the Deaf and Dumb, vol. iii.

(13) James Wood's (D.D., of Ely) Algebra (rev.), vol. iii.
( L4) Quetelet on Probabilities (rev.), vol. iv.

(15) Young's Elements of Mechanics (rev.), vol. iv.

(16) State of Mathematical and Physical Sciences in the

University of Oxford, vol. iv.
(1 7) Von Turk's Phenomena of Nature (rev.), vol. iv.

1833. (18) On Teaching Arithmetic, vol. v.

(19) Cunning-ham's Arithmetic (rev.), vol. v.
D D

402 MEMOIR OF AUGUSTUS DE MORGAN.

(20) On the Method of teaching Fractional Arithmetic,

vol. v.

(21) On the Method of teaching the Elements of Geometry,

vol. vi.

(22) The School and Family Manual (rev.), vol. vi.

(23) Method of teaching Geometry, No. 2, vol. vi.

(24) Busby's Catechism of Music (rev.), vol. vi.

(25) Geometry without Axioms (rev.), vol. vii.

(26) Ritchie's Principles of Geometry (rev.), vol. vii.

(27) Elementary Works by M. Quetelet (rev.), vol. vii.

(28) Cambridge Differential Notation, vol. viii.

(29) Gravitation, Airy's article, Penny Cyclop, (rev.),

vol. viii.

(30) Peacock's Treatise on Algebra (rev.), vol. ix.

(31) Peacock's Treatise on Algebra, No. 2, vol. ix.

(32) Progress of Physical Science, vol. x.

(33) Ecole Poly technique, vol. x.

MEMOIRS IN THE CAMBRIDGE PHILOSOPHICAL TRANSACTIONS.

(1) On the General Equation of Carves of the Second Degree,

read Nov. 15, 1830.

(2) On the General Equation of Surfaces of the Second Degree,

read Nov. 12, 1832.

(3) Sketch of a Method of introducing Discontinuous Con-

stants into the Arithmetical Expressions for Infinite
Series, where they admit of several values, read May 16,
1836.

(4) On a Question in the Theory of Probabilities, read Feb. 1837.

(5) On the Foundations of Algebra, read Dec. 9, 1839.

(6) On the Foundations of Algebra, No. 2, read Nov. 29, 1841.

(7) On the Foundations of Algebra, No. 3, read Nov. 27, 1843.

(8) On Divergent Series, and Points connected with them,

read March 4, 1844.

(9) On the Foundations of Algebra, No. 4, On Triple Algebra,

read Oct. 24, 1844.

(10) On Divergent Series, and on Various Points of Analys

connected with them, read 1844.

(11) On a point connected with the Dispute between Keill and

Leibnitz, read Jan. 1846.

(12) On the Structure of the Syllogism, and on the application

of the Theory of Probabilities to questions of Argument
and Authority, read Nov. 9, 1846.

LIST OF WRITINGS. 403

(13) Method of Integrating Partial Differential Equations, read

June 1848.

(14) On the Symbols of Logic, the Theory of the Syllogism, and

in particular of the Copula, and the application of the
Theory of Probability to some questions of Evidence,
read Feb. 1850.

(15) On some Points of the Integral Calculus, read Feb. 1851.

(16) On some Points in the Theory of Differential Equations,

read 1854.

(17) On the Singular Points of Curves, and on Newton's Theory

of Co-ordinated Exponents, read 1855.

(18) On the Question : What is the Solution of a Differential

Equation, Supplement to No. 3, read April 1856.

(19) On the Beats of Imperfect Consonances, read Nov. 1857.

(20) A Proof of the Existence of a Root in every Algebraic

Equation, read Dec. 1857.

(21) On the General Principles of which the Composition or

Aggregation of Forces is a Consequence, read 1859.

(22) On the Syllogism, No. 4, and on the Logic of Relations,

read 1860.

(23) On the Theory of Errors of Observation, read Nov. 1861.

(24) On the Syllogism, No. 5, and on various points of the

Onymatic System, read 1863.

(25) On the Early History of the Signs + and — , read 1864.

(26) A Theorem relating to Neutral Series, read 1864.

(27) On Infinity and the Sign of Equality, read May 1864.

(28) On the R.oot of any Function, and on Neutral Series, No. 2,

read May 1866.

(29) On a Theorem relating to Neutral Series, read Oct. 1868.

IK THE PHILOSOPHICAL MAGAZINE.

(1) On Taylor's Theorem, 1835.

(2) On the Relative Signs of Co-ordinates, 1836.

(3) On the Solid Polyhedron, 1838.

(4) On the Rule for finding the value of an Annuity for three

lives, 1839.

(5) Suggestion on Barrett's Method, 1841.

(6) On Fernel's Measure of a Degree, Nos. 1 and 2, 1841.

(7) On the reduction of a Continued Fraction to a Series, 1841.

(8) On Fernel's Measure of a Degree, Nos. 3 and 4, 1842.

(9) On Leonardo da Vinci's Use of + and -, 1842.

(10) On Torporley's Anticipation of part of Napier's Rule, 1843.

D D 2

404 MEMOIR OF AUGUSTUS DE MORGAN.

(11) On the almost total disappearance of the earliest Trigono-

metrical Canon, 1845.

(12) Derivation of the word Theodolite, 1846.

(13) Derivation of Tangent and Secant, 1846.

(14) Account of the Speculations of Thos. Wright, of Durham,

1848.

(15) On the Additions made to the Second Edition of the Com-

mercium Epistolicurn, 1848.

(16) On a Property of the Hyperbola, Jan. 1848.

(17) On Anharmonic Ratio, 1849.

(18) On the Early History of Infinitesimals in England, 1, 1852.

(19) On Indirect Demonstration, 1852.

(20) On the Authorship of the Account of the Comniercium

Epistolicum, 1852.

CAMBRIDGE MATHEMATICAL JOURNAL.

(1) On the Perspective of the Co-ordinate Plane, pp. 92, '.»">,

1841.

(2) On a simple property of the Conic Section, pp. 201-3, 1841.

(3) Remarks on the Binomial Theorem, pp. 61, 62, 1843.

(4) On the Equation (D + a)M3 = x, pp. 60-62, 1845.

(5) On a Law existing in the successive approximations of a

Continuous Fraction, pp. 97-99, 1845.

CAMBRIDGE AND DUBLIN MATHEMATICAL JOURNAL.

(1) On Arbogast's Formulse of Expansion, pp. 238-255, 1846.

(2) Suggestion on the Integration of Rational Fractionp, Nov.

1848.

(3) On a Point in the Solution of Linear Differential Equa-

tions, 1849.

(4) Extension of the word Area, May 1850.

(5) Application of Combinations to the explanation of Arbogast's

Method, Feb. 1851.

(6) On the Mode of using the signs + and — in Plane Trigo-

nometry, May 1 85 1 .

(7) On the Connection of Involute and E volute in Space, Nov.

1851.

(8) On Partial Differential Equations of the First Order, Fel

1852.

(9) On the Signs + and — in Geometry, and on the interpi

tation of the Equation of a Curve, Nov. 1852.
(10) Mathematical Notes, pp. 93, 94, 1853.

LIST OF WRITINGS. 405

QUARTERLY JOURNAL OF MATHEMATICS.

(1) On the Dimensions of the roots of Equations, 1857.

(2) On the Fractions of Vanishing or Infinite Terms, 1857.

(3) Historical Notes on the Theorem respecting the Dimen-

sions of Boots, 1857.

(4) Notes on Euclid i. 47, 1857.

(5) On the Integrating factors of Pd + 2dy + R,dz, 1858.

(6) On the Classification of Polygons of a given number of

sides, 1858.

CENTRAL SOCIETY OF EDUCATION.

On the Mathematics ; their value in Education.
On Professional Mathematics, 1837-38-39.

THE MATHEMATICIAN.

(1) Remarks on General Equations of the Second Degree, pp.

242-246, 1850.

(2) Organised Method of making the resolution required in the

integration of Rational Fractions, pp. 242-246, 1850.

(3) Remarks on Homer's Method of solving Equations, pp.

289-291, 1850.

BRITISH ALMANAC AND COMPANION.

1831. On Life Assurance.

1832. On Eclipses.

1833. On Comets.

1834. On the Moon's Orbit.

1835. Halley's Comet.

1836. Old Arguments against the Motion of the Earth.

1837. Notices of English Mathematical and Astronomical Writers

between the Norman Conquest and the year 1 600.

1838. On Cavendish's Experiment.

1839. Progress of the Problem of Evolution.

1840. On the Calculation of Single Life Contingencies.

1841. On the use of small tables of Logarithms in Commercial

Calculations, and on the practicability of a Decimal
Coinage.

1842. On Life Contingencies, No. 2.

1843. References for the History of the Mathematical Sciences.

1844. Ou Arithmetical Computation.

406 MEMOIR OF AUGUSTUS DE MORGAN.

1845. On the Ecclesiastical Calendar — Easter.

1846. On the earliest printed Almanacs.

1847. Recnrrence of Eclipses and Full Moon.

1848. On Decimal Coinage.

1849. Short Supplementary on the First Six Books of Euclid's

Elements.

1850. On Ancient and Modern Usage in Reckoning.

1851. On some points in the History of Arithmetic.

1852. A Short Account of some recent Discoveries in England

and Germany, relative to the Controversy on the Inven-
tion of Fluxions.

(See Life of Newton in Knight's ' British Worthies/
Arts. Commercium Epistolicum and Fluxions, P. Cyc.,
Dispute between Keill and Leibnitz, Cambridge Memoirs.)

1853. On the difficulty of correct descriptions of Books.

1854. On a Decimal Coinage.

1855. The Progress of the Doctrine of the Earth's Motion between

the times of Copernicus and Galileo, being notes on the
Ante-Galilean Copernicans.

1856. Notes on the History of the English Coinage.

1857. Notes on the State of the Decimal Coinage Question.

IN SMITH'S CLASSICAL DICTIONARY.

Diophantus. Sosigenes.

Eucleides. Theon.

Heron. Ptolomaeus.
Hipparchus.

TRACTS PUBLISHED BY THE SOCIETY FOR THE DIFFUSION OF
USEFUL KNOWLEDGE.

(1) Study and Difficulties of Mathematics, vol. i., 1836.

(2) Arithmetic and Algebra, 1831, vol. i., 1836.

(3) Examples of the Processes of Arithmetic and Algebra, vol. i.,

1836.

DUBLIN REVIEW.

Laplace on Probabilities, No. 1, April 1837.
Laplace on Probabilities, No. 2, July 1837.
On Legislation for Life Assurance, Aug. 1840.
Review of Jones on the value of Annuities (published by
Diffusion Society), August 1841.

LIST OF WRITINGS.

407

Peyrard's Elements of Euclid, Nov. 1841.

Weights, Measures, and Coinage, May 1841.

Science and Rank, Nov. 1842.

Baily's Repetition of the Cavendish Experiment, March 1845.

Speculators and Speculations, Sept. 1845.

Book-keeping, Dec. 1845.

Mathematical Bibliography, Sept. 1846.

Helps to Calculation, March 1847.

ENCYCLOPEDIA METROPOLITANA.

Calculus of Functions, 1835.
Theory of Probabilities, 1837.

LIST OF ARTICLES IN ' PENNY CYCLOPAEDIA.'

(This list of articles in the * Penny Cyclopaedia ' is taken
partly from a copy in the British Museum, in which all the articles
have the names of their authors appended by the donor ; and
partly from the marked copy in Mr. De Morgan's possession.
The constellations and planets not included in this list are also by
him, if the Museum copy is correct.)

Abacus, 2 Advowsons, value of

Abatis Aeolipyle

Abauzit, Firmin Aero-dynamics
Abbreviation, mathl. Aerostatics
Abel, Niels Henri Agnese, Maria
Aberration Air

Aberration (in optics) Air-gun
Abscissa Air-pump

Absurdum, reductio Aliquot part
ad D'AIembert

Accelerated motion
Accent (mathl.)
Achromatic
Acoustics
Acronychal
Act (University)
Actuary

Addition
Addition of ratios

Algebra

Algebraic

Algebraic geometry

Algorithm

Almacanter

Almagest

Almanac

Alonsine tables

Alternate

Altitude

Amphiscii

Amplitude

Analysis

Anaxagoras

Anaximander

Anaximenes

Anemoscope

Angle

Anker

Annuity

Annulus

Anomalistic year

Anomaly (astronl.)

Antecedent

Antecedentia

Antilogarithm

Antinomians

Antipodes

408

MEMOIR OF AUGUSTUS DE MORGAN.

Antiscii

Antoeci

Aphelion

Appian, Peter

Apogee

Apollonius Pergreus

Apparent (astron.)

Apparent magnitude

Apparent motion

Approximation

A posteriori, a priori

Apsides

Aratus, astronomer

Arbogast, Louis
Fred.

Arc

Arch

Archimedes

Architrave

Archivolt

Arctic circle

Are

Area

Argument

Aristarchus

Aristoxenus

Arithmetic

Arithmetical com-
plement

Arithmetical mean

Arithmetical pro-
gression

Arithmetical pro-
portion

Armillary sphere

Arroba

Ascension, ascen-
sional difference

Aspect (astronl.)

Asterism

Astrolabe

Astrology

Astronomy
Asymptote
Atmosphere
Atmospheric air
Attraction in

physics

Attwood, George
Aurora borealis
Autolycus
Automaton
Auzout, Adrien
Average
Avoirdupois
Axiom
Axis
Azimuth

Bacon, Roger
Bailly, Jean Sylvain
Bainbridge, John

(astron.)
Balance

Ballistic pendulum
Balloon
Barlaam

Barlowe, William
Barometer
Baroscope
Barrel

Barrow, Isaac
Barter (arithmet.)
Bartholinus
Bassantin, James
Bayer, John
Bearing (nautical)
Beccaria, Giovanni

Battista
Belidor
Bellows
Berkeley, Goo. (the

latter half)

Bernard, Edward

Bernoulli

Berosus (the latter

half)
Binomial
Binomial theorem
Biquadratic
Bombelli, Raphael
Bonnycastle, John
Borda, Jean Charles
Borel and Borelli,

part

Boscovich, R. J.
Bossut, Charles
Bouguer, Pierre
Bouillaud, Ismael
Boyle, Robert
Bradley, James
Brahe, Tycho
Briggs, Henry
Brouncker
Burning-glass
Bushel

Cagiioli

Calculating machine

Calculus

Calibre

Calippus

Callet

Camera In c it la

Campaiii, M. and J.

Campanus, J,

Camus

Cancer (sign)

Canon (mathl.)

Canton, John

Capacity

Capillary attraction

Capricortius (sign)

Carat

LIST OF WRITINGS.

409

Cardan

Colson, John

Corvus

Carnot

Combinations and

Costard, George

Cassini

Permutations

Cotes, Roger

Castelli

Comet

Coulomb

Catalogue (astron.)

Comet of Biela

Craig, John

Catenary

Commandine

Cramer, Gabriel

Cause

Commensurable

Crux

Caustic (optics)

Commercium Epis-

Ctesibius

Cavalieri

tolicum

Cube

Cavendish, Henry

Common measure

Culmination

Celsius

Compass, azimuth

Cunitz, Maria

Centigrade

Compass, mariners'

Curtate

Centre

Compasses

Curvature

Centrifugal forces

Complement

Curve

Centripetal force

Composition

Cusp

Chain (surveying)

Compound quantities

Cycle

Chaldron

Concave and convex

Cycloid

Chance

Concentric

Cylinder

Chappe d'Auteroche

Conchoid

Characteristic (of a

Condition (mathcs.)

logarithm)

Condorcet

Data, Datum

Chastellet

Cone

Day

Chiliad

Conic sections

Decagon

Chord

Conical projection

Declination

Church rates

Conjugate

Deferent

Circinus

Conjunction and

Definition

Circle

opposition

Deflection

f\T rlofMTn I'f ion

Conoid

Degree of an equation

&c.

Conon of Alexandria

Deism

Circular parts

Constant

Demoivre's hypothe-

Circulating decimals

Constellation

sis

Cissoid

Construction

Demonstration

Clairaut

Contact

Deneb

Clavius

Content

Denominator

Cleomedes

Contrary and con-

Density

Clepsydra

tradictory

Departure

Cloud

Convergent

Depression

Cocker, Edward

Converse

Derivation

Coefficient

Co-ordinates

Determinate

Cohesion

Copernicus

Development

Collins, John

Cord

Diagonal

Collision

Corollary

Diagonal scale

410

MEMOIR OF AUGUSTUS DE MORGAN.

Diagram

Diameter

Differential calculus

Differential co- effi-
cient

Digit

Dimension

Direct and retrograde Equimultiples

Direction Equinoctial

Directrix

Disc

Discontinuity

Discount

Dividend (arithl.)

Division

Dodecagon

Dome

Drachm, or Dram

Duodecimals

Duplicate ratio

Duplication of the
cube

Equation of payments Geometer
Equations, algebraical Geometrical
Equations, difft rential Geometry
Equations, functional Globe
Equator and ecliptic Globular projection
Equiangular, Equi- Globular sailing

lateral

Equinoxes

Euclid

Excentricity

Factor, in algebra
Fall of bodies
False position
Fellowship (in

arithmetic)
Ferrei and Ferrari

Gnomon

Gnomonic projection

Golden number

Graduation

Gravity, centre of

Gruldinus

Gunter

Gyration, centre of

Hachette

Halley

Hal ley's Comet

Harmonic proportion

Figure (in geometry) Harmonics

Dynamics
Dynamometer

Firkin

Flam steed

Flexure, contrary

Fluxions

Force

Forces, impressed
and effective

Forces, parallelo-
gram of

Fourier

Fractions, common
and decimal

Height, measurement

of

Heliacal

Herschel, William
Heteroscii
Hevelius, partly
Hogshead
Homogeneous and

Heterogeneous
Homologous
Horary
Horizon

Earth (astronl.)

Earth, density of

East

Easter, method of

finding
Eclipse

Elimination (algebc.)
Ellipse Fractions, continued Horologium

Elliptic compasses Fractions, vanishing Horrocks, Jeremiah
Ellipticity Functions,calculus of Hour, Hour-circle,

Klongation (astronl.) Functions, theory of Hour-line
Encke's Comet Huyghens

Epoch (astronl.) Hyperbola

Equal Gage Hyperbole

Equation Gallon Hypothenuse

Equation (astronl.) Generating functions Hypothesis

LIST OF WRITINGS.

411

Impact

Impenetrability
Impulse
Inclined plane
Incommensnrables,

theory of

Increment and de-
crement
Indefinite
Indeterminate
Induction (mathl.)
Inequality
Inertia
Infinite, Infinity,

Infinitesimal

calculus
Integer
Integration, Integral

calculus
Interest
Interpolation
Interpretation
Invariable
Inverse, Inversion
Involute and

E volute
Involution and

Evolution
Irrational quantity
Irreducible case
Isochronous

Julian period

Kalendar

La Caille
Laplace

League

Leap Year

Least squares

Legendre

Lemma

Lemniscata

Lens

Lever

Libration

Life, mean duration

Light, barometrical

Light-equation

Lights, Northern ?

Line

Limits, theory of

Litre

Logarithms

Logarithms, Gauss's

hyperbolic
Logarithmic curve

and spiral, use of
Longitude and

latitude
Lubienietske

Maclaurin

Magic square

Magnitude

Map

Mario tte

Ma seres, Francis

Maskelyne, Nevil

Mass, in physics

Mathematics

Maurolico, or

Marullo

Maxima and Minima
Menelaus
Mensuration
Mercator, Nicholas
Mercator's projection
Meridian

Meton, Metonic cycle

Metre

Middle latitude

Mile

Milky Way

Momentum, or

Moment
— — or Moment

of inertia
Money
Monge
Moon

Mortality, law of
Motion

• direction of

of the earth

Moving force
Multiple, Submul-

tiple

Points

Musa, Mohamed Ben

Napier's bones, or
rods

Negative and impos-
sible quantities

Node

Nothing

differences

of

Nucleus of a comet

Number

Numbers, appellations
of

Numbers, theory of

Numbers of Ber-
noulli

Numeral characters

Numeration

Numerator

Numerical

412

MEMOIR OF AUGUSTUS 1)E MORGAN.

Oblate
Oblique
Obliquity-
Oblong
Observation and

experiment
Occupation
Octans
Offsets
Operation
Orb, Orbit
Order
Ordinate
Oscillation and centre Proportion

Precession and nuta- Reduction

Regular figures,
polygon, solids,
polyhedrons
Relation (mathl.)
Residual phenomena

tion

Pressure
Prime

Primum mobile
Principia

Probability, theory of Resistance ?
Problem Reversion

Process ? Reversion of series

Progression Revolution

Projection Rhomb, Rhombus,

Projection of mathe- Rhomboid

matical diagrams Rhumb, or Rumb

of oscillation

Pace

Parabola

Paradox

Parallelepiped

Parallelogram

Parallels

Parameter

Penumbra

loara-

Proportional

rithms

Proportional parts
Ptolemaic system
Pyramid

Quadrant
Quadrature
Quadrature of the
circle

Percussion, centre of Quantity

Perimeter Quarter

Periodic functions Quartile

Periods of revolution Quintal

Piccolomini, A. Quintile

Piling of shot

Pipe

Planet

Planisphere

Point of contrary
flexure

Pole, Polar

Polygon and poly-
hedron

Pond, John

Power (mechanics)

Practice

Radix
Ratio
Ratios, composition

of
Ratios, prime and

ultimate
Reciprocal
Rectangle
Rectification
Recurring scries

Right angle
Root
Rotation
Round
Rule, Ruler

Sagittarius

Salient

Saros, Neros, Sosos

Satellite

Scale, musical

mathematics
Scholium
Scruple

Seasons, change of
Segment
Series

Sexagesimal
Sextans (constell.)
Side
Sidereal

Sign, astronomy
Sign, mathematics
Similar, similar

figures

Sine and Cosine
Sine and Cosine,

curves of

LIST OF WRITINGS.

413

S lide, or Sliding rule

Solar system

Solid, Solidity

Solid angle

Solid, surface, line,
point

Solid, superficial,
and linear dimen-
sions

Solstices

Solution

Space and Time

Species, mathematics

Sphere, or globe

Sphere, doctrine of
the

Spherical trigono-
metry

Spheroid

Spiral

Square

Square root

Stable and unstable

Star, double star,
cluster of stars

Statics

Stationary, mecha-
nics

Stationary, astro-
nomy

Stereographic

Sterling ?

Straight, straight
line, plane

Sturm's Theorem

Subcontrary

Sublime (geometry)

Subsidiary

Substitution

Subtraction Subtra-
hend, Minuend

Siifficient reason

Sum and difference

Sum, Summation

Sun

Sun-dial

Sun, eclipse of

Surd

Surface, Surfaces,
theory of

Surfaces of the
Second Degree

Syllogism ?

Symbols and
Notations

Symmetry, Sym-
metrical

Sympathetic sounds

Synodic, Synodic
Revolution

Synthesis

System, mathema-
tics

System, astronomy

Table
Tangent
Taylor, Brook,

theorem
Term (algebra)
Theodosius of

Bithynia ?
Theon, the elder
Theorem

Theory and practice
Theory of couples
Theory of equations
Three, rule of
Time

Time of descent
Toledo, tables of
Transcendental
Transformation

Transformation of
co-ordinates

Transits of Mercury
and Venus

Transversal

Trapezium, Trape-
zoid

Traverse tables

Triangle

Triangula and Tri-
angulum Australe

Trigonometrical co-
ordinates

— curves

— series

— survey
tables

Trigonometry

Trisection of the angle

Trochoidal curves

Troy weight

Tube

Tuning

Twilight

Ullage
Ulugh Beg
Undetermined
Universal and Parti-
cular ?
Universe
Unlimited
Uranus

Vacuum, or Void

Vanish (mathematics)

Variable

Variations, calculus of

Varignon, Pierre

Velocity

414

MEMOIR OF AUGUSTUS DE MORGAN.

Vernal and Equi- Wager

nox

Vibration
Vieta

Viga Ganita
Virtual velocities
Vitello
Volume
Volute
Vortex

Wallis, John

Wingate, Edward
Wrangler

Weight Wright, Edward

of earth

of observa-
tions

Weights and mea- Year

sures Young, Thomas

Winston, W.

SEPARATE WORKS.

Elements of Arithmetic, 8vo, 1835.

Algebra, Prelim, to the Differential Calculus, 8vo, 1835.

Connection of Number and Magnitude: an attempt to explain
the Fifth Book of Euclid, 8vo, 1836.

Essay on Probabilities, and on their Application to Life Con-
tingencies and Insurance Offices, Cabinet Cyclopaedia, small
8vo, 1838.

The Differential arid Integral Calculus, one vol. 8vo, pp. 770,
1842.

Arithmetical Books, from the invention of printing to the present
time, being brief notices of a large number of works, drawn
from actual inspection, 8yo, 1847.

First Notions of Logic, preparatory to study of geometry, 8vo,
1839.

Formal Logic, or the Calculus of Inference necessary and pro-
bable, 8vo, 1847, pp. 336.

The Globes, Celestial and Terrestrial, for Malby's Globes, 8vo,
1845.

Syllabus of a Proposed System of Logic, 8vo, 1860.

Trigonometry and Double Algebra, 1849.

The Book of Almanacs, with an index of reference, by which the
almanac may be found for any year up to A.n. 1000, with
means of finding the day of any new or full moon from
B.C. 2000 to A.D. 2000, compiled by A. De Morgan, 8vo, 1850.

MISCELLANEOUS.

Correspondence of Scientific M^n of the Seventeenth Century,
by S. P. Rigaud. Contents and Index by A. De Morgan,
1841.

LIST OF WRITINGS. 415

Treatise on the Problems of Maxima and Minima, by Ram-

chundra, Calcutta, edited, with Introduction, 1850.
Decimal Association Proceedings, with Introduction, 1854
Debate on the Decimal Coinage Question, with remarks on the

speech of the Member for Kidderminster, 1855.
Reply to Facetiae of the Member for Kidderminster, 1855.
Journal of a Tour in the Unsettled Parts of North America, by

Francis Bdly, edited with Preface, by A. De Morgan, 1856.
Preface to From Matter to Spirit, by Sophia De Morgan, 1863.
Notes on Colonel W. H. Oakes's Table of the Reciprocals of

Numbers, 1865.
Seven Figure Logarithms of Numbers 1 to 108,000, corrected,

with a description of the Tables added by Prof. De Morgan,

8vo. (Trans, of Lndwig Schroen Siebenstellige. Gemeine

Logarithmen der Zanten.) 1865.
The Eleventh Chapter of the History of the Royal Society, with

additions, by Prof. De Morgan, 1849.
General Information on Subjects of Chronology, Geography,

Statistics, &c., References for History of Mathematical

Science, 1842.
Statement in answer to an assertion made by Sir W. Hamilton

in reference to a discovery of a new principle in the Theory

of Syllogism, 1847.
English Science, Report of the British Association, vols. i. and ii.,

written for a Review, edited by Mr. Beaumont (title for-
gotten), 1835.
Tables, C. Knight's English Cyclopaedia, a new edition of Useful

Knowledge, London, 1861.

In addition to the above there were numerous contributions
to the ' Memoirs ' and ' Obituary Notices ' of the Astronomical
Society, to the Journal of the Institute of Actuaries and
Insurance Record. I do not find any contribution to the
North Biitish Review except the Review of ' Brewster's Life of
Newton.' Among the smaller writings which I know to be
omitted from the above list are some to Charles Knight's

* Library of Anecdote,' biographies in the same publisher's

* Portrait Gallery,' &c., &c.

The voluminous contributions to the ' Athenaeum,' ' Notes
and Queries,' &c., I have been obliged to omit on account of their
number.

INDEX OF NAMES, ETC.

ABA

ABACUS, 235
Abracadabra, 381

Adams, Professor John, 126, 129-136

Adelaide Eoad, N.W., 271, 364

Affleck, Lady, 101, 305

Agathocles (eclipse of), 232

Airy, Sir G. B., 15, 19, 24,42, 48, 62,
77, 107, 118; 127-130, 134-138,
237, 241,248, 252, 273, 333

Albert Life Assurance, 279

Alderson, Baron, 390

Algebra Nova, 59

Alliance Assurance Company, 363

Alvescot, 215

Amicable Life Assurance,60, 181

Appledore, 2

Arago, 126, 130, 176-178

Argelander, 136

Aristotle, 350

Arithmetic and Algebra, 29

Arnauld, 384

Ashburnham, Lord., 203

Astronomia Philolaica, 75

Astronomical Club, 250

Astronomical Society, Eoyal, 19, 41 -
63,76, 81-83, 106-108, 118, 124,
181, 191, 194, 273, 277, 292, 301

— Annual Report, 232

— Obituary Notices, 110
Athanasian Creed, 322
Athenaeum Newsp., 179, 192-194, 210
Aubert, J., 382

Austin, 350

BABBAGE, Charles, 48, 60, 89, 133,
235, 243, 324, 333, 335, 387,
Bacon, Lord, 296, 303, 305
Bacon, Roger, 218, 302
Bagehot, Walter, 97, 359
Baily, Francis, 41-46, 49, 76, 78, 81,
104-109, 110, 117, 120, 140, 145,
148, 231, 256, 301-335

BOU

Baily, Miss, 45, 301
Baily, Richard (Selim Effendi), 335
Bain, Prof. Alexander, 306, 339
Bampton Lectures, 296
Bardin's Globes, 120
Barnstaple, 23
Barrow, Isaac, 296
Barton, Catherine, 264, 288
Baynes, Professor Spencer, 212
Beaufort, Admiral, 2, 64, 77, 293
Bengal Hurkaru, 280
Bentham, George, 162
Bentham, Jeremy, 350
Bentinck, Lord W., 321
Berkeley, Bishop, 15, 115, 164
Bernoullis (The), 286
Bertrand, M., 312
Bessel, — , 82, 127
! Bethune, Drinkwater, 61, 268
Bhascara, 269
Bideford, 2
Biot, M., 32, 131, 231, 257, 262, 264,

278, 290, 298
Biran, Maurice de, 300
Bird, William, 77
Birkbeck, Dr. George, 23
Bishop, George, 49, 137
Bishop, Mrs., 49
Blackburne, Archdeacon, 104, 109,

113

Blanchard (priest), 382
Blandford, — , 3
Eland's Quadratic Equations, 7
Board of Longitude, 49
Bolland (Baron), 388
Bompas, Henry, 359
Bonnycastle's Algebra, 335
Boole, George, 165-168, 212
Boucly, M., 179-211
Bouillaud (or Bullialdi), 59, 75
Bourdon's Algebra, 29, 32
Bouvard, A., 127
Bouvard's Tables, 127

E E

418

MEMOIR OF AUGUSTUS DE MORGAN.

BOW

Bowriug, Sir John, 236, 238, 240

Bradley, 108

Brewster, Sir David, 199, 257, 261-

263

Briggs, Dr., 31
Briggs, General, 21, 31-33
Bright, John, M.P., 241
British Association, 69
British Museum, 176
British Worthies (Knight's), 176
Brougham, Lord, 23, 51, 125, 269,

312, 332, 358

Brown, William, 238, 241,243, 255
Browne, J. Baldwin, 101
Budget of Paradoxes, 58, 70
Bunyan, John, 305
Burdett, Sir F., 109
Butler, Charles, 55
' Butler's Analogy,' 194
Byron, Lady Noel, 89

pABINET Cyclopaedia, 92

\J Cacciatore, M., 127

Calculus of Functions, 82

Cambridge Philosophical Society, 286
- Transac-
tions, 113

Camden Street, 96

Campbell, Thomas, 23, 358

Campden Hill Observatory, 61

Camus Musical Club, 16

Gary's globes, 120

Case William, 359

Cassini, Count, 153

Catalogue of stars. 42, 75, 83

Cavendish Experiment, 45, 106, 108,
111 „

Cayley, George, 297

Censorinus, 204

Challis, Professor, 129, 132, 135,
138

Chasles, M., 396

Chevallier, JRev. Temple, 68

Chillingworth, 194

Chladni, 32

Church rates, 87

City of London School, 190

Clarke, Dr E. D., 109

Clarke (an'i-Trinitarian), 261

Cleaaby, Sir R. (third wrangler), 18

Clifton, Professor R. B., 97, 359

Clough, A. H., 173

Coates, Thomas, 53

Cobbett, 220

Cobden, Richard, 241

Coudington, Professor, 15, 24

Colenso, Bishop, 325, 327, 378

ELL

Coleridge, Samuel Taylor, 321, 363

Colin, Melanie, 181

Companion to the Almanac, 50, 53,

107, 123, 234, 264
Comptes Rendus, 68 .
Comtism, 116
Connection of Number and Magnitude,

65 .

Conolly, Dr., 53
Constellations (names of), 63
Convocation, 299
Cornelius Agrippa, 379
Cousin, Victor, 300
Crotchet Castle, 66
Crowe, Catherine, 173
Gumming, Rev. Dr., 325

DAVY, Sir Humphry, 335
Day schools (his), 30
Dealtry, Rev. — , 387
Decimal Association, 235-240
Decimal coinage, 235-255
De Blainville, 163
Defoe, Daniel, 20
De Gasparis, 217
Delambre, 59, 108, 168
Dela Rue, Warren, 2/1
De Moivre, 233

De Morgan, Mrs. (s^n.), 2, 11-15
— Campbell Greig, 234

Edward Lindsey. 116,281

Elizabeth Alice, 189, 197

George Campbell, 34, 112,

281, 286, 363

George, 234. 281, 286

Helena Christiana, 367

William Frend, 108

Des Cartes, 108, 257
Dickens, Charles, 93, 265
Differential and Integral Calculus, 52,

65, 113
Digges, 291
Dodson, James, 233
John, 234

Dollond, 108
Drummond, Sir W., 21
Druse Trinity, 328
Dumas (priest), 382
Dunlops Nebulee, 120, 148

EASTER Question, 125
Ebury, Lord, 266
Edleston, J., 257
Edmonds, T. R., 279
Elements of Arithmetic, 54
Ellenborough, Lord, 87

INDEX OF NAMES, ETC.

419

ELL

Elliotson, Dr. John, 323
Ellis, Leslie, 9, 103, 318

— Sir Henry, 201
Encyclopaedia Metropolitana, 92
Essay on Probabilities, 92
Evening amusements, 109
Exeter, 108

FABEICIUS, 295
Falconer, Thomas, 16

Falloux, M., 179

Family Endowment Offices, 110

Fanshawe, Colonel, 1

Faraday, Michael, 82, 192

Farish, Professor, 388

Fenner, Eev. J., 3

Ferishta, 21, 31

Financial Keform Association (Liver-
pool), 247

Finlaison, 87

Flaherty Scholarship, 144

Flamsteed, John, 120, 256

Follen, Mrs., 173

Formal Logic, 111, 157-168

Forman, Captain, 77, 78

Foster, Professor Michael, 190, 222

Fouchy, 151

Franklin,J. B., 248, 252

Fraser, Peter, 103

Free Christian Union, 365

Frend, William, 19, 21, 23, 28, 31,
39, 81, 89, 109, 235, 312

Fry, Elizabeth, 90

n ALILEO, 290

\J Galle, M., 128

Galloway, Thomas, 45, 60, 150, 155,

171, 180

Gardiner's Logarithms, 381
George III., 82, 322, 333
Ghetaldi, 76
Ghuleim Hassein, 31
Gilbert, Davies, 217
Gladstone, William Ewart, 239, 241
Goethe, 321, 362
Goldsmid, Sir Isaac, 53
Gompertz, Benjamin, 279
Good Words, 265
Gordon (Senior Wrangler), 17
Gordon, Jemmy, 321, 391
Graham, Professor, 292
Greathead, Samuel, 376
Greenwood, J. G., 359
Gregory, D. F, 151

Olinthus, 64, 312

Guizot, M., 177

Gunning, Esquire-Bedell, 391

INT

HACHETTE, M., 32, 58, 64, 75
Halifax, Lord, 245, 264, 288

Hallam, Henry, 111, 201

Halley, 108, 256, 258

Halliwell, J. 0., 124

Hamilton, Eev. H. Parr, 15

Hamilton, Sir W., 104, 160-162, 204,
212, 331

Sir W. Eowan, 333

Hardy, Cozens, 359

Harrison, 108

Hartog, N. E., 102

Harwood, Sir Busick, 388

Haussen, Professor, 127, 136

Hayden, Mrs., 221

Heald, Eev. William, 16, 206, 214,
218-221, 293

Hencke, 136

Hensley, Lewis (sen.), 41

Mrs., 85, 143

Herschel, Sir J. W., 41-45, 67, 152,
170, 193,209, 213,216, 231,237,
248, 287, 289, 291, 302 309, 320-
326, 333, 369, 371, 376, 395-400
Sir W., 85, 108, 148

Hervey, T. K., 176, 202, 2JO

Hey wood's Analysis of Kant, 315

Higgins, Godfrey, 21, 31

Higman, John, 12, 15

Hill, Sir John, 172

Octavia, 265

Eowland, 176, 201, 241

Hind, John, 137

E., 49, 122, 136, 217

Historical Society of Science, 1 24
Hobbes, Thomas, 350

Hood, Thomas (A.D. 1500), 67

Hoppus, Eev. J., 327

Hornbuckle, 388

Horner, L., 31

Horrocks, 301

' Household Words,' 265

Houtmann, F., 299

Howard, C., 120

Hume, David, 350

Jacobus, 153

Joseph, M.P., 51

Husenbeth, Eev. Dr., 322
Hussey, Dr., 127
Hustler, 388

Hutton, Dr., 106
E. H., 54

] NSTITUTE of Actuaries, 45
JL Insurance Eecord, 279
International Association for Weights
and Measures, 240, 247

420

MEMOIR OF AUGUSTUS DE MORGAN.

INT

International Statistical Congress,

269
Introductory Lecture, 10, 29, 183, 278

JANE, Duchess of Gordon, 2
Jephson, 389
Jessel, George, 97, 359
Jevons, Prof. Stanley, 97
Johnson, Prof. Manuel, 138, 191
Julian Calendar, The, 205

TTALEIDOSCOPE, The, 262
J\. Kane, Sir .Robert, 168
Kant, 315, 332
Kastner, 75
Kempt home, 387
Keynes, Rev. T., 3
King, Lady, 89
King's College, 174
Knight, Chas., 108, 256
Knight's 'British Worthies,' 126, 256,
261

T ACROIX, 203

_LJ Ladies' College, 94

Lagrange, 108, 113, 114

Laing, Rev. D., 264

Lalande, 382

Lamb, Charles, 321

LangJale, Lord, 390

Laplace, 92, 108, 306

Lardner's Cyclopaedia, 145

Lee, Dr.. 49, 271-333, 390

Lefort, M., 278

Leibnitz, 108, 256, 262, 294, 317

Leopold, Duke of Tuscany, 69, 75

Leverrier, 126-136, 395

Lewis, Sir George Cornewall, 244

Library of Useful Knowledge, 267

Libri Guglielmo,59, 84, 126, 130, 173,

176, 203, 210, 264-286, 299, 396
Life Assurance, 279
Lindsey, Theophilus, 116
Literarium, The, 253
Liverpool Observatory , 122
Locke, John, 141, 218, 261
Logan, Rev. Dr., 103
London University, 50
Long, George, and Mrs. Long, 103
Louis Philippe, 177
Lowe, Robt., 243, 249
Lowndean Professorship, 297
Lubbock, Sir John, 66, 136, 237, 267
Ludovicus Vives, 378
Lyndhuret, Lord, 109

NIC

MACAULAY'S Essays, 101
Macaulay, Lord, 288-328
Maclear, Sir T., 77, 84, 333
Madge, Rev. T., 88
Madura, 1
Main, R., 138
Maitland, Rev. Samuel, 124, 219,

376

Majendie, 184
Malby's Globes, 120, 148
Malcolm, Sir John, 31
Malthus, Rev. T., 109
Manchester New College, 355, 372
Manners, Admiral, 45
Mansel, Dean, 54, 296, 317, 331
Maps of the Stars, 66-68
Marshman, Adam, 290
Marston, Westland, 173
Marti neau, James, 337-356
Maskelyne, Neville, 108
Mason, Bev. William, 16, 376, 393
Mathematical Canon, The, 233
Mathematical Club, 123
Mathematical Society, 280-286, 363
Maule, Judge, 61, 387
Maurice, Rev. F. D., 174
Maxima and Minima, 268
Menabrea, 89
Mersenne, 75
Milbourne, 152
Mill, James, 33, 115
Mill, John Stuart, 33, 114-116, 163,

328-332, 378-383
Miller, Professor, 237, 248, 252
Miller, William, 248, 252
Mitchell's Apparatus, 107
Monro, Cecil, 158
Monteagle, Lord, 241
Montucla, 59, 75, 111
Morland, Sir Samuel, 59
Mulock, Miss, 173
Murphy, 150

NAPOLEON BUONAPARTE, 250
Napoleon III., 299
National Address to America, 182
Naudet, M., 179

Nautical Almanac, 19, 42, 49, 333
Neate, Rev. A., 16, 79, 170, 215, 294
Neptune, The Planet, 126-128
Newman, Francis, 174
Newman, Thos. Henry, 323
Newton, Isaac, 198, 231, 257-264,

288, 301-303, 323
Nicholas Nickleby, 265
Nicolas of Cusa, 290
Nicolas, Sir Harris (Letter to), 70-73

INDEX OF NAMES, ETC.

421

NIC

Nicolay, Rev. William, 174
Ninth Bridgwater Treatise, 90
Noel, Hon. and Rev. Baptist, 142
North British Review, 261-263
Notes and Queries, 219

0 SCOTT College (St. Mary's), 133
Overstone, Lord, 248, 251-253
Owen, Robert, 325

T)ALEY, Archdeacon, 109, 350

-L Pancras, St., 323

Panizzi, Antonio, 203, 211

Parsons, Rev. J., 3, 6, 11, 19

Pascal, 125

Pasley, Gen., 236, 241

Pattison, Prof., 34, 37, 39

Peacock, Dean. 12, 15, 16, 24, 82, 144,

202, 217, 237, 297, 328
Peacock, Thomas, 298
Pearson, Dr., 41
Peccam, Abp., 291
Peene, Dr. W. Ghirdon, 185-188, 340,

375
Penny Cyclopaedia, 46, 60, 107, 123,

194, 235, 255
Penny Magazine, 51
Perrott, Mr., 150
Perry, Mr., 45
Petrus Hispanus, 378
Pettigrew, Mr , 124
Petty, Sir William, 251
Philosopher (definition of), 95
Philpotts, Bishop, 378
Physiology (teaching of), 184, 225
Pickwick, 93

Pilgrim's Progress, The, 59
Ploucquet, 103
Poinsot, M., 129
Pollock, Frederick (L, C. Baron), 168,

332, 334, 385-392
Poole, Mrs., 3
Porson, Richard, 45
Porter, Jane, 24
Powell, Rev. Baden, 170
Prickett, Mr., 219
Probabilities, Tract on, 267
• Essay on, 75, 92

QUARTERLY Journal of Educa-
tion, 53

Quetelet, 60, 65
Quilon, 3

STE

RAMCHUNDRA, 268
Ranke, M., 312

Ranyard, A. Cowper, 281, 282, 285
Raper, Lieutenant, 64
Redland School, 3, 5, 7, 8
Reece, Robert, 5, 6, 9
Rees, Joseph, 120
Reid, Mrs. Elizabeth, 173
Reynolds, H. Russell, 120
Rheticus, 151

Rigaud, Stephen Peter, 257
Robertson, Mr. Groom, 339, 349
Robinson, Dr. (of Armagh), 333
H. Crabb, 3, 321, 332, 361

Robert, 321

Ross, Captain, 76
Rosse, Lord, 299
Royal Astronomical Society, 270,

277

Royal Society, 76, 81, 181, 294
Rutherford, Dr., 154

SADLER, Rev. Thomas, 363
St. Helena, 3
St. Michael's, Bristol, 8
Schinderhaussen, Olearius, 320
Schoolmaster (The), 54
Scott, Rev. A. J., 173
Sedgewick, Adam, 104
Serenus Samonicus, 380
Shaftesbury, Lord, 265, 333
Sharp, Abraham, 256
Sharpey, Professor, 267
Sheepshanks, Anne, 191, 300

Richard, 45, 61, 104,

112, 118, 134, 153, 190, 232, 237
Simeon, Rev. J., 13
Smith, Rev. James, 1 73

Mr. J. B., M.P., 243-246

Smith's Harmonies, 152, 287
Smyth, Adi., 43-49, 79, 83, 150, 152,

171, 204, 208-230, 272, 29J, 308,

333

Mrs , 324

Piazzi, 84, 324

South, Sir James, 43-48, 61, 82, 333-

335

Southey, 321
Spencer, Herbert, 162
Spring-Rice, T., M.P., 236
Standard scale, 50, 111
Standert, Hugh, 4, 17
Stanley, Dean, 398
Lord, 243

Starkie, Sergeant, 61
Stephenson (engineer), 80
Stevinus, 111

422

MEMOIR OF AUGUSTUS DE MOKGAN.

STE

Stewart, Mr., 83

Stoke Newington, 20, 31, 41

Stratford, William Samuel, 20, 80,

312

Striive, Professor, 12, 131
Swedenborg, 173
Sylvester, Professor, 144, 286, 311

TATE, Eev. James, 104
Taunton, 23

Tayler, Eev. John James, 384
Taylor, Sedley, 08, 124, 398

Richard, 124

Temple, Rev. Dr., 104
Templeton, Mr., 77
Thelwall, John, 23
Thompson, General Perronet, 332
Thorp, Archdeacon, 15, 24, 56
Tooke, Home, 109, 362
Towneley, Richard, 331
Troughton and Simms, 61
Tyrwhitt, Rev. Robert, 109

TTLUGH Beg, 335
U Uncle Tom's Cabin, 182
Unitarians, 86, 342
University College, 34-38, 40, 50-53,

69-72, 85, 91-98, 102, 105-190,

336-361, 374
Mathematical So-

ciety, 282

School, 286

University Hall, 363, 374
University of London, 34-38, 50, 58,

91, 102. 222-228, 269, 363
Uranus, 127
Useful Knowledge Society, 51,54, 67,

113, 120, 126, 144

VAPEREAU, 397
Vaughan's Treatise, 249
Vellore, 1
Victa, 59, 75, 290

YOU

Vija Ganita, The, 269
Vince, Professor, 387, 301
Vivisection, 184
Vossius, 33, 75

WALEY, Jacob, 97, 101, 359
Wallis, Professor, 305
Warburton, M.P., 292, 312
Waring, Dr., 391
Warren, Dr., 328
Warren's blacking, 83
Wartmann, M.f 1 27
Watts, Dr. Isaac,
Weisse, Mr., 136

Weld's ' History of R. Society,' 257
Whewell, Rev. Dr., 12, 16, 113, 151,

158, 170, 172, 193, 198, 200, 207,

212, 228, 231, 290, 296, 302, 305,

315, 318,391
Winston, 199, 261
White, Professor, 69, 79
Wilkinson's 'Ancient Egyptians,' 119
William III., 261
Williams, Mr., 154

Miss, 3

Wingate's Arithmetic, 201

Wollaston, Dr., 217

Wollaston's Catalogue, 120

Woodhouse, 391

Woolley, Dr., 363

Wcollgar, J. W., 81, 120

Worcester, 2

Wordsworth, Christopher, 321, 363

Wright's ' Theory of the Universe,'

152
Wrottesley, Lord, 108, 138, 235, 237,

270, 333

- Hon. Mrs., 108
— Sir John, 235
Wyatt, Digby, 45
Wyvill, Christopher, M.P., 104

YOUNG, Dr. Thomas, 82, 145, 217
Young, John, 218
Young, Robert, 5, 217

t.OSDOH : PIUSTKD IIT

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INDEX

Abbey & Overtoil s English Church History 14

Abney's Photography 10

Acton s Modern Cookery 20

i Alpine Club Map of Switzerland 17

; Guide (The) 17

, A moss Jurisprudence 5

Primer of the Constitution 5

50 Years of English Constitution 5

Anderson's Strength of Materials 10

Armstrong's Organic Chemistry 10

Arnolds (Dr.) Lectures on Modern History 2

M i scellaneous Works 6

Sermons 15

r (T. ) English Literature 6

Poetry and Prose ... 6

Amotfs Elements of Physics 9

Atelier (The) du Lys

Atherstone Priory

Autumn Holidays of a Country Parson
Ayre's Treasury of Bible Knowledge ..,

Bacon's Essays, by Whately

Life and Letters, by Spedding

Works

18

18

7

20

5
5
5

Bagehot's Biographical Studies 4

Economic Studies 21

Literary Studies

Bailey's Festus, a Poem 18

Bain's James Mill and J. S. Mill 4

Mental and Moral Science 5

on the Senses and Intellect 5

22

WORKS published by LONGMANS 6- CO.

Bain's Emotions and Will 5

Bakers Two Works on Ceylon 17

Balls Alpine Guides *7

Baits Elements of Astronomy 10

Barry on Railway Appliances 10

. & Bramwdl on Railways, £c 13

Bauerman's Mineralogy 10

Beaconsfield's (Lord) Novels and Tales 17 & 18

. Speeches i

. Wit and Wisdom 6

Beckers Charicles and Callus 7

Beeslys Gracchi, Marius, and Sulla 3

Bingham's Bonaparte Marriages 4

Black's Treatise on Brewing 20

Blackleys German- English Dictionary 7

Bloxam's Metals 10

Bolland and Lang's Aristotle's Politics 5

Boultbee on 39 Articles 15

's History of the English Church... 14

Bourne's Works on the Steam Engine 14

Bawdier s Family Shakespeare 19

Brabournes Fairy-Land 18

Higgledy-Piggledy 18

Bramley-Moore' s Six Sisters of the Valleys . 18

Brande's Diet, of Science, Literature, & Art 1 1

Brassey's British Navy 13

Sunshine and Storm in the East . 17

Voyage in the ' Sunbeam ' 17

Bray's Elements of Morality . 16

Browne's Exposition of the 39 Articles 15

Brownings Modern England 3

Buckle's History of Civilisation 2

Buckton's Food and Home Cookery 21

Health in the House I2&2I

Bull's Hints to Mothers 21

Maternal Management of Children. 21

Burgomaster's Family (The) 18

Cabinet Lawyer 20

Culver fs Wife's Manual 10

Capes' s Age of the Antonines 3

. Early Roman Empire 3

Carlyle's Reminiscences 4

Gates' s Biographical Dictionary 4

Cayleys Iliad of Homer 19

Changed Aspects of Unchanged Truths ... 7

Chesneys Waterloo Campaign 2

Christ our Ideal 16

Church's Beginning of the Middle Ages ... 3

Colenso's Pentateuch and Book of Joshua . 16

Commonplace Philosopher 7

Comte's Positive Polity 4

Conders Handbook to the Bible 15

Conington's Translation of Virgil's yEneid 19
• - Prose Translation of Virgil's

Poems l8

Contanseau's Two French Dictionaries ... 7

Conybeare and Howson's St. Paul 15

Cotta on Rocks, by Lawrence n

Counsel and Comfort from a City Pulpit... 7

Cox's (G. W.) Athenian Empire 3

— — — — Crusades 3

. Greeks and Persians 3

Creighton's Age of Elizabeth 3

. England a Continental Power 3

.- — Papacy during the Reformation 14

Shilling History of England ... 3

. Tudors and the Reformation 3

Cresy's Encyclopaedia of Civil Engineering 14

Critical Essays of a Country Parson 7

Culleys Handbook of Telegraphy 13

Curteis's Macedonian Empire 3

Davidsons New Testament 14

Dead Shot (The) 19

De Caisne and Le Maout's Botany n

De Tocqueville's Democracy in America... 4

Deives's Life and Letters of St. Paul 15

Dixon's Rural Bird Life , 11^:19

Dun's American Farming and Food 21

Irish Land Tenure 21

Eastlake's Hints on Household Taste 13

Edmonds's Elementary Botany ; n

Ellicott's Scripture Commentaries 15

Lectures on Life of Christ 15

Elsa and her Vulture 18

Epochs of Ancient History 3

English History 3

Modern History 3

Ewalds History of Israel 15

Antiquities of Israel 15

Fairbairris Applications of Iron
. Information for

13

Information for Engineers 13

Mills and Milhvork 13

Farrar's Language and Languages 7

Fitzwygram on Horses 19

Francis's Fishing Book 19

Freeman's Historical Geography '

Froude's Caesar 4

English in Ireland X

History of England X

" ort Studies 6

Thomas Carlyle |

Gairdner's Houses of Lancaster and York
Ganot's Elementary Physics

• Natural Philosophy

Gardiner's Buckingham and Charles I. ...

•Personal Government of Charles I.

Fall of ditto

•Outline of English History ...

•Puritan Resolution

•Thirty Years' War

(Mrs.) French Revolution

Struggle against Absolute i

Monarchy

Goethe's Faust, by Birds 1

bySelss '

by Webb :

Goodeve's Mechanics

Mechanism

Gore's Electro-Metallurgy :

Gospel (The) for the Nineteenth Century . :

Grant's Ethics of Aristotle

Graver Thoughts of a Country Parson

Greville's Journal

Griffin's Algebra and Trigonometry

Grove on Correlation of Physical Forces...
Gwill's Encyclopaedia of Architecture

Hales Fall of the Stuarts

Halliwell-Phillipps s Outlines of Shake-
speare's Life

WORKS published by LONGMANS 6- CO.

23

Hartwig's Works on Natural History,

&C IO&IT

Hassall's Climate of San Remo 17

Haughtoris Physical Geography 10

Hayward's Selected Essays 6

Heer's Primeval World of Switzerland 1 1

Helmhollz's Scientific Lectures 9

Herschels Outlines of Astronomy 8

Hopkins s Christ the Consoler 16

Horses and Roads 19

Hewitt's Visits to Remarkable Places 19

Hullahs History of Modern Music n

Transition Period n

/fume's Essays 6

Treatise on Human Nature 6

Ihne's Rome to its Capture by the Gauls... 3

History of Rome 2

Ingelow's Poems 18

fagds Inorganic Chemistry 12

Vamesoris Sacred and Legendary Art 12

Jenkins Electricity and Magnetism 10

Verrold's Life of Napoleon i

Johnson's Normans in Europe 3

Patentee's Manual 21

'Johnston s Geographical Dictionary 8

Jukes s New Man 15

Second Death 16

Types of Genesis 15

KaliscJis Bible Studies 15

Commentary on the Bible 15

Path and Goal 5

Keary's Outlines of Primitive Belief 6

Keller's Lake Dwellings of Switzerland.... n

Kerts Metallurgy, by Crookes and Rohrig. 14

Landscapes, Churches, &c 7

Latham's English Dictionaries 7

Handbook of English Language 7

Lecky's History of England i

• European Morals 2

Rationalism 2

Leaders of Public Opinion 4

Leisure Hours in Town 7

Leslie's Political and Moral Philosophy ... 6

Lessons of Middle Age 7

Lewes' s History of Philosophy 2

Lewis on Authority 6

Liddell and Scott's Greek-English Lexicons 8

Lindley and Moore's Treasury of Botany ... 20

Lloyd' s Magnetism 9

Wave-Theory of Light 9

Longmans (F. W.) Chess Openings 20

Frederic the Great 3

• German Dictionary ... 7

(W.) Edward the Third 2

Lectures on History of England 2

St. Paul's Cathedral 12

London's Encyclopaedia of Agriculture ... 14

. Gardening ...ii & 14

Plants ii

Lubbock's Origin of Civilisation ii

Ludlow's American War of Independence 3

Lyra Germanica 16

Macalister's Vertebrate Animals ............ 10

Macaulay's (Lord) Essays ..................... i

— - - History of England ... i

- Lays, Illus. Edits. ...12 & 18
--- Cheap Edition... 18
--- Life and Letters ........ 4

- ; - Miscellaneous Writings 6

- - Speeches .................. 6

-- Works ..................... i

--- Writings, Selections from 6

MacCullagh'sTi'a.c\.s ........................... 9

McCarthy's Epoch of Reform ............... 3

McC^llloch's Dictionary of Commerce ...... 8

Macfarren on Musical Harmony ....... ..... 12

Macleod's Economical Philosophy ............ 5

--- Economics for Beginners ......... 21

-- Elements of Banking ............... 21

--- Elements of Economics ............ 21

- Theory and Practice of Banking 21
Macnamara's Himalayan Districts ......... 17

Mademoiselle Mori .............................. 18

Mahaffys Classical Greek Literature ...... 3

Marshman's Life of Havelock ............... 4

Martineau's Christian Life ..................... 16

- Hours of Thought ............... 16

- Hymns .............................. 16

Maunder s Popular Treasuries ................ 20

Maxwells Theory of Heat ..................... 10

May's History of Democracy .................. I

' History of England ..................... r

Melmlle's (Whyte) Novels and Tales ...... 18

4

Merivale's Fall of the Roman Republic ... 2

- General History of Rome ...... 2

- Roman Triumvirates ............... 3

- Romans under the Empire ...... a

Merrifields Arithmetic and Mensuration... 10

Miles on Horse's Foot and Horse Shoeing 19

- on Horse's Teeth and Stables ......... 19

Mill (].} on the Mind ........................... 4

S.) Autobiography .................. 4

Dissertations & Discussions 5

Essays on Religion ............ 15

Hamilton's Philosophy ...... 5

Liberty ........................... 5

Political Economy ............ 5

Representative Government 4

Subjection of Women ......... 5

System of Logic ............... 5

Unsettled Questions ......... 5

Utilitarianism .................. 5

Millard's Grammar of Elocution 7

Miller's Elements of Chemistry 12

Inorganic Chemistry IO&I2

Wintering in the Riviera 17

Milncr's Country Pleasures ii

Mitchells Manual of Assaying 14

Modern Novelist's Library 18

Monck's Logic 5

Monselts Spiritual Songs 16

Moore's Irish Melodies, Illustrated Edition 12

Lalla Rookh, Illustrated Edition.. 12

Morris's Age of Anne 3

Mozley's Reminiscences of Oriel College... 3

Mutter's Chips from a German Workshop. 7

Hibbert Lectures on Religion ... 16

Science of Language 7

Science of Religion 16

Selected Essays 6

WORKS published by LONGMANS 6- CO.

Nelson on the Moon 8

Ncvile s Horses and Riding 19

New Testament (The) Illustrated 12

Newmans Apologia pro Vita Sua 3

Nicols's Puzzle of Life n

Northcott's Lathes & Turning 13

Oliphanfs In Trust 17

Orsi's Fifty Years' Recollections 4

Our Little Life, by A. K. H. B 7

Overton's Life, &c. of Law 4

Owen's (R.) Comparative Anatomy and

Physiol ogy of Vertebrate Animals 10

i Experimental Physiology ... 10

(J.) Evenings with the Skeptics ... 6

Perry s Greek and Roman Sculpture 12

Payen's Industrial Chemistry 13

Pewtners Comprehensive Specifier 20

Piesses Art of Perfumery 14

Pole's Game of Whist 20

Powells Early England 3

Preece & Sivewright 's Telegraphy i o

Present-Day Thoughts 7

Proctors Astronomical Works 8&9

— - — Scientific Essays u

Public Schools Atlases 8

Rawlinsoris Ancient Egypt 2

Sassanians 2

Recreations of a Country Parson 7

Reeve's Cookery and Housekeeping 20

Reynolds' s Experimental Chemistry 12

Rich's Dictionary of Antiquities 7

Rivers' s Orchard House n

• Rose Amateur's Guide n

Rogers' s Eclipse of Faith and its Defence 15

Roget's English Thesaurus 7

Ronalds' Fly-Fisher's Entomology 19

Rowley's Rise of the People 3

Settlement of the Constitution ... 3

Rutley's Study of Rocks 10

Samuelson's Roumania 16

Sandars' s Justinian's Institutes 5

Sankey's Sparta and Thebes 3

Seaside Musings 7

Scott's Farm Valuer 21

Rents and Purchases 21

Seebohm's Oxford Reformers of 1498 2

Protestant Revolution 3

Sennet fs Marine Steam Engine 13

Sewelfs Passing Thoughts on Religion ... 16

. Preparation for Communion 16

. Private Devotions 16

Stories and Tales 18

Shelley's Workshop Appliances 10

Short's Church History 14

Smith's (Sydney] Wit and Wisdom 6

(Dr. R. A.) Air and Rain 8

(K. B.)Carthage& the Carthaginians 2

Rome and Carthage 3

( J.) Shipwreck of St. Paul 15

Southey's Poetical Works 19

& Bowles's Correspondence 4

Stanley's Familiar History of Birds n

Steel on Diseases of the Ox 19

Stephen's Ecclesiastical Biography 4

Stonehenge, Dog and Greyhound 19

Stubbs's Early Plantagenets 3

Sunday Afternoons, by A. K. H.B 7

Supernatural Religion 16

Swinburne's Picture Logic 5

Tancock's England during the Wars,

1765-1820 3

Taylor's History of India 2

Ancient and Modern History ... 3

(Jeremy] Works, edited by Eden 16

Text-Books of Science 10

Thome"s Botany 10

Thomson's Laws of Thought 6

Thorpe's Quantitative Analysis 10

Thorpe and Muir's Qualitative Analysis ... 10

Three in Norway 16

Thitdichum's Annals of Chemical Medicine 12

Tilden s Chemical Philosophy 10

Practical Chemistry 12

Todd on Parliamentary Government 2

Trench's Realities of Irish Life 6

Trevelyan'sLifeofFox i

Trollope's Warden and Barchester Towers 18

Twiss's Law of Nations 5

Tyndalls (Professor) Scientific Works... 9& 10

Unawares 18

Unwin's Machine Design 10

Ure's Arts, Manufactures, and Mines 14

Ville on Artificial Manures 14

Walker on Whist 20

Walpole's History of England i

Warburton's Edward the Third 3

Watson s Geometery 10

Watts' s Dictionary of Chemistry za

Webb's Celestial Objects 8

Weld' s Sacred Palmlands 17

Wellingtons Life, by Gleig 4

Whatelys English Synonymes 7

Logic and Rhetoric 5

White's Four Gospels in Greek 15

and Riddle's Latin Dictionaries ... 8

Wilcockss Sea-Fisherman 19

Williams' s Aristotle's Ethics 5

WillicKs Popular Tables 21

Wilson's Studies of Modern Mind 6

Woods Works on Natural History 10

Woodward' s Geology ir

Yonge's English-Greek Lexicons
Youatt on the

e Dog and Horse 19

Zellers Greek Philosophy

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