Fourier
The Man
and the
Physicist
John Herivel
JOSEPH
FOURIER
THE MAN AND
THE PHYSICIST
BY
JOHN HERIVEL
Sketch of Joseph Fourier as a young man by his friend Claude Gautherot. An ardent
Jacobin like his master David, Gautherot was one of a deputation of three who pleaded
for Fourier's release from prison before the Committee of Public Safety at the height
of the 'Great Terror' in Messidor Year II. (Original in possession of the Municipal
Library of Grenoble)
CLARENDON PRESS • OXFORD
I97S
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© OXFORD UNIVERSITY PRESS 1975
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means,
electronic, mechanical, photocopying, recording or otherwise, without
the prior permission of Oxford University Press
FOR ELIZABETH
AND IN
MEMORY OF MY PARENTS
access:
82074
GI976 T~
1 Q
CAi tbubcY
\-\\ r
PRINTED IN GREAT BRITAIN BY
WILLIAM CLOWES & SONS, LIMITED
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ACKNOWLEDGEMENTS
My primary debt is to certain institutions and individuals for the preserva-
tion of historical material. As regards persons, I am particularly aware of
my debt to C. L. Bonard and his son Alphonse who out of feelings of respect
and affection were responsible for preserving the magnificent set of early
letters from Fourier to Bonard which make up the essential kernel of the
biographical part of this book. As regards institutions, I am indebted to
the Bibliotheque Nationale, the Archives Nationales, the archives of the
Academie des Sciences, the Bibliotheque de l'lnstitut, the departmental
archives of Isere, Rhone, and Yonne, and the municipal libraries of
Auxerre, Grenoble, Lyons, Nantes, and Orleans. I am also indebted to
many individuals in these institutions for the help they so willingly gave
me to locate, copy, and, on occasion, photograph the various manuscripts in
question. Special mention, however, must be made of Madame Gauja and
her assistants in the archives of the Academie des Sciences, and of M. Hohl
and his assistants in the departmental archives of Yonne.
I am indebted to the Research Committee of the Academic Council of
the Queen's University of Belfast for generous grants over a period of years
towards visits to various archives and libraries in France, and to the Publi-
cation Fund for help towards the expenses of publication: to a succession
of assistants in the Library of Queen's University for inter-library loans,
and to Michael Henry for help in certain bibliographical matters. To
Anne Toal, Anne Dickson, Carol Powell, and Elizabeth Gregg for typing
and re-typing the various drafts of this book up to and including the final
version. I am also indebted to various colleagues: to Henry Barnwell for
helpful advice on the English translation of Fourier's letters to Bonard:
to Charles Gillispie, Henry Guerlac, Roger Hahn, and Pearce Williams
for their comments on an earlier version of Part I of this book. Also to
certain colleagues in the Societe des Sciences Historiques et Naturelles de
l'Yonne including Mssrs. Durr, Richard and, above all, Andre Casimir. To
M. Casimir's indefatigable help over a period of years I am indebted either
directly or indirectly for the location of a great part of the material on
which I have based my account in Chapter 2 of Fourier's part in the
Revolution in Auxerre.
L.
CONTENTS
List of plates xii
Abbreviations xii
Introduction 1
PART I
FOURIER THE MAN
i. Early life 5
1. Auxerre 5
2. St. Benoit-sur-Loire 8
3. Return to Auxerre 13
Notes 17
2. Fourier and the Revolution: Auxerre 27
1. The revolutionary vortex 27
2. The Orleans affair 30
3. Imprisonment of Messidor Year II 38
Notes 46
3. Fourier and the Revolution : Paris 51
1. The Normalien 51
2. Imprisonment of Prairial Year III 54
3. The terrorist 57
4. The Polytechnicien 61
Notes 65
4. Years of exile : Egypt and Grenoble 69
1 . Permanent secretary of the Cairo Institute 69
2. The prefect of Isere 76
3. Friendship with Bonard 82
Notes 85
5. Years of exile: Grenoble and Lyons 96
1. Extra-prefectorial duties 96
2. The first Restoration 104
3. Flight from Grenoble 106
4. Prefect of the Rhone IIO
Notes in
CONTENTS
6. Last years : return to Paris
The pension campaign
The Academicien
Friendships old and new
The Egyptian Society
Female relations
Last years
Notes
PART II
FOURIER THE PHYSICIST
7. Chronological account of researches in heat
Notes
8. Derivation and solution of the equation of motion of heat
solid bodies
1. Derivation of equations
2. Solution to equations
Notes
9. Expression for the flux of heat in solid bodies
Notes
10. Miscellaneous topics
1. Communication of heat between discrete bodies
2. Terrestrial heat
3. Radiant heat
4. Movement of heat in fluids
5. Papers not on analytical theory of heat
Notes
EPILOGUE
1. Fourier's achievement as a physicist
2. The influence of Fourier's analytical theory of heat
3. Fourier the man and the physicist
Notes
APPENDIX
LETTERS
1. Fourier to Bonard, May 1788
11. Fourier to Bonard, March 1789
in. Fourier to Bonard, September 1789
in
118
118
122
128
130
*34
136
138
149
159
162
162
171
177
180
190
192
192
197
202
205
206
206
209
216
229
238
243
250
253
CONTENTS
iv. Fourier to Bonard, October 1793
v. Fourier to administrators of the Department of Yonne,
January 1794
vi. Fourier to Bonard, January/February 1795
vii. Fourier to Bonard, March 1795
viii. Fourier to Bergoeing, June 1795
IX. Fourier to Villetard, June/July 1795
x. Fourier to Bonard, October 1795
xi. Fourier to Bonard, November 1797
xii. Fourier to Bonard, November 1801
xiii. Fourier to Bonard, November 1802
XIV. Fourier to Bonard, January 1804
xv. Fourier to Bonard, no date
xvi. Fourier to Bonard, no date
xvii. Fourier to an unknown correspondent, around 1810
xviii. Fourier to an unknown correspondent, around 1810
xix. Fourier to an unknown correspondent, around 18 10
xx. Fourier to Laplace, around 1808-9
xxi. Fourier to an unknown correspondent, around 1808-9
xxii. Fourier to Bonard, February 1810
xxiii. Fourier to Minister of the Interior, March 1815
xxiv. Fourier to Minister of the Interior, March 181 5
xxv. Fourier to sub-prefects of the Department of the Rhone,
May 1815
xxvi. Fourier to the Ministers of War, Police, and the Interior,
May 1815
xxvn. Fourier to the Minister of the Interior, March 1816
xxvi 1 1. Fourier to the president of the first class of the Institut.
Provenance of letters
BIBLIOGRAPHY
Primary sources :
Fourier
Other authors
Secondary Sources
Index
255
258
259
270
276
280
287
289
292
297
298
299
301
302
305
307
316
3i8
322
323
324
325
326
327
33i
333
334
334
335
336
337
343
LIST OF PLATES
A sketch of Fourier by Claude Gautherot
The interior of the Abbey St. Germain
The Cathedral St. Germain
A street in Auxerre
Portrait of Fourier by an unknown artist
Portrait of Fourier by Boilly
frontispiece
facing page
5
») >»
36
JJ 1)
37
J> )>
116
>> )»
117
ABBREVIATIONS
Aim. Yon. Almanac de V Yonne.
AN Archives Nationales, Paris.
Bib. Inst. Bibliotheque de l'lnstitut de France.
Bib. Mun. Bibliotheque Municipale.
BN Bibliotheque Nationale, Paris.
Bio. Univ. Biographie Universelle. With supplement 86 Vols, Paris, 181 1-
1862.
B.S.S.H.N.Y. Bulletin de la Sociite des Sciences Historiques et Naturelles de
V Yonne.
Gde. Encycl. Lagrande encyckpidie. Paris, 1885-1891.
Gd. Lor. Grand Larousse encyclopedique. With supplement 1 1 Vols.
Paris, 1 960-1 968.
Ind. Bio. Index Biographique des membres et correspondants de I'Academie
des Sciences. Paris, 1954.
J. Ecol. Poly. Journal de I'tcole Poly technique.
Proc. Verb. Proces verbaux des stances de I'Academie des Sciences, 1795-1835.
10 vols. Hendaye, 1910-1922.
INTRODUCTION
Joseph Fourier, one of the most outstanding theoretical physicists France
has produced, belonged to that very select band including Galileo, Newton,
Maxwell, Planck, and Einstein, who by the originality, importance, and
influence of their work effected revolutions in various branches of the
subject. Great achievements in theoretical physics inevitably presuppose
adequate mathematical powers. In Fourier's case these powers amounted
to genius and his influence in both pure and applied mathematics was per-
haps even greater than in the case of theoretical physics. Nevertheless his
activities and achievements by no means ended with mathematics and
theoretical physics. He led a most varied and interesting life. In the period
1793 to 1794 he played a leading part in the Revolution in his native town
of Auxerre, was imprisoned twice and was fortunate to escape with his life.
He was professor for a time at the Ecole Polytechnique where he succeeded
Lagrange, was a member of the Egyptian campaign and Permanent
Secretary of the Institute of Cairo. In Egypt under successive commanders
in chief, Bonaparte, Kleber, and Menou, he filled the most important
civilian administrative positions. He made an outstandingly successful
Prefect of Isere from 1802 to 18 15, and was Prefect of the Rhone for a time
following a dramatic encounter with Napoleon during the Hundred Days.
Later he was elected a member of the Academie des Sciences, and as one of
the two permanent secretaries of that body was at the centre of French
scientific life from 1822 until his death in 1830. Fourier would therefore
seem to present the ideal subject for that fully integrated biographico-
scientific study of which historians of science sometimes dream. Unfor-
tunately such a study is impossible in Fourier's case. In the first place,
during the years between 1804 and 181 1 which witnessed his most im-
portant and creative work in the subject, Fourier was a part-time physicist
only. It was Fourier the prefect who supplied the money for Fourier the
physicist to carry out his experiments and who somewhat miraculously
found the time and intellectual energy to develop his theories on top of a
host of important and onerous administrative duties. During all this time
Fourier resided outside Paris which was then, as now, the almost exclusive
centre of French scientific activity, and judged by the small number of
surviving letters his relations with his colleagues in the metropolis were
tenuous in the extreme.
What is more serious is that apart from one interesting but relatively
unimportant paper published in 1798 there is absolutely no evidence of
2 INTRODUCTION
Fourier having engaged in any serious theoretical physical researches be-
fore around 1804, that is for more than half of his total life span, and after
he had already had interesting careers in local revolutionary politics and
as the leading civilian administrator during the Egyptian campaign. Unless
one were to devote a whole chapter to the 1798 paper— which would
hardly be justified— the first serious technical discussion of Fourier the
physicist would come roughly halfway through the account of his life.
Moreover, as the greater part of all Fourier's work in theoretical physics
was contained in his 1807 memoir, once the topic of Fourier the theoretical
physicist had been broached it would be difficult to find any good reason
to discontinue it until the greater part of the story had been told. The net
outcome would be a biography in which roughly the first quarter up to
Fourier's appointment as prefect of Isere was purely biographical, the next
half purely scientific, and only the last quarter of mixed biographico-
scientific content, with the scientific part of much less importance than in
the preceding section. Faced with such an unconvincing and disconnected
pastiche it seemed preferable to make a clean division into two parts, Part I
on Fourier the man, and Part II on Fourier the physicist.
The biography of Fourier in Part I is the first to be based on all the
currently available documentary and other evidence. It contains much
new and hiterto unpublished material, especially on Fourier's part in the
French Revolution, his defence of his 1807 memoir, and certain aspects of
his. life on his return to Paris in 181 5. It would have been possible to pro-
duce a longer and more detailed biography of Fourier. The actual level of
detail has been decided with an eye to maintaining a rough balance between
the two parts of the present work. The resulting study of Fourier's life is
certainly not to be regarded as definitive, though I hope that it will be
accurate and reasonably complete, and that it will contribute ultimately to
a definitive study in French by one of Fourier's own compatriots.
Unlike the case of Fourier's achievements qua theoretical physicist —
which have been almost entirely neglected — his achievements and in-
fluence in pure mathematics have now been the subject of study by his-
torians of mathematics for almost a century, and I am only concerned in
Part II of the present work with Fourier the mathematician in so far as this
is necessary for an understanding of Fourier the physicist. A topic-by-topic
approach has been followed in Part II as being far superior to a chrono-
logical account as regards both presentation and insight afforded into
the development of Fourier's thought. This separation into individual
topics, though convenient, is nevertheless artificial, and to compensate for it
a detailed historical survey is given in Chapter 7 covering the whole sweep
of the development of Fourier's thought in the analytical theory of heat, a
subject in which almost all his work in theoretical physics was concentrated.
INTRODUCTION 3
While many of the facts presented in this chapter are not in themselves
new, no complete chronological account of the whole of Fourier's work in
the analytical theory of heat had been given before, and the present account
contains new material based on documentary evidence which is here pre-
sented for the first time. The first part of Chapter 8 considers the formula-
tion of the equations of motion for the various solids treated by Fourier,
beginning with the crucially important case of the thin bar. This part of
Chapter 8 is largely novel, whereas the second part, which deals with his
solutions to these equations, a topic to which much attention has already
been devoted, is given a much more summary treatment. Chapter 9 con-
tains new insight into the gradual perfection of Fourier's treatment of the
rate of flux of heat problem. Chapter 10 is devoted to a number of miscel-
laneous, unrelated topics which are simultaneously too important to be
omitted and yet in no case necessitate a sufficiently extensive treatment to
require separate chapters to themselves.
The division of this book into two parts should not be taken to imply
that I believe that Fourier's rich and varied experience of life was entirely
divorced from his work in theoretical physics, and in the last part of the
Epilogue, where a summing up is made of Fourier's career both as a man
and a savant, consideration is given to the question of possible interactions
between Fourier the man and Fourier the physicist.
It proved impossible to find an entirely satisfactory consistent policy for
the location of the rather large number of biographical notes. The solution
of putting these notes together in a separate appendix was rejected on the
grounds that they would then tend to be ignored both in the text and in the
letters. The alternative of giving a biographical note at the first occurrence
of the person concerned whether in the text or in the letters would have
involved many tiresome backward references in the letters which in any
case had to be given priority over the text on scholarly grounds. It seemed
best therefore to give biographical notes to all persons appearing in the
letters as part of the notes to the letters themselves, and to provide appro-
priate forward references to any appearances of the same persons in the text.
The lengths of these biographical notes were determined largely by the im-
portance of the persons concerned for the present work, as opposed to their
own intrinsic importance as historical figures. Thus Bonard, a mathe-
matician of no importance but the teacher and close friend of Fourier,
receives considerable space, whereas Francois Arago, Fourier's successor
as permanent secretary at the Academie des Sciences, and one of the fore-
most French physicists of his day, but neither a friend nor an enemy of
Fourier, is dismissed in a few lines, as are Ampere and Fresnel, and for the
same reasons. On the other hand, Laplace and Lagrange, important both
for themselves and for Fourier, receive lengthy notices. At the other
4 INTRODUCTION
extreme certain figures such as Robespierre and Danton are too well known
to require biographical notes, and Lazare Carnot only qualifies because of
his eminence as a scientist.
Belfast
September 1973
J.H.
PART I
FOURIER THE MAN
I
EARLY LIFE
1. Auxerre
Joseph Fourier, by turns novice, abbe\ Jacobin, secretary to the Institute
of Cairo, prefect of Isere under Napoleon and the First Restoration, and of
the Rhone for a time during the Hundred Days, permanent secretary of
the Academie des Sciences, and remembered today as the author of the
epoch-making Analytical Theory of Heat, was born on 21 March 1768 in
the ancient town of Auxerre. His father Joseph Fourier, a master tailor of
Auxerre, had been born in the small town of RaviUe in Lorraine where his
parents Simon and Anne Marie Fourier had been shopkeepers. Nothing is
known of the year in which Joseph left Lorraine, his reasons for so doing,
or why he ended his westward journey in Auxerre in preference to other
nearby towns such as Sens, Troyes, or Tonnerre. If he shared his famous
son's love of elegance and beauty he could simply have been attracted by the
town itself, magnificently situated on its height dominating the river
Yonne, with its many fine buildings including the ancient clock tower,
the Abbey St. Germain, and the Cathedral St. Etienne, all happily still
standing today. Or he could equally have been attracted by the people of
Auxerre themselves, by the striking beauty of its womenfolk and the sound
common sense, independence, and civic pride of its male citizens. For al-
though Auxerre had endured its fair share of the ills to which European
towns in general, and French towns in particular, were in the past heir-
barbarian invasions, plague and pestilence, occupation (though not de-
struction) by English forces for a time during the Hundred Years War, and
the attentions of Huguenot iconoclasts during the wars of religion in the
sixteenth century — it had escaped other major calamities including destruc-
tion by the Normans, 1 and by 1751 was as prosperous and independent a
town as the general situation and government of France at that time would
allow. Joseph Fourier might finally, and perhaps most probably, have been
attracted to Auxerre by the ecclesiastical standing of a town which had had
6 EARLY LIFE
its own bishop since Gallo-Roman times and which besides a great number
of parish churches, some of them very large and fine, also boasted the
magnificent gothic Cathedral St. Etienne.'and the even more ancient and
more famous Abbey St. Germain, the special pride of the town since its
foundation by St. Germain himself in the fifth century a.d. Such a rich and
powerful ecclesiastical establishment would necessarily afford tailors much
lucrative trade, in which Joseph Fourier might have expected some special
consideration in pious memory of his paternal great uncle, the Blessed
Pierre Fourier, 2 one of the leading figures of the Counter-Reformation in
Lorraine in the sixteenth and early seventeenth centuries. In any event,
Joseph Fourier's famous son Jean Joseph Fourier does seem to have been
treated with special consideration by the ecclesiastical authorities in
Auxerre, though this could simply have been due to his own intellectual
brilliance rather than the saintly connection on his father's side, a con-
nection, however, of which Fourier himself seems to have been very proud
in later life.
By his first wife Marie Colombat, whom he married in Auxerre in 175 1,
Joseph Fourier had three children. On her death aged thirty-six in 1757
he married, secondly, Edmie Germaine LeBegue by whom he had twelve
further children, the first born in 1759, the last in 1774. The ninth of these
children, and the subject of the present study, was born on 21 March 1768
and christened Jean Joseph 3 the same day. Edmie Fourier died on 26
October 1777 at the age of forty-two. At the time of her death she resided
in the Place de la Hotel de Ville, her husband and she having moved there
from their previous residence in the rue Notre Dame (now rue Fourier)
where Jean Joseph Fourier was born. Three days later, distraught by his
wife's death, Joseph Fourier abandoned his two youngest children, aged
three and four years, to the Foundling Hospital (Hotel de Dieu). Early
the next year (1778) he followed his wife to the grave. Jean Joseph was
therefore left an orphan a little before his tenth birthday.
Fortunately for Fourier, his parents' deaths seem to have caused little
interference with his education. He received his first lessons in Latin and
French in a small preparatory school kept by Joseph Pallais, 4 organist and
master of music at the Cathedral St. Etienne. Later, attracted by his
quick mind and winning ways, a number of local worthies 5 made it possible
for him to proceed from Pallais' school to the local Fcole Royale Militaire. 6
The ficole Royale Militaire of Auxerre was one of eleven such provincial
schools which had been given this special designation in 1776 on being
required to take each some fifty to sixty poor pupils of noble birth destined
for the army. 7 Each school was placed under the direction of a religious
teaching order: those at Soreze, Tiron, Rebais, Beaumont-en- Auge, Pon-
levoy, and Auxerre were under the Benedictine congregation of St. Maur, 8
EARLY LIFE 7
those at Vendome, Effiat, and Tournon were directed by the Oratorians,
and those at Brienne — Napoleon's college — and Pont a Mousson by the
Minimes and the Chanoines of St. Sauveur respectively. The reputations
of the various ficoles Royales Militaires naturally varied from one school
to another depending largely on their standings prior to their change in
status. Thus among the Benedictine schools, that at Soreze 9 was by far the
best known with a long-established reputation for progressive methods of
teaching and emphasis on science and mathematics, and of the remaining
schools that at Pont a Mousson was perhaps the most highly regarded.
However, a certain measure of uniformity was ensured by regular visita-
tions from a panel of inspectors — set up by the Minister of War in 1776 —
which included the Chevaliers Keralio 10 and Charbonnet, 11 and the
academiciens Legendre 12 and Bailly. 13 The presence of the last two indi-
cated the special importance attached to the teaching of science and mathe-
matics in the Fcoles Militaires by reason of the requirements of those pupils
who entered the specialist corps of artillery and engineers. The use of certain
textbooks, especially those of Bezout 14 and Bossut 15 in mathematics, also
helped to maintain uniform standards and to improve the levels of instruc-
tion by enabling more time to be devoted to teaching as opposed to lectur-
ing. 16
The declaration converting the college at Auxerre into an Fcole Royale
Militaire was dated 31 October 1776, though it was not registered by the
Parlement of Paris till 10 June 1777, 17 and the college — which had been
closed on 1 November 1776 — was reopened under its new title in October
of the same year. Under the Benedictines it soon regained a great measure
of its previous prosperity though the total number of pupils never exceeded
120 as opposed to the maximum of around 200 in the earlier college.
Fourier entered in 1780 18 and quickly distinguished himself by the happy
ease and quickness of his mind, being said always to have been at the head
of his class, so that he was soon received free as an internal student, the
Benedictines no doubt seeing in him a possible future recruit to their teach-
ing order. At first he is said to have shone most in literary studies, and
Challe relates how in his own school days at the College of Auxerre he
heard of Fourier's marvellous facility for composing verses, especially
those of a light and playful nature. At about the age of thirteen, however, a
growing passion for mathematics began to dominate all other interests.
According to both Cousin and Mauger he was at this time in the habit of
collecting candle ends by day in order to steal down to the classroom at
night and devote long hours to the study of mathematics in some sort of
store room or large 'cupboard'. One night the then deputy principal, Dom
Laporte, while making the rounds of the school saw a light through the
keyhole of the 'cupboard'. Fearing a fire he rushed in only to discover the
1
8 EARLY LIFE
young Fourier absorbed in mathematical problems. 19 History does not
relate if Fourier was thereafter prevented from burning his candles at both
ends.
In this way by the early age of fourteen he is said to have completed his
rhetoric and mathematics and to have become intimately familiar with the
six volumes of Bezout's course of mathematics. Mauger's account here is
confirmed by the records, 20 for at the prize giving on 29 August 1782
Fourier divided the prix d' excellence in Rhetoric and obtained a prix de
composition in mathematics. He also obtained first prize for singing, while
the next year he obtained first prize for Bossut's Mechanics. Thereafter
there is no trace of Fourier in the prize lists. It is known 21 that he had a
prolonged illness from December 1784 to November 1785, the result, per-
haps, of his excessive application to study, and possibly the beginning of a
tendency towards insomnia, dyspepsia, and asthma from which he suf-
fered much in later years.
According to Mauger, Fourier's success had now inspired a lively
interest among the notabilities in Auxerre, with the Benedictines and the
bishop, de Cice, 22 disputing the honour of being his patron. Eventually
he was placed in the College Montaigu at Paris by the beneficence and under
the protection of the prelate. There he repeated with distinction his
rhetoric course and took his philosophy, completing his studies at the early
age of seventeen. At this time, or possibly at the end of his studies at the
ficole Militaire, and before the long illness referred to above, he wished to
enter the artillery or the engineers, his application to the Minister of War
having the support of the then inspectors of the school including the mathe-
matician Legendre. Fourier's application, however, met with the crushing
reply that as he was not noble he could not enter the artillery (or the en-
gineers) 'even if he were a second Newton' ! 23 In any event, on returning to
Auxerre he at first assisted in the teaching of mathematics. He then de-
cided to enter the Church, and in 1787 proceeded to the Benedictine abbey
of St. Benoit-sur-Loire to prepare for his vows while acting as professor of
mathematics to the other novices.
2. St. Benoit-sur-Loire
In the course of the second half of the eighteenth century the regular
(monastic) orders in France found themselves in an increasingly precarious
position. Combining great wealth in land, buildings, and treasure with
steadily dwindling numbers of inmates, they provided a standing tempta-
tion to a government which was continually poised on the verge of bank-
ruptcy. This temptation became irresistible once the Revolution had broken
out, though during the immediately preceding decades many monasteries
had already been closed down as redundant. St. Benoit-sur-Loire had been
EARLY LIFE 9
spared, not, it may be surmised, because of its architectural splendours
— the famous basilica built between 1067 and 1 281 is today one of the finest
surviving examples of French Romanesque with little or no regional
influence. The reason was more probably the continued contribution of
the congregation of St. Maur to teaching and learning, or the peculiar
sacredness of an Abbey which had been one of the foremost shrines of
Christendom ever since the body and relics of St. Benedict had been trans-
ferred there from Monte Cassino in the seventh century, or even possibly
the long connection of the Abbey with the Crown in the Middle Ages —
hence the prefix 'royal' — when it had often acted as host to the Kings of
France at a time when royal chateaux such as those of Blois and Fountain-
bleau still remained to be built.
Nothing would be known of Fourier's life at St. Benoit from 1787-9
were it not for three letters written by him from there to his friend and
former Mathematics Professor at Auxerre, Bonard. 24 The period from the
beginning of the year 1787 when he entered St. Benoit and the first extant
letter to Bonard in May of the following year was hardly conducive to
meditation, teaching and research, even behind the high walls of the Abbey
St. Benoit. All France, not least Fourier who was invariably well-informed
of events in spite of an assumed indifference to external affairs, watched
with mingled hope and fear the dramatic incidents of the so-called 'Aristo-
cratic Revolution' in which much of the remaining authority of the
Crown was destroyed by the refusal of the notables to grant those reason-
able financial and fiduciary reforms, which alone could have prevented the
final bankruptcy of the King and the consequent convocation of the States
General. February 1787 saw the meeting of Calonne's notables, April
the replacement of Calonne by Brienne, August the revolt of the Parlement
and its exile to Troyes, September its recall, November the dramatic
imposition of taxes by the King and the exile of the Duke of Orleans
answered by the vote of Parlement against lettres de cachet in January, and its
declaration of fundamental laws of the realm to which the inevitable reac-
tion was the armed coup of 5-6 May. The transfer of many of the powers
of Parlement by the edict of 8 May was then the signal for riots in Paris and
elsewhere.
It was against this increasingly menacing situation that Fourier wrote to
Bonard on 22 May. 25 Ever an erratic correspondent, Fourier opens with
an elaborate apology for his dilatoriness:
On occasion others have graciously forgiven me too long a silence ; I hope for
the same indulgence from you. This accursed habit follows me everywhere, call
it what you will ; the fact remains that I like and infinitely esteem people, and yet
do not write to them. However, I only wrong myself, it is one pleasure the less
and you know that I have said goodbye to pleasures for the moment.
10 EARLY LIFE
Fourier continues with an account of his life at St. Benoit. The picture
he paints is not a very happy one. He is evidently a trifle uncertain if he
was not after all mistaken in entering St. Benoit 'against the advice of many
persons'. Having wished to devote himself to 'study and religion' he finds
himself immersed in the 'petty concerns' of studies, classes, arithmetic
lessons in which last he will soon be at 'fractions' ! 26 He modestly confesses
himself uncertain whether he will be able to live up to the high reputation
with which he entered the Abbey. He admits that one solid advantage
compared with Auxerre is the regularity of his life at St. Benoit including a
nightly eight hours' sleep. But this, alas, leaves him 'no time for living',
especially as his nights are not illuminated by Cartesian type dreams.
Above all he longs to hear news of his paper on algebra which Bonard had
evidently sent for an opinion to various Parisian mathematicians of the day
including a certain Montucla. 27 He would, he says, be 'enchanted' to know
the opinion of these mathematicians. He chats of various mathematical
matters including an elegant solution of some little problem in analysis
provided by Bonard whose memoir on a 'curve with double curvature'
he promises to return soon, and he challenges Bonard to find a way of
arranging 17 lines in a plane so as to give 101 points of intersection. As well
as news of his precious paper he also desires to be sent 'mathematical,
physical and astronomical news'. Has the Marquis de Condorcet 28 pub-
lished what he is said to have written on modern calculus ? Is it true that M.
de la Grange [Lagrange] and other academiciens employ eight months of
the year in visiting the Fxoles Militaires ? 29 He rightly cannot persuade him-
self to believe such a tall story. As to political news, he feigns his usual
indifference: 'those who fight each other tear themselves to pieces'. As an
earnest of this indifference he has surrendered his subscription to the
Journal of Geneva: 30 'the world and I' he declares somewhat pompously
'will have to grow several years older without knowing each other' — a
rash prediction to hazard in the France of May 1788, and in Fourier's case,
as it turned out, a singularly inaccurate one. At this point he concludes
with a pious prayer for the simultaneous epistolatory reformation of
Bonard and himself:
I end a letter which is already too long, you could revenge yourself by the
length of yours; there would also be a way of correcting my negligence, namely
by setting me an example of the opposite quality. I recommend you to try this
method, you will oblige him who with sentiments of esteem and attachment has
the honour to be
Your very humble and obedient servant,
Fourier.
Between this and Fourier's next extant letter, the descent to the Revo-
lution had gathered irresistible force. The disturbances of May 1788 had
EARLY LIFE
11
made way for insurrection in June, and opposition to proposed reforms
so widespread and formidable that Brienne had first retreated and then
retired, Necker had been recalled, Parlement reinstated, and the King's
credibility having been destroyed, battle was joined between the notables
and the third estate. Chaos was everywhere, in Brittany there was civil war,
and the whole country was full of a flood of conflicting pamphlets. Amid all
this turmoil the letters of convocation of the States General went out on
24 January, and throughout the land the three orders met to draw up their
lists of grievances and elect representatives for the States. It was against
this background — when the father Prior, Dom Charpentier, was absent
from St. Benoit to take part in the preliminary assembly of clergy at
Orleans, 31 when, as Fourier so vividly puts it: 'Everything resounds with
the news of the day' — that he wrote to Bonard on 22 March 1789. 32
Once again Fourier affects a tone of lofty, even callous indifference to
events outside the Abbey. It is not to be expected that he, Fourier, will dis-
cuss such matters with Bonard any more than the accidents caused by a
serious flooding of the Loire, which 'frightened many, and did harm to
some, but to me neither one nor the other'. Judging by this attitude it
might be surmised he has been reading the works of the Stoic philosophers.
In fact, apart from a 'miserable copy of Montaigne' there is evidently an
almost total lack of books in the Abbey :
Is it not to be condemned to ignorance not to be able to read any other books
but one's own? It is a privation not to be consoled by all philosophy. I have
no books to read but a miserable copy of Montaigne lacking certain pages
which I am reduced to guess at; I busy myself a little with Greek; you can well
believe that it is for reading Euclid and Diophantus rather than Pindar and
Demosthenes.
As to his health, it has not been too good and for the last five months
he has constantly had a 'weak stomach and difficulty in sleeping'. This
sets him thinking that he has bought very dearly some 'rather fragile
knowledge' not easily marketable. As for his mathematical studies, they,
too, evidently hang fire :
Alone and without help one can meditate but one cannot make discoveries;
often by flying the world one becomes better, but not wiser; the heart gains
and the mind loses.
Not that he has lost faith in the paper on algebra sent to Paris. On the
contrary he is confident that his methods are the 'true methods' and the
Italian ones 'absurd and opposed to all that is most certain in analysis'. So
that it is 'impossible that a genuine mathematician should reject such
powerful evidence'. In spite of all this no answer has yet come from Mon-
tucla whom Fourier suspects of having lost interest in 'learned analysis'.
I
12 EARLY LIFE
Having referred to an incorrect enunciation of a theorem in another memoir
on numerical equations — to be presented in person by Fourier to the
Acad6mie des Sciences the following November — and having somewhat
pompously cautioned Bonard that 'one must not replace errors by errors'
Fourier concludes :
Forgive me the trouble this letter has caused you, all the disorder and bitter-
ness you will find in it. If you only knew the effect of a passion for the truth
when it is constrained to be sterile, and all the treachery which ungrateful truth
reserves for her devotees. But if it is hard to suffer her caprices, it is very pleasant
to complain of them. And who would grudge me this pleasure? For me pleasures
are so rare.
From this passage it is evident that in spite of the lack of books at St.
Benoit, Fourier had somehow managed to come by the works of Jean-
Jacques Rousseau, provided, of course, he had not already read them at
Auxerre. But if one dismisses the tone of this passage as being due more
to the prevalent climate of opinion than to Fourier himself, it is impossible
to doubt the genuine anguish expressed in the postscript to the letter :
Yesterday was my 21st birthday, at that age Newton and Pascal had [already]
acquired many claims to immortality.
One further letter 33 to Bonard from St. Benoit has survived. Taken up
entirely with the lack of news about the paper on algebra supposedly
communicated to Paris by Bonard and the latter's failure to reply to his
last letter, it provides a good example of Fourier's ability to bring pressure
to bear on recalcitrant correspondents :
On this occasion I shall no longer complain of your silence ; I must declare
myself since you have done so. This correspondence with which you yourself
had charmed me was no more than a pleasing chimera; but what is there that
cannot be consoled by time and reason ? . . .
... If you were to put between your reply and my letter too long an interval I
might perhaps lose the opportunity which is going to present itself to send what I
have written to Paris.
Judging by the lack of any reference to the great events which were
sweeping away the old order of things in France, Fourier would seem to
have been somewhat indifferent to the Revolution. But if this was really the
case — which may be doubted — he was unable long to escape its conse-
quences. On 28 October the Constituent Assembly took the first step
towards the abolition of monastic orders by a decree forbidding the taking
of any further religious vows. This was followed on 2 November by a
decree putting the property of the regular congregations at the disposal of
the State. Finally, on 13 February 1790 the suppression of all religious
EARLY LIFE
13
orders was decreed in principle with the striking exception of Fourier's own
congregation of St. Maur which was deemed to have deserved well of the
State by its virtues and love of letters. Sometime earlier, however, Fourier
had said farewell to St. Benoit and returned to Auxerre to take up a posi-
tion as assistant to Bonard in the teaching of mathematics at the Fxole
Royale Militaire.
3. Return to Auxerre
Accounts differ as to when Fourier left St. Benoit. According to Cousin 34
it was just before the outbreak of the Revolution, whereupon he is said to
have discarded his Benedictine habit without regret, having in any case
never taken his vows. However, from the letter of September 1789 to
Bonard it appears that Fourier was at that time still at St. Benoit. Challe 35
is more circumstantial. According to him Fourier was preparing to take
his vows in Auxerre on 5 November 1789, when news had reached the
town the previous day of a provisional order 36 of the Constituent Assembly
prohibiting the taking of any further such vows. Fourier was thus unable
to take his vows at that time, and never did so subsequently, the Assembly
later confirming the provisional order, making it definitive and final. 37
Mauger 38 has still another version, according to which the Prior of St.
Benoit, foreseeing the imminent suppression of all religious orders, ad-
vised Fourier to take his vows since he would then be entitled to a pension
if the orders were suppressed! Fourier's refusal then provided the first
recorded example of his disinterestedness.
There are, finally, two hard pieces of information about Fourier's
whereabouts towards the end of 1789 and the beginning of 1790: in the
first place he is known 39 to have been in Paris on 9 December 1789 to read a
paper on algebraic equations to the Academie Royale des Sciences, pre-
sumably after he had left St. Benoit. In the second place there is the account
of Fourier himself in a declaration of 30 April 1790:
J. B. J. Fourier aged 22 years declares that having completed his noviciate at
St. Benoit-sur- Loire it was in respect of the decree of the Assembly National
that he did not pronounce his vows, but that called to Auxerre to profess rhetoric
and mathematics he has the intention of remaining in the congregation of St.
Maur. 40
This declaration of 30 April 1790 was on the occasion of a visitation the
same day to the Abbey St. Germain by two representatives of the muni-
cipality of Auxerre sent to enquire the intentions of the inmates in the
light of the decree of 13 February relating to the suppression of religious
orders. Of the remaining eleven members of the ancient Abbey, nine,
I
14 EARLY LIFE
including 'the novice Fourier', declared their intention of observing their
vows in the Congregation of St. Maur. The Benedictines thus continued to
direct the college of Auxerre which now had the double title College
Nationale and Ecole Royal Militaire.
Later the same year Fourier appears as the Abbe Fourier in charge of
the third class at the college on a list 41 of teachers submitted to the munici-
pality by the Principal, Dom Rosman. 42 In addition to the teaching of
rhetoric and mathematics referred to in the declaration of 20 April 1790,
Fourier is said later to have filled the chairs of history and philosophy, 43
and to have given special courses in astronomy for advanced pupils. 44
He was active, too, in the town where he was the first president of a
'Society of Emulation'. 45
It is uncertain 46 whether Fourier continued to teach in the college at
Auxerre during the whole period from April 1790 till his appointment or
reappointment in June 1793, following the dismissal of all the so-called
professor-priests including the Principal, Dom Rosman. In any case,
after the declaration of 30 April 1790 life seems to have continued at the
college much as before apart from a new plan of studies 47 — said to have
been drawn up by Fourier himself— submitted to the municipality by Dom
Rosman, the principal, sometime in the year 1790. In the early part of 179 1
the Abbey was in danger of being sold as a result of the decree placing all
ecclesiastical property at the disposal of the State. To avert this calamity
Dom Rosman petitioned the local authorities on 20 March 1791 for per-
mission to transfer the college and Ecole Militaire to the Abbey, to which a
number of pupils had already been transferred in 1788 when the buildings
of the old College d'Amyot had become inadequate. The petition was
granted, and on 31 July 1791 the commission of dispossession of ecclesiasti-
cal properties allowed the building of the Abbey to be turned over to the
use of the pupils, the church being preserved as a public oratory and a
chapel of the college.
In the same year there was a visitation of the college by a commission of
the municipality, possibly in connection with Dom Rosman's petition.
Once again, as on the occasion of an earlier visitation in 1783, the financial
affairs of the college were found to be in a chaotic state :
No order in the accounts of which the greater part are neither made up nor signed.
Gaps in almost all matters relating to accounts. Loose leafs for the receipt of
pensions in a state of disorder. In short an almost inextricable chaos. 48
But a wise municipality turned a blind eye to such unimportant failings,
and the college continued its pedagogically useful and successful life.
A commissioner 49 of the local directory who visited the college on the
morning of 30 October 1792 reported favourably on its physical state, the
EARLY LIFE
15
health of the pupils, and the education received by them. Everything was
clean and proper, in an excellent state of organization, the air salubrious,
the children well-fed and strong and healthy for the most part. In the
classes there was a free, progressive, and liberal atmosphere, the old written
exercises having largely been replaced by discussion. The standard of
teaching was particularly striking in mathematics and physics, and the
report even deplored the tendency to drive out Latin and other classical
studies to make way for the mathematics so much in demand at the time by
the parents of pupils. Latin, it was pointed out, was important for teaching
precision of thought and an understanding of human nature, and it would
be a pity if it were to be reduced too much.
Reading the commissioner's report on his visit to the school on 30
October 1792 and his apparent unconcern at the fact that the majority of
the teaching staff at the school were in holy orders, albeit of the juring
variety, it is difficult to believe that some two months before hundreds of
priests had been massacred in the prisons of Paris. Not that Auxerre had
escaped entirely unscathed from the shock-wave emanating from Paris
after the fall of the Throne on 10 August. On the nineteenth of that month
there had been a riot in the town in the course of which two innocent men
were murdered by a mob in the Hotel de Ville. 50 But this was fortunately
an isolated incident. These seem to have been the only two violent deaths
in Auxerre directly attributable to the Revolution, and whatever the reason,
good fortune, lack of involvement in the Federalist revolt in 1793, or the
wise moderation of Nicolas Maure, 51 deputy for the district of Auxerre at
the Convention, the town was never disgraced by the guillotine, nor were
any of its citizens brought before the Revolutionary Tribunal.
However, if there was little or no bloodletting in Auxerre during the
Revolution this is not to say that the town was in any way isolated from
the events in the rest of the country, something which was in any case only
possible, if at all, for a few odd individuals or families in a few corners of
the country. In fact the local Society of the Friends of the Republic (later
the Popular or Patriotic Society) was one of the best known and most
active and most militant provincial clubs in the country. It appears 52 that
this society had been founded by that curious and enigmatic figure,
Michel Lepelletier, 53 one of the so-called martyrs of the Revolution. When
Lepelletier arrived in Auxerre in the autumn of 1791 with the painter
Claude Gautherot 54 in tow as his secretary and general factotum, he found
there a Society of the Friends of the Constitution which seems to have
been established towards the end of 1790, and which continued in existence
under the same name in 1791 and 1792. The democratic ideas of Lepelletier
had need of a more efficacious, wider and less elevated base for their propa-
gation than that provided by the well-to-do members of the essentially
16
EARLY LIFE
bourgeois Society of the Friends of the Constitution. As a result of the fatal
self-denying ordinance of the preceding Constituent Assembly, Lepelletier
was not eligible for election to its successor the Legislative Assembly, and
he wished instead to obtain for himself a high post in the departmental
administration to which he already had an aristocratic claim through his
vast possessions in St. Fargeau, one of the regions of the department of
Yonne. In this he was eminently successful, being elected president of the
departmental administration, a position which he then continued to occupy
till his election to the Convention in September 1792. The wider base
sought by Lepelletier and Gautherot could only be provided with the
support of 'little people' including artisans, shopkeepers, workmen, and
small-salaried people who lacked the necessary financial means and leisure
to belong to the Society of the Friends of the Constitution. There resulted
the foundation of a new society, the Popular or Patriotic Society of Auxerre,
or the Society of Friends of the Republic — the title was somewhat flexible
— of which Gautherot continued to be the leading light until 9 Thermidor
when he discreetly slipped away to Paris never to return to Auxerre again.
The Popular Society of Auxerre was dynamic, definitely sans-culotte and
even verging towards Hebertism, for if it could not be regarded as an organ
of Hebert in the strict sense, at least it was enthusiastic for the sort of
political, social, and economic ideas found in Hebert's infamous magazine
the Pere Duchesne. Thus when the question of the King's trial began to
agitate the country the Society at Auxerre sent a passionately worded
address 55 to the Convention demanding the trial of Louis:
Legislators.
We are disturbed to see that having received the express desire of the people
united in all the debates of the Republic that Louis should be tried, the National
convention has decreed nothing in regard to the matter. Deputies have recog-
nized the justice of this demand, and have promised to carry it out. Why have
they not done so ? This is what we ask you to explain.
On the day of 10 August the will of the people expressed itself in this unani-
mous cry: that Louis should pay the penalty of his heinous crime. Your decree
on the Republic implies a second one which demands the beginning of the trial
of this traitor ...
Gautherot was one of the more prominent signatories to this address. There
was no trace, however, of the signature of either Bonard or Fourier. In
Bonard's case the absence of his signature was possibly due either to
moderation or prudence, since he was signatory to another less inflamma-
tory address 56 of the Society to the Convention a few days later on 15
October. As for Fourier, it seems that his entry onto the local revolutionary
scene did not occur until February 1793.
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17
Notes
1. Although the Normans penetrated the Yonne as far as Auxerre in 887, 889,
and 911 they never succeeded in capturing the town. But they laid waste the
surrounding countryside and pillaged the abbey of St. Marien.
2. Pierre Fourier (1565-1640). Known as the good father of Mattaincourt, he was
born at Mirecourt, in Lorraine, and educated at the College of Pont a Mousson.
He became Canon in the Abbey of Chaumousey, and was ordained in 1589
but was later ordered to return to Pont a Mousson to become learned in patristic
theology. Like his great-grand-nephew he had an exceptional memory and
knew the summa of St. Thomas Aquinas by heart. In 1597 he was appointed
parish priest of the 'corrupt' parish of Mattaincourt where he soon restored
morals and religion. He also looked after the temporal interests of his flock
founding a kind of mutual-help bank. In 1598 he founded the congregation of
Notre Dame for teaching poor girls, and in 1621 he undertook the reformation
of the regular canons in Lorraine which led to the formation in 1629 of the
Congregation of Our Saviour. On account of his attachment to the House of
Lorraine he was driven into exile at Gray where he died in 1640. In 1730 the
Pope Benedict XIII published a decree for his beatification, and in 1897 he
was canonized by Pope Leo XIII. (Cath. Encycl. : these are lives of Pierre
Fourier by Bedel, Derreal, and Vuillemin).
3. In the baptismal records of the Parish of St. Regnobert, Auxerre, Fourier is
entered as Jean Joseph. When Champollion-Figeac first knew him in Grenoble
he employed the first names Jean Baptiste Joseph. Later he employed Joseph
only.
4. Born around 1706, Joseph Pallais was appointed organist of the cathedral
St. Etienne in 1734. He was still in service at the time of the profanation of the
cathedral in 1790. Pallais was a friend of Jean-Jacques Rousseau to whom he
had taught the first elements of music, and whom he is supposed to have hidden
in Auxerre when Rousseau was fleeing from Montmorency. His contribution
to Rousseau's musical education prompted the directory of the department to
award him a retirement pension of 800 livres per annum, a sum far in excess of
his salary as an organist. Pallais was the author of Les Principes d'accompagne-
mentpour Vorgane et le claireau (Gardien; Mauger; Quantin.).
5. According to Mauger (p. 1) it was a certain Madame Mouton and several other
generous persons in Auxerre who enabled Fourier to continue at Pallais's
school when he had become an orphan and then to enter the ficole Royale
Militaire as an external pupil. Cousin (p. 2) refers to a 'good lady', — evidently
the Madame Mouton of Mauger's account — who recommended him to the
Bishop of Auxerre (De Cice) who then had him placed at the Ecole Royale
Militaire.
6. The educational tradition in Auxerre was a very ancient and honourable one:
it extended back in unbroken succession as far as the fifth century A.D., and
included a period in the ninth and tenth centuries when Auxerre was the fore-
most centre of learning in France with outstanding teachers such as Heribald,
Herac, and Remie, the last named being the renovator of the school of Chartres.
After their period of brilliance in the ninth and tenth centuries the schools of
Auxerre suffered a steady decline as the centre of French learning shifted back
first to Chartres, then to Paris, and by the middle of the sixteenth century little
remained of their former glory beyond the title Grandes Ecoles of the local
college where the humanities were taught by a principal and four professors. In
18 EARLY LIFE
the second half of the century a new college was built through the munificence
of Jacques Amyot (1513-93) Bishop of Auxerre, one of the most brilliant
scholars of the French Renaissance whose translation of Plutarch played an
important role in the creation of written French. Amyot had originally intended
his college to be under the Jesuits whose education was at that time increasingly
in demand by the French middle-classes. But the formation of the League
under the instigation of the Jesuits against the King Henry III whom Amyot
had taught and later served as grand almoner, and whom he greatly loved,
changed his attitude to the Jesuits and their direction of his school. When
Amyot died in 1593 after cruel persecutions and almost a prisoner in his own
see — for Auxerre had sided with the League against the King — his kinsmen
tried to let the new building against the wishes of the municipality. The ensuing
law suit dragged on for many years until it was ultimately settled by the
Parlement of Paris in favour of the town, and in 1622 the Jesuits at last took
over control of Amyot's college. To the original teaching of grammar and the
humanities philosophy was added in 1651, but the school never seems to have
been very prosperous under the Jesuits and at the time of their expulsion from
France in 1762 it had no more than fifty-five pupils.
Following the expulsion of the Jesuits the college at Auxerre was taken over
by a mixed band of teachers, lay and clerical, under whose direction it had
soon attained a state of prosperity far beyond anything enjoyed previously, the
number of pupils having risen to 200 by 1765. The college continued to
flourish until 1772 when it underwent a sudden and catastrophic change of
fortune following the victory of the pro-Jesuit party in Auxerre over the
opposing Jansenist party which had been particularly strong in Auxerre as a
result of the long reign of the universally admired and respected pro-Jansenist
de Caylus, Bishop of Auxerre from 1704 to 1754. Attempts by the strongly pro-
Jesuit Bishop de Cice to have all remaining pro-Jansenist professors at the
college dismissed and even sent to the galleys were ultimately unsuccessful.
But the disturbance in the life of the college was very great and it never entirely
recovered its earlier prosperity under the Benedictines, the total number of
pupils never exceeding 120 as opposed to a maximum of around 200 in the
earlier college (Gde. Encycl; Challe (1); Moiset).
7. This move had followed the closing by the Minister of War, the Count of St.
Germain, of the Ecole Royale Militaire in Paris. Opened in 1753 to provide
education for up to 500 pupils of noble birth with insufficient means to obtain
their education elsewhere, it had been closed by St. Germain because of the
small number of its pupils who had entered the artillery or engineers in spite of
a large outpouring of funds, and also because it had never been possible to
take more than about half of the 500 pupils originally envisaged, once again
on the score of expense. St. Germain evidently hoped that the new system of
Ecoles Royales Militaires scattered over the country would provide a cheaper
method of catering for a larger number of pupils. He was concerned too with
the somewhat exclusive attitudes engendered by the school in Paris with its
pupils made up entirely of the sons of the nobility. He hoped that in the new
schools these pupils would learn to mix with others of less distinguished pedi-
gree. Evidently the spirit of the Enlightenment had even penetrated the corri-
dors of the Ministry of War. St. Germain seems to have been genuinely
interested in the educational, physical, and moral well-being of the military
pupils. Glaring gaps in the most elementary aspects of education had shown
EARLY LIFE
19
up in the French officer classes during the Seven Years War. These had to be
remedied. Special attention was to be paid to those subjects which would later
be important to officers, especially in the artillery and the engineers. Room had
therefore to be found for more mathematics, if necessary at the expense of
Latin. But St. Germain's plan sought to avoid falling into the opposite extreme
of excessive and self-defeating application to studies. It was essential to pay
attention to the physical well-being of the pupils. Suitable sports were to be
encouraged, and excessively long periods of enforced stillness in class were to
be forbidden or at least reduced. No aspect of the pupils' well-being was
neglected even down to their clothes which were to be 'large and loose in order
not to impede movement' and care was to be taken about cleanliness and
appearance. Pupils were to be allowed the greatest possible freedom in recrea-
tion hours 'for youth has need of movement, and to form men capable of action
they must not be too restricted in infancy'. Finally, pupils were never to be
cruelly used either verbally or by corporal punishment.
If St. Germain's noble plan of education for the pupils of the Ecoles Royales
Militaires must have remained — like all such plans — something of a pipe dream
in the inevitable absence of a sufficient number of enlightened teachers to carry
it into effect, nevertheless it must have helped to soften some of the more
objectionable features of the old, spartan, system of education which then ob-
tained in France and elsewhere. In the case of those colleges under the direction
of the congregation of St. Maur — as at Auxerre — it reinforced attitudes and
methods which had already been put forward some twenty years earlier by
Dom Fougeras at a general chapter of the Benedictines at Marmontiers in
1758 (Challe (1); Moiset; Taton (3)).
The Benedictine teaching congregation of St. Maur, under whose control the
Ecole Militaire at Auxerre had been placed, had been founded by letters patent
of 1 61 8 confirmed by papal bull of 162 1, and had been effectively instituted by
Dom Gregoire Tarisse (born Cassenon 1571) who gave the new congregation
its solid foundation and first lustre. This was later increased by Dom d' Archery,
the founder of the Benedictine historical school, whose first and best-known
pupil was Dom Mabillon. The centre of the congregation was in Paris, the
residence of the superior general being in the Abbey of St. Germain des Pres
which also housed the magnificent library of the order. St. Germain des Pres
thus ultimately became the centre of a vast co-operative work of historical
research leading to the gradual publication of imposing scholarly works such as
Gallia Christiana (1715-1725) and Histoire Litteraire de la France (1733-1768).
Fourier's strong historical sense was no doubt derived from the Benedictines.
The considerable destruction of records and manuscripts of all kinds during
the Revolution rendered the historical labours of the Benedictines doubly
valuable. The members of the congregation of St. Maur moved freely from one
Benedictine college to another, one reason, no doubt, for the active and pro-
gressive pedagogical attitude of the congregation. This became especially
marked in the second half of the eighteenth century particularly after the
expulsion of the Jesuits from France in 1762. The most progressive centre
seems to have been in Soreze beginning with the advent of Dom Fougeras as
principal in 1757. Some idea of his enlightened attitude to education can be
gleaned from the following extract from a memoir presented by him to the
general chapter of the Benedictines at Marmontiers in 1758 :
In a well-regulated college amusement should be mingled with work; it is essential
20 EARLY LIFE
that children acquire the habit of work without becoming disgusted by it: and one
may avoid this happening by allowing them to distract themselves by some quarters
of an hour of real recreation.
Other indications of the progressive attitude of the teaching at Soreze and at
other colleges of the congregation of St. Maur were the reduction, and in certain
cases abolition, of Latin, the introduction of 'courses' in which pupils were free
to follow subjects of their own choice, and also the emphasis given to the
teaching of mathematics and science. This last tendency had already manifested
itself before 1776, but became more marked with the arrival of pupils destined
for the artillery and engineers for whom these subjects were of much greater
importance than for the average pupil (Gde. Encycl. Taton (3)).
9. A seminary or college was opened in the priory of Soreze in 1683. It was closed
under various pretexts in 1722 and was not reopened again until 1757. The
then prior, Dom Fougeras, was too daring in his reforms and was recalled in
1760. But on the insistence of parents his successor was ultimately forced to
reintroduce some of the measures of his predecessor, and under Dom Des-
paulx, prior from 1766 to 1769 and 1 771 to 1790, the enlightened reforms of
Dom Fougeras were completely reinstated. By 1767 the college had become
famous throughout France and beyond. In that year there were 220 pupils of
whom seventy-two were foreigners. In 1789 there were no fewer than eighty
Americans at the school. In 181 2 the number of pupils was 223 of whom only
six were Americans and eleven Spaniards, but by 1 8 1 6 the total number of pupils
had increased to 410, forty-three being Americans and eighteen Spaniards.
In 1790 the school was split over the question of the oath of allegiance to the
State ; twelve of the original total of about twenty-four teaching staff refused to
take the oath, while five swore it with reservations. Dom Despaulx left at this
time and ultimately there remained only 4 brothers including Francois Ferlus
under whose guidance the school managed to survive the storms of the Revo-
lution. Some idea of the standing of the school can be seen from the fees which
were 700 livres per annum compared to 500 at the school attended by Na-
poleon at Brienne, while the fees at other colleges of the Congregation of St.
Maur were considerably less. Soreze had many distinguished pupils; as Ferlus
said during the Revolution: 'the pupils of Soreze people all the corps of en-
gineering, artillery, and marine and all classes of society which require extended
knowledge'. Between 1805 and 1840 the school sent no fewer than 113 pupils to
the Fxole Polytechnique (Combes; Taton (3)).
10. Keralio, L. F. G. Chevalier de (1731-93). After service in the army he took up
writing and acted for a time as tutor to the young Don Ferdinand of Parma in
company with the philosopher Condillac. He was appointed professor of
fortifications at the old Ecole Militaire in Paris where he was very successful. A
supporter of moderate reform at the time of the Revolution he was appointed a
commandant of a battalion of the national guard in Paris. He was a member of
the Academie des Inscriptions and was one of the editors of the Journal des
Savants up to its suppression in 1792 (Bio. Gen.; Bio. Univ.; Gde. Encycl.).
ii. Charbonnet, P. M. (1733-1815). He entered the Church and became professor
at the College Mazarin. In 1762 he carried off the prize of master of arts at the
University of Paris of which he was elected rector in 1781. At the Revolution
he took the oath of allegiance to the state and occupied several municipal
positions. He was chosen to oversee the imprisonment of the royal family in the
Temple. Opinions have differed on the manner in which he carried out this
EARLY LIFE
21
delicate mission. On the creation of the Ecoles Centrales he was appointed
professor at Aube, and later at the College Charlemagne where he continued to
teach till his retirement (Bio. Gen.; Gde. Encycl.).
12. See below Letter III, n. 4.
13. Bailly, J. S. (1736-93). By 1760 he had become immersed in his true vocation of
astronomy. He entered the Academie des Sciences in 1763 and ran for the
position of permanent secretary with the support of Buffon, but was defeated
by Condorcet who was supported by d'Alembert. His great Histoire de I'Astro-
nomie appeared between 1775 and 1787. In 1777 he made the acquaintance of
Benjamin Franklin who appreciated his taciturnity and whose friendship and
counsel prepared Bailly for his role in the Revolution. In 1783 he entered the
Academie Francaise. He was elected first deputy of Paris to the States General,
and as president of the National Assembly guided the Revolution through its
first vital stages. He presided over the great day of the Tennis Court, claiming
the right as president to be the first to take the oath. He was elected the first
mayor of Paris on the same day (15 July 1789) as Lafayette was put in command
of the Garde Bourgeoise (later National Guard). In spite of his glorious part in
the early days of the Revolution he rapidly lost his popularity with the people of
Paris as a result of his support for the King after the flight to Varennes, and
even more for his part in the death of the republican 'martyrs' of the fusillade
of the Champs de Mars on 17 July 1791. He resigned his position of mayor in
November 1791 and retired to Nantes. Later he moved to Melun to be near
his friend Laplace. Towards the end of June 1793 he was arrested and later
condemned to death by the Revolutionary Tribunal and guillotined (Bio.
Gen.; Gde. Encycl.; see also Brucker, Hahn (2), and Smith).
14. Bezout, E. (1730-83). He became a member of Academie des Sciences in 1758.
In 1763 he was appointed examiner of the gardes de la marine, and was charged
by the minister to compose a suitable textbook for the use of pupils. There
resulted his Cours de mathematiques a I'usage des gardes de la marine (4 Vol.,
Paris 1764-7). In 1768 he succeeded Camus as examiner for the artillery. His
Cours complet de mathematiques a I'usage de marine et de Vartillerie (6 Vol.,
Paris 1780) was immensely and deservedly popular and up to the end of the
century was almost obligatory reading for pupils ambitious to enter the Ecole
Polytechnique. His Theorie generate des equations algebraiques (Paris, 1779)
opened up the way to further advances and was probably the starting point
for Fourier's own researches in the same field (Bio. Gen. ; Gde. Encycl. ; see also
Vinot).
15. Bossut, C. (1730-1814). After a brilliant career with the Jesuits he became a
student of d'Alembert with whom he later collaborated on the mathematical
part of the Encyclopedic In 1762 a memoir on the resistance of fluids to the
motion of planets gained him a prize of the Academie des Sciences of which
body he became a member in 1768. His Cours complet de mathematiques ap-
peared in 1765, and his Mecanique en general in 1792. As professor of mathe-
matics at the school of Mezieres he transformed the quality and content of the
courses. Among his pupils at Mezieres were Borda and Coulomb (jBjo. Gen. ;
Gde. Encycl. ; Ind. Bio. ; see also Doublet).
16. At Soreze we know that the course of Camus was followed from 1758 onwards
till its replacement by the course of Bezout in 1769. That Bezout was used at
Auxerre as well as Soreze is evident from the reference to that work in the
second letter of Fourier to Bonard. In 1774 Bossut's course was added at
1
22
EARLY LIFE
Soreze and it was evidently also in use in Auxerre for in 1783 a certain Bonard
the elder obtained first prize for 'le grand cours de Bossut'. In the same year
Fourier was awarded equal first prize in Bossut's Mecanique. The works of
Bezout and Bossut prove that the teaching of mathematics in the Ecoles Royales
Militaires was capable of reaching what would still today be regarded as an
advanced school level. There can be no doubt that through their teaching and
writing Bossut and Bezout made an important contribution to the great
flowering of French mathematics and science in the revolutionary period. As
regards the teaching of calculus this was facilitated in Soreze (and possibly in
other schools) by the introduction of Antelemy's French translation of Agnesi's
work on the differential and integral calculus (Taton (3)).
17. Challe thought this long delay was due to opposition to the school at Auxerre
being put under a religious body again, whereas Moiset considered it was
simply an expression of the displeasure at certain pro-Jesuit measures intro-
duced by the King. Whatever the reason for delay the edict was ultimately
registered only at 'the very express commandment of the King'.
18. Nicolas Davout (1770-1823), later marshal of France, entered the same year.
Fourier is said to have protected Davout's mother during the Terror.
19. This detail of the candle story is taken from Fortin (p. 106).
20. Municipal Library Auxerre item SZ 171.
21. Fourier Dossier, AN.
22. J. B. M. Champion de Cice (1725-1805) was deputy for the bailiwick of
Auxerre at the States General where he voted for the right. His much more
famous brother J. M. Champion de Cice (1735-1810) Archbishop of Bordeaux
(1781) was a member of the Assembly of Notables in 1787. He showed himself
a strong partisan of the popular cause in the debates on verification of powers
of May/June 1789, and was one of the clergy who joined the third estate on
22 June. He was rewarded by the position of Lord Privy Seal in the liberal
ministry formed by the King after the recall of Necker, and continued in
office till November 1790. After ten years of exile he returned to France under
the consulate and died as Archbishop of Aix, unlike his brother who died in
exile {Gde. Encycl.).
23. Although Roux insisted on the veracity of this story, Cousin (p. 2, n. 1)
argued that there was in fact no such boycott of non-noble students entering
the specialized corps of the army, a view confirmed by a statement of the
Abbe Proyart, principal of the college of Puy, in 1785 ; 'today the great ambition
of the commoner is to see his son appear in uniform beside the nobleman's son'
(Taton (3), p. 104).
24. Bonard, C. L., born around 1765. Commenced teaching at the Ecole Militaire
at Auxerre around 1784. He figures as professor of mathematics on a list of
teachers at the college proposed by the director Dom Rosman in 1790. Bonard
was a moderate republican, one of the signatories of the patriotic address to the
National Assembly of the Society of Friends of the Revolution in Auxerre on
15 October 1792, and a member of the Revolutionary Committee of Auxerre.
He was 'disarmed' in the spring of 1795 for his part in local government during
the Terror, but was reinstated the following autumn. He did not attend the
ficole Normale, presumably due to family commitments. He was appointed
mathematics teacher in the new ficole Centrale at Auxerre in 1796, and was a
member of the council of that school in 1800. In April 1804 he refused the
position of professor of mathematics offered to him at the projected secondary
EARLY LIFE
23
school of Auxerre. Thereafter he gave lessons in mathematics till his retirement.
He died in 1819 (Arch. Yon. ; Cestre (3)).
25. See below Letter I, Appendix, p. 243.
26. It must be remembered that Fourier went to St. Benoit in a double capacity:
to study for his noviciate, and to assist with (or more probably direct) the
teaching of elementary mathematics to the other and less mathematically
qualified novices. So that when he says 'we shall soon be at fractions' he is
speaking as teacher rather than taught.
27. See below Letter I, n. 9, Appendix, p. 246.
28. See below Letter I, n. 11, Appendix, p. 247.
29. Lagrange was never an inspector of the ficoles Militaires as opposed to Bailly
and Legendre. It is inconceivable that the latter would have spent so much time
visiting the various schools. For a biographical note of Lagrange see below,
Letter I, n. 12, Appendix, p. 247.
30. There were two Journal de Geneve appearing in 1788. One only appeared
between August 1787 and January 1791 and was purely a depot of facts and
information relating to the district of Geneva. The other, founded by Panc-
koucke under the title Journal historique et politique (45 Vol., 1772-83), and
continued by Mallet du Pan the elder (16 Vol., 1784-7), was given the title
Journal historique et politique de Geneve (18 Vol., 1788-92). During its last
period the printed cover bore the sole title Journal de Geneve. Fourier is
evidently referring to this latter journal. According to E. Hatin (Bibliographie
historique et critique de la presse periodique francaise (Paris 1866, p. 73)):
The long duration of this sheet, founded by Panckoucke, which had the advantage of
appearing three times a month, sufficiently proves the regard in which it was held by
contemporaries : it can be consulted as a faithful resumee of all the gazettes and public
papers of the period.
Fourier would therefore have been well informed of events in the external
world at least up to the time of the surrender of his subscription.
3 1 . The meeting of the assembly of clergy took place in the church of the Cor-
deliers, Orleans, from 17 March to 2 April, 1789. From the minutes of this
meeting (which have been preserved in MS. 993 Bib. Mun. d'Orleans) it
appears that the prior of the Abbey of St. Benoit, Dom Charpentier, played a
leading part in the proceedings : he was a member of one of the bureaux for
verifying the credentials of delegates, was one of twenty-six commissioners
responsible for drawing up the Cahiers de doleances of this assembly, and was
elected scrutineer at the election of delegates from the assembly to the States
General. He himself proclaimed the results.
32. See below Letter II, Appendix, p. 250.
33- See below Letter III, Appendix, p. 253.
34- Cousin, p. 2.
35- Challe (1), p. 227.
36. 28 October 1789.
37. It was confirmed in principle at the sitting of the Assembly of 13 February
1790.
38. Mauger, p. 271.
39. See Navier's Introduction to Fourier's Analyse des equations determinees. Paris,
1831.
40. Arch. Dep. Yon. Serie. L, Reg. p. 223.
41. Idem.
.
24
EARLY LIFE
42. See below Letter XII, n. 5, p. 294.
43. In his letter of 24 Nivoise Year II demanding the place of librarian in a pro-
jected new municipal library Fourier states that he had occupied successively
the chairs of mathematics, history, eloquence, and philosophy.
44. Mauger, p. 271.
45. The Society of Emulation of Auxerre was founded in 1790 by thirteen young
men of the town. Fourier was first president and probably the moving spirit
of the foundation. The society was dispersed towards the end of 179 1, no
doubt due to widening political rifts between its members. The aim of the
society was the culture of letters and arts. Its papers are in the possession of the
Societe des Sciences Historiques et Naturelles de V Yonne (Quantin).
46. According to a curriculum vitae in his application for a retirement pension
after the Hundred Days, Fourier was professor of mathematics for a time at the
Ecole Royale Militaire at Rebais, also under the congregation of St. Maur.
47. It is reproduced in Cestre (1) and embodies the liberal traditions of the Congre-
gation of St. Maur.
48. Challe (1), p. 227.
49. By name Paradis, in the absence of Michel Lepelletier by that date deputy of
Yonne at the Convention for the district of St. Fargeau. These and other
details of the visitation are taken from Schmidt. For some indications of
Lepelletier's curious career see note 53 below.
50. Lebeuf, vol. 2, p. 538.
51. Maure, Nicolas Sylvestre (1743-95)- A grocer in his native town of Auxerre.
While an administrator of the department of Yonne he was elected to the Con-
vention through the influence of Michel Lepelletier. An unsuccessful mission
to Eure et Loir in November 1792 led to a rebuke from the Convention, but he
was supported by the Jacobin Society of which he was an active member. He
voted for the death of the King and against an appeal to the people, or a stay of
justice. He was president of the Jacobin Society on the day of the King's
execution on 21 January 1793. He attempted a reconciliation between the
Girondists and the Montagnards in March, but when he saw that this was
impossible he demanded that the Society of Jacobins should inform the people
of the situation in the Convention. He became a member of the Committee of
General Security on 25 March 1793 and was largely responsible for its
'purification' and renewal the following September. He oversaw the levee en
masse of 23 August 1793 in the department of Yonne, and on 29 December 1793
he was charged with the organization of revolutionary government in the
departments of Yonne, Seine, and Marne. He remained faithful to the Moun-
tain during the reaction after 9 Thermidor defending the former members of
the Committee of Public Safety in a writing entitled ' Un mot a la decharge des
trots membres de Vancien Comite de salut public' . Having shown himself favour-
able to the insurrection of 1 Prairial Year III (20 May 1795) he was denounced
by Le Hardy on 1 June as a former friend of Robespierre and Dumas and a
defender of Carrier. On 4 June the municipality of Auxerre revealed a series of
(supposed) cruelties and exactions committed by its own representative. Maure
then knew what fate awaited him and blew out his own brains.
Although Maure was for a time a close follower of the bloodthirsty Marat,
and congratulated himself at a sitting of the Jacobins on 26 January 1794 that
Marat had called him his son, he seems to have been very moderate in his
actions. Thus he had the French diplomat E. de Maulde acquitted on a charge
EARLY LIFE
25
of treason on 22 June 1793, while on October 1794 he was actually denounced
by Gamier of Aube for having released from prison twenty-six non-juring
priests and eleven wives of emigres. The fact that he was painted as a blood-
thirsty monster by Freron a few days later can safely be discounted. The judge-
ment of Kucinski seems closer to the truth: 'Such was Maure in his missions,
protector of the poor, the unfortunate, he did nothing but good in the depart-
ments where he had to exercise power' (Bio. Univ. ; Bio. Gen. ; Kucinski).
52. I am indebted to Monsieur Andre Casimir of Joigny, Yonne, for the following
details of the Popular Society of Auxerre. Unfortunately the scarcity of docu-
ments has made it impossible for Monsieur Casimir to write a detailed history
of the society.
53. Le Pelletier de St. Fargeau, Louis Michel (1760-93). A member of one of the
most distinguished families of the legal aristocracy, he occupied successively
the positions of advocate-general and president of the Parlement of Paris. He
was nominated to the States General by the nobility of Paris and was one of
those who refused to obey the King's order of 27 June 1789 to join the third
estate, eventually remaining alone in the noble's chamber with the Count
Mirepoix. But the events in Paris of 12 July, and the pleadings and menaces
(it is said) of the party of the Duke of Orleans persuaded him to make an abrupt
change of front. From being an extreme reactionary he became a fervent
revolutionary. On 13 July he strongly supported the recall of Necker saying:
'Let us represent the people if we do not wish the people to represent them-
selves.' In January 1790 he became a member of the Committee of Criminal
Jurisprudence, and presented a sort of penal code to the Constituent Assembly
in April 1791. Like Robespierre he was at this time a fervent opponent of the
death sentence. On the dissolution of the Constituent Assembly he had himself
elected president of the administration of the department of Yonne in which he
had great influence through his vast domains in the district of St. Fargeau.
Later he was elected one of the representatives of Yonne at the Convention
where he played a leading part in the judgement and sentence of the King.
Said originally to have been in favour of imprisonment, it has been conjectured
that the same fear which had changed his mind on 12 July 1789 now led him to
support the death penalty. In addition he showed himself one of the most
vigorous opponents of an appeal to the people, publishing a pamphlet which
Petion — previously more of an opponent of the King than Lepelletier —
denounced in the Convention as seditious. Lepelletier was assassinated on the
eve of the King's execution. He seems to have been a curious mixture of
genuine concern for his fellow men — among whom he had the capacity for
inspiring deep loyalty and affection, as in the case of Maure — and a cynical and
utterly realistic regard for his own interest: 'what do you expect,' he is supposed
to have said, 'when one has 600 000 pounds of rent one has either to be at Co-
blentz or at the top of the Mountain'. Lepelletier, like Phillipe figalite, Duke of
Orl6ans, chose to be at the top of the Mountain. Whether, unlike the Duke, he
would have been able to retain his seat there if he had not been assassinated on
20 January 1793 provides an interesting topic for historical speculation (Bio.
Gen. ; Bio. Univ.).
54- Gautherot, Claude (1769-1825). A painter and sculptor, he became popular
for his busts of Voltaire, Rousseau, Turgot, and Bailly. He entered the atelier
of the painter David in 1787 and became his friend. In 1790 he was a member
of the administrative commission of the Jacobin Society where he presided
L
26
55
56
EARLY LIFE
over the important sitting of ai June 1791 at the time of the return of the royal
family from Varennes. Having arrived in Auxerre with Michel Lepelletier in
the autumn of 1791 he became a member of a departmental surveillance com-
mission set up following a visit of two commissaires of the Pans commune
after 10 August 1792. Later it required a special decree of the Convention
(13 Vendemiaire Year IV) to free Gautherot from the attention of a judge of
the peace curious to know the role he had played in the riot of 19 August 1792
in which two innocent men were murdered. He was attached to Maure in his
mission to Seine, Marne, and Yonne. After 9 Thermidor he left Auxerre and
installed himself in Paris. He was wounded by a bullet when defending the
Convention on 13 Vendemiaire Year IV and thereafter devoted himself entirely
to painting. He collaborated as editor in a collection of portraits of famous men
and women of the seventeenth and eighteenth centuries in Gallerie Fratifaise,
3 Vol. (Paris, 1830) (Bio. Gen.; Casimir).
Arch. Nat. C 238, dossier 242, p. 14.
Reproduced in Poree, vol. 1, p. 115. It is against the motion— many times
passed in the Convention and as many times repealed— to set up a special
guard made up of recruits from the departments to take the place of the Parisian
national guard and the armed guards of the sections which (rightly) inspired no
confidence in their ultimate loyalty to the Convention among the Girondists
and their allies.
FOURIER AND THE REVOLUTION:
AUXERRE
1. The revolutionary vortex
In a letter written later 1 from prison, in justification of his part in the
Revolution in Auxerre in 1793 and 1794, Fourier describes the growth of
his political views :
The first events of the Revolution did not change my way of life. Because of
my age I was still unable to speak in public; and impaired by night studies my
health scarcely sufficed for the work my position required of me.
From another point of view I will admit frankly that I regarded these events
as the customary disturbances of a state in which a new usurper tends to pluck
the sceptre from his predecessor. History will say to what extent this opinion was
justified. Republican principles still belonged to an abstract theory. It was not
always possible to profess them openly. 2 As the natural ideas of equality de-
veloped it was possible to conceive the sublime hope of establishing among us a
free government exempt from kings and priests, and to free from this double
yoke the long-usurped soil of Europe. I readily became enamoured of this cause,
in my opinion the greatest and the most beautiful which any nation has ever
undertaken.
In such a mood of generous enthusiasm it was but a short step for Fourier
to enter politics itself. The occasion of this would seem to have been a
speech about conscription before the local Assembly following the Decree
of 21 February 1793 for the raising of 300 000 men. On 1 February 1793,
on the report of Brissot, war had been simultaneously declared on England
and Holland. The previous day the annexing of Belgium had been decreed
by the Convention on the motion of Danton. These new threats to the
European status quo had led in turn to the formation of the first coalition
against France. At the same time massive desertions by the volunteers of
1 79 1 and 1792 had reduced the Army of the Republic to around 228 000
men as against the 400 000 under arms in December 1792. It was to
remedy this perilous situation that it was decided to raise a levee of 300 000
men. But the Convention only fixed the individual totals from the various
departments and left it to local bodies within departments to decide by the
vote of citizens how their individual quotas should be filled, whether by
lot, by volunteering, or other means. This large uncertainty as to the means
of choosing 'volunteers' inevitably led to heated discussions in local
28 FOURIER AND THE REVOLUTION: AUXERRE
assemblies throughout the country. In Auxerre the question was debated
in a general assembly of the sections of the commune, and it was apparently
at this meeting that Fourier intervened with a plan for filling the local
quota which was later adopted by the assembly. It was as a result of the
favourable impression thus created that Fourier was then invited to join
the local Popular or Patriotic Society. 3
Fourier himself gives a different— though not necessarily contradictory
account 4 of the manner of his involvement in local politics in the spring
of 1793 : although he had already become strongly imbued with republican
ideals his duties as a teacher had prevented him from undertaking any
additional duties. But when the law of 21 March 1793 had decreed the
establishment throughout France of sectional committees to receive the
'declarations of strangers and travellers' he was invited to become a mem-
ber of the local committee in Auxerre by a general assembly of the sections.
Fourier might conceivably have turned down this invitation, and later he
must often have wished that he had. But at the time the temper of patriots
everywhere had been raised to fever pitch by the military reverses in
Belgium culminating in the defeat of Dumouriez at Neerwinden. The
mounting military threat from without, combined with the internal threat
posed by the rebellion in the Vendee, then led to a series of revolutionary
measures— including the institution of the Revolutionary Tribunal-
carried in the Convention against the fierce opposition of the Gironde.
For Fourier to have refused to accept the position offered him on the local
committee of surveillance would therefore have branded him as an oppo-
nent of the patriot party. In fact, what is known of his later involvement in
local politics makes it likely that he eagerly embraced the chance to play his
part in the defence of the Republic 'one and indivisible' against all its
enemies, internal and external.
Once a member of this committee, however, he inevitably found himself
sucked into the revolutionary whirlpool, in the first place, perhaps, in
putting into practice his own plan for local recruitment. It was one thing,
in fact, to decree the raising of 300 000 men, and even to agree in local
assemblies (as in Auxerre) on methods of meeting local quotas. It may not
even have been too difficult to raise the local quotas in towns such as
Auxerre where there were strong radical tendencies and no great opposition
to the central government. It was quite another matter to persuade recruits
to come forward in many of the country areas. In the hope of ironing out
these tiresome local difficulties some eighty-two members of the National
Convention were sent out from Paris on 9 March to oversee the levee. An
insurrection in Brittany was quickly suppressed, but in the Vendee the
opposition of the peasant masses soon led to a full-scale royalist revolt
which only began to be controlled in October 1793, and then only by means
FOURIER AND THE REVOLUTION: AUXERRE
29
i
of the most draconian measures, and after government forces had suffered
a number of major reverses. Thus the attempt to raise 300 000 men led to
an even more pressing need for recruits in those parts of France which had
not suffered from insurrections, arising in part out of the very attempt to
impose the levee. This helps to explain a mission on which Fourier was
sent in June 1793 from Auxerre to the neighbouring district of Avallon 'to
invite, and if necessary require, citizens to take arms against the rebels of
the Vendee'. 5
Fourier had been sent to Avallon by the conventionel Meaule, 6 then on a
mission to oversee the levee in the departments of the centre and west. A
little later, on 1 July, he was representing Meaule at a meeting of all con-
stituent authorities in Auxerre. 7 By this time, therefore, when the struggle
between the Federalists and the Jacobins had reached a new paroxysm of
fury, Fourier had evidently fully committed himself to the Jacobin cause.
Things had moved a long way since the decree of 21 February for the
raising of 300 000 men: on 10 March the Revolutionary Tribunal had been
instituted ; on 1 1 April the rate of the assignat had been pegged ; a maximum
price for grain had been laid down on 4 May; and finally the insurrection
of the 31 May-2 June had led to the fall of the Gironde followed by the
Federalist revolt. At one point this revolt had spread to no less than sixty
departments. During June and July both the Federalists and the Vendeens
continued to prosper and for a time in July the life of the Republic was in
jeopardy. All this time, as Fourier remarks in his letter to Villetard:
the duties of these committees [of surveillance] were successively modified, and
various laws entrusted them with a universal surveillance which soon degenerated
into very extensive powers since the law of 17 September ordered them to
proceed to the arrest of suspects. 8
Thus by 17 September the committees of surveillance — originally
entrusted with the comparatively inoffensive task of keeping an eye on the
movements of strangers and travellers — had become an integral part of the
apparatus of the Terror which had itself been forced on an unwilling
government and Convention by the mounting tide of popular agitation
impelled forward by near famine conditions and the continuing military
threat from within and without. At this point Fourier prudently attempted
to withdraw from the committee feeling 'less suited than many others to
execute this law' 9 (that of 17 September) to the extent of submitting his
resignation in writing. But his attempt was in vain, willy-nilly— and it is
not certain that the feelings expressed in Fourier's letter to Villetard in
1795 were exactly the same as those he harboured in the heady days of
September 1793 — he was inextricably caught up in the revolutionary vor-
tex. For as he relates :
This move [his letter of resignation] produced an effect opposite to what I had
30 FOURIER AND THE REVOLUTION: AUXERRE
intended. In the reply sent to me I was reminded of a law which forbade any
official from abandoning his post, and my resignation was rejected. At the same
time other persons openly accused me of abandoning my colleagues at a moment
when my help was about to become most useful to them. I was reproached with
the feebleness of my conduct, and some even doubted the purity of my
intentions. 10
Thereafter one might have expected his zeal for the revolutionary cause
to have abated somewhat. Nevertheless on 12 October, some three weeks
after the promulgation of the notorious law of 17 September, Fourier was
sent by Nicolas Maure on a mission to the neighbouring town of St. Brie
'to bring the people back to a sense of duty' 11 — in all probability in con-
nection with the excessively unpopular measures for raising men for the
levee en masse of 23 August 1793. It is not known how successful Fourier
was in his attempt to reform the people of St. Brie, or even if he went there
at all, for a few days later he was sent on another, much more important
and as it turned out far more dangerous, mission to collect horses for the
war effort in the neighbouring department of Loiret.
2. The Orleans affair
Fourier had been delegated by the conventional Ichon, 12 one of a number
of representatives of the people sent out by the National Convention
following its decree of 17 Vendemiaire Year II (8 October 1793) relating
to the raising of horses in urgent demand as a result of continuing military
operations in the Vendee and elsewhere. Ichon was assigned to the 19th
military division comprising the departments of Yonne, Aube, Cote d'Or,
Nievre, Loiret, Cher, and Indre, and set up his headquarters at Auxerre.
With the help of the local Popular Society 13 he chose six agents, one of
whom was Fourier, to oversee the collection of horses, the terms of refer-
ence of their mission being laid down in an order 14 dated 23 Vendemiaire
(14 October 1793): they were to be responsible solely for the raising of
horses (article 3), were to concert with local popular societies and envoys of
popular assemblies (article 4), and were also expected to act with great
speed as their powers were to expire a little less than a month later on 21
Brumaire (11 November 1793).
Fourier evidently carried out his duties in Loiret with commendable
dispatch for his mission had already been completed 'with every possible
success' by 7 Brumaire (28 October 1793), as appears from a letter 15 of that
date written by Fourier to Bonard from the Angel Inn at Montargis, a
small town some seventy kilometres from Auxerre. But on his way through
Orleans in the course of his mission Fourier had unfortunately become
involved in a local dispute which was to have the most distressful conse-
FOURIER AND THE REVOLUTION: AUXERRE 31
quences. He alludes to this affair somewhat obliquely in his letter to
Bonard :
You will have heard that the Department of Loiret is not absolutely quiet and
the town of Orleans is somewhat disturbed: I played some part in this matter and
I behaved in it in conformity with the principles of the Revolution.
But the 'principles of the Revolution' varied considerably not only from one
'party' to another but even within a given 'party'. To understand why
Fourier's revolutionary principles had led him into such serious trouble the
reasons for the 'somewhat troubled' state of the town of Orleans in the
autumn of 1793 must first be elucidated. Thanks to Lefebvre, 16 these
reasons are known in great detail and provide one of the more curious and
interesting examples of the actual working of the French revolutionary
process in a specific case.
Like many other French towns, Orleans had been in an increasingly
troubled state from at least March 1793 onwards due in large part to local
antagonism between the wealthy Bourgeoisie, supporters (faut de mieux)
of the Girondin cause, and the sans-culottes, the small tradesmen and
artisan class who were equally firm supporters of the revolutionary groups
to the left of, and including, the Jacobins of the spring 1793 variety. 17 The
antagonism had been exacerbated by rising prices, shortage of bread, and
recruitment for the levee of 300 000 men. On 15 March the situation took
an ugly turn when two (radical) representatives on mission (Jeanbon- Saint
Andre and Lacoste) were insulted by members of the Bourgeoisie on their
way through the Faubourg Saint-Marceau. A much more serious incident
occurred the following day when the representative Leonard Bourdon —
later to play a leading part in the downfall of Robespierre — was set upon
and wounded in the centre of the town. His wounds were not grave and he
soon recovered, but word went round that there had been an attempt on his
life. In the circumstances of the time — the Vendee was then on fire — the
'assassination' of Leonard Bourdon seemed part of a great counter-
revolutionary plot. On 18 March the Convention voted Orleans in a state of
rebellion, suspended the municipality, and decreed that the guilty be sent
to the Revolutionary Tribunal. It also detailed three representatives of the
people, Bourbotte, Julien of Toulouse, and Prieur of the Marne, to proceed
to Orleans. However, two other representatives, Collot D'Herbois and
Laplanche, 18 already on mission for recruitment in Nievre, reached Orleans
first and set about 'revolutionizing' the town. On 24 March the Girondins
with the aid of Tallien had the decree of the Convention lifted only to see it
re-imposed on 27 March following a protest from Collot and Laplanche.
Thereafter the municipal authority was in the hands of the sans-culottes
and although the Bourgeoisie of Orleans moved heaven and earth to have
I.
32 FOURIER AND THE REVOLUTION: AUXERRE
the decree of the Convention withdrawn they were unable to do so before
the insurrection of 31 May finally consolidated the power of their oppo-
nents. On 13 July— the day of Marat's assassination— nine of the suspects
of the 'assassination' of Leonard Bourdon who had been sent before the
Revolutionary Tribunal were condemned to death and guillotined.
Laplanche returned to Orleans on 1 September, this time entrusted
with the overseeing of the levee en masse of 23 August and with orders to
renew the administration and purge those suspected of federalism. During
August the power of the sans-culottes and their more extreme leaders,
especially Taboureau, the so-called enrage of Orleans, had increased
steadily due mainly to a chronic shortage of food accompanied by a
vertiginous rise in the prices of all basic commodities and a corresponding
devaluation of paper money. In these respects the situation in Orleans was
typical of that in other parts of France. On 26 July, under pressure from
the near-starving populace, the Convention had been forced to bring in a
law against hoarding according to which merchants were required within
eight days of its proclamation to declare their stocks of merchandise to the
authorities and display a notice of the list of the various items outside their
premises. Anyone who failed to fulfil either of these provisions, or who
gave false information, was to be declared a hoarder and as such was liable
to the death penalty. In Orleans the feverish attempts of merchants to sell
their stock within the eight days allowed by the law led to the institution of
forty-four commissaries who proceeded to domiciliary visits. These visits
were very fruitful and resulted in the seizure of much undeclared stock,
though no-one was prepared to pursue delinquents for hoarding and thus
send them to the scaffold. Instead they were fined and their stocks confis-
cated.
Throughout August the crisis continued so that when Laplanche arrived
in Orleans on 1 September the town was in a great state of ferment. At first
it seemed that his arrival would assure the total and final triumph of the
sans-culottes. He chose his advisers from among them in the Popular
Society of the town. He declared that he was surrounded by twelve members
of the 'club' whom he regarded as 'pure', that is, in a state of revolutionary
grace. On 3 September and subsequent days he assembled the adminis-
trative corps of the city before the people in the church of St. Paterne and
proceeded to 'purge' them after subjecting them to a torrent of vituperative
abuse— no doubt from the pulpit of the church, a peculiarly appropriate
'platform' for an ex-member of the Benedictine order. He took the upper-
middle class especially to task, and threatened to dismiss the whole depart-
mental administration. He taxed the rich and distributed some— but not all
—of the proceeds among the poor. He made numerous arrests including
Bigot, the arch-hoarder in the eyes of the sans-culottes. On 9 September,
FOURIER AND THE REVOLUTION: AUXERRE
33
at his third seance in St. Paterne, he even threatened to form a revolutionary
army with a moveable guillotine like that in Paris. But in spite of his violent
language and his war on the rich — which was real enough at first — La-
planche seems quickly to have taken a strong personal dislike to certain of
the sans-culottes leaders, especially Taboureau, who may well have offended
his vanity by their independent and truculent bearing, the special badge of
the militant poor in all ages. On the other hand, those whom he had
punished pocketed their pride and inundated him with humble supplica-
tions for the lifting of fines or terms of imprisonment. They found support
among certain Montagnards — or self-styled Montagnards — in the adminis-
tration. Especially helpful to the Bourgeoisie was Aignan, 19 a young and
able man who acted as secretary to Laplanche in the seances at St. Paterne.
Aignan seems quickly to have insinuated himself into the good graces of
Laplanche to the point of becoming procureur-syndic of the district, no
mean achievement for a former 'Feuillant' who was rumoured to have
been the author of a tragedy on the death of King Louis XVI which had
circulated clandestinely earlier in the year, and who was reproached — rightly,
it seems — for having become a Montagnard in order to escape conscription
for the levee en masse.
But the major influence in turning Laplanche against the sans-culottes in
favour of the better-off members of society seems to have been the con-
ventionel Delaguelle de Coinces. 20 By August 1793 De Coinces was taken
for a backer of the sans-culottes but this had not always been the case. In
1789 he had been one of the judges who had condemned to death the
notorious Rimbert. 21 After the 'Revolution' of 10 August 1792, the sentence
on Rimbert had been quashed as illegitimate by the court of appeal, and
after the fall of the Gironde on 2 June 1793 the court had taken a further
step to the left by allowing his widow to take an action against her late
husband's judges, her lawyers suggesting the sum of 150 ooo 22 livres as
adequate indemnity for the loss of her husband, not forgetting legal costs.
Rumour even had it in Orleans that the widow would only be satisfied with
the blood of her husband's judges, and that the affair was to be taken up by
the Revolutionary Tribunal. Since Taboureau had already defended the
memory of Rimbert, de Coinces had a pressing interest in causing his
downfall, an eventuality which became more probable in October when
he gave his beautiful daughter Adelie in marriage to Laplanche. In the event
Taboureau suddenly found himself not only without his promised place on
the departmental administration but even excluded from the general coun-
cil of the commune. Laplanche also attacked him at a meeting of the
Popular Society of which Taboureau was at that time president. But the
debate was adjourned and many of Taboureau's supporters continued to
hold positions. And so having raised the expectations of the sans-culottes,
I.
34
FOURIER AND THE REVOLUTION: AUXERRE
Laplanche ended by disappointing and irritating them by his actions
against Taboureau and his new-found gentleness towards their hated
opponents among the merchant class. When Laplanche left for Bourges the
sans-culottes returned to the attack, and when he returned to Orleans on n
October the Popular Society pointedly failed to send a delegation to com-
pliment him on his safe return. The representative of the people answered
by freeing the arch-hoarder Bigot from whom he even obtained a loan for
grain destined for the Navy, an act which caused the most intense annoy-
ance. Laplanche in turn was furious at the sans-culottes who had, he said,
profited by his absence to destroy the peace and quiet he had left behind
him on his departure for Bourges. On 13 October, having assembled the
people and authorities for one of his famous sessions in St. Paterne, he
attacked two of the leading sans-culottes, Chamouillet and Besserve, for
being oppressors of Bigot : 'It will be on the top of his sacks of corn that he
will appear before you. Butcher him [there] if you dare!' The next day
(14 October) there was a strong movement in the town against Bigot, and a
violent altercation between some of the sans-culottes leaders and Laplanche,
who thereupon rushed to the town hall where he dismissed Laguette,
Billet, Chamouillet, and Besserve and had the first three arrested. The
next day the .most militant of the sans-culottes leaders, Taboureau, was
arrested on the order of the Department and sent to Paris. It was at this
singularly inappropriate point that Fourier chose to intervene and air his
eloquence on the side of the sans-culottes. According to Fourier himself 23 it
was 'the defence, perhaps imprudent but at least disinterested' which he
dared make of 'three paterfamilias' which led to his disgrace. There can be
little doubt that the paterfamilias in question were the above mentioned
trio Laguette, Billet, and Chamouillet. Fourier's 'defence' of them at the
Popular Society, before their arrest or afterwards at the time of their 'trial',
was certainly imprudent. For these three had evidently incurred La-
planche's special wrath, so that by defending them Fourier was attacking
the dreaded representative of the people on mission in the very capital of
his district, a most unwise procedure, and one liable to lead to unpleasant
consequences. These were not long in developing. By the time of his letter of
7 Brumaire to Bonard from Montargis he had already learnt that his ad-
versaries in Orleans intended to denounce his conduct to Ichon as the per-
son responsible for sending him on his mission to Loiret. In reality this
denunciation had already reached Ichon the previous day as appears from a
letter of 12 Brumaire to the Committee of Public Safety from the conven-
tionel Nicolas Maure :
Liberty or death 12th day of Brumaire Year II
I was at Joigny, citizen colleagues, the sixth day of this month with Ichon
when he received from a mounted gendarme a letter from the administrative
FOURIER AND THE REVOLUTION: AUXERRE
35
body of Orleans demanding the recall of citizen Fourrier [sic] agent of Ichon
in that department for disturbing the public order. My colleague immediately
ordered the recall of Fourrier. However, he had seen his conduct reproved, and
Fourrier recalled, without having been heard. I owe you an account of the
method employed by Ichon for the nomination of his agents. When he arrived
he said to me : tell me of someone in whom I can trust to speed up my operations
in the departments assigned to me. I sent him to the Popular Society of Auxerre
which is excellent. It chose six citizens who were presented to him and whom he
accepted. Citizen Fourrier, a young man full of intelligence, eloquence and zeal,
was sent to Loiret. Ichon conferred on him powers restricted to the collection of
horses. It seems that Fourrier, finding no opportunity to display his eloquence
before such audiences, got up on certain popular platforms. He can talk very
well and if he put forward the views of the Society of Auxerre he has done no-
thing blameworthy; but he is awaited to give an account which will be examined
severely.
Citizen colleagues, Ichon is a brave man. He is afflicted with this censure. He
has done nothing to merit it. Let the Convention thunder at evil men but let her
encourage the good. Listen to the voice of him who always speaks the truth and
who loves you all after his own dear land. Give some consolation to Ichon who
has already hired more than 600 fine horses and who takes infinite pains. Let
the Convention be strong in the confidence of French men. Eight hundred
thousand men, horses, munitions, all are ready at the moment, at the hour. So
that were all the despots united as many again, I should not fear them.
Brotherly greetings
Maure the Elder. 24
The reference in Maure's letter to the censure of Ichon is explained by
the fact that the administrative body of Orleans complained about Fourier's
behaviour not only to Ichon, but also to the Committee of Public Safety.
This in turn led directly to a decree 25 presented to the Convention on behalf
of the Committee by Barere 26 on 8 Brumaire. Article 1 of this decree re-
minded representatives of the people sent to departments for the raising
of cavalry (such as Ichon), that neither they nor their delegates (such as
Fourier) could countermand measures of representatives of the people
already sent to departments (such as Laplanche). Article 2 stated that:
The commission given by the representative of the people sent into the depart-
ment of Loiret to citizen Fourrier [sic] is revoked. The citizen Fourrier is de-
clared incapable of receiving such commissions [in the future].
Although Ichon was not explicitly named in the decree he was referred
to by name in the account given in the Moniteur 27 in which Barere was
reported to have taxed him with exceeding the terms of his mission. This was
as good as a public rebuke by the Committee, and an unjustified one at that,
for although Fourier had certainly exceeded the powers conferred on him
36 FOURIER AND THE REVOLUTION: AUXERRE
by the terms of Ichon's order of 23 Vendemiaire, Ichon had certainly not
exceeded his, the appointment of agents to oversee the raising of horses
being allowed for explicitly in Article 10 of the Convention's decree of 17
Vendemiaire. Ichon, who in any case seems to have been an excitable fellow,
was not unnaturally upset to read of the rebuke meted out to him by
Barere, all the more so as he apparently first learnt both of the decree of 8
Brumaire and of Barere's strictures not in a letter from the Committee but
in the Journal des Debats. 28 His displeasure at this unwarranted rebuke
may possibly even have been mixed with fear, if not for his head, at least
for his position. In any case he wrote 29 post-haste on 1 1 Brumaire to justify
himself to the committee: he pointed out that the individual who had
abused his powers in the Department of Lolret (that is, Fourier) had been
appointed on the advice of the foremost patriots of the Popular Society of
Auxerre; that he was justified in appointing agents by Article 10 of the law
regulating his mission; and that his order regulating the powers of these
agents gave them no mandate for 'contradicting or opposing the measures
already taken by representatives of the people' in the department in ques-
tion. There was, in fact, only one fault with which Ichon felt he could re-
proach himself, his failure to inform the Committee of the contents of this
order. Otherwise the report of the Committee to the convention would
necessarily have restricted itself to Fourier's errors. As it was, Ichon was
evidently deeply wounded at what he interpreted as the censure of the
convention :
Citizens and colleagues; the decree handed down by the Convention at the
conclusion of the report of the Committee touches me at present to the quick. I
am struck with the severity of its provisions.
He was evidently concerned above all with his reputation as a good
Montagnard: 'I beg you', he said to the Committee, 'not to forget that I am
entirely devoted to the cause of the state, and that there is nothing more
precious to a Montagnard than to retain himself pure in public opinion.'
As an additional precaution he thoughtfully enclosed with his letter to
the Committee an address 30 to the National Convention itself in which he
briefly related the facts of Fourier's misconduct, the remonstrance by the
'regenerated administrative corps of Orleans', and his subsequent recall of
Fourier. A reference at the end to 'several details of great interest' which
made it necessary for the National Convention to 'order its Committee of
Public Safety to take the most exact cognisance of the whole affair' might
have sent an additional shiver down Fourier's spine if Ichon's address had
been published in the Journal des Debats. But the address itself is next to
his letter to the Committee in the Archives, and there is no indication it was
ever read to the Convention.
FOURIER AND THE REVOLUTION: AUXERRE
37
Fourier's intervention in Orleans had evidently stirred up a regular
hornets' nest and given him most unwelcome national press coverage as a
man 'incapable of holding such commissions in the future'. October 29,
thirteen days after the execution of the Queen, and two days before that of
the Girondists, was hardly the best of times to be denounced in the Con-
vention by Barere who had himself played a leading part in the proceedings
against both the Queen and the Girondists. Nevertheless, judging by the
tone of Maure's letter of 12 Brumaire, Fourier was by then no longer in any
real danger. There is good reason to believe, however, that he had been in
considerable, even grave, danger for a short time immediately after word
of Barere's decree reached Ichon in Joigny. According to Cousin, Ichon
then
lost his head, and for fear that he would be accused of complicity with Fourier
directed an order against him according to which he was to be arrested wherever
he was and be guillotined on the spot. 31
It might be difficult to attach much credence to this account if it were
not for another — considerably later — letter of Maure to the Committee of
Public Safety in which he enclosed
an order of the representative Ichon which, among other dispositions, takes away
the powers given to citizen Fourier sent by him [Ichon] as national agent into
the department of Loiret, orders his transfer to Orleans and execution there,
makes the most complete eulogy of this citizen, gives details of the events which
led to this order being made, demands his punishment if he is guilty, his libera-
tion if he is innocent. 32
Unfortunately Ichon's order has been either destroyed or misplaced.
Nevertheless Maure's abstract of it still conveys a vivid impression of
Ichon's alarm and confusion at the news of the Convention's decree of
8 Brumaire and the criticism of himself contained in Barere's presentation
of the decree. We gather that at some stage after Fourier's intervention in
Orleans Ichon actually ordered his arrest, even his execution, though there
is an evident contradiction between Fourier being executed and simply
being tried and punished or released according as to whether he were guilty
or innocent.
Cousin then rounds off the story: according to him when Fourier had
completed his mission in Loiret he returned to Auxerre
where he would have run the greatest possible danger if the Popular Society and
the Committee of Surveillance had not interposed themselves between Ichon and
him. Maure, deputy of the department of Yonne at the Convention, who was then
at Auxerre, successfully intervened on behalf of his young and learned com-
patriot.
38
FOURIER AND THE REVOLUTION: AUXERRE
Cousin's account requires possible modification in one respect only. If
in spite of being at Montargis on the seventh, Fourier had not returned to
Auxerre at the time of Maure's letter of 12 Brumaire, it was because he too
had got word of the Convention's decree of the eighth removing him from
his commission (he could after all, like Ichon, have read of it in the Journal
des Debats) and that he thereupon wisely decided to hide 33 for a while
until he learnt how things had gone in Auxerre. No doubt the sum of 400
francs demanded from Bonard in his letter from Montargis was to cover
just such a contingency.
As for Ichon, once he had cooled down he no doubt felt something of a
fool for having over-reacted in such an excessive way to Fourier's behaviour
in Orleans. Nevertheless, he was evidently still in no mood to exonerate
Fourier completely, as appears from an order 34 promulgated by him at a
seance of the departmental directory at Auxerre on 19 Brumaire. Having
referred to his (Ichon' s) order of 23 Vendemiaire (laying down the duties
of the six commissioners appointed to oversee the collection of horses) and
to the decree of the Convention of 8 Brumaire which declared Fourier
incapable of holding such a commission in the future and directed the
immediate recall of all commissioners, and considering that Fourier had
betrayed the confidence of Ichon by exceeding the limits of his powers, it
was ordered that
citizen Fourrier [sic] sent by the representative of the people Ichon into the
department of Loiret, and suspended from the exercise of his powers by Ichon
on 7 Brumaire is and remains definitely dismissed . . .
Judging by the tone of this order, on 19 Brumaire (9 November, 1793)
Ichon was evidently still smarting from his censure by the Convention.
In fact from a letter 35 of 29 Brumaire from Maure to the Committee of Public
Safety, we learn that although Ichon had been 'consoled' by a letter 36 sent
him by the Committee, his peace of mind had not yet been restored and
Maure felt he needed a rest. As for Fourier, the date of his return to Auxerre
is unknown, nor is it known whether he was 'disciplined' in any way beyond
being dismissed from his commission and declared incapable of holding
any similar ones in the future. In any case he must have hoped — vainly as it
turned out — that he had heard the last of his 'imprudent' defence of the
three paterfamilias of Orleans.
3. Imprisonment of Messidor Year II
On his return to Auxerre, Fourier continued to teach in the college and
remained a member of the local revolutionary committee. When he next
appears on the scene it is in the guise of applicant for the new position of
FOURIER AND THE REVOLUTION: AUXERRE
39
Municipal Librarian in Auxerre — a somewhat unexciting and stay-at-
home assignment eminently suitable for a citizen forbidden to hold any
further roving commissions. To the several reasons advanced by Fourier
in favour of his candidature 37 — wide teaching experience, irreproachable
morals, well known civic virtue attested by his election to a public position
(membership of local Revolutionary Committee)— Fourier added a some-
what unorthodox 'need of several years repose' necessitated by his 'having
devoted' himself 'since childhood, and possibly with too much ardour, to
the study of the exact sciences', passing his nights in instructing himself,
and his days in instructing others. A certain tone of lassitude is detectable
in Fourier's 'need of several years repose' and the reasons advanced in its
favour are not entirely convincing. Had he grown weary of the Revolution
which he had embraced so eagerly in the preceding spring? Or was he
simply suffering from exhaustion as a result of his horse-raising and other
activities in Loiret ? It is impossible to say : no letters written by Fourier in
the year 1794 have been found beyond the one just referred to. Residing all
that time in Auxerre, he would in any case have had little or no occasion to
write. There is therefore no indication of his attitude to the political and
other developments of the year. Was he perturbed at the so-called drama
of Germinal, the execution of the Hebertists on 24 March and of Danton
and his associates a few days later on 5 April ? No doubt these events were as
confusing to the 'patriots' in the provinces as they were to those in Paris.
Had he begun to question the justification of a Revolution which could
hound the mathematician and philosophe Condorcet to his death, 38 or
which was soon to have no need of a scientist of genius like Lavoisier ? 39
Both these events must surely have touched Fourier the mathematician
and scientist more than other men. What were his feelings at the mounting
holocaust of terror after the law of 22 Prairial had removed the last remain-
ing checks of the due process of law before the Revolutionary Tribunal,
so that the appearance of a name on the daily list of the State prosecutor
Fouquier-Tinville was almost equivalent to a death sentence? Once
again there is no way of knowing, no evidence beyond what Fourier himself
wrote afterwards when he claimed that he had spoken out in Auxerre
against the worst excesses of the Revolution. 40
Although his application for the position of librarian was unsuccessful,
he was designated in May by the Popular Society of Auxerre as one of the
'bibliographical commissioners' 41 responsible for overseeing the preserva-
tion and cataloguing of the many books which were at that time in danger of
destruction following the suppression of the regular monastic orders and
the break up of libraries belonging to emigres and those whose goods had
been confiscated by the state. In addition he continued to teach in Auxerre.
In April 1793 the college had suffered its first major change of personnel
40
FOURIER AND THE REVOLUTION: AUXERRE
since the outbreak of the Revolution when all the remaining so-called
professor-priests apart from the principal, Rosman, were forced to resign
through pressure brought on them by the Popular Society of the town.
Rosman somehow managed to continue in office — possibly in a caretaking
capacity — but in June he too had to step down. His place was then taken by
Balme on the recommendation of Nicolas Maure. 42 The fact that the
appointment was by the Minister of War, Bouchette, indicates that the
college still continued as an Fcole Militaire, but on i November 1793 it
lost this status following a decree of the National Convention abolishing
all such schools. From 1 November 1793 onwards the college continued as a
National College and it was still in existence in June/July 1794 when a list
of the staff included Fourier, Roux, and Bonard. 43 Soon afterwards it was
closed down, as is attested by an order 44 of 29 Thermidor Year II (16
August 1794) requiring the settling of the accounts of the sale of furniture
of the college — a good measure of the straightened circumstances of the
departmental administration under whose control it then lay. Judging by
his invariable position at the head of the list of professors of the school,
Fourier acted as professor of the first class and possibly as vice-principal
during the whole of Balme's principate.
In addition to his teaching and bibliographic duties Fourier continued
as a member of .the revolutionary committee of Auxerre. After his unsuccess-
ful resignation bid around September 1793 he would have known better
than to make a second attempt during the far more dangerous period of the
spring and summer of 1794. A few glimpses of Fourier's revolutionary
activities in Auxerre and district have survived, one in a story given by
Cousin :
as a member of the revolutionary committee of Auxerre Fourier had been en-
trusted with some mission or other to the neighbouring town of Tonnerre. On his
way there he entered into conversation with another traveller in the public
coach; seduced by the amiability of his questioner, this man told Fourier that
he was also entrusted with a political mission to Tonnerre, but one of the gravest
kind. It was a matter of having arrested and transferred to the Revolutionary
Tribunal — which usually meant being sent to the scaffold — a person from
Tonnerre whom Fourier scarcely knew but whom he had every reason to believe
innocent. On leaving the coach at Tonnerre the agent was to demand the arrest
of the person in question. Fourier attached himself to this man, insinuated
himself more and more into his confidence, and on arrival at Tonnerre invited
him to lunch at his inn : there he exerted all his charm to retain him and make
him forget his mission. It was impossible to warn the intended victim, for it
would have been necessary to confide in a servant who could have betrayed him;
on the other hand if Fourier were to leave his man for a moment the latter would
have gone straight to the municipality to demand the necessary armed guard to
effect the arrest. Faced with this difficulty, and having exhausted every means of
FOURIER AND THE REVOLUTION: AUXERRE
41
retaining his guest voluntarily, Fourier left the room where they were dining
under some pretext. On going out he gently locked the door and ran to warn the
person who was menaced with so imminent a danger. When Fourier failed to
return the agent grew restless, made to leave the room, and finding himself locked
in flew into a violent rage. Soon afterwards Fourier returned, excused himself as
best he could for the silly joke he had played on the agent, and offered to lead him
to the municipality. On the way they met the very man whom Fourier had
warned who was now on his way out of the town. To distract the attention of his
companion Fourier stopped before a newly painted shop sign and began to extol
its beauty with an eloquence which held the eyes and mind of the agent on one
side of the street while the suspect slipped past unnoticed on the other. 45
Another glimpse of Fourier, this time as a somewhat embarrassed agent
of the Terror in Auxerre, is contained in a passage from a letter, written in
prison to his son, by a Francois Leblanc, former procureur du roi for waters
and forests in Auxerre.
About fifteen days ago, my good friend, Fourier came here with a second member
of the Committee. He gathered us together and informed us that within eight
days they had to send off everyone's interrogations and the reasons for their
arrest, and that the representative Maure would shortly judge us either yonder or
here : in order to save time he gave us a series of questions to answer on a pro-
forma consisting of our names, titles, number of children, fortune before and
since the Revolution. He warned us that further questions would be asked, that
among others would be added questions on our voyages to Paris since May 1789
and on the various outstanding occasions [of the Revolution], on the petitions
we may have signed, on our connections; the interrogations were commenced
the same evening but were not exhaustive : for everybody they were restricted to
very few things, to nothing at all as far as I was concerned. I was asked if I had
been in Paris on any of the following occasions? No; where was I at the death of
the tyrant ? At Auxerre or in my country house ; if I had signed any petitions ?
No ; if I had done anything for the Republic ? Some patriotic gifts and others to our
brothers in arms, recently a bedcover and a horse saddle. Why had I given up my
employment ? Because I had for a long time intended to transfer my position to
you, that I was not able to carry it out any longer because of my leg; since that was
all, I suggested to them that they were doubtless going to ask me some questions
on the offence which had given rise to my arrest. After looking at each other,
especially Fourier who was asking the questions and writing notes at the bottom
of my form, Maure spoke up and told me that there were no further questions
and that I could give a memoir. I asked him on what. On my life since 1789 he
replied; the whole thing went off very reasonably for everyone. Fourier said to
me, you have a son in the armed forces of the Republic? You know I have, I
replied. He wrote it down although it was already given as a reply to their ques-
tions concerning the number of children . . .* 6
By Messidor Year II Fourier had become president of the revolutionary
committee in Auxerre. As such he was the foremost local agent of the
42
FOURIER AND THE REVOLUTION: AUXERRE
Terror in that town, and so might reasonably have expected to enjoy some
immunity from the Terror himself. But in fact we only learn of his elevated
position from an entry in the local Archives which reports his arrest. 47
As is usual in the case of such entries no indication is given of the reasons for
the arrest. These must be sought for elsewhere, first in the account of
Cousin. 48 According to this account it must be supposed that even after
relations between Fourier and Ichon had been smoothed over by the
combined intervention of the Popular Society, the revolutionary committee,
and the conventional Nicolas Maure, Fourier continued to smart from a
feeling of injustice at the decree of the Convention — which is not surpris-
ing when it is remembered that this decree declared him unfit to hold
'similar commissions' in the future (that is similar to the one he had held in
Loiret), and thus evidently considerably reduced his possible range of
usefulness at a time when he presumably burned to make himself useful
to the Republic 'one and indivisible' of which he had recently been a
national agent. And so he visited Paris to plead his own case, was presented
to the Jacobin Society — possibly with a letter of introduction from Maure
who was an active member of the society — and introduced to Robespierre. 49
But he evidently made a bad impression on the latter, for soon after his
return to Auxejre he was imprisoned by order of the Committee of Public
Safety. Every 'decent' person in Auxerre then interceded in his favour and
he was released, only to be re-arrested eight days later. So great was the
esteem enjoyed by Fourier at Auxerre that an official deputation was then
sent to Paris to demand his release. 50 Saint- Just received the deputation
with great hautiness. He admitted Fourier's talents and did not even
deplore his sentiments; but he reproached him with lukewarmness : 'yes,'
he said, 'he speaks well, 51 but we no longer have any need of musical
patriots' and in fact he (Saint- Just) was preparing to act when 9 Thermidor
intervened and delivered France and Fourier.
The departmental archives partly confirm, sometimes expand, and no-
where directly contradict Cousin's account. Fourier was arrested for the
first time on 4 July 1794 by order of the Committee of General Security
dated 1 Messidor (19 June 1794). 52 He was subsequently freed by order of
the Committee of Public Safety and then re-arrested on 29 Messidor
(17 July) on a further order of the Committee of Public Safety dated
23 Messidor (11 July). 53 As for the deputation sent to Paris to intercede
for Fourier before the Committee of Public Safety, this is referred to in a
report in the departmental archives 54 where the members concerned
describe how Fourier was first released by the Committee as a result of
their intercession, only to be re-arrested a few days later.
The reasons for Fourier's arrest are not in doubt: according to the
delegation who interceded for him before the Committee of Public Safety
FOURIER AND THE REVOLUTION: AUXERRE
43
it was the intervention of a certain commissioner Demaillot which led to
the order for Fourier's re-arrest. Demaillot reminded the Committee of
Barere's report to the Convention declaring Fourier unfitted for public
office, claimed that Fourier was an Hebertist, and was believed by the
Committee. Interesting light is thrown on the activities of the agent
Demaillot in the following passage in Lefebvre :
in Germinal (Year II) the leaders of the sans-culottes [of Orleans] hawked round
the Popular Society and in the sections an address demanding that the little
Capet [that is the Dauphin, son of Louis XVI] should be put to death. The day
after the fall of the Hebertists such an action was calculated to draw lightning.
They were denounced to the Committee of Public Safety. Aignan [of Orleans]
came to Paris and in company with Laplanche was received by the committee
and sent to Robespierre. Leblois [of Orleans] who happened to be present related
after 9 Thermidor that Robespierre had bitterly criticized the conduct of the sans-
culottes of Loiret. He sent Demaillot there, one of the agents of the committee,
who up to the eve of 9 Thermidor savagely pursued the terrorists. From 21
Floreal to 20 Messidor a series of orders of the Committee effected the arrests of
the terrorists in Orleans, in Beaugency, Pithiviers, Montargis, Chateau Renard.
At Orleans twenty-eight were thus imprisoned and sent to Paris. The Committee
of Surveillance of the Council General of Orleans was suppressed and the per-
manence of the sections abolished ... At the same time Demaillot obtained the
liberation of a certain number of suspects. He even tried to obtain the creation
at Orleans of a Popular Commission ... So the sans-culottes who had prema-
turely seized power in March 1793 were chased out more than 2 months before
9 Thermidor. 55
Fourier was therefore evidently arrested on the grounds of his support in
October 1793 of the sans-culottes of Orleans, who by the time of his arrest
in Messidor Year II had for some time been regarded by the Committee
of Public Safety — or at least by Robespierre and his associates Saint-Just
and Couthon — as dangerous terrorists worthy of liquidation. Fourier who
had sided with them in October 1793 was by implication an equally
dangerous terrorist. Hence the charge of Hebertism levelled against him by
Demaillot and accepted by the Committee.
Regardless of the justice or otherwise of the charge of Hebertism levelled
against Fourier — not to speak of the justification of Robespierre's policy of
employing terror to suppress terror and usher in the reign of truth and
virtue — the fact remains that 29 Messidor, the date of Fourier's re-arrest,
was a most uncomfortable time to be in prison in France on a political
charge. In reality, it was of course only a few days before 9 Thermidor and
the fall of Robespierre and his associates. But Fourier was not to divine
this. For him it would simply have been the time of the 'great Terror',
when the guillotine devoured its daily batch of victims and heads fell
'like tiles' — to use the picturesque phrase of the public prosecutor
r
44
FOURIER AND THE REVOLUTION: AUXERRE
Fouquier-Tinville. Fourier must therefore have been a prey to extreme
anxiety at least up to 9 Thermidor. If we are to believe his own account in his
letters 58 to Bergoeing and Villetard he also 'suffered every indignity and was
even condemned to death'. There is no documentary evidence for this last
assertion. He could only have been condemned to death if he had been
brought before the Revolutionary Tribunal in Paris as there was no mech-
anism for this sentence for a political offence in Auxerre itself. But if he had
been condemned to death by the Revolutionary Tribunal, then as there was
a gap of at most twelve hours between sentence and execution he would
certainly have been guillotined. So that it seems that Fourier's assertion
must be interpreted in the sense that imprisonment by order of the Com-
mittee of Public Safety on 29 Messidor was effectively equivalent to a
death sentence. Certainly, if Robespierre's own head had not fallen on
10 Thermidor Fourier could well have been brought before the Revolu-
tionary Tribunal, and in that case he would almost certainly have been
guillotined. Happily for Fourier it was not only those in prison at this time
who feared for their lives. There were also many outside who went in fear
and trembling, especially a small group of ex-terrorists including Fouche,
Tallien, and Freron who had soiled the purity of Robespierre's Revolu-
tion by their acts of savage and wanton barbarity, who rightly feared that
they were next on the list to be arrested and brought before the Revolu-
tionary Tribunal, and who in desperation had formed a conspiracy to
overthrow Robespierre and his associates. In the event it was, of course, the
conspirators who won the day, and no doubt Fourier must have breathed a
deep though somewhat confused sigh of relief when news of the executions
of Robespierre and his associates 57 reached Auxerre. He may even have
imagined that he would himself be freed immediately. In the event he had
to wait till 24 Thermidor before an order of the Committee of General
Security commanding his release reached Auxerre. 58
After his release Fourier at first seems to have continued to play his part
in local politics, being listed as a member of the provisional revolutionary
committee on 23 Fructidor (9 September 1794). 59 On 27 Vendemiaire (18
October 1794) a new and presumably definitive committee was elected
from which Fourier resigned on 2 Brumaire 60 (23 October 1794) in order
to become a teacher in the new system of education in Auxerre, although he
did not actually take up his position until the 26 Brumaire (16 November
J 794)- 61 On 21 Frimaire Year III (1 1 December 1794) he was nominated to
the Fcole Normale. 62 The somewhat peculiar circumstances under which
this nomination occurred were related by Fourier himself in a passage in his
letter to Villetard:
In the month of Frimaire last when I was professor of mathematics at the
College of Auxerre, and unbeknown to me, the administrators of a neighbouring
FOURIER AND THE REVOLUTION: AUXERRE 45
district nominated me as a pupil to the Ecole Normale. I did not wish to accept
without the authorization of the constituted bodies of the commune of Auxerre. I
informed the district administration of this nomination, they confirmed it, and in
the order addressed to me included a fair testimonial of my civisme and prin-
ciples. 63
Was Fourier's nomination by a neighbouring district entirely unsolicited,
or had he perhaps discreetly let it be known that he would not be averse to
a change of air ? In any case it is interesting to view his nomination in the
light of a passage from a work of one of his fellow students at the Fcole
Normale :
When the pupils [of the ficole Normale] gathered together France had only just
emerged from beneath the axe of Robespierre. The agents of this tyranny were
everywhere regarded with abhorrence: but the fear which they had inspired,
joined to a fear of their return to power, retained them some vestige of credit.
They profited from this by seizing the opportunity of quitting the scenes of their
vexatious acts. Several had themselves named pupils of the Ecole Normale.
They carried there with the ignorance proper to them the hate, distrust, and
contempt which followed them everywhere. Beside them were men full of wis-
dom, talents and enlightenment, men whose names were celebrated in all
Europe. But the respect with which the latter were clothed could not extend to
the former . . , 6i
Fourier would have had few regrets at the prospect of leaving Auxerre.
Then as now Paris was the mecca for all aspiring young Frenchmen.
Though he was an experienced teacher of many years, and could not
expect to derive much benefit from the Fcole Normale in that respect,
nevertheless he must have hoped that through attending the school he
would at last get in touch with the outstanding French mathematicians of
the day, Laplace, Lagrange, and Monge. He may also have had other reasons
for wishing to leave Auxerre not unconnected with the so-called post-
Thermidorian reaction. 65 In fact some time before his departure he must
already have been thoroughly alarmed at the way things were moving in
Auxerre. There had been warnings of the impending storm considerably
earlier. Thus Balme and he had been 'purged' for a time from the Popular
Society though they were later re-admitted. 66 By the time he left Auxerre
Fourier must have wanted to forget all about his part in the Revolution.
His participation in the government of the Terror would have made him
many enemies. As ex-president of the revolutionary committee he was a
marked man. Now he might hope, like so many other 'ex-patriots' including
his friend Gautherot, to be allowed to lose his revolutionary past in the
great wen of the metropolis. In this he was to be sadly disappointed. But
for a time any anxiety on that score must have been forgotten in the intoxi-
cating excitement of the opening seances of the Fcole Normale in Paris.
46
FOURIER AND THE REVOLUTION: AUXERRE
Notes
1. See below Letter IX, Appendix, p. 280.
2. The open emergence of an active republican party can be effectively dated from
the flight of the King to Varennes (20 June 1971). The next day Paris was
plastered with pro-republican posters of which Thomas Paine later claimed
the authorship. On 8 July Condorcet went over to the republican camp. On
17 July the riot of the Champ de Mars supplied the necessary martyrs to the
republican cause. The next day the anti-republican members of the Jacobin
Society marched off the stage of history in a body to form the Society of
Feuillants. Contrary to their confident expectation it was the Jacobin Society
which flourished and the Feuillants Society which withered away.
3. This is the story given by Mauger (p. 272). Cousin (p. 4) also mentions the same
speech although he does not say it was the occasion of Fourier entering the
Popular Society of Auxerre. Challe (2) p. 112 has a rather different story.
According to him Fourier's speech before the Popular Society was to gain
exemption himself from military service, not to encourage others to enlist as
stated by Cousin.
4. See below Letter IX, Appendix, p. 281.
5. Aim. Yon., 1793. P- i°9-
6. Meaulle, J. N. (1757-1826). Representative of Loire-Inferieure at the Con-
vention where he voted for the death of the King. Was a member of the Com-
mittee of General Security and went on various missions in which he was
noted for his moderation. He was a member of the Council of 500 and occupied
various positions under the Empire. He was banned as a regicide in 1 816 and
died in exile (Bio. Gen. ; Gde. Encycl).
7. Arch. Yon. Serie L, Reg. 490.
8. See below Letter IX, Appendix, p. 281.
9. Idem.
10. Idem.
11. Poree, vol. 6, p. 93.
12. See below Letter IV, n. 3, Appendix, p. 256.
13. According to Maure's letter of 12 Brumaire. See above p. 34.
14. Arch. Nat. AF II 151, C6te 1221.
15. See below Letter IV, Appendix, p. 255.
16. Lefebvre (2), vol. 2, pp. 97-157.
17. Though revolutionary from its original inception in 1789 the dominant political
tone of the society had shifted steadily to the left from constitutional through
republican to Montagnard.
18. Goyre-Laplanche, J. L. (1755-1817). Originally a member of the Benedictine
order, he was elected to the Convention for Nievre. In the trial of the King he
voted for immediate execution. The letter of 13 October 1793 from the Com-
mittee of Public Safety recalling Laplanche from Orleans and instructing him to
proceed to Caen to take the place of Robert Lindet — judged too moderate in
his putting down of the federalist revolt in Calvados — talked of the necessity for
'striking acts of severity which spare none of those guilty'. The letter was signed
by Collot d'Herbois who would have had personal experience of Laplanche's
capacity for such acts at the time when Laplanche and he first set about
'revolutionizing' Orleans in the preceding March. According to Kucinski
Laplanche was much more severe than d'Herbois, who later, however, was far
FOURIER AND THE REVOLUTION: AUXERRE
47
to outstrip any of Laplanche's acts of severity by his bloody partnership with
Fouche in Lyon from 7 November 1793 onwards when over 1500 persons —
including the father of the physicist A. M. Ampere — were executed, often in
batches, for their supposed part in the insurrection in the town earlier in the
year. If we are to believe Kucinski, although Laplanche was essentially loud-
mouthed and boastful rather than evil, nevertheless 'he sent to the Revolutionary
Tribunal men and women from Orleans who were condemned to death'. He is
also said (Cuissard) to have sent many priests to Nantes where they were
drowned. After 9 Thermidor, Laplanche — to his credit — remained faithful to
the Mountain. He was ordered to be arrested on 22 Thermidor Year III but
managed to hide and ultimately benefited from the general amnesty passed at
the last seance of the Convention on 4 Brumaire. He is said to have lived out his
life thereafter close to the Chateau de Rivande, home of his wife Adelie de
Coinces, who, if Cuissard is to be believed, married Laplanche in spite of her
loathing for him only to save her parents from the guillotine. Cuissard states
that Laplanche was a prey to continual fears for his life and that before his
death he made a public retraction of his conduct and did homage to the religion
which he had abjured (Bio. Gen. ; Cuissard; Kucinski).
19. Aignan, E. (1 773-1 824). The author of several tragedies and of Extraits des
memoires relatifs a I'histoire de France depuis 1767 a la Revolution (Paris 1825)
written in collaboration with Norrins. Elected to Academie Francaise in 1824.
20. De Coinces, Delaguelle (1736-1809). Descended from an ancient bourgeois
family of the Salogne. He entered law and took up a position in Orleans. He
embraced the Revolution and was elected to the Convention where he sat
with the Mountain. In the trial of the King he voted for death without stay
or appeal to the people. He was a member of the Jacobin Club and was main-
tained a member at the seance of 12 December 1793. His political career ended
with the Convention and thereafter he lived in Paris until his death (Kucinski).
21 . No trace could be found of the unfortunate Rimbert.
22. The sanctity of property and the right of holding and acquiring wealth con-
tinued to be respected, at least in principle, throughout the most violent and
radical phases of the French Revolution.
23. See below Letter IX, Appendix, p. 283.
24. Arch. Nat. AF II 146B, Doss. 1 179, piece 22.
25. Proc. Verb. Conv. Nat., vol. 24, p. 198.
26. Barere, B. (1755-1841). A barrister by profession, he was elected to the States
General and later to the National Convention. At first he voted with the
Girondins, pouring ridicule on Robespierre on the occasion of Louvet's
attack on 5 November 1792. Later by his services he performed the miracle of
calming Robespierre's normally inexorable rancour. As president of the Con-
vention in December 1792 he encouraged the trial of the King: 'the tree of
liberty', he said, 'will not know how to grow unless it be watered by the blood
of Kings'. He voted for the immediate death of the King without stay or
appeal to the people. He became a member of the Committee of Public
Safety, remaining neutral up to the insurrection of 31 May and the fall of
the Gironde, after which all his actions were directed towards living down his
past moderation. On 5 September it was Barere who decreed the Terror to be
the order of the day. He played a leading part in the judgement of the Queen
and demanded the death sentence on the Girondins. Above all he made himself
the ingenious flatterer of Robespierre, all the minutes and orders of the
48 FOURIER AND THE REVOLUTION: AUXERRE
Committee of Public Safety relative to the diffusion and printing of Robe-
spierre's discourses being in his hand. Without any ideas of his own, if he had a
subject to treat he would approach in turn other members of the Committee of
Public Safety who would later be surprised to find their own ideas issuing from
him as from a faithful mirror. But he was a brilliant orator — Burke dubbed him
the Anacreon of the guillotine — and an equally brilliant drafter of reports and
minutes, and played a key role in the working of the dictatorship of Year II.
In the session of 9 Thermidor he was very perplexed to know which side to
support, and tradition has it that he had two speeches in his pocket, one for and
one against Robespierre. His embarrassment became extreme when from all
sides arose the cry: 'Barere to the platform.' Without mentioning Robespierre
by name he attacked him at his most vulnerable point by ordering the arrest
of the commandant of the National Guard Henriot, and later he submitted the
report on the outlawing of Robespierre and his fellow associates. Following
the rising of March he was sentenced to be deported in company with Collot
d'Herbois and Billaud Varenne. But Barere managed to escape and remained
in hiding till the general amnesty of 4 Brumaire. In 18 16 he took refuge in
Belgium as a regicide, only returning to France after the July revolution. He was
elected a deputy in 1832 but the election was declared void on a technical
point and he never sat. No doubt the King, Louis Phillipe, did not relish the
idea of one of those who had 'betrayed' his father, Phillipe Egalite, sitting in the
assembly (Bio. Gen. ; Gde. Encycl.).
27. Le Moniteur Universel (anc. Ed.) No. 39, 9 Brumaire Year II.
28. We learn of this hurtful detail in Ichon's letter to the National Convention.
29. Arch. Nat. AF II 151, C6te 121.
30. Idem.
31. Cousin (1), p. 6.
32. Arch. Nat. AF II 164, Cdte 1345.
33. As related in the accounts of both Mauger and Challe.
34. Arch. Yon. Serie L, MS. 203.
35. Arch. Nat. AF II 146B, Doss. 1179, piece 25.
36. The present whereabouts of the letter of the Committee of Public Safety to
Ichon is unknown. It would seem to have been available to Kucinski who relates
how the Committee 'invited Ichon to return to the bosom of the Convention
to enjoy a needed rest'.
37. See Letter V, Appendix, p. 258.
38. 29 March 1794.
39. The words supposedly applied by one of Lavoisier's judges before the revolu-
tionary Tribunal — La Revolution n'a pas besoin des savants — may be apocryphal
but they certainly applied to Lavoisier himself.
40. See Letter IX, Appendix, p. 282.
41. Arch. Yon. Serie L, Reg. 229.
42. Moiset, p. 16. For a biographical note on Balme see below Letter XII, n.io,
Appendix, p. 295.
43. Arch. Yon. Serie L, Reg. 223.
44. Moiset, p. 19.
45. Cousin, p. 6.
46. Arch. Yon. Serie L, MS. 1420.
47. Arch. Yon. Serie L, Reg. 322.
48. Cousin, p. 6.
FOURIER AND THE REVOLUTION: AUXERRE
49
49-
50-
Si-
52.
53-
54-
55-
56.
57-
58,
59
60.
61,
62
63
64
I can find no trace of Fourier's presentation to the Jacobin Society or of his
introduction to Robespierre. Cousin appears to have originated this detail
which he probably had from Roux.
The sending of such a deputation from Auxerre to Paris, a distance of some
180 kilometres, at the most dangerous period of the great Terror was at one and
the same time a measure of the esteem in which Fourier was held in Auxerre —
as Cousin himself notes — of the real (and justified) fear for Fourier's life, and
of the bravery of the deputation. In Messidor Year II the whole of France was
gripped by fear and sensible people took good care not to draw themselves
to the attention of the Committee of Public Safety.
If Cousin's account can be trusted, Saint-Just would seem to have heard
Fourier speak, presumably at the Jacobin Society. Robespierre was notoriously
intolerant of any rivals to his oratorical ascendancy, and if Fourier pleaded his
case too eloquently either to Robespierre himself or in his presence before the
Jacobin Society he might have attracted Robespierre's suspicious jealousy. A
good example of the latter's touchiness in this respect is provided by his un-
successful attempt to have Couthon announce the victories of the Republic to
the Convention in place of the too eloquent Barere.
n. 47, above.
Ibid.
Arch. Yon. Serie L, Reg. 637.
Lefebvre (2), vol 2, pp. 162-3.
Letter VIII, Appendix, p. 276: Letter IX, Appendix, p. 280.
In his letter to Villetard (Letter IX, Appendix, p. 283) Fourier mentions that
one of the two commissioners responsible for his arrest in Messidor was
declared an outlaw on 10 Thermidor.
Arch. Nat. F 7 4575, quoted in Poree, vol. 2, p.
Arch. Yon. Serie L, Reg. 557.
Ibid.
Arch. Yon
Arch. Yon
165.
Serie L, Reg. 219.
Serie L, Reg. 399.
Letter IX, Appendix, p. 281.
J. B. Biot (4), p. 67. Quoted in Alain, p. 174.
65. This reaction had begun immediately after 9 Thermidor with a spontaneous
movement in the Convention to reduce the power of the Committee of Public
Safety culminating in a decree of 24 August 1794 which reduced its status to
one of equality with all the other committees of the Convention, and required
it in future to restrict itself exclusively to foreign affairs and the conduct of the
war. Up to this point there can be no doubt that the majority in the Convention
had no desire to attack all the remaining members of the 'great' Committee of
Public Safety and other Jacobins. But the movement which had begun by a
reduction in the power of the Committee of Public Safety could not stop there.
The Revolution had gone into reverse, the highwater mark of sans-culotte and
Jacobin influence was past, and soon there was a general movement to discredit
and remove from office former Jacobins of all kinds. For a time the Jacobins
in Paris counter-attacked strongly, especially after the expulsion from the
Jacobin club of the renegade terrorists Tallien and Freron, and the mother
society in Paris also drew support from other societies in the provinces. But
from around September onwards the tide began to flow ever more strongly
against the Jacobins. There was a strong revulsion of public feeling against them
50
66.
FOURIER AND THE REVOLUTION: AUXERRE
at the time of the trial and release of the 132 prisoners from Nantes. This was
accentuated still further through the subsequent trial and execution of the
terrorists Carrier and Joseph-le-Bon. All this time the power of the shock troops
of the right, the so-called Jeunesse-Doree— led by the ex-Jacobin Freron well
schooled in all the tricks of street and other intimidation— was increasing
steadily until ultimately they wrested control of the centre of Paris from the
Jacobin supporters. A critical stage was reached with the closing of the Jacobin
club in November 1794. At the same time the reaction began to spread into the
provinces where it took a much uglier turn. Extensive massacres of Jacobins
commenced in various places in the South, especially, as in Lyons and Nimes,
where repression in the autumn of 1793 following the federalist revolt had
been most severe. Although there are indications that the Thermidorian
reaction took longer to reach Auxerre than most places, nevertheless by the end
of Ventose Year II the Thermidorians were evidently in full control. By this
time Fourier had already left Auxerre, for according to the departmental archives
'In Ventose Year III [February/March 1795] the college at Auxerre has become
completely disorganized by the departure of professors Balme, Fourier
(Arch. Yon. Serie L, Reg. 224 1 .).
Arch. Yon. Serie L, Reg. 559.
FOURIER AND THE REVOLUTION:
PARIS
1. The Normalien
The Fcole Normale (Year III) 1 was called into being 2 by a decree of the
National Convention dated 9 Brumaire Year III (30 October 1794) with a
view to increasing the number of elementary school teachers of which
there was at that time an acute shortage in France. This decree was then
executed with impressive — and as it turned out excessive — dispatch and on
1 Pluviose (20 January 1795) the school was inaugurated amid great en-
thusiasm 3 and with all due pomp and ceremony in the grand amphitheatre
of the Museum d'Histoire Naturelle under the presidency of the represen-
tatives of the people Lakanal 4 and Deleyre. 5 Fourier was certainly the
ablest — and later the most distinguished — of all the pupils who crowded
the banks of the grand amphitheatre on that memorable scene. Unlike some
of the other pupils he was also assiduous in his subsequent attendance. In
an undated letter 6 to Bonard he gives a vivid impression of the early sessions
of the school.
The tcole Normale holds its sessions at the Jardin-des-Plantes, 1 in a middling-
sized place of circular shape; daylight only enters from above; the pupils who
are very numerous, are seated in rows on the tiers of a very high amphitheatre;
there is not room for everyone, and every day there are a fair number who find
the door closed; if one is obliged to leave during the session, one cannot enter
again. Only pupils are admitted, on presentation of their cards to the officer on
guard or the sentry. Some exceptions are made, however, in the case of a small
number of loyal citizens and of several women. At the back of the room, and
within an enclosure separated by a railing, are seated several Parisian scientists
and the professors. In front, and on a slightly higher platform are three arm-
chairs for the professors who are to speak and their assistants. Behind them, and
on a second, still higher platform, are the two representatives of the people
Lakanal and Deleyre, in the uniform of deputies on detached service. The session
opens at 1 1 o'clock when one of the deputies arrives ; there is much applause at
this moment and when the professor takes his place. The lessons are almost al-
ways interrupted and terminated by applause. The pupils keep their hats on,
the professor who is speaking is uncovered ; three quarters of an hour or an hour
later, a second professor takes his place, then a third, and the usher announces
that the session is ended. The names of the professors are familiar to the men of
letters who attend the sessions and conferences. I have noticed Cousin, 8
52
FOURIER AND THE REVOLUTION: PARIS
Lalande, 9 Brisson, 10 the bookseller Panckoucke, 11 several professors of the Lycee.
Several are brought in official carriages or with the deputies ; the professors never
come any other way. Here are some particulars about the professors: these
minutiae may appear superfluous, but I am writing them because the papers give
no account of them.
Doubtless the particulars given by Fourier did not appear 'superfluous'
to Bonard, and they certainly constitute one of the very few first-hand
accounts of the appearances, idiosyncrasies, and lecturing habits of a
quite extraordinarily gifted group of men including the leading contempo-
rary Parisian mathematicians and scientists of the day. Qua mathematician,
Fourier was inevitably particularly moved and impressed to see before him
Lagrange, 12 'the first among European men of science'. The majority of
students, innocents at least as regards mathematics, gave Lagrange 'a
rather poor reception'. For them, no doubt, he was just a comic old boy
incapable of preserving order, who showed his Italian birth by pronouncing
s like z: but for Fourier he was the author of the Mecanique Analytique,
the creater with Euler of the Calculus of Variations, an analyst of genius,
and the fact that there was in his speech 'the hesitation and simplicity of a
child' would only have made his true greatness more apparent to Fourier's
discerning eye. Laplace, 13 who unlike Lagrange, was only among the first
rank of men of science, evidently made much less of an impression on
Fourier, and he may already have taken a personal dislike to a man whose
excessive — and quite unnecessary — deference to authority had recently led
him to pocket his pride by accepting nomination as a pupil at the Ecole
Normale as a result of an 'administrative error' later 'repaired' by the
government. As a teacher of long standing himself, and former Professor
of Eloquence in Auxerre, Fourier judged the professors' success or failure
to communicate with a practised and critical eye. Thus he found that
Hauy 14 spoke with extreme precision and clarity: 'it would be impossible
to express oneself better'. But he was unable to cope with questions,
becoming confused and answering 'badly or not at all'. D'Aubenton, 15 a
'broken old man' who was almost carried to his chair, spoke and read
alternately and was understood by no-one. And yet the touch of humour
in his speech was sufficient to inspire the respect of the students. Berthollet, 16
'the greatest chemist we have either in France or abroad', found it exces-
sively difficult either to speak or to perform experiments, and was under-
stood only by those 'who study much or understand already'. Monge, 17
on the other hand, who had a loud voice, and was 'active, ingenious, and
very learned', fell into the opposite extreme of excessive clarity: 'One
finds even that he is too clear, or rather that his method is not sufficiently
rapid.' Of the representatives on the Arts side, La Harpe, 18 with his
'bantering and decisive way of speaking', was of all the professors the one
FOURIER AND THE REVOLUTION: PARIS
53
that Fourier liked best to listen to, and after him Garat. 19 Volney, 20 who
spoke slowly and seemed to take a pleasure in it, and who astonished the
audience by the 'glitter of his diction' evidently tried to stuff too much
philosophy into his course which lost its principal object in the process. Of
the accounts of the various professors the most vivid and amusing is that of
the teacher of deaf-mutes, Sicard : 21
Sicard is well known as a teacher of deaf-mutes. Of short stature, still young, he
has a strong voice, distinct and vibrant. He is ingenious, interesting, active, and
knows how to keep the attention of a large audience. He pleases the crowd who
bring down the roof in applause. He praises his subject, his method and his
principles, and at every turn talks of the natural man, whom he claims to be
deaf and dumb. He is a man of great wit, without genius, who seems to be very
sensitive and, is I think, in reality modest, but he has been beguiled by some sort
of grammatical system which he claims to be the clue to the sciences. He often
speaks for a long time and pompously, and there is something capricious in his
accent and diction. His theory of grammar, which is brilliant in certain respects,
is one of the craziest I know of. In spite of this there is talk of adopting it, and
even prescribing it in all the schools of the Republic. If this comes about we
shall have something to laugh at. Apart from this, Sicard is full of enthusiasm
and patience and is a paragon of all the virtues, but he is mad : that makes me
think that he pleases the ladies, although he is small and rather ugly.
Inaugurated on i Nivose the Fcole Normale was officially closed on
30 Floreal following, though most of the pupils had probably departed for
their several homes sometime earlier as on 5 Floreal only forty-nine had
voted to continue the courses. No doubt Fourier was among the faithful
forty-nine, 22 more especially as he had previously been appointed one of
the mditres des conferences in mathematics. 23 For the majority of the pupils
the Ecole Normale had been largely a waste of time. Many in fact were
quite incapable of following the courses offered and soon found more
entertaining ways of passing their time at public expense in a Paris which
was reacting furiously from a regime of terror, virtue, and fixed prices in a
whirl of gaiety, dissipation, and inflation. Fourier was an outstanding
exception. The Fcole had provided him with the opportunity of meeting
some of the foremost French mathematicians of the day including Lagrange,
Laplace, and Monge. This was the turning point in his career, and pro-
vided in retrospect one of the few justifications for adding fuel to the in-
flationary fire to the tune of some z\ million francs of public money. 24 Un-
fortunately Fourier's success at the Ecole Normale was soon clouded by
anxiety engendered by rumours of action against him in Auxerre for his
part in the government of Year II. By 28 Ventose (18 March 1795) he was
sufficiently alarmed to write to Bonard for information and advice on the
matter. 25
54
FOURIER AND THE REVOLUTION: PARIS
2. Imprisonment of Prairial Year III
Fourier had heard vague news that he had been accused and condemned
in the sections and that he had been held up as a peculator and a drunkard,
a laughable charge if he had not known the excesses of which the 'armed
vengeance of the factions' were capable. What he desperately needed from
Bonard were precise details of any charges which had been levelled against
him. In fact, in typical Fourier style, he was not so uninformed as he had
made out. He had heard that the assembly of the sections had decided to
denounce him and demand his exclusion from the Fxole Normale. But he
required details of the accusations brought against him. In any case he
thought the denunciation irregular and unlikely to succeed. Was he not
employed by the Government at the College de France ? What could harm
him except material facts ? Where would these facts be found ? Who could
reproach him with 'an act unauthorized by the law'? His conscience was
clear:
I voluntarily did what I thought was just and useful to the cause which I em-
braced: what went beyond this I did not impede, but for the most part I could
not have done so without rushing to certain ruin.
Of course he could be blamed for not risking his life rather than tolerate
injustice, but he demanded at least that he should only be blamed by
those who would have done so themselves in his place. Poor Fourier,
everything had been going so well at last ; his health had been fairly good,
Laplace and Lagrange had promised to publish a new proof he had given
of the 'famous rule of Descartes', he was 'on very good terms with these
two mathematicians', he was devoting himself to study with more en-
thusiasm than ever, and would have been perfectly happy if only he had
been left in peace. But this miserable affair of his denunciation at Auxerre
had greatly disturbed him — as he put it to Bonard:
Whatever it is, mental uneasiness or excessive work, I am not at all well : I have
been obliged to keep to my room today.
At the time (28 Ventose, 18 March 1795) of writing this letter Fourier
was evidently a prey to the most gloomy forebodings. These were only too
well justified. His enemies in the commune of Auxerre had no intention of
leaving him in peace. In an address to the National Convention dated 30
Ventose (20 March 1795) inveighing against former 'terrorists' the follow-
ing ominous passage occurred :
We shudder when we think that the pupils of the Fxole Normale were chosen
under the reign of Robespierre and his prot igis. It is only too true that Balme and
Fourier, pupils of the department of Yonne, have long professed the atrocious
principles and infernal maxims of the tyrants. Nevertheless they prepare to be-
FOURIER AND THE REVOLUTION: PARIS
55
come teachers of our children. Is it not to vomit their poison in the bosom of
innocence . . .? 26
No doubt Fourier, who always seems to have been singularly well in-
formed, would have heard of this address, and also that of 10 Germinal
(30 March 1795) 27 which called for the disarming of terrorists. The
insurrection of 12 Germinal 28 would then have done nothing to still his
apprehensions, nor the Convention's own decree of 21 Germinal (10 April
1795) for the disarming of terrorists.
However, there is no trace of the address of 30 Ventose having reached
the floor of the Convention, and Fourier would have begun to breath more
freely again when the same address was suddenly presented by a commis-
sioner of the commune of Auxerre to the Committee of Public Instruction
at their seance of the 22 Germinal (11 April 1795). 29 Denunciations of for-
mer terrorists were flying thick and fast at the time and the Committee was
evidently not prepared to take any action against Fourier and Balme on the
basis of so generalized and undocumented a condemnation. They therefore
simply sent the address back for comments to Mailhe, 30 at that time repre-
sentative of the people on mission in Yonne. Given Fourier's special
position teaching mathematics in the College de France and his relations
with Lagrange, Laplace, 31 and Monge it is probable that he would have
learnt of what had taken place and once again he would have been thrown
into a state of nervous uncertainty. Again nothing happened for a long time.
Finally on 26 Floreal (15 May 1795) Mailhe's report on Fourier and Balme
found its way back to the Committee. 32 It was not very encouraging. It
found Fourier and Balme among the chief of those responsible for the
'tyranny which had recently weighed on the town of Auxerre' and recom-
mended that they be prevented from entering the teaching profession.
This could evidently not be ignored, and though the committee may have
been loath to take action against such well-qualified persons as Balme and
Fourier it nevertheless recommended the Treasury to suspend the in-
demnities 33 due to them as pupils at the licole Normale. At the same time
it passed on the report of Mailhe to the Committee of General Security. 34
Two days later, however, as a result of the personal intervention of Maure
and Villetard, two of the representatives of Yonne at the Convention, the
committee countermanded the suspension of the indemnities of Fourier
and Balme. 35 It was the last service Maure would do Fourier. A few weeks
later, having been implicated in the Romme conspiracy following the
insurrection of 1 and 2 Prairial, 36 and his arrest having been decreed by the
Convention, he committed suicide.
As repression grew following the surrender of the Faubourg St. Antoine
on 4 Prairial (23 May 1795) Fourier's fears must have grown even sharper.
Moreover he now had an additional cause for alarm apart from the original
56
FOURIER AND THE REVOLUTION: PARIS
condemnation contained in the address of 30 Ventose and the unfavourable
comments of Mailhe, both presumably irretrievably lodged in the files of
the Committee of General Security, for on 23 Floreal (12 May 1795) an
order 37 had been issued at Auxerre demanding the disarmament of a
number of terrorists including Fourier and Balme. On hearing of this
through his relatives, Fourier wrote to the Municipality on 12 Prairial
(31 May 179s) 38 pointing out that although he had had no official notifica-
tion of the order, and no chance to defend himself from the charge of
terrorism, nevertheless he would hasten to conform to it. But the day
before, unknown to Fourier, Mailhe had issued a second order dated
11 Prairial (30 May 1795) 39 ordering the detention of all those so-called
terrorists who had failed to comply with the original order of 23 Floreal.
Before hearing of this new order Fourier again wrote to the Municipality
asking before which duly constituted authority he should present himself
in order to effect his disarmament in a regular manner. Elsewhere 40
Fourier describes how he attempted to disarm the enmity of his opponents
in Auxerre by resigning a new position given him at the Fcole Centrale des
Travaux Publiques (later Fcole Polytechnique). But even this despairing
move was in vain. The reply of the municipality was not long in coming.
On the night of 18/19 Prairial (7/8 June 1795) 41 he was awakened by
Bayard, chief of the armed guard of the section of Social Contract, and
marched off to prison in the Rue des Orties having scarcely been granted
the time to dress himself. 42 According to Cousin, who probably had the
story from Roux, Fourier never forgot the reply given by Bayard when the
concierge expressed a hope that Fourier would be back soon — 'Come and
get him yourself — in two pieces!' 43
A few days after his arrest Fourier addressed a letter 44 to the chairman
of the Committee of General Security in which he gave a detailed account
of the events leading up to his arrest, and defended himself vigorously
from any possible charge of terrorism. He asked to be interrogated either
by Bergoeing himself or in his presence. 'I address my complaints to you
confidently,' he said, 'and I beg you to excuse the disorder and length of
this letter. I have scarcely enough freedom of mind to justify myself; your
humanity will make up for that.'
Fourier's protest, however, with its urgent demand for an interrogation
was either unnecessary or immediately effective, for on the same day (24
Prairial) he was freed provisionally by order of the Committee of General
Security. 45 But Fourier's provisional liberation was evidently not confirmed
as appears from a letter addressed to the Committee of General Security
by one of his brothers :
To the citizen members composing the Committee of General Security.
Citizens, Jean Baptiste Fourier, tailor of Auxerre, at present at Paris for reasons
FOURIER AND THE REVOLUTION: PARIS
57
of business, No. 27 Rue David at the house of citizen Moutron, points out that
he has just been informed that the citizen Joseph Fourier his brother, former
pupil of the Fxole Normale, living at No. 5 Rue de Sauvage Maison de Bour-
gogne, was arrested there and has been made prisoner in the jail of the Rue des
Orties.
Assured of the innocence of his brother by the principles which he knows to be
his, the petitioner is unaware of the reasons for his detention, but he hopes,
citizens, that your justice will find itself concerned to order his prompt interroga-
tion. This is why he presents his request to you. 46
Jean Baptiste's letter was minuted in the margin: 'Fourier demands the
liberty of his brother who is arrested. Find the denunciation. Find the
papers and the motives and join them to this to make the report.' It was
then evidently sent to the committee of the section of Social Contract —
where Fourier had resided previously — who returned it to the Committee
of General Security with a letter 47 dated 16 Messidor (4 July 1795) in
which they detailed their part in Fourier's arrest on the night of 18/19
Prairial. Having been released provisionally Fourier had thus evidently been
re-arrested and was still in prison on 16 Messidor almost a month after his
original arrest on the night of 18/19 Prairial.
3. The terrorist
It is not known if Fourier was ever brought before a court during his
imprisonment in Prairial Year III, or even if he was interrogated. In any
case it is evident that the two main charges brought against him would have
been his failure to comply with Mailhe's order of 23 Floreal to present
himself at Auxerre to be disarmed, and that of having inspired terrorism.
As to the first charge, it is evident that his enemies in Auxerre used his
failure to present himself there to be disarmed as a pretext for having him
arrested in Paris. But what of the far more serious charge of having inspired
terrorism in the year 1793-4? Here it is known with certainty what his
defence would have been. It is given in considerable detail in a letter to
Joseph Villetard written from prison, and in more summary form in the
last part of his letter to Bergoeing:
As to the charge of terrorism, I am unable her e to advance all the reasons
which will convince you that these charges are unfounded. I shall only insist on
the incontestable facts that no-one in the commune of Auxerre was condemned
to death or judged by the Revolutionary Tribunal at Paris; that no revolutionary
tax was established of any kind whatsoever, that the property of those detained
was never confiscated, that no cultivator, artisan, or merchant was arrested, that
in what concerns me personally I believe that I introduced into my conduct and
my opinions a moderation which I did not find in my adversaries, that far from
58
FOURIER AND THE REVOLUTION: PARIS
having shared the revolutionary madness of many men I regarded it with horror
and blamed it publicly; that I have experienced terror more than I inspired it,
as I was the victim of it precisely on the same date a year ago, that I was arrested
and even condemned to death, delivered by the unanimous demands of the
assembled sections, the same which abandoned me or pursued me today, arrested
again so that I owed to 9 Thermidor both life and liberty, so that there is no
one of my compatriots who has known more danger than I. 48
Fourier's experience as an advocate before the popular Tribunals in
Auxerre and elsewhere had evidently given him useful practice in preparing
a case. He wisely confined himself to important matters of fact which
Bergoeing, as the then chairman of the Committee of General Security, the
body responsible for all police matters throughout France, would have
been in an unrivalled position to check. It can be assumed therefore that
during the Terror no-one in the commune of Auxerre was executed, or
brought before the Revolutionary Tribunal, that no revolutionary taxes
were levied and no goods of detainees confiscated. In other words that
there were no major acts of terror in the commune of Auxerre during the
period 1793 to 9 Thermidor 1794.
But if Fourier could thus exonerate himself from any major acts of
terrorism, what of his part in the regime of the Terror, especially the arrest
and detention of suspects, in the commune of Auxerre ? To this charge he
would no doubt have replied in the regular manner of all subordinates of a
dictatorship before and since:
Let them take it as certain that I have done nothing arbitrarily and nothing
that does not emanate directly from a law 49
or
I was entrusted by their own votes with a surveillance determined by the law. I
received this position without soliciting it, I continued it without the power of
withdrawing from it, and I exercised it without passion. 50
Fourier was certainly not a Fouche or a Joseph-le-Bon. Having con-
tinued, or, as he argued in his letter to Villetard, having been forced to con-
tinue a member of the Committee of Surveillance after the Law of Suspects
of 17 September 1793 had transformed it into a revolutionary committee
and the primary agent of the apparatus of the revolutionary and terrorist
government in the neighbourhood, he was more aware than most of his
colleagues of the possibility of a day of reckoning. 'I respected', he says in
his letter to Villetard, 'the power which had been given me, and repeated a
thousand times that we should render an account of it one day.'
But Fourier in office was not only careful to act in perfect conformity
with the law, he also — if his own account is to be believed — did everything
FOURIER AND THE REVOLUTION: PARIS
59
he could to temper the rigour of that law. Thus in regard to the interior
regime in the local detention centre he argued 'that everything not expressly
forbidden by the law should be allowed'. 51 He also claimed to have
argued constantly against those who were in favour of confiscating the
goods of detainees. Nor did he confine himself to negative actions. Accord-
ing to his letter to Bonard of 28 Ventose Year III there were 'several
persons' who were indebted to him for the tranquillity 'which they always
enjoyed'. In his letter to Villetard he also refers to certain citizens whom he
defended against unjust denunciations, and others whom he protected by
secret warning — calling to mind the story of the mission to Tonnerre
related by Cousin.
The picture of Fourier which emerges from all these accounts is far from
the 'monster of immorality and inhumanity' conjured up by his opponents
in the commune of Auxerre. Nevertheless a doubt evidently remained even
in Fourier's own mind as appears from a passage in his letter of 28 Ventose
Year III to Bonard.
However, my opponents can leave it to my conscience, and I am judged by it
much more rigorously than they themselves would judge. Let them take it as
certain that I have done nothing arbitrarily and nothing that does not emanate
directly from a law. That is enough for me to feel no anxiety under a good
government. But it is perhaps not enough to satisfy myself, and so I can add that
my heart was never party to the evil produced by circumstances. I voluntarily
did what I thought was just and useful to the cause which I had embraced: what
went beyond this I did not impede, but for the most part I could not have done
so without rushing to certain ruin. It will be said that I should have taken the
risk rather than tolerate injustice and act as its instrument; that may be true,
but at least let me be blamed only by those who would have done so themselves
in my place. 52
Fourier's defence will readily be accepted, especially when account is
taken of the measures he took to save the innocent, the feeble, and those
who had fallen into 'error'. But those who suffered the indignity of deten-
tion on the strength of warrants signed by Fourier were inevitably not
disposed to forgive him so easily. As he put it in his letter to Villetard:
There remain, therefore, those citizens who being noble or priests or relations
of emigres found themselves included under the law of 17 September and who ex-
perienced a temporary detention when they showed themselves declared enemies
of the Revolution. They accuse me of not having been opposed to their arrest and
will never pardon me for having signed the warrants for their arrests. They pre-
tend to believe that I could have released them and wanted me to make this use
of the trust which had been placed in me. 53
As it turned out, Fourier was the only member of the former revolu-
tionary committee whom they could reach. The others listed as terrorists
60 FOURIER AND THE REVOLUTION: PARIS
were disarmed in conformity with Mailhe's order of 23 Floreal. Fourier
alone, either for the reasons given in his letter to Bergoeing, or because he
feared to return to Auxerre, failed to comply with the order of Mailhe.
His adversaries in Auxerre evidently seized on this exultantly, and pursued
him with implacable hatred and 'boundless revolutionary fury' until they
had effected his arrest.
If Fourier, therefore, was evidently not a terrorist in the true sense of
the word, it still remains to place him in the rather broad political spectrum
of the 'patriots' of Year II stretching from enrages such as Varlet and
Roux on the lunatic fringe of the left, through the Hebertists, the followers
of Marat and the Robespierrists to the Dantonists and Indulgents on the
right. Now it is certain that Fourier was arrested in Messidor Year II
(July 1794) on the grounds of his intervention on the side of the sans-
culottes of Orleans in the previous October. 54 By July 1794 these same sans-
culottes had come to be regarded by the Committee of Public Safety — or at
least by Robespierre and his associates — as dangerous terrorists worthy of
liquidation. Fourier who had sided with them in October 1793 was by
implication an equally dangerous terrorist. Hence the charge of Hebertism
levelled against him by the agent Demaillot and accepted by the Committee.
This charge, however, need not be accepted at its face value. No doubt the
sans-culottes whom Fourier had supported in Orleans in October 1793 were
very extreme. What is known of Taboureau makes it probable that at the
very least they were Hebertists, and their action in calling for the death of
the Dauphin the following spring confirms it. But this, of course, by no
means proves that the Fourier of October 1793 was himself an equally
extreme revolutionary. It is in fact impossible to believe that in October
1793 (or at any other time) Fourier was a committed follower of Hebert
with his bloodthirsty appeals in the Pere Duchesne for so many noble heads
(including that of Bailly), just as it is impossible to believe that he would
not have been revolted by the call of the sans-culottes of Orleans for the
death of the Dauphin in the spring of 1794. 55 Nevertheless, while he might
even have shared some of Laplanche's personal dislike for the sans-culottes
leaders, he could still have sympathized with their pitiful plight, and have
been moved to intervene on their behalf against Laplanche out of a feeling
of natural justice 'in conformity with the principles of the Revolution'. 56
In any case, it is clear that although Fourier's political convictions of
October 1793 must inevitably have lacked the bloodthirsty frenzy of Hebert
and the enrages they were still very radical. This conclusion does not seem
as surprising as it might otherwise appear in the light of what is known of
the post-revolutionary Fourier, when account is taken of what is known
of Fourier's political intimates in Auxerre. If some, like Balme 57 and
Bonard 58 were comparatively moderate, no more than republican (though
FOURIER AND THE REVOLUTION: PARIS 61
both serving on the revolutionary committee), others including Milon, 59
Gautherot, 60 Maure, 61 and Defrance 62 were much more radical. Thus
Milon, who is said to have been a relation of Fourier, and who was one of
the principal signatories of the savage address 63 of the Popular Society of
Auxerre calling for the trial — and by implication — death of the King, was
undoubtedly a sans-culotte, that is, more radical than the average member
of the patriot or Montagnard party. Gautherot, who was also a signatory
of this address, was probably even more extreme than Milon. It will be
recalled, 64 for example, that there was a strong suspicion that he had played
some part in fomenting the riot in Auxerre on 19 August 1792 in which
two innocent men were murdered. As for Defrance and Maure, they would
seem to have been more radical than republicans like Balme and Bonard but
less radical than real sans-culottes such as Milon and Gautherot. On the
whole it seems most probable that Fourier was closest to Defrance and
Maure, and that he was like them a committed Montagnard. When account
is taken of his presidency of the revolutionary committee in Messidor
Year II there is therefore no reason to be surprised at the action taken
against him by his Thermidorian opponents in the commune of Auxerre in
the spring of 1795.
4. The Polytechnicien
The reasons for Fourier's final release from prison are not known.
According to Cousin 65 it was due to the intervention of his pupils in the
ficole Centrale des Travaux Publiques, but if it was due to any intervention
this is more likely to have been that of Laplace, Lagrange, or Monge
especially the latter two who must by this time have been well aware of
Fourier's talents as a mathematician, and, what was even more important,
as a teacher of mathematics. Alternatively, and more probably, his release
may simply have been due to the changing political climate in the Con-
vention, which after the end of the repression following the Jacobin in-
surrection of 1 and 2 Prairial veered to the left again in face of a royalist
threat which mounted steadily before it was finally crushed on 13 Vende-
miaire by Napoleon's 'whiff of grape-shot'. As Fourier (and Balme) were
're-armed' in Fructidor Year III 66 by an order of the Committee of
General Security of the eleventh of the same month, it may be assumed that
Fourier was released by the former date at the latest. No doubt he then
went straight back to teaching in the ficole Centrale, and when he next
writes to Bonard it is from the ficole Polytechnique, the same school under
the new, and now familiar, name it had acquired by a decree of 1 September
*795-
The decree establishing the school had been laid before the Convention
62 FOURIER AND THE REVOLUTION: PARIS
by Fourcroy on 24 September 1794 and adopted four days later. Due to
various delays— occasioned in part by a particularly severe winter which
reduced many of the pupils to a state of near starvation — the school did not
open until 21 December. In September 1795, at the end of the first year of
studies, it was deemed to have passed its probationary period satisfactorily
and was confirmed in its establishment. By a law of 1 September its name
was changed from the 'ficole Centrale des Travaux Publiques' to 'Fcole
Polytechnique'. By a succeeding law of 22 October the status of the school
as the sole preparatory school for all the so-called schools of application was
likewise confirmed. By that time Fourier had found a very congenial niche
for himself as teacher and administrator. In a letter to Bonard 67 — who had
been appointed one of the provincial examiners for intending entrants to
the Fcole — he describes the method of choosing successful candidates by a
jury of 'several distinguished scholars' on the basis of marks by examiners
from all over the country. A measure of Fourier's standing in the school
is given by the fact that if there were to be a further examination of in-
tending pupils on reaching Paris he thinks that he would probably be the
one chosen to do it. As for Fourier himself, what he most looked for in
entrance candidates was that they should have 'outstanding talents regard-
less of how much they have actually been taught'— an opinion remarkably
similar to one expressed by Monge at the time of the setting up of the
school. What was necessary above all was a 'marked taste for mathematics
and extraordinary aptitudes together with an aversion, or at least indif-
ference to, the frivolities of which Paris offers so many opportunities'.
Whatever the state of Fourier's religious convictions at this stage, he had
evidently not lost his serious, Jansenist attitude to life, with its emphasis
on the importance of devoting one's energies to study and self-improve-
ment.
Throughout the letter Fourier adopts a tone of new-found importance
and weighty judgment which could have been a little galling to his old
teacher who is begged 'not to neglect this correspondence' nor to doubt
the pleasure it gave Fourier. So that even if Fourier's star was in the ascen-
dent he was full of good intentions to keep in contact with his old friends.
In closing he especially asks to be remembered not only to Mme Bonard
but also to 'little Rene' whom he had baptized, presumably in his quality
as Abbe rather than in his more recent role as president of the revolutionary
committee of Auxerre. All in all there is a strong impression that the scars
of the Terror were being forgotten and that Fourier was at last settling
down to his true vocation of teaching mathematics.
The years 1795-8 spent by Fourier at the Fxole Polytechnique were
marked by periodic crises as the political pendulum continued to oscillate
violently from left to right and back again. These crises sometimes left
FOURIER AND THE REVOLUTION: PARIS 63
their mark on the ficole. Thus after 18 Fructidor Year V (4 September 1797)
when the pendulum swung to the extreme left and a large number of right-
wing members of the Council of Five Hundred were proscribed, the
administration of the school thought it prudent to give a mark of their
republican sympathies — those of the pupils being somewhat suspect at the
time — by planting a tree of liberty. Fourcy has preserved an amusing
account of the ceremony at which Fourier himself participated :
The Minister of the Interior, who had been invited to this ceremony, was
represented by the Director General of Public Education. An attempt was also
made to have Bonaparte (who was then at Paris) present: he promised, but did
not come. As a result Desaix and several other distinguished officers including the
generals Andreossy of the artillery, and Caffarelli-Dufulga of the engineers, were
all the more conspicuous. After a ceremonial gathering in which Monge as
director and after him Fourrier [sic], Neveu, and Chaussier, made speeches about
the branches of teaching for which they were responsible, the whole assembly
moved into the courtyard of the laboratories where an Athenian poplar had just
been planted. The director (Monge) attached a tricolour to the tree and in the
roots was implanted an hermetically sealed bottle containing an account of the
inauguration, together with details of the size of the tree and the various names
given to it by Linneaus, Jussieu, Weston, Ayton, Lamarck, and the Jardin des
Plantes. Verses were sung, strophes recited full of warmth and enthusiasm; in
sum nothing was omitted which could stir the heart. A shower unfortunately
intervened, and the republican fervour of the pupils did not prevent them from
immediately dispersing to seek shelter in the classrooms from whence they
watched the remainder of the ceremony through the windows. The incident
undoubtedly detracted from the effect which it was hoped to produce on the
external world, and produced in the Director General of Public Education a dis-
pleasure which he made no attempt to hide. 68
The school was also affected by the Directory's changing policy towards
it which was in turn largely determined by the ups and downs of the
financial position of the nation. Thus in a letter 69 of 20 Brumaire Year VI
(10 November 1797) to Bonard, Fourier relates how the number of candi-
dates admitted to the school was to be 'greatly reduced by the government'
just at a time when not only the number of candidates for entry had in-
creased, but also their quality, a fact which the examiners were pleased to
attribute in part to the 'spreading abroad' of Fourier's lectures. One thing
which had not changed was the rigid impartiality of the methods of choosing
candidates. Thus when Villetard, like Fourier a native of Auxerre, asked
Fourier's advice about a young man of the district of Avallon who wished to
enter the school he got the following rather dusty answer :
I replied that there was only one door by which to enter this school, and that it
6 4 FOURIER AND THE REVOLUTION: PARIS
was neither his business nor mine to introduce the young man there other than
by way of examination.
Nevertheless Fourier was not above giving members of the election jury
'advance notice of the candidates they will receive from Auxerre' and was
happy to inform Bonard that 'Laplace in particular, whose opinion carries
most weight, agrees with me that special attention should be paid to those
candidates (that is the ones from Auxerre) since their recommendations
originate from a just and very learned man' — Bonard. The same letter
mentions 'a young pupil of citizen Billy, Professor at Fontainebleau'. This
was S. D. Poisson 70 who was to be successively Fourier's pupil at the
ficole, his deputy as Professor of Analysis during his absence in Egypt, the
protege of Laplace, and finally Fourier's bitter opponent over some
questions in connection with the analytical theory of heat.
There is no trace of Fourier having submitted any memoirs to the
Academie des Sciences during his years at the ficole Polytechnique, and
apart from one paper in the Cahiers of the Fxole there is no indication of his
having commenced or continued any major mathematical researches. It
must be concluded, therefore, that apart from any administrative duties —
and knowing Fourier it is difficult to believe that he could have kept out of
either administration or college politics during the years 1795-8 — he was
devoting most of his energies to the preparation and delivery of his lectures.
Two sets of lecture notes have been preserved 71 and display the sort of
elegance and clarity of thought one would expect from Fourier, together
with a lively interest on occasion in the history of the topic under considera-
tion. Given Fourier's eloquence it may be imagined that these lectures
were of outstanding interest and charm and very influential. By 1798
he must have been firmly settled in the chair of analysis and mechanics in
which he had succeeded Lagrange in 1797. At this stage he would surely
have begun to turn his attention again to his own private research in mathe-
matics which had been interrupted some nine years previously by the
Revolution. But once again, as in 1793, his career was to take a new and
unexpected turn, this time as a result of a letter received from the Minister
of the Interior :
The Minister of the Interior to Citizen Fourier Professor at the Ecole Poly-
technique.
Citizen, the executive directory having in the present circumstances a particu-
lar need of your talents and of your zeal has just disposed of you for the sake of
public service. You should prepare yourself and be ready to depart at the first
order. If you are actually charged with any employment or if you occupy any
place at the expense of the Republic you will conserve them during your mission
and the salary attached to them will be paid to your family. 72
FOURIER AND THE REVOLUTION: PARIS
65
Notes
1. This addition is necessary if the short-lived school of Year III is not to be
confused with the present Ecole Normale going back with certain interruptions
to 1808. The inscription referring to the school of Year III on the front of the
present Ecole Normale would seem to imply a connection between the two
schools. But as Alain (Chapter 5) conclusively shows, the two schools were
entirely distinct as regards both origin and purpose. For the Ecole Normale
(Year III) was set up by the Convention to train teachers for primary education,
while the forerunner of the present Ecole Normale was set up some sixteen
years later as an integral — though rather minor part — of the Napoleonic system
of education to train professors for secondary and higher education.
2. The idea of such a school, like so much else in revolutionary and post-revolu-
tionary France, as de Tocqueville was the first to realize, went back to the
ancien-regime. Following the expulsion of the Jesuit order from France in
1762 the college of Lisieux was transferred to the college of Louis le Grand
with the intention of providing an education 'capable of supplying professors
to the University of Paris, masters for the residential colleges and teachers for
the children of citizens'. In the following year all the 'little colleges' of the
University were united to Louis le Grand to form 'an abundant nursery of
masters, of which the state has need, and which will spread emulation through-
out the land'. The status of Louis le Grand as predominately a training college
for teachers of all sorts was strengthened in 1766 by the institution of three
degrees (aggregations) in grammar, rhetoric, and philosophy, and by the pro-
vision of scholarships for those wishing to prepare for such degrees. Thus some
twenty years before the institution of the Ecole Normale (Year III) we find
not only the idea but also the creation of such a school, something which no
doubt contributed to the excellence of much of the pre-revolutionary educa-
tional system. What was in fact new in 1794 compared with 1766 was not the
idea of an Ecole Normale, but the grave shortage of teachers of all kinds,
especially of elementary school teachers (instituteurs) following the destruction
of a great part of the old system of education by the Revolution and the failure
to replace it by anything new.
The seriousness of the actual situation was frankly expressed by Barere
in a report to the Convention on 13 Prairial Year II. In spite of all attempts to
open primary schools, to introduce different grades of instruction, to revive
science and literature, to encourage the arts and to train up the younger
generation as good republicans, nothing had yet been done, and as a result the
Republic was menaced in both her civilian and military functions. In order to
combat this situation the Committee of Public Safety considered that a school
should be set up in Paris to train teachers to be sent out into all parts of the
country. Barere ended by promising a further report on the subject from the
Committee of Public Safety.
The promised report, however, was somewhat slow in coming, which was
not surprising considering the ever increasing tempo of the Terror and the
growing split in the Committee of Public Safety from 22 Prairial onwards
between Robespierre and his supporters and the other members of the com-
mittee. In the event it was only after 9 Thermidor that the question of an
Ecole Normale was again raised in the Convention, this time by Robert Lindet
in his famous state of the nation speech of 20 September 1794 in the brief calm
66 FOURIER AND THE REVOLUTION: PARIS
between 9 Thermidor and the full violence of the thermidorian reaction which
was soon to sweep away all the remaining members of the 'great committee'
including Lindet himself. Referring to education as the surest way of dissipat-
ing ignorance and attaching the people to the Revolution Lindet continued:
Why should you not order that there be opened in Paris a course of studies to form
teachers and that a certain number of citizens from all districts capable of fulfilling
such [teaching] functions should come to Paris to follow this course ?
The Convention embraced this idea with its customary gallic enthusiasm
and decreed that its Committee of Public Instruction should present a project
for 'Ecoles Normales' within twenty days! On 3 Brumaire Lakanal accordingly
laid before the Convention a plan for the setting up of Ecoles Normales aimed
at teaching, not the individual sciences or arts, but the art of teaching itself,
first at Paris by means of the foremost savants of the day, then by means of the
pupils thus taught throughout France (Gde. Encycl; Alain; Barnard; Dupuy;
Fayet).
3 . A vivid account of the opening seance has been preserved :
the seance was begun by the reading of the decrees of the National Convention for the
establishment of the ficoles Normales. At the announcement of this law all the pupils
and spectators raised their hats and rose spontaneously to listen respectfully . . . The
citizens Laplace, Hairy, and Monge occupied the chair in turn. Having read out their
programmes they gave their first lessons. They were listened to in the deepest silence
and on several occasions ware warmly applauded.
{Seances des'Ecoles Normales, t. 1, p. VI-VII).
4. See below Letter VI, n. 2, Appendix, p. 262.
5. See below Letter VI, n. 3, Appendix, p. 263.
6. See below Letter VI, Appendix, p. 259.
7. Founded in 1635, the J or din des Plantes had at first been a centre for the
culture and study of medicinal plants. With the appointment of Buffon as
Director in 1739 the field of study was gradually extended to the whole of
botany. The Jar din des Plantes was reorganized by the Convention's law of 10
June 1793 and had had its name changed officially to Museum d'Histoire
Naturelle under which name it had been opened to the public on 7 September
1794. But the old name lingered on.
8. See below Letter VI, n. 4, Appendix, p. 263.
9. See below Letter VI, n. 5, Appendix, p. 263.
10. See below Letter VI, n. 6, Appendix, p. 263.
11. See below Letter VI, n. 7, Appendix, p. 264.
12. See below Letter I, n. 12, Appendix, p. 247.
13. See below Letter VI, n. 10, Appendix, p. 264.
14. See below Letter VI, n. 12, Appendix, p. 265.
15. See below Letter VI, n. 14, Appendix, p. 266.
16. See below Letter VI, n. 15, Appendix, p. 266.
17. See below Letter III, n. 3, Appendix, p. 253.
18. See below Letter VI, n. 19, Appendix, p. 267.
19. See below Letter VI, n. 26, Appendix, p. 268.
20. See below Letter VI, n. 20, Appendix, p. 267.
21. See below Letter VI, n. 22, Appendix, p. 268.
22. Allain, p. 194.
23. Guillaume, vol. 5. p. 478.
FOURIER AND THE REVOLUTION: PARIS
67
24. There was one other possible justification for the Ecole Normale. It provided
almost the first example in France of an educational establishment under
government auspices in which lectures were given by the foremost scientists
and mathematicians of the day. Formerly there had been an almost complete
divorce between science and the universities. In this sense the Ecole Normale of
Year III can be regarded as a curtain raiser to the Paris Faculty of Science of
the Napoleonic University.
25. See below Letter VII, Appendix, p. 270.
26. Arch. Nat. F 7 4439.
27. Ibid.
28. The insurrection of 12 Germinal (1 April 1795) was precipitated by an acute
shortage of bread which began to be felt in January and reached near famine
proportions by the end of March. The demonstrators marched on the Con-
vention where they broke in and demanded bread. Once the demonstrators
had been dispersed the insurrection was put down ruthlessly. Paris was put in a
state of siege and the armed forces placed under the command of General
Pichegru. Local leaders were arrested together with twelve deputies including
the anti-Robespierrists Leonard Bourdon, Amar, and Cambon, and the three
'terrorists' of the old 'great' Committee of Public Safety, Barere, Billaud-
Varennes and Collot d' Herbois who were sentenced to deportation.
29. Guillaume, vol. 6, p. 71.
30. See below Letter VIII, n. 2, Appendix, p. 278.
31. Laplace was a member of the Committee of Public Instruction.
32. Guillaume, vol. 6, pp. 203-4.
33. This could have referred to subsistence paid to pupils of the Fxole Normale
during their stay in Paris (indemnite de sejour), or to travelling expenses to and
from Paris (indemnite de route) or possibly to the salary paid to each of the
maitres des conferences in mathematics.
34. The Committee of General Security was responsible for all internal security
and police matters throughout France.
35. Guillaume, vol. 6, p. 204.
36. On 1 Prairial the tocsin rang in the Faubourg Saint Antoine and the Jardin des
Plantes. This time the women led the march on the Convention, and the cry
was bread or death. The demonstrators entered the Convention in sufficient
numbers and with sufficient arms to encourage the small remnant of the
Mountain to voice their principal demands including the release of Jacobin
prisoners. This, the so-called Romme conspiracy, led later to the deaths of six
deputies including Romme. Lacking leaders the insurgents were later driven
away from the Convention by the loyalist sections. The next day the insurgents
marched again on the Convention but returned home lulled by false promises.
On 3 Prairial the Faubourg Saint Antoine was surrounded by military forces
and on the next day an army under General Menou was about to advance
against it when the Faubourg and its starving inhabitants surrendered without a
fight. A military commission was then set up to try those implicated in the
insurrection. Of 132 persons who appeared before this commission nineteen
were condemned to death and committed suicide or were executed including
the six deputies of the Mountain referred to previously. These were the so-
called martyrs of Prairial, the last of the Montagnards.
37. This order is referred to in Letter VIII (to Bergoeing). It would seem to have
68
38-
39-
40.
41.
42.
43-
44.
45-
46.
47-
48.
49-
SO-
5i.
52-
S3-
54-
55-
56.
57-
58.
59-
60.
61.
62.
63.
64.
6S.
66.
67.
68.
69.
70.
7i-
72.
FOURIER AND THE REVOLUTION: PARIS
been a somewhat tardy local reaction to the Convention's decree of 21 Germinal
for the disarming of terrorists.
See below Letter VIII, Appendix, p. 276.
Ibid.
See below Letter IX, Appendix, p. 284.
Arch. Nat. F 7 4710, Doss. 5.
Fourier's house at the time of his arrest, No. 5 Rue de la sauvage peuple de
Bourgogne, was not actually in the section of Social Contract. From other
documents in the same dossier (F 7 4710) as the letters of Fourier and his
brother given below, it appears that when the order of the commune of Auxerre
reached the committee of the section of Social Contract they ordered the chief
of the armed guard of the section, Bayard, to effect Fourier's arrest. When it
appeared that Fourier (possibly as a precaution) had changed his domicile to a
residence in another section. Bayard proceeded to the Committee of General
Security where he deposited the papers from Auxerre and obtained permission
to arrest Fourier at his new residence.
Cousin, p. 6.
See below Letter VIII, Appendix, p. 276.
Arch. Nat. F 7 4710, Doss. 5.
Ibid.
Ibid.
See below Letter VIII, Appendix, p. 277.
See below Letter VII, Appendix, p. 271.
See below Letter IX, Appendix, p. 282.
Ibid, p. 282.
See below Letter VII, Appendix, p. 271.
See below Letter IX, Appendix, p. 282.
See above, p. 43.
Ibid.
See below Letter IV, Appendix, p. 255.
See below Letter XII, n. 10, Appendix, p. 295
See above Chapter I, n. 24.
See below Letter IV n. 4.
See above Chapter I, n. 54.
See above Chapter I, n. 51.
See below Letter XII, n. 9, Appendix, p. 295.
See above, p. 16.
See above, p. 26.
Cousin, p. 6, though he actually uses the later title of the school.
Arch. Yon. Serie L, Reg. 324 1 .
See below Letter X, Appendix, p. 287.
Fourcy, pp. 129-30.
See below Letter XI, Appendix, p. 289.
See below Letter XI, n. 7, Appendix, p. 290.
See Grattan-Guinness (3), pp. 5-8, for an interesting brief account of these
lectures.
Fourier Dossier AN.
YEARS OF EXILE: EGYPT AND
GRENOBLE
1. Permanent secretary of the Cairo Institute
In writing to Fourier, the Minister of the Interior was obeying the orders
he had received in a private and confidential letter from the Directory
instructing him to 'put at the disposition of General Bonaparte the en-
gineers, artists, and other subordinates of your ministry together with the
different things he will demand of you for the purpose of the expedition
to which he has been assigned'. 1
The letter from the Directory to the Minister of the Interior was dated
26 Ventose Year II (16 March 1798), and the letter from the Minister of
the Interior to Fourier 7 Germinal Year II (27 March 1798). On the
following 19 May in company with Bonaparte, his fellow generals and
officers, and members of the scientific and literary commission 2 together
with 30 000 soldiers and sailors, all stowed into some 180 ships (including
thirteen ships of the line), Fourier, in all probability at sea for the first time
in his life, found himself being carried away from Toulon bound for some
unknown destination. That Egypt was the actual destination of this great
armada was a secret which had been somewhat miraculously restricted to a
small group of men, and which certainly had not reached the ears of
Nelson who remained as ignorant of the true destination of the expedition
as he was of its actual position throughout the passage to Egypt.
For a great part of the voyage many members of the expedition including
Bonaparte suffered cruelly from sea-sickness. In the days of relative calm
the latter was fond of holding his so-called 'institutes' in which he would
discuss all manner of questions with members of his staff and of the scienti-
fic and literary commission. 3 It was presumably on such occasions that
Bonaparte came to know Fourier and to assess his worth and potential
gifts as an administrator. As professor at the Fcole Polytechnique Fourier
was one of the senior members of the scientific commission, and would have
dined at the Captain's tables of his own and other ships. 4 There he would
have had a chance of meeting other senior members of the scientific and
literary commissions and naval and military officers. In fact we know that
he became friendly with General Kleber 5 during the voyage, a circum-
stance which was later to have unfortunate consequences. The former
conventionel and ex-terrorist Tallien, 6 one of the leaders in the conspiracy
70
YEARS OF EXILE: EGYPT AND GRENOBLE
against Robespierre, would have had a special interest for Fourier, who
may, however, have been discreet about his own part in the Revolution in
the years 1793-4-
Throughout the voyage, Nelson with his squadron of thirteen 74 poun-
ders frantically scoured the Mediterranean for the French armada, coming
as close as two miles to it on 22 June. The proximity of the English fleet
proved nerve-racking to most members of the French expedition apart
from Bonaparte who was too busy preparing for Egypt to bother about the
possibility of an encounter with Nelson. Apart from the capture of Malta
with its timely contribution of some 7 000 000 gold francs to Bonaparte's
war chest following the suppression of the ancient order of the Knights of
Malta, the journey was uneventful if full of discomfort and suffering for
the lesser ranks owing to their cramped quarters and indifferent rations.
On 1 July 1798 Pompey's pillar at Alexandria was at last sighted, and the
following day the city was captured after a brief resistance.
Amidst the frenzied preparations for the march on Cairo the members
of the commission of arts and science tended to be forgotten. Alexandria
turned out to be an uninspiring slum and some members of the commission
—including Fourier — were fortunate to be given temporary quarters in
the much more pleasant and salubrious town of Rosetta. Here Fourier took
up his first administrative position in Egypt as a member of the provincial
purchasing commission. In the meantime the main body of the army were
pushing on towards Cairo. In their march through the desert they suffered
terrible hardships due in part to a lack of proper equipment especially
water bottles. On 21 July the Mameluke forces under Murad Bey were
routed at the Battle of the Pyramids, and on 24 July Bonaparte entered
Cairo. But a few days later these brilliant successes were more than
cancelled by the annihilation of the French fleet in Aboukir Bay. Regardless
of anything Bonaparte could say the ordinary soldier no doubt shared the
feelings of the physicist Malus 7 on learning of this catastrophe :
From then on we realised that all our communications with Europe were broken.
We began to lose hope of ever seeing our native land again. 8
Equally serious, on learning of the disaster of Aboukir Bay, the Directory
ceased to make any sustained or serious attempt to assist Bonaparte or
even to communicate with him.
Magnificently undeterred by the destruction of his fleet, Bonaparte set
to work to bring some sort of order out of the incredible confusion, poverty,
disease, filth, and decay which were the most prominent characteristics
of the Cairo scene. Thus he soon set up a municipal 'divan' or council in
the hope of persuading the native leaders to run their own affairs, subject,
of course, to the ultimate control of the French. The Thermidorian Tallien
YEARS OF EXILE: EGYPT AND GRENOBLE
71
was appointed French commissioner or observer at the meetings of this
body, a position later held by Fourier.
Among a multitude of other tasks Bonaparte still found time to oversee
the foundation of the Cairo Institute, a body which had no doubt been
much discussed during the passage to Egypt, and which was formally
created by an order dated 20 August 1798. Following the procedure at the
setting up of the Institut in Paris — a body of which Bonaparte was still
at this time inordinately proud to be a member, always signing himself:
'Bonaparte, member of the Institut' — seven foundation members were
first agreed on who were then responsible for drawing up a list of further
members chosen from the Commission of Arts and Science. There were to
be four classes of twelve members each in mathematics, physics, political
economy, and literature and the fine arts. Only the mathematics class was
ever filled, and it also contained the most distinguished collection of
members including Monge, 9 Fourier, Malus, and Bonaparte himself. The
best-known members of the other classes were Berthollet, 10 Conte, 11 and
Geoffroy Saint Hilaire 12 (Physical class) and J. B. Say 13 (Political Eco-
nomy). In the section of Literature and Fine Arts was the artist Denon 14
who brought back with him to France a large collection of drawings which
provide an invaluable pictorial record of many aspects of the Egyptian
expedition.
The first meeting of the Institute took place on 25 August 1798, Monge
being elected president, Bonaparte vice-president, and Fourier permanent
secretary, 15 a position which he continued to hold throughout the whole
period of the French occupation of Egypt. Monge — no doubt aided by
Fourier — seems to have played the chief part in the organization and
activities of the Cairo Institute from its foundation till his return to France
with Bonaparte in August 1799. The Institute was located in the former
palace of the Beys, the great room of the harem serving for the seances, and
the rest of the building was used for lodging the members and for labora-
tories, workshops, and a museum of Egyptian natural history. The garden
of the palace became the botanical garden of the Institute.
Napoleon had envisaged a three-fold purpose for the Institute: the pro-
gress and propagation of the sciences in Egypt ; the collection and publica-
tion of natural, historical and other data on Egypt; last, but not least, the
Institute was expected to act on occasion as a sort of think-tank to advise
the civil and military administration on any questions with which they
might need assistance. Bonaparte — who retained a real interest in the work
of the Institute for the remainder of his stay in Egypt — propounded a
number of questions 16 at the first meeting of the Institute all stamped
with his own severely practical, unphilosophical caste of mind : could the
army's baking ovens be improved, and if so how? Was there a way of
72
YEARS OF EXILE: EGYPT AND GRENOBLE
brewing beer without hops ? What methods were in use to purify the Nile
water ? Which was more practical in Cairo — windmills or watermills ? Were
there any resources for manufacturing gunpowder ?
Although committees were duly set up to study these and other ques-
tions, the activities of the Institute's members were not exclusively devoted
to such practical matters. Thus natural historians like Geoffroy Saint
Hilaire were much more concerned with scientific study of the fauna and
flora of Egypt, and although Fourier read a note on a proposed wind-
activated watering machine to the Institute on the first complementary 17 day
of Year VI, a few days earlier, on 21 Fructidor of the same revolutionary
year, he read a memoir on his old love, the general resolution of algebraic
equations: and so, as Cousin 18 remarks, on the banks of the Nile Fourier
still occupied himself with the problem which had already so greatly
exercised him at Auxerre, and Navier (to whom Fourier's papers were
entrusted at his death) claimed that certain of Fourier's papers on the
subject were written with Egyptian ink on Egyptian papyrus. Unlike
Geoffroy Saint Hilaire and other members of the Commission of Arts and
Science who sometimes found time hanging heavily on their hands,
Fourier seems always to have been fully occupied either on his adminis-
trative duties as permanent secretary of the Institute, or in writing papers
to be read before that body. Among these Cousin 19 notes four mathematical
memoirs.
Sometime in the first half of 1799 Fourier took part in the expedition
to Lake Natron under General Andreossy, 20 Berthollet being the other
principal civilian member of this expedition besides Fourier. Earlier he had
been fortunate to miss the ill-fated Syrian campaign in which French
casualties 21 were more than a third of the original number which had set
out from Egypt in February 1799. On 14 June Bonaparte made his 'trium-
phal' re-entry into Cairo with the remnants of his Syrian army. On 25
July following, he annihilated a Turkish invasion force at the battle of
Aboukir. He then learnt through newspapers thoughtfully supplied him by
the British naval commander, Sir Sidney Smith, 22 of the troubled situation
in France. Determined to risk all on a return to France, Bonaparte left
Egypt on 18 August accompanied by a small party including the insepar-
able Monge and Berthollet. Inevitably rumours got about before the actual
departure, and at a meeting of the Institute Monge and Berthollet found
themselves acutely embarrassed to deny their imminent departure from
Egypt. Fourier, in particular, was so agitated at the thought of their leaving
him behind that he followed them into the street and could hardly be
persuaded to let them go, 23 while the poet Grandmaison 24 — who had
served with Fourier on the Rosetta purchasing mission before they were
both called to the Institute in Cairo — followed Bonaparte to his port of
YEARS OF EXILE: EGYPT AND GRENOBLE
73
embarkation, rowed out to the General's frigate, and begged to be taken
back to France. Much amused, Bonaparte relented and took him on
board.
In spite of pressing military and administrative duties Bonaparte
characteristically found time immediately before his return to France to
plan an expedition by a mixed scientific and literary commission to Upper
Egypt under the joint leadership of Fourier and Costaz. 25 On the return
of the expedition Fourier was put in charge of the collation of its discover-
ies. Later this formed the basis of the Description of Egypt for which
Fourier supplied an historical introduction which was later to cost him
much anxiety and labour while Prefect of Isere.
Before leaving Egypt Bonaparte had left a letter to Kleber nominating
him as commander in chief. Kleber, who detested the politician in Bona-
parte as much as he admired the general, accepted the position with mingled
rage and scorn, for Bonaparte had not been able to bring himself to face
Kleber in person before his departure, possibly fearing that Kleber would
have refused the position offered him and thus have made it much more
difficult for Bonaparte to leave Egypt. Under Kleber Fourier was appointed
president of a bureau set up to collect information relating to modern
Egypt. Fourier's work in this position and as secretary of the Institute was
carried on against a constantly troubled military and civilian background. 26
Thus following the countermanding by the British government of the
convention of El-Arish entered into by Kleber and Sir Sidney Smith on
28 January 1800, fighting broke out between the French and Turkish
forces. Although the main Turkish forces were routed by Kleber at the
Battle of Heliopolis (20 March 1800) nevertheless there was an insurrection
in Cairo which began in March and only ended on 22 April when the
Turkish forces in the city were evacuated.
On 14 June 1800 the French expedition suffered an irreparable military
loss through the assassination of Kleber. It was Fourier who read the funeral
oration, a speech 'whose hollow bombast' 27 may have suited the occasion
and audience but which does little to enhance Fourier's memory. This
speech also contained some rather fulsome flattery of Bonaparte who by
this time had established himself in Paris as First Consul. It is to be hoped
that Fourier was not obliged to witness the impaling of Kleber's assassin, a
proceeding which took place on the route of the funeral procession to the
grave of Kleber.
Under Kleber's successor Menou, 28 Fourier was appointed to a number
of additional administrative positions including that of French representa-
tive on the divan of Cairo — a position which had earlier been filled by the
Thermidorian Tallien — chief of the administration of justice in Egypt,
and examiner of naval cadets who had passed through the mathematical
74 YEARS OF EXILE: EGYPT AND GRENOBLE
school at Cairo. Fourier was also entrusted with delicate diplomatic
negotiations with Murad Bey, the formidable leader of the Mamelukes
who had evaded capture by both Bonaparte and Desaix. 29 His success in
persuading the wily Murad to sign an alliance with the French command at
a time when they were none too strong militarily represented a not in-
considerable diplomatic achievement.
Following the landing of a British Expeditionary Force under General
Abercrombie at Aboukir Bay on 8 March 1801, and the repulse at Canopus
(21 March) of a French attempt to drive the British forces back into the
sea, the position of the remaining French forces in Egypt deteriorated
rapidly. Menou withdrew to Alexandria and was cut off by a flooding of
the surrounding country by the British. At this point the members of the_
Institute felt it was time to go home. As a preparatory move they had
themselves transferred from Cairo to Alexandria prior to embarking for
France. Understandably, those who were to be left behind did not view
the retirement of the savants with any great enthusiasm. Thus General
Menou wrote to Fourier as follows :
Good citizen, I did not indicate any discontent regarding your departure either
to the army or to the government . . . but your departure in the actual circum-
stances appeared to me, and still appears to me, and will always appear to me,
immoderate and ill-conceived. But the lively manner in which I have expressed
myself on this subject is entirely for your own personal attention. 30
When the boat with the members of the Institute on board left the port
of Alexandria it was immediately arrested by the British Fleet, apparently
much to the surprise of its passengers. Following the persuasive arguments
of Fourier, the commander of the fleet, Sir Sidney Smith, agreed to release
all the members of the Institute apart from Fourier himself whom he
retained as a hostage. The other voyagers were very upset by this turn of
events, but not nearly as upset as when they discovered that General
Menou would not allow them to re-enter the port of Alexandria because of
their contact with the enemy! Ultimately, when Menou relented and
allowed the members of the Institute to return to Alexandria, Sir Sidney
Smith released Fourier while retaining his papers. In the meantime the
French position had deteriorated still further. Belliard, 31 the commander
of the French forces besieged in Cairo, had capitulated. For a while Menou
hung on, but he too was soon forced to surrender and the terms of capitula-
tion were signed on 30 August 1801.
After the capitulation the officer in command of the British forces,
General Hutchinson, attempted to commandeer the scientific collections of
the French expedition. But when Geoffroy Saint Hilaire threatened to
follow them to England Hutchinson changed his mind and allowed the
YEARS OF EXILE: EGYPT AND GRENOBLE
75
French to keep their collections. He was, however, adamant about the
Rosetta stone which Menou was forced to surrender. This stone neatly
epitomizes the French expedition to Egypt: its position in the British
Museum symbolizes the military failure of the expedition, while the stone
itself is a perpetual reminder of the enormous scientific importance of an
expedition which laid the foundations of modern Egyptology.
On the passage to Egypt Bonaparte had promised each of his soldiers
enough money on their return to France to buy six acres of land. This was
to become the subject of ribald comment by the troops in Egypt, and those
who were fortunate enough to return to France carried with them little else
than an inexhaustible supply of stories of their triumphs and tribulations
in Egypt. Fourier was more fortunate than most. His war had been at the
least a very successful administrative experience which seemed certain to
mark him out for some important appointment on his return to France. As
to the impression which he had made on his colleagues of the Commission
of Arts and Science, little has survived beyond two somewhat contradictory
records. The first, a contemporary account, is found in a letter written to
Cuvier by Geoffroy Saint Hilaire while waiting in quarantine at Marseilles
on his return to France from Egypt: having referred to Fourier as a man 'of
great intelligence and merit' he continued :
we were so close together, and his claims became so overweaning, that we often
came in conflict : however there was finally a relationship between us which was
sufficiently large, frank, and intimate on my side, perhaps political on his.
His plan since the departure of Berthollet had been to prove by hurtful
sarcasms that all his colleagues of the Institute were ignoramuses, and that his
pupils, who were then civil engineers, were the only ones who had any knowledge.
You can imagine that he was strongly supported by the latter and that he mounted
a concealed attack which threatened to have some effect until the good people
without pretensions took offence at it. Fourier's aim was to have a name for the
same superiority and understanding which it is customary to afford in Paris to
Lagrange and Laplace. 32
Another, rather different, impression was given many years later by
Jomard in a funeral oration at Fourier's graveside:
which of us has forgotten his conduct so full of justice and generosity towards the
natives ? How much his mind, his understanding, and his graciousness gained us
followers and contributed to maintaining the authority of a handful of men over a
population then so fanatical, and so stirred up by rich, strong, and powerful
enemies, and by leaders, religion, and arms. Who would have said that this man
of so lofty a mind, so sure a judgement, and so profound a knowledge would have
had an exquisite sensibility for the beauties of art ? And yet there is none among
either his disciples and friends or the companions of his dangers and hardships
who does not render homage to the delicacy and purity of his taste. It was the
76
YEARS OF EXILE: EGYPT AND GRENOBLE
same tact, the same wisdom, which then shone in his judgements and conversa-
tion as has since in all his works. What a charm he could bring to every subject,
what ingenious comparisons, what an inexhaustible memory, what gentle
philosophy animated his conversations whether under the silent monuments of
the town of a hundred gates or in the sound of the cataracts! To the great
memories of the historian are henceforth joined those of a bold enterprise which
will always honour France. Fourier hallowed them one and all in a discourse that
should not die; all except the part which he himself played in the expedition.
But posterity will add his name to those whom his eloquent pen has immor-
talised. 33
Discounting somewhat both the evident animus of the natural historian
for the theoretical physicist, and the nature of the occasion of Jomard's
remarks, it may be assumed that the 'permanent' secretary of the Cairo
Institute was neither as prejudiced as Geoffroy Saint Hilaire made out,
nor such a paragon of all the virtues as presented in Jomard's oration.
Having returned to France Fourier immediately reopened his corres-
pondence with Bonard : 34 the voyage itself from Egypt had left him with
'nothing but the most agreeable memories' though the 'prolonged hard-
ships' during his stay in Egypt had left their mark on his health. The study
of the 'antiquities of Egypt' and his many administrative duties had not
diverted him from mathematics though he had not yet published any of his
researches. But he intended to do so as soon as he had published his work
on the 'astronomical monuments' of Upper Egypt, provided he was
'fortunate enough to enjoy a substantial period of leisure in Paris'. After a
brief indication of the nature of his work on the 'astronomical monuments'
it was the turn of Bonard and his family :
Present my regards to Madame Bonard and embrace in my name all your
charming family. But I retain an altogether special affection for that one of your
children whom I baptized. If M. Rosman still lives in Auxerre express to him
the token of my regards and unalterable attachment which reflection and age can
only increase.
2. The prefect of Isere
On his return to Paris Fourier immediately took up his teaching duties
again as Professor of Analysis at the ficole Poly technique. But not for long.
On 1 8 Pluviose Bonaparte wrote to his trusty chemical henchman Ber-
thollet as follows :
Citizen Senator, the Prefect of the Department of Isere having recently died, I
would like to give an earnest of my confidence in citizen Fourier by appointing
him to this place. Please be good enough to speak to him about it and let me
know if this would answer his expectations. 35
YEARS OF EXILE: EGYPT AND GRENOBLE 77
Berthollet's line of communication with Fourier led through Gaspard
Monge to whom Berthollet then wrote as follows:
My dear friend,
Please find Citizen Fourier and get him to promise to be at your house this
evening between eight and nine o'clock. I have a proposal to make him on behalf
of the First Consul about an urgent matter. I embrace you
Signed Berthollet. 36
If we are to believe Cousin 37 the First Consul's proposal was in fact a
command which Fourier would have ignored at his peril. It is difficult to
credit this, since Fourier was firmly established in the Exole Polytechnique
and even Bonaparte would have been unable to have him dismissed from
that position simply because he had declined to accept the prefecture of
Isere. 38 But Fourier could well have found that after his large administra-
tive responsibilities in Egypt his chair at the Ecole had shrunk somewhat
since 1798, and that he may in fact have been looking for a new, and more
responsible, position is suggested by Bonaparte's request to be informed
if the proposed position answered Fourier's 'expectations'. In that case, if
he were to refuse the position offered to him, he might never have been
offered another, although he could hardly have been attracted by the
position of prefect in a town such as Grenoble so remote from Paris as
to amount to virtual exile. Whatever his feelings of disappointment on this
score he seems quickly to have stifled them, and a few days later he was
appointed Prefect of Isere by an order of the First Consul dated zt. Plu-
viose.
Having accepted the position of Prefect of Isere Fourier seems to have
been in no hurry to leave Paris to take up his position, for on 12 Germinal
we find the minister of the Interior, Chaptal, 40 writing to him at his Paris
address as follows :
The First Consul requests me, citizen Fourier, to inform you that the affairs of
the Department of Isere require that you proceed to your residence. Please inform
me of the time of your departure and when you have arrived at Grenoble notify
me of your installation. 41
But Fourier had already left Paris, and Chaptal's letter only caught up
with him after he had been installed as prefect in Grenoble. From there he
replied 42 on 29 Germinal excusing the lateness of his departure from Paris
on the grounds of the difficulty of winding up his personal affairs in Paris
and Auxerre in less than three months, while assuring the minister of his
unreserved devotion to duty and his desire to 'reply to the benevolent and
consoling views of the Government so justly honoured throughout Europe'.
The department of Isere to which Fourier had been appointed prefect
78 YEARS OF EXILE: EGYPT AND GRENOBLE
was one of eighty-three such regions into which France had been divided
by a decree of the Constituant Assembly of 3 February 1790. The Assembly
had been concerned to cut through the tangled web of the administration
of the ancien regime based on provinces and replace it by something new,
more efficient, and more democratic. Thus each department was headed by
an elected assembly with a 'general council' of thirty-six members and a
'procureur syndic' representing the King. Under the revolutionary govern-
ment of Year II the assemblies and their general councils, almost entirely
composed of well-to-do Bourgeoisie, were rightly suspected of Girondin
sympathies, and government agents were appointed to watch over them.
Under the Directory each department had its own ruling body with an
accompanying 'general commissioner' appointed by the central govern-
ment to supervise its working including the enforcement of laws. Finally,
by a law of 28 Pluviose Year VIII inspired by the First Consul, the de-
partmental directories were abolished and replaced by a single person, the
prefect, who was thereafter the sole representative of the executive power
in the department. And thus, with the substitution of prefects for inten-
dants and departments for provinces the system of centralization adopted in
France after the Revolution was very similar to that which had been in
force before it^a striking illustration of de Tocqueville's principle.
Once installed as prefect, Fourier's first care was the administrative
machinery of his prefecture. He found the four counsellors already in
position not entirely to his liking and had them replaced over a period by
others including a certain high-sounding Joseph Marc de Gratet du
Bouchage, doubtless a relative of the Du Bouchage who as Minister of
Marine under King Louis XVIII was to be such a staunch supporter of
Fourier. As his principal private secretary he appointed a certain Auguste
Lepasquier, a person with extensive literary training, the local poet laureate,
whose commemorative verse extended from a quatrain commemorating
the marriage of the Emperor Napoleon with Marie Louise of Austria to an
ode to the Count D'Artois, the future King Charles X, on the occasion of
his passage through Grenoble in 18 14. Lepasquier had particular responsi-
bility for all literary affairs and for education. A second private secretary,
Raynaud, looked after other administrative affairs. These were the two
key men of Fourier's administration and between them they saw to the
execution of all his instructions. As third secretary he chose a certain
Professor Alexis Michallet, a stylistic purist intended for the writing of
specially important dispatches. But Michallet became too fond of the vin du
pays and had to be dropped. All Fourier's secretaries and clerks had at least
one onerous task in common, the decipherment of his handwriting:
abominable at the best of times, except in the most fateful letters such as
that written from prison to the Representative of the People Bergoeing, it
YEARS OF EXILE: EGYPT AND GRENOBLE
79
degenerated in notes and minutes — with which, according to Letonnelier,
Fourier was in the habit of covering drafts — into 'a villainous little scrawl' 43
which must have been the despair of his officials.
Fourier's tasks as prefect were exceptionally varied. His first duty as sole
representative of the executive power in the department was to see to the
promulgation and enforcement of the various laws and directives which
flowed in a steady stream from Paris, especially those concerned with
taxation and recruitment for the consular and imperial armies. He was also
expected to keep the central government constantly informed about the
state of the department, especially as regards the morale of its citizens
and the preservation of law and order. This he did by a series of reports
covering every conceivable subject from the cutting down of trees of
liberty 44 and the activities of vandals in the gardens of ex-Ursuline nuns, 45
to the difficulties encountered in recruitment 'principally in the most
mountainous part of the department'. 46 Another of Fourier's important
early tasks was to effect a reconciliation between the warring parties which
were the aftermath of the Revolution. For it was the settled — and in this
case wise — policy of Napoleon to unite the maximum number of French-
men regardless of their original sympathies, republican, royalist, or ecclesi-
astical, in support of his policy and person. 47 In the event Fourier seems
soon to have succeeded in gaining the support of the more important
members of society. From the beginning he was on excellent terms with the
nobility whose support for the regime Napoleon prized so highly. If the
nobility were first drawn to Fourier by his pleasant old world manners and
the charm of his conversation — a former president of the Parlement of the
Dauphine said of Fourier that 'he could give lessons in theology to bishops,
and in politeness to pre-1790 parlementarians' 48 — they soon had better
reasons for supporting him, for he was always ready to do them a service.
For example, Cousin 49 tells the story of the emigre returning from exile
who had the chance to buy back his original property which was being
auctioned as a national holding. The property, which was worth much
more than the nominal figure put on it, was to be auctioned in public, and
there was in reality no hope of the original holder buying it back. In
desperation he approached Fourier and won his sympathy. The auction was
fixed for 8.00 a.m. on the unwritten, but universal, understanding that bidd-
ing was unlikely to commence before about 10.00 a.m. Fourier, however, in
his capacity as prefect turned up precisely at 8.00 a.m. when only a handful
of interested parties were present including, of course, the former owner.
At 8.15 a.m. the prefect instructed the usher to commence the bidding
making a great show of anger at the small attendance. In the event the
former owner was then able to buy back his ancient property. Doubtless no
one was much deceived by Fourier's show of anger, on the other hand there
80 YEARS OF EXILE: EGYPT AND GRENOBLE
was no public outcry since the emigre in question was personally respected
and liked by all classes.
Another service rendered the nobility by Fourier was in the matter of
the guards of honour. 50 These were to be recruited from the better families
of the country. But many of these families had little inclination to provide
recruits, having already lost too high a proportion of their members in the
Revolution. Fourier therefore arranged that they should buy themselves
immunity, the money provided being used to raise a body of paid volun-
teers. Thus the demands of the central government were met while the
nobility retained their sons at home.
Apart from the nobility, the other main class whose support Fourier
sought was that of the wealthy middle class made up largely of self-made
and mildly republican members of society, the so-called Bourgeoisie.
Among these he is said to have been popular for himself and also because of
his excellent administration devoid of red tape, excessive paper work, and
general humbug and tomfoolery of all kinds, for Fourier evidently had the
knack — essential to all first-rate administrators — 'of doing much without
any great stir'.
As for the local clergy, he apparently soon succeeded in establishing good
relations with them by his skilful and sympathetic treatment, no doubt
assisted by Claude Simon, 51 Bishop of Grenoble, a former tutor of Joseph
Bonaparte, and ardent supporter of his brother Napoleon. On 3 July 1803
Fourier visited the Cathedral of Notre Dame in Grenoble to receive the
oaths of cures nominated in the diocese. 52 After the ceremony, which was
carried out with great pomp and before a considerable assembly including
Bishop Simon, mass was celebrated while incense was given to the prefect.
Perhaps the fragrance of the incense evoked in Fourier the memory of the
last mass he had communicated in the Abbey St. Germain before the rising
tide of the Revolution had terminated the life of the Abbey and scattered
its remaining handful of inmates including the abbe Fourier.
History does not relate Fourier's relations with members of the extreme
Jacobin party in Isere. They were probably of little importance, but we can
imagine that it was perhaps with this group that he showed least sympathy.
His own Jacobin past was something he probably wished to hide.
Fourier's major achievement as prefect of Isere lay in his decisive con-
tribution to the draining of the swamps of Bourgoin. Covering an area of
some twenty million acres these swamps had been useless except for a little
rough grazing and had been responsible for annual epidemics of fever
which ensured that few of the surrounding inhabitants ever passed their
fiftieth birthday. On the advice of Colbert, Louvois, and Vauban the
swamps had been ceded by Louis XIV to the Marechal Turenne on the
understanding that he had them drained. A number of attempts were
YEARS OF EXILE: EGYPT AND GRENOBLE 81
subsequently made to begin the operation of draining. But in spite of the
support of the various intendants of the Dauphine all these attempts broke
down over the impossibility of achieving among the forty communes
bordering the swamps agreement sufficient to justify the commencement
of draining operations. It was Fourier's signal achievement to succeed
where his predecessors had failed. After negotiations stretching over a
period of some four years, he finally had the satisfaction of seeing the
mayors of all the communes subscribe to a common treaty executed at
Bourgoin on 7 August 1807. His success was due to a combination of
persuasiveness, charm, persistence and endless patience, for he was
apparently obliged to visit all the communes in turn and meet most of the
inhabitants individually before he could persuade them to give up, at least
temporarily, their immemorial rights of pasturage for the sake of the future
betterment of the land. Augustin Perier, 53 one of the foremost citizens of
Isere during Fourier's prefecture, was particularly well acquainted with
the various aspects of the draining of the swamps. When Cousin met him in
1 83 1 he was still full of admiration for Fourier's handling of the negotiations
leading to the signing of the 1807 treaty. 54 Once this treaty had been signed
it was possible for the draining to begin. The company Bimar responsible
for the operation of the draining was well aware of its debt to Fourier
for the 'marks of goodwill which made it fitting that the Company should
witness its gratitude to him in a special manner'. 55 This it did in a suitably
worded flowery address which later proved useful to Fourier when he came
to claim a pension on his return to Paris in 181 5. Equally grateful,
though at a somewhat later date, were the proprietors holding land in the
marshes, this time for services rendered to protect them from the 'unjust
and constantly renewed pretentions of the company Bimar' ! 56
The draining of the swamps was completed in 18 12. The cost was
1 200 000 francs, the increased value of the reclaimed land alone without
allowing for any later improvements in its condition was of the order of
4 000 000 francs. Even more important, if incapable of precise monetary
assessment, was the striking improvement in the health of the inhabitants
following the cessation of the annual epidemics of fever. All in all, Fourier
seems to have been fully justified when he claimed the draining of the
swamps of Bourgoin was the greatest public work which had been com-
pleted in France in 'these last years'. 57
Fourier's other major administrative achievements as Prefect of Isere
was the opening up of the French section of the road from Grenoble to
Turin via the Lantaret and Mount Geneva. Although the original route
was much longer it naturally contributed to the wealth of the countryside
through which it ran, and the project for a new route was vigorously
opposed not least by the then Minister of the Interior 58 — Fourier's direct
82
YEARS OF EXILE: EGYPT AND GRENOBLE
superior as Prefect — who was himself a native of the countryside in ques-
tion. Eventually Fourier had a memoir presented directly to Napoleon
by a number of local notables setting forth the advantages of the new
route including the shortening of the journey between Lyons and Turin
with its not unimportant implicit military advantages. Knowing with whom
he had to deal through first-hand experience in Egypt, Fourier restricted
his memoir to a single page containing nothing but the essential features of
the scheme and the principal advantages to be expected from it together
with a map of the route. His insight into Napoleon's character was fully
justified and two days later the request was granted. 59 Thereafter all
opposition, including that of the Minister of the Interior, melted away and
by 1 8 14, when work had to be stopped following the downfall of Napoleon,
the road had been opened up as far as the Italian frontier. Thereafter its
continuation hung fire to the chagrin of those who had expended
so much work and money on its execution. That part of the road
opened up was eventually completed providing a carriageway as far as
Briancon.
3. Friendship with Bonard
A number of letters written by Fourier during his time in Isere bear
witness to his continued friendship with Bonard up at least to the year
1 8 10. These letters deal mostly with matters of purely personal interest to
Fourier and Bonard only. Thus in one letter 60 Fourier asks Bonard to
carry out a number of small tasks including payments to a friend and to a
nephew. He also requests Bonard to help buy one of his brothers out of the
army. This particular brother may have been the black sheep of the family
because Fourier states that 'as soon as he has retired from the service I shall
give him a small pension and inform him how I wish him to use it; it is
also my intention that he remain at Auxerre'. Fourier was very evidently the
head of the family. In another (undated) letter 61 he announces his im-
minent arrival at Auxerre where he hopes to stay with Bonard. Un-
fortunately no account has survived of his reunion with Bonard and other
friends in Auxerre. No doubt they had many experiences to exchange, and
many reminiscences of the old days in Auxerre, especially during the Terror.
In two other letters 62 he mentions the question of placing one or two of
Bonard's children in a Lycee. Bonard, who had been Professor of Mathe-
matics at the Ecole Centrale in Auxerre, was offered the same position
in the Secondary School which was planned to take its place under the
Napoleonic reorganization of French education. But Bonard declined this
position. His letter of refusal has been preserved and is worth quoting in
YEARS OF EXILE: EGYPT AND GRENOBLE 83
full for the vivid impression it gives of the integrity and independence of
the man:
I have been informed that I was nominated by the Minister of the Interior as
Professor of the 5th and 6th classes of mathematics at the Secondary school.
I am very flattered by the pleasant things which you have seen fit to say about
me. I should like to justify the confidence with which I have been honoured. But
various considerations require me to take a line which if not conformable to my
tastes is at least authorized by circumstances.
To continue a career which I have followed for 24 years would seem to imply
that I could not but accept. Should I accept ? It would be necessary for me to
have an idea of the extent of the duties which I would be required to fulfil and
of the advantages which I should derive from them, [for] my position requires me
to take account of my own interests in the employment of my time. I have also
other motives. My physical facilities would not permit me to employ in this
position all the zeal and activity that it requires. Although mathematics is a
science of reflection its teaching is susceptible of action and passion. To convince
young people it is necessary to show the same warmth which is required in
oratorical declamations. The feebleness of my constitution warns me that it is
time to renounce a position which could have an unhappy influence on my health
which I wish to retain for my children's sake.
Moreover, I will state frankly that filled with a sense of the importance and
dignity of the calling of those who instruct youth, I see with displeasure that in
the actual organization the teacher will not be given all the consideration which
alone makes up for the pains and sacrifices to which he is condemned in fulfilling
the task imposed on him.
Moreover the government establishes the uniformity of teaching to give it a
good direction. This is wise. But I would have some observations to make on the
choice which has been made for mathematics.
My decision is therefore unequivocal, I return my nomination. I hope that the
bureau of administration whose good opinion I greatly prize will not find it
reprehensible that I do not accept a place which suits neither my moral nor my
physical dispositions. I am grateful, and I would regard any circumstance as
fortunate in which I could convince the administration of my veneration and
gratitude. 63
It is not known how Bonard employed his time after his retirement from
official teaching. He probably continued to teach mathematics privately,
and his own mathematical ambitions, long dormant in favour of his pupils,
especially Fourier, evidently revived momentarily as appears from the
following letter to Lalande, 64 then one of the permanent secretaries to the
Academie des Sciences:
I take the liberty of addressing to you the result of some researches which have
as principal object the properties of parallels. This theory has not yet been treated
as one would like it to be: if I have managed to present it in a more satisfactory
84
YEARS OF EXILE: EGYPT AND GRENOBLE
manner than has been done up to the present my work will contribute to per-
fecting an important part of elementary geometry and will not be useless.
To fulfil my object I have believed it necessary to take the elements of geo-
metry from the beginning because of the preliminary propositions which I have
to bring out, and there are certain parts which I present in a new way. The whole
treated very succinctly is the fruit of reflections that a long practice in teaching
have put me in a position to make.
If you consider, Sir, that this essay would not be unworthy of the attention
of the most able mathematicians, please be good enough to present it to the class
of mathematical sciences of the Institut; it is the right way to find out the degree
of interest which it merits. Full of confidence, Sir, in your wisdom and indulgence
I am persuaded that you will know how to appreciate my work, and if there is any
indiscretion in my initiative I hope you will be good enough to excuse me.
Please receive, Sir, the homage of my consideration and respect.
Bonard 65
The paper referred to is entitled 'First notions of elementary geometry',
and has been preserved. 66 It is remarkable only for the extreme clarity of
its presentation. A note by Lalande praises one happy construction,
points out an error in another, and the incompleteness of a further one,
and ends with the judgement: 'all told, this work hardly merits being
presented to the Institut'.
Thus ended Bonard's private mathematical ambitions. Thereafter, he
had to content himself with the success of Fourier and possibly other of his
pupils, and of his own children.
The last extant letter from Fourier to Bonard was dated 25 February
1810. Unlike the other letters which are mostly little more than hurried
notes, this one is full of an affectionate tenderness which speaks of Fourier's
real feelings for his friend :
Paris, 25 February 1810
My dear old friend,
I do not know how to ask your forgiveness for the continual delays in my
correspondence, though they can only in part be blamed on my negligence; for
the circumstances in which I have found myself for several months have de-
manded my exclusive and total attention. 67
I have written today to Grenoble and instructed the person responsible for my
affairs to send you immediately the sum of 800 francs to which you refer in your
letter.
My letter will arrive on 1 February (sic) and you will certainly receive the sum
in question by the 6th or 7th of next month. If, however, you find this delay
somewhat inconvenient please be good enough to write to M. Guichard the
post office director, and request from him on my behalf the sum of 800 francs. I
know his friendship for me well enough to be certain that he will accede to your
request. Please give my regards to Mme Bonard and thank her for what she has
YEARS OF EXILE: EGYPT AND GRENOBLE
85
done for my niece. I shall do my best on my return to spend a day or two at
Auxerre. When you remember me to M. Guichard, tell him how much I regret
not having seen him when he was last at Paris; I often meet M. Dumoland, his
friend, at court and we talk about him.
At last I am coming to the end of my troubles, the printing of my discourse will
soon be finished. I shall then devote more time and care to my personal affairs.
In continuing to have recourse to your kindness I shall try to repay it better
than I have done up to the present. Please remember me to M. Roux and give me
news of his health.
Accept the assurance of all the feelings of gratitude which I owe to your long
standing friendship.
J. Fourier
Prefect of Isere 88
With this affectionate letter we say goodbye to Bonard. The demand for
800 francs may have been in payment of a debt owed him by Fourier who
was remarkably disorganized in his financial affairs. If it was due to Bonard's
own impecuniosity we can be sure that Fourier would have helped him
generously during the last years of his life up to his death in 18 19, un-
fortunately three years before the publication of the Analytical Theory of
Heat. Of these years nothing is known. Bonard would certainly have had
friends in Auxerre, his wife who was still alive in 1810 may well have out-
lived him. As for the children for whose sake he had wished to safeguard
his health in 1804, one son Alphonse 69 became the owner of a hotel in
Auxerre while another — the same Rene whom the abbe Fourier had
baptized — had a successful career in the army medical service ending as
medical officer in charge of the military hospital at Calais. As successful a
father as he was a teacher, Bonard was evidently one of those on whom the
health of the res publica ultimately depends.
Notes
1. As Professor of Mechanics and Analysis at the Ecole Polytechnique Fourier
could certainly have been regarded as a 'subordinate' of the Ministry of the
Interior under whose control the school then lay. So that it is just possible that
he was not asked whether or not he wished to be 'disposed of for the sake of
public service*. This was certainly the case with the physicist E. L. Malus, who
as a serving engineer was simply ordered to proceed to Toulon — much to his
chagrin as he was just about to marry Fraulein Koch, the daughter of the
Chancellor of the University of Giessen, in which town he happened to be
stationed as a member of the French army of occupation. In other cases pre-
liminary soundings were first made. Thus so important a person as Gaspard
Monge was invited to join the expedition in a letter signed by all five Directors.
Monge at first refused, no doubt much to the chagrin of Bonaparte, who not
only appreciated Monge's rare gifts as a mathematician and scientist — not to
say as a collector of objets d'art in enemy territory — but also genuinely loved
him as a friend, an emotion fully reciprocated by Monge who never wavered in
86
YEARS OF EXILE: EGYPT AND GRENOBLE
his devotion to Bonaparte. The latter, however, was not the man to accept a
simple refusal. He soon realized that it was Madame Monge who stood in the
way of Monge joining the expedition. She was evidently a formidable woman
who had no intention of allowing her 'silly old husband' to join the expedition.
But after two personal visits by General Bonaparte she was forced to capitulate,
and Monge later embarked at Civitta-Vecchia with the contingent under
General Desaix. At Bonaparte's suggestion he carried with him a number of
useful effects including the Arabic press of the Holy Office and 800 bottles of
the finest wine from the cellar of Napoleon's brother Joseph.
In other cases possible recruits for the scientific side of the commission were
approached by either Berthollet or Caffarelli who had been charged with this
task by Bonaparte. Not all those approached accepted. Thus when Berthollet
visited Cuvier and Geoffroy Saint Hilaire in the Museum d'Histoire Naturelle
and invited them to join the expedition with the irresistible words 'Come, Monge
and I will be your companions and Bonaparte your general', the impetuous,
warm-hearted Saint Hilaire accepted while the more reserved and calculating
Cuvier refused. Certainly Cuvier had a good excuse, being deputy to a very
ancient professor whose days were evidently strictly numbered and whose
chair Cuvier had every intention of occupying at the first possible moment.
But Cuvier, shrewd man that he was, may also have calculated that an expedi-
tion to unknown parts under the mercurial and unpredictable Bonaparte —
wasteful, as Herold notes, of nothing but human lives — might not have been
very profitable from an academic point of view.
2. Although Bonaparte may well have discussed the organization of the com-
mission of arts and science to be attached to an eventual Egyptian expedition
with Monge in Italy in 1797, it seems that the idea of such a commission — as
opposed to that of the expedition itself — was Bonaparte's own, though he
almost certainly had in mind the scientific contingent of Alexander's expedition
to the East. Bonaparte's interest in science seems to have waned somewhat in
later years, but in 1798 he had a genuine enthusiasm for the subject, and
imagined that he might have made an alternative career in it for himself. (An
interesting discussion of Bonaparte and French science is given in Crosland,
chapter 1. See also Barral.)
3. See Crosland, p. 15.
4. On leaving Paris the members of the Scientific and Literary Commission had
fondly imagined they would form an homogeneous group. In the event they
were divided into five classes, the first class being paid at the rate of 6000 francs
per annum, each subsequent class being paid 1000 francs less than the next
one above. In letters to Cuvier from Toulon of 9 and 18 May 1798, Geoffroy
Saint Hilaire describes how unhappy many members of the commission were
at their lowly classification. He himself was one of six members of the top class
. and as such dined at tables of ships' captains where he ranked as a superior
officer. No doubt Fourier, then a full professor at the Ecole Polytechnique, also
travelled first class, though there appears to be no specific indication that this
was the case.
5. Kleher, Jean Baptiste (1753-1800). He was trained as an architect in Paris and
later served for a time in the Austrian Army. He returned to Alsace and joined
the Republican forces in 179a serving with distinction in the war of Vendee.
He was dismissed for the crime of having spared the lives of 4000 prisoners
taken at St. Florent, but was recalled in 1794 and sent to the Army of the
YEARS OF EXILE: EGYPT AND GRENOBLE
87
North under Jourdan where he played a decisive part in the battle of Fleurus
and in the capture of Frankfort in July 1796. He then retired for a while and
wrote his memoirs but returned for the Egyptian Campaign where he greatly
distinguished himself especially in Syria and at the battle of Aboukir. In
company with Desaix, Hoche, Joubert, and Marceau, Kleber was one of the
greatest of the generals of the Republic {Bio. Gen. ; Gde. Encycl. ; Gd. Lar.).
6. Tallien, J. L. (1767-1820). Elected to the National Convention where he sat
with the Mountain and became a member of the Committee of General
Security. He was the leader with Fouche in the conspiracy against Robes-
pierre and was one of the most active Thermidorians. He was saved from
exile in 1816 through the friendship of Decazes, the favourite of Louis
XVIII.
Napoleon seems somehow to have got wind of Fourier's revolutionary past
— possibly from Fouche, who could have seen Fourier's dossier in the files of
the Committee of General Security — for during his passage through Grenoble
during the Hundred Days he first accused Fourier of having voted in the
Convention for the death of the King, and when he was assured that Fourier
had never been a member of that body he persisted in maintaining that Fourier
had signed a document in Auxerre calling for the trial of Louis. J.J. Champollion-
Figeac, who relates this story, later took the trouble to verify that Fourier was
not a signatory of the address in question, probably the one of October 1792
of which part is reproduced above in chapter 2, p. 16.
7. Malus, Etienne Louis (1775-1812). He was the son of Louis Malus du Mitry,
treasurer of France. Educated at home in literature and mathematics, he was
sent to the school of Mezieres but was dismissed as a suspect in 1793 when he
enrolled in the army and was sent to Dunkerque. There his talents were
noticed by the engineer Lepere who had him sent to the Ecole Polytechnique.
Monge had already noticed him at the school of Mezieres and chose him as
one of the special band of brigade chiefs, taught by himself, who were destined
to instruct others. Malus was perhaps Fourier's most brilliant pupil at the
Ecole Polytechnique. During three years he devoured works on mathematics
and began to write original papers on the path of light in media of variable
refractive index. He then returned to the army and was present at the passage
of the Rhine in 1797. He took part as an engineer in the Egyptian Campaign
where he repeatedly distinguished himself. On his return to France he took
up his work in science again and was awarded a prize for physics at the Aca-
demie des Sciences in 1810 for a memoir on double refraction. The previous
year he had published an account of his discovery of polarization by reflection.
He was elected to the Academie des Sciences in 18 10 and in spite of the war
between England and France was awarded the highest honour of the Royal
Society of London, the Rumford medal, on 22 March 1811. His death the next
year at the age of thirty-seven was a grievous loss to French science {Bio.
Univ.; Bio. Gen.; Gde. Encycl.; Ind. Bio.).
8. Malus, p. 88.
9. See Letter III, n. 3, Appendix, p. 253.
10. See Letter VI, n. 15, Appendix, p. 266.
11. Conte, Nicolas Jacques (1755-1805). Orphaned at an early age, he took up
portrait painting from which he derived considerable profit but later devoted
himself to mechanical arts and the study of science and mathematics. In
Paris he followed the lessons of Vauquelin and presented to the Academie
I
88 YEARS OF EXILE: EGYPT AND GRENOBLE
des Sciences a hydraulic machine of his own invention which was much
praised. After the outbreak of the Revolution, especially after war had been
declared against England, he exercised much ingenuity in finding substitutes
for materials which could no longer be imported. From 1796 onwards he was
associated with Monge and Berthollet in researches into balloons and became
the Director of the Aerostatic School at Meudon. He also played a part in the
setting up of the Conservatoire des arts et metiers. He took part in the Egyp-
tian Expedition as head of the ballooners. After the disaster of Aboukir and
the revolt of Cairo — when a great part of the instruments and material brought
by the French to Egypt were destroyed — he exercised miracles of ingenuity
in constructing utensils and machines of all kinds from simple windmills to
money mints. Thanks in great part to his activity and genius the expedition
was provided with bread, linen, arms and munitions, engineers were provided
with precision instruments, and doctors with surgical instruments. According
to Monge he had 'all the sciences in his head and all the arts in his hand'.
Napoleon found him 'good for everything'. On returning to France in 1803 he
was charged by the Minister of the Interior Chaptal with the direction of the
publication of the work of the scientific and literary commission of Egypt. He
invented a printing machine which considerably reduced this work but did not
live to see it completed. He was one of the first members of the Legion of
Honour (Bio. Gen. ; Gde. Encycl).
12. Geoffroy Saint Hilaire, Etienne (1772-1844). After receiving his early education
at the College de Navarre he intended to enter the Church, being appointed
to a canonry in the chapter of Saint Croix at his native town of Etampes with
permission to stay in Paris to study law in which he took his primary degree
in 1790. By this time he had already been much attracted to science by the
lectures in experimental physics of Brisson and had begun the study of medi-
cine. After the fall of the Throne on 10 August 1792 all the masters of the
College du Cardinal-Lemoine where Saint Hilaire was then in residence were
arrested as non-juring priests. Following vigorous representation Saint
Hilaire managed to have two of these priests released including his teacher and
friend the Abbe Haiiy. On 2 September he penetrated the prison of Saint-
Firmin in disguise and tried to persuade the other professors to escape. But
they refused and were all massacred. The same night Saint Hilaire managed
to save the lives of twelve other prisoners. Overcome with fatigue and sorrow
he returned to Etampes where he fell dangerously ill. When he eventually
recovered he returned to Paris where he took up the study of botany on the
advice of Haiiy, and on the reorganization of the Jardin des Plantes as the
Museum d'Histoire Naturelle he was appointed to one of the twelve new chairs
sharing the teaching of zoology with Lamarck. It was he who recognized
Cuvier's genius and had him appointed to a position in Paris in 1794. In Egypt
. he investigated the flora and fauna of the Nile delta and was a member of the
commission set up to organize the Institute of Cairo. He is said to have saved
the collections of the scientific commission for France by threatening to burn
them rather than give them up to the British in conformity with the terms of
the capitulation of 31 August 1801. After the Convention of Cintra in 1808 he
once again persuaded the British to allow him to retain a collection he had
made during a visit to Portugal. He became Professor of Zoology at the
Faculty of Science in 1809 having been called to the Institute in 1807. In 1830
he opposed Cuvier in a famous controversy over the question of the fixity of
YEARS OF EXILE: EGYPT AND GRENOBLE
89
species which played an important part in the pre-history of the theory of
evolution (Bio. Gen. ; Gde. Encycl.).
13. Say, Jean Baptiste (1767-1832). After a period of apprenticeship with a Lon-
don businessman he became a journalist. Adam Smith's 'Wealth of Nations'
interested him in economics and his Traite d'ficonomie Politique (1803) was
very influential. The famous law of supply and demand bearing his name was
the central tenet of orthodox economics until the great depression of the 1930s.
After the Restoration he taught political economy at the Athenee (1816), the
Conservatoire des arts et metiers (1821), and the College de France (1830)
(Bio. Gen. ; Gd. Lar.).
14. Denon, Dominique Vivant (1747-1825). French designer, engraver, and diplo-
mat. He was destined for the law but turned instead to arts and literature. He
distracted the aged Louis XV by his brilliant conversation and was given
various diplomatic tasks. While in Switzerland he slipped unnoticed into
Ferney and drew the famous Dejeuner a Ferney and the portrait of Voltaire.
He became a member of the Academie de Peinture in 1787. At the outbreak of
the Revolution he was in Italy and he owed his omission from the list of
emigres to the intervention of David, for whom he then drew the famous
Serment du Jeu de Paume. He also drew a striking picture of Barere at the
Tribune. He attached himself in due course to General Bonaparte and made
himself pleasant to Josephine. He accompanied the Egyptian expedition and
made an important contribution to the Description of Egypt by his drawings
and descriptions of ancient Egyptian monuments. He was the director of all
Napoleon's major monumental works and accompanied him on his most
important campaigns. He initiated the policy of enriching the Louvre with
works taken from conquered lands. He was one of the first to practise litho-
graphy (Gde. Encycl.; Bio. Gen.).
15. Fourier was elected permanent secretary at the first seance. He was then at
Rosetta and his place was temporarily taken by Costaz who had obtained the
next largest number of votes after Fourier. The minutes of the first two seances
(6 and 1 1 Fructidor Year VI) are signed by Costaz alone, the next two minutes
are signed by Costaz and countersigned by Fourier, and the next minutes
(26 Fructidor) by Fourier alone (Bib. Inst. MS. 3818).
16. Some of the greatest urgency following the destruction of the French fleet
and along with it instruments and appliances of all kinds.
17. The additional five or six days beyond the 360 provided by the twelve revo-
lutionary months of thirty days were originally, and appropriately, termed
jours sans-culottidiens. By Year VI the sans-culottes had long been out of favour,
and the term had been changed to the politically neutral complementer es.
18. Cousin, pp. 13-14.
19. Ibid., pp. 19 and 22.
20. Andreossy, Antoine Francois, Count (1761-1828). He gained rapid promotion
in the Italian and Egyptian campaigns. He was a distinguished member of the
Commission of Arts and Sciences in Egypt, and published several memoirs in
the Description of Egypt including one on the valley of Lake Natron. He re-
turned to France with Napoleon and actively assisted him in his subsequent
rise to power, being rewarded with the control of artillery and engineering in
the Ministry of War. He retired after the second Restoration and devoted
himself entirely to scientific work of a geographical and geological nature. He
was elected to the Academie des Sciences in 1824 (Bio. Gen.; Ind. Bio.).
90
YEARS OF EXILE: EGYPT AND GRENOBLE
21. Caffarelli was one of the heaviest losses to the expedition. Malus contracted
plague, and though he cured himself by the exercise of indomitable willpower,
his health was broken and he died early in 1812. Monge also took dangerously
ill but recovered.
Caffarelli, Louis Marie Joseph Maximilien (1756-99). He was a member of
an Italian family which had settled in France in the reign of Louis XIII. He
was educated at Soreze where he distinguished himself especially in mathe-
matics, and later he entered the engineers. In 1792 he served as an officer of
the engineers in the army of the Rhine. At first he was an enthusiastic revo-
lutionary but was later dismissed for having protested against the day of 10
August and the deposition of the King. On his return home he was imprisoned
for fourteen months, but was reinstated in his position in 1795 when he served
with distinction in the army of the Sambre and Meuse and had a leg carried
away by a bullet on the banks of the Nahe. He retired to Paris for a while and
became a member of the Institut. He took part in the Egyptian Expedition as
chief engineer and died before Acre from a wound to one of his arms which had
to be amputated. He was renowned for his bravery, and was very popular with
the soldiers who called him 'wooden leg'. Caffarelli published a number of
memoirs on public education and several scientific works (Bio. Gen.; Gde.
Encycl.).
22. Smith, Admiral Sir William Sidney (1764-1840). He entered the Royal Navy
in 1777 and saw service in the American War of Independence. In 1785 he
went to France where he resided for two years, mostly at Caen, and acquired a
liking for French civilization along with a complete mastery of the French
language. In 1787 he took a journey through Morocco and in the summer of
1789 proceeded to Sweden where he took a prominent part in a naval war
between Sweden and Russia as a result of which he was made a Knight Grand
Cross of the Swedish Order of the Sword. He next proceeded to Constantinople.
Finding himself without transport when ordered home in 1793 he bought a
sloop at Smyrna at his own expense, and with a crew of forty other benighted
British seamen sailed to Toulon to join Lord Hood in his operations against
the republican forces besieging the town. During the evacuation Smith was
put in charge of the burning of French ships in the port, an operation which
was not entirely successful. He made himself extremely unpopular at this time
with other officers through his high-handed manner and excessive self asser-
tion. From 1795 onwards he was employed on various harrying operations on
the French coast in the course of which he was captured at Le Havre in 1796.
Proposals for his exchange were refused by the French government who were
by this time thoroughly exasperated at his activities, and he was imprisoned
for a period of two years in the Temple prison in Paris. Ultimately he escaped
with the help of a Colonel Phillepeaux, a former officer of the royal French
army and class-mate of Napoleon at Brienne. With Phillepeaux Smith played a
memorable part in the defence of Acre against Bonaparte, and for his services
received the grateful thanks of both houses of parliament and a pension of
£1000 per annum. Smith's success at Acre rekindled his thirst for independent
command and he took it upon himself to sign with General Kleber the Con-
vention of El-Arish (24 January 1800) according to which the French forces in
Egypt were to be transported bag and baggage to France at the expense of the
Sultan and his allies. But Lord Keith disowned the Convention and the war
was recommenced. Ultimately, however, the terms for the capitulation of the
YEARS OF EXILE: EGYPT AND GRENOBLE
91
French forces in Egypt differed little from those originally agreed with Kleber
though many thousands of lives, including that of Kleber himself, had been
lost in the meantime. Smith returned home in 1801, was promoted rear-
admiral in 1805, and vice-admiral in 18 10 when he was placed second in
command of British naval forces in the Mediterranean. He returned to England
in 1 8 14 in very bad health but nevertheless characteristically managed to be
present as an observer at the Battle of Waterloo, and had the curious distinction
of being invested with the k.c.b. by the Duke of Wellington in the Palace
Bourbon in Paris on 29 December 1815. He was promoted admiral in 1821.
He spent the last years of his life in Paris where he became head of the Order
of St. John of Malta in France, and died in Paris on 26 May 1840 being buried
close to his wife in the cemetry of Pere Lachaise where a monument was
erected to his memory (D.N.B.; Gde. Encycl.; Barrow; Herold).
23. Herold, p. 325.
24. Idem.
25. Costaz, Louis, Baron (1767-1842). He was a maitre des conferences at the
Ecole Normale in 1795, and became an examiner at the Ecole Polytechnique
in 1796. He played a large part in the foundation of the Conservatoire des arts
et metiers. In Egypt he was assistant secretary to the Cairo Institute and
contributed to the Description of Egypt. He was successively Prefect of the
Manche (1804), Director General of Ponts et Chaussees (1813) and Counsellor
of State (18 1 4). After Waterloo he devoted much time to the encouragement of
French industry. He was elected to the Academie des Sciences in 183 1 as a free
academicien (Bio. Gen. ; Gde. Encycl. ; Ind. Bio.).
26. For example, before Bonaparte's departure there had been an insurrection in
Cairo in October 1798 in which the Institute, then housed in the palace
Qassin Beg, had only been saved by the resolute action of Monge and Berthollet
who insisted in holding out till help arrived from the army.
27. Herold, p. 368.
28. Menou, Jacques Francois, Baron de (1750-1810). Of an ancient family of the
nobility, he entered the army and was elected to the States General, where he
played a leading part in army reforms and in the Constituent Assembly.
After the flight from Varennes he was one of the founders of the Society of
Feuillants. He was in command of the troops in the Chateau of the Tuilleries
on the night of 9-10 August, but was nevertheless continued in his command
and fought in the Vendee. His defeat there led to an act of accusation against
him by Robespierre. He appeared at the bar of the Convention but was saved
by Barere. He was made a general after 9 Thermidor. He repressed the Fau-
bourg Saint Antoine after the insurrection of 1 and 2 Prairial Year III and as
a result was put in command of the Army of the Interior. But he was replaced
by Bonaparte on 13 Vendemiaire for his conciliatory attitude to right-wing
insurgents on that day and remained in retirement till the Egyptian Campaign
when he was put in charge of a division. After succeeding Kleber as comman-
der-in-chief in Egypt he married a Mohammadan and was converted to Islam
taking the title Abdallah. He was defeated by the British invasion force at
Canopus (21 March 1801) and finally capitulated on 31 August of the same
year. By the terms of the capitulation he was able to bring back the French
army to France. Through the favour of Napoleon he was then given various
positions in Italy including that of Governor General of Tuscany (1808) and
Venice (1809). According to the Duke of Ragusa, Menou was devoid of almost
92 YEARS OF EXILE: EGYPT AND GRENOBLE
all military virtues except bravery, was an incurable procrastinator — after he
left Piedmont 900 unopened letters were found in his office — ceaselessly
absorbed with trivia of all kinds, and he seems to have owed his continued
employment after his return to France to the fact that he had constantly put
himself at the head of the pro-Bonaparte party in Egypt. Napoleon would also
have been unlikely to forget that it was Menou's indecision on 13 Vendemiaire
which made possible his own rise to power. (Bio. Gen.; Gde. Encycl.).
29. Desaix, Louis de Veygoux (1768-1800). He belonged to a noble family in
straitened circumstances. After attending the Ecole Royale Militaire at
Effiat he entered the army in 1783, and in 1789 he embraced the revolutionary
cause. He fought under Jourdan and Moreau and played a brilliant part in the
campaigns of the Army of the Rhine. On a visit to Italy he allied himself with
Bonaparte whom he followed to Egypt. He led the operations against Murad
Bey in Upper Egypt where his wise government earned him the title of 'The
Just Sultan' among the Arabs. Disapproving of the Convention of the El-
Arish he returned to France in March 1800 and died gloriously on the field of
Marengo after his last minute intervention had saved Bonaparte from defeat.
The latter regarded Desaix as the most able of all his lieutenants (Gde. Encycl.).
30. Champollion-Figeac, J. J., p. 18.
31. Belliard, A. D. (1769-1832). He entered the Army and was in charge of Du-
mouriez's headquarters at Jemmapes where he displayed great bravery. After
the defection of Dumouriez Belliard was arrested and dismissed from his
position. Thereafter he enlisted as a private soldier and had begun to reclimb
the military ladder when he was given back his previous position by Hoche.
He fought through both the Italian and Egyptian campaigns with great dis-
tinction. Besieged in Cairo by greatly superior enemy forces, he nevertheless
managed to obtain very favourable terms and was given command of the 24th
military division on his return to France. In 1805 he was made chief of staff
to Murat and took part in the Spanish and Russian campaigns where he again
distinguished himself. On the First Restoration he was named Major General
and Peer of France. On the return of Napoleon he accompanied the royal party
as far as Beauvais, refusing to leave them until ordered to do so by Louis
XVIII himself. For the remainder of the Hundred Days he again supported
Napoleon and was arrested after the Second Restoration but was pardoned
and readmitted to the Chamber of Peers three years later. Louis Philippe
appointed him Ambassador to Belgium where he was French Signatory to the
Treaty which separated Holland and Belgium (Bio. Gen.; Gde. Encycl).
32. Geoffroy Saint-Hilaire, p. 216.
33. Fourier Dossier AdS.
34. See below Letter XII, Appendix, p. 292.
35. Fourier Dossier AN: Item 5 of Appendix to Fourier's Letter of 20 Nov. 1815
• to Minister of Interior.
36. Champollion-Figeac, J. J., p. 22.
37. Cousin, p. 28.
38. We remember also that Cuvier's firm refusal to accompany Bonaparte to
Egypt seems to have had no adverse effect on his rapid promotion under the
Napoleonic regime.
39. Fourier Dossier AN : nomination of Fourier as Prefect of Isere.
40. Chaptal, Jean Antoine (1756-1832). On graduating in medicine at Mont-
pellier he went to Paris to complete his studies. He returned to Montpellier in
YEARS OF EXILE: EGYPT AND GRENOBLE
93
1 78 1 to take up a new chair of Chemistry in the School of Medicine. He early
adopted Lavoisier's new theory of chemistry which he expounded with great
clarity and power. He made many important contributions to applied chemistry.
On inheriting his uncle's fortune he devoted his wealth to founding factories
where chemistry could be applied to industry. The Government rewarded
all his many services to the State by letters of nobility and the order of Saint
Michel. In the Revolution he took the side of the Girondins against the
Montagnards in his 'Dialogue entre un Montagnard et un Girondin' which led
to his arrest after the insurrection of 31 May. But his friends in Montpellier
easily obtained his release and he left for Paris where he was made director of
the manufacture of saltpetre at Grenelle. He was charged with the reorganiza-
tion of the Ecole de Medecine where he lectured in chemistry until 1797.
After 18 Brumaire he became Minister of the Interior on the retirement of
Lucien Bonaparte. In this position he made important improvements in
hospitals, and in industrial and technical education. He retired in 1804 partly
through dissatisfaction with the loss of public education to his ministry. On
Napoleon's return from Elba Chaptal accepted the direction of commerce and
manufacture. For this defection Louis XVIII had him struck off the roll of
peers, but he was reinstated several years later, and thereafter contributed as
Counsellor of State to the improvement of commerce and industry. He was
elected to the Institut in 1796. (Bio. Gen.; Gde. Encycl.; Ind. Bio.; Pigeire).
41. Fourier Dossier AN: nomination of Fourier as Prefect of Isere.
42. Ibid.
43. Letonnelier, p. 137.
44. Champollion-Figeac, A. L. (2), p. 141.
45. Ibid., p. 163.
46. Ibid., p. 149.
47. In this task Fourier was assisted by the history of the ancient province of the
Dauphine to which the region of the department of Isere had originally be-
longed. The Dauphinois, in fact, had played a memorable part in the events
immediately preceding the convocation of the Estates-General in March 1789
only rivalled by the turbulent Bretons. Thus the parlement of Grenoble had
been the first to demand (21 August 1787) the convocation of the Estates-
General. The reforms of Lamoignon, including the suspension of provincial
parlements, produced a popular uprising in Grenoble on 7 June 1788, the
famous 'day of tiles' on which the angry populace rained down tiles on the
King's soldiers massed in the narrow streets of the town. Soon after the so-
called Assembly of Vizille (21 July 1788), composed of representatives of the
three estates, especially the third, demanded the re-establishment of the
parlements and the convocation of the Estates -General. In that latter body
representatives of the Dauphine again played a leading part, and two of them,
Mounier and Barnave, were leading figures in the Constituent Assembly. But
the Revolution eventually went too far for the early representatives of the
Dauphine and the constituents who elected them. Although there was a
strongly held local tradition of freedom of thought — possibly related to the high
proportion of Protestants in the province who still made up a quarter of the
population as late as 1720 — this love of freedom went with an equally strong
belief in good government natural to a province which had been exceptionally
prosperous from around 1730 onwards, and which contained no concentrations
of urban proletariat as in Paris or Lyons. From all this it followed that it was
94
48.
49-
5°.
Si-
52
53-
54'
55'
56.
57.
58
59
60
YEARS OF EXILE: EGYPT AND GRENOBLE
quite natural for the Dauphine as a whole, and Isere in particular, to welcome
the Napoleonic regime with its promise of strong and stable government, and —
equally important — its guarantee of the retention of the important gains which
the Revolution had brought to the lower and middle classes at the expense of
the nobility. Statistics bear out this supposed initial popularity of the Na-
poleonic regime. Thus when a plebiscite was taken in 1804 regarding hereditary
establishment of the imperial throne in the family of Napoleon, the voting in
the department of Isere was 80 000 to 12 in favour. And when Napoleon passed
through Isere in 1805 on his way to Milan more than 10 000 people from the
department turned up at Bron to cheer him on his way (Gd. Lar. ; Letonnelier).
Champollion-Figeac, A. L. (1), p. 79.
Cousin, p. 32.
Ibid., p. 32.
And possibly by discreet reference to the Blessed Pierre Fourier, of whom he
is said (Champollion-Figeac, J. J., p. 41) to have spoken with great pleasure
in Grenoble. He was indebted to Champollion-Figeac for obtaining both a
biography and a portrait of his saintly great-great-uncle. Fourier made good
use of this portrait during a stay of King Charles IV of Spain at the prefecture
on his way through Grenoble. With a somewhat un-Jacobin regard for royalty
Fourier had personally supervised all the arrangements of the King's visit with
great care, but had forgotten to provide a crucifix. The King had unfortunately
forgotten his too, and asked to borrow Fourier's. The latter had probably
disposed of his by 1793 at the latest, and to cover up his embarrassment pro-
duced the portrait of the blessed Pierre Fourier while a crucifix was being
fetched from a nearby church (Champollion-Figeac, J. J., p. 41).
Letonnelier, p. 138.
Perier, Augustin (1773-1833). He was counsellor in the parlement of Grenoble
and entered the Ecole Polytechnique at its foundation, returning later to his
native town where he occupied himself actively with industry. In 1815 he was
elected representative of the Rhone in the Chamber of the Hundred Days where
he sat with the majority. He stood without success for Isere in 1819 and 1820
but was elected by the same department in 1827 sitting to the left of centre. He
signed the address of the 221 and was re-elected in 1830, co-operating actively
in the establishment of the July government and in the revision of the Charter.
But he opposed any extension of political liberties and consequently failed to be
re-elected in 1831. Created a peer of France in 1832, he took an important part
in debates and in parliamentary work (Bio. Gen. ; Gde. Encycl.).
Cousin, pp. 29-30.
Fourier Dossier AN: item 9 of appendix to Fourier's letter of 20 Nov. 1815
to Minister of Interior.
Ibid., item 7.
Fourier Dossier AN: Letter of 28 March 18 16 to Minister of Interior.
Cretet, E. (1747-1809). Deputy of the Cote-d'Or in the Council of Five Hun-
dred, he became counsellor of state after 18 Brumaire, director of Ponts et
Chaussees, governor of the Banque de France (1806) and Minister of the Interior
(1807).
Cousin, p. 30.
See below Letter XIII, Appendix, p. 297.
61. See below Letter XVI, Appendix, p. 301.
62. See below Letters XIV and XV, Appendix, pp. 298, 299.
YEARS OF EXILE: EGYPT AND GRENOBLE
95
63. Cestre (3) (1915), p. 454.
64. See below Letter VI, n. 5, Appendix, p. 263.
65. Bib. Inst. MS. 2041 fol. 383. The letter is dated 30 Ventose Year XIII.
66. Ibid., item 66.
67. Fourier was in Paris for a number of months towards the end of 1809 and the
beginning of 1 810 to supervise the printing of his introduction to the Descrip-
tion of Egypt.
68. Bib. Mun. Aux. MS. 335. For completeness' sake it is reproduced below as
Letter XXII, Appendix, p. 322.
69. It was he who presented to the Municipal Library of Auxerre the precious
collection of letters from Fourier to Bonard.
YEARS OF EXILE: GRENOBLE AND
LYONS
1. Extra-prefectorial duties
The draining of the swamps of Bourgoin and the opening of the French
part of the new road from Grenoble to Turin were the major public works
carried out in Isere during Fourier's prefecture, and he had a right to be
proud of the part he played in both projects, especially the former. But he
also contributed as prefect in many other ways to the life of the depart-
ment. For example, he interested himself in individuals of promise in the
department and did what he could to see them launched on their careers.
Thus he used his position as prefect to prevent Champollion-Figeac the
younger 1 from being conscripted by the simple expedient of ignoring
repeated letters from the Minister of War while at the same time writing
himself to various influential people on behalf of Champollion. 2 Eventually
Fourier carried the day, the Minister was forced to retire, and Champollion
was saved for his true metier of Egyptology, a subject to which he had in fact
been introduced by Fourier himself.
As an ex-member of the bibliographic commission at Auxerre during
the Terror, and as candidate for the position of director of the projected
municipal library in that town in 1794, it is not surprising to find Fourier
the prefect active in acquiring books for the municipal library in Grenoble.
Indeed his policy of a rapid build up of books put the library heavily in
debt for a number of years. This, however, as Champollion 3 wisely ob-
serves, was but an illustration of Fourier's discernment of the difference
between public and private bodies in the matter of indebtedness.
He also took a keen interest in the Society of Arts and Sciences at
Grenoble having been elected to the first place to fall vacant after his
appointment as prefect. 4 He was apparently not very assiduous in attending
ordinary meetings of the Society though he was always present at public
seances and at extraordinary meetings. To this society he communicated
all matters of interest which came to his attention through correspondence
and reading, and he also read several memoirs at public meetings including
a discourse 5 on the sciences remarkable for its Baconian emphasis on the
obligation of science to serve the good of mankind. He founded two prizes
in the Society, one in mineralogy, an appropriate subject in a region as rich
in mineral deposits as Isere, and one in statistics. 6
YEARS OF EXILE: GRENOBLE AND LYONS
97
One of the most troublesome and time-consuming of Fourier's under-
takings during his stay in Isere was his contribution to the Description of
Egypt. The idea of this work went back at least to a letter 7 of Kleber of
22 November 1799 to the Institute of Cairo following the return of the
expedition to Upper Egypt under the joint direction of Fourier and Costaz.
Having referred to
the truly liberal and patriotic idea of joining together so many fine things in one
great work, and where possible placing the objects in the national collections . . .
Kleber continued,
In consequence I desire that prompt measures be taken to ensure the writing
of the various works, the distribution of topics, and the choice of the person
responsible for directing the whole of this fine work and for linking together its
various parts. The Institute will feel the need for a general introduction written
all of a piece.
By the almost unanimous vote of a joint meeting of the commissions and
the Institute, Fourier was chosen to 'unite and publish the collection of
works'. The exigencies of war inevitably delayed the project, but it had
been known to the French government in a letter of 23 June 1800, and
after the return of the expedition to France the idea of a general description
of Egypt was renewed by an order of 6 February 1802, the production of
the work to be at the expense of the State and the contributors to be paid
their former salaries as members of the Egyptian expedition. They were
also to share among themselves the proceeds of the sale of the work.
According to a letter from Monge, Fourier was to be charged with
forming a list of the persons who should make up the assembly of savants and
artists returned from Egypt ; all the members of the Institute of Cairo were to
belong to the assembly except those who could not contribute to the required
labours. 8
After the plates of the work had been put in hand the question of writing
arose, especially of the preliminary discourse, and of the editing of the
whole work. Once again, as in Egypt, the assembly of contributors chose
Fourier as editor of the general introduction. 9 According to Champollion-
Figeac, 10 Fourier composed this introduction with painstaking care — no
doubt realizing how carefully Napoleon would scrutinize the result.
Towards the end of his task he isolated himself in a country residence 11
some two leagues from Grenoble where he could devote himself entirely
to the final polishing of his work. In the autumn of 1809 the preliminary
discourse was at last completed and brought to Paris for Napoleon's
approval. This was slow in coming. The then Minister of the Interior, the
Count of Montalivet, 12 tried several times to retrieve from Napoleon the
98
YEARS OF EXILE: GRENOBLE AND LYONS
preliminary printed copy which he had constantly kept on his desk. But
each time, even though he was reading something else, the Emperor
silently retained Fourier's volume by placing his hand on it. At last he
called Fourier to an interview and returned his copy emended in various
places in his own hand to make Fourier's description of the Egyptian
campaign conform more closely to his own view of it — something not
always in complete accord with the actual facts. 13 After the necessary
amendments had been made the work was finally published in 1810. Later,
at the time of the Restoration, a new edition came out in which all references
to Napoleon had been suppressed.
Fourier's general introduction 14 was essentially a survey of the history
of Egypt from Antiquity up to the time of the French expedition. One
interesting detail 15 from the general background to this expedition was his
reference to the memoir presented to Louis XIV by Leibniz detailing the
advantages which would have been derived from the French occupation
of Egypt. A manuscript containing this memoir evidently came to the
attention of the French commander in Hanover during the French occupa-
tion of that town. In the revised version of his Introduction Fourier was at
pains to prove that the idea of an invasion of Egypt, and the subsidiary
idea of a survey of that country, could not have been suggested to Na-
poleon from a reading of Leibniz's memoir. In other words, that the notion
of the expedition was an original idea with Napoleon. At various places
Fourier also makes somewhat fulsome references to Napoleon the 'hero
of the expedition', his enthusiasm for the victories of the French forces
under his leadership making it difficult for him to account for the final
capitulation and the enormous losses suffered in both men and material.
One curious aspect 16 of Fourier's contribution to the Description of
Egypt was his absolute refusal to be rewarded in any pecuniary way for his
labours. Whether he was hoping to be rewarded in some other way —
perhaps by an appointment to a position in Paris — is not clear, but in any
case this time he stood his ground against Napoleon, refused to yield, and
was ultimately 'rewarded' by Napoleon's minute 'granted' against his
name on the list of contributors.
In spite of all the pains lavished on its composition, Fourier's prelimi-
nary discourse is little more than a pastiche written in what appears today
as a rather flowery early nineteenth century style. But it struck a sym-
pathetic echo in at least one of Fourier's contemporaries as appears from
the following letter to Fourier from Fontanes, 17 Grand Master of the
Imperial University.
I do not doubt, Sir, that the work being prepared on Egypt will be worthy of the
savants who are carrying it out, but in waiting for this work I have to tell you
that your preliminary discourse by itself alone is a fine monument. You write
YEARS OF EXILE: GRENOBLE AND LYONS
99
with the grace of Athens and the wisdom of Egypt. Everything is elegant and
grave in your style. It is a long time since I have had anything so good and so
solid. I am not flattering you. I am expressing my real opinion and I write to you
after a second reading which has given me greater pleasure than the first.
Receive, Sir, all my thanks, and the assurance of my highest regard. 18
Finally, apart from his contribution to the Description of Egypt, and his
many administrative and other duties as prefect, Fourier somehow found
time and energy during his stay in Grenoble for his major life work on the
analytical theory of heat.
By the time of his appointment as Prefect of Isere in 1802 the subject of
heat had become one of pressing concern to Fourier. It is not known
whether his extreme need of, and sensitivity to, heat was a long-standing
characteristic; what is certain is that he never managed to acclimatize
himself to the change from Egypt to Isere. Thus in a letter of 1810 to the
Minister of the Interior he said :
The prefect of the department of Isere points out that having changed suddenly
from the climate of Egypt to that of the Alps, following the long and distressful
siege of Alexandria, he contracted several years ago chronic rheumatic pains
which without depriving him of an healthy appearance become more and more
serious and threaten him with a grave illness. 19
In fact, if we are to believe Cousin, Fourier brought back with him to
France from Egypt — whose climate he is said always to have regretted— a
need for great heat at all times which amounted almost to a disease. Thus
he never went out, even in the hottest weather, without his overcoat, and
often accompanied by a servant with another coat in reserve. When he
finally returned to Paris the excessive warmth of his rooms is said to have
hastened his death. In Grenoble, where the winters are far more severe than
in Paris, his concern with adequate heating of his rooms must have been
all the greater. In short, the question of heat, its loss by propagation in
solids and radiation in space, the problem of conserving it — on which
Fourier advanced interesting suggestions in his Analytical Theory of Heat
— can never have been out of his mind for long.
Whether this peculiar personal interest in heat had anything to do
with his theoretical work in the subject must remain a matter of surmise.
What is certain is that some early work 20 around 1804-5 on tne subject of
the propagation of heat had grown by the end of 1807 into a full-scale
memoir 'On the Propagation of Heat in Solid Bodies'. 21 This memoir
contained essentially the whole of Fourier's Analytical Theory of Heat as
published in 1822 apart from the treatment of the diffusion of heat in
infinite solids. By 1807 the Prefect of Isere had thus added to his many
achievements in the administrative field a contribution of the first order in
100 YEARS OF EXILE: GRENOBLE AND LYONS
the rather different field of theoretical physics. Fourier's theory put forward
methods for solving two distinct kinds of problems: first, given a steady
supply of heat at some point or points of a body, to find the eventual steady
distribution of the temperature at all points of the body — the case of a thin
bar, heated by a furnace at one end and immersed in air held at a given
temperature at its surface, provided the simplest (and the most ancient)
example of this type of problem. In the second kind of problem a body was
originally heated throughout according to a certain given temperature
distribution, and was then allowed to cool in an environment whose tem-
perature was given. For example, a uniform sphere initially everywhere at a
given temperature was suddenly plunged in a current of air held constantly at
zero temperature, and it was required to find the temperature at every point
of the sphere at all subsequent times. The great Earth itself provided another,
and far more complex, example of the same kind of problem, and one
which had apparently stimulated Fourier in his search for a general theory
of the propagation of heat in solid bodies. 22 Both classes of problems were
based on a single set of equations governing the movement of heat within
solids, and supplemented in every case by special equations, the so-called
boundary conditions, governing the flow of heat at the bounding surfaces
between the bodies and the surrounding environment.
Fourier read an abstract of his memoir before the First Class of the
Institut on 21 December 1807. 23 The commission set up to report on the
memoir consisted of Lagrange, 24 Laplace, 25 Monge, 26 , and Lacroix. 27
The composition of this commission would seem to have guaranteed a
fair hearing for the memoir. None of its members were in any way antago-
nistic to Fourier and there was no reason for the first two to have altered
the high opinion they had formed of him during his time at the Ecole
Normale and the Ecole Polytechnique. 28 As a veteran of the Egyptian
campaign, and the distinguished 'permanent' secretary of the Cairo Insti-
tute, he could also expect special support from Monge who had been the
first president and one of the prime movers in the foundation and early
organization of the same body, and who had in any case known Fourier
previously at the Ecole Polytechnique during the years 1795-7. The first
reaction to his memoir came in a review 29 by S. D. Poisson in the Bulletin
of the Philomath: Society which if not exactly enthusiastic was perfectly
correct and fair. But Poisson's review was the only public reference to
Fourier's memoir outside the proceedings of the First Class of the Institut
and certain references by Fourier himself at a much later date, and in spite
of a request by the First Class to the commission to hurry up its work no
report ever appeared. In fact, far from receiving the universal acceptance
and acclaim it can now be seen to have deserved, the memoir gave rise to a
lively, many sided, and at times acrimonious controversy. There were two
YEARS OF EXILE: GRENOBLE AND LYONS
101
major criticisms of Fourier's memoir, one on the mathematical side, the
other on the physical side, and between them they struck at the very founda-
tion of the whole work. The major criticism on the mathematical side was
directed at Fourier's use of trigonometrical expansions, or as it would be
termed today, at his use of Fourier series. This criticism was probably
first made in 1808, Laplace and Lagrange being the principal persons in-
volved. Nothing has survived of their actual criticisms which in any case
could have been made orally during an extended visit to Paris by Fourier
in 1808-9 m connection with his Introduction to the Description of Egypt.
However, Fourier's replies to their criticisms have been preserved in the
partly legible drafts of two letters to Laplace 30 and (possibly) Lagrange 31
respectively, together with a mathematical note on the topic under con-
sideration. All these are written with such exemplary clarity — from a logical
as opposed to a calligraphic point of view — that their inability to persuade
Laplace and Lagrange, especially the.latter, provides a good index of the
originality of Fourier's views. The tones of the two letters also provide an
interesting contrast between the almost brutal directness of the letter to
Laplace and the deferential, almost reverential, tone of the letter to
Lagrange with its somewhat emotional ending:
'I desire, above all, to recommend my work to your attention for other reasons
and to remind you of the tokens of benevolence you have given the author. My
heart will always guard their memory . . . Excuse, Sir, the length of this letter,
and be sure that it is written by one who honours and admires you . . . 32
Unfortunately Fourier's logic and rhetoric were both lost on Lagrange who
continued up to his death to disbelieve at least in the rigour of Fourier's
use of trigonometrical expansions.
The second major criticism of Fourier's work was directed against his
derivation of the equations of motion of heat in a continuous solid. Biot
was here the chief opponent aided and abetted at first by Laplace and later
by Poisson. Conceivably this attack might have been avoided if Fourier
had taken care to make a graceful reference in his memoir to his undoubted
indebtedness to Biot's paper of 1804, 33 with its qualitative description of
the process of propagation of heat in a thin bar of which a first incomplete
and erroneous mathematical formulation was given in the Draft Paper of
1 804-5 . 34 There is some reason to believe 35 that Biot was sent a copy of this
paper or of an early draft of the 1807 memoir which still contained the
erroneous derivation. In any case, in 1809, in the course of a review in the
Mercure de France of a work by Prevost, Biot referred to 'an analytical
difficulty which has up to the moment held up all those who wished to sub-
mit the propagation of heat through bodies to calculation'. 36 No doubt there
had already been some criticism of Fourier's derivation of the equation of
r
102
YEARS OF EXILE: GRENOBLE AND LYONS
YEARS OF EXILE: GRENOBLE AND LYONS
103
propagation of heat in his 1807 memoir on the score of its incompleteness.
But to criticize it thus, even if only by implication, in a public journal was an
entirely different matter especially since the whole question was still, as it
were, sub-judice. Fourier's angry response can be seen in two letters to
unknown correspondents :
To treat with such lack of care one of the most important questions in analytical
physics, to rush into publishing in periodical works speculations which are still
uncertain, and even erroneous, ... to make use of public newspapers to foist on,
and attribute to, others his own errors, and to predispose others against a work
which he dare not attack directly. 37
These were faults which Fourier found it impossible 'to observe without
scorn'. In the same letter he also directed a very sharp attack against
Laplace whose method of obtaining an analytical expression for the flux
of heat in the case of a heated bar had been praised by Biot in his Mercure de
France article. Laplace was said to have aided Biot in his 'pretended' dis-
covery of a ridiculous iron bar effect, and to have been the object of Biot's
'servile and calculated flattery' which displayed Laplace as the inventor of
an idea to which he could not in fact lay claim. Fourier even went so far as
to 'sincerely regret' that Laplace did not realize that he was himself thus
supporting an attitude 'so false and so contrary to the progress of the
sciences' : 'the artifices', he added somewhat tartly, 'that an author adopts
to exalt his own reputation beyond that which is reasonable never have
lasting success and often involve him in bitter regrets'. Fourier ended this
letter by a dramatic gesture of renunciation towards his 1807 memoir. T
would prefer', he said, 'to lose so just a cause rather than defend it by
means of public papers', and he declared his intention of abandoning this
'noble theatre' to those who desired it for a career 'equally worthy'.
The controversy over Fourier's work in heat took a new turn at the
beginning of 1810 when the propagation of heat in solid bodies was an-
nounced as a subject for the Institut's grand prize in mathematics for the
year 181 1. 38 Almost total obscurity surrounds the manoeuvrings which
finally led to the decision to set this subject for the prize. Fourier himself
may have given the first impulse in one 39 of the letters concerning Biot's
criticisms where he suggests that the question could be cleared up by set-
ting the subject as a prize memoir. Elsewhere, in some unpublished manu-
script notes 40 on the historical background to his work in heat, he suggests
that attempts were made to prevent the subject being set for a prize essay on
the grounds that no report had yet been made on the 1807 memoir. Pre-
sumably the First Class of the Institut was divided on the merits of pro-
posing the subject. The supporters of Biot, of whom Laplace at this stage
was probably a member, may have argued that if the subject were set as a
prize essay Fourier would inevitably be the winner, and that it would then
be impossible to pass over his work as in the case of the memoir by simply
failing to make a report. In any event, the subject was set and Fourier sent
in his memoir. According to Champollion-Figeac 41 he then continued in a
state of extreme trepidation till word reached him at Grenoble of the safe
arrival of his submission at the secretariat of the Institut.
The commission set up to examine submissions for the prize consisted
of Lagrange, Laplace, Malus, Haiiy, and Legendre. There was one other
candidate apart from Fourier. Fourier's submission consisted of the memoir
of 1807 together with new sections on the cooling of infinite solids, and on
terrestrial and radiant heat. In spite of these important additions the Prize
Essay was still identical with the 1807 memoir as regards its essential
contents on both the physical and mathematical sides. The unresolved
differences of opinion over the earlier memoir might then have been ex-
pected to extend to Fourier's submission for the Prize Essay. Nevertheless
the Prize was awarded to Fourier. The Institut might thus have been
thought to have set the final seal of its approval on Fourier's work. But
while the commission was in no doubt of the superiority of Fourier's sub-
mission and of its great originality and interest, it was still not entirely
reconciled to its validity in certain vital respects. This ambivalence towards
Fourier's essay was clearly expressed in the committee's report:
This theory contains the true differential equations of the transmission of heat
both in the interior of bodies and at their surface; and the novelty of the subject
combined with its importance has determined the class to crown this work, in
observing, however, that the manner in which the author arrives at these equa-
tions is not exempt of difficulties and that his analysis to integrate them still
leaves something to be desired on the score of generality and even rigour. 42
Understandably Fourier read the commissions' report with very mixed
feelings. What the commission gave with one hand it took away with the
other. All his resentment at what would have seemed to him to be the
shabby manoeuvrings of Biot, Laplace (and Poisson) must have welled
up again, and he apparently wrote a stiff letter of protest. 43 The letter itself
has disappeared but not the diplomatic reply 44 of the permanent secretary,
Delambre: 45 the commissioners had full powers in such matters, though
Fourier could evidently write to them himself if he desired, or add a
supplement to the printed version provided it was made clear that the
supplement had been written after the period of the competition. There
the matter seems to have rested. The Institut appeared to be in no hurry
to publish Fourier's masterpiece with or without supplement, and it was
not till after his return to Paris in 18 15 that he could get the publication of
the Prize Essay under way, and then only after further vigorous prodding of
Delambre.
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YEARS OF EXILE: GRENOBLE AND LYONS
2. The first Restoration
Fourier's life in Isere as prefect, writer, and mathematician was evidently
a busy and useful one. Yet in spite of this he was apparently always secretly
unhappy at his position in Grenoble. 46 The climate as we have seen,
especially that in winter, was not at all to his liking; according to him Isere
was the 'native land of rheumatism'. 47 He must also have greatly missed the
company of his scientific peers and colleagues of his polytechnic days, men
like Lagrange, Monge, and Laplace. Fourier, in fact, was the one major
French physical scientist of the period 1800-25 who did not spend the
greater part of that time in Paris. We know 48 that his friends in Paris
including Monge, Berthollet, and Costaz were well aware of his desire to
return there from Grenoble, and they apparently made this known to
Bonaparte. But the latter always turned a deaf ear to their suggestions, and
the post of Director General of Mines which Fourier would have considered
as his 'marshal's baton', and a position which he would have filled with
ease and distinction, was given to another.
Champollion-Figeac 49 suspected that the reason for Bonaparte's ap-
parent indifference towards Fourier may have originated in the latter's
rather too open support for Kleber's criticism of Napoleon at the time of
the latter's return to France from Egypt in 1799. For although Kleber had
admired Napoleon as a general he had greatly disliked his political oppor-
tunism, and the letters written by him to the Directory after Napoleon's
return were filled with blame of the latter's precipitate departure from
Egypt. These letters, however, were opened by the First Consul himself.
Whatever the exact reasons for Fourier's 'exile' in Grenoble, as the
years slipped by it must have begun to seem to him that he would continue
as Prefect of Isere until his retirement. But fate was to give one final, un-
expected, twist to his career. After the disastrous Russian campaign, and
even more after Leipzig, Fourier could not have been the only one of the
army of imperial officials who had begun to wonder what the months ahead
held in store for him. Would the Emperor be able to continue in power ? If
not, who would take his place, and in that case would he himself be able to
retain a position which he had loyally occupied for more than ten years
under the Consulate and Empire ? The answer was to come unexpectedly
soon. By January 1814 foreign troops were fighting on French soil again
for the first time since 1795, and although Napoleon's masterly campaign
of February-March gave a final lustre to his military fame by proving his
greatness in adversity, it could not prevent the surrender of Paris to allied
troops on 31 March. In the meantime Grenoble was besieged by Austrian
forces. One of the generals commanding these forces had served under the
officer in command of the defences of the city, General Marchand. 50 The
YEARS OF EXILE: GRENOBLE AND LYONS
105
two entered into a friendly correspondence and in due course Marchand
learnt of the surrender of Paris and the abdication of Napoleon. A con-
vention was then agreed on and the Austrian forces occupied Grenoble
on behalf of Louis XVIII who had since become King of France. Under
the new regime Fourier continued provisionally as prefect, his high stand-
ing with the different classes of society, especially with the members of the
old nobility, contributing greatly to a smooth transfer of power. Although
the return of the King was unexpected — it had been largely engineered by
Talleyrand — it turned out at first to be reasonably popular. The promise
of a constitutional charter to guarantee the rights of Frenchmen under the
new regime went some way towards stilling the fears of the more republican
members of society, and in any case Napoleon's interminable wars had
produced a general, if temporary, indifference to the exact nature of
authority provided only it ensured a long and uninterrupted period of
peace. Fourier himself, however, was soon faced by an acutely embarrassing
situation on learning that Napoleon was to pass through Grenoble on his
way to Elba. How was he to treat the Emperor about whom still clung some
remnants of former greatness ? How would Napoleon react to finding his
old servant Fourier still Prefect of Isere? Stripped of his power his anger
could still be as terrible as ever. Somewhat maliciously Champollion-
Figeac 51 suggested that Fourier should follow the Emperor into exile, a
prospect which he did not relish in the least, and which visibly upset him
still further. On the day on which Napoleon was due to enter the city all
preparations had been made for his stay in the prefecture and Fourier was
in a state of extreme upset and despondency. Suddenly a messenger arrived
to announce that Napoleon would not pass through Grenoble after all, that
instead he was to take the route du midi through Bourgoin. Fourier's relief
at this news was enormous and he retired for the rest of the day to recover
his composure. Later Champollion discovered that Fourier had himself
engineered the change of route by warning the prefect at Lyons that it
would be dangerous for Napoleon to pass through Grenoble owing to the
excited condition of the people in the region.
Some time later Fourier visited Lyons where he had an audience of the
Duchesse d'Angouleme in which he made clever use of the term 'legiti-
macy' at this time much in vogue. 52 Although he was not at first politically
acceptable he made a good impression on the courtiers who in turn sup-
ported Fourier with the Duchesse and he was confirmed in his position as
prefect. Soon after, Fourier's new status as loyal servant of the crown was
consummated by a visit of the King's brother, the Count d'Artois, later
King Charles X, who thereafter and in spite of the unfortunate happenings
of the Hundred Days always retained an excellent opinion of Fourier.
By the beginning of 181 5 Fourier's administration in Isere had doubtless
1
106
YEARS OF EXILE: GRENOBLE AND LYONS
settled down again into very much the same grooves as before. True, there
were some signs of unrest due to the wild statements of the Ultras — the
followers of the Count D'Artois — and of some of the higher clergy who
urged the government to return to their rightful owners the noble and
clerical lands sold during the Revolution; and J. J. Champollion-Figeac 53
relates how several inhabitants of Grenoble received a proclamation dated
22 February 1815 which played cleverly on these and other complaints of
the people under the royal regime and predicted that 1 March at 5 a.m.
would see the first act in a new drama. But this was only one of many
canards and rumours circulating at the time, and no doubt Fourier dis-
missed it in company with the others. He could not, however, so easily
dismiss a letter from the prefect of the neighbouring department of Var
dated Frejus 2 March:
My dear Sir and Colleague,
I have the honour to inform you that Bonaparte at the head of 1,700 men dis-
embarked yesterday at Gulf Juan, reached Grasse this morning, and according
to those soldiers who have been questioned is heading for Lyons by Saint- Vallier,
Digne, and Grenoble. No matter how extraordinary this news may seem to you it
is entirely true. 54
3. Flight from Grenoble
Fourier's feelings on receiving this totally unexpected and indeed
terrifying note can be imagined. The Emperor, who as First Consul had
originally appointed him Prefect of Isere and whose abdication route to
Elba he had diverted from its original path through Grenoble — ostensibly
in the interests of public order, in reality to avoid the exquisite embarrass-
ment of having to entertain Napoleon in his (Fourier's) continuing capacity
as Prefect — the same Napoleon grown terrible again was now retracing his
steps from Elba to Paris but this time by the geodesic path through
Grenoble, and this time without any possibility of diversion.
Faced not only with a question of personal danger and embarrassment,
but one possibly affecting the future of both France and Europe, Fourier
acted with commendable dispatch. The letter from the Prefect of Var had
reached him at 4.00 p.m. By 7.00 p.m., when he commenced a letter to the
Minister of the Interior in Paris, he had not only made up his mind to
oppose Napoleon but in collaboration with the mayor of Grenoble, the
commanding officer of the garrison, General Marchand, and the Inspector
of the local National Guard he had worked out various contingency plans,
including the disposition of forces to prevent crowds of seditiously inclined
persons from moving on the residences of the principal authorities of the
town or seizing public money for the enemy cause.
YEARS OF EXILE: GRENOBLE AND LYONS
107
Having somewhat optimistically assured the Minister that the inhabitants
of Grenoble and the surrounding area were firmly behind the King, and
having expressed himself confident of the outcome of a trial of strength
with Napoleon by reason of the loyalty of the citizens of the neighbourhood
and of the soldiers, Fourier concluded :
I beg your Excellency to transmit to me the instructions you will deem appro-
priate. Be assured that I will carry them out zealously and faithfully, no motive of
fear will turn me from my duty towards King and country. I know personally the
audacious enemy who threatens us and I do not doubt that before very long he
will send us emissaries . . , 55
Fourier's letter is minuted as having been completed at 7.00 a.m. on the
following morning and we may surmise that he passed a troubled night. In a
postscript he informed the Minister of the Interior of letters received from
surrounding prefects, and of how the inhabitants of Grenoble who had at
first been thrown into confusion by the news of Napoleon's disembarkation
had now in great numbers declared against him.
In the afternoon of 5 March Fourier had a proclamation 56 put up in the
town containing an official admission of Bonaparte's disembarkation at
Gulf Juan, reminding citizens of their duty to the King, and warning those
who might be inclined to forget it that they would be 'arrested immediately
and severely punished in conformity with the laws of the constitution'.
That the views expressed by Fourier in his proclamation were no empty
words, but were intended seriously by him at this time, is proved by a
letter 57 of the prefect appointed by Bonaparte to replace Fourier which
describes the latter's 'frenzied anger' at the treasonable activities of Bona-
parte's supporters in Grenoble. Fourier, it appears, had even threatened to
have them executed if they helped the Emperor's entry into Grenoble. But
in spite of all the genuine efforts of Fourier and other prefects and authori-
ties in the southern part of France Napoleon's progress was irresistible. On
the whole he was welcomed by the majority of the population who had
grown restive under the increasingly reactionary policy of the King's
government. As he passed through the surrounding countryside opposition
melted away. There was no overt act against the King's regime, but on the
other hand there was no determined support for it. There was no group of
citizens, for example, in Grenoble, who stood up for the King with sufficient
strength to affect public opinion. By 7 March Napoleon was drawing near
Grenoble. The previous day he had had his famous confrontation with
soldiers of the 5th Regiment of line. On the sixth there was a dramatic
defection from the King when the 7th Regiment of line rode out of Gre-
noble with their colonel at their head, drew up on the roadway in full view
of the city walls, replaced the royal colours by the tricolour, and rode off to
join Napoleon.
108
YEARS OF EXILE: GRENOBLE AND LYONS
On 7 March Fourier had an official proclamation published announcing
the imminent arrival at Lyons of the King's brother, the Count d'Artois, to
take over command of a royalist army to oppose Napoleon. It also reminded
officials and all others under Fourier's administration of the 'sentiments of
fidelity which should bind them to the King'. 58 In retrospect this looks like
one last despairing effort on Fourier's part to rally the inhabitants of
Grenoble and the still unoccupied part of Isere behind the King's govern-
ment. In fact it was still at this stage uncertain whether or not Grenoble
would fall without a fight. If it had stood out against Napoleon his bid to
regain power might well have failed. But in the event he bluffed his way
into the town without a shot being fired. 59 As he entered triumphantly at
one gate General Marchand and Fourier left the town by other gates,
Fourier on the road to Lyons, and Marchand on the road to Cambery.
Before leaving Fourier had prudently taken out an insurance policy against
possible future developments by preparing a room for Napoleon in the
prefect's residence. 60 Besides fresh linen on the beds etc., he left a letter to
Napoleon in which he managed to express both his feelings of obligation
towards the King and his wish not to offend his old master. He
likewise left a letter for General Bertrand 61 whom he had known in
Egypt-
Fourier left Grenoble on the night of 7 March. By the twelfth he was in
Lyons. When he left Grenoble he was still Prefect of Isere under the King.
When he reached Lyons he had become Prefect of the Rhone under Bona-
parte. Accounts differ somewhat as to exactly how this unexpected meta-
morphosis took place. According to Cousin 62 it was Napoleon who sought
out Fourier. According to Arago, 63 Fourier proceeded straight to Lyons
where he had a stormy interview with the King's brother, the Count
d'Artois, who ordered him back to Grenoble. According to Champollion-
Figeac 64 and Fourier 65 himself it appears that Fourier was on the road to
Lyons when he received a dispatch from that town which caused him to
halt. The dispatch in question, dated Lyons 8 March and from the then
Prefect of the Rhone the Count Chabrol, has been preserved 66 and bears
out the account of Fourier and Champollion-Figeac.
If we are to believe Fourier 67 he then waited where he was on the road
until the arrival of the Count De Polignac, 68 the aide de camp of the Count
d'Artois. Sometime latter he turned towards Grenoble on the basis — as he
later claimed — of the instructions in Chabrol's dispatch. But his actual
instructions in that dispatch were to move towards Lyons or Grenoble
'depending on developments', the intention evidently being that if things
were going badly for the royal cause he should retire to Lyons, whereas if
the royal cause was in the ascendant he should advance to Grenoble. By the
evening of 8 March Napoleon was sweeping towards Lyons with an ever
YEARS OF EXILE: GRENOBLE AND LYONS
109
increasing army. It must have been obvious to anyone who knew the com-
parative merits of Napoleon and the Count d'Artois in the field, and who was
aware of the feeling of the majority of the people towards the royal regime,
that the King's cause was lost in that part of France, and that even if the
Count d'Artois were to stand and fight he would be brushed aside by Napo-
leon. The Count had in fact no intention of risking a battle with Napoleon
and quickly retired from Lyons. According to Champollion-Figeac 69
Fourier learnt of this from a courier. Although Fourier understandably
makes no mention of it, circumstantial evidence points strongly towards
this being the real reason for him turning back towards Grenoble. Accord-
ing to Fourier 70 he was soon surrounded by a group of soldiers and brought
before the Emperor at Bourgoin where he was received with great hostility
because of his known attempts to cut communications across the Rhone.
Helpless and under the most extreme duress he finally gave in to Napoleon's
plans and accepted the prefecture of the Rhone. Champollion-Figeac's
account 71 is somewhat different and rather more plausible than Fourier's :
according to him Fourier proceeded to Cessieux where he spent the night of
8 March. He also sent a message to Champollion-Figeac in Grenoble, no
doubt to sound out Napoleon. Napoleon had at first been enraged by
Fourier's failure to greet him on his entry to Grenoble and by what he re-
garded as Fourier's ungrateful conduct. An order issued at Grenoble on
9 March bears witness to the Emperor's displeasure:
The Prefect of the department of Isere is suspended from his office. He is
required to have evacuated the territory of the 7th military division within the
space of 5 days on pain of being arrested and treated as an enemy of the nation. 72
Thereupon Figeac, who is the hero of his own account, set to work to
mollify Napoleon's attitude to Fourier. He first made sure that a copy of
Fourier's 'Historical Introduction' to the Description of Egypt was pro-
minently displayed on Napoleon's visit to the municipal library. Then he
drew the Emperor's attention to the letter written by Fourier to him be-
fore his departure from Grenoble, for Napoleon had stayed not in the
prefecture but in a small hotel and the letter had not been forwarded.
Napoleon was thus at first unaware of Fourier's thoughtful action. Gradu-
ally his anger cooled until finally he told General Bertrand to find Fourier
and bring him to him. Immediately on hearing this Champollion-Figeac
sent the good news to Fourier who was sheltering at a safe distance from
the route which Napoleon would take between Grenoble and Lyons. On
receiving the all-clear from Figeac Fourier then proceeded to Bourgoin
where he was presented to Napoleon. The latter's reception was in no way
hostile and the next day Fourier heard from Bertrand that he had been
made Prefect of the Rhone.
110
YEARS OF EXILE: GRENOBLE AND LYONS
4. Prefect of the Rhone
Bonaparte's order appointing Fourier Prefect of the Rhone was dated 12
March, and he was installed at Lyons the same day in a ceremony carefully
documented 73 by the Secretary General of the prefecture, one of those
indestructible bureaucrats whose continued devotion to duty and adminis-
trative punctilio provided so powerful an element of continuity during the
kaleidoscopic dynastic changes of the 1st and 2nd Restorations. Fourier
later claimed 74 that he was full of uncertainty as to whether or not he
should exercise the powers thus thrust upon him by the 'usurper' Napoleon.
If he did he would be carrying out the orders of 'an enemy authority', if he
did not he would be unable to use his considerable powers as prefect to
intervene on behalf of innocent citizens threatened by the pro-Bonaparte
party. In the event he decided — once again according to his own account —
to appeal to the King for instructions, and for this purpose had dispatched
from Lyons on 15 March an entirely trustworthy (but unnamed) messenger
whom he had called from Grenoble for the purpose. But this messenger
was turned back at Fontainebleau before reaching Paris and returned
without instructions to Fourier at Lyons on 23 March. Nothing then re-
mained for Fourier but 'to retire quietly (from his position as prefect),
having stopped the first effects of personal vengeance and political fana-
ticism'. Unfortunately for this account, however, there is a considerable
body of documentary evidence which points to a prefect who was by no
means an unwilling servant of the new Imperial Government up to his
'quiet' retirement sometime after 17 May. Thus on 30 March 18 15 he is
writing 75 to the newly appointed Minister of the Interior, Lazare Carnot, 78
to congratulate him on his appointment — 'a new proof of the clear view of
his majesty' — and to inform him that the inhabitants of the Rhone had
rallied to Bonaparte apart from some partisans of the previous government
who were 'few in number and without influence'. Far from waiting on
instructions from Paris Fourier had anticipated them by taking all necessary
steps to 'strengthen public opinion still capable of being led astray by some
new lies spread intentionally'. The curious analogy between Fourier's
actions as Prefect of Isere at the end of the first reign of Louis XVIII, and
his actions as Prefect of the Rhone at the beginning of Bonaparte's second
reign would not have passed unnoticed by anyone who examined the docu-
ments in question in the Archives of the Ministry of the Interior on the
occasion of Fourier's first application for a state pension in December 18 15.
On 1 May Fourier is writing 77 to the sub-prefects of his department
instructing them about arrangements for voting in accordance with an
Imperial Decree relating to the so-called 'Acte Addittonel' 78 to the im-
perial constitution. This letter is a model of bureaucratic thoughtfulness in
YEARS OF EXILE: GRENOBLE AND LYONS
111
which nothing is overlooked down to the smallest details and Fourier had
probably little to do with it apart from signing his name. This he does as
Count Fourier, a shortlived title conferred on him by imperial decree
which he understandably did not employ after the Hundred Days, reverting
instead to his old title of Baron. On 6 May he is writing 79 a much more
compromising letter to the Minister of War (with copies to the Minister of
Police and the Minister of the Interior) on the question of recruitment for
the grande armee. From this letter it is evident that part of the prefecture
was being used as a recruiting office :
The recruiting officers occupy one of the offices of the prefecture, and I have
them supplied with the material necessary for their writing. There are already
some white forms left by the former recruiting captains, but they will not be
enough to provide for duplicate copies : I am having others printed . . .
The decree relieving Fourier of his position as prefect was dated Paris
17 May. 80 But it would seem to have been somewhat slow in reaching him
since on 22 May we find him writing 81 as prefect to the Mayor of Lyons
concerning the surveillance of two persons 'suspected of having been the
principal instigators of the seditious movements which appeared in the
Department of Herault'.
The evidence presented so far points to a Fourier who was perfectly
willing to carry out all reasonable administrative requests, even those con-
cerned with recruitment for the Imperial armies or the surveillance of
political suspects. Nevertheless at the same time there is no reason to doubt
his own claim 82 to have lost no opportunity of reducing as far as possible
all injustice and suffering associated with the change of regime following
Napoleon's return from Elba. Fourier himself supplied an example of this
in one of his applications for a pension after Waterloo in the form of a
written testimonial of a certain Count of Saint Vallier who was freed from
prison as a result of a letter written by Fourier on his behalf to the local
military commander Marshal Suchet :
Paris 27 October 1815.
Some of the facts contained in the memoir of M. the Baron Fourier, former
prefect of Isere, were already known to me, and I find that M. Fourier relates
them with too much modesty since he makes no mention of the esteem and
gratitude of those formerly under his administration which he has merited in so
many ways.
I cannot pass over in silence a matter concerning myself which happened
sometime between the months of March and July last. I was arrested in my
house in the month of April of that year and transferred to Lyons with the Mayor
and the commandant of the National Guard of the town of Saint Vallier by
order of General Grouchy to appear before General Corbineau, special commis-
sioner of Bonaparte. Some considerable time after the said General Corbineau
112
YEARS OF EXILE: GRENOBLE AND LYONS
had left, I presented myself to Marshal Suchet, commandant of the army, to
demand from him our liberty. This Marshal appeared astonished and pained
with such an arbitrary act executed without any apparent motive ; but he added
that as all three of us had been arrested by an authority other than his own he
could not free us unless this were demanded by the Prefect of Lyons who would go
bail for us. The prefect was then M. Fourier, who did not hesitate to write a very
strong letter to Marshal Suchet to obtain our release which he took all necessary
steps to ensure, and which did ensue, and it is to M. Fourier that three citizens
arbitrarily and unjustly arrested owed their liberty which would long have been in
jeopardy without him. 83
Accounts differ on the reasons for Fourier being relieved of his position
as Prefect of the Rhone. According to Cousin 84 it was due to Fourier's
unwillingness to comply with certain harsh orders emanating from Carnot
in Paris. But Champollion-Figeac, 85 who is very circumstantial and quotes
verbatim at considerable length from Fourier and the other persons con-
cerned, claims that his resignation was due not to orders emanating from
Carnot but from a certain Count Maret, 86 one of a number of extraordinary
commissioners sent by Napoleon throughout France to ensure compliance
with his commands. In particular Fourier is said by Champollion-Figeac
to have refused to carry out a purge of certain administrators including
some in his own prefecture who were suspected of royalist sympathies.
There seems however to be no extant documentary evidence bearing on this
question and in a letter 87 of 15 May to Count Maret we find him expressing
agreement with certain measures proposed to him by Maret.
Whatever the reasons for Fourier's removal from the prefecture of the
Rhone they do not seem to have entirely destroyed his credit with Carnot
or Napoleon, for on 10 June Napoleon decreed as follows :
At Imperial Palace of Elysee
10 June 1815.
Napoleon, Emperor of the French, on the report of our Minister of the Interior,
we have decreed as follows: —
1. There is granted from 1st July, 1815 a retirement pension of 6,000 francs to
each of the following :
Fourier ex-Prefect of Isere and of the Rh6ne.
2. These pensions will be inscribed in the great book of public debt. They cannot
under any pretext be added to any other pensions or salaries paid by the state
in such a manner as to exceed the level fixed by the present decree. 88
However by 1 July, the day on which the first payment was due, Napoleon
had been defeated, the King had returned, and Fourier never touched a
franc of the pension. It was to be at least six years before he received any
money in the way of pension for all his many educational and administra-
tive services to the State.
YEARS OF EXILE: GRENOBLE AND LYONS 113
Notes
1. Champollion-Figeac, J. F. Called Champollion lejeune. French Egyptologist,
1790-1832. While Professor of History at Grenoble (1812-15, 1818-21) he
prepared himself for his epoch-making work on the decipherment of Egyptian
hieroglyphics announced in his Lettre a M. Dacier of 1822. The extent if any of
Champollion's debt to the earlier work of Thomas Young on the Rosetta
Stone has never been established. Champollion was made keeper of the
Egyptian department of the Louvre in 1826. In 1831 he became professor at
the College de France.
2. Arago, (1), p. 329.
3. Champollion-Figeac, J. J., p. 26.
4. Ibid., p. 28.
5. This somwhat dull and uninspiring piece is reproduced in Champollion-
Figeac, J. J., pp. 333-7-
6. His personal interest in this subject dated at least from his years in Egypt, but
now there was a powerful additional reason for collecting statistics relating to
the department of Isere as a result of the insatiable appetite of the Ministry of
the Interior for such information. At this time (1804) there was no official
almanac and an administrative annual was not to appear till 1809. Fourier
therefore addressed himself to various savants of the region to undertake the
work and supply him with material. He also, as we have seen, requested the
Society of Arts and Sciences of Grenoble to make statistics of the region the
subject of one of their prizes. But the response to his requests were disappoint-
ing, and having discovered that a certain Berriat-Saint-Prix had written a
statistical account which the Society judged to be very exact and interesting
he asked for a copy. The learned Professor of Law, however, was even more
meticulous than Fourier in matters of accuracy, and kept putting off the day of
sending Fourier his collection. In desperation Fourier asked a certain Perrin
Dulac to complete a statistical survey which he, Fourier, had himself begun.
On 10 June 1806 Fourier was at last able to inform the Minister of the dis-
patch of the first volume of Perrin Dulac's work. But it turned out that Fourier
had either not read, or — as he himself claimed — had not received the detailed
instructions from the minister regarding this statistical survey. It should in
fact have been in manuscript and not in printed form. Fourier hastened to
apologize for this error. The relevant order had not reached him. If it had he
would have conformed to it 'scrupulously'. In fact although Fourier had had
the statistical survey printed he had not had it published though his letter may
have given this impression to the Minister. But as soon as he was aware of
the details of the missing order he had given rigorous orders himself to see that
the work should not be published, and he intended to produce a statistical
account of his own on the exact lines laid down in the ministerial order. As for
the second volume of Perrin Dulac's work, when Fourier examined it he found
many errors. He complained of these to the author and asked the inexorable
Berriat-Saint-Prix to examine the work. The latter found many more errors
which he detailed in full in a note to Fourier. Fourier then took over the whole
printing of both works at his own expense and had them suppressed. In the
event the minister never received the completed statistical memoir on Isere. As
an experienced administrator of long standing Fourier may simply have played
for time until the attention of the Minister was occupied elsewhere. One
114
YEARS OF EXILE: GRENOBLE AND LYONS
unexpected outcome of the suppression of the edition of Perrin Dulac's work
was to make the book itself an excessively rare collector's piece, only four
examples being known to Champollion-Figeac (Champollion-Figeac, A. L. (2),
pp. 323-8).
7. Reproduced in Champollion-Figeac, J. J., pp. 73-4.
8. Ibid., p. 75-
9. As appears in a letter from Berthollet to Fourier preserved in Fourier Dossier
AN. But Fourier was apparently unable to accept and the position as editor was
taken by Jomard.
10. See Champollion-Figeac, J. J., pp. 76-81.
11. The chateau of Beauregard, where Fourier guarded his solitude jealously. But
exceptions were occasionally made including a certain Mme Lallier, wife of the
chief engineer of bridges and roads in Isere, who visited Fourier on several
occasions to paint his portrait. Unfortunately this 'departmental masterpiece',
as A. L. Champollion-Figeac somewhat maliciously terms it, seems to have
disappeared. Fourier had already had his portrait painted in Paris by Girodet.
The portrait, which still existed in the study of a M. Storelli at the time of
composition of A. L. Champollion-Figeac's Chroniques Dauphinoises, was said
to have been one of the masterpieces of the French school.
12. Montalivet, J. P. B., Comte de (1766-1823). Counsellor at Parlement of
Grenoble. He became acquainted with Bonaparte and was successively appoin-
ted prefect, director of Ponts et Chaussees (1806) and Minister of the Interior
(1809). During the Hundred Days he was intendant general of the Crown.
This account is taken from Champollion-Figeac, J. J., p. 82.
The text of the first version submitted to Napoleon is reproduced in Cham-
pollion-Figeac, J. J., pp. 88-172.
Ibid., p. 89.
Ibid., p. 84.
Fontanes, Louis Marquis de (1757-1821). He published some early poems and
a French translation of Pope's Essay on Man. At first he embraced the Revolu-
tion but his courageous protest against the bloody acts of Collot d'Herbois
and Fouche in Lyon obliged him to go into hiding. He emerged after 9
Thermidor and became a member of the Institut and Professor at the Ecole
Centrale in Paris. He was proscribed again on 18 Fructidor and lived for a
while in London where he became friendly with Chateaubriand. He returned
to Paris after 18 Brumaire and by his writings in the Mercure de France became
the leading opponent of the Ideologues of the Decade Philosophique. He pro-
moted the establishment of the Empire and gained the favour of Bonaparte. He
was appointed Grand Master of the Imperial University in 1808 and Senator in
1 810. Under Louis XVIII he was made a member of the Privy Council and a
Marquis. He was official orator of the Legislative Corps and Senate under
Napoleon, and of the Chamber of Peers under Louis XVIII. Nevertheless he
had a mind of his own, was not afraid to oppose Bonaparte on occasion, and was
one of the judges who refused to vote for the death of Marshal Ney (Bio. Gen. ;
Gde. Encycl.).
18. Ibid., p. 85.
19. Letonnelier, p. 136.
20. Preserved in the Draft Paper.
21. 1807 memoir.
22. Thus in his 'Memoir sur les Temperatures du Globe Terrestre' (CEuvres, 2,
13
14
IS
16
17
YEARS OF EXILE: GRENOBLE AND LYONS
115
23-
24.
25-
26.
27.
28.
29-
30.
3i-
32.
33-
34-
35-
36.
37-
38.
39-
40.
4i-
42.
43-
44.
45-
46.
47.
48.
49
S°.
5i
pp. 97-125) he states 'The question of terrestrial temperatures always seemed
to me one of the most important objects of cosmological studies, and I had it
principally in mind in establishing the mathematical theory of heat.' (op. cit.,
p. 114).
This is the date written on the text of the memoir itself by Delambre, then
permanent secretary (mathematics) to the First Class of the Institut. It is also
given in Proc. Verb. 3, p. 632.
See below Letter I, n. 12, Appendix, p. 247.
See below Letter VI, n. 10, Appendix, p. 264.
See below Letter III, n. 3, Appendix, p. 253.
See below Letter X, n. 4, Appendix, p. 288.
In his letter (VII) to Bonard, Fourier had said that he was on very good terms
with these two mathematicians.
Poisson (2).
See below Letter XX, Appendix, p. 316.
See below Letter XXI, Appendix, p. 318.
Ibid., p. 320.
Biot (1).
Draft Paper, fol. 124.
See below Letter XXI Appendix, p. 318.
Biot (2), p. 336.
See below Letter XVII, Appendix, p. 302.
There appears to be no trace in the Proces Verbaux of the decision to set the
subject of propagation of heat in solid bodies as a prize essay.
See below Letter XVIII, Appendix, p. 306.
Historical Notes.
Champollion-Figeac, J. J., p. 45.
Quoted in CEuvres, 1, p. vii.
According to Champollion-Figeac, J. J., p. 47, n. 1.
Bib. Nat. MS. ff. 22529, fol. 119.
Delambre, Jean Baptiste (1749-1822). He acquired early a passion for study
which was first directed to history and literature. Later his interest turned to
mathematics and astronomy and he became the assistant of the astronomer
Lalande. He carried off prizes at the Academie des Sciences in 1790 and 1792
for his tables of Uranus and the satellites of Jupiter. In 1792 he was elected to
the old Academie des Sciences and in 1795 to the First Class of the Institut and
the Bureau des Longitudes. In 1803 he became Permanent Mathematical
Secretary to the Institut. He succeeded Lalande at the College de France in
1807 and was appointed treasurer of the Imperial University in 1808. His most
important works were his Astronomie theorique et pratique (1814) and his
Histoire de V Astronomie (six volumes: 1817 to 1827) (Bio. Gen.; Gde. Encycl.).
Champollion-Figeac, J. J., p. 30.
Letonnelier, p. 136.
Champollion-Figeac, J. J., p. 34.
Ibid., p. 31. Crosland, p. 60, gives an interesting example of another scientist,
Prony, who incurred Napoleon's displeasure, this time by refusing to join in
the Egyptian campaign, and who thereafter was passed over for any honours
during the whole of the Napoleonic regime.
See below Letter XXVII, n. 2, Appendix, p. 330.
Recounted in Champollion-Figeac, J. J., p. 37.
116
52-
S3-
54-
55-
56-
57-
58.
59-
6o.
6i.
YEARS OF EXILE: GRENOBLE AND LYONS
Ibid., p.
Ibid., p.
Ibid., p.
Ibid., p.
Ibid., p.
62.
63-
64.
65-
66.
67.
68.
69.
7°-
71-
72.
73-
74-
75-
76.
77-
78.
79-
80.
81.
82.
83.
84.
37-
182.
187.
192.
196.
Fourier Dossier AN: item 16 of appendix to Letter of 20 Nov. 1815.
Copies of this proclamation are found in the Fourier Dossier AN.
Arago, (1), p. 356.
Champollion-Figeac, J. J. p. 207.
Bertrand, Henri Gratien, Count (1773-1844). He took part in the Egyptian
campaign being wounded at Aboukir. He was made aide de camp by Napoleon
after his brilliant conduct at Austerlitz. Thereafter he accompanied Napoleon
on all his campaigns, saving the French army after Leipzig. He became grand
marshal of the Imperial Palace, and took part in Napoleon's campaign of
February-March 18 14. He was present at Waterloo, and afterwards refused to
leave Napoleon accompanying him to St. Helena where he stayed till the Em-
peror's death in 1821. Condemned to death in absentia in 1816, he was later
pardoned by Louis XVIII and restored to his rank. After 1830 Bertrand became
a deputy and constantly defended the liberty of the press. In 1840 he was
entrusted by Louis Philippe with bringing back Napoleon's remains to France
{Bio. Gen.; Gde. Encycl.).
Cousin, p. 35.
Arago (1), p. 357.
Champollion-Figeac, J. J., p. 210.
Fourier Dossier AN: supplement to letter of 20 November 1815.
Fourier Dossier AN: item 15 of appendix to letter of 20 November 1815.
Ibid., note added by Fourier.
Probably Comte Armand Jules de Polignac, 1771-1847, brother of the Minister
of Charles X.
Champollion-Figeac, J. J., p. 210.
Fourier Dossier AN: supplement to letter of 20 November 1815.
Champollion-Figeac, J. J., p. 210.
Fourier Dossier AN: supplement to letter of 20 November 181 5.
Fourier Dossier AN : proces-verbal of Fourier's installation as Prefect of the
Rh&ne.
Fourier Dossier AN.
See below Letter XXIV, Appendix, p. 324.
See below Letter XXIII, n. 1. Appendix, p. 323.
See below Letter XXV, Appendix, p. 325.
This act, which was in imitation of the charter of Louis XVIII, established a
parliament composed of two chambers, a chamber of peers elected by the
sovereign, and a chamber of representatives elected by a form of universal
suffrage. It was solemnly promulgated in Paris at a champ de mai on 1 June
1815.
See below Letter XXVI, Appendix, p. 326.
Fourier Dossier AN.
Bib. Mun. Lyon MS. 2274.
See below Letter XXVII, Appendix, p. 328.
Fourier Dossier AN: item 19 of appendix to letter of 20 November 1815.
Cousin, p. 35.
4. A portrait by an unknown artist, possibly Claude Gautherot, of Fourier in prefectorial
uniform. (In the possession of the Musee St. Germain, Auxerre. Photograph by R. G.
Phelipeaux of Auxerre)
IT i;;\, I .- I
5. A portrait of Fourier by Boilly. (Taken from a copy in the possession of the Archives
of the Acad.em.ie des Sciences)
YEARS OF EXILE: GRENOBLE AND LYONS
117
85. Champollion-Figeac, J. J., p. 25iff.
86. Possibly J. P. Maret, 1758-1827, brother of the more famous H. N. Maret,
Due de Bassano, Napoleon's chef de cabinet.
87. Bib. Mun. Lyon, MS. 2273.
88. Fourier Dossier AN.
LAST YEARS: RETURN TO PARIS
1. The pension campaign
Following his dismissal as Prefect of the Rhone Fourier returned to Paris.
There he is said greatly to have enjoyed his new-found freedom from
administrative duties, and the opportunity of mingling again with scientific
and mathematical colleagues such as Laplace, Monge, and Berthollet. But
his pleasure at returning to Paris was to be shortlived ; Waterloo and the
downfall of Napoleon soon placed him in a desperate financial position.
Generous to a fault, and in the habit of living up to the top of his income
and beyond, he had little money in his pocket when he came to Paris, and
never touched a franc of the annual pension of 6000 francs of which the
first instalment was due on July 1 . To these pressing financial difficulties
was added justified anxiety over the attitude of the King's government
to his acceptance of the position of Prefect of the Rhone during the Hun-
dred Days. For a time it seems 1 that he even thought of emigrating to
England where he would at least have been free of any political persecutions
and could have hoped to make a living by teaching mathematics. Mercifully
he was not forced to take this extreme step. As always, there was a friend
ready to help, this time in the person of the Count de Chabrol, 2 Prefect of
the Seine, a pupil of Fourier's at the Fxole Polytechnique and his com-
panion on the Egyptian campaign. Disregarding any unfavourable reactions
from the extreme right, Chabrol had Fourier appointed Director of the
Statistical Bureau of the Seine. He thus similtaneously relieved Fourier
of any pressing monetary anxieties and ensured that the statistical reports
emanating from his department in the next fifteen years or so should be
the envy of the world and serve as models of their kind.
Safely ensconced at the Bureau of Statistics of the Department of the
Seine in a post for which he was pre-eminently suited on both the practical
and theoretical sides, 3 Fourier could give up — no doubt without much
regret — the idea of emigrating to England. But there was still much to be
done to establish himself firmly in Paris; above all he had to have himself
elected to the Academie des Sciences and he had to persuade the govern-
ment to replace the 'stillborn' pension of 1 June. Fourier lost little time
in applying for a pension. On 20 November 1815 he sent a lengthy memo-
randum* to the Ministry of the Interior in which he set out his major
services to the State in teaching, in the Egyptian campaign, and as Prefect
LAST YEARS: RETURN TO PARIS
119
of Isere, naturally drawing particular attention to his part in the draining
of the swamps of Bourgoin and his contributions to the Description of
Egypt. If Fourier had confined his activities to teaching and administration
this application for a pension would in all probability have been favourably
received — provided, of course, his Jacobin activities in the years 1793-4
had not come to light. But his support for Napoleon during the Hundred
Days inevitably endangered the success of his application. Aware of this
danger himself, he evidently decided it would be best to give a separate
justification of his actions in the Hundred Days independent from the
original application based on his services to the state in education and
administration. This accounts for a supplement 5 to the original memoir
dated 22 November 181 5 which stresses his efforts to put down sedition
in Grenoble prior to Bonaparte's arrival, citing as evidence a letter 8 of his
successor at Grenoble, Boissonnett, and the order 7 of Napoleon requiring
him to quit the territory of the 7th military division within five days on
pain of being treated as an enemy of the State : the rather more doubtful
thesis was also advanced that it was in pursuance of the order of the royal
authorities that he had turned back to Grenoble and thus fell into the
hands of Napoleon ; as for his brief tenure of the prefecture of the Rhone,
it had preserved the town of Lyons 'from the greatest disasters', while his
dismissal had been due to his opposition to the 'unjust and arbitrary'
measures required of him.
Fourier's application was duly acknowledged 8 by the Minister of the
Interior. Some considerable time then elapsed before he learnt that his
application had been refused. 9 Fourier was much too experienced an
administrator to accept this rejection as final. He replied immediately with
a proper show of feeling in a letter of 28 March 1816; having expressed
'the keenest sorrow' over the Minister of the Interior's reply, Fourier
proceeded once again to retail his various services to the state in education,
administration, and scholarship. He also pointed out — which was true-
that he was the only one who had received no payment for his part in the
production of the memoirs on Egypt, and that in the process of draining
the swamps of Bourgoin he had been put to considerable personal expenses
which had never been repaid.
Referring to his activities during the Hundred Days he suggested that:
No political motive should efface the memory of so many services from which
the State and many generations will receive real and lasting advantages. I realise
how out of place it is to speak thus of oneself, and it is as painful to me as it is
contrary to good manners thus to recall the outcome of my efforts; but I may
be excused if one remembers the absolute obligation under which I find
myself to make the most of my services by all means consistent with the
truth. 10
r
120
LAST YEARS: RETURN TO PARIS
The original of the letter of 28 March is minuted at the top:
M. Pannellir. Keep this letter. The Prefect of Grenoble at the time of the arrival
of Bonaparte should not be surprised not to have a pension.
While the supplementary memorandum dated 8 April 1816 (in which he
again gave a separate justification of his conduct during the Hundred
Days) is minuted :
Place these documents in the file of the conduct of M. Fourier during the most
disastrous epoch of our history.
Both minutes seem to be in the same hand, probably that of the then Minis-
ter of the Interior Vaublanc 11 or possibly the King himself, and evidently
neither boded much good for Fourier's application. Not surprisingly the
pension had still not been granted by the time of a visit by Fourier to the
Minister of the Interior on 9 May 181 6. This demarche was likewise un-
successful though the advent of a new Minister of the Interior, Laine, 12
delayed a reply to Fourier until June. Laine then wrote to Fourier as
follows :
Baron Fourier,
You have reminded me of the request which you presented to my predecessor
to obtain a retirement pension as former prefect.
His majesty having recently adjourned his decision on this matter I cannot
allow myself to resubmit your request to him at present. I regret that this circum-
stance prevents me from doing anything in your favour. 13
This letter was evidently not very encouraging and gave Fourier little
grounds for hope. He would have been more hopeful if he had known that
his good friend the Minister of Marine, Dubouchage 14 had queried whether
the King had in fact adjourned consideration of Fourier's demand, and that
an earlier version 15 of the letter of June from the then Minister of the
Interior had been minuted by the King or his first minister the Due de
Richelieu as follows :
I desire that the Minister sign this letter and that M. Pannellir add a note to know
if the new Minister (Laine) is not disposed to treat M. Fourier more favourably.
Evidently it had been the former, and very reactionary, Minister of the
Interior Vaublanc who had chiefly opposed the granting of a pension to
Fourier. Nevertheless the pension had still not been awarded by November
1 81 6 as appears from a letter of Laine to Fourier on the twenty-ninth of
that month :
Baron Fourier,
I have not forgotten what you told me last July and what I myself replied to
you then.
I spoke of my desire to obtain for you a pension for all your administrative and
literary labours. I am constantly aware of the need for this and I shall eagerly
LAST YEARS: RETURN TO PARIS
121
seize any opportunity which may present itself for proposing it (to the King).
I have your memoir before my eyes. The important service which you ren-
dered to the state by the considerable draining operations carried out and com-
pleted under your directions is not the kind of service which can remain
unrewarded. 16
This must have raised Fourier's hopes very high. But once again he
was to be disappointed and thereafter there is no record of any further
demands by Fourier before a letter 17 to Laine of 10 March 18 18 in which he
refers to Laine's encouraging letter of 29 November 1 816, to his interven-
ing election to the Academie des Sciences (May 1817), and joins a me-
morial 18 supporting his request from a deputation of four persons from
the department of Isere. Again there was no response, since there is a fur-
ther application 19 of 9 September 1821 in which Fourier briefly goes over
the (now) familiar grounds of his claim for a pension. This time the
application was backed up by a letter 20 from Fourier's friend Chabrol the
Prefect of the Seine. To Chabrol's letter Laine's very reactionary succes-
sor Corbiere 21 did not even deign to reply himself. Instead with calculated
coolness he instructed the Director of the Ministry to reply on his behalf:
The Minister of the Interior has passed to me the letter you have written him
in support of Baron Fourier who solicits a retirement pension by reason of
services rendered in education and administration. His Excellency, who ap-
preciates the merits and services of this former official, would like to have been
able to give you some hope for the success of his demand, but the strict provisions
of our legislation on pensions absolutely prevent it. As a necessary condition for
obtaining a retirement pension the relevant decree of 13 September 1806
requires 30 years of salaried service, and 60 years of age at the moment of ter-
mination of duties. M. the Baron Fourier seems to have fulfilled the first con-
dition, but he had not reached 60 years of age on quitting the administration in
181 5. His demand is therefore inadmissible according to the terms of the decree
in question. I regret, personally, being unable to advance the interest which you
have for him. 22
No doubt the discouraging message in this letter found its way back to
Fourier. It must have seemed to him at this stage that there was no point
in making any further applications. The refusal to grant him a pension on
the purely technical grounds of his having retired before reaching the age
of sixty, especially since that retirement was in the form of a dismissal
during the Hundred Days, must have made it clear to him that the then
Minister of the Interior was inflexibly opposed to his demand. In fact he
was awarded a pension at some subsequent date, but curiously the pension
was granted by the Minister of Police for 'important services of informa-
tion' 23 rendered him by Fourier. The information in question is unspecified
and one can only hope that Fourier had not been acting as a police informer,
122
LAST YEARS: RETURN TO PARIS
and that the information transmitted by him to the Minister of Police was
of a statistical nature which in his position as Director of the Statistics
Bureau of the Department of the Seine he would have been in a good
position to provide.
2. The Academicien
Apart from the pension campaign, Fourier's other major preoccupation
in the first years of his return to Paris was his election to the Academie des
Sciences. In April 1816 word reached him of a proposal to elect several
new members as 'free academiciens' , 2i that is as opposed to the ordinary
procedure in which election had to await the vacation of a 'chair' through
the death of a sitting member. A commission 25 was set up to compile a list
of possible candidates for the free positions. When Fourier called on
members of this commission some of them were not at home. This gave him
a useful excuse to write 26 to the President of the First Class of the Institut
with a request to bring before the commission his claims for consideration
on the grounds of his contributions to science ; 'my attachment to science'
he said 'is in truth the only claim which I should advance to win your vote'.
Nevertheless he shrewdly added a reference to the prize awarded him by
the Institut itself.
. Fourier's case was a strong one on purely scientific grounds if only
on the score of his Prize Essay of 181 1. Moreover, although Lagrange 27
had died, and Monge 28 had been forced out as a supporter of Bona-
parte, Laplace 29 still remained very powerful and would doubtless
have supported Fourier's candidature. It is probable, too, that Fourier's
charm would have had its effect on those members of the election com-
mission whom he had been able to find at home. In the event, however, his
election on 27 May 1 816 to one of the two free positions was anything but a
walkover: at the seance of 20 May 191 6 he was one of eight candidates
shortlisted for the two places of free academiciens out of the original list of
thirty-four presented to the Academie by its election commission. 30 At
the first round of voting at the seance 31 of 27 May de Rosily 32 obtained 16
votes, de Cubieres 33 12 and Fourier n ; at the second round de Rosily 20,
de Cubieres 13 and Fourier 1 1 . On a straight vote between de Rosily and de
Cubieres the former was elected to one of the free places by 39 votes to 14.
At the first round of voting for the second place Fourier obtained 27 votes
and de Cubieres 18, and Fourier was then elected to the second place at
the second round when he obtained 38 votes against de Cubieres 17. The
Minister of the Interior, Laine, 34 was informed of Fourier's election the
same day by letter from the Permanent Secretary (mathematical sciences)
Delambre, 35 with a request that the election be submitted for approval to
LAST YEARS: RETURN TO PARIS
123
the King. In more normal times such approval would have been no more
than a formality. But the times were by no means normal in May 18 16.
Admittedly they were more normal than they had been in the summer of the
previous year when the White Terror had been active again in France,
especially in the south and west, and when many former Jacobins,
Napoleonists, and other 'non-conformists' had been murdered by gangs
of 'royalist' assassins. But as long as the ultra-reactionary Vaublanc 36 con-
tinued as Minister of the Interior Fourier's chances of entering the
Academie des Sciences were as dim as his chances of obtaining a retirement
pension. The replacement of Vaublanc by the comparatively liberal Laine 37
on 8 May 1816 immediately improved his chances, but the ultra-royalist
'introuvable' chamber of deputies still sat — it was not to be dissolved till
the following September — and as long as it continued both the King and his
ministers had to moderate whatever inclination they may have had to-
wards a sympathetic treatment of those who had gone over to Napoleon
in the Hundred Days, even in a comparatively 'mild' way, as in the case of
Fourier. In the event the King refused to confirm Fourier's election to the
Academic 38
Neither Fourier nor the Academie, however, were prepared to take this
rebuff lying down. On 3 June the top brass of the Academie including the
president, vice-president and both permanent secretaries wrote 39 to the
Minister of the Interior Laine giving the reasons of the Academie for
electing Fourier, at the same time enclosing a letter which had been sent to
the Academie in support of Fourier's candidature by the King's own
Minister of Marine, Dubouchage : 40
M. Fourier, gentleman, author of various mathematical and physical works
and of the preliminary discourse of the Description of Egypt desires to be
nominated to one of the vacant places in the Royal Academie des Sciences. It is
not for me to justify to you the literary claims of M. Fourier, they are known to
you, and you are in a better position than I am to appreciate them; but I am glad
to render him as administrator (Prefect of the department of Isere) all the justice
which he merits : M. Fourier acquired a real claim to the esteem and gratitude of
this department by the services which he rendered it as administrator, and by his
constant efforts to moderate or modify the harsh dispensations of the tyranny
under which France groaned. This conduct has won him the especial gratitude
of the families most devoted to the royal cause who found themselves most
exposed to oppressive measures; I desire that this justice which I am happy to
render to M. Fourier may contribute to ensure him the vote of the Academic 41
In his letter 42 of acknowledgement of 4 June, Laine promised to inform
the King of the reasons for Fourier's election and from this time on it
appears that he and Dubouchage worked steadily to predispose the King in
favour of Fourier's election to the Academie.
124
LAST YEARS: RETURN TO PARIS
Fourier did not have to wait long for his next chance of membership.
On 5 April 1817 Rochon, 43 a member of the physics section, died and
Fourier again threw his hat into the ring. By 27 April the King's opposition
had evidently been overcome as we learn from a letter of that date from
Fourier to the academicien Huzard : 44
I presented myself today at M. Huzard's to have the honour of seeing him and
asking him to give me a new proof of his kindness in the next election of the
Academie des Sciences. The minister has been good enough to inform the
president of the Academie that the obstacle which had annulled the first nomina-
tion has been lifted. 45
Fourier was this time elected by an overwhelming majority, no doubt
mainly because he was now competing for a position in the physics section
only open to those with certain specific scientific qualifications as opposed
to the previous positions of free academiciens in which the 'qualifications'
were much less restricted. Of the 50 votes cast at the seance* 6 of 12 May,
Fourier obtained 47. The Academie was evidently determined to leave the
King and his minister in no doubt of its feelings about the merits of
Fourier's candidature, and of its displeasure at the rejection of its original
choice of Fourier in the preceding May. The Minister was informed of
Fourier's election by letter 47 the same day. This time the election was not
opposed by the King. But unintentionally or otherwise he put Fourier on
the rack for over a week, not giving his approval until 21 May, Delambre
being informed on 23 May. 48
Much water had flowed under many bridges since November 1789 when
the young novice Joseph Fourier had read his first paper to the Academie
Royale des Sciences of King Louis XVI. Now some twenty-eight years
later, the Revolution, the Consulate, the Empire, the First Restoration, and
the Hundred Days having intervened, this same Fourier was at last safely
elected to the Academie Royale des Sciences of that unfortunate King's
brother Louis XVIII. There can have been few other examples in the
history of the Academie des Sciences of so long a gap between the first
memoir and the election of so distinguished a savant as Fourier. This pro-
vides a good measure of the magnitude of the impediment produced by the
Revolution in the fulfilment of the scientific ambitions expressed in the
postscript to his letter 49 of 22 March 1789 to Bonard: 'Yesterday was my
21st birthday; at that age Newton and Pascal had [already] acquired many
claims to immortality'.
Once elected to the Academie Fourier was relieved of any nagging
uncertainty as to his scientific standing. Now at last he could devote himself
entirely to his true mitier. The result was a period of intense activity which
made the years between his election to the Academie in May 18 17 and his
LAST YEARS: RETURN TO PARIS
125
election to the position of permanent secretary (mathematical sciences)
in November 1822 one of the most scientifically useful in his life. He
immediately threw himself wholeheartedly into the life of the Academie,
sitting on a large number of commissions set up to examine a variety of
matters especially the consideration of memoirs submitted to the Academie.
In no fewer than ten cases 50 as reporter, or secretary, Fourier was
responsible for drawing up the final report of the commission in question.
At the same time he actively pursued his own researches, and during the
period in question he submitted a total of eight original memoirs to the
Academie, two on statistical 51 topics, two on mathematics, 52 and four on
the analytical theory of heat. 53
In August 1822 Delambre, 54 the permanent secretary of the Academie
for the mathematical sciences, died. At the seance 55 of 11 November 1822
Fourier was placed on the list of candidates for the vacant position along
with Biot 56 and Arago. 57 Fourier seems to have been already quietly con-
fident of the outcome of the contest, for in a letter to Sophie Germain 58 he
states:
I cannot doubt now but that the wish of the greater number of my colleagues will
be to choose me and that that one 69 of my opponents who flatters himself the most
is very much mistaken. But he has resource to so many artifices that it would be
imprudent not to fear him. 80
As usual Fourier was well briefed on the current state of opinion. Arago
withdrew his name at the same seance on the grounds that his other occupa-
tions would not permit him to serve, and at the election 61 on 18 November
Fourier obtained 38 votes against Biot's 10. At the seance 62 of 6 January
1823 it was announced that Fourier's election to the position of permanent
secretary had been approved by the King.
After he became permanent secretary to the Academie Fourier's life as an
academicien inevitably changed somewhat. He was now responsible for all
the official correspondence of the society on the mathematical side with
other learned societies and with individuals of all kinds. He also continued
to serve on commissions though he no longer acted as reporter. The last
such commission to which he was elected was in May 1830, a few days
before his death. 63 He also naturally continued to attend seances 6 * of the
society. He was also responsible for composing a number of eloges 65
including those of Delambre — his predecessor as permanent secretary —
and Laplace. He was likewise responsible for producing the annual reports
on the state of the mathematical sciences. 66 Finally, in addition to all this
activity he somehow found time (as in Isere) to continue with his own
private researches in mathematics and physics and during the period
126 LAST YEARS: RETURN TO PARIS
1822-30 he published a number of papers in both pure and applied mathe-
matics.
Fourier's life as a savant was enlivened by a number of fierce contro-
versies with certain of his colleagues. The first and most important of these
was a recrudescence of that over the period of 1807-10 concerning the
Analytical Theory of Heat. This time his opponents were Biot and Poisson
with Laplace acting more as a judge than a participant.
Biot's attack on Fourier's treatment of the problem was contained in a
footnote of his Traite de Physique 61 in which he claimed that in his 1804
paper he had been the first to 'enunciate and apply' the equation for the
steady state distribution of temperature in an iron bar at one end. Fourier
had no difficulty in exposing the falsity of this claim in a note 68 in his
unpublished Historical Precis devoted specially to Biot's misdeeds in which
he also took Biot to task, as in 1809, for omitting any reference to the
earlier work of Amontons and Lambert — a regrettable departure from an
'invariable usage founded on the most just principles'.
Poisson's criticisms were more serious than Biot's and understandably
gave Fourier considerable cause for alarm. For Poisson did not restrict
himself to a criticism of Fourier's methods, but attempted to give a treat-
ment of the propagation of heat in solids alternative to that of Fourier, and
this at a time, 181 5, when Fourier had himself published nothing on the
subject. In his first paper, 69 said to have been an abstract of a memoir
presented to the Academie des Sciences earlier in the year, Poisson referred
specifically to Fourier's Prize Essay of 181 1 which he had seen in the
Secretariat of the Institut. He admitted that Fourier had found the correct
equations of the propagation of heat in solid bodies, and that the solutions
given in various particular cases were sound, but, in terms curiously
similar to those of the report of the commission on the Prize Essay, he
maintained that Fourier's treatment left something to be desired both as
regards his method for deriving the equations of propagation and the
generality of his solution.
Fourier responded to Poisson's attack by a three-pronged counter attack.
In the first place, to safeguard his priority in the subject until the publica-
tion of the Analytical Theory of Heat — whose printing had apparently
begun by 181 6 — he had a short paper 70 published in various journals con-
taining brief, non-technical accounts of his own achievements in the subject
in the still unpublished Prize Essay of 181 1. In the second place, he gave a
considered reply to the criticism of Poisson in his Historical Precis. 11 This
work was apparently intended for publication though it never in fact ap-
peared. It may however have been shown to various colleagues, especially
Laplace, with its devastating replies to the criticisms of Biot and Poisson.
In the third place, Fourier was fortunate enough to be able to show that an
LAST YEARS: RETURN TO PARIS 127
application by Poisson of his method to a particular problem was mathe-
matically unsound. This had nothing to do with the validity of the method
itself, but it must have seriously undermined its credibility with Laplace to
whom Fourier sent a copy of the paper 72 in which he exposed Poisson's
errors.
The covering letter to Laplace is in the soothing tones of Fourier the
diplomat and peacemaker :
I would not permit myself such reflections if they were [directed ?] to anyone
other than M. Poisson himself, and if they were not submitted to M. Laplace,
that is to say a benevolent judge equally inclined to both combatants, and who
knows that this great controversy is not in the least serious, and not being public
can only have advantages without any awkwardness. 73
But his true feelings to Poisson (and Biot) were given in another passage :
Seven or eight years ago M. Biot and M. Poisson expressed themselves in the
same way on the subject of my work. Having contested the various results they
recognize now that they are exact but they protest that they have invented another
method of expounding them and that this method is excellent and the true one.
If they had illuminated this branch of physics by important and general views
and had greatly perfected the analysis of partial differential equations, if they had
established a principal element of the Theory of Heat by fine experiments such as
those of the calorimeter, they would have the right to judge my work and to
correct it. I would submit with much pleasure and I would recognize that their
discussion was a source of precious illumination. But one does not extend the
bounds of science by presenting in a form said to be different results which one
has not found oneself and, above all, by forestalling the true author in publica-
tion. 74
As usual Fourier had the last word, and although Poisson continued to
work on the theory of the propagation of heat, and ultimately published a
work on the subject after Fourier's death, there is good reason to believe
that henceforward Laplace adopted the role of 'benevolent judge equally
inclined to both combatants' which Fourier had so neatly suggested for him
in his letter.
Apart from this major controversy with Biot, and more especially
Poisson, over the Analytical Theory of Heat, there is evidence for other
and less important controversies in which Fourier was involved : one with
Cauchy 75 over the question of priority in the discovery of the so-called
Fourier transforms, and later controversies with Poisson over certain
mathematical questions 76 and some relating to Fourier's treatment of
radiant heat. 77 All in all, it was with his old pupil and deputy that Fourier
had the most frequent controversies, and in each case Fourier seems to have
128 LAST YEARS: RETURN TO PARIS
had the better of him. But this did not affect his high opinion of Poisson's
talent. For at the end of the long passage quoted above he says:
M. Poisson has too much talent to exercise it on the work of others, he wastes
it by employing it to discover that which is known. Science waits for, and will
obtain from him, discoveries of a greatly superior order. 78
3. Friendships old and new
Apart from fulfilling his obligations to Science and the Academie,
Fourier found time to cultivate old friendships and form new ones both
within and without the Academie. Among the list of particular friends given
by Mauger appear the names of the academiciens Lagrange, 79 Monge, 80
Humboldt, 81 Cuvier, 82 and Navier. 83 Of these Lagrange was doubtless the
one most admired by Fourier. Of their relations in the period 1795-8
nothing is known, and thereafter Fourier could only have met Lagrange
again on the rare occasions of his visits to Paris in the period 1802 up to
Lagrange's death in 1813. Still, we can be sure that in spite of Lagrange's
reservations about certain mathematical features of Fourier's Prize Essay
of 181 1 Fourier would have had no reason to revise the opinion he formed
of Lagrange when he first saw him attempting to lecture at the short-lived
ficole Normale of 1795: 'everyone knows that he is an extraordinary man,
but it is necessary to have seen him to realise that he is a great man'. As for
Monge, who had encouraged Fourier at the time of the submission of his
first memoir to the old Academie des Sciences in November 1789, whom
Fourier had known in the early years of the ficole Polytechnique, and in the
Cairo Institute where their collaboration as President and Permanent
Secretary must have been particularly close, it is to be hoped that Fourier
did not desert him when, dismissed from the Institut and forbidden
to enter his beloved ficole Polytechnique, he lived out the remaining melan-
choly years of his life in retirement.
Once he became permanent secretary of the Academie on the mathema-
tical side Fourier must have seen more of Cuvier, his opposite number on
the 'physical' side, than any other of his colleagues in the Academie.
Their friendship, in fact, would have contributed much to the efficient
running of the Academie, and considering Cuvier's enormously powerful
position in that body — he had been permanent secretary on the physical
side since 1803 — it is reasonable to surmise that good relations between the
two men had been established prior to Fourier's election as permanent
secretary and were a not unimportant factor in that election. In one respect,
at least, there was a curious, and possibly significant, similarity between the
outlooks of Fourier and Cuvier to their respective sciences : Cuvier believed
in a rigid separation between plant and animal species which was the basis
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of his ineradicable hostility to the 'permissive' evolutionary views of
Geoffroy Saint Hilaire, while Fourier believed in an equally rigid and
apparently preordained separation between at least two of the most
important theories of physical science, that of dynamics and Fourier's own
analytical theory of heat. 84
Although Fourier is said to have lived a rather retired life on his return
to Paris after Waterloo, he no doubt made an exception occasionally to
attend the Cuvier salon, the most distinguished 'scientific' salon 85 of the
day. There he would have met not only non-scientific members such as
Henri Bayle (Stendhal) but also fellow academiciens such as Geoffroy
Saint Hilaire and Humboldt. There is no evidence for the closeness of his
friendship with Humboldt. Geoffroy Saint Hilaire he had known in
Egypt where, as we have seen, 86 they had not always seen eye to eye.
Apart from Cuvier and Humboldt the only other member of the Aca-
demie des Sciences who is known to have been a particular friend of
Fourier in his last years was the engineer and applied mathematician
Navier to whom Fourier's papers passed on his death. According to
Cousin, 87 Navier was one of a number of young men including Dirichlet, 88
Libri, 89 Duhamel, 90 and Pouillet 91 whom Fourier delighted to have around
him in his old age. Either Fourier was an exceptionally good judge of
mathematical talent — which would not have been surprising — or else
Cousin only listed the more distinguished of Fourier's young friends,
for all of these four later joined Navier as members of the Academie des
Sciences. Dirichlet, elected to one of the coveted positions of foreign
associates reserved for the most distinguished non-French scientists and
mathematicians, was one of the outstanding pure mathematicians of the
first half of the nineteenth century, and made particularly important
contributions to the development of some of Fourier's own ideas in pure
mathematics.
It is rather striking that among Fourier's particular friends in the Aca-
demie des Sciences we find none of the other outstanding French mathema-
tical physicists of the day, Laplace, 92 Poisson, 93 Biot, 9 * Arago, 95 Fresnel, 96
and Ampere. 97 If we exclude Ampere on the grounds of his excessive
eccentricity — something hardly likely to appeal to the level-headed Fourier
any more than to his level-headed friends Cuvier and Humboldt — and
Fresnel on the score of his age, and the fact that unlike Navier he happened
to be the protege of Arago rather than Fourier, we are left with the first four.
There is every reason to believe that Fourier's relations with Arago were at
least correct, if not actually friendly — they had after all a mutual friend in
Humboldt — though perhaps Arago was a trifle too revolutionary for the
liberal but cautious Fourier of the Second Restoration. There remain
Laplace, Poisson, and Biot. Judging by his eloge of Laplace's achievement
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in science and mathematics Fourier was in no doubt of Laplace's genius
for the subject. He was not the only person, however, who seems to have
had certain reservations about Laplace the man: 'Laplace has done much,
he said to Cousin, 'but he would like to have done everything'. 98 A hint of
an incipient dislike for Laplace can even be detected as far back as Fourier's
letter to Bonard early in the year 1795 in the somewhat malicious
account" of how Laplace was nominated as a pupil at the Ecole Normale
and how the great man — always unnecessarily in awe of authority — had
accepted the humble position offered him though the government had
later 'corrected this administrative error'. The fact that Fourier excused
himself at very short notice on the grounds of indisposition 100 from
reading the graveside oration required of him as permanent secretary on
the mathematical side at Laplace's funeral provides another possible
indication of a certain lack of cordiality in his relations with Laplace.
Against this, a letter 101 of Laplace to Fourier of 1824 nas survived which
ends on a very cordial note: 'I embrace you, and renew to you all my
feelings of esteem and friendship'. As for Biot and Poisson, the reasons
for the rather cool relationship between them and Fourier will be suf-
ficiently evident from what has gone before. 102
4. The Egyptian Society
The scientists, artists, and literary men who had shared the splendours
and miseries of the Egyptian campaign formed a natural fellowship which
was renewed by the survivors through their combined work on the Des-
cription of Egypt on their return to France. Fourier's closest friends among
his fellow 'Egyptologists' were said to have been Jomard 103 and Chabrol. 104
Both had been pupils at the Ecole Polytechnique during Fourier's time
there, and no doubt Fourier had had a hand in choosing them (as well as
Malus and others) as part of the large contingent from the Ecole
Polytechnique to the scientific commission. But their real friendship with
Fourier would have dated from the campaign itself when Fourier is said
to have encouraged Jomard in the study of historical remains which was
later to become the ruling passion of his life. Fourier and Chabrol — his
other close friend from the Egyptian campaign — had had another ex-
perience in common, that of acting as prefect under the Napoleonic
regime. But Chabrol had wisely refused to support Napoleon during the
Hundred Days, and had made quite certain of not being faced with the
kind of agonized decision Fourier was forced to make at Bourgoin by
fleeing the country, perhaps a fortunate event from Fourier's point of view
since otherwise Chabrol might not have been in a position to come to his
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131
rescue in the dark days after Waterloo by appointing him to the direction of
the statistical bureau of the Seine.
Among Mauger's list of Fourier's particular friends appears the some-
what unexpected and very colourful figure of the British sea-dog, Admiral
Sir Sidney Smith, k.c.b., 105 a sort of foreign associate of the Egyptian
'Society'. Fourier had, of course, first made Smith's acquaintance under
exceptional and distressing circumstances 106 at the time of the attempted
return to France of the members of the Commission of Sciences and Arts
of the Egyptian campaign. In 1820 Smith migrated to Paris, probably to
escape the attention of debt collectors in England, and here he evidently
renewed his acquaintance with the Commission, this time under more
peaceful and auspicious circumstances. To their credit the members of the
Commission did not forget their debt to Smith for saving their collections
on the high seas off Alexandria. They showed their gratitude to him in a
peculiarly appropriate and charming manner as the following letters 107
relate :
The president and members of the Commission of Egypt to His Excellency the
Minister and Secretary of State for the Interior.
Sir,
As the members of the Commission of Sciences and Arts of Egypt were
setting sail for France the vessel which carried them was in the power of the
British fleet for a time. Their papers and collections were about to be lost to their
country, they found themselves in a critical position and their lives were men-
aced. They would doubtless have succumbed, and the results of their laborious
researches would have been destroyed, if a generous Englishman had not come
to their aid. Animated by a love of science, Admiral Sir Sidney Smith saved their
collections and their persons. They cannot forget the noble devotion of this
worthy stranger who was not frightened to compromise himself to assure to their
country the results of their labours. As if it were a sacred duty, he religiously
looked after the papers of one of us, the perpetual secretary of the Institute of
Egypt; and as soon as the commission had returned to France he hastened to
send back these papers intact.
We believe, Sir, that this generous conduct merits a signal mark of public
gratitude, and we come to propose that your Excellency offers him a token of this
in requesting the King that Admiral Sidney Smith should be given a copy of the
Description of Egypt.
We have the honour to be with respect, Sir, Your Excellency's very obedient
servants.
signed: Fourier etc.
26 January 1826
Mr. Admiral,
Forgive my extreme haste for not waiting for a time when I would be free to
come and see you to tell you that yesterday, Thursday, the King has signed the
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order which accords you the Description of Egypt. It is less you that I congratu-
late than my country which has known how to appreciate by this slight mark of
public gratitude generous sentiments and magnanimous loyalty.
Please accept the renewed and sincere expression of my regards.
Signed Jomard.
Paris, i February 1826
Sir,
I hasten to inform you that by royal order of 25 January his Majesty has been
gracious enough to accord you a copy (in fine paper) of the Description of Egypt.
I congratulate myself in being able to announce this act of royal munificence,
and I beg you to take the matter up with M. Jomard, representative of the govern-
ment on the Commission of Egypt.
Receive, Sir, the assurance of my distinguished consideration, the Minister,
Secretary of State for the Interior.
signed Corbiere 108
Fourier had evidently a special reason for being grateful to Sidney
Smith for the safe keeping and prompt return of his mathematical papers,
though it is not clear why Smith retained the papers when Fourier and the
other members of the Commission had returned to Alexandria. Perhaps
Fourier feared for their safety and calculated that they would be safer in the
keeping of the British Admiral than in the French ship. If so, it shows that
on. occasion Fourier was a shrewd judge both of situation and character.
Unfortunately, no other evidence of the friendship between Fourier and
Smith has survived, or of the conversations they must often have had to-
gether in Paris about the Egyptian campaign in which they both played
such distinguished though different parts.
Among his circle of close friends Fourier also counted a number of
administrators and politicians, men like Laine 109 too honest to be a good
politician and so generous that when he became a minister he had to borrow
the uniform of his office; or Augustin Perier, 110 a former pupil of Fourier's
at the ficole Polytechnique, wealthy industrialist and politician, the trusted
friend and confidant of Fourier during his stay in Isere as prefect. Also
Augustin's younger brother Casimir, 111 the most brilliant French politician
of the third decade of the nineteenth century, who by his firm, and on
occasion ruthless, policy as Prime Minister probably prevented the out-
break of civil war in the first two critical years of the July Monarchy.
Not all Fourier's friends during his last years in Paris were as grand as
Casimir Perier or Admiral Sir Sidney Smith, k.c.b. We learn from Cousin
that he had a brother in Paris— probably the same Jean-Baptiste who had
written 112 to the Committee of General Security on Fourier's behalf at
the time of his imprisonment after the Prairial Days of 1795 — who kept a
shop, not very successfully it seems, 113 and with whom Fourier always
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remained very friendly, and whom he helped from time to time, eventually
settling a small pension on him. There was also his devoted man-servant
Joseph who was entrusted with all his financial affairs, who had followed
Fourier from Grenoble and Lyons to Paris, and who was to follow his coffin
to the grave. There were still a few old friends left in Auxerre including
Roux 114 and Ame, 115 and at least one other young Parisian friend not a
mathematician, Victor Cousin, 116 who was eventually to take Fourier's
place in the Academie Francaise. If Cousin's philosophical stock has
fallen somewhat since the great days of his extraordinarily popular public
lectures in Philosophy in the Sorbonne, nevertheless by any standards he
was an exceptionally intelligent and enlightened man who had a lively
appreciation of historical accuracy — as his researches into seventeenth
century biography show — and the reminiscences and accounts of Fourier
which we find in his biographical notes provide many valuable, and often
unique, sources of information about various aspects of Fourier's life and
his attitudes to science, education, philosophy, and religion. 117
Cousin relates 118 how he first met Fourier in 1824 at the house of Laine.
He encountered Fourier several times before they became at all friendly.
Cousin had just returned from Germany where he had undergone a term of
imprisonment on suspicion of being a member of the secret society of
Carbonari. On his return to France he continued in disgrace for a time, and
not unnaturally Fourier was rather cautious about entering into any sort of
intimate relations with such a 'revolutionary' character. But gradually they
became more intimate, and when Fourier moved towards the end of his
life to a house in the Rue D'Enfer only a short distance from that of
Cousin they became much more friendly. Cousin relates how he took care
to humour the older man, to be suitably deferential towards him, how
Fourier was touched by his attentions, and how gradually he became much
freer in his conversation. He delighted to tell stories of his experiences in
the Revolution, in Egypt, as Prefect of Grenoble. Understandably, Cousin
found particularly interesting any references by Fourier to Bonaparte.
Fourier emphasized the benevolence and charm of Bonaparte, and one
account he gave Cousin proved so interesting that the latter took an exact
note of it. It related to the attitude of Bonaparte towards classical studies :
Like all great minds Bonaparte passionately loved literature. He had brought
to Egypt a collection of literary works entirely disconnected with the object of
the expedition and he used to read these in the little leisure which was left to
him by the works and cares of command. One day in Cairo as we walked on the
banks of the Nile, he took from his pocket a Lucan and began to read to me
several passages from it, among others the famous passage on Caesar and Pom-
pey. He greatly admired it, but he did not always understand it very well, and
from time to time made mistakes which I corrected for him. 119
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It seems, according to Cousin, that the good Fourier hesitated and lost
his way in his early days on the banks of the Nile in trying to translate Lucan
to Bonaparte in just the same way as thirty years later when trying to
translate Cornelius Nepos and Horace to Cousin in the Luxembourg
gardens in Paris. But Bonaparte, who was much less philosophical than
Cousin, grew impatient at not advancing more quickly, and after about
half an hour he threw down the book on the sand in a rage complaining
that Latin was not better taught in his young days. Apparently he envied
Garat 120 and others their facility to read Lucan, and he was dumbfounded
to learn from Fourier that these gentlemen were almost as embarrassed by
the subject as he was himself: 'Is Latin not known any more in France ? Ah,
one day I'll put that right.' And, as Cousin remarks, he was already dream-
ing of the restoration of classical studies which played so prominent a part
in the structure of the Napoleonic lycees.
5. Female relations.
Fourier never married but is said, inevitably, to have been extremely
fond of the company of intelligent women. Certainly he was not the only
mathematician of the day who courted the friendship of Sophie Germain, 121
one of the select band of female mathematicians of note of which history
bears record. A self-taught mathematician of very considerable talent
who had held her own in correspondence with Gauss and Lagrange,
Sophie was also a person of great charm and vivacity. Fourier's friendship
with her extended over the period from at least 1820 until his death, and a
considerable number of his letters 122 to her have survived. Most of these are
little more than notes dealing with such matters as the reading of Sophie's
papers to the Academy, and their interest lies largely in the indication
they provide of a certain light-hearted, gallant side to Fourier's physiog-
nomy. For example, on 1 June 1823 he wrote as follows:
I have the honour to recall myself to the memory and esteem of Mile Germain.
I have, for long been very desirous of calling on her, but have been prevented
from doing so by certain pressing business.
I send to her enclosed 1° an official letter 2° a ticket for the person who will
accompany her. If Mile Germain does not intend to be present at the stance, I
beg her to dispose of the ticket as she thinks fit, and if it were necessary I could
send one or two more [tickets] but not centre ones.
Alas, I would have much preferred to have been able to retain one of those
[centre] tickets myself. I am condemned to speak in public, a great bore, and I am
going to appear tomorrow like a feeble light in the midst of a firework display.
But I am resigned to bearing invidious comparisons. It has seemed reasonable
to me to adopt from the start a grave and simple tone which I shall be able to
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keep to, and to eschew any pretensions to a success which I would not obtain
and which I do not wish for: what I do wish for is to retain the esteem and
remembrance of Mile Germain. I beg her to receive the expression of my respect.
Fourier. 123
In spite of Fourier's evident warm feelings of friendship for Sophie,
up to at least 1827 his letters continue to open and close in the same formal
sort of way which the French adopt in all but the most intimate corre-
spondence. A note 124 in very broken handwriting addressed to Ch[ere],
Sfophie]. and signed J[osep]h suggests that it required the imminent
approach of death itself to effect a relaxation in this iron rule.
A delightfully light and playful letter to Madame Cuvier has also been
preserved :
I make haste to send Madame the Baroness Cuvier several samples of the
recent discovery of M. Renard of Vivienne Street. I would like to have included a
sample of his prose which is neither less soft nor less clear than his lemonade
but I have not been able to find it. It states that the entire contents of a packet
should be thrown into a glass of water. The word entire is underlined because the
packet apparently contains two parts both necessary for the success of the experi-
ment. Mme Renard told the servant that this composition of her husband is made
of nectar. Without being entirely of this opinion I have found the liquor agree-
able if a little aromatic. She stressed the advantage of the low price, a thing
indifferent to the Gods but not to mortals.
I beg Madame Cuvier to allow me to enclose two letters of the celebrated
mathematician Monge. I hope later to acquit completely the commission of Mile
Clementine and I shall try to find other pieces worthy of augmenting [her
collection?].
I have the honour of offering to Madame Cuvier the honour of my respect.
Joseph Fourier.
Paris, Sunday morning. 126
There is, however, nothing playful about the letter of unknown date
from Fourier to a certain Doctor l'Herminier, 126 full of an anxious and
delicate concern for a person endowed with the 'rarest and most beautiful
qualities' whom Fourier says that he 'tenderly loves' :
Monday evening
Paris.
Sir and dear colleague in Philosophy,
I received today a letter from the person of whom I spoke to you this morning.
She has taken the salutory but unfortunately tardy decision to have recourse to
your superior knowledge. She will go to you on the day you will appoint. I
thought that Wednesday next at exactly two o'clock or a little earlier. If you
would prefer it she could find you at No. 14 Rue Caumartin. She is very keen not
to be named or even to be known, and I was able to calm her entirely on this
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score because you did not even know her name, and if you were to know it it is
very certain that you would be inclined to ignore it entirely even if she herself
allowed some questions on that score.
With all my heart I desire that you should receive all details of as many circum-
stances as possible, and all those that would be useful. In the first conversation
that I had with this same person I did not insist on the gravity of the illness, and I
only spoke of an analogous principle which could be different though it would
produce similar effects. I was frightened in my first interview of producing too
strong an impression. However, it is absolutely necessary that she should no
longer be in any doubt in this respect, for this illness seems to be deeply rooted
and to have become bearable to some extent, so that if there were to remain any
uncertainty she might perhaps not make up her mind to the indispensible treat-
ment. In any case, all this is confined to your customary discretion and I con-
gratulate myself that this same person has decided to choose you. She is worthy
of all your interest by reason of the rarest and most beautiful qualities. For myself,
who love her tenderly, in so much as this entirely unforeseen event may bring
to nothing the feelings which I have had for her, I would be most deeply grateful
for anything you could do for her and for me.
Receive sir, and dear colleague, the expression of all the feelings of gratitude
and attachment which I owe you. I am going to reply tomorrow morning to her
letter of yesterday and I will tell her Wednesday at two o'clock at No. 14 Rue
Caumartin unless I hear from you to the contrary. I will send my reply to her
letter only at two o'clock tomorrow afternoon, Tuesday. If by that time I have
received no advice from you it will be expressly understood that she will find
you at your home on Wednesday at two o'clock.
Joseph Fourier 127
Unfortunately, as in the case of so many of Fourier's later letters, this
letter is undated, though by the writing it was evidently not written in his
very last years. The use of the style Monsieur in place of Citoyen on the
envelope also effectively rules out the possibility of it being written before
1804. It would seem, therefore, most probably to have dated from the
early years of Fourier's return to Paris after Waterloo and just conceivably
the person concerned could have been Sophie Germain herself who died
of cancer at a comparatively early age in 1831.
6. Last years
In his position as permanent secretary of the Academie Fourier led a full
and satisfying academic life. He was at the centre of scientific activity in
France. He was recognized and respected by his fellow scientists. There
was little more for him to ask for. At last he had reached his final and en-
tirely satisfying niche as a man and a scientist. Honours crowded in on him
during his last years. He was elected to various foreign scientific societies
including the Royal Society of London. In 1826 he was called to the
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137
Academie Francaise in succession to Lemontey. 128 On the death of Laplace
in 1827 he was elected president of the conseil de perfectionnement of the
Ecole Polytechnique. Fate had no more unforeseen twists in store for him.
His last years were to be as quiet and happy as the constantly troubled
political scene in France and the precarious state of his health would
allow. His health had never been good. It would appear that excessive study
— presumably around the age of thirteen when he became intensely
interested in mathematics — had damaged it and that this was accentuated
by the serious illness which he had in the years 1784-5. In coming back
from the East to Europe he had also caught rheumatism which was re-
newed with the slightest cold. He had always had a certain difficulty in
breathing — possibly dating from the hours spent in nocturnal study in the
'cupboard' in Auxerre— and at the end of his life this had become so great
that he was forced to sleep almost standing up, and when writing or speak-
ing — for fear of bending down and provoking an attack of breathlessness —
he put himself into a sort of box which kept his body upright and only
allowed his head and his arms to protrude. From the minutes 129 of the
Academie des Sciences it appears that he had a serious illness in the year
1825 when a deputation of the Academie was sent to wait on him and bring
him its good wishes for a speedy recovery. He recovered from this illness
but no doubt afterwards he was much enfeebled.
In a passage at the end of a letter to Auger, 130 permanent secretary of the
Academie Francaise, evidently written some time after his own election to
that body in 1826, Fourier wrote:
Receive the thanks which I have long owed you and the homage of my wishes.
You have neither cough nor pulmonary complaints. You are surrounded with a
pleasant family, you are happy, be so perpetually. As for me, I already see the
other bank where one is healed of life. May I find there Descartes and Berthollet.
Joseph Fourier
Tuesday morning 131
But appearances can be deceptive, and when Auger disappeared from his
home in January 1829 and was later found drowned in the Seine, Fourier
must have recalled this passage in his letter with a pang. The other bank of
the river, as it turned out, was closer for Auger than it was for Fourier. Still,
he did not have long to wait. The call came suddenly on 16 May 1830
towards 4 o'clock in the afternoon when he had a heart attack from which
he died soon afterwards. Dr. Larrey, 132 who looked after him during his
short illness, qualified his complaint as a nervous chronic angina complicated
by a nervous disease of the pericord and the principal organs of the chest.
After his death a subscription was opened to collect money to erect a
suitable memorial. The largest contributors (in francs) were Blanchin 133
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(ioo), Chabrol and Dupuytren 134 (50), and Cuvier, Jomard, Navier and
Augustin Perier (30). Sophie Germain, who was herself to die soon after-
wards, gave 10 francs, and Biot and Poisson nothing.
Notes
1. Cousin, p. 36.
2. Chabrol, Gilbert Joseph Gaspard, Count de Volvic (1773-1843). During the
Terror he was imprisoned with all his family but was freed in 1794. He became
a pupil at the Ecole Polytechnique where he opted for Ponts et Chaussees and
was placed first both in the entrance examination and the final examination
for his promotion. He was attached as an engineer to the Egyptian expedition
and was a member of the commission of arts and sciences contributing to the
Description of Egypt. He was named under-prefect at Pontivy where he
rapidly planned a new town, and later became Prefect of Montenotte in Italy.
He was a very able administrator and was distinguished by the zeal with which
he carried out Napoleon's commands especially as regards conscription.
Happening to be in Paris at the time of the Malet conspiracy in December
1 81 2 he was appointed Prefect of the Seine by Napoleon in place of Frochot.
But in 1814 in company with other members of the municipal council he
deserted Napoleon and was one of those who greeted Louis XVIII at the
gates of Paris. He was then retained as prefect. On Napoleon's return from
Elba he went into hiding. After Waterloo he was reappointed prefect of the
Seine and for the next eighteen years devoted himself to the administration of
Paris. When certain of his enemies attempted to have him removed from this
position King Louis XVIII remarked: 'He has married the town of Paris
and I have abolished divorce.' He was retained as prefect by Charles X and
retired after the July Revolution in 1830. Chabrol made notable contributions
to the improvement of Paris including the building of the Bourse, and of
hospitals, abattoirs, and markets. He contributed particularly to the advance-
ment of education in the city. When he was appointed prefect there were 1700
primary school pupils, when he left there were 26 000. He was a great patron
of the Arts. He became a member of the Institut in 1820 (Bio. Gen.; Gde.
Encycl).
3. He had already had much practical experience of gathering statistical infor-
mation in both Egypt and Isere.
4. Fourier Dossier AN.
5. Ibid.
6. Ibid.
7. Ibid.
8. Ibid.
9- Ibid.
10. See below Letter XXVII Appendix, p. 328.
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139
11. See below Letter XXVII, n. 1, Appendix, p. 329.
12. Laine, Etienne Henri Joachim (1767-1835). A leading advocate in his native
town of Bordeaux, he was made a member of the Senate in 1808. Becoming
disgusted with the bellicose policy and dictatorial ways of Napoleon he allied
himself with the royalists and argued for a just and honourable peace in a
celebrated report of a commission of the Legislative Assembly in December
1 81 3. As a result he was publicly accused of treason by Napoleon. He retired
to Bordeaux and accepted the provisional title of Prefect of the Gironde from
the Due D'Angouleme in March 18 14. Returning to Paris at the First
Restoration he was made President of the Chamber of Deputies by Louis
XVIII. During the Hundred Days he went into hiding returning after Water-
loo as President of the Chamber of Deputies where he fought against the
reactionary policy of the ultra-royalists. Appointed Minister of the Interior
on 7 May 1816, he played a great part in the ordinances of 5 September 1816
which dissolved the Chambre 'introuvable' . A new assembly elected under his
influence showed itself willing to end reaction and voted the electoral law of
5 February 18 17 in favour of the middle classes. An honest man, he retired
from power in December 181 8 as poor as when he entered office. Louis XVIII
said of him : 'I would never dare to demand anything unjust of my minister.'
Recalled to the cabinet as Minister without portfolio in December 1820 he
remained in office for one year only. Thereafter he maintained a discreet
opposition to the minister Villele. Under Charles X he opposed the policy of
Polignac. He was made a member of the Academie Francaise by royal
ordinance of March 1816. He recognized the July Government but played
little part in the chamber of peers under Louis Philippe (Bio. Gen.; Gde.
Encycl.).
13. Fourier Dossier AN.
14. Dubouchage, Francois Joseph, Viscount de Gratet (1749-1821). A soldier by
training he was appointed Inspector General of Artillery but reluctantly
accepted the position of Minister of Marine in July 1792. A devoted royalist,
on 10 August 1792 he urged the King not to put himself in the hands of the
National Assembly, but when the King gave in it was Dubouchage who
escorted Marie Antoinette through a hostile crowd to the Assembly. After this
he fled from France and did not return before the Directory. He opposed
Napoleon and was arrested for a time in 1805 as an agent of the Bourbons. In
1816 he became Minister of Marine again. In this position he did much
damage by appointing those who had little to recommend them beyond their
royalist zeal. He disapproved of the Ordinance of 5 September 1816 and the
moderate policy of which it was an index, and left office in June 1817 to be-
come Minister of State and enter the Chamber of Peers where he usually
voted with the ultra-royalists (Bio. Gen. ; Gde. Encycl.).
15. Fourier Dossier AN.
16. Ibid.
17. Ibid.
18. Ibid.
19. Ibid.
20. Ibid.
21. Corbiere, J. J. G. P., Comte de (1767-1853). During the Consulate and the
Empire he maintained close links with royalist supporters in Brittany. He
was a close supporter of the ultra-royalist Villele in the Chambre 'introuvable'.
140 LAST YEARS: RETURN TO PARIS
In December 1816 he became minister of state and president of the royal
council of education. When he retired a few months later he had already
'terrorized' the University. On his return to office in December 1821 he
showed himself without pity to all those who had proved themselves insuf-
ficiently ultra. Under Charles X his unpopularity grew daily with that of
Villele. The failure of his notorious 'law of love' by which he had hoped to
muzzle the press contributed to the downfall of the Villele ministry. After the
July Revolution he retired to Brittany and succeeded in being forgotten
(Gd. Lar.).
22. Fourier Dossier AN.
23. Ibid.
24. This new category of membership, which was not explicitly restricted to a
particular section, was introduced in the reorganization of the Institut
following a royal ordinance of 21 March 1816.
25. Proc. Verb., vol. 6, p. 44. Seance of 27 March 1816.
26. See below Letter XXVIII, Appendix, p. 331.
27. See below Letter I, n. 12, Appendix, p. 247.
28. See below Letter III, n. 3, Appendix, p. 253. He was replaced by Cauchy.
29. See below Letter VI, n. 10, Appendix, p. 264.
30. See Proc. Verb., vol. 5, p. 58.
31. Ibid., p. 59.
32. Rosily-Mesros, Count F. E. de (1748-1832). He was elected a free Academicien
in May 1816. He was a vice-admiral, director of the general depot of the
navy. He was also member of the Academie de marine and the Bureau des
longitudes.
33. Cubieres, S. L. P., Marquis de (1747-1821). He was elected correspondent
for the section of Rural Economy and Veterinary Science of the first class of
the Institut in 1810 and free Academicien in June 1816. He was keeper of
external monuments of the palaces of Versailles and the Trianon.
34. See above n. 12.
35. Fourier Dossier AdS. For a note on Delambre see above, chapter 5, n. 45.
36. See above n. 11.
37. See above n. 12.
38. Fourier Dossier AdS. Letter of 29 May 1816 from Laine to Delambre.
39. Ibid., referred to in Letter of 4 June from Laine to Delambre.
40. See above n. 14.
41. Fourier Dossier AdS.
42. Ibid.
43. Rochon, A. M. de (1741-1817). Elected to the ancient Academie des Sciences
in 1 77 1, and to the experimental physics section of the Institut in 1795. He
was a traveller and a marine astronomer.
44. Huzard, J. B. (1755-1838). Elected to the rural economy and veterinary
section of the first class of the Institut in 1795. He was Inspector General of
veterinary schools and a member of the Academie de medecine and the
Soci6t^ d'agriculture. He was also a well-known bibliophile.
45. Bib. Inst. MS. 1976.
46. Proc. Verb., vol. 6, p. 187.
47. Fourier Dossier AdS.
48. Ibid., marginal note in letter of 12 May to Minister of Interior.
49. See below Letter II, Appendix, p. 251.
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141
5°-
Si-
52.
S3-
56.
57-
The reports in question will be found in Proc. Verb., vol. 6, pp. 238, 257,
287, 344, 361, 453; ibid., vol. 7, pp. 168, 231, 264, 378.
See Proc. Verb., vol. 6, p. 469; ibid., vol, 7, p. 347.
See Proc. Verb., vol. 6, p. 329; ibid., vol. 7, p. 270.
See Proc. Verb., vol. 6, p. 236; ibid., vol. 7, pp. 52, 88, 274.
54. See above, chapter 5, n. 45.
55. Proc. Verb., vol. 7, p. 386.
See below Letter VII, n. 10, Appendix, p. 273.
Arago, F. 1786-1853. He was a student at the Ecole Polytechnique and was
elected to the first class of the Institut in 1809 in which year he succeeded
Monge as professor of analytic geometry at the Ecole Polytechnique. He
resigned from this position in 1 830 on succeeding Fourier as one of the per-
manent secretaries of the Academie des Sciences. He entered politics the same
year and sat on the extreme left of the Assembly. Arago is remembered for his
discovery of the solar chromosphere and for his contributions to electricity
and magnetism. He also played a leading part in the promotion of Fresnel's
wave theory of light.
58. Germain, Sophie (1776-1831). At the age of thirteen she became inspired
with a love of mathematics through reading about the death of Archimedes
in Montucla's Histoire des Mathematiques. She had to teach herself out of
books and against the wishes of her parents. She managed to obtain lecture
notes from pupils of various professors at the Ecole Polytechnique and sent
these with comments to Lagrange under pretence of being a pupil at the Ecole.
Lagrange was full of praise for these comments and when he learned the real
author he was surprised but encouraged her. She took up the study of Gauss's
Disquisitiones Arithmeticae — having learnt Latin for the purpose — and entered
into correspondence with Gauss, again under pretence of being a pupil of the
Ecole Polytechnique. Once again she received every encouragement. She
took up the study of elastic surfaces in which she won a prize at the Institut
in 1 81 5. With the encouragement of Fourier and Legendre her researches
into the theory of elastic surfaces were published in 1820. She was passionately
fond of literature and poetry. Her Considerations sur I'Etat des Sciences et des
Lettres aux differentes epoques de leur culture was published posthumously in
1833 after her death from cancer in 1831 (Bio. Gen.; Gde. Encycl.).
Obviously referring to J. B. Biot.
Reproduced in Stupuy, p. 319.
Proc. Verb., vol. 7, p. 394.
Ibid., p. 413.
Ibid., vol. 9, p. 443. Seance of 10 May.
One of the most historic of these as regards the physical sciences was that on
26 July 1824 when an account of Sadi Carnot's masterpiece 'Reflexions sur la
puissance motrice du feu' was read by the engineer Girard before an audience
which included, besides Fourier, Arago, Laplace, Ampere, Fresnel, Poisson,
Navier, and Dulong. The failure of any one of these to recognize the value of
Carnot's work is a good indication of its originality.
Delambre's eloge is given in Mem. Acad. Roy. Sci. (2), vol. 4 (Historical
section) pp. cciv-ccxxvii, that of Laplace, Ibid., vol. 10, pp. lxxxi-cii. Fourier
also read eloges of Herschel (Ibid., vol. 6, pp. lxi-lxxxi), Breguet (Ibid., vol. 7,
pp. xcii-cix), and Charles (Ibid., vol. 8, pp. lxxiii-lxxxviii).
59-
60.
61.
62.
63-
64.
65-
! T
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143
66. These are found in Mem. Acad. Roy. Sci. (2nd series) Historical sections: for
year 1822, vol. 5, pp. 231-320; year 1823, vol. 6, pp. i-lx; year 1824, vol. 7,
pp. 1-xci; year 1825, vol. 8, pp. i-lxxii; year 1826, vol. 9, pp. i-xcv; year
1827, vol. 10, pp. i-lxxx; year 1828, vol. 11, pp. i-lix.
67. Biot (3), p. 669, n. 1.
68. Op. cit., fol. 157 ff.
69. Poisson (3).
70. 'Theorie de la Chaleur'. Ann. Chimie Physique, 3 (1816), 350-75. In the same
category were a 'Note sur la chaleur rayonnant', Ibid., 4 (1817), 128-145, and
'sur la temperature des habitations et sur le mouvement varie de la chaleur
dans les prismes rectangulaires', Bull. sci. soc. philomatique Paris (1818) 61-7.
71. Op. cit., especially fol. 161-2.
72. Bib. Nat. MS. ff. 22525, fol. 82-84V, 98-98V.
73. Ibid., fol. 91V.
74. Ibid., fol. 98V.
75. See Grattan-Guinness (3), pp. 461-2.
76. Ibid., pp. 463-5. See also Fourier's paper 'Note Relative aux Vibrations des
Surfaces Elastiques' (CEuvres, 2, pp. 257-67).
77. See Fourier's paper 'Remarques sur la Theorie Mathematique de la Chaleur
Rayonnante' (CEuvres, 2, pp. 427-49).
78. Bib. Nat., MS. ff. 22525, fol. 98V. Poisson had in fact already amply proved
his talent if only by his fundamental 1812 paper on Electrostatics, and he was
to prove it again by his equally brilliant paper of 1824 on Magnetism.
79. See below Letter I, n. 12, Appendix, p. 247.
80. See below Letter III, n. 3, Appendix, p. 253.
81. Humboldt, Alexander, Baron von (1769-1859). After some geological studies
in Freiburg where Werner was one of his teachers, and a period as director
of mines in Franconia, he moved to Paris in 1797 to buy the necessary instru-
ments for extended explorations in the tropics. In Paris he made the acquain-
tance of various savants including Laplace and Berthollet, and formed lasting
friendships with Arago and Gay-Lussac. He intended to accompany the
French Expedition to Egypt but was diverted by chance and in company
with Aime Bonpland undertook instead a voyage to South America which
lasted from 1799-1804. The extraordinarily rich and important results of this
expedition were published from 1805-32 in thirty volumes under the title of
Voyage aux Regions Squinoxiales du Nouveau Continent fait en iygg-1804.
The preparations and overseeing of this vast work, to which many other
savants contributed besides Humboldt and Bonpland, retained Humboldt in
Paris almost continuously from 1808 to 1827 when he at last acceded to the
repeated requests of the Prussian government and returned to Berlin. In 1829
he undertook a major voyage to Central Asia at the request of the Czar
Nicolas I. Thereafter he devoted his energies to the composition of his
Kosmos (4 Vol. 1845-58). Although Humboldt's most important work was in
physical geography, of which he was effectively the founder, he also made
important contributions to geology and economics (Bio. Gen. ; Gde. Encycl).
82. Cuvier, Georges Dagobert (1769-1832). Son of a protestant minister he was
himself originally destined for the Church. After attending the College of
Stuttgart — where he acquired a knowledge of administrative law which later
stood him in good stead — he spent six years from 1788-94 as tutor to the
children of a Norman nobleman. He occupied his leisure hours in the classifi-
cation of insects, plants, and animals, especially marine animals of which his
increasingly expert knowledge soon led him to recognize many errors in the
Linnaean classification. Through the intermediary of Tessier, a member of the
ancient Academie des Sciences who had escaped revolutionary persecution by
becoming a military surgeon, and who encountered Cuvier by chance in
Normandy, the latter entered into correspondence with Geoffroy Saint
Hilaire who soon recognized Cuvier's genius: 'Come to Paris,' he wrote, 'you
will play the role of another Linnaeus amongst us, of a second legislator of
natural history.' In 1794 Cuvier came to Paris where he was appointed
anatomy assistant in the Jardin des Plantes. He was elected to the Academie
des Sciences in 1795 before Geoffroy Saint Hilaire had himself become a
member. He replaced D'Aubenton at the College de France in 1799, and
Mertrud at the Musee d'Histoire Naturelle in 1802. He was elected Per-
manent Secretary of the Academie des Sciences for the physical sciences in
1803. He prospered both under Bonaparte and Louis XVIII, the latter
appointing him 'minister of dissident cults' and chancellor of the university,
while under Louis-Philippe he was made a Peer of France. He was elected
to the Academie Francaise in 1818. Cuvier was effectively the creator of
comparative anatomy and palaeontology, and thus ultimately contributed
powerfully to the establishment of the theory of evolution though he himself
believed in the fixity of species and was the uncompromising opponent of the
evolutionary views of Geoffroy Saint Hilaire (Bio. Gen. ; Gde. Encycl.).
83. See below, Letter I, n. 1, Appendix, p. 245.
84. See below, Epilogue, pp. 226-227. f° r a discussion of this curious aspect
of Fourier's philosophy of science.
85. The salons of the restoration period are described in Ancelot. Fourier would
also have attended the salon of Chabrol, and possibly that of the painter
Gerard of which his friends Humboldt and Cuvier were members.
86. See Saint Hilaire's impression of Fourier in Egypt given above, chapter 4, p.
75-
87. Cousin, p. 38.
88. Dirichlet, Peter Gustav Lejeune (1805-59). He completed his studies in
Paris where he entered into close relations with the leading mathematicians
of the day. Later Fourier recommended him to Alexander von Humboldt
who had him named assistant at the University of Breslau. He became
successively professor at the General Military School of Berlin (1828), and
extraordinary and then ordinary professor at the University of Berlin (1839).
In 1855 he succeeded Gauss to the chair of higher mathematics at Gottingen.
His researches were mainly in the theory of partial differential equations, the
theory of numbers, and the theory of trigonometrical series and integrals.
He was elected a Foreign Associate of the Academie des Sciences in 1854
(Gd. Lar.).
89. Libri, Guglielmo-Brutus, Count (1803-69). A member of one of the most
ancient Florentine families. He was nominated Professor of Mathematical
Physics at Pisa in 1823. During a visit to Paris in 1824 he was very well re-
ceived by all the leading French scientists of the day. He was implicated in a
conspiracy and sought refuge in France in 1830 where he became naturalized
in 1833 in which year he was elected to the Academie des Sciences in succes-
sion to Legendre. He became professor at the College de France and was
appointed inspector of the libraries of France. But at each visit to a library
l T
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145
the loss of rare books and manuscripts was reported. An investigation was
actually begun and then discontinued. On the outbreak of the Revolution of
1848 he was warned of his impending arrest and fled to London where he was
received as a martyr. Two years later he was sentenced in abstentia in Paris to
ten years' imprisonment. Libri arrived in England almost penniless but by the
sale of his inexhaustible collection of stolen books and manuscripts he raised
more than one million francs. His innocence was protested for many years
by a party in France led by Prosper Merimee. In 1888 the French government
was able to buy back some of the stolen works. Libri's own most important
work was his Histoire des Sciences Mathematiques en Italie (Gde. Encycl.;
Gd. Lar.).
90. Duhamel, Jean Marie 1797-1872. He was assistant, then professor (1834)
at the Ecole Polytechnique where he had the name of being an excellent
lecturer. He was Director of Studies at the ficole Polytechnique from 1848
to 1 85 1 when he took up the chair of analysis again. He was appointed Pro-
fessor at the Paris Faculty of Science in 1851. He published a number of
memoirs on analysis and rational mechanics. He was elected to the Academie
des Sciences in 1840 (Gd. Lar.).
91. Pouillet, Claude (1790-1868). He was a pupil at the Ecole Normale where he
became a maltre des conferences. He was appointed physics professor to the
children of Louis Philippe (1827), a position which may have helped his later
appointments as professor at the Ecole Polytechnique (1831), director of the
Conservatoire des arts et metiers (1833), and professor of physics at the Sor-
bonne (1838). He served for a time as deputy for the Jura and occupied
himself with scientific and industrial matters, playing an important part in
committees concerned with railways and other technical matters. A disciple of
Gay-Lussac and Biot, he is said to have been an excellent lecturer. He made
some important experiments on the compressibility of gases. He was elected
to the Academie des Sciences in 1837. He retired from all his positions in
1851 following his refusal to take the oath required by the new regime (Gde-
Encycl. ; Gd. Lar.).
92. See below Letter VI, n. 10, Appendix, p. 264.
93. See bi;low Letter XI, n. 7, Appendix, p. 290.
94. See below Letter VII, n. 10, Appendix, p. 273.
95. See above, n. 57.
96. Fresnel, A. J. (1788-1827). He had a brilliant career at the Ecole Polytechnique.
In 1814 he commenced his researches in light with the encouragement of
Arago who became his constant champion in the promotion of his new
theories against the criticisms of Laplace, Poisson, and Biot. He was elected
to the Academie des Sciences in 1823. Fourier's letter informing him of this
election has been preserved.
97. Ampere, A. M. (1775-1836). He was appointed inspector general of the
Imperial University in 1808, Professor of Mathematics at the Ecole Poly-
technique in 1809 and elected to the first class of the Institut in 1814. Re-
membered for his fundamental contribution both to the experimental and
theoretical sides of electricity and magnetism.
98. Cousin, p. 39.
99- See below, Letter VI, para, r, Appendix, p. 260.
100. As described by Biot who had himself to extemporize an oration in place of
Fourier.
101. Bib. Nat., MS. ff. 22529 fol. 123.
102. See above chapter 5, pp. 101-3, and section 2 of present chapter.
103. Jomard, Edme Francois (1777-1862). On completing his studies at the Col-
lege Mazarin he entered the Ecole Polytechnique at its foundation and pro-
ceeded from there to the Ecole Geographique. He was a member of the
Egyptian Expedition. With the help and advice of Fourier he concentrated on
topographic work and the exploration of ancient monuments. He became a
member of the Institute of Cairo and concentrated on the reconstruction of
ancient palaces from their ruined remains. He made important discoveries
in numerical hieroglyphics. He was sent to the Palatinate by Napoleon to
direct geographical studies including, no doubt, the provision of better maps.
By his geological investigation he contributed to the debate between vulcanists
and neptunists. He was recalled from Germany in 1803 and made an im-
portant contribution to the Description of Egypt for which he directed all the
works of engraving and printing. He was hard working, modest, simple,
obliging and his advice was constantly sought by archaeologists and geogra-
phers from all parts of Europe (Bio. Gen. ; Gde. Encycl.).
104. See above, n. 2.
105. See above, chapter 4, n. 22.
106. See above, chapter 4, p. 74.
107. Barrow, 2, pp. 436-8.
108. See above, n. 21.
109. See above, n. 12.
no. See above, chapter 4, n. 53.
in. Perier, Casimir (1777-1832). He was a witness of the Revolution in Paris and
later served for a time in the Army of Italy. Under the Empire he founded a
bank with his brother which did much to encourage industrial activity in
France and from which he acquired immense wealth. He played a notable
part in the Chamber of Deputies under the Restoration. He was forced un-
willingly into the party of revolt against the policy of Charles X and his
ministers and played a leading part in the July Revolution, entering the
government of King Louis Philippe in August 1830 as minister without port-
folio. In March 1831 he became President of the Council and it was due to his
firm — and on occasion ruthless — use of force that France was prevented from
falling again into a bloody revolution and civil war within and war with the
combined powers of Europe without. Worn out by incessant labours he was
carried off in the cholera epidemic of 1832 (Bio. Gen.; Gde. Encycl.).
112. See above chapter 3, p. 56.
113. Cousin, p. 38.
114. See below, Letter IV, n. 2, Appendix, p. 256.
115. See below, Letter XII, n. 8, Appendix, p. 295.
116. Cousin, Victor (1792-1867). The son of a poor artisan, he had no regular
education up to about the age of eleven, and it was only by chance through
protecting a pupil who was being attacked by his schoolmates of the Lycee
Charlemaigne that Cousin came to the notice of the mother of this pupil
who then had him entered at the Lycee. There he rapidly went to the top and
passed out the best pupil of his year. He entered the Ecole Normale becoming
assistant in literature at the age of twenty. Later he was drawn to philosophy
through the lectures of Laromiguiere. From 1815 to 1821 he was assistant
in philosophy to Royer-Collard at the Sorbonne where his lectures attracted
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great attention by their eloquence and forcefulness. Following the rightwing
reaction after the assassination of the Due de Berri he was dismissed from his
position in company with Guizot and Royer-Collard. At this time he paid his
second visit to Germany and was imprisoned on suspicion of being a member
of the secret society of the Carbonari. On his return to France he was received
as a public hero. In 1828 he was appointed by the relatively liberal cabinet
under Martignac to the position of Professor of Philosophy at the Sorbonne.
Here his lectures were immensely popular and drew large and enthusiastic
audiences. At the time of the Revolution of 1830 he was made a Councillor of
State and in the same year became a member of the Academie Francaise in
succession to Fourier. He entered the royal council of public education and in
1832 was made a peer of France. He became Director of the Ecole Normale
where he expounded to his pupils the philosophy of Aristotle and completed
his translation of Plato. In 1840 he was appointed Minister of Public Instruc-
tion in the cabinet of Thiers, a position which he occupied for eight months.
During this time he flooded Paris with proclamations, pamphlets, decrees etc.
and played a prominent part in the debates in the Chamber of Peers where
he made many impressive speeches. At the time of the Revolution of 1848
Cousin was against the insurgents and thereafter he disappeared from public
life. All that was left to his position in Paris were his rooms in the Sorbonne,
and he resigned his lectureship and all his public positions to devote the
remainder of his life to writing. Cousin was an eclectic constructing his
philosophy from many other philosophical systems following the principle
that 'every system is true by what it affirms, and false by what it denies'.
The German idealist philosophers, especially Hegel, whose acquaintance
Cousin had made in Germany, exercised a particularly strong influence on
his thought. But he lacked the patience and perseverance necessary for any
real achievement in philosophy. Of much more lasting value than Cousin's
philosophy were his contributions to scholarship, especially his criticism of
the styles of writers such as Pascal and Rousseau, and his studies of certain
little-known historical figures of the seventeenth century. In these fields he
was able to exercise all his skill in literary criticism, his delight in discussing
points of taste, and his passion as a scholar for fine editions and for the dis-
covery of variants and manuscripts (Bio. Gen. ; Gde. Encych).
117. Cousin, pp. 39-41.
118. Ibid., p. 38.
119. Ibid., p. 42.
120. See below, Letter VI, n. 26, Appendix, p. 268.
121. See above, n. 58.
122. Arch. Nat. MS. ff. 91 18 and na. 4073.
123. Ibid.
124. Ibid.
125. Fourier Dossier AdS.
126. I have not been able to find any information on l'Herminier.
127. Bib. Mun. Nantes MS. 281.
128. Lemontey, P. (1762-1826). A deputy at the Leglislative Assembly and later
an historian, he was elected to the Academie Francaise in 1819.
129. Proc. Verb., vol. 8, p. 213.
130. Auger, Louis Simon (1772-1829). From 1799-1812 he was an official in the
Ministry of the Interior. His first literary efforts had little success. His mental
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131-
132.
133-
134-
characteristics were clarity and perseverance rather than vivacity, force, or
grace, and he changed to tasks more suited to his powers including laborious
and critical works. He worked on the Decade Philosophique and the Journal de
VEmprie in which he constantly showed himself an admirer of the seventeenth
century. He was elected a member of the Academie Francaise in 181 6 at a
time when royal ordinance had banished several distinguished members.
This irritated liberal writers against him and the irritation was later increased
by his nomination to the commission de censure which led to repeated attacks
against him from which he suffered much. He was very happily married, his
wife being a niece of Berthollet and Monge, but he developed a nervous
malady which produced profound melancholy. He disappeared from his
home on 5 January 1829 and was discovered drowned in the Seine near
Meulan on 17 February (Bio. Gen.; Gde Encycl.).
Bib. Inst., MS. 4501.
Larrey, D. J., Baron (1766-1842). In 1792 he joined the Army of the North
where he was later appointed principal surgeon. He took part in the Egyptian
Expedition and in many other of the military campaigns of the Republic.
During the Empire he was surgeon in chief to the Grande Armee. His care for
the feeding and hygiene of hospital patients earned him the nick-name 'La
Providence' among the simple soldiers. He was shunned at first at the Second
Restoration but was recalled and became a member of the Academie de
medecine (1820) and was elected to the Institut (1829). He wrote a number of
important works in military surgery (Gde. Encycl. ; Gd. Lar.).
Blanchin, J.-B. (? 1836). Educational writer. Author of a number of
popular school books.
Dupuytren, G. (1777-1835). French surgeon famed for his innovations, his
mastery of operating techniques, and his ruthless pursuit of power. He was a
member of the Institut and a professor at the Paris Faculty of Medicine to
which he left on his death the sum of 200 000 francs for the foundation of the
museum bearing his name.
PART II
FOURIER THE PHYSICIST
CHRONOLOGICAL ACCOUNT OF
RESEARCHES IN HEAT
The beginning of Fourier's theoretical researches in heat cannot be dated
with any certainty. It could have been as early as 1802 soon after his move
to Grenoble, and it was certainly not later than around 1804. 1 What is
certain is that his first theoretical approach to the subject was through con-
sideration of the movement of heat between a finite number of discrete
bodies arranged in a straight line. 2 His solution to this problem is preserved
in a manuscript form in his Draft Paper, 3 a work which was possibly
intended for publication and which was in any case completed around
1804-5. The same problem, later much extended, appears in the 1807
memoir, 4 the Prize Essay 5 and the Analytical Theory. 6 Physically it was a
blind alley though it led to important mathematical advances in the treat-
ment of trigonometrical expansions, and it appears in the Prize Essay and
the Analytical Theory largely as an historical monument to Fourier's
earliest work in the theory of heat in much the same way as the second
proof of the law of centrifugal force in the Principia 7 is a memorial to
Newton's earliest work in dynamics.
Apart from the transmission of heat between a finite set of discrete
bodies, and an unsuccessful though suggestive attempt to extend the solu-
tion to the case of an infinite set of bodies, the Draft Paper of 1804 contains
a first incomplete, and largely erroneous, treatment of the distribution of
temperature in a thin bar heated at one end. 8 A nattering reference 9 to a
paper of 1804 by J. B. Biot 10 on the same topic makes it reasonably certain
that it was this paper — of which the contents may have been communicated
to Fourier before the publication of the paper itself— which first stimulated
Fourier to turn his attention from the physically unimportant if mathe-
matically interesting problem of the transmission of heat between discrete
bodies to the real problem at issue — the propagation of heat in continuous
bodies. The other problem treated in the draft paper of 1804, this time in a
r
150
CHRONOLOGICAL ACCOUNT OF
definitive way requiring no significant alterations in all subsequent ver-
sions, was that of the semi-infinite strip with its edges and end held at
constant temperatures. 11 The treatment is memorable for Fourier's first
use of trigonometrical expansions in the theory of heat, for his brilliant
treatment of the question of convergence of such expansions, and for the
heroic manner in which the coefficients of the various cosine terms in the
expansion are determined by purely algebraic means. Prior to the treat-
ment of semi-infinite strip partial differential equations are given for the
general, non-steady, motion of heat in one, two, and three dimensions. 12
These are incorrect as regards omission of the specific heat in the term
involving the time rate of change of the temperature, and the appearance in
the equations of a term corresponding to heat loss at the surface of the solid
— though Fourier does express uncertainty as to whether or not the latter
term should be included. By chance or design both errors are avoided in the
case of the semi-infinite strip since the temperature distribution is assumed
to be steady while the fixing of the temperatures at the edges and end
obviates the need for any separate consideration of heat loss.
It seems probable that the draft paper was completed around the period
1804-5. His next work, the 1807 memoir, was said 13 to have been completed
towards the end of 1807, and was in any case read before the Institute on
21 December of that year. This memoir represents an enormous advance
on the draft paper as regards physical and mathematical understanding of
the underlying problems, and the number and variety of applications. No
manuscript evidence has survived of the manner and pace of the develop-
ment between the two works, though the draft paper itself contains definite
indications in its introduction — evidently written in the manner of intro-
ductions after the body of the paper — which point towards a very rapid
development on both the physical and mathematical sides beyond the level
of the ensuing text. For example, a reference to the treatment of discrete
bodies states that they are arranged in a circle, whereas in the body of the
paper the discrete bodies are arranged in a straight line, and it is only from
the 1807 paper onwards that consideration is given to bodies arranged
circularly. Likewise, in the introduction it is stated that on making the num-
ber of separate masses tend to infinity while the size of each tends to zero
the result obtained is 'in agreement with that given by the principle of
Newton', whereas once again in the body of the paper itself this limiting
process is imagined to apply to bodies arranged in a straight line and is
certainly not carried through to a conclusion. Another indication of a
major advance in Fourier's treatment of the mathematical problems
involved is his comment in the introduction that he had originally ob-
tained trigonometrical expansions by means of very laborious eliminations,
but that now he employed a much more general and much more expedi-
RESEARCHES IN HEAT
151
tious rule to resolve an arbitrary function into series of sines and cosines.
Once again this method was not used in the body of the paper itself.
Reference to the need for experimental investigations as an aid to the
elucidation of certain outstanding obscurities relating to the problem of a
heated bar is also to be found in the body of the paper. 14 Elsewhere 15
Fourier refers to a series of very careful experiments carried out over a
period of two years before the writing of the 1807 memoir in which he
repeated all important experiments which had been carried out previously
in England, France, and Germany and added experiments of his own con-
cerned with the propagation of heat in solids and liquids. If these experi-
ments were originally directed towards the elucidation of particular prob-
lems associated with a heated bar, they ultimately had the much more
important function of making Fourier thoroughly conversant with the
various physical aspects of the phenomena of the propagation of heat
including the role of specific heat in the full, time-dependent equation of
motion of heat. By 1807, the pure mathematician of the draft paper,
interested in the problem of the flow of heat with as superficial an under-
standing of the physical side of the problems involved as Biot in 1804 or
Laplace in 1809, had become the complete theoretical physicist in the
manner of Newton and Fresnel, his genius for mathematical manoeuvre
now firmly based on an intimate understanding of the relevant physical
concepts including specific heat, 16 conductivity, 17 and heat flow. 18
Fourier's experimental investigations in the two years or so preceding the
completion of the 1807 memoir had one further outcome: by careful
choice of the most suitable experiments they enabled him to give a number
of striking experimental confirmations of his new theory. These — as he
modestly noted in the introduction to the 1807 memoir — 'contributed to
give to the theory an authority which one might have been inclined to refuse
in a matter still obscure and apparently subject to so many uncertainties'. 19
The 1804 draft paper is a curiously uneven work: the treatments of a
finite set of discrete bodies and of the semi-infinite strip are so definitive
and complete as to require no essential changes in all later versions, and
both are stamped with the elegance, clarity, and daring characteristic of
Fourier's genius in pure mathematics. But this mathematical mastery
exists in uneasy partnership with an equally great uncertainty on the phy-
sical side epitomized by the failure to realize the need for a knowledge of an
exact quantitative expression for the heat flux across any given section, the
totally erroneous derivation of the equation governing the steady distribu-
tion of temperature in a 'thin' bar, the absence of the specific heat in the
general non-steady equation of propagation of heat, and the uncertainty as
regards the appearance in this same equation of a surface heat-loss term.
In the 1807 memoir the situation is transformed: this is no longer a paper
1
152 CHRONOLOGICAL ACCOUNT OF
but a treatise. It is incomplete compared with the Prize Essay only as
regards a certain residual inadequacy in the treatment of the heat flux and
the derivation of the equations of motion, in the omission of a treatment of
the cooling of infinite solids, and in discussions of terrestrial and radiant
heat, so that it is difficult not to agree with Fourier's view 20 that the setting
of a Prize Essay was unnecessary since the problems it propounded had
already been solved in the 1807 memoir.
Apart from the fact that the treatment of discrete bodies in a straight line
immediately after the introduction as in theDraft Paper, the structure of the
1807 memoir is already very close to the Prize Essay and the Analytical
Theory of Heat. Following a discussion of fundamental physical concepts
including conductivity and the expression for flux of heat, 21 the equation
for the propagation of heat in a thin rod is formulated and solved for the
steady state, 22 followed by a similar treatment for a thin ring. 23 Then
follows the derivation of the full interior equations of propagation of heat in
a sphere 24 and a cylinder 25 : in both cases the derivation of the equation is
ad hoc making use of special symmetries, but consideration of a finite
cube 26 leads to the derivation of the general equation of propagation of heat
within any solid, 27 the previous equations for the cylinder and the sphere
being re-derived as special cases of this general equation. 28 Up to this
point no solutions have been obtained except in the trivially simple cases
of the thin rod and the thin ring. Apart from the final section on experi-
mental investigations, 29 the remainder of the memoir is taken up with the
derivation of solutions starting with the case of the semi-infinite strip, 30
followed, as in the case of the Prize Essay and the Treatise, by a prolonged
discussion of trigonometrical expansions of various functions. 31 The gene-
ral (time-dependent) solution of the thin ring is considered next, 32 and
subject to certain plausible identifications between parameters, this is
shown 33 to be the same as the limiting solution for a set of discrete bodies
arranged circularly as the number of bodies tends to infinity and the mass
of each tends to zero in such a way as to lead to a continuous circular dis-
tribution. Discussions of the cooling of a sphere, 34 a cylinder, 35 and a cube, 36
and the steady-state distribution for an infinite prism 37 complete the
contents of the memoir apart from the final section on experimental
investigations.
The sheer size and range and diversity of application is so much greater
in the 1807 memoir than in the Draft Paper that it is at first sight difficult
to distinguish the really fundamental advances in the former over the latter
work. But a careful comparison reveals that these advances were almost all
on the physical side. In the Draft Paper Fourier clearly displays the sort of
mathematical mastery which will be equal to any of the problems likely to
be thermal phenomena. 38 What is lacking is a thorough understanding of
RESEARCHES IN HEAT
153
the underlying physical processes. Having acquired this understanding and
having hit on the correct expression for the heat flux at any point of a
heated body, the way was then open for him to formulate correctly the
equations of the propagation of heat in the interior of any solid body. It
then only remained to formulate separately the appropriate boundary
conditions at the surface of the solid in question — the direct involvement
of a heat-loss factor in the equations of propagation in a thin rod being evi-
dently an idealization resulting from the assumption of a constant tem-
perature over sections perpendicular to the length — for the whole subject
of the propagation of heat to be reduced to a matter of mathematical
analysis which Fourier then proceeded to apply to one case after another.
Fourier read an abstract 39 of his memoir before the First Class of the
Institut on 21 December 1807. The commission set up to report on the
memoir consisted of Lagrange, Laplace, Monge, and Lacroix. The com-
position of the commission, the experimental confirmation of his theory,
and the fact that he had reached many of the principal mathematical results
by independent methods 40 must have made Fourier confident of the out-
come of the commission's work. In fact, the first reaction to his memoir
came in a review by S. D. Poisson 41 in the Bulletin of the Philomatic Society.
It stated the prime objective of the work, the determination of the tem-
perature at all points of a heated body both in the steady state and in the
case of cooling, referred to the equations for the propagation of heat both in
the interior and at the surface of solids, listed the special cases treated by
Fourier, and noted the experimental confirmation of the theory, especially
the remarkable case involving the temperatures at diametrically opposite
points in the cooling of a heated ring. The review, if not enthusiastic, was
perfectly fair and correct in manner, 42 and there were only two points at
which any sort of criticism implied or otherwise could be read into Poisson's
comments, and then only with hindsight in the light of his subsequent
criticism of Fourier's work: the first was the fact that he reproduced Biot's
erroneous treatment of a thin bar, something which might have been taken
to imply that Fourier's ostensibly similar but actually quite different treat-
ment was incorrect; and the second was his comment that the investigation
of the new equations of propagation of heat posed 'delicate questions in the
theory of heat deserving the attention of mathematical physicists' 43 which
could have been taken to imply that Fourier's own investigations of these
questions were not altogether satisfactory.
Poisson's review was the only public reference to Fourier's memoir
outside the proceedings of the First Class of the Institut and certain
references by Fourier himself at a much later date, and in spite of a request
by the First Class to the commission to hurry up its work 44 no report ever
appeared. Instead a lively controversy arose involving two major criticisms
154
CHRONOLOGICAL ACCOUNT OF
of Fourier's work which between them struck at its very foundations on
both the mathematical and physical side. The first was directed at his use
of trigonometrical expansions, the second at the validity of the method he
had employed to derive the fundamental equations for the propagation of
heat in the interior of continuous bodies. The chief critics of his use of
trigonometrical expansions seem to have been Laplace and Lagrange. It
appears that Laplace had maintained that the expansions given by Fourier of
cosine * in terms of sines, and of sine * in terms of cosines were 'contrary
to the principles of the calculus'. 45 Fourier corrected this misapprehension
in a letter to Laplace of which a partly legible draft has survived. 46 On the
contrary he maintained against Laplace that the results could be 'demon-
strated rigorously' spelling out exactly what was meant by the claim that a
given function was equal to the sum of an infinite number of trigono-
metrical terms, referring to his brilliant method of expressing the sum of
the first m terms of the infinite series as a function of i/m, which tended in
the limit of large m to the sum in question. In a letter, 47 probably to
Lagrange, he made the same point at greater length — and in a more tact-
ful manner — referring especially to the series
\x = sin x-\ sin zx+\ sin ^x. . .
whose convergence was 'clearly' established by a note accompanying his
letter. It seemed to Fourier that if such demonstrations were to be for-
bidden it would be necessary to give up writing 'anything exact in mathe-
matics'. While apologizing for the absence of any reference to earlier work
on the same subject by Euler and d'Alembert due to his inability to consult
any mathematical works during the researches leading to the 1807 memoir,
he also made it clear that he regarded Euler and d'Alembert's use of trigo-
nometrical series as inadequate compared with his own on the grounds,
firstly, that they were 'both persuaded that an arbitrary and discontinuous
function could never be resolved in series of this kind', and secondly that
no mention was made of limits within which a given trigonometrical
expansion held. In any case Fourier's use of trigonometrical functions was
only a 'particular case' among others which he had to treat, which later
'offered analytical difficulties of a very different order' and he referred
specifically to the section on motion of heat in a cylindrical body 48 which he
regarded as the only part of his work worthy of Lagrange's attention.
The second major criticism of Fourier's work was directed against his
derivation of the equations of motion of heat in a continuous solid. The
polemical aspects of this side of the controversy have already been noted, 49
especially Fourier's angry reaction to an implied criticism of his work con-
tained in a certain passage in an article by Biot appearing in the Mercure de
France. 50 The 'analytical difficulty' somewhat obscurely referred to by
RESEARCHES IN HEAT
155
Biot in this passage had already been expressed explicitly in an appendix
to a paper by Laplace 51 in which the problem of the flow of heat in a
narrow bar was treated by 'molecular' considerations similar to those he
had employed in the body of the paper in the case of the refraction of light.
Such a treatment was necessitated by the fact that one based on considera-
tion of three consecutive 'points' of the bar led to a differential equation in
which the two sides were of different orders of magnitude. This was cer-
tainly true of the quantitative treatment of the same problem in Fourier's
draft paper of 1804-5 which had itself arisen out of the qualitative treat-
ment in Biot's paper of 1804. There is some reason to believe that Fourier
sent Biot and Poisson a copy of this draft paper, or possibly an early draft
of the 1807 memoir which may still have contained the erroneous treatment
and it may have been this treatment which Laplace had in mind. 52 But he
was quite unjustified in applying the same criticism to Fourier's 1807
memoir, and his own treatment, though typically ingenious, compared
unfavourably in certain physical respects with that given by Fourier. 53
Nevertheless, although the criticism of Biot and Laplace was unjustified,
and was made in a somewhat underhand manner calculated to cause the
maximum annoyance to Fourier, it had the virtue of stimulating him to a
justification of his method of deriving the equation of motion for heat
which led to a significant improvement over the treatment given in the
1807 memoir. This improvement was later incorporated in the Prize Essay
and the Analytical Theory of Heat. Traces of it were given in certain
marginal notes to the 1807 memoir, 54 and it was then fully worked out in a
long letter to an unknown correspondent dating from around 1809-10. 55
It corresponded to the transition from the 'three slice' approach found
throughout the 1807 memoir — itself reminiscent of the 'three point'
approach of Biot's qualitative treatment of 1804, and Fourier's erroneous,
quantitative treatment in the draft paper — to the 'single slice' approach
found in the Prize Essay and the Analytical Theory of Heat. 56 This
transition also met the criticism of Biot 57 and Laplace 58 that the 'analytical
difficulty' could not be surmounted unless account was taken of 'points'
other than those immediately adjacent to the 'point' at which the heat flow
in the bar was to be calculated.
Apart from these two major criticisms of Fourier's work there were at
least two of lesser importance directed, respectively, against his form
of the surface equations, 59 and against the reality of the roots of the trans-
cendental equation involved in the problem of the cooling of a heated
sphere. 60 Fourier's form of the surface equations — as compared with a sur-
prisingly naive suggestion put forward by Laplace 61 — was ultimately
accepted but once again Poisson maintained the superiority of his own
derivation of the same equations. The other question proved more
156 CHRONOLOGICAL ACCOUNT OF
recalcitrant and led to papers by both Fourier and Poisson after the
appearance of the Analytical Theory itself. 62
The controversy over Fourier's work in heat took a new turn at the be-
ginning of 1810 when the propagation of heat in solid bodies was an-
nounced as a subject for the Institut's grand prize in mathematics for the
year 181 1. The committee set up to examine submissions for the prize
consisted of Lagrange, Laplace, Malus, Haiiy, and Legendre. 63 There was
one other candidate apart from Fourier. Fourier's submission consisted of
the memoir of 1807 together with certain new sections, especially those on
the cooling of infinite solids, and on terrestrial and radiant heat. 64 The
treatment of the cooling of infinite solids was an obvious omission from the
1807 memoir, probably due to Fourier's inability at that stage to handle the
mathematical problems involved, since treatments are given of several
cases of the steady distribution of temperature in infinite solids. It is
possible that Fourier was stimulated in a search for solutions of the full
diffusion equation for the infinite line by a paper of Laplace in which a
solution to the equation was given in terms of an integral. 65 But he could
have developed his own method 66 involving Fourier integrals independent-
ly, and the only major use made of Laplace's solution in the Prize Essay is
as a check of Fourier's own methods. As regards the section on terrestrial
heat, 67 according to Fourier this topic provided one of the major incentives
for the development of his analytical theory of heat in the first place, 68 and
the section on radiant heat 69 could well have been stimulated by Fourier's
reading of a work by the Swiss physicist Prevost. 70 In spite of these
important additions the Prize Essay was still identical with the 1807
memoir as regards its essential contents on both the physical and mathe-
matical sides. The unresolved differences of opinion over the earlier
memoir might then have been expected to extend to Fourier's submission
for the Prize Essay. Nevertheless the prize was awarded to Fourier. The
Institut might thus have been thought to have set the final seal of its
approval on Fourier's work. In fact, the report 71 on Fourier's essay con-
tained serious reservations which made it plain that the commission, in
other words Laplace and Lagrange, who were not only its most powerful
and influential members, but also much more familiar with Fourier's
work than any of their colleagues, were still unreconciled either to Fourier's
method of deriving the fundamental equations for the propagation of heat
or to his use of trigonometrical series in their solution.
The serious reservations contained in the referees' report elicited a
letter 72 of protest from Fourier to the permanent secretary Delambre,
apparently without effect. 73 At the same time the Institut seemed in no
hurry to publish the essay. As long as he remained 'exiled' from Paris and
unable to become a full member of the Institut there was little Fourier
RESEARCHES IN HEAT
157
could do about this. In any case he must have been much too preoccupied
with prefection duties during the decline of the Napoleonic regime, the
First Restoration, and the Hundred Days to do any work on the theory of
heat. But on his return to Paris in June 18 15 he would have been alarmed
to read an article by Poisson in the Journal de Physique. 1 * In this article
Poisson referred to Fourier's Prize Essay of 181 1 which he had been al-
lowed to consult at the secretariat of the Institut. While conceding that
Fourier's essay contained the correct equations of propagation of heat as
regards both the interior and the surface of conducting bodies, and that
the experimental confirmation of the results obtained in the case of a
sphere and certain other solids provided a simultaneous justification of the
results themselves and the theory on which they were based, it seemed to
Poisson that the analysis employed by Fourier was not 'devoid of difficul-
ties' and did not appear to have 'all the rigour and generality required by
the importance of the question'. 75 The similarity between this criticism
and that contained in the report on the Prize Essay is striking and may not
have been entirely fortuitous. It appeared that Poisson's criticism was
partly directed against the use by Fourier of solutions to differential
equations in terms of trigonometrical expansions, and he recalled Euler,
d'Alembert, and Lagrange's criticism of Daniel Bernouilli's similar use of
trigonometrical solutions in the problem of the vibrating string. 78 Poisson
himself favoured a solution to the differential equation of propagation of
heat in terms of a single arbitrary function as originally shown by himself
in 1806 77 and confirmed later by Laplace 78 in 1809. By extending Laplace's
form of solution from one to three dimensions Poisson claimed that he
was able to treat in his own, and supposedly more general, manner all the
cases for which solutions had been provided by Fourier in terms of trigono-
metrical series. This he regarded as 'the true solution to the problem' 79 in
implied contrast to the method employed by Fourier. To this claim
Fourier gave an unanswerable response in his unpublished Historical
Precis 80 in which he pointed out that any solution of the full heat propaga-
tion equation taking given arbitrary values at all points at an initial time
must be the only solution. So that any two correct solutions which appear
to be different must in fact be identical. To drive the point home he went
on to prove 81 that the solution in terms of trigonometrical functions for a
ring of radius R gave the same solution as R tended to infinity as that given
by Poisson for an infinite bar. The same argument was later reproduced in
the Analytical Theory of Heat. In another paper 82 Poisson gave an
example of his approach to the solution of the heat propagation equation by
providing a solution for the case of a bar initially heated in some arbitrary
manner over a given finite length and then allowed to cool. Unfortunately
for Poisson his analysis was invalidated by an elementary error which
158 CHRONOLOGICAL ACCOUNT OF
Fourier had no difficulty in pointing out in a letter to Laplace. 83 This
probably represented the final turning point in Fourier's struggle for recog-
nition.
In his first paper Poisson had also criticized Fourier's work on the
familiar grounds that although the equations of propagation were correct
the derivation given them in the simplest case of a thin bar led to an
incompatibility of differentials on the two sides of the equation. Echoing
Biot's opinion, he said that this difficulty could not be overcome except by
employing Laplace's method for deriving the expression for the rate of
flow of heat in terms of the temperature gradient from certain plausible
suppositions regarding the passage of heat between individual 'molecules'.
Using this method Poisson had obtained the same results as those given by
Fourier whose demonstration, however, 'left something to be desired'. 84
The next year (1816) Biot 85 advanced exactly the same argument as Poisson
for overcoming the supposed difficulty. In a footnote 86 he even claimed that
he (Biot) had been the first both to 'enunciate and apply' the correct
equation for the propagation of heat in a stationary case. In the same foot-
note he also criticized Fourier's use of trigonometrical expansions while
praising the methods adopted by Poisson. These charges, which had of
course been advanced before by Biot in his Mercure de France review of
1809, were dealt with by Fourier in a separate note of his Historical
Precis 87 in which he had little difficulty in showing up the falseness of
Biot's claim to have been the first 'to enumerate and apply the correct
equation'. Indeed, as Fourier remarked, he could not have done so without
a knowledge of the correct expression for the flux of heat. Being ignorant of
this he was in no position to find the equation. He then proceeded to go
over the usual argument in favour of the expression he had adopted for the
flux of heat, and to expatiate at considerable length on the nature of the
double error which led Biot to the correct equation.
Nothing more is heard of the criticisms of Biot and Poisson after
Fourier's withering reply in his letter to Laplace and his unpublished
Historical Precis. Thereafter their 'conspiracy' seems to have collapsed.
Nevertheless Fourier could not have felt entirely confident as long as his
Prize Essay remained unpublished. This may account for a number of
papers 88 published in various journals between 1816 and 1822 which are
largely in the nature of extracts from the Prize Essay. It is commonly said
that Fourier was himself responsible for having his Prize Essay published
as soon as he became permanent secretary of the Academie des Sciences.
Although it is true that the Essay was published in succeeding numbers 89 of
the memoirs of the Academie des Sciences after he had become permanent
secretary, nevertheless the actual publication was put in hand at an earlier
date as is evident from a letter of Delambre to Fourier, 90 and also by a
RESEARCHES IN HEAT
159
reference by Fourier himself in notes following the reproduction of his
Essay. 91
A little before he became permanent secretary of the Academie des
Sciences for the mathematical sciences Fourier had the pleasure of pre-
senting his Analytical Theory of Heat to the Institut. 92 This omits the
chapters on terrestrial and radiant heat, and on experimental results found
in the Prize Essay, but otherwise differs in no really important respect from
that work. Like the Prize Essay this work had also been very slow in
printing. 93 With the publication of his Analytical Theory and of the Prize
Essay Fourier's fears about possible priority claims or plagiarism of his
work must have come to an end. In the remaining years of his life he pub-
lished a number of further papers on the theory of heat including applica-
tions to terrestrial heat, to the theory of radiation, and to the motion of heat
in fluids. 94
Notes
1. Because of a reference to a paper of 1804 by J. B. Biot (Biot (1)) in the Draft
Paper.
2. In the notes at the end of the published version of the Prize Essay Fourier
states that 'the first analytical researches of the author on the communication of
heat were concerned with its distribution between disjoint masses : they have
been preserved in the first part of the memoir'. CEuvres 2, p. 94.
3. Draft Paper fol. 109 bis-122.
4. 1807 memoir, arts. 1-13.
5. Prize Essay, arts. 38-43.
6. Analytical Theory, chapter IV, sect. 2.
7. Newton Principia, Book I. Prop. IV, Theor. IV, Scholium.
8. See below, chapter 8, pp. 164-5.
9. Draft Paper, fol. 124-4 v -
10. Biot (1).
11. Draft Paper, fol. i28ff.
12. Draft Paper, fol. 125-5 v.
13. According to Historical Notes.
14. Draft Paper, fol. 127V.
15. Historical Precis fol. 162.
16. 1807 memoir, art. 15.
17. Ibid., arts. 16, 17.
18. Ibid., arts. 17, 18.
19. Ibid., fol. 3.
20. Historical Notes.
21. 1807 memoir, arts. 15-18.
22. Ibid., art. 19.
23. Ibid., art. 24.
24. Ibid., art. 25.
25. Ibid., art. 26.
26. Ibid., art. 28.
160
27-
28.
29-
3°-
3i-
32.
33-
34-
35-
36.
37-
38.
39-
40.
41.
42.
43-
44-
45-
46.
47.
48.
49.
So.
Si-
52.
S3-
54-
55-
56.
57-
58.
59'
60.
61.
62.
CHRONOLOGICAL ACCOUNT OF
Ibid., art. 29.
Ibid., arts. 30, 31.
Ibid., arts. 159-67-
Ibid., art. 32.
Ibid., commencing at art. 34.
Ibid., arts. 76~94-
Ibid., arts. 95, 96.
Ibid., arts. 97-1 14-
Ibid., arts. 116-39.
Ibid., arts. 152-8.
Ibid., arts. 140-51.
With the possible exception of the treatment of diffusion in infinite solids
which had to await the Prize Essay and represented a definite advance mathe-
matically over anything found in the 1807 memoir.
This abstract has been preserved in MS. 1851, Ecole des Ponts et Chaussees,
Paris.
As he states in Letter XXI to Lagrange, Appendix, p. 318.
S. D. Poisson (2).
I can find no reasons for Grattan-Guinness's opinion that this review repre-
sented 'the ultimate in denigration' of Fourier's work. See Grattan-Guinness
(1), p. 250.
Poisson (2). See (Euvres, 2, p. 215.
See Proc. Verb., vol. 4, p. 299: seance of 15 Jan. 1810.
See below, Letter XX to Laplace, Appendix, p. 316.
Ibid.
See below, Letter XXI, Appendix, p. 318.
In this section Fourier for the first time treated the cylindrical or Bessel
functions.
See above, chapter 5, pp. 101-2.
Biot (2).
Laplace (3), pp. 290-5.
In Letter XXI to Lagrange(?) Fourier states that he transmitted part of his work
'two years ago to M. Biot and M. Poisson*. It is evident from the context that he
is referring to a time before the submission of the 1807 memoir.
For example, there was no indication in Laplace's treatment of how the constant
involved in the expression for the heat conduction depended on the dimensions
of the bar or the material of which it was made up.
1807 memoir, art. 18.
See below, Letter XIX, Appendix, p. 307.
This topic is discussed below in chapter 8, pp. 166-7, and chapter 9, p.
185.
Biot (2), p. 336.
Laplace (3), p. 291.
This is referred to in item 6 of notes to abstract of memoir contained in MS.
1 85 1, ficole des Ponts et Chaussees, Paris, also in Historical Notes.
Ibid., item 5.
Laplace (3), p. 294. See discussion of this below, chapter 8, p. 170.
See especially Fourier's 1829 paper 'Remarques Generates sur 1' Application
des Principes de l'Analyse Algebraique aux Equations Transcendantes'.
(Euvres, 2, pp. 185-210.
RESEARCHES IN HEAT
161
63.
64.
65-
66.
67.
68.
69.
70.
7i-
72.
73-
74-
75-
76.
77-
78.
79-
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93-
94-
Proc. Verb., 4, p. 544: seance of 7 Oct. 181 1.
See (Euvres, 2, p. 94, for Fourier's description of the contents of the Prize
Essay.
Laplace (2). Fourier refers to this paper in his Historical Precis, fol. 155.
Given in Prize Essay arts. 66-79.
Prize Essay, arts. 80-8. See below chapter 10, pp. 197-202.
See above, chapter 5, n. 22.
Prize Essay, arts. 89-100. See below chapter 10, pp. 202-5.
Prevost (1).
Reproduced in (Euvres, I, p. vii.
The letter itself seems to have disappeared.
See letter from Delambre to Fourier in BN MS. ff. 22529, fol. 119.
Poisson (3).
Ibid., p. 434.
See Fourier's own reference to this controversy in 1807 memoir, fol. 1 14-15.
For critical accounts see Bose (2); Langer; Mach, pp. 93-7; Grattan-Guinness
(3), chapter 10; Ravetz (2). The last named work contains a useful biblio-
graphical note at p. 71.
Poisson (1).
Laplace (2).
Poisson (3), p. 435.
Op. cit., fol. 161-2.
Ibid., fol. 161-161V. The question of uniqueness is discussed below in chapter
8, PP. 175-7-
Poisson (4).
BN MS. ff. 22525, fol. 82-2V, 83-4V, 98.
Poisson (3), p. 439.
Biot (3).
Ibid., p. 669, n. 1.
Historical Precis, fol. 157-8V.
Especially the first of these : 'Theorie de la Chaleur', Ann. Chimie Physique,
3 (1816), 350-75-
Memoires de I'Academie Royale des Sciences, 4 (1819-20: publ. 1824), 185-555 ;
ibid., 5 (1821-2: publ. 1826), 153-246.
BN MS. ff. 22529, fol. 121.
(Euvres, 2, p. 94.
Proc. verb., vol. 7, p. 274.
In his letter of 11 April 1 816 to the President of First Class (see below Letter
XXVIII) Fourier claimed that 360 pages of his work had already been printed.
See below, chapter 10.
8
DERIVATION AND SOLUTION OF THE
EQUATION OF MOTION OF HEAT IN
SOLID BODIES
In discussing Fourier's derivation and application of the equations govern-
ing the propagation of heat within continuous solids we shall follow
Fourier's own method from the 1807 memoir onwards of making a sharp
division between the derivation of the equations of propagation in various
cases and the solution of the same equations subject to certain initial and
boundary conditions. Section 8.1 of this chapter will therefore be devoted
to the derivation of the equations of propagation of heat and section 8.2 to
their solution. Fourier gives no reason for this separation between deriva-
tions and solutions. Probably it was simply an index of his orderly mind and
a tendency to separate the largely physical thought processes of the deriva-
tions, above all in the critical case of the thin rod, from the purely mathe-
matical processes involved in their solution. It has proved an appropriate
division for the purpose of the present book which is principally con-
cerned with Fourier the physicist rather than Fourier the mathematician.
Much consideration has already been given 1 to the mathematical aspects of
Fourier's work in the theory of heat and the account given in section 8.2
is intentionally concise. In contrast, very little attention has been given to
the physical aspects of Fourier's work and the treatment in section 8.1,
especially in the case of the thin bar, is much more detailed and contains
new insights into Fourier the theoretical physicist.
1. Derivation of equations
It seems reasonably certain that Fourier was first stimulated to turn his
attention from consideration of discrete bodies to that of a continuous body
by Biot's paper of 1804. 2 This paper was principally concerned with the
steady state temperature distribution in a thin bar heated at one end and in
contact at its surface with air or other medium contained at constant
temperature assumed zero. On the basis of careful observations it appeared
that the decrease in temperature with distance from the heated end always
followed a logarithmic law. This explained why a thermometer placed at a
distance of six feet from the heated end showed no observable temperature
rise above that of the surrounding air. For Biot calculated that a difference
EQUATION OF MOTION OF HEAT IN SOLID BODIES 163
of one degree would have required a temperature of some 23 984 Reaumur
at the heated end, that is a temperature of the order of four times the tem-
perature of melting iron as measured in the experiments of Wedgwood.
On the basis of this result for the particular iron bar employed Biot con-
cluded :
Thus it is physically impossible to heat to one degree the end of an iron bar of
two metres or six feet in length by heating the other end, because it would melt
before this. 3
This rash generalization to all iron bars of the result true for a particular
one was later to lay Biot open to a devastating attack by Fourier.
Biot's paper was largely concerned with observational results and he
gives references by various earlier works on the same topic by Newton and
Ingenhouss. 4 Curiously, however, it contained no references to two papers
by Amontons 5 and Lambert. 6 Amontons work was apparently the first in
which the variation in temperature of a bar heated at one end was employed
as a 'thermometer' for measuring the melting points of various solids. To
this end he assumed that the temperature decreased linearly with the dis-
tance from the heated end. An important advance over this position was
then made by Lambert. From a passage in Lambert's work it is clear that he
achieved a pretty complete qualitative understanding of the process of con-
duction of heat in the bar. For example at one point he says :
However, the heat flows gradually to the more distant parts, but at the same
time travels from each part into the air. So that when the fire has burnt and been
maintained long enough at the same strength, every part of the bar finally
acquires a definite degree of heat because it constantly acquires as much heat
from parts of the rod nearer the fire as it transmits to the more distant parts and
the air. This stationary state will now be considered separately. 7
Lambert then gave a fairly plausible though incomplete justification for
a logarithmic decrease of temperature with distance which he proceeded to
test experimentally.
It was only some considerable time after reading Biot's paper that
Fourier learnt of the existence of the papers of Amontons and Lambert. He
was later 8 inclined to blame Biot for failing to give any reference to their
work in his 1804 paper, the implication being that Biot had been indebted
to them, especially to Lambert, for the ideas in his own paper. There is no
way of deciding if Fourier's poor estimate of Biot was justified. What is
certain is that the short section in Biot's paper in which he attempted to
give a theoretical investigation of propagation of heat in a thin bar bore a
striking resemblance in part to the discussion of Lambert. Each point of
the bar, he argued, 9 received heat from the point which preceded it, and
communicated some of it to the point which followed. The difference of
164 DERIVATION AND SOLUTION OF EQUATION
heat was what remained to the point as a result of its distance from the
source and its loss to the air by immediate contact and by radiation. In the
equilibrium state, when the temperature of the bar was stationary, the
increase of heat in each point of the bar by reason of its position would
equal that which it lost to the air, and by Newton's law this loss was pro-
portional to its temperature. In a non-steady state the increase of tempera-
ture in a given interval would equal the quantity of heat gained by reason
of position minus the quantity lost by radiation. The condition for tem-
perature equilibrium being reduced to calculation gave an ordinary
differential equation of the second order between the increase of the tem-
perature and the distance from the source of heat. This equation had con-
stant coefficients and could be integrated. In the non-stationary state an
extra variable, the time, was introduced to give a partial differential equa-
tion of the second order. This second equation contained the first as a
special case. Only the steady state problem was considered in which the
integral contained two arbitrary constants, and a non-arbitrary constant
which depended on the ratio of the 'conductivity' to the 'radiation'. 10
These three constants depended on the special conditions of the bar and
could then be determined by observation. At a great distance from the
source there would be no effect, and the temperature would be equal to that
of the surrounding air or other medium. This condition eliminated one of
the exponential terms. In practice there were no infinite bars but for bars
which were sufficiently long the temperature difference at the end would
be approximately zero.
Contrary to what Biot was to claim later, 11 the theoretical arguments in
his 1804 paper were of a purely qualitative nature. The first known attempt
at a quantitative treatment of the same problem, albeit of a very tentative
and incomplete nature, is contained in section 3 of Fourier's Draft Paper. 12
There he considers three consecutive slices of the bar at temperatures
y lt y 2 , y 3 , and argues that, other things being equal, the heat entering the
middle slice from the left slice will be proportional to y x -y 2 or 8y lt
and the heat leaving the middle slice for the right-hand slice will be
proportional to y 2 —y a or 8y 2 . So that the net heat which remains in the
middle slice will be proportional to 8y x - 8y 2 or 8 2 y 2 . But since the state
of the bar is assumed to be steady there must be an exact balance between
the net gain of heat in the middle slice and the net loss of heat to the air
at the corresponding portion of surface. The air is evidently assumed to be
at temperature zero and the loss in question will therefore be proportional to
the temperature y 2 of the middle slice, assuming that the cooling follows
Newton's Law. Expressing the heat balance for the assumed steady state
would then lead to 8 2 y 2 ~y 2 . But this poses a serious and apparently insur-
mountable difficulty, for the left-hand term is of the second order of small
OF MOTION OF HEAT IN SOLID BODIES
165
quantities, while the right-hand term is of zero order of small quantities.
Something else must therefore be taken into account. In the first place,
argues Fourier, a cylindrical slice has with a succeeding slice a contact
'incomparably more extended' than that which it has with the surrounding
medium (air). This leads to an additional term 8x on the right-hand side of
the equation. But the equation is still unbalanced as regards order of mag-
nitude, and to right this Fourier has to make the curious assumption that
since consecutive slices across which the heat flow takes place are 'infinitely
thin' the heat will be conveyed across them 'infinitely more easily' than in
the case of the heat lost to the air at the curved surface of the bar. This
yields a further additional term 8x on the left-hand side leading to an
equation of the correct form
&y
8x 2
= const, y.
The unsatisfactory nature of this derivation needs no stressing, and no
doubt Fourier himself did not feel very happy about it. A possible indica-
tion of this is provided by the fact that he makes no attempt to solve the
equation in spite of its simplicity. This could have been accounted for by
Fourier's uncertainty at this time of the actual nature of the sign of the
right-hand side whether positive or negative. In this connection a reference
to Biot's paper in the introduction to the draft paper is of interest:
Moreover the calculation does not suffice to remove all the uncertainties of this
theory of the movement of heat. There are those which will only be resolved by
means of experiment. This is what M. Biot has already undertaken with the
greatest success. He has been good enough to communicate to me the first
results obtained in his printed memoir. 13
Or again referring to the heat loss at surface of the bar :
I particularly desire to know how the figure, polish, or dullness of the surface
modifies the effect of this property. 14
Although Fourier's derivation of the equation for the propagation of
heat in a thin rod in the draft paper was erroneous, it did contain the germs
of a more satisfactory treatment as regards consideration of consecutive
slices and the notion of heat balance in the steady case. What was missing
was a knowledge of the rate of flow of heat across a given element of area.
This was first supplied in the 1807 memoir 15 where he gives a careful
justification of the assumption that the heat flow per unit of area is pro-
portional to the gradient of temperature, the constant of proportionality K
(the internal conductivity) depending on the substance in question. Armed
with this result he then considers a bar having a square cross-section of
side / sufficiently small for the temperature to be assumed constant over
166 DERIVATION AND SOLUTION OF EQUATION
any section perpendicular to the length of the bar. The prism is divided
into an infinity of slices of thickness 8x perpendicular to its length. He con-
siders three consecutive slices at x, x+8x, x+28x at which the tempera-
tures are y, y', y" . Then the rate of flow of heat into the middle slice from
the first slice is
-K.4\y' -y)\hx = -4KP(dy/dx)
And the rate of flow of heat from the middle slice to the right-hand section
is
-K.^l 2 (y"-y')/8x = - 4KI 2 (dy'/dx).
Therefore the net rate of gain of heat of the middle slice is 4KI 2 d(dy/dx).
The rate of loss of heat to air for the same slice is 8/ dx hy, where h is
coefficient of external conductivity. Therefore for a steady state
that is
«*■<($
8/ dx hy,
d 2 y _ zh
dx 2 ~ Kl y '
One important aspect of this derivation of the equation of motion for the
thin bar memoir is the way in which it becomes clear that (d 2 y/dx 2 )ly must
be positive in contrast to the earlier treatment which gave no grounds for
rejecting a solution with a negative value for this ratio, leading to a trigo-
nometrical solution in which one term could not be ignored as in the case of
a positive value for the same ratio. Equally important was the explicit
dependence of the constant of proportionality on the dimensions of the bar
and on its coefficients of internal and external conductivity.
The treatment of the thin bar in the 1807 memoir gave the correct
equation of motion and was based on the correct expression for the heat
flux. But there was still one remaining imperfection originating from
the treatment of heat flux as between consecutive slices of infinitesimal
width S* as compared to the Prize Essay and the Analytical Theory where
the flow of heat is always imagined across a geometrical section of zero
thickness. In the case of the thin bar the transition from the standpoint of
the 1807 memoir to the final, correct standpoint of the Prize Essay and the
Analytical Theory is epitomized by the transition from the employment of
the term tranche in the former work to that of section in the two latter
works. What may well have represented Fourier's first use of section as
opposed to tranche is contained in a letter 16 written to an unknown cor-
respondent in the period 1809-10, one of the three 17 extant letters to an
unknown correspondent or correspondents in which Fourier defended
OF MOTION OF HEAT IN SOLID BODIES
167
himself against the claim of Biot 18 and Laplace 19 that all those who had
attempted to derive the equation of propagation of heat had run up against
an analytical difficulty which could only be surmounted by following the
method employed by Laplace in the annex on heat in his light diffraction
paper of 1809. 20 The treatment given by Fourier in his draft paper was sub-
ject to this analytical difficulty, and it may have been this paper of which
Biot had been thinking. But there was no justification for levelling the same
criticism against the derivation of the equation of propagation of heat in the
1807 memoir. Fourier was therefore at great pains to bring out the dif-
ference between his former, erroneous derivation and that given in the
1807 memoir. To this end he gives a careful account of the original treat-
ment in which he uses the tranche approach throughout and shows how its
error resides in the assumption that the heat flow between tranches is
proportional to temperature differences, as opposed to temperature gra-
dient. This error had, of course, been corrected in the 1807 memoir. But
in the letter he removes the remaining imperfection of the 1807 memoir
and bases his treatment entirely on consideration of a single slice bounded
by sections at * and x + 8x respectively. Now he considers 21 a section at
distance * and denotes by z the quantity of heat traversing the given
section from left to right in unit of time. Since the temperature of the bar is
steady z must equal the quantity of heat lost in the same time over the
whole surface area to the right of x. It follows that if x' is another section to
the right of that at *, and z' is the corresponding value of z, z — z' =
quantity of heat lost per unit of time over the part of the surface contained
between * and x'. If x' = x+8x it follows that
8z = — chy 8x,
that is dz/dx = — chy,
c being the circumference of a section of the rod perpendicular to its length.
To determine the actual temperature distribution equation in the steady
state it only remained to determine z.
An equally striking example of the transition from tranche to section is
contained in two extensive marginal entries in the original text of the 1807
memoir itself. The first 22 is concerned with heat flux and talks throughout
of heat flow across sections, and the second 23 is concerned with the equation
of motion which is now obtained by equating the flux across a given section
at distance * to the integral representing the total surface heat loss to the
right of the given section. By differentiation of this equation the equation
for the temperature distribution follows.
In the Prize Essay and the Analytical Theory there is no further use of
three tranches either in the treatment or the derivation of the equations of
motion. In the Prize Essay 24 the equation for temperature distribution for
168
DERIVATION AND SOLUTION OF EQUATION
the thin bar is derived in the same way as in the second marginal entry 23
described immediately above. As for the method of derivation previously
employed in Letter XIX, Fourier contents himself with noting that one
'obtains the same result by considering the equilibrium of heat in the single,
infinitely thin slice contained between two sections whose distances are x
and x+8x'. 25 In the Analytical Theory 26 he gives the integral approach
first but now follows with the actual details of the alternative, 'sectional'
derivation.
The derivation of the equation for steady temperature distribution in a
thin bar was not only the first problem of the flow of heat in solids to be
considered by Fourier but undoubtedly also the problem to which he
first gave a definitive solution some time between the 1807 memoir and the
Prize Essay. But the fact that there was a flaw in the derivation in the 1807
memoir did not prevent him from obtaining the correct equation for the
thin bar. Also the method employed, unlike the faulty method followed
in the 1804 draft paper, was now applicable to other and more important
cases. Following the treatment of the thin rod the derivations of the
equations for heat propagation in these cases all employed the three slice
approach. The first problem considered after the thin rod, that of the
motion of heat in a thin ring, 27 though effectively in three dimensions could
be treated as one dimensional on the assumption that the ring was so thin
that there was no appreciable variation in temperature over any section
perpendicular to the central axis, the only variable being the distance *
measured along this axis. Unlike the case of the thin rod, a non-steady state
was considered. Previously, when considering the non-steady state in the
Draft Paper, 28 Fourier had followed Biot's qualitative argument in his
1804 paper and had erroneously set the net rate of increase of heat in the
element under consideration equal to the rate of change of temperature.
This error was also remedied in the 1807 paper by the introduction of the
specific heat capacity per unit volume of the substance, a quantity which
was carefully defined earlier in the same work. 29
In the next case treated, that of homogeneous sphere 30 heated to a given
uniform temperature and then allowed to cool in a medium at zero tem-
perature, the equation of propagation of heat could be written down by
slicing up the sphere into thin spherical shells and assuming that the heat
flow was necessarily everywhere in a radial direction. The same kind of ad
hoc treatment making use of special symmetries could also be employed in
the case of an infinite circular cylinder, 31 but in the case of an infinite
prism 32 the equation of propagation of heat in the steady case required a
full three-dimensional discussion. This time the division was by three sets
of slices parallel to the co-ordinate planes yz, xz, and xy. Attention was
directed to an infinitesimal cube situated at x, y, z and surrounded by six
OF MOTION OF HEAT IN SOLID BODIES
169
neighbouring cubes. In considering the flow of heat into the interior cube
from the two cubes immediately above and below it relative to the yz co-
ordinate plane, Fourier simply assumed this flow would be proportional to
dT/dx (where T is temperature), without giving any separate justification.
This lacuna was first made good in the Prize Essay. 33 Apart from this the
equation of propagation of heat in the steady case followed in the usual
way as
v 2 r = o.
In the next case considered, that of the cooling of a finite cube, the addi-
tional term corresponding to a change in temperature led to the full
general equation
CD(8TI8t) = KWT
for the propagation of heat in the interior of a continuous solid, where D
was the density, and C the specific heat per unit of mass. 34 This general
equation was then applied ab initio to re-derive the same equations for
the sphere and the cylinder which had been obtained previously by ad
hoc methods. 35
The derivations of the equations of motion in cases other than the thin
bar in the Prize Essay 36 and the Analytical Theory 37 differed from those
given in the 1807 memoir in the replacement of three consecutive slices by
a single slice, and in the corresponding shift in attention from transmission
of heat between neighbouring slices to transmission of heat into a single
element across its bounding surfaces.
In the 1804 Draft Paper the problems considered — a finite number of
discrete bodies, a thin bar, and a semi-infinite strip, precluded the con-
sideration of true boundary conditions involving the external conductivity.
In the case of discrete bodies the question did not arise, whereas in the case
of the thin bar the surface entered directly via the term hy into the equation
of propagation itself; this was a result of the ideal assumptions concerning
the thinness of the rod which made it possible to ignore any variation in
temperature over a given section perpendicular to the length of the bar. In
the case of the semi-infinite strip the assumption that the edges were at
temperature zero likewise obviated the necessity of considering physical
boundary conditions since it was only necessary to put the temperature
equal to o when y equalled ± a. This case was quite different from the
situation at the surface of a sphere or a cylinder in air at temperature T= o.
In the first case the temperature of the solid was held at T= o, whereas now
it was the temperature of the surrounding medium which was held at
T=o, and as a result there was an abrupt discontinuity in temperature at
the surface. In the case of the semi-infinite strip the edges would have had
to be in contact with infinite reservoirs at temperature T= o, whereas in the
170 DERIVATION AND SOLUTION OF EQUATION
case of the temperature discontinuity the temperature of the air or other
medium would have to be kept constant by keeping it moving at the surface
as in Newton's original experiment. 38
Fourier's uncertainty about the question of boundary conditions is
indicated in the draft paper by the fact that in writing down the general
equation of propagation in three dimensions he questions whether or not a
term involving the exterior conductivity h should appear in the interior of
the solid. This, he says, can only be determined 'by the results of experi-
ments'. 39 In the 1807 memoir all such uncertainties have disappeared. If
a term involving h remains in the equations for the thin bar or the thin ring
this is a consequence only of their thinness and corresponds to the ideal
assumption of no variation of temperature over the section. But in the case
of a heated sphere allowed to cool freely in air at temperature zero, Fourier
specifically comments in the text 'the value of the coefficient h is not found
in this equation ; but one first introduces it into the calculation when one
expresses the conditions relating to the surface'. 40 The relevant surface
conditions, namely, K(dT/8r) + hT=o is duly given when the problem is
considered later 41 with a view to obtaining an analytical solution relative
to the given initial conditions. It is given without any fuss, and as though
Fourier were unaware of its revolutionary nature, by simply expressing the
flux of heat across the surface in two ways, first in terms of Fourier's own
law of heat flux, and secondly in terms of Newton's law of cooling. Since
Fourier's boundary condition does no more than tie together the flow of
heat up to, but just beneath, the surface with the actual flow at the surface,
it is surprising to find that it was one of the aspects of the 1807 memoir
criticized by Biot and Laplace, 42 as we learn from the following passage:
Unless I am mistaken myself the temperature of the extreme envelopes of a
body are not as M. Laplace or he [Biot] represent them to be.* 3
Laplace's (and presumably Biot's) views on the question are given at the
end of the section on heat in Laplace's 1809 paper on diffraction. 44 There 45
he assumes that the surface of a heated body rapidly reaches that of the
surrounding medium, and that a law is then quickly established governing
the rise of temperature within the body up to a certain maximum value U.
The loss of heat is then proportional to U. This is opposed to the views of
those (including Fourier and Newton!) who thought that the temperature
of the surface was above that of the surrounding medium, thus breaking the
law of continuity. But if Laplace had examined carefully the writings of
Newton and subsequent writers on the subject, he would have seen that
they all took care to state that the air surrounding the heated body was
moving rapidly past it, thus maintaining a constant temperature. The rather
wild nature of Laplace's hypothesis in this matter is in striking contrast with
OF MOTION OF HEAT IN SOLID BODIES
171
sober, simple, and correct condition formulated by Fourier, and provides
another example of his superior physical intuition in this particular topic
compared with that of Laplace, Poisson, or Biot.
Considerations similar to those employed in the case of a sphere sufficed
to determine the boundary conditions in all the other cases considered in
the 1807 memoir, and there is no change in this respect in the Prize Essay
(or the Analytical Theory) except that now the boundary conditions are
given immediately after the derivation of the interior equations of propaga-
tion instead of later when analytical solutions of these same equations are
being considered. However, the Prize Essay 46 and the Analytical Theory 47
do differ from the 1807 memoir in containing the general expression for the
boundary condition at any point of a solid of given shape which is equiva-
lent to the modern expression
kT+KVT.n = o,
where n is the unit vector in the direction of the normal at the point in
question.
2. Solutions to equations
Although there was a superficial similarity between Fourier's mathe-
matical treatment of the equations for the steady state and the non-steady
state, there were in fact profound differences between the two kinds of
problems both on the physical and the mathematical side which makes it
necessary to consider them separately.
Steady state
Disregarding the mathematically trivial cases of the steady states for a
thin bar and a thin ring the only steady state cases considered by Fourier
were those of the semi-infinite strip and the infinite prism. In each case
there were heat sources over which the temperature was held at a given
fixed temperature, and heat 'sinks' at y= ± 1 for the semi-infinite strip, and
y= ±1, z— ±1 for the infinite prism, over which the temperature was
artifically maintained zero.
Separation of variables alone in each case led to special trigonometrical
solutions involving parameters whose possible values were then deter-
mined by the necessity of T=o at the heat sinks. The complete solution
was then expressed as a linear combination of the allowable special solu-
tions with undetermined coefficients whose values were derived from the
necessity for T= 1 over the heat sources, at first by algebraic elimination
(semi-infinite strip, Draft Paper) 48 and then by the far more convenient
method of integration based on the orthogonal properties of the basic
solutions. 49
172 DERIVATION AND SOLUTION OF EQUATION
What does not seem to have been stressed is the highly artificial and
cunning choice of T= o at the heat sinks. In the case of the heat sources it
would still have been possible to find the undetermined coefficients if one
had had T=any constant or even T= T(y) for — i< v< i, in the case of
the semi-infinite strip, or T=u{y).v{z) for arbitrary u, v in the case of the
prism, though of course it would have rendered the physical status of both
these problems increasingly unrealistic. But in the case of the heat sink
there was no choice other than T=o if trigonometrical series were used.
For the choice T=o was the only one which could be satisfied both
individually and collectively by all the special trigonometrical solutions and
at the same time determine the allowable values of the undetermined para-
meters in these solutions. Ultimately Fourier could have dealt with a heat
sink distribution of heat given by T=cf>(x) by means of Fourier integrals
subject to satisfactory behaviour of <f>(x) at infinity. But when he first
treated the problem of the semi-infinite strip such a treatment would have
been beyond him. The innocent looking choice T=o, devoid of any
physical significance for the temperature scale used by Fourier, had thus a
hidden mathematical significance of tremendous importance.
Given the physical artificiality and idealization of the semi-infinite strip
problem its essential significance was on the mathematical side, above all
for its introduction of Fourier's use of trigonometrical functions expanded
in the 1807 memoir into a general treatment of the problem of expressing
an arbitrary function in trigonometrical series of sines or cosines or mix-
tures of both. 50 It was, of course, just the question of the adequacy of these
trigonometrical functions for this purpose which constituted one of the
two major criticisms of Fourier's 1807 memoir. This aspect of Fourier's
work has already been given extensive treatment including a recent dis-
cussion by Gratton- Guinness of the bearing of the eighteenth-century string
problem for Fourier's own work. 51 Relevant here is an interesting passage
in a letter of Fourier which evidently constituted a reply to a charge of his
having failed to refer to earlier works 53 on the subject of trigonometrical
series:
I transmitted this part of my work two years ago to M. Biot and M. Poisson who
then knew the use I was making of it to express the integrals of partial differential
equations in trigonometrical or exponential series : they did not point out to me that
d'Alembert or Euler had employed these integrations to develop a trigono-
metrical solution. I was ignorant of the fact myself or I had entirely forgotten it ;
it was in attempting to verify a third theorem that I employed the procedure
which consists in multiplying by cos ix dx the two sides of the equation
<j>{x) = a + a i cos x + a 2 cos 2*H
and integrating between a = o and x=ir. I am sorry not to have known the mathe-
matician who first made use of this method because I would have cited him.
OF MOTION OF HEAT IN SOLID BODIES
173
Regarding the researches of d'Alembert and Euler could one not add that if they
knew this expansion they made but a very imperfect use of it. They were both
persuaded that an arbitrary and discontinuous function could never be resolved
in series of this kind, and it does not even seem that anyone had developed a con-
stant in co-sines of multiple arcs, the first problem which I had to solve in the
theory of heat. It was also necessary to know the limits between which this
development took place. For example it has to be realized that the equation
x/z = sin x— \ sin 2x+% sin %x- • •
is no longer true when the value of x is between -n and 277. However, the second
side of the equation is still a convergent series but the sum is not equal to x/2.
Euler, who knew this equation, gave it without comment. It is very clear that if
the method used to develop certain functions in trigonometrical series had been
entirely exact it would have made known the limits between which the equations
held true. Finally this development of a function in sines or co-sines of multiple
arcs is only a particular case among those which I have had to treat, and these
latter offered analytical difficulties of a very different order. It was necessary, for
example, for determining the movement of heat in a cylindrical body to develop
an arbitrary function in a series whose terms depended on a transcendental
function given by a differential equation of the second order. I beg you, Sir, to be
good enough to examine this part of my work which is really the only part
worthy of your attention.
I did not intend to denigrate the work which had been done before me by
mathematicians as illustrious as Messrs. d'Alembert and Euler for I hold their
memories in the deepest respect. But I have wished to make it clear that the
procedure which they made use of was not adequate to solve the problems relating
to the theory of heat. 63
Non-steady state
The assumption of a normal mode time-dependence of the form
exp (ar) was first made by Fourier in his treatment of the transmission of
heat between a finite number of discrete bodies. 54 This, as he remarked,
was 'a known method' 55 so that he evidently was familiar with at least this
aspect of the treatment of the string problem by his predecessors in the
eighteenth century. The same assumption formed the invariable point of
departure for his consideration of all non-steady problems of the propaga-
tion of heat in continuous solids. Combined with the separation of the
spatial variables among themselves and from the temporal variable there
resulted separate ordinary differential equations in each of the spatial
variables. The solution to all these equations were given in terms of trigo-
nometrical functions involving undetermined parameters, with the excep-
tion of the cylinder. 56
At this point boundary conditions had to be taken into account which
with the exception of a thin ring took the form K(dTjdr) + hT=o. Once
174 DERIVATION AND SOLUTION OF EQUATION
again this boundary condition was satisfied for each particular solution and
led in turn in all cases (including that of cylinder) to transcendental
equations for the undetermined parameters. However, unlike the case of
the steady state in which the condition T=o was necessary for trigono-
metrical solutions to be possible, these transcendental equations in no
way restricted the particular solution in question. However their mathe-
matical treatment, especially that of the reality of the roots, and especially
that corresponding to the cooling of a sphere, proved troublesome and led
to papers by both Fourier and Poisson even after publication of the Ana-
lytical Theory. 57
Having determined, at least in principle, an enumerable infinity of
allowable parameters, general solutions could then be written down
involving arbitrary coefficients whose values could be determined from
the arbitrary initial distribution of temperature for t = o by multiplication
and integration in which the vanishing of 'mixed' terms was guaranteed by
the transcendental equations determining the boundary conditions.
A word needs to be said about the special case of non-steady propagation
in a thin ring. 58 Here the allowable values of the undetermined parameters n
in the spatial part of the solutions (viz. sin nx) were determined by the
necessity for the distribution of heat to be periodic of period zirr, where r
was the radius of the ring. Since the corresponding solution with cos nx
was. equally permissible the general solution in this case involved a mixed
expansion in terms of both sines and cosines, the coefficients being deter-
mined by integrations in terms of the initial distribution of temperature at
time f = o. According to Fourier 59 he first derived these formula for the
coefficients by the 'method of elimination', that is algebraically, and then
independently by consideration of the results obtained previously for a
finite number of discrete bodies arranged circularly between which heat
could be communicated by a shuttle mechanism. 60
The elucidation of the connection between the pure sine and cosine
expansions valid in the region o to tt of a function periodic with period 2tt
with mixed sine-cosine expansions in the region — tt to it was one of the few
aspects in which the analytical theory marked a significant advance over the
Prize Essay. 61 This exposition has not always been properly understood.
For example, Kelland 62 made a number of errors because — as William
Thomson 63 later pointed out — he did not realize that a sine/cosine expan-
sion of a given function in the range o to 77 necessarily implied it was odd/
even in the range — tt to o compared with the range o to it. More recently
Grattan-Guinness 64 has made the surprising suggestion that :
the purpose of this reasoning (that in the Analytical Theory) was clearly to avoid
reliance on the integration term-by-term method of obtaining its co-efficients
whose fallibility Fourier had seen all too clearly.
OF MOTION OF HEAT IN SOLID BODIES
175
In fact, as the function is necessarily assumed to be periodic of period 2tt
then if it is given over the whole range — tt to tt it will be determined every-
where else, and the fact that its Fourier expansion must involve both cosines
and sines is to prevent it being either even or odd in the range — tt to o
compared to o to tt which is, of course, not necessarily the case. As for the
coefficients of the various sine and cosine terms these are determined in the
usual way by integrals as Fourier specifically states in direct contradiction
to the statement of Grattan-Guinness.
One aspect of Fourier's work in the Analytical Theory of Heat to which
little or no attention seems to have been given hitherto was his proof of
uniqueness of solution for the heat conduction equation. It appears in
section 280 of the Analytical Theory 65 immediately following his solution
for the motion of heat in a ring. He gives an essentially step-wise proof:
knowing the initial temperature distribution at time t = o that at a short
time A* later follows uniquely, and from this that at time 2 At and so on.
This is obviously equivalent to the employment of a Taylor expansion in
the time about t = o of the form
#f : x,y, z) = <}>{o: x,y, *) + *(^ o + ^ (f|), =0
+ ■■
each partial differential coefficient of order n with respect to the time t = o
being determined by means of the conduction equation in terms of the initial
spatial distribution of the temperature.
A comparison with the Prize Essay and the 1807 memoir reveals no
trace of uniqueness considerations in either of these two works. There can
be little doubt that it was introduced into the Analytical Theory because of
criticisms of Fourier's work by Poisson and Biot in 18 15 and 1816.
Poisson' s criticism deserves quotation in full :
As the partial differential equation to which it corresponds is linear and has con-
stant coefficients, one can also satisfy it by an integral composed of an infinity of
exponentials of sines and cosines containing an infinite number of arbitrary con-
stants : this integral is contained in the preceding one ; but it would be difficult to
decide a priori if it has the same degree of generality and if it can replace it
identically, something which necessarily throws doubt and obscurity on all
solutions deduced from this second form of the integral. M. Fourier, who did not
go beyond a solution of this kind, remarks himself that it is similar to that which
Daniel Bernouilli gave to the problem of vibrating strings ; but it is well known
that Euler, d'Alembert, and Lagrange, who occupied themselves at the same
time with the same problem, and who differed among themselves on various
points, were at one nevertheless in regarding Bernouilli's solutions as incomplete
and less general than that containing arbitrary functions. This is not true of the
formulas of M. Fourier : I am sure that all the results he obtains are correct ; but
176 DERIVATION AND SOLUTION OF EQUATION
against his analysis can be advanced the same objections as those advanced
against that of Bernouilli and repeated in other similar cases.
In general it seems to me that whenever an unknown quantity depends on a
partial differential equation, and when its values should reduce in fact to a sum
of particular integrals, the only way of disposing of all doubts and retaining for
the mathematical certainty result is not to suppose in advance such a form for the
unknown quantity, but to deduce it, on the contrary, from the general integral by
a succession of direct and rigorous transformations. This is what I have attempted
to do in this memoir . . .
... I leave it to mathematicians to judge if I have attained the end that I have set
myself. 66
Biot echoed Poisson :
. . . M. Fourier has since reproduced the same partial differential equation in a
large work which has been crowned by the Institut of France. He satisfies it
generally by an exponential integral which he applies to straight bars and to rings,
both in the steady and non-steady states. In addition he has found an equation
for the condition which must hold at the surface of an extended body when the
heat excited in its interior comes to dissipate itself at this surface by radiation and
contact with the air. But since exponential integrals do not in general allow in an
applicable manner the discontinuities which are included in the general integral
of partial differential equations, it remains to show that all possible methods of
heating always produce in the end, and after a greater or lesser time, effects of
this nature. This is what M. Poisson has achieved in a very fine memoir whose
results I shall soon detail. 67
Fourier's devastating reply to these criticisms of the form of his solution
is contained in his unpublished Historical Precis. 68 He refers to Poisson's
approach to the theory of heat based on a three-dimensional version of
Laplace's solution to the one-dimensional heat-conduction equation con-
taining an arbitrary function under the integral sign. Employing this type
of solution Poisson reached the same results as Fourier. But this was
necessarily the case. He illustrates this 69 by proving that the exponential
solution for the motion of heat in a ring radius r whose temperature is a
given function of position tends in the limit of r ->• oo to the solution for a
straight bar given by Poisson in terms of Laplace's solution. As he puts it
more generally :
The integral of the equation of the movement of heat can be presented in very
different forms. The application to the theory of heat consists in discovering in
the simplest way that which is most appropriate to the question proposed. One is
assured that the solution is exact when the function of * and t which satisfies the
differential equation represents the given initial state, and this solution is applic-
able when one deduces simply from the same function the numerical values of
the temperature. The physical question remains imperfectly resolved if the
OF MOTION OF HEAT IN SOLID BODIES
177
second condition is not fulfilled. In general every expression of x, y, z, and t that
satisfies the equation of the second order
8v 8 2 v 8 2 v 8 2 v
ft = fx 2 + 8y^ + 8z 2
and which reduces when one puts t = o to an arbitrary function f(x, y, z) of the
three variables x, y, z is the complete integral proposed. Such expressions are
always identical, no one of them can be considered as more general than another,
and in whatever manner they are obtained they certainly have the same range. If
in solving diverse questions of the theory of heat one restricts oneself to deducing
solutions of a certain form of the integral one makes the calculation infinitely
more complicated, and it will be more difficult to discover these solutions when
one treats entirely new questions. 70
The point could not be put more clearly, and it only remained to supply
a general proof of uniqueness as found in the Analytical Theory itself.
Notes
i. See especially Bose (2), Grattan-Guinness (1), (2), Jourdain (1), (2), Langer,
Van Vleck.
2. Biot (1).
3. Ibid., p. 9.
4. He probably had in mind the works by Newton and Ingenhouss given in the
bibliography.
5. Amontons.
6. Lambert.
7. Lambert, p. 184. Quoted in Mach, pp. 78-9.
8. Thus in the unpublished Historical Precis (fol. 157), Fourier wrote:
The researches of M. Biot had the same object as that of Amontons and of Lambert
and they gave certain numerical values consistent with the law proposed by the latter.
After that one would have expected that the works of these physicists would have
been cited in M. Biot's work. We looked for this citation without success both in the
work published in 1804 and in the new treatise of Physics. The author thus departs
from an invariable usage and one founded on the most just motives.
9. Biot (i), p. 317.
10. The exact meanings of these terms were evidently not clear to Biot.
11. Biot (3), p. 669, n. 1.
12. Draft Paper, fol. 124-124V.
13. Ibid., fol. 108.
14. Ibid., fol. io8v.
15. 1807 memoir, art. 17. The development of Fourier's thinking on the question of
heat flux is considered in chapter 9 below.
16. See below Letter XIX, Appendix, p. 307.
17. The other two are reproduced in the Appendix as Letters XVII and XVIII.
18. Biot (2), p. 336.
19. Laplace (3), p. 291.
20. Ibid., pp. 291-5. See below, chapter 9, p. 184 for an account of this method.
1
178 DERIVATION AND SOLUTION OF EQUATION
21.
22.
23-
24.
25-
26.
27.
28.
29.
3°-
31-
32.
33-
34-
35-
36.
37-
38.
39-
40.
41-
42.
43-
44-
45-
46.
47-
48.
49-
So.
Si-
52.
S3-
54-
55-
56.
57.
58.
59.
60.
61.
62.
See below Letter XIX, p. 308.
1807 memoir, fol. 38.
Ibid., fol. 40.
Prize Essay, pp. 217-18.
Ibid., p. 218.
Analytical Theory, pp. 51-2.
1807 memoir, art. 23.
Draft Paper, fol. 125.
1807 memoir, art. 15.
Ibid., art. 25.
Ibid., art. 26.
Ibid., art. 27.
Prize Essay, pp. 212 and 235.
1807 memoir, art. 28.
Ibid., arts. 30, 31.
Prize Essay, arts. 1 1-14.
Analytical Theory, arts. m-31.
Newton, p. 828.
Draft Paper, fol. 127V.
1807 memoir, fol. 51.
Ibid., art. 98.
Also a criticism by Poisson referred to in Historical Notes.
See below Letter XVII, Appendix, p. 303.
Laplace (3).
Ibid., p. 294.
Op. cit., art. 15.
Op. cit., arts. 146-54.
Draft Paper, fol. 128-49.
A method referred to in the introduction to the draft paper and first employed
in the 1807 memoir. See 1807 memoir, arts. 62-3.
1807 memoir, arts. 50-74.
Grattan-Guinness (3), chapter 10.
See also Ravetz (2), for an account of these including bibliographical indica-
tions.
See below Letter XXI, Appendix, p. 318.
Draft Paper, fol. 109-20V.
Ibid., fol. 114V.
1807 memoir, arts. 122-39. Fourier's treatment of this case by the introduction
of the so-called cylinder or Bessel functions has already been exhaustively
studied, most recently in Grattan-Guiness (3), chapter 16.
See especially Fourier's 1829 paper 'Remarques generates sur l'application des
principes de l'analyse algebraique aux equations transcendantes', CEuvres, 2,
pp. 185-210.
1807 memoir, arts. 76-94.
See Letter XXI, Appendix, p. 318.
See Prize Essay, p. 398 foot.
Analytical Theory, arts. 231-4.
Kelland, p. 64. The copy of Kelland's work consulted on loan from University
Library, Glasgow has the following marginal comment: 'This is a mistake.
Fourier formulae are quite right' W[illiam] Tfhomson]. Kelland's statement
OF MOTION OF HEAT IN SOLID BODIES
179
'There can be little doubt to anyone who carefully examines the subject, that
all Fourier series on this branch of the subject are erroneous' has been crossed
out.
63. Thomson, W. 'On Fourier's Expansions of Functions in trigonometrical
Series', Camb. Math. J., 2, pp. 258-62.
64. Grattan-Guinness (3), p. 281.
65. Analytical Theory, p. 299.
66. Poisson (3), p. 440.
67. Biot (3), p. 669 n. 1.
68. Op. cit., fol. 161V-162.
69. Ibid., fol. i6iv.
70. Ibid., fol. 162.
EXPRESSION FOR THE FLUX OF HEAT
IN SOLID BODIES
The familiar expression for the heat flux in solid bodies involving the
partial spatial derivatives of the temperature distribution was probably
taken very much for granted once the opposition of Biot and Poisson had
been stilled by the presumed defection of Laplace to the enemy camp, 1 and
little if any attention can ever have been given thereafter to what must
always have seemed to the majority of readers of the Analytical Theory of
Heat the rather tedious and longwinded justification given by Fourier of
his expression for the heat flux. 2 But this is not an attitude which the his-
torian of science can afford to take if he wishes to understand the process
which leads to the creation of the Analytical Theory of Heat. On the con-
trary, he must put himself in the position of Fourier for whom it was of
vital and anxious concern not only that the expression for the heat flux
should be of the correct form — otherwise the theory itself would inevitably
be incorrect — but also that it should be possible to justify this expression
by deriving it from one of those fundamental simple principles or general
facts to which the scientists of the eighteenth and early nineteenth century
attached such overwhelming importance. By great good fortune there is
sufficient material available to make it possible to follow in fairly close de-
tail the gradual sharpening of Fourier's attitude to the heat flux from the
original vague intuition that in the one-dimensional case the communica-
tion of heat between adjacent parts was proportional to a temperature
'difference', to the final careful and compelling justification for the general
three-dimensional expression given in the Analytical Theory. One can thus
come to appreciate both the great importance which Fourier attached to
this element of his theory and the magnitude of his achievement in deriving
and justifying the expression for the flux of heat.
The first essential step towards deriving an expression for the heat flux
was the realization of the necessity for such an expression in the derivation
of the equation for the propagation of heat starting with the simplest
possible case of the thin bar. It was the failure to introduce such an expres-
sion which led to the inhomogeneity in the 'equation' derived by Fourier
in the Draft Paper. 3 And the purely heuristic introduction of the term 8x on
the grounds that the conductivity of an infinitely thin slice would be
infinitely great can perhaps be regarded as the first faint move in the direc-
EXPRESSION FORTHE FLUX OFHEAT IN SOLID BODIES 181
tion of the introduction of the correct expression for the heat flux. A
measure of the conceptual difficulties involved at this point is given by the
fact that neither Biot nor Poisson seemed able to grasp this aspect of
Fourier's approach, and as a result continued to harp on a supposed 'analy-
tical difficulty' in Fourier's derivation — referring to the supposed existence
of an inhomogeneity in the equation itself — as late as 1816.
Fourier had evidently hit on the correct temperature dependence of the
expression for the heat flux before the completion of the Draft Paper, for in
a check of his solution for the semi-infinite plate based on heat balance
considerations,* he assumes that the heat flow per unit length across
sections of the bar perpendicular to the x- and j>-axis will be proportional
to (8T/8y), (BT/Bx) respectively. However, he gives no indication of any
justification for the use of this result, and his first proof of the proportionality
of heat flux on the spatial temperature derivative is found in the 1807
memoir in the process of giving a precise definition of heat conductivity
within a solid body. There 5 he considers a prism of finite given cross
sectional area and infinite length which has attained a steady state of tem-
perature distribution in which the temperatures over two given sections a,
A at a certain distance apart are 1 and o respectively. In that case it is 'easy
to see' that the temperatures will decrease from 1 to o 'according to the
ordinates of a straight line'. For imagine the prism divided into an infinite
number of equal slices by planes perpendicular to the axis. Each slice has
a vanishingly small thickness and the temperature throughout it is assumed
to be the same. According to hypothesis the difference of temperature
between consecutive slices will be the same for any two consecutive slices
throughout the length of the prism between a and A. At this point he
makes an implicit appeal to the principle of Newton— already referred to
explicitly in a marginal note 6 in his earlier discussion of radiation at the
surface of a heat body — from which it follows that 'the quantity of heat
which passes from one portion of matter to another depends (other things
being equal) on the excess of the temperature of one body over the tem-
perature of the second'. 7 The heat which flows between any two consecu-
tive slices will therefore always be the same, and so the prism will conserve
its actual state unchanged. He then considers a prism of the same substance
with the same temperature difference between two sections a, A at half the
distance apart of the earlier one. Now the flow of heat will be twice as great
as before, since the temperature difference between consecutive slices in
the second prism will be twice that in the first, and the quantity of heat
transmitted is — again by Newton's principle — 'other things being equal,
independent of the absolute temperatures and proportional to the excess of
temperature of one body over the other'. 8 Finally, in the general case of the
division of a prism of the same material into slices of equal thickness, the
182
EXPRESSION FOR THE FLUX OF
heat flow will be proportional to the temperature difference between
consecutive slices, and will therefore vary directly as the temperature
difference B — b, and inversely as the distance A — a, between the ends of
the prism. The heat flow may therefore be set equal to
-K.{B-b)/(A-a) = -K(dyldx).
If B = o, 6=1, and A — a= i the quantity of heat which flows in unit of
time across a given cross-sectional area will be K. This is the required
precise definition of the conductivity K in terms of which the heat flux is
now determined for one-dimensional flow in an infinite prism of the sub-
stance in question.
The case considered by Fourier up to this point was purely that of a
steady distribution in a bar in which there was a linear fall off of the
temperature from one surface to another. In a note at this point in the
memoir he goes on to consider the more general case where the temperature
distribution is no longer linear :
We shall consider again the case where the different sections of the prism are sub-
jected to fixed temperatures. Suppose that the section which corresponds to the
abscissa a preserves the temperature b, that an intermediate section which cor-
responds to the abscissa x is maintained by some external cause or other at
temperature v, that another section at distance x' is maintained at temperature
y', and that it is the same for various other sections which being placed at dis-
tances x",. . ., x'",. . . by the effect of some cause or other preserve the tempera-
tures y" y, . . . finally that the last section at distance A preserve the tem-
perature B. It follows from what has been said above that the solid subjected to
these conditions will reach a permanent state in which the temperatures will be
represented by the ordinates of a polygon. Therefore the flux of heat which tra-
verses any section will not have the same value throughout the prism. It will not
vary with the time for the same section, but it will in general be proportional to
the tangent of the inclination of a side of the polygon.
The preceding conclusion does not depend on the shape of the polygon, and it
follows, therefore, that if every section of the prism were maintained by an
external cause at a permanent temperature in such a way that the law of the tem-
peratures was represented by the ordinates of any curve whatsoever of which x is
the abscissa and y the ordinate, the quantity of heat which flows according to this
assumption in a given time through a section of the prism which has reached a
fixed state, will be proportional to the tangent of the inclination of the curve, and
will have for exact measure — K(dy/dx). 9
Although the result obtained by Fourier for the heat flux in one-
dimensional flow was correct, and led to the true equations for the propa-
gation of heat for various cases beginning with that of the thin rod, the
derivation of this expression was vitiated by the division of the prism into
infinitesimally thin slices. At first sight this assumption appears to be no
HEAT IN SOLID BODIES
183
more than an idealization of the kind constantly employed in theoretical
physics from Galileo onwards. Such idealizations, however, have to be
physically realizable, at least in principle, and apart from the difficulty of
accepting the notion of a slice of non-vanishing but infinitesimal thickness
for which the temperature is everywhere the same, with the accompanying
assumption of a temperature jump between successive slices, there is the
quite unacceptable notion that all the heat transmitted to a given slice
originates from the two neighbouring slices. This focusing of attention not
on a single slice, but on a given slice in company with its two immediate
neighbours, is found without exception in all the cases considered in the
1807 memoir and was in all probability inherited from the same 'three
slice' aspect of the erroneous treatment of the thin bar in the Draft Paper 10
which in turn bears an obvious resemblance to Biot's consideration 11 of
three successive 'points' on the bar. It may have been this aspect of Fouriers
treatment of heat flow in a thin bar which gave rise to a criticism by Biot
and others that the transfer of heat was assumed to be by immediate con-
tact only. In Biot's case this particular criticism seems first to have ap-
peared in print in his Mercure de France review of Prevost's book and then
in more detail in his Traite de Physique. 12 Having discussed the condition
governing propagation of heat in a bar and the ultimate attainment of a
steady state in much the same qualitative way as in his paper of 1804, Biot
continued :
The algebraic enunciation of the preceding condition immediately furnishes a
differential equation whose integral determines, for any given time, the tem-
perature of each thermometer as a function of its distance from the source and
the temperature of the latter. 13
But the attempt to form this equation led to an 'inhomogeneity' which
could not be removed as long as one supposed
that each infinitely small material point of the bar only receives heat by contact
from the point immediately preceding it, and only transmits heat to the point
immediately succeeding it. 14
It is important to note that Biot does not claim that the inhomogeneity
difficulty is insuperable, but only that it cannot be removed by this special
'contact' hypothesis. Since this, as we have just seen, was the method
employed by Fourier in his 1807 memoir, Biot is evidently making a veiled
reference to that work.
However this immediate contact hypothesis is unacceptable to Biot for
he continues:
This difficulty can only be surmounted by admitting, as has been done by M.
Laplace, that one and the same point is influenced, not only by those which
184
EXPRESSION FOR THE FLUX OF
touch it, but by those which surround it at a small distance before and after.
Then homogeneity is re-established, and all the rules of the differential calculus
are preserved. 15
The reference to Laplace was to his treatment of the conduction of
heat in a bar given in an appendix 16 to his famous 1809 paper on double
refraction. Having — as he thought — given a successful treatment of light
based on intermolecular forces, he turned to the case of heat where he
believed an application of the same methods should have led 'by a clear
and precise manner to the true differential equation of motions of heat in
solid bodies, and of their variations at its surface' and thus 'bring back
the subject of heat into the domain of analysis'. 17 Considering that all this
had been effected by Fourier some two years earlier in a memoir which
was still being considered by a commission of which Laplace was a mem-
ber, it is not surprising that Fourier reacted somewhat angrily to Laplace's
contention. 18
Before giving his own treatment Laplace argued 19 for its necessity by
describing the inhomogeneity which arose in the treatment based on suc-
cessive sections (as in Fourier's 1807 memoir) namely, that as the heats
received by an 'infinitesimally thin' section of the bar from the sections to
the left and right of it were both of the first order, their difference, which
gave the total heat received by the intermediate section, would be of the
second order, and this would not in a finite time produce a finite elevation
of the temperature.
Laplace's method 20 — applied only to the case of a thin bar — consisted in
considering two sections at the same distance S on either side of a section at
position x. Then if u', u, and u 1 were the temperatures of the three sections,
the heat received and communicated to the middle section would (by
Newton's principle) be proportional to
k(u' — u) — k(u — u x ) = k(u' — ZU + U X ).
It followed that the total heat received and communicated by the middle
section, that is the flux across that section, was
r
kiu'-zu + u^fW&S,
where the function f(S) determined the way in which the heat action of one
section on another varied, with their separation S, R being the radius of
'sensible action' of the heat. Setting u' - zu + u x ~ (d 2 «/d* 2 ) S 2 and replacing
R by 00 owing to the rapid decrease in/(S) with increasing S, there resulted
Ax 2
/•oo
Jo
S 2 /(S)dS=ag
where a was a constant.
HEAT IN SOLID BODIES
185
Fourier refers to this implied criticism of his manner of deriving the
equation of propagation of heat in a passage in one of two letters to un-
known correspondents in which he strongly criticizes Biot for his implied
criticism of his (Fourier's) memoir :
As to the general principle about which M. Biot talks which consists in the fact
that the molecules of bodies which are immediately adjacent to each other act the
one on the other for the transmission of heat, I do not understand why one would
wish to set it up as a new truth. It has seemed inconceivable to me that the action
in question could be restricted solely to surfaces in contact, and it is evident, or so
it appears to me, that each point of an element should act on every point of
neighbouring elements. It is no less certain that when the surface of a body is
heated the heat which dissipates itself into the colder air comes not only from
the extremity of the surface, but also from points which are beneath it at a very
small distance. I can assure you that I have often employed these considerations
in my researches. But I have recognized very clearly that it was not necessary [to
employ them?] for founding the theory of heat. 21
The criticisms by Biot and Laplace of Fourier's method of deriving the
equation of propagation of heat in a bar were evidently misdirected. For
both authors ignored the fundamental fact that Fourier's derivation did not
assume that the heat interchange across a given section was proportional
to the temperature difference but to the gradient of the temperature. Never-
theless their criticisms may have had the effect of leading him to
re-examine his use of successive slices of non-vanishing but infinitesimal
thickness in his derivation of the formula for the heat flux. In any case, in
the Prize Essay the transmission of heat between successive slices has dis-
appeared, and in its place all transmission of heat is across mathematical
sections within the solid. A possible shift from this use of slice to that of
section can be seen in a marginal note to the 1807 memoir quoted above, 22
but the first full exposition of the correct treatment is found in part of the
long letter of around 1809 to an unknown correspondent, 23 possibly
Lagrange or Laplace. Nowhere else does Fourier bring out with such com-
plete clarity the impossibility of determining the equation of propagation
of heat in a thin bar — and by implication in other and more complex
cases — without a knowledge of the exact expression for the heat flux across
a given section. For 24 if z is the unknown expression for the heat flux as a
function of the distance x along the bar, then consideration of the heat
balance in the steady state for that part (slice !) of the bar between x and
x+ox gives — 8z=chy 8x, where c is the circumference of the bar, h its
coefficient of exterior conductivity, and y the temperature. In the limit as
8x — > o this gives the equation dz/dx = —chy. So that unless z was known
as a function of the temperature y the equation of the propagation of heat
186
EXPRESSION FOR THE FLUX OF
would equally remain unknown. As Fourier put it in the unpublished
Historical Precis with Biot in mind :
One sees by that which precedes that without knowing the analytical expression
of the quantity of heat transmitted one cannot form, and consequently one can-
not enunciate or apply, the equation of the linear motion of heat. 25
The remainder of the letter is largely taken up with the determination of
the actual expression for z in the case of a thin bar. For this he imagines the
solid contained between two infinite parallel planes held at different con-
stant temperatures. Once the movement of heat has been determined in
such a case it will be easy to apply the result to a slice of thickness Sx. As in
the 1807 memoir, but now in a much more sophisticated and satisfactory
way, he proves that if the temperature decreases between the two planes
'as the ordinates of a straight line' then the temperature distribution will be
steady. For consider any two intermediate sections m, n parallel to the
bounding planes. He will show that the heat flow across m equals that
across n. Therefore, the section between m and n will receive as much as it
loses. It will therefore retain its state unchanged, and the same will be true
of all other parts, and therefore for the solid as a whole. To prove that the
heat flows across sections m and n are equal he considers a part AD of the
solid which is divided at C into the equal parts, AC, CD so that m is the
section through the midpoint of AC and n is the section through the mid-
point of CD. By adding a common temperature to all the points of CD the
mutual action of 'molecules' is unchanged, and therefore the heat flow is
the same as before. But by a suitable addition the resulting temperatures of
CD can be made equal to those of AC. Therefore the heat flow across m
equals that across n. But m and n were any two intermediate sections.
Therefore the heat flow across any section must be the same, and the solid
will retain its steady state.
It remains to determine the value for this common flow of heat across any
section. In order to do this he imagines a second, equal, solid whose
bounding temperatures are in each case twice that of the first one. If p, q
are two neighbouring points on either side of a given section in the first
solid, and p', q' are the corresponding points on either side of the corres-
ponding section in the second, then evidently the heat 'action' between p'
and q' will be twice that between p and q. It follows generally that for any
two solids of the same material and of equal thickness the heat flow across
corresponding sections will simply vary as the ratio of the temperature
differences between the bounding planes. From this it follows that the
expression for the heat flow across a given section will be proportional to
the difference of the bounding temperature divided by the distance be-
tween the two planes. The multiplying factor will naturally depend on the
HEAT IN SOLID BODIES
187
conductivity of the material in question. For an infinitesimal slice Sx whose
end temperatures are v and y + Sy he deduces the heat flow across the sec-
tion at x to be — K(dy/dx). This is the required result from which the
equation of propagation of heat in a thin bar immediately follows. 26
In the Prize Essay 27 the derivation of the fundamental result for the heat
flow in the one-dimensional case is essentially identical with that given in
the 1809-10 letter. It is now prefaced, however, with some discussion 28
of the basic (Newtonian) principle on which the whole argument rests,
namely that, other things being equal, the interchange of heat between any
two molecules m, n is proportional to their temperature difference. In
Letter XIX Fourier had already presented an ingenious derivation of this
Newtonian principle based on the assumption that the transmission of heat
between two 'molecules' will be unaltered if each temperature is increased
by the same amount. For 29 let the 'quantities of heat' of the two 'molecules'
p, qbe [/and V respectively, where U— V=a is infinitely small compared
with U or V. Suppose the quantity of heat sent by p to q equals <f>(U, r)
where r is the distance between the two molecules, and that that sent by q to
p equals <j>(V, r). The mutual action tending to change the temperature
equals <j>(U, r)-<f>(V, r) or a<f>'(U, r). But if one adds the same constant
quantity AtoV and U there will be no change in the mutual action of the
two molecules. Therefore, acf>'(U+A, r) is the same as a<f>'(U, r). Therefore,
<f>'(U, r) is independent of U, and the mutual action between the molecules
is simply proportional to the temperature difference, other things (including
the distance) being equal, which is the Newtonian principle. He does not
reproduce this argument in the Prize Essay, confining himself to citing
some of the evidence in favour of the principle. Thus it would follow 30
from the principle that a common augmentation of the temperatures of all
points of a body and its surroundings would make no difference to the
flow of heat — a result so fully confirmed by experiments that it can be
regarded as an 'invariable fact'. Also 31 that if a body sufficiently small for
all its points to be regarded as at the same temperature were placed in a
medium of given constant temperature the rate of loss of heat at any
instant would be proportional to the temperature difference. This would
lead to a logarithmic law of cooling against the time, a result once again
amply confirmed by experiment. Or again, 32 if several points of a body in a
medium held at temperature zero, were originally at temperatures a, j8, y
and after a given interval of time at tempatures a', fi', y ', then if they had
been originally at temperatures ma, mp, my they would, after the same
lapse of time as before, be at temperatures ma', m/3', my'. And so the final
temperatures in the second case would be m times the final temperatures in
the first case. Once again this is confirmed by experiment, and could only
hold if the quantity of heat which passes from one molecule to another is
188
EXPRESSION FOR THE FLUX OF
proportional to the difference of the temperature between them. The agree-
ment between observation and theory for the permanent temperatures of
bars and rings, and for the movement of heat in the same bodies, and in
those of spherical or cubical form, lent additional confirmation to the
principle from which the theoretical results were deduced. This principle
'proposed by Newton, explained by Mr. Lambert of Berlin and accepted
by all Physicists' 33 might require certain corrections in the light of further
experiments, and it would then be easy to modify the form of the theory.
But up to date, no precise observations had indicated the need for such a
revision.
One respect in which the Prize Essay went beyond anything given in
either the 1807 memoir or the 1809-10 letter was in the treatment of
heat flow in the general case in which it could no longer be regarded as
one-dimensional, as in the case of a solid bounded by two infinite parallel
planes held at constant different temperatures. For this he first considers 34
the motion of heat in a prism in which the actual temperature is given by
ax+fiy + yz, the temperatures on the faces of the prism being maintained
by some exterior cause at those given by the equation. He claims that this
will represent a possible steady distribution of temperature. To see this
it suffices to compare the flow of heat across two planes perpendicular to
the direction of the z-axis at a distance c apart. The two molecules m, rri
co-ordinates (x, y, z), (x', y', z') are infinitely close together above and
below the first plane, and M, M', two similarly situated molecules with
respect to the second plane, that is with co-ordinates (x, y, z + c), (#', y',
z' + c). Evidently the distance between m, rri, and M, M' will be the same,
and from the equation of temperature distribution the temperature
difference is the same in each case. Therefore the mutual action between M
and M' will be the same as that between m and rri. This will be true of all
corresponding pairs of molecules above and below the two planes. There-
fore the heat flow across the second plane will equal that across the first,
and the same will likewise be true for planes perpendicular to the *- and y-
axis respectively. Therefore any interior portion of the prism bounded by
six planes parallel in pairs to the faces of the prism will receive as much
heat as it loses. Therefore no part of the solid can change its temperature,
so that the original temperature distribution will be a steady one.
It remains to determine the heat flow across a section of the prism per-
pendicular to the #-axis. For this he considers 35 two molecules m and rri
'infinitely close' to the given section such that the line joining m, rri is paral-
lel to the sections, and /x. is a point below the section at an infinitesimal dis-
tance lying on the perpendicular bisector of m, rri . Then since the distances
of (j, from m and rri are the same, the action of m and rri on /x will be
q{v — w) and q{v' — to) respectively, where q is a multiplying factor depend-
HEAT IN SOLID BODIES
189
ing on distance between m, rri, and fi and v, v', and to are the temperatures
of m, rri , and \x respectively. Therefore the total action of m and rri on \i will
be q(v + v' — 2w). But this latter result would be the same as if the temperature
distribution were v = A + yz. This would be true for all pairs m, rri, so that
the total heat action across the section of the part above the section on that
below the section would be the same as if temperature distribution were
given by v = A + yz. But in this case the result is known to be a heat flux
— K(8v/dz), and similar results will hold for sections perpendicular to the
x- and y-axes respectively. As for the heat flow for any temperature dis-
tribution 36 <f>{x, y, z: t) in a given solid, the temperature at a given time at
point x+8x,y + 8y,z+ 8z infinitesimally close to the point x, y, z will be
given by
This gives the same linear dependence of the variation of temperature in
the immediate neighbourhood of xyz with respect to the co-ordinates
8x, 8y, 8z relative to xyz as was assumed originally in the case of a finite
prism. It follows that the heat flux per unit area over a section perpendicular
to the z-axis will be - K{8(f>}dz) with similar results for the other two co-
ordinates. By these ingenious considerations Fourier made good in the
Prize Essay a serious lacuna in the 1807 memoir where in his treatment of
the full three-dimensional case of a rectangular prism he had simply
assumed these results without adequate justification. 37
Fourier evidently regarded his treatment of the heat flux in the Prize
Essay as satisfactory since he added no new features to it in the Analytical
Theory where the treatment 38 differs from that in the Prize Essay only in
being spelt out in greater detail for the benefit, no doubt, of less gifted
readers than in the case of the Prize Essay. However, at the time of the
renewed criticism of his work by Poisson and Biot in 1815 and 1816 res-
pectively, he brings out in rather more detail than previously his reasons for
preferring his approach to that of Laplace — as advocated by Biot and
Poisson — in which it was assumed that the propagation of heat within
bodies takes place by radiation between 'molecules' as was the case outside
bodies. To Fourier it seemed important 'not to give to the principle of
communication of heat any hypothetical extension'. For the principle
alone was sufficient to establish the mathematical theory of heat, and it was
quite unnecessary
to examine if the propagation is carried out by way of radiation in the interior of
the solids, whether or not it consists in the emission of a special matter that the
molecules interchange with each other, or if it results, like sound, from vibrations
190
EXPRESSION FOR THE FLUX OF
of an elastic media. It is always preferable to restrict oneself to the enunciation of
the general fact indicated by observation, which is no other than the preceding
principle. One shows thus that the mathematical theory of heat is independent of
all physical hypothesis ; and in effect the laws to which the propagation is subject
are admitted by all physicians in spite of the extreme diversity of their sentiments
on the nature and the mode of its action. 39
Notes
i. After the final controversy of the years 1815, 1816 and Fourier's letter to Lap-
lace. See above chapter 7, pp. 157-8.
2. For example in Analytical Theory, chapter 1, sections 4 and 7.
3. See above chapter 8, pp. 164-5.
4. Draft Paper, fol. 145V.
5. 1807 memoir, art. 17.
6. Ibid., fol. 34.
7. Ibid., fol. 36.
8. Ibid., fol. 37
9. Ibid., fol. 38.
10. Draft Paper, fol. 1 24-1 24V.
n. Biot (1), p. 317.
12. Biot (3).
13. Ibid., p. 667.
14. Ibid., p. 667.
15. Ibid., p. 668.
16. Laplace (3), pp. 291-5.
17. Ibid., p. 290.
18. See above chapter 5, pp. 101-2, for an account of Fourier's angry reaction to
the criticisms of Biot and Laplace.
19. Laplace (3), p. 291.
20. Ibid., pp. 291-4.
21. See below Letter XVII, Appendix, p. 303.
22. See above, p. 182.
23. See below Letter XIX, Appendix, p. 307.
24. Ibid., p. 309.
25. Historical Precis, fol. 158.
26. See below Letter XIX, Appendix, p. 309.
27. Prize Essay, p. 203 ff.
28. Ibid., pp. 200-3.
29. See below Letter XIX, Appendix, p. 312. By 'quantity of heat' he clearly
intends temperature.
30. Prize Essay, p. 201.
31. Ibid., p. 201.
32. Ibid., pp. 201-2.
33. Ibid., p. 202.
34. Ibid., p. 209.
35. Ibid., p. 210.
36. Ibid., p. 235 ff.
37. 1807 memoir, art. 27.
HEAT IN SOLID BODIES
191
38. Analytical Theory, chapter 1, sections 4, 7.
39- Historical Precis, fol. 158. Fourier's attitude, consistently maintained throughout
all his work in heat, makes it unnecessary to give any consideration to con-
temporary views on the nature of heat as described, for example, in Fox.
IO
MISCELLANEOUS TOPICS
1. Communication of heat between discrete bodies
Careful readers of Fourier's Analytical Theory of Heat must often have
been puzzled by the fact that the second largest section 1 in the whole work,
that on the communication of heat between discrete bodies, seems at first
sight to have precious little to do with the rest of the book. Admittedly, a
closer inspection reveals two actual connections: in the first place it is
shown 2 in this section that the result found by purely algebraic methods for
a finite number of discrete bodies arranged circularly can be made to give in
the limit the same result as that obtained in the preceding section by purely
analytical methods for the case of a continuous ring, and this could be
taken as providing an independent justification both for the latter result and,
more significantly, for the equations from which that result was derived ; in
the second place, the same limiting process leads 3 to the analytical formula
for the expansion of a periodic function F(x) of period 2tt given arbitrarily
in the interval o to 2tt in terms of a mixed series of sines and cosines of
integral multiples of *. But these two results by themselves would scarcely
justify the inordinate space given by Fourier in his treatise to this somewhat
outlandish topic. The true explanation was probably a historical one,
namely that Fourier's first researches in the theory of heat were on the sub-
ject of the transmission of heat between discrete bodies. The appearance
of a long section on the same topic in the Analytical Theory of Heat can
thus be regarded as an implicit monument to these earlier researches in
much the same way as Newton's second proof of the law of centrifugal
force in the Principia was a monument to his earliest researches in dyna-
mics. Fortunately for historians of science, Fourier had a lively historical
sense and no inclination to cover up his traces by the destruction of early
drafts of his finished work, and it is therefore appropriate to find a section
on the transmission of heat between discrete bodies in the early Draft
Paper.
The treatment there, 4 as far as it goes, is identical with that given
from the 1807 memoir onwards. Thus he first considers two equal bodies
mass m of perfect conductivity at different temperatures a and b, and
imagines a transmission of heat between them by means of an ingenious
ideal shuttle mechanism consisting of an infinitesimally small section dm
which moves to and fro in a fixed time dt between the two masses. By
MISCELLANEOUS TOPICS
193
entirely clear and straightforward assumptions he then shows that, to the
first order of small quantities, the changes in the temperatures of the two
bodies from their original values a, B at any time t as a result of a complete
to and fro motion of the shuttle are given by
da =
(a-B)
m
dm, d/J
{a-B)
m
dm.
Putting k = dmjdt 5 he obtains
da = - i ^- dt, dB = i £2- dt
m m
and argues that k can be taken as a measure of the speed of transmission of
heat, or reciprocal conductivity, between the two bodies since it increases
as dm increases or dt decreases. Putting a — B=y
dv = — 2{kjm) y dt,
y = (a — b) exp ( — zkt\m),
where a and b were the initial values of the temperatures of two bodies,
and it is assumed silently that a is greater than b. It follows that
a = %(a + b) + %{a — b) exp ( — zktjm),
B = %{a+b)-%{a-b) exp (-zktjm).
Therefore as the time increases both bodies tend to the same common
temperature \{a + b) which they would have acquired according to the
accepted theory of specific heats if they had been put in direct permanent
contact at the beginning.
Having given a complete solution for the case of two discrete masses,
Fourier proceeds 6 to consider the general case of n separate equal masses
arranged in a straight line and initially at arbitrary temperatures a, b,
c, . . . in which transmission of heat takes place by the same shuttle
mechanism between successive bodies as in the case of two bodies only. By
precisely similar arguments he finds that the first-order changes of tem-
peratures of the masses which at the beginning of a new round of heat
transmissions were a, B, y, 8, . . . , i/r, a> are given at the end of a complete to
and fro movement of the shuttles by
a-B
m
dm,
B+ {(°-V Z (P-r)} dm _^ + (±^ dm;
m
m
He proceeds to look for a normal mode solution 7 of the form
a = a x exp {hi), B = a 2 exp {hi), . . . , 00 = a n exp {hi).
19 4 MISCELLANEOUS TOPICS
The corresponding equations for the coefficients a lt a 2 , . . . are then
a = a x
a x = a ±
a 2 = a x (q-\-2)-a
"a = «2(?+2)-fli
«n + l = «n(? + 2)-«n-l
where
<7 = Am/£,
a recurrent series whose solution may be written in the form
a m = A sin mu + B sin (m — i)m.
Putting M? = o and i gives a = — B sin u and a ± = A sin w. Therefore
a m = . * {sin mu — sin(#z — i)m).
sin m
On substituting this solution in the general term he then obtains q =
2(cos u— i). Equating a n+1 = a n then gives sin nu = o yielding n different
eigenvalues
ttj = iir/h, i = o, i, . . . , n— i.
The general solution of the original set of equations is then obtained by
combining arbitrary linear combinations of the special solutions and he
shows that as t — >■ oo this always tends to the mean initial temperature.
This general solution for the case of heat communication for a finite
number of separate bodies is followed (as in the Prize Essay and the
Analytical Theory of Heat) by the comment that as the number of bodies
tends to infinity, u — > o and the term {sin mu — sin {m — i/«}/sin u tends to
cos mu.
At this point, however, there is a significant difference between the Draft
Paper and the 1807 paper or the Prize Essay. In the draft he gives 8 an in-
complete and unconvincing attempt to apply the above limiting solution
to the case of a continuously heated line for which he suggests an equili-
brium temperature distribution varying as cos x at distance x, a result
which would appear to have been introduced in Fourier's handwriting
after the original composition of the draft. He concludes :
the analysis which we have employed could be used to determine the laws of the
propagation of heat in bodies of several dimensions. But this transition from the
solution which is appropriate to a finite number of bodies to an infinitesimal
solution (if we can speak thus) requires complicated calculations. 9
MISCELLANEOUS TOPICS
195
In the 1807 memoir 10 and beyond he repeats the analysis of the n body
problem almost word for word and symbol for symbol up to the point
where consideration is given to the passage to the limit of n -> 00. He
notes again that u — > o and {sin mu — sin (m— i)u}/sm u — s- cos mu, but now
he only considers the first term of greatest order depending on the time
derived from u^Trjh which gives the difference between the final tem-
perature (2 ajh) and the actual temperature for large values of t. The dis-
crete bodies can now be imagined to be arranged around the semi-peri-
meter of a circle, the angular position of body r being m/n (see Fig. 1).
The body 'in the middle' (that is nearest to njz) reaches the mean tem-
perature most quickly, while all those on one side of it exceed the mean
temperature, all those on the other side of it are less than the mean tem-
perature, the time dependence of all being the same. He has evidently
wisely given up the attempt of the Draft Paper to make a transition to the
case of a continuous rod, while he is equally 'half way' towards considering
Fig. 1
the problem of a number of bodies spaced equally round a circle to which
he immediately turns his attention. 11
Once again the transmission of heat takes place by the usual shuttle
mechanism. But now there is a vital difference between the earlier treat-
ment of the same number of masses in that the last mass communicates
heat with the first. In other words the circle is closed, which makes a
fundamental difference to the equations of motion and their solution.
After the end of a further to and fro movement at time t, the first-order
changes in the temperatures of the bodies which at the beginning of this
movement were a f , i= 1, 2, . . . , n are given by
&&! = (klw)(a n -2a 1 + a 2 )dt
da ( = (k/w)(a { _ i - 2«,+ <x <+ i) dt i = 2, 3, . . . , n - 1
da n = (*/»)(«„_! -2a n + a 1 ) dt,
where w is the mass of the shuttle and k = w/dt. The same normal mode
solution <>!,= £( exp (ht) is attempted as before which once again yields a
196
MISCELLANEOUS TOPICS
recurrent series. The solution of this series can be expressed in one of n
different forms
b, i = sin*M,l , ., .
j iyj = simuj
= cos iui
where
and
u i = *■"{)- J )l n > J = i, 2, . . . , »,
h } = (2k/m)(cosUj—i).
Any linear combination of the normal mode solutions is also a solution
giving finally a most general solution :
f zkt 1
a, = V (Aj sin (t — i)uj + Bj cos (i— i)m ; ) exp < (i — cos u,) >■
i = i, 2, — n
To complete the solution it remained to determine the values of A jt B jt
j = i, 2, . . . , n, in terms of the initial values a l3 a 2 , . . . , a n of c^, a 2 > • • • > <V
By an elementary though rather subtle argument he shows 12 that contrary to
appearances there are only n different constants to be determined. These
he obtains by setting the time equal to zero, multiplying each equation by
an appropriate sine or cosine term, and adding, when all the sums on the
right-hand side go out except the term involving the constant whose value
is to be determined.
After considering two particular examples of no great importance, he
proceeds to consider 13 the passage to the limit of infinitely large n carried
out in such a way that nm = 2n where m is the mass of each body. In place
of separate masses he sets elements of length 8x. The initial temperatures
a u a 2 , ■ ■ ., a n become an arbitrary function of * where x is the distance
along the arc. The following substitution is then set up :
n m k a { i a ; - j
zrrjbx Sx Trh*l8x <f>(x) x/8x ifi(x, t) x/Sx
After some straightforward reduction including the replacement of sums
by integrals this leads to
a i -> ^{x, t) = — (j>(x) dx+ ^ - \ (I <f>( x ) sinjx dx\ sinjx
+ 1 <f>(x) cosjx dx J cosjx > x exp ( —j 2 irgt)
* h is the value of k when there are only two bodies. See Fourier's discussion of
this on fol. 138 of the 1807 memoir.
MISCELLANEOUS TOPICS
197
Putting hir = K gives identification 14 with equations already obtained
for non-steady motion in a thin ring based on purely analytical considera-
tions, provided — and Fourier omits to point this out — the exterior con-
ductivity is set equal to zero, i.e. provided there is no exterior radiation.
For Fourier this identification showed that it was not necessary to have
recourse to the analysis of partial differential equations to determine the
propagation of heat in a ring: one could solve the problem for an infinite
number of bodies and let the number tend to infinity. According to
Fourier this approach had a clarity which was peculiar to it and which
directed the first researches'. 15 It brought out the 'separateness' of the
particular values satisfying the partial differential equation which made up
the general solution.
He notes 16 finally that on putting the time equal to zero in the general
equation the formula obtained is that which he had already obtained for the
decomposition of a function arbitrary in the interval o to 277 and periodic
of period 2w into a sum of cosines and sines of multiple arcs.
2. Terrestrial heat
Fourier published three papers on the subject of terrestrial heat. The
first was published in the Prize Essay of 181 1 17 and in company with the
treatment of radiant heat was one of two substantial additional sections in
that work compared with the 1807 memoir. The other two papers on the
same subject were published in 1820 18 and 1824 19 respectively. The latter
work was largely expository in character and added nothing essentially
new. It will not be considered separately from the first two which for con-
venience will be referred to as papers I and II respectively.
On several occasions Fourier maintained that from an early stage he
regarded the problem of terrestrial heat as one of the most important
which could be treated by the Analytical Theory of Heat and even one
which he had had principally in view in establishing the theory. 20 In the
introduction to paper I Fourier lists the various effects to be considered. In
its diurnal motion, and its passage round the sun, the surface of the earth
experiences a variation in temperature due to the effect of the sun. These
two motions together produce periodic movements in the temperature at
any given point of the surface. Observation shows that these oscillations
rapidly die out at quite a short distance beneath the surface where the tem-
perature becomes effectively constant. On the other hand, this constant
temperature is different for different latitudes, an effect due to the inclina-
tion of the axis of the earth to the ecliptic. There are therefore two prob-
lems to be considered. The first is concerned with periodic changes in
temperatures at a point of the surface. The second is concerned with
198
MISCELLANEOUS TOPICS
changes in temperature from one latitude to another. Fourier considers these
two problems separately. In the first place he considers 21 the problem of
temperature variation in a vertical line given that the surface point is
subject to periodic variation. And in the second case 22 he considers the prob-
lem of variation in temperature with latitude under the surface envelope of
the earth due to the existence of the poles, that is, due to the fact that, regard-
less of small variations, the temperature at the north and the south poles is
always extremely low, whereas that nearer the equator is always much
higher.
To consider the first problem Fourier takes the equations of motion of
the movement of heat in a sphere derived earlier in the Prize Essay, 23 and
ignores the term containing the reciprocal of the distance u from the centre.
This approximation will of course only be true at very great distances
from the centre, but it will be justified in this particular problem since
he is considering a sphere, the earth, of a very great radius. When this
term has been dropped it follows that the equation of motion
dv _ , 8 2 v
is that for a line or an infinite prism. He now looks for a solution to this
equation which is periodic in the temperature.
He suggests 24 the solution
v = a. exp (—gu). cos (2g 2 kt—gu).
It is easy to check that this in fact does satisfy the equation. Likewise for
sine in place of cosine. This solution must be periodic in the time, and if d
is the period of the variation in question then we must have
2g r 2 kd = zriT (r integral)
The general solution is obtained by combining all such special solutions for
all allowable values of the g's, including g=o:
v{t, u) = a+ 2 exp (-g r u).{a r cos (2g 2 kt-g r u) + b r sin (2g 2 kt-g r u)}.
Evidently all non-constant terms fall off rapidly with increasing distance
below the surface. So that at a short distance one can confine oneself to the
first non-constant term. The coefficients of the various terms are easily
obtained by supposing v(t , u = o) = <f>(t ) is known and then in the usual way
multiplying by an appropriate trigonometrical term and integrating over
the period of the variation. It follows 25 from this that the constant
MISCELLANEOUS TOPICS
199
term is equal to the mean temperature at the particular point of the surface.
It is this mean surface temperature which the temperature in the interior
rapidly attains with increasing distance below the surface owing to the
rapid fall off of all the other terms.
In order to compare theory with experiment it would be necessary to
insert particular values for the interior conductivity. He takes 26 the case of
iron for which substance these parameters have been determined by
experiments based on the Analytical Theory of Heat, namely with a ring
and with a cooling sphere. By comparing the results obtained this leads to
an approximate value K= 3/2 for iron. 27 The values for the specific heat C
and D the density are approximately 5/24 and 7800 respectively. Inserting
these values he finds that at a depth of 2-3025 metres and assuming a value
for 6 equal to 1440 minutes (that is for the diurnal variation) then the value
of exp ( — g x u) is about 1/100. Consequently at a depth of 2*3025 metres the
diurnal variations are very small. In the case of the annual variations for
which 0=365 x 1440 it is easy to see that the variations are practically
insensible at a depth of about 60 metres. As for the earth itself, whose
interior conductivity is much less than that of iron, the variations would
penetrate to much smaller depths both for the annual and the diurnal
variations, and this in fact is found to be the case. And thus the observations
which had been known for a long time are explained in terms of the theory.
As Fourier puts it: 'If these facts had not been known they would have been
deduced as simple and obvious consequences of the general equation which
we have put forward.' 28 He then goes on to consider the question of heat
loss at the surface and restricting himself to the first of the periodic terms
by straightforward and obvious calculations based on the expression for the
heat flux he deduces that regardless of particular values of the parameters in
question the heating of the surface commences one-eighth of a year before
the temperature of the surface has reached its mean value, and the cooling
of the surface begins one-eighth of a year after the temperature of the sur-
face has again fallen to its mean value. For the particular case of iron, he
also calculates the approximate amount of heat which passes in the course
of half a year from the atmosphere to the interior of the earth over a given
area of one square metre, and finds that it would be equivalent to that
which would melt about 2856 kilograms of ice or a column of ice having a
base area of one square metre and a height of 3-1 metres.
He now turns 29 to consider the quite different problem of the steady
distribution of temperature in the interior of the earth due to the existence
of the poles, that is due to the unequal heating of the surface of the earth
by the sun.
He assumes that the temperature at any point of a given sphere is a
function only of its distance (y) from the axis, and its distance (x) from the
200
MISCELLANEOUS TOPICS
v = cos nx
plane of the equator. In terms of these variables the steady-state equation
becomes :
8 2 v 8 2 v i 8v
dx 2 By 2 y dy
He shows that a particular integral of this equation is given by
exp (ny cos r) dr
where the parameter n is undetermined. The general solution is then
obtained by a superposition of all possible particular solutions for different
possible values of the parameter n. He studies the heat balance correspond-
ing to this particular result, showing that the heat at any particular point
flows perpendicularly to the parallel towards the poles, and that this loss
of heat is exactly compensated by a flow of heat inward towards the axis. In
general therefore the heat penetrates by parts near the equator and is
dissipated at the poles.
In the introduction to paper II 30 Fourier goes over previous ground
sorting out the various problems which go to make up the total problem of
terrestrial heat. He explains how the problem of terrestrial heat can be
divided up into three parts :
i. The action of the sun's rays produces oscillations in the surface
Jayer. Below this the temperature is constant in a vertical line to a great
depth and equal to its mean value at the surface multiplied by a
decreasing factor involving the distance from the surface. During part
of the year the earth loses heat to space and during part of it it gains it
back again.
2. The motion of heat in the interior, that is away from the surface layer,
consists of a slow flow — very much slower than the periodic changes —
from the equator inwards and then upwards towards the poles. This
was the second problem treated in paper I.
3. There is also a flow of heat due to the primitive store of heat in the
earth. This corresponds to the secular cooling of the earth. It is
evidenced (according to Fourier) by an increase of temperature as
one descends deeply into the earth. It is this effect which is considered
in paper II.
The idea is to approximate to the surface of the earth, or a particular
region of the surface of the earth, by an infinite slab at whose free end there
is a surrounding medium corresponding to the air at temperature zero.
Initially the temperature distribution in the slab as a function of the
distance u from the free end is given by an arbitrary function F(u). The
MISCELLANEOUS TOPICS
201
.F'(a) > sin ^>a . da,
problem is to find how the temperature changes with the time. His
solution 31 to this problem is as follows :
, , , C x exp(-p 2 Kt/CD) (h .
v = (^ J p 2 + h 2 IK* \K SmpU+P C ° SpU .
where p is a variable of integration, and h is an exterior conductivity.
He then investigates a number of special cases. In the first case he
assumes that the temperature is constant and equal to a value b up to a
depth A and thereafter is zero. In the second case he assumes the tempera-
ture is b everywhere up to an infinite distance. In the second case he
investigates the variation of the temperature at the surface. By means of
an ingenious transformation of the integral, he shows that for large values
of the time t the surface temperature is approximately given by the for-
mula 32
v = (blh)V(CDInKt)
He notes that exactly the same approximate formula would be obtained
from the solution for a sphere when the radius is very large and for large t.
Once again it is impossible to make a proper comparison between theory
and observation since the values for the parameters in the case of the
earth are unknown and in any case there is reason to believe that at great
pressure these equations would have to be altered. But by taking the values
for iron one can get an idea of the correct order of magnitudes. The paper
ends with a number of 'consequences' 33 all concerned with the primitive
heat of the earth and its gradual loss by radiation at the earth's surface. If
there had been no such primitive heat then the temperature at great depths
would either be constant (if the permanent heating of the earth by the sun
were completed) and otherwise would decrease. The fact that the tem-
perature actually increases at great depths argues powerfully in favour of
the existence of a primitive heat in the earth. An important factor in the
cooling of the earth is the actual temperature of surrounding space disre-
garding the heat of the sun. The excess, v, of the surface temperature of the
earth over that of surrounding space has a necessary connection with the
rate of increase of temperature with depth at the surface, (8vj8x) x = ,
namely,
K{8vj8x) xss0 + hv = o.
For iron, an increase of one degree in 30 metres would correspond to the
temperature of the surface being J degree above that of surrounding space.
Lacking parameters for this earth the excess of its surface temperature over
that of surrounding space can only be estimated roughly but it is in any
202
MISCELLANEOUS TOPICS
case very small. From the theory it is possible to deduce a formula for the
time of cooling of the earth in terms of the rate of temperature decrease at
the surface and the original temperature of the earth, and also a formula for
the rate of cooling of the surface temperature in terms of the time of cooling
and the rate of decrease of temperature with distance at the surface. From
this latter formula it appears that the rate of cooling at the surface is now
excessively small and in any case less than 1/57 600 of a degree per century.
The smallness of the residual effects due to the primitive heat of the earth
are in striking contrast to the much larger effects produced by changes in
surface conductivity due to natural and human causes, the height of the
sun, presence of waters, direction of winds, etc. It is these accidental
effects which Fourier considers to be responsible for the difference of
climates in the two hemispheres. On the other hand, in spite of the small-
ness of the observed effects due to a residual primitive heat of the Earth it
still leads to a vast loss of heat by radiation at the surface and may still be
associated with a very elevated temperature at the centre.
Fourier ends this paper by contrasting the paucity of observational
material on the values for terrestrial parameters with the certainty of the
Analytical Theory of Heat from which all consequences relating to the
earth must be derived and which is independent of any supposition regard-
ing the actual nature of heat itself.
Paper III, 34 in which Fourier is inclined to ramble from one topic to
another, and which is lacking in any definite structure, is largely an expo-
sition in general non-mathematical terms of the results obtained in the
two earlier papers. It does, however, give a much more detailed discussion
of the notion of interplanetary temperature. 35 He suggests that the exis-
tence of a temperature of interplanetary space different from absolute zero
is due to heat reaching the solar system from the innumerable stars sur-
rounding it. If these stars were absent, so that only the sun and the planets
were in the skies, then the phenomena would be very different from those
observed. Thus when the sun went down the temperature at the surface of
the earth would suddenly drop to absolute zero. The slightest changes in
the distance of the sun or the eccentricity of the orbit of the earth about the
sun would produce major changes in the climate. The fact that these
changes do not occur is due, according to Fourier, to the existence of an
interplanetary temperature different from absolute zero.
3. Radiant heat
Fourier published a total of five papers 36 on the subject of radiant heat.
The first, and much the most important, of these was given in sections
89-100 of the Prize Essay. The other papers published at various later
MISCELLANEOUS TOPICS
203
dates are concerned largely with a further exposition of the ideas contained
in the Prize Essay or with the discussion of explanations of experimentally
observed results, and add little new to the original paper. They will only be
referred to insofar as they clear up certain obscurities in that paper. In the
second part 37 of his Historical Precis Fourier traces the historical back-
ground of the experimental work in the subject preceding his own theo-
retical investigations in the Prize Essay. Among other works he cites certain
by Leslie, Pictet, and Prevost. Probably Prevost's work was the most
important for Fourier since it contained one of the basic assumptions on
which Fourier's own work was based, namely, that if a body surrounded by
other heated bodies maintains its temperature unchanged it must receive as
much heat by radiation from the surrounding bodies as it loses to them by
its own radiation.
The Prize Essay paper is concerned essentially with two topics.
1. The law connecting the intensity of emission of radiant heat from a
heated surface with the angle of emission.
2. Allowance for partial reflectibility and partial emissivity of radiation in
the case of thermal equilibrium between a number of bodies in a
hollow container whose surface temperature is given.
Fourier approached the law of emission from three separate standpoints.
From the experimental side it had been shown by the experiments of
Leslie that within the limits of experimental error the intensity of heat
radiation emitted from a given surface varied with the sine of the angle
of inclination of the radiation to the surface. From the theoretical side the
law could be approached in two different ways. In the first place, one could
attempt to derive it from the experimentally observed fact that in equili-
brium the temperature of a body always took up the same value as that of its
surrounding container. Fourier based his derivation 38 of the law here on the
additional assumption that the total heat radiated per unit time from an
element of surface, area S, temperature a, was aSh where h would be a con-
stant characteristic of the surface in question. He then introduced an
angular dependence of the radiation emitted by the introduction of a
function .F(sin </)) so that if all the radiation were of the same intensity as
that making an angle <f> with the surface, the total radiation emitted per
unit surface area would be G = agF (sin <f>), where g is another constant. It
followed that the actual amount of radiation emitted per unit surface area
would be ag fg' 2 F(sin <f>) cos <f> d<f>. So that h=g fg' 2 .F(sin <j>) cos <f> d<j>.
At this point 39 Fourier made a considerable deviation to prove that if the
intensity of emission were in fact proportional to sin </>, then bodies placed
within different enclosures would ultimately take up the same temperature
204 MISCELLANEOUS TOPICS
as the enclosure. However, if this law did not hold then in certain other
cases this result would not follow.
Having thus provided some evidence in favour of the assumption
F(sin (j>) ~ sin <f> he returned 40 to the general case of a body within a given
enclosure at a certain temperature. By considering two surface elements
S, a, one, a, belonging to the body at temperature a, and the other, S,
belonging to the surface of the container also at temperature a, he showed
that the radiation sent from the first to the second would be
agSoF (sin cf>) sinpjziry 2 ,
while the radiation sent from the second to the first would be
agSaF(sin p) sin <j>J2Try 2 ,
where y was the distance between the two elements and <f>,p were the angles
which the line joining the two elements made with S, a respectively. For
the heat sent from the first to the second to be equal to the heat sent from
the second to the first it was necessary for F(sinp) sin <f> = F (sin <j>) sin p.
For this to be true of all such pairs of elements the function .F(sin <f>) would
need to be proportioned to sin <f>. This is the sine law, but it is clear that
Fourier has not proved its necessity based on the single initial assumption —
itself a physical fact — that in equilibrium the temperature of the body must
be equal to that of the enclosure in which it is placed. In addition he has
had to make a much more serious assumption of a detailed balance of
radiation between any surface element of the body and any element of the
surrounding surface. Nor can Fourier's assertion that 'it is easy to see that
the equality of the two reciprocal actions is precisely that which constitutes
the equilibrium of temperature' 41 be accepted.
The second method 42 of deriving the sine law of theoretical means was
based on ingenious 'molecular' considerations. He supposed that all the
interior layers of an emitting surface contributed to the emission of heat
from the surface, but that owing to an extinction effect they contribute ever
less as one proceeds away from the surface into the interior of the body.
This results from the fact that any point within the body emits radiation
with the same intensity in all directions, which falls off, however, with the
distance from the point in question. It follows that radiation emitted in an
oblique direction from a point within the body will have further to travel
before reaching the surface and will therefore be less intense on emerging
than will be the case for radiation directed perpendicularly to the surface. He
puts this idea on a quantitative basis (see Fig. 2). He lets 0(a) express the
contribution at a point O of the surface of the radiation emitted from a point
Q within the solid at distance a from O. The assumption of a cut-off
implies that O(a) = o for a ^ a. Then the whole line om (see diagram) con-
MISCELLANEOUS TOPICS
O P
205
Fig. 2
tributes at O an intensity perpendicular to the surface of amount J" 0(a) da.
But for a point Q on Om at a distance a from O the contribution at P in an
oblique direction <j> will be 0(a/sin<£). Therefore the total contribution
from Om at the surface in oblique direction <f> will be
/•a/sin <t> = a
0(a/sin <j>) da.
J a/sin d>-0
Putting a/sin <f> = P this gives 43
sin0. To^djS
which is proportional to sin <j> as desired.
4. Movement of heat in fluids
Fourier presented a memoir 44 on the motion of heat in fluids to the
Academie des Sciences and read an abstract of it to the Academie in the
usual way. This was printed in the Memoires of the Academie along with
notes on the subject found among Fourier's papers after his death by
Darboux. The essence of Fourier's argument amounts to a correction of
the normal equation of propagation of heat in solids, namely
cee/dt = kv 2 8
by a term to take account of transfer of heat by conduction. Assuming
that the amount of heat in a volume V of the fluid at temperature 8 is CV
where C is the constant value of the specific heat per unit volume, Fourier
206
MISCELLANEOUS TOPICS
finds by the usual argument that the rate of gain of heat due to convection
in an elementary box of side 8x, 8y, 8z at x, y, z will be 45
where v x , v y , v z are the components of fluid velocity. Assuming that the
transfer of heat by conduction and convection act independently it follows
that the equation of propagation of heat is given by
VI,S,2 J
Characteristically he derives the same result by slightly different con-
siderations. 46
5. Papers not on analytical theory of heat
Apart from his work on the analytical theory of heat, Fourier published
only two papers on other topics in theoretical physics. The first was a
paper 47 of 1798 on the principle of virtual velocities. In it Fourier attempts
to deduce this principle from the principle of the lever which he in turn
deduces from the assumption that three equal, and equally inclined, con-
current forces are necessarily, and self evidently, in equilibrium. This is
the central object of the paper but there is also some additional discussion
of the application of the principle of virtual velocities to the movement of
fluids and the oscillation of systems of bodies about positions of equilibrium.
A short study of this paper has been given by Costabel 48 who is of the
opinion that apart from its undoubted interest and freshness of approach it
would be impossible to assess its true originality, importance, or influence
without a careful historical study of the whole subject including the con-
tribution of Fourier's predecessors and contemporaries.
The other published paper 49 on theoretical physics was on the subject of
wave motions in elastic laminae. Fourier does not concern himself here
with the derivation of the basic equation, and the paper is of purely mathe-
matical interest.
Notes
1. Analytical Theory, chapter IV, section 2.
2. Ibid., pp. 293^7.
3. Ibid., p. 297.
4. Draft Paper, fol. 109-23.
MISCELLANEOUS TOPICS
207
This argument and all subsequent uses of it by Fourier, is open to the criticism
that although dt is the time for a single to and fro shuttle movement it is later
regarded as a variable differential of the time for the purpose of integration.
This difficulty can be avoided as follows. Let At be the fixed time for a to and
fro shuttle movement. Then, as before,
a (*-*>) ,,
da&t = dm,
db At = dm.
For a time dt small compared with unit of time but large compared with At
the change of temperature would then to the first order be
da = —
(a
-b), dt
dm . -T-'
m At
,, (a-b) , dt
do = dm -j—
m At
If now we put K/dm= i/At that is dm\Cu = K it follows that
da= _(£Z*L> X dt,
db = ^Z^ K dt,
9-
10.
11.
12.
13-
14-
IS-
16.
17-
19.
20.
21.
22.
23'
24-
25-
26.
and we only need assume this give a sufficiently good approximation to the
differential equations.
da/dr = -(fl-b)K/m, db/dt = (a-b)K/m.
Draft Paper, fol. 113 ff.
This, he notes, is the usual solution, so that he must have been familiar with at
least this aspect of discussion of the string problem in the eighteenth century.
Draft Paper, fol. 12 1-3.
Ibid., fol. 123.
1807 memoir, arts. 3-5.
Ibid., arts. 6-13.
Ibid., art. 10.
Ibid., arts. 95-6. Fourier only returns to the question of the passage to the
limit after obtaining a solution for a ring by analytical means in arts. 76-
94. His treatment of the limiting process is very beautiful.
Ibid., fol. 140.
Analytical Theory, p. 296.
Ibid., p. 297.
Prize Essay, arts. 80-8, 'Des temperatures terrestres et du mouvement de la
chaleur dans l'interieur d'une sphere solide, dont la surface est assujettie a des
changements periodiques de temperatures', Oeuvres, 2, pp. 3-28).
'Le refroidissement seculaire du globe terrestre.' Bull, des Sci. par la Societe
Philomatique de Paris (1820), 58-70 (Extract in Oeuvres, 2, pp. 271-88).
'Remarques generates sur les temperatures du globe terrestre et des espaces
planetaires'. Ann. Chimie Physique, 27 (1824), pp. 136-67 {Oeuvres, 2, pp. 97-
125)-
See Oeuvres, 2, p. 114.
Ibid., pp. 5-20.
Ibid., pp. 20-8.
Prize Essay, art. 44.
Oeuvres, 2, p. 8.
Ibid., p. 11.
Ibid., p. 14.
H
208 MISCELLANEOUS TOPICS
27. Idem.
28. Ibid., p. 16 ff.
29. Ibid., pp. 20-8.
30. Ibid., pp. 271-3.
31. Ibid., p. 275.
32. Ibid., p. 277.
33. Ibid., pp. 282-8.
34. Oeuvres, 2, pp. 97-125.
35. Ibid., pp. 106-8.
36. 'Note sur la chaleur rayonnante'. Ann. Chimie Physique, 4 (1817), pp. 128-45
{Oeuvres 2, pp. 331-348); 'Questions sur la theorie physique de la chaleur
rayonnante*. Ibid., 6 (1817), pp. 259-303 {Oeuvres, 2, pp. 349-86); 'Resume
theorique des proprietes de la chaleur rayonnante'. Ibid., 27 (1824), pp. 236-81
{Oeuvres, 2, pp. 387-424); 'Remarques sur la theorie mathematique de la
chaleur rayonnante'. Ibid., 28 (1825), pp. 337~65 (Oeuvres, 2, 425-49).
37. Loc. cit., fol. 163-8V.
38. Oeuvres, 2, pp. 29-46.
39. Ibid., pp. 32-43-
40. Ibid., p. 43.
41. Ibid., p. 45.
42. Ibid., p. 54 ff.
43. Ibid., p. 57.
44. 'Memoire d' Analyse sur le Mouvement de la Chaleur dans les Fluides'. Mem.
Acad. Roy. Sci., xii (1833), pp. 507-30. It is reproduced in Oeuvres, 2, pp.
595-6I4-
45. Oeuvres, 2, p. 606.
46. Ibid., pp. 607-9.
47. 'Memoire sur la Statique contenant la Demonstration du Principe des Vitesses
Virtuelles et la Theorie des Moments'. Journal de l'£cole Poly technique, Cah.
5 (1798), pp. 20-60. Oeuvres, 2, pp. 475-521.
48. Costabel, P. 'Fourier et le Principe des Vitesses Virtuelles'. Sciences, 3,
pp. 235-8.
49. 'Note relative aux Vibrations des Surfaces Elastiques, et aux Mouvement des
Ondes'. Bull. Sci. par la Societe Philomatique (1818), pp. 129-36. Oeuvres, 2,
pp. 257-67.
EPILOGUE: FOURIER THE MAN
AND THE PHYSICIST
1. Fourier's achievement as a physicist
Fourier was an experimental as well as a theoretical physicist. We know 1
that he spent two years prior to the publication of his 1807 memoir in
repeating all previous experiments in connection with heat conduction,
and adding some new ones of his own. His experiments were admittedly
not creative in the sense of leading to new discoveries and theories in the
manner, for example, of Faraday or Ampere. Instead he used them to con-
firm his theory, to give it 'an authority which one would have been inclined
to refuse it, in a subject which is still obscure and subject to so many
uncertainties'. 2 Nevertheless, one cannot refuse the title physicist to Fourier
in the sense of a scientist who is involved with physics at first hand on one
or other or both of the experimental or theoretical sides. For the term
physicist does not exclude theoretical considerations, and these in turn
need not necessarily be cast in a mathematical form ; the example of Fara-
day, though very exceptional, is sufficient to establish this point, for nobody
could deny that Faraday was a great theorist though he certainly was not a
theoretical physicist in the usual, mathematical, sense of that term.
Fourier, on the other hand was obviously, and pre-eminently, a theoretical
physicist in just this sense. To assess his achievement as a theoretical
physicist would therefore inevitably entail a judgment on his achievement
as a mathematician. But this would fall outside the terms of reference of the
present work in which I am only concerned with Fourier the mathemati-
cian in so far as this is necessary for an understanding of Fourier the
physicist. The present section will therefore be concerned with Fourier's
achievement as a (theoretical) physicist on the physical side, the mathe-
matics involved being all of a trivial nature — as opposed, of course, to the
ability to apply this mathematics, an entirely different matter.
In the light of what has been said above little or no account need be taken
of the 1798 paper on virtual velocities. For this paper is a part of mechanics,
contains no new principles, and is chiefly interesting for the ingenuity which
Fourier displays in attempting to derive the principle of virtual velocities
from other, and supposedly, more basic principles. In any case, a thorough
investigation would be necessary 3 before any sort of reliable judgment
could be made on the originality, importance, and possible influence of
this paper. Fourier's work on elastic surfaces will also be ignored on the
grounds that he himself played no part in the derivation of the basic
210
EPILOGUE
equation of motion, his own contributions to the subject being purely on
the mathematical side. The papers on terrestrial and radiant heat merit
more careful attention, especially the latter. Those on terrestrial 4 heat are
all based directly on the equation of propagation of heat in solid bodies.
As such they fall essentially under the heading of mathematical physics or
even applied mathematics. Nevertheless they are interesting from a
physical point of view. Thus they provide useful evidence of Fourier's
ability to deal with a problem which is essentially complex by reason of the
number of physical factors involved including the interior heat of the earth,
the loss of heat at its surface, the heat received from the sun, the effects of
both the diurnal and annual rotation, the influence of the seas, and so on.
Fourier's approach to this very complex problem was based on a number
of extremely bold idealizations. These have been criticized as unrealistic,
but at the same time they provide excellent evidence for Fourier's pos-
session of what seems to have been one of the prime ingredients of true
creativity in theoretical physics from Galileo onwards. Again, the papers
on terrestrial heat display another attitude characteristic of the creative
theoretical physicist, Fourier's awareness 3 that he was concerned with
problems in which progress would ultimately depend on the collection of
new observations and a continued interplay between theory and obser-
vations: the theory controlling the observations, and the observations
leading to a gradual expansion and deepening of the theory. So that
although his instinctive approach to this and other problems was through a
very bold process of idealization, there was never any danger of him being
carried away by the resulting theory. As regards physical problems,
Fourier the mathematician was always very firmly under the control of
Fourier the physicist who never lost sight of the need for a final appeal to
observation.
More immediately relevant than his papers on terrestrial heat to
Fourier's achievement as a physicist was his work on radiant heat. 6 Here
there was no mathematical connection with, or use of, the basic equations
of propagation of heat. This was a case of Fourier breaking entirely new
ground by laying the mathematical foundations of a subject in which all
previous work had been entirely experimental. His major achievement in
the field was undoubtedly his derivation of Leslie's experimentally deter-
mined 'sine law' for emission of radiation at the surface of heated bodies.
He gave two derivations 7 of this law, one based on a principle of detailed
balance, the other based on 'molecular' considerations. Both derivations
display Fourier's physical understanding and mathematical ingenuity in a
flattering light. This work is certainly original and creative ; what is quite
uncertain at present is its importance historically by reason of its influence,
if any, on successors such as Kirchhoff or Stefan. Given Fourier's great
EPILOGUE
211
reputation in the mid-nineteenth century one would be inclined to assume
that any work of his in radiant heat must have influenced all later work in
the subject. But against this it must be remembered that there is almost
nothing on radiant heat in the Analytical Theory of Heat itself, and it is not
clear to what extent, if at all, his other published work was influential apart
from the very special case of William Thomson, 8 Lord Kelvin, who seems
to have had a peculiarly detailed knowledge of Fourier's work as a
whole.
Of the cases considered so far the only one in which there was no doubt of
an original, creative contribution by Fourier was that of radiant heat. But
the physical aspect here was perhaps rather less prominent than the mathe-
matical. Thus it must be remembered that in the case of the 'sine law' for
emission of radiation Fourier was not searching for a new law but for a
mathematical justification of one which had already been established ex-
perimentally. Also that he based the first of his two derivations on a physical
principle — that of detailed balance — which had already been effectively
given by Prevost. The situation was entirely different in the case of his
formulation of the equations of motion of heat within and at the surface of
solid bodies. Here there can be no doubt whatsoever of either the originality
or importance of Fourier's achievement nor of its predominantly physical
nature. It is on a study of the formulation of these equations that an esti-
mate of the physical side of Fourier's achievement as a theoretical physicist
must be based.
It was a profound physical understanding of the problem of the thin
bar which led to the whole development of Fourier's analytical theory of
heat. A detailed account had already been given of Fourier's treatment of
this problem in the Draft Paper, 9 the 1807 memoir, 10 and in Letter XIX. 11
The one factor common to all three versions was the notion of the inde-
structibility or conservation of heat. This concept was found in Biot's
1804 paper, and before that — and unacknowledged by Biot — in Lambert,
so that Fourier could evidently lay no claim to any originality here. Nor
did his treatment of the problem in the draft paper show any real advance
over that given by Biot except in a closer approach to physical reality by his
replacements of Biot's 'points' by 'slices' of the bar. For although Fourier
'derived' an equation, whereas Biot only implied its existence, Fourier's
derivation, as he himself makes plain in the Letter XIX, 12 was entirely
unjustified. It was presumably the patently unsatisfactory nature of this
derivation which stimulated Fourier to look for a better one, and this in
turn inevitably led to what must be regarded as his most critically impor-
tant and original single insight into the physical nature of the conduction of
heat in solid bodies, namely, the concept of heat flux, and the concomitant
realization that without a knowledge of the expression for the heat flux as a
212 EPILOGUE
function of the temperature the problem of the thin bar — and by
implication all other more complicated problems — would necessarily
remain unamenable to rational treatment.
The notion of a flux of heat or other 'substance' as a rate of flow per unit
time per unit area is such a familiar and central one in modern theoretical
physics, that it is difficult if not impossible to assess the measure of origi-
nality involved in its original formulation by consideration of the concept
itself. Contemporary evidence is fortunately available to make good this
lacuna. Fourier's contemporaries, it will be remembered, 13 found it
excessively difficult either to understand or to accept this concept. Thus
Laplace, by any reckoning the foremost theoretical physicist among
Fourier's contemporaries in France or elsewhere, certainly did not under-
stand this basic element of the analytical theory of heat when he first
encountered it as a member of the commission set up to report on the 1807
memoir, and the criticism of the derivation of the basic equations in the
report on Fourier's Prize Essay proves that he still had not accepted it by
February 1812. Biot and Poisson were even more obtuse than Laplace. As
late as 1816 they were still insisting on the existence of an 'analytical
difficulty' which could only be overcome by adopting Laplace's 'molecular'
approach, whereas Fourier had proved — conclusively as it appears today —
that it could equally be overcome by the use of his notion of heat flux.
Admittedly this evidence for the originality of the concept of heat flux is
somewhat weakened by the fact that Laplace, Biot, and Poisson had each
to varying extents an emotional blockage which stood in the way of a ready
acceptance of Fourier's work, including the basic concept of heat flux. Not
so, however, Fourier himself, and perhaps the best measure of his achieve-
ment in arriving at an absolutely clear formulation of the notion of heat
flux and its function in the phenomena of heat conduction is provided —
somewhat unexpectedly — by a comparison between his treatment of the
thin bar problem in the 1807 memoir and in Letter XIX. This comparison,
it will be remembered, 14 reveals a fundamental transition from a 'three
slice' to a 'one slice' approach. On examining this transition it is clear that
even at the time of composing the 1807 memoir Fourier himself had still not
attained to a perfectly clear conception of heat flux. Admittedly there was
an interchange of heat between consecutive 'slices'. But one could not
really talk of a flux, since this is something which occurs not between two
extended parts but across a geometrical section. And as Fourier is at pains
to emphasize in Letter XIX 15 — possibly, as we have seen, in response to
criticism of his treatment in the 1807 memoir — the heat in question must
be thought of as originating not just in the parts of the bar immediately on
either side of the section, but from other more distant parts as well, though
the influence of these latter parts will, of course, be very small. The modern
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213
notion of heat flux therefore occurs for the first time in Letter XIX, and
thereafter in the Prize Essay and the Analytical Theory of Heat. If we date
Letter XIX to around 18 10, it can then be said that some five years elapsed
between the time that Fourier first entertained the notion of heat flux, and
the absolutely clear exposition found in Letter XIX. Given the difficulty
which Fourier himself experienced in clarifying this concept, Laplace,
Biot, and Poisson must not be judged too harshly for their failure to
welcome it with open arms, and in any case they must all be given some
credit for having stimulated Fourier to make his formulation of the concept
more precise and physically acceptable. All in all this is surely another
example of one of those apparently simple, almost trivial, concepts in
theoretical physics which nevertheless seem to require for their formula-
tion the intervention of a Galileo or a Newton.
The realization of the need for the concept of heat flux led immediately
to the need for an explicit, functional expression for this flux in terms of
the variables of the problem. This was necessary for the true solution of
the thin bar problem in the 1807 memoir, 16 and the proper expression for
the heat flux in terms of the interior conductivity and the gradient of the
temperature is found in that paper. However, just as Letter XIX contains
both a more satisfactory treatment of the concept heat flux than the 1807
memoir and a much clearer exposition of the need for an explicit functional
expression for this flux, so it also contains a far more satisfactory proof 17 of
the actual expression for the heat flux than that given in the 1807 memoir.
This new proof was in any case necessitated by the transition from the
'three-slice' to the 'one-slice' approach. The method followed was both
interesting and ingenious, and was remarkable for the bold use of idealiza-
tions especially that of an infinite slab with steady heat flow as already found
in the 1807 memoir. Noteworthy, too, was the manner in which the proof
was based not on the Newtonian principle of heat interchange propor-
tional to temperature difference, as in the 1807 memoir, but on the more
fundamental principle — from which Fourier attempts to derive the New-
tonian principle — that phenomena of heat conduction in bodies depend
only on temperature differences between parts, and so will be unchanged if
all temperatures are increased by the same amount. The somewhat wild
nature of this idealization from a physical point of view needs no stressing.
But once again it proves Fourier's flair for just the right sort of idealization
required to simplify an essentially complex problem and make it amenable
to mathematical treatment while simultaneously providing a solution
yielding a good approximation to the actual physical situation in a wide
range of cases.
An important, and original, aspect of Fourier's thinking on heat flux
was his introduction of a precise definition of the interior conductivity, K.
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This was given with great care in the 1807 memoir, 18 and it was an aspect
which required no clarification or emendation in Letter XIX or in the
Prize Essay. The first thing to be noticed about the definition is its com-
plete novelty. To see this one has only to examine the welter of conflicting
views on conductivity of heat held by experimentalists prior to Fourier. 19
In particular, the complete confusion which reigned as regards conduc-
tivity of a substance as measured by its ability to conduct heat, and its
ability to radiate heat. Admittedly Biot 20 refers in his 1804 paper to the
ratio of conductivity to radiation, but he gives no indication whatsoever
of what precisely he means by either term. In a few pages in the 1807
memoir Fourier banishes all such confusion and uncertainty. But though
Fourier's definition is perfectly clear it has simultaneously a peculiarly
indirect character. It would be impossible to measure the value of the K for
a given solid directly by means of this definition. Fourier, in fact, had
introduced a parameter for which a numerical value was required if pre-
dictions were to be derived from the theory, but which itself could only be
measured through application of the theory. Thus the definition of the
internal conductivity K established a particularly intimate link between
theory and experiment. K was a parameter whose value could never be
given by the theory alone, only with the aid of experiment. But equally it
was a parameter whose value could never be given by experiment alone,
only with the aid of the theory. The obvious comparison here is with the
mass parameter in Newtonian dynamics which necessitated a linkage be-
tween theory and observation in the application of the theory to specific
cases. Unlike Newton, however, Fourier himself seems to have been well
aware of this peculiar relationship between the conductivity and the theory.
What has just been said of Fourier's definition of interior conductivity
applies pari-passu to his definition of surface radiating power 21 : it was
utterly clear, entirely novel, dissipated previous confusion, and resulted in
a necessary linkage between theory and observation. The definition of
these two parameters in the 1807 memoir provides another striking example
of Fourier's profound physical understanding of the true nature of the
process of heat conduction. It also provides an equally striking example of
his ability to express new physical concepts with admirable clarity and
precision of thought and language.
Equally important, and complementary to, Fourier's definitions of
interior and exterior conductivity was his separation of the process of
interior conduction and exterior radiation of heat. Fourier, it will be
remembered, 22 was at first uncertain whether or not a term involving the
exterior conductivity, h, should always figure in the equation of propagation
of heat within solids. The origin of this uncertainty was the justified pres-
ence of such a term in the equations for a thin bar or a thin ring. But when
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215
writing down the general equation of heat conduction in two or three
dimensions in the draft paper he also included a term in h. 23 At the same
time he expressed his uncertainty as to whether the presence of this term
was justified, and in the case of the semi-infinite strip he left it out alto-
gether. But this was an artificial case in which the boundary condition did
not involve h, since the edges of the strip were held at given fixed tempera-
tures through contact with infinite reservoirs unaffected by any finite inflow
or outflow of heat. However, in the case of a sphere originally heated
throughout to a given temperature and then plunged in air held at a
different temperature it was impossible to avoid a decision on the actual
part played by radiation at the surface of the sphere. The outcome was the
beautiful boundary condition expressing the flow of heat across a surface
element in two ways : as a heat flux immediately within the surface, and as
a flow of heat radiated immediately above the surface. In the 1807 memoir
Fourier introduces this epoch-making boundary condition in such a casual
and unassuming way as to give the impression that he did not himself
realize what a brilliant and original contribution it was. But once again
contemporary evidence is supplied by Laplace 24 whose own condition was
not only inferior physically to Fourier's, but would seem to have been quite
incapable of any precise mathematical formulation. Fourier's condition, on
the other hand, was not only amenable to mathematical formulation, but
through its mathematical treatment, first by Fourier himself, then by his
disciples Sturm and Liouville, and after them by an army of other workers,
it opened up the whole field of eigenvalues and eigenfunctions of such
enormous importance for modern applied mathematics and theoretical
physics.
The boundary condition for the cooling of a heated body immersed in an
infinite medium maintained at constant temperature neatly epitomizes and
sums up the various factors which underpinned the physical side of Fou-
rier's achievement in the analytical theory of heat : a complete grasp of the
underlying physical processes, a formulation of the corresponding physical
concepts and their embodiment in definitions of compelling simplicity and
clarity, an idealization of the problem at once bold and mathematically
amenable, leading in turn to an elegant mathematical formulation of the
process in question. There is nothing surprising or unfamiliar about these
factors. What is uncommon — or what was at least in the past uncom-
mon — is the simultaneous possession by one and the same individual of the
necessary physical understanding, right philosophical approach, analytical
powers, clarity of mind, and mathematical ability which seem essential
for the fundamental creative acts which are at the root of all revolutionary
advances in theoretical physics. Although the analytical theory of heat did
not turn out to be as important from a physical point of view as Fourier
T
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217
had thought, and although the theory itself was eventually taken over by
mechanics — albeit of the statistical variety— in direct contradiction to
Fourier's unilateral declaration of independence in the Preliminary
Discourse, nevertheless it is clear that the physical side of Fourier's achieve-
ment in theoretical physics must be rated of the very greatest importance if
only because it made possible the creation of the analytical theory of heat
with its very important influence in both pure and applied mathematics in
the remainder of the nineteenth century and beyond. In any case, apart
from the importance of the physical side of Fourier's achievement in
theoretical physics, there remains the beauty and completeness of the
achievement itself. Fourier's problem was at first a small one, in essence
that of the conduction of heat in a thin bar. But the formulation he gave of
it left nothing to be desired as regards clarity, completeness, and elegance.
As presented in the Analytical Theory of Heat, and in the light of the
supporting historical documents necessary for its proper understanding, it
constitutes a wonderful example of creativity in theoretical physics, a rock-
like foundation able to support the vast superstructive raised on it in the
leisure hours of the Prefect of Isere by the mathematician Fourier.
2. The influence of Fourier's analytical theory of heat
Fourier's analytical theory of heat is largely mathematical in content
involving the application of pure mathematical theorems and formulae to
various thermal problems. But it does contain various physical elements,
above all the derivation and justification of the basic equations of the pro-
pagation of heat, which alone would justify the application of the term
theoretical physics to the work as a whole. It follows that the influence of
Fourier's work must be considered under two main headings, its influence
in mathematics and its influence in theoretical physics.
There is, of course, no necessity for a great and original work in theor-
etical physics such as Fourier's to have any influence whatsoever in either
pure or applied mathematics. The contrary has almost invariably been the
case. Thus few works either literary or scientific had a greater or more varied
influence in eighteenth century Europe than Newton's Principia, but its
influence certainly did not extend to mathematics, except in the negative
sense of exerting a somewhat unfortunate influence on British mathe-
matics through its use of synthetic rather than analytical methods. Or
again, the contribution of Maxwell in electricity and magnetism, or Planck
in radiation, or Einstein in relativity, were all enormously important and
influential in theoretical physics, but were almost entirely derivative and
uninfluential from a mathematical point of view. In fact Fourier's Analyti-
cal Theory of Heat was enormously influential in both pure and applied
mathematics, more so, perhaps than any other important work in theoreti-
cal physics before or after up to the present day. When we ask the reason
for this we find that the short answer resides in the fact that Fourier was
the first person to give a reasonably thorough and detailed treatment of a
whole class of problems based on a partial differential equation involving
both temporal and spatial variables subject to non-trivial boundary
conditions on both the temporal (initial) and spatial (surface) variables. In
the process of dealing in succession with a series of problems of increasing
complexity all based on the same (heat propagation) equation, he was faced
in turn with a series of mathematical challenges to each of which he was
able to give an adequate answer. His ability to do so proved his genius as a
mathematician. His manner of doing so provided a harvest of original
mathematical discoveries and techniques, which in turn provided a rich
mine of material for many of the most important developments in pure
mathematics in the rest of the century. At the same time the methods he
had adopted for solving problems in the theory of heat proved immediately
applicable to other branches of theoretical physics, so that his work was
greatly influential also from the point of view of applied mathematics, all
the more so because of his clarity of expression both literary and mathe-
matical, and his great pedagogical skill born of a long and varied experience
of the teaching of mathematics at various levels from that of the novices at
St. Benoit-sur-Loire to the most brilliant students at the ricole Polytech-
nique. Fourier's work, in fact, was at one and the same time a treatise
of great originality, and a text book of marvellous and compelling
clarity.
Considerable attention has already been given to Fourier's influence in
mathematics and there is no need to go over all the ground again in
detail. 25 It seems to be agreed that Fourier's most important, and indeed
revolutionary, contribution to pure mathematics was to the concept of
mathematical function. His realization that the most 'unruly' and 'irregular'
functions — even including those containing actual discontinuities in the
modern as opposed to Eulerian sense — could be represented by trigono-
metrical functions, can be looked at in two ways. It could be regarded as a
final and long-delayed resolution of the problem of the vibrating string in
favour of the intuition of David Bernouilli against the views of Euler,
d'Alembert, and Lagrange. 26 Alternatively, and perhaps more justly, one
can regard Fourier's extension of the power of representation of trigono-
metrical series not as the closing of one chapter in the history of mathe-
matics, but as the opening of a new and more exciting chapter in which the
concept of function achieved its modern form through the successive
contributions of Dirichlet, Riemann, Weirstrass, and others. 27 Certainly
it is clear that Fourier himself perfectly understood the extraordinary
218 EPILOGUE
nature and true importance of his discovery. Thus in the 1807
says:
memoir he
says
It is quite extraordinary that one can determine the value of the coefficients (of
the various trigonometrical terms) although the given function may not be sub-
ject to any determinate law, and although one obtains the analytical equation of a
curve composed of arcs of different kinds. One is led in this way to admit into
analysis functions which have the same value whenever the variable has any
value between two given limits ; whereas if one substitutes in the two functions in
place of the (previous) variable a number contained in another interval, the
results of the two substitutions are different one from the other. The functions
which enjoy this property are represented by different curves which only co-
incide in a certain portion of their extent and offer a peculiar kind of osculation
which has not been considered hitherto. 28
Of the other developments in pure mathematics which have been attributed
to Fourier, perhaps the one which can be traced back most unmistakably to
the Analytical Theory of Heat was the theory of orthogonal functions.
Once again Fourier seems to have been well aware of the importance and
generality of the new idea. Thus in Letter XXI (to Lagrange ?) he states :
Finally, this development of a function in sines or cosines of multiple arcs is only
a particular case among those which I have had to treat, and these latter offered
analytical difficulties of a very different order. It was necessary, for example, for
determining the movement of heat in a cylindrical body to develop an arbitrary
function in a series whose terms depended on a transcendental function given by
a differential equation of the second order. I beg, you, Sir, to be good enough to
examine this part of my work which is really the only part worthy of your
attention. 29
Other developments in pure mathematics which can be traced back with
varying degrees of certainty to the Analytical Theory of Heat include the
reintroduction and sharpening of the definition of the definite integral as a
sum, 30 the notion of uniform convergence, 31 and the theory of infinite
determinants. 32 Less plausible, perhaps, is the view 33 that Cantor was
indebted to Fourier for the use of trigonometrical functions in the early
development of his theory of point sets.
In applied, as opposed to pure, mathematics Fourier's work was equally
influential. Particularly important here were the use of Fourier series and
Fourier integrals as two of the prime tools in the solution of mathematical
problems occurring in applied mathematics, the methods employed for the
first time by Fourier (at any rate in a consistent way) for treating problems
in applied mathematics involving partial differential equations subject to
boundary and initial conditions, and Fourier's treatment of the full time-
dependent conduction or diffusion equation. These methods, first
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219
consistently and clearly employed by Fourier in his Analytical Theory of
Heats have become such a familiar part of modern methods in applied
mathematics that it is difficult to realize how revolutionary and novel they
were at the time of the publication of Fourier's book. No doubt an exhaus-
tive dredge of all previous writings in the eighteenth and early nineteenth
century in both pure and applied mathematics would show up some earlier
uses of Fourier's methods and techniques apart from the known example of
trigonometrical series. Nevertheless, there can be no question that the use
by Fourier of all these methods was so consistent and so clear that their
simultaneous publication in his work affected a revolution in applied mathe-
matical techniques, and that thereafter they rapidly became accepted as
standard methods. 34
When we turn to consider Fourier's influence in theoretical physics we
immediately notice a striking contrast with the cases of pure and applied
mathematics. Whereas in the latter cases Fourier's most profound and
original discoveries, especially in relation to trigonometrical and other
expansions, had a direct, explicit, and conscious influence on later
developments in pure mathematics, his most original achievements on the
theoretical-physical side — his derivation of the correct heat flux expres-
sion 35 and the equations of the propagation of heat including the boundary
conditions — seem to have passed without comment and to have had little
influence either explicit or implicit on his contemporaries or successors
once his theory had been generally accepted, for it must be remembered
that with the exception of his use of trigonometrical expansions no aspect of
his work had given rise to greater controversy 36 before the acceptance of his
theory by Laplace had finally stilled the carpings of Biot and Poisson.
There would seem to have been two main reasons for this at first sight
curious and paradoxical situation, the first a general one, shared with many
other original developments in theoretical physics, the second more
peculiar to the Analytical Theory of Heat. In the first case, Fourier's
fundamental achievements on the theoretical physical side were largely
ignored once the theory as a whole had been accepted because this is the
almost inevitable fate of any successful theory in theoretical physics, and in
direct proportion to the success of the theory. Thus, as opposed to his
law of gravitation and his 'explanation' of planetary motions, Newton's
development of the concept of force and his application of the second law
of motion seem to have been undervalued by everyone in the eighteenth
century including Newton himself — as witness his attribution 37 of the
first two laws of motion to Galileo. The same could be said in large measure
of Maxwell's derivation of his equations for the electromagnetic field, or of
Einstein's formulation of the dynamical equations of motion in Special
Relativity. In each case the theoretical physical achievement resided almost
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entirely in the original, creative, inductive process which led to the for-
mulation of the appropriate mathematical equation governing the process
in question. Insofar as the resulting theory was correct it was incapable
of modification or extension as regards its basic structure, and to that
extent was never influential directly but only indirectly through its applica-
tion to other problems, that is in an applied mathematical sense. This is
assuming, of course, that the theory in question was complete : insofar as
Newton did not formally deal with rotating bodies in any of his published
work 38 there remained original theoretical physical contributions to be
made to the subject by Euler and others. Insofar as Ampere's contributions
to electromagnetism were incomplete they stimulated further original
contributions to the subject. But insofar as Maxwell's theory came at the
end of a long line of previous investigations of which it was the final and
complete crown it left little room for any further really creative develop-
ments on the physical side within the domain of classical physics. Fourier
himself was probably well aware of his own achievement in deriving the
correct equations of motion of heat, especially in the light of the contro-
versy they had given rise to with Biot, Poisson, and for a time, Laplace.
There appears, however, to be no evidence that any of the later admiration
for his work was directed to this aspect of it, though allowance must be
made for the possibility of an almost unconscious — and possibly very
important — influence of Fourier's whole handling of the physical founda-
tion of his theory, especially his definitions of the various new concepts in-
volved in its formulation discussed in section ii.i above.
There are, of course, good reasons for this tendency for the fundamental
physical achievement in any original development in theoretical physics to
be disregarded. In the first place, the finished work by itself usually gives
little indication of the process leading to the final formulation of the basic
equations 39 for the topic in question — for this, earlier drafts, often un-
published, are essential. In the second place, it is only comparatively
recently, especially with the work of Koyre, 40 that historians of science
have begun a fundamental reappraisal of the process of discovery in
theoretical physics based on the growing realization that some apparently
simple and hitherto neglected conceptual advances may actually have
represented the most characteristic, original, and difficult steps in the
creation of various branches of theoretical physics.
The other particular reason in Fourier's case why his achievement on the
theoretical-physical side had so little direct influence was due to the very
thoroughness and completeness of his formulation of the basic physical
principles of the theory. Thereafter, there remained little for his successors
to do but to apply Fourier's equation and methods to problems not con-
sidered by Fourier himself. In one obvious sense, of course, Fourier's work
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221
was influential in theoretical physics as a whole insofar as it represented the
conquest of a branch of experimental physics by mathematical treatment.
In this respect Fourier's success in the subject of heat encouraged others to
attempt a like conquest by similar methods in other branches of physics.
For example, George Greene, one of the very earliest British theoretical
physicists to be fully aware of the significance and importance of Fourier's
work, in the introduction to his Essay on Electricity and Magnetism
instances the success of Poisson and Cauchy in applying Fourier's methods
to the subject of water waves. 41
Another respect in which Fourier's work was important was as a model
of right method in mathematical physics. As Poincare commented :
Fourier's theory of heat is one of the first examples of the application of analysis
to physics. Starting from simple hypotheses, which are nothing but generalized
facts, Fourier deduced from them a series of consequences which together make
up a complete and coherent theory. The results which he obtained are certainly
interesting in themselves, but what is still more interesting is the method which
he used to arrive at them and which will always be a model for all those who
wish to cultivate any branch of mathematical physics. 42
Another evident influence of Fourier's work in theoretical physics was his
treatment of his problem of terrestrial heat, 43 which provided the starting
point for later investigations, especially those of William Thomson. 44 It is
possible, too, though to my knowledge unproven, that Fourier's work on
radiant heat, especially his use of the principle of detailed balance to derive
the sine law of emission, 45 may have influenced later work in that field
also.
Account must finally be taken of possible influences of the Preliminary
Discourse to Fourier's Analytical Theory of Heat. This differs from most
other parts of the treatise in having effectively no antecedents in the Prize
Essay or the 1807 memoir. Both these latter works have introductions, but
they are almost exclusively concerned with the contents of the succeeding
texts whereas the Preliminary Discourse ranges far beyond the bounds of
the Analytical Theory of Heat to touch on general aspects of the philosophy
of both mathematics and science. The reason for this greater generality
of outlook can only be guessed at, but it could well have been due simply to
Fourier's sense of occasion on publishing the final, printed version of his
masterpiece and a felt need to preface it by some sort of scientific credo
in the manner of the prefaces to the first and second editions of Newton's
Principia, or of the introduction to Huygens's Traite de la lumiere. As for
the title itself, Discours Preliminaire as opposed to the more customary
'preface', it may have had overtones in Fourier's mind with such epoch-
making and revolutionary works as the Discours Preliminaire of d'Alembert
or that of Lavoisier in his Traite Elementaire de la Chimie.
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Absolute clarity of expression was one of the great virtues of all but the
latest of Fourier's published work in some of which he becomes a trifle
rambling and obscure, but in the Preliminary Discourse this clarity is
somewhat surprisingly found in company with a rather confused structure
reminiscent of a similar lack of structure in the Introduction to the
Description of Egypt — in which Fourier alternates between straight des-
criptive passages, philosophy of mathematics, philosophy of science, and
expressions of opinion relating to his own work.
The descriptive passages serve much the same purpose as the introduc-
tions to the 1807 memoir and the Prize Essay. But they not only tell the
reader what to expect in the body of the work, they also tell him something
of Fourier's attitude to science in general and his own theory in particular.
Thus, as might be expected from so convinced a Baconian as Fourier,
repeated stress is laid on the utility of the theory for the civilian economy
and the arts 46 apart from its application to the physical sciences including
the great question of terrestrial temperature. 47 A measure of this severely
practical approach is given by his emphasis on the necessity of the theory
leading to numerical application 'a necessary condition of all research,
without which one never reaches beyond useless transformations' 48 — a
possible reference to the approach of Poisson in terms of a Taylor expansion
in the time, which though mathematically equivalent to Fourier's approach
was scientifically useless owing to the impossibly slow rate of convergence
of the resulting series. For numerical applications the measurement of the
basic quantities of thermal capacity, and interior and exterior conductivi-
ties was essential, 49 an enterprise which could only be successfully
carried out by a union of theory and experiment which was equally vital for
any further progress of the theory. 50 As to the analysis on which the whole
theory was based, in a beautifully concise but complete manner he describes 51
how it consists of the general conditions governing the motion of heat, i.e.,
the equation of motion of heat, the accidental but continuing effects of the
figures or state of the surfaces, and the non-durable effects of the original
distribution of heat. He also refers to various problems not considered in
the 'present work' including radiant heat, terrestrial temperatures, the
comparison of theory with experiment, and the equations of the movement
of heat in fluids. 52 All but the last of these had already appeared in the
Prize Essay of 181 1, and were to reappear in the published version of that
work. Finally, as regards descriptive passages, and as befits a great scientist
who had always a deep interest in the history of his subject, he gives a
brief autobiographical account 53 of the historical development of the
subject beginning with the treatment of the transmission of heat between
separate masses.
In his references to mathematics Fourier makes the customary remarks
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on its universality, simplicity, and clarity: 'There cannot', he believes, 'be a
more universal or simple language, one more exempt from errors and
obscurities.' 54 The principal attribute of mathematics is clarity. She has
'no signs to express confused notions'. 55 More debatable was his belief that
'the profound study of nature is the most fruitful source of mathematical
discoveries'. 56 Fourier's fellow mathematicians would have had to admit
that this belief had worked exceptionally well in Fourier's own case. But
some would have taken strong exception to Fourier's utilitarian attitude to
mathematics agreeing with Jacobi that 'the only end of science is the honour
of the human mind, and that consequently a question about numbers is
worth as much as a question about the system of the world'. 57 All would
have been agreed, however, on the striking way in which mathematics
'follows the same path in the study of all phenomena: interprets them by
the same language, as if to attest the unity and simplicity of the plan of the
universe, and to render even clearer this immutable order which presides
over all natural causes'. 58
As regards philosophy of science, Fourier reveals himself already in the
introductory paragraph of the Discourse as a confirmed positivist :
The primordial causes are unknown to us, but they are subject to simple and
constant laws which can be discovered by observation and whose study is the
object of natural philosophy. 59
Elsewhere he refers to the small number of 'general facts' to which all
thermal phenomena may be reduced, or to the possibility of deducing the
'principles' of the theory from a small number of
primordial facts whose causes are not considered by mathematicians, but which
they admit as resulting from ordinary observation and confirmed by experi-
ments. 60
On several occasions he refers to the importance of experiment and
observations and their blending with theory. For example, no progress is
to be expected in so complex a subject as terrestrial temperatures without
many more measurements of the various observed effects. Nevertheless the
theory itself will still play a vital part:
the theory itself will direct all these measures and will assign to them their
precision. There cannot be henceforth any considerable progress which will not
be founded on these experiments; for mathematical analysis is able to deduce
from general and simple phenomena expressions of laws of nature: but the
special application of these laws to effects which are very complicated requires a
long theory of exact observations. 61
Finally there was his attitude to his own theory. Here again he brings out
his strongly Baconian, utilitarian attitude to science in general and his own
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theory in particular with its 'multiple connections' 62 with civilian uses and
technical arts. Most important, and I shall suggest most influential, was his
dogmatic attitude to the 'independence' of his Analytical Theory of Heat,
and the impossibility of a 'take-over' by mechanics: in spite of the im-
pressive range of applicability of the principles of mechanics stretching
from the movements of the stars, their shape, the equilibrium and oscilla-
tion of the seas, the harmonic vibration of air and sounding bodies, the
transmission of light and the vibration of liquids — ample confirmation of
Newton's homage to mathematics : 'ac gloriatur Geometria quod tarn paucis
principiis aliunde petitis tarn multa praestet' 63 — in spite of all this Fourier
was of the opinion that:
whatever may be the extent of mechanical theories, they do not apply to the
effects of heat. These [effects] make up a special order of phenomena which can-
not be explained by the principles of movement and equilibrium. 84
On the other hand the 'new theories' explained in Fourier's work:
were united forever to the mathematical sciences and rest like them on immov-
able foundations : they will retain all the elements they possess today, and will
continually acquire further application. 65
Now it must be confessed that with one exception to be discussed pre-
sently, none of Fourier's views on the philosophy of either mathematics or
science sound particularly original, and in any case they are no more than a
characteristically concise Gallic sketch as opposed to a more fully worked
out and suitably obscure Germanic exposition. His attitudes to the nature
of mathematics and its remarkable role in the interpretation of phenomena
could have been original, but they have a flavour which is either markedly
Cartesian — simplicity, clarity, universality — or which remind us strongly
of the Great Book doctrine of Galileo as echoed by Newton, d'Alembert,
Laplace, and a host of others. And although his belief that 'the profound
study of nature is the most fruitful source of mathematical discoveries', had
perhaps never been put in so memorable a form before, it was scarcely an
original view; one finds exactly the same attitude, for example, with Lap-
lace and Poisson. 66
Likewise, his emphasis on facts could be paralleled many times in the
writings of Maupertuis, d'Alembert, and others from the victory of the
Newtonian camp in the 1730s onwards, 67 and it certainly represented the
core of the philosophic attitude which dominated French scientific thought
immediately before the Revolution as expressed, for example, in the writ-
ings of Lavoisier 68 and his disciples, or in those of 'ideologues' 69 such as
Cabanis or Destut de Tracy. Fourier would certainly have been exposed
to this influence during his time at the College Montaign around 1786
when he could scarcely have avoided coming in contact with the writings
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of Condillac 70 which had contributed so largely to the strongly 'positivist'
attitude of French science in the 70s and 80s.
Although there was a great deal of common 'Newtonian' ground among
philosophically minded French scientists from Maupertuis onwards — an
emphasis on observed facts, an aversion to hypotheses of a speculative,
Cartesian kind frowned on by the implacable Newton, an appeal to the
method of analysis and resolution and so on — there was nevertheless a
striking amount of variation in their attitude to causes. Some, like d'Alem-
bert and Laplace inclined towards a belief in a single, ultimate cause, itself
unknowable but from which everything else would be derived, though
Laplace had no false illusions about the likelihood of finding this cause, at
any rate in the foreseeable future. 71 Others like Lavoisier 72 and his dis-
ciples took a much more positivist line, putting greater emphasis on facts
and turning away from the search for causes as not only dangerous but
unnecessary. A possible explanation of the origin or Fourier's somewhat
surprising adherence to this second school is provided by his under-
standably hostile attitude towards Laplace's attempt in 1809 to derive the
equation for the propagation of heat in a thin bar from 'molecular' con-
siderations. It will be remembered that Laplace and Biot had claimed that
this was the only way to surmount a supposed difficulty relating to incom-
patible terms in Fourier's quite different treatment. Although Biot had
much the worst of the ensuing controversy, nevertheless Poisson and he
renewed the same criticism in 181 5 and 1816 respectively. In his unpub-
lished Historical Precis completed in 1816 Fourier gave a considered reply
to their criticisms and in the course of his arguments brought out more
clearly than in any of his published writings the reason for his apparent
aversion to first causes, at least as regards heat:
It is not enough to allege that a physical hypothesis is necessary to surmount
certain difficulties which would be insoluble without this explanation. Questions
of this type are not decided by authorities. It is necessary again to base oneself on
special reasons and positions. To us it seems more important not to give to the
principle of communication of heat any hypothetical extension, and we think that
this principle suffices to establish the mathematical theory. For the fundamental
equations are demonstrated in the most clear and most rigorous manner without
it being necessary to examine if the propagation is carried out by way of radiation
in the interior of the solids, whether or not it consists in the emission of a special
matter that the molecules interchange with each other, or if it results, like sound,
from vibrations of an elastic medium. It is always preferable to restrict oneself to
the enunciation of the general fact indicated by observation, which is no other than the
preceding principle. One shows thus that the mathematical theory of heat is
independent of all physical hypotheses; and in effect the laws to which the pro-
pagation is subject are admitted by all physicists in spite of the extreme diversity
of their sentiments on the nature and the mode of its action. 73
T
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As opposed to his largely derivative views on the philosophy of science
and mathematics, it does not seem possible to point to any very convincing
precedent for the dogmatic, separatist attitude of Fourier towards his own
theory expressed in the curious assertion:
whatever may be the extent of mechanical theories, they do not apply to the
effects of heat. These [effects] make up a special order of phenomena which can-
not be explained by the principles of movement and equilibrium. 74
This is perhaps the most puzzling statement in the Preliminary Dis-
course, and one which goes clean against Fourier's habitually careful,
level-headed, and almost uniformly correct judgements in matters scientific
and mathematical. It thus calls for some explanation, especially in the light
of its possible influence on Auguste Comte, and through him on French
philosophical attitudes to Science in the second and third quarters of the
nineteenth century.
There seem to be at least two possible explanations of this attitude : the
first on technical, mathematical grounds, and the second on largely per-
sonal grounds having little to do with either physics or mathematics.
The Analytical Theory of Heat developed by Fourier was based mathe-
matically on a general equation of propagation of heat together with initial
and boundary conditions. The latter changed from one problem to
another; the former might take different forms depending on the co-
ordinates chosen or on special symmetries or other features of the heated
bodies under consideration, but the basic equation was always the same. It
was, as it were, though Fourier himself does not express it in this way, an
invariant feature of his theory, just as the form of the equations of motion
was an invariant feature of Newtonian dynamics or — and more relevant —
just as the motion of continuous bodies, as in the propagation of sound or
in the vibrations of a flexible string, were governed by 'invariant' partial
differential equations which could themselves be derived under certain
plausible simplifying assumptions from the more basic Newtonian
equation of motion.
Now both the equations of propagation of heat and the propagation of
waves in air or strings were of the second order as regards the spatial
variables. But here the similarity between the two ceased: whereas the
dynamical equations, such as that of d'Alembert which must have been
particularly familiar to Fourier, were of the second order in the time
derivative, Fourier's equation for the propagation of heat was of the first
order, and there was no example then known to science of a dynamical
equation referring to continuous bodies with a first order partial derivation
in the time. It could — one is inclined even to say it must — then have
seemed to Fourier that his theory, with its entirely different type of
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227
equation, could never be brought under the sway of mechanics all of whose
branches were based on Newton's equation which in every case led to a
partial differential equation of the second order in the time. If this was
Fourier's argument — and it is difficult to believe that it could have escaped
him — then one must have every sympathy with his judgement. It is sur-
prising that, contrary to Fourier's belief, the theory of heat can be brought
under the sway of dynamics but only, of course, if one is prepared to intro-
duce statistical or quantum statistical mechanics.
The other possible explanation of Fourier's attitude is more speculative,
and can be regarded in any case as at most a minor contributory factor
towards his final attitude, though it may well have played a more important
part at an earlier stage, namely the fact that during the whole of Fourier's
most active work in the theory of heat from around 1805 up to the publica-
tion of the analytical theory in 1822 the subject of mechanics (in the sense
of dynamics) was entirely dominated by Laplace. If, as I shall suggest
later, 75 this may have explained the otherwise somewhat curious absence of
any contribution by Fourier to the subject of celestial dynamics, it might a
fortiori explain, if only at the subconscious level, his reluctance to see his
own theory taken under Laplace's Newtonian umbrella, more especially
as he had had to fight off an attempt by Laplace to take over the whole
subject for himself, or for his disciple Biot, by his derivation of the expres-
sion for the heat flux from 'molecular' consideration in the annex to his
paper on diffraction.
As regards the question of a possible influence on Comte as opposed to
an 'explanation' of the statement itself, the facts are simple and not open
to dispute. Comte was acquainted with Fourier who attended some, at
least, of his second course of lectures on the positivist philosophy. Little
is known beyond that of the relations between the two men, 76 but regardless
of Fourier's views of Comte — and during the increasingly reactionary
reign of Charles IX a vaguely revolutionary figure like Comte would have
been inclined to instil a mild alarm into the liberal-minded but very
cautious Fourier of the last years — the fact that Comte dedicated the pub-
lished version of his lectures to Fourier leaves little room for doubt on his
attitude to Fourier and this is explicitly confirmed by a passage in the
'exposition' where Comte claims that Fourier's researches on heat supply
striking verification for his own views:
In fact, in this work, of which the philosophical characteristic is so eminently
positive, the most important and precise laws of thermal phenomena are dis-
covered without the author having once enquired about the intimate nature of heat 11
[italics added].
Many passages could be cited which prove that Comte extended
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Fourier's antipathy to enquiring into the intimate nature of heat to all
phenomena:
Thus:
Today all discerning intellects recognize that our real studies are rigorously
restricted to the analysis of phenomena in order to discover their effective laws,
that is to say their constant relations of succession and similarity, and that these
studies can in no way concern the intimate nature of phenomena, nor their cause,
either first or final, nor their essential method of production. 78
Finally there are certain passages in Comte which remind one strongly of
the separatist attitude of Fourier towards the theory of heat for example :
Because of the variety and complication of its phenomena physics will be greatly
inferior to astronomy whatever its future progress may be. In spite of all arbitrary
suppositions optical phenomena will always form a category sui generis neces-
sarily irreducible to any other: a light will always be heterogeneous to a move-
ment or a sound. In default of other motives, physiological considerations oppose
themselves invincibly to such a confusion of ideas by the unalterable characteris-
tics which profoundly distinguish the sense of sight whether from the sense of
hearing or from that of contact or pressure. If such radical separations could be
arbitrarily effaced according to certain gratuitous hypotheses, be they more or less
ingenious, it is impossible to see where such aberrations would be halted. 79
It may be, of course, that the separatist attitude to physics evinced by
Fourier and Comte represented some deeper and more fundamental
attitude of French scientists which would still have been influential in
French theoretical physics in the absence of the expression of this attitude by
Fourier and Comte. One is reminded, for example, of the equally dogmatic
separatist attitude towards species of Georges Cuvier, Fourier's close
colleague as the biological permanent secretary of the Academie des
Sciences during the whole of Fourier's tenure of the mathematical secre-
taryship in the period 1822 to 1830. In any case, the whole question of the
role of positivist attitudes in the apparent decline of certain branches of
science — including theoretical physics — in France from around 1830 on-
wards is still very much an open one. 80 And while it may be true that
Fourier's influence in this respect in France may not have been an alto-
gether happy one, there are good reasons for believing that elsewhere
Fourier's whole work, including the Preliminary Discourse, exerted an
entirely healthy influence. This seems to have been particularly true in the
case of William Thomson, Lord Kelvin, a life-long devotee of Fourier,
through whom Fourier influenced the whole development of nineteenth-
century theoretical physics in Britain culminating in Clerk-Maxwell's work
in electromagnetism. 81
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3. Fourier the man and the physicist
From his letters, his scientific and mathematical writings, the reports he
edited as a member of the Academie des Sciences, and the eloges he was res-
ponsible for as the permanent mathematics secretary to that body, we get a
clear impression of Fourier's intelligence, incisive clarity of thought,
originality, and sound common sense. In his personal correspondence there
is evidence of more human qualities : a sense of humour, interest in others,
generosity, genuine affection on occasions, especially in certain letters to
Bonard and in the enigmatic letter to Dr. l'Herminier. 82 All these impres-
sions are confirmed by contemporary accounts such as those of Jomard and
Cousin which also speak of his great personal charm, his fabulous memory,
his persuasive eloquence, his pleasant old-world manners, his wide
interests, liberal views and genuine love of humanity. The account of
Geoffroy Saint Hilaire 83 also reminds us that Fourier had another, harsher,
side to his character, something which was to prove useful in his defence of
the Analytical Theory of Heat.
Nevertheless, in spite of brilliant personal and intellectual qualities
which made Fourier at once welcome and at ease in the best Parisian circles
of the Restoration, not to speak of that citadel of Gallic wit and culture the
Academie Francaise, it would be unrealistic to attempt to strike any sort
of historical balance between Fourier the man and Fourier the savant. As a
savant he achieved an international position, and increasingly dominated
the theoretical physical scene in Paris — itself still the world centre of the
subject — from his election in 1822 to the position of permanent secretary
of the Academie on the mathematical side till his death in 1830. As a man
he never achieved anything beyond local fame or notoriety : no doubt the
president of the revolutionary committee of Auxerre in 1794 was both
admired and feared by many of his fellow citizens, but they all resided in
Auxerre or its immediate vicinity. Admittedly Fourier the revolutionary
appeared for a brief moment on the national scene, albeit ignominiously,
when named in Barere's decree to the Convention of Brumaire 1793. As for
the Orleans affair which had prompted Barere's decree with its near fatal
consequences for Fourier, apart from Fourier and his immediate friends
and enemies in Auxerre and the all-seeing eye of the Committee of General
Security it must have passed unnoticed amid the great political storms of
1793 and 1794 and would be completely forgotten today if it were not for
the fortunate survival of many of the documents of the case and Fourier's
eminence as a mathematician and a physicist. Certainly we are entitled to
speculate that Fourier might have played a much more important part in the
Revolution if he had been elected to the National Convention. There his
charm and persuasive oratory could just conceivably have succeeded, for
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example, in turning the tide in favour of Louis where the turgid rhetoric
of Condorcet was of no avail. But in September 1792 Fourier was barely
twenty-three, was still almost too young to enter local politics let alone the
national arena, and would in any case have stood no chance of election in
Yonne against candidates like Michel Lepelettier or Nicolas Maure. In
Egypt, again, his position as permanent secretary of the Cairo Institute and
his many administrative functions made him the most important civilian
member of the expedition. But little was heard of anyone but Bonaparte
before the latter's return to France, and thereafter the expedition passed
into virtual oblivion forgotten by almost everyone apart from the friends
and relatives of its unfortunate members. Finally, as Prefect of Isere
Fourier was admired, respected, and perhaps even loved by the great
majority of the citizens of the department. But in that position he was no
more than one among eighty-three Napoleonic prefects — though he may
well have been the most able and successful as he certainly is almost the
only one of them remembered today with the possible exception of Chabrol
— and during his many years in Grenoble he was known in Paris only to a
select band of savants and administrators, his path to any further advance-
ment blocked by Napoleon's unswerving secret aversion dating from
Fourier's too open support for Kleber in Egypt. As a politician, an admini-
strator, a prefect of the Napoleonic regime, Fourier can therefore merit no
more than a footnote in the history of the period, whereas both as a physicist
and a mathematician he was undoubtedly one of the major figures of the
nineteenth century and beyond.
Nevertheless the fact that according to normal historical standards
Fourier the man hardly measures up to Fourier the savant does not mean
that the former should be ignored in comparison with the latter. At the
very least Fourier provides an intensely interesting example of one of a
rather small number of eminent savants — the majority, as it happens, and
no doubt not purely by chance, fellow Frenchmen, who, like Fourier, lived
through the storms of the Revolution — who have also played a more or less
distinguished part in the general life of their times. It is not unreasonable,
then, to ask to what extent, if at all, Fourier's rich and varied experience
of life conditioned his achievements as a savant beyond his obvious and
unavoidable dependence on his local, national, and European environments
for the satisfaction of those early physical, spiritual, emotional, and edu-
cational needs which necessarily underpinned all his later achievements in
science.
Fourier appears to have been the only one of a family of fifteen brothers
and sisters who distinguished himself in any way. The conclusion is
irresistible that in Fourier's case it was a favourable combination of genes
rather than any environmental factors which determined his initial intel-
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231
lectual advantage, and no doubt this was due in the first place to a memory
which by all accounts would seem to have been of quite extraordinary
accuracy and tenacity. This may have been partly hereditary, for it will be
remembered that this gift had emerged at least once before in the Fourier
family in the person of the Blessed Pierre Fourier who is said to have had
the summa of St. Thomas Aquinas by heart. By itself such a phenomenal
memory was, of course, no guarantee of anything beyond a parrot-like
ability to repeat without effort whatever he heard or read. But as Fourier
himself said in his eloge of Laplace: 'memory is a precious gift which is not
genius but serves it for acquiring and retaining'. Allied in Fourier's case to a
quick understanding and wide interests it enabled him to excel in all his
studies until his encounter with mathematics around the age of thirteen
marked the first turning point in his career. Without this youthful passion
for mathematics Fourier would doubtless still have distinguished himself
in some way or other, but it would not have been as a theoretical physicist.
The encouragement and stimulation of Bonard, by all accounts an out-
standing mathematics teacher, may have been, indeed probably was, a
decisive factor here, and it is perhaps significant that the year 1781 in
which Fourier attained the age of thirteen was also the year in which
Bonard began to teach mathematics in Auxerre.
The advent of the Revolution then marked the next turning point in
Fourier's career. Otherwise he would certainly have taken his vows and
spent the rest of his life in the Congregation of St. Maur. Perhaps he would
still have acquired some fame as a mathematician, have become a corres-
pondent of the Academie des Sciences, or even a member if he could have
managed to have himself transferred to the Congregation's Paris house at
St-Germain-des-Pres. Or he might have found an outlet for his adminis-
trative talents as Father Superior of some great abbey such as St. Benoit-
sur-Loire. As it was, the Revolution put an abrupt end to his ecclesiastical
career and opened up entirely new vistas outside his continuing work in
teaching as assistant to his old master Bonard. His conversion to Republi-
canism and entry into local politics via the popular society of Auxerre, his
membership of the local revolutionary committee and his various missions
to the surrounding regions, above all that to Loiret, then sucked him into
the maelstrom of local revolutionary politics and led directly to his two
imprisonments from both of which he evidently suffered deeply, especially
the first imprisonment in Auxerre when he seems to have been fortunate
to escape with his life.
But the Revolution not only left its mark on Fourier by the suffering it
imposed on him, not to speak of the resulting large increase in his ex-
perience of life and dealings with his fellows, it was also directly respon-
sible for opening up a career for him in mathematics at a level he could
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never have hoped for as a teacher in the Congregation of St. Maur or at the
licole Royale Militaire in Auxerre. For his attendance at the ficole Nor-
male — that short-lived child of the Revolution — brought him to the atten-
tion of Laplace, Lagrange, and Monge which in turn led to a position at the
ficole Polytechnique where his subsequent appointment to Lagrange's
chair of analysis and rational dynamics then opened up the most promising
of prospects for a professional career in mathematics. Whether Fourier
would have achieved his present fame if he had continued uninterruptedly
at the Fxole Polytechnique must remain a matter of speculation, and con-
ceivably he might then never have become interested in the analytical
theory of heat. Certainly it is a curious fact that during a stay of almost
three years at the Fcole Polytechnique between September 1795 and May
1798 he only contributed a single paper to the 'cahiers' of the school. This
could have been an indication that teaching and administration were taking
up an undue proportion of his time and energies at an age — around thirty —
when according to Hardy's (doubtful) hypothesis he should already have
passed the peak of his inventiveness as a mathematician. In any case his
experience in Egypt was certainly very different from any he could have
had in Paris, and his important administrative and other responsibilities
in that country may have made it difficult for him to settle down to a
sheltered academic life on his return to France, and thus have led him to
accept the position of Prefect at Grenoble in the hope that, in spite of its
obvious disadvantages, it would be a stepping stone to some other larger
and more congenial position in Paris.
Fourier took up his position as Prefect of Isere early in 1802. A year later
in the middle of 1803 he must have been thoroughly at home in Grenoble.
No doubt he found the administrative problems with which he was faced
there comparatively simple compared with those to which he had impro-
vised solutions amid the continuing chaos and alarms of the Egyptian
scene. The French prefect was — and to some extent still is — an absolute
monarch in his own domain for whom all material aids and comforts of
life are supplied without question. As prefect Fourier could always com-
mand the best servants from domestic helpers to the members of his own
special 'cabinet'. For intellectual stimulation he had the pick of the most
intelligent and entertaining citizens of Grenoble, men like Champollion-
Figeac, the municipal librarian, and his more brilliant younger brother who
was later to unlock the key to the Egyptian hieroglyphics. And from time to
time if life in Grenoble itself palled somewhat, there were always visits to
the different corners of his kingdom and beyond. All in all however much
Fourier may have grumbled from time to time about his 'exile' in Isere,
life in Grenoble, especially in the early years before he had given up all
hope of an eventual move to a larger post in Paris, had its very decided
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advantages. There must have been evenings then, when there were no
callers and no visits to be paid, after dinner when his aides had been dis-
missed, when he drew up his chair before the fire and allowed his mind to
turn back to his ambition of earlier years to become a great mathematician
in the manner of 'Newton and Pascal'. 84 This ambition had been sub-
merged by other and more pressing commitments, increasingly by the
Revolution from 1789 onwards, totally from 1793 to 1795 and again to
some extent by the Egyptian campaign from 1798 to 1801 — though even in
Egypt the ambition had never been forgotten and he had somehow
found both the time and the energy to take up his researches into the theory
of equations again, for according to Navier one of the mathematical papers
on that topic found among Fourier's papers after his death was written in
Egyptian ink on Egyptian paper. When he finally returned to France in the
autumn of 1801 it was with the express intention of devoting himself again
to mathematics once he had cleared away some work on the Egyptian
zodiacs. It is not then surprising to have clear documentary evidence 85
that Fourier had become active again in pure mathematics by the middle of
1804. What calls for an explanation is not this quite natural renewal of his
former work in pure mathematics under the favourable conditions in
which he found himself in Grenoble once he had become firmly estab-
lished as Prefect of Isere, but the fact that he became interested in the
problem of heat conduction. Granted that his reputation as a physicist is
based entirely on his Analytical Theory of Heat, and that this is largely true
also of his reputation as a mathematician which would have been immeasur-
ably less if based solely on his work in equations, it is evident that his
encounter with the analytical theory of heat was the central event in his
career as a savant.
A considerable prior interest in theoretical physics as opposed to pure
mathematics is of course evident from the paper of 1798. But it is an
interest in the subject from the formal, mathematical point of view, and
under the obvious influence and inspiration of the Lagrange of the Mecani-
que Analytique. At this point a curious fact about Fourier comes to mind.
When we look at all the most outstanding French theoretical physicists
born in the eighteenth century — Clairaut, d'Alembert, Lagrange, Laplace,
Fourier, Ampere, Poisson, and Fresnel — then we find that Fourier and
Fresnel were the only ones who made no contribution to Analytical
Dynamics, a subject which had been largely monopolized by the French
School from the time of Clairaut onwards. That Fourier was familiar with
the basic Newtonian system is clear from his lectures, and he must have
been familiar with Lagrange's Mecanique Analytique and some at least of
Laplace's voluminous writings in the subject. Why then did he at no stage
show any sign of contributing himself? Two possible explanations suggest
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themselves: in the first place, around 1803 so much work had already been
done in the subject that it could have appeared somewhat vieljeu to a dis-
cerning onlooker such as Fourier, though Poisson 86 was soon to show that
there was still room for contributions sufficiently original to renew Lag-
range's long lapsed interest in mechanics and lead to his final burst of
creativity as a mathematical physicist. The other and possibly more likely
reason was a natural antipathy to Laplace. This is perhaps already evident
from Fourier's first assessment of him at the Ecole Normale Year II as
'among the first of European savants' 87 as opposed to Lagrange who was
quite definitely 'the first', or of his comment that Laplace's method of
lecturing was undistinguished, or of the malicious story of Laplace's
'election' to the Ecole Normale. Fourier's apparent lack of enthusiasm for
analytical dynamics could then have been arisen in part from a disinclination
to enter a field which around 1803 was entirely dominated by Laplace. It is
interesting to note here en passant that although Fourier was always respect-
ful to Laplace, and was not above making a graceful compliment to him
on occasion, 88 he was never in any way deferential to him, as is evident, for
example, in the whole tone of the letter of 1808/9 m which he quite firmly
put Laplace in his place over the question of trigonometrical series. 89
If plausible reasons can be found for explaining a lack of any contribu-
tion to, or apparent interest in, analytical dynamics on the part of Fourier,
what of the other branches of theoretical physics apart from heat in which
important developments took place in the first quarter of the nineteenth
century, namely, in electricity and magnetism, and in the theory of light?
No very good reason can be given in the case of electricity and magnetism.
For against the argument that the great burst of creativity in electro-
magnetism led by Ampere had to await Oersted's discovery of 1820, we
have the fact of Coulomb's brilliant work in both electricity and magnetism
which can scarcely fail to have been known to Fourier, 90 and which
influenced Poisson's fundamental contribution of 1806. In the case of light
a much stronger case can be made out for Fourier's failure to participate,
namely it would have been necessary for him either to have been able both
to read and to understand the original papers of Young, a formidable
undertaking of which he was in any case almost certainly linguistically
incable, or he would have had to rediscover the basic phenomena for him-
self hke Fresnel, but before Fresnel, and without the invaluable assistance
of Arago or the stimulation of the discoveries of Malus, once again a
somewhat improbable proceeding. As for heat, for some years prior to
1804 there had been considerable experimental activity in thermal pheno-
mena, both on the question of propagation of heat in solid bodies, and in
thermal radiation. It seems, however, that Fourier knew nothing of this
work before he learnt of it through Biot's paper, which in turn directed
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his attention to study the propagation of heat in a thin bar, the real begin-
ning of his Analytical Theory of Heat. 91 But Biot's work was not respon-
sible for arousing Fourier's initial interest in a theoretical treatment of
thermal phenomena in the first place. This interest had already shown itself
in his earlier researches in the subject into the communication of heat
between discrete bodies. Without this prior interest it seems unlikely that
Biot's somewhat pedestrian paper of 1804 would have aroused anything
more than a transient response in Fourier, whereas in the light of his earlier
researches he was in a position to respond critically to the incomplete, but
very suggestive, sketch for a theoretical treatment of the thin bar problem
in Biot's paper, incorporate it in his draft paper of 1805, and then transform
it into one of the cornerstones of the memoir of 1807. It is evident, there-
fore, that the first decisive step in Fourier's Analytical Theory of Heat
was his original treatment of the communication of heat between discrete
bodies. His reproduction of the whole of this topic in the 1807 memoir, the
Prize Essay, and the Analytical Theory of Heat, is a good indication that
Fourier himself was of the same opinion. As for the reason for Fourier being
drawn to this particular topic in theoretical physics soon after his arrival
at Grenoble, this must remain a matter of speculation though it is tempting
to suppose that it was simply due to the almost pathological personal
susceptibility to cold which he experienced on his return from Egypt, 92
and which ensured that the question of heat, its loss by propagation in
solids and radiation in space, the problem of conserving it — on which
Fourier himself advanced interesting suggestions in his Analytical Theory 93
— can never have been out of his mind for long, at least during the winter
months.
If this were the only point at which Fourier the man impinged on
Fourier the mathematician and physicist, the search for some sort of
meaningful rapport between the human and the scientific sides of his life
would have proved abortive. But when we take into account the contro-
versy 94 arising out of the 1807 memoir we find other more profound and
interesting ways in which Fourier's experience of life contributed to his
achievement in science. The more closely this controversy is looked at the
more apparent is the extreme gravity of Fourier's position. Laplace and
Lagrange on whose good opinion and support he must have counted, and
whose influence in the commission was dominant, had both turned against
him. Nor was it simply a matter of a number of rather narrow questions to
which precise yes or no answers could eventually be found. The two major
criticisms of Fourier's work were both of a somewhat nebulous and
intangible nature. His derivation of the basic equation of motion was
supposedly lacking in 'rigour', this could be supplied, but even if Laplace
could be persuaded to accept Fourier's derivation he still preferred his
236
EPILOGUE
own. The question of the use of trigonometrical expansions was much
more subtle and difficult and in spite of all Fourier's persuasive arguments
Lagrange could never bring himself to accept the validity of Fourier's
procedures. The whole work was therefore at stake. Laplace and Lagrange
remained openly opposed to it and Biot lost no opportunity of sniping at it
from the side lines. The danger of an absolutely damning report was there-
fore very great. It was at this point that a long experience of pleading
difficult cases came to Fourier's aid. To ward off the attacks of Biot and
Laplace, to neutralize if not remove the misgivings of Lagrange, required
the protracted exercise of all Fourier's considerable powers of persuasion
both literary and mathematical. It was here that Fourier the man inter-
vened most decisively in the career of Fourier the savant. The persuasive
eloquence which had pleaded the case of the innocent before the popular
tribunes in Auxerre during the Revolution, or which had pleaded for his
own life and liberty in the letters from prison to the conventionels Bergoeing
and Villetard during the Prairial days of 1795, was now pressed into service
to defend a theory which was fighting for its life against the conspiracy of
Biot, Laplace, and Poisson. The letters 95 to Lagrange, Laplace, and other
unnamed correspondents provide the only extant evidence for this defence,
but no doubt Fourier found the opportunity to defend his memoir even
more persuasively in person on the occasion of his extended visit to Paris
in 1809/10 to oversee the printing of his Introduction to the Description of
Egypt. It would be tempting to argue with hindsight that truth is great
and must prevail, that Fourier's theory was in all essential respects correct,
and would, therefore, inevitably have triumphed regardless of whether or
not he had defended it. But if he had not reacted vigorously, and on
occasion ruthlessly, against the Biot-Laplace conspiracy, if he had not had
the daring and effrontery to criticize Laplace openly in a letter 96 to some
unknown, but obviously influential person — an action as dangerous
scientifically in 1809, when Laplace was very much the 'dictator' of the
physical sciences in France, as Fourier's action in criticizing the conven-
tional Laplanche had been dangerous politically in 1793 — then there is
every reason to believe that Fourier's paper would have been forgotten, the
subject of the propagation of heat would not have been set as a Prize Essay,
or that if it had Fourier would have been too discouraged by the reception of
his earlier memoir to submit another. In that case no doubt all the results
in the analytical theory of heat would ultimately have been discovered
independently and the theory of the conduction of heat in solids would be
little different today from what it actually is. Nevertheless the loss to
mathematics and theoretical physics in the nineteenth century through the
non-appearance of Fourier's work would have been immense, for the
chances of another single work combining at one and the same time so
EPILOGUE
237
much mathematical originality with so many new methods and results in
applied mathematics and theoretical physics would have been vanishingly
small. Certainly Poisson's 97 ponderous work on the subject would have
supplied no sort of acceptable alternative to Fourier's Analytical Theory of
Heat. What would have been so sorely missed would have been the
enormous impact on both mathematics and theoretical physics of Fourier's
treatise, as a result of its compelling elegance and clarity, and its simul-
taneous presentation of so many original results. Science and mathematics
would have had to make do instead with a patchwork of independent
results as opposed to a single, connected masterpiece.
Compared with some of his contemporaries, especially Lagrange,
Laplace, and Cauchy, Fourier's collected works take up a rather modest
space on the shelves which carry the forgotten writings on which the
triumphs of modern theoretical physics are largely based, and in Fourier's
case his collected works were almost entirely made up of a single work, the
Analytical Theory of Heat, and deductions therefrom. Few works, how-
ever, have contained so many original results or have had so great an
influence in both pure and applied mathematics and in theoretical physics.
Fewer still have represented such a rounded, human achievement. To the
creation, composition, exposition, defence, and publication of this work he
devoted all his gifts of intellectual energy, creativity, persistence, clarity,
eloquence, and persuasion as a mathematician, a physicist, a writer and an
advocate, so that the Analytical Theory of Heat must be regarded not only
as a memorial to Fourier the mathematician and physicist but also to
Fourier the man. Perhaps at this point Fourier still has something to say
to the present age when all his purely mathematical and physical achieve-
ments have long since been inextricably interwoven into the fabric of
modern mathematics and science. To the romantic argument that great
achievements in art, literature, and science are reserved for those who
sacrifice everything to their chosen subject Fourier, as a true son of the
French Enlightenment, provides the example of one who succeeded in
combining achievements of the highest order in mathematics and science
with a profound interest in life, literature, and art not to speak of a successful
career in administration. At a time when the experimental way of the
seventeenth century is increasingly under attack for its contributions to cer-
tain of the ills of modern society, Fourier reminds us of the Baconian
message that the true end of science is not the advancement of knowledge —
important though that is — but the increase in the real happiness and well-
being of mankind, and that if we have to choose — as now seems likely —
between depth of knowledge and quality of living we shall have to choose
the latter rather than the former. Also that an essential factor in this quality
of living is supplied by the old classical notion of that delicate balance
1
238
EPILOGUE
EPILOGUE
239
between conflicting subjects, interests, and occupations which makes up
true culture, that if the arts man without some knowledge of science is an
'ignoramus', the scientist without a living interest in literature and art is a
'barbarian', 98 and that the proper function of education as in Fourier's
own ficole Royale Militaire in Auxerre is to prevent the production of
narrow specialists while still fostering a love of individual excellence in all
its varied forms.
Notes
i. Historical Precis, fol. 162.
2. 1807 memoir, fol. 3.
3. See above, chapter 10, p. 206.
4. See above, section 10.2.
5. For example,
These theories [those on terrestrial heat] will expand greatly in the future, and nothing
will contribute more to their perfection than numerous sets of precise experiments :
for mathematical analysis (if we may be permitted to reproduce* this reflection) can
deduce from general and simple phenomena the expression of the laws of nature : but
the application of the laws to very intricate effects requires a long sequence of exact
observations.
Oeuvres, 2, p. 125, *Preliminary Discourse to the Analytical Theory of Heat.
6. See above, chapter 10, pp. 202-5.
7. Ibid., pp. 204-5.
8. See, for example, his reference to Fourier's work on terrestrial heat in his
'On the secular cooling of the earth', Trans. Roy. Soc. Ed., 23 (1864), 157-69.
9. See above, chapter 8, pp. 164-5.
10. Ibid., pp. 165-6.
11. See Appendix, pp. 308-9.
12. See Appendix, p. 308.
13. See above, chapter 9, pp. 183-5.
14. See above, chapter 8, pp. 166-7, chapter 9, pp. 185-6.
15. Appendix, pp. 312.
16. Loc. cit., art. 19.
17. See above, chapter 9, pp. 186-7.
18. See above, chapter 8, p. 182: 1807 memoir, arts. 17, 18.
19. See, for example, Rosenberger, F., Die Geschichte der Physik, vol. 3, pp. 110-11.
20. Biot (1), p. 321.
21. 1807 memoir, art. 16.
22. See above, chapter 8, p. 170.
23. Loc. cit., fol. 1 27V.
24. See above, chapter 8, p. 170.
25. See especially Bose (2), Grattan-Guinness (1), (2), Jourdain (1), (2), Langer,
Van Vleck.
26. For this controversy see Bose (2), Langer, Mach, pp. 78-114, Grattan-
Guinness (3), chapter 10, Ravetz (2).
27. See, for example, Monna, A. F., 'The Concept of Function in the nineteenth
and twentieth centuries'. Archive for History of Exact Sciences, 9 (1972), 57-84.
28.
29.
3°-
31-
32.
33-
34-
35-
36.
37-
38.
39-
40.
4i-
42.
43-
44-
45-
46.
47-
48.
49-
S°-
Si-
S3-
S3-
54-
55-
56.
57-
58.
59-
60.
61.
62.
63.
64.
65-
66.
67.
Op cit., fol. 116.
See below, Letter XXI, p. 320.
Jourdain, p. 250; Van Vleck, pp. 1 16-17.
Van Vleck, pp. 1 18-19.
Ibid., pp. 120-1.
Ibid., p. 120.
For evidence of the introduction of these methods into British mathematics
see Herivel (2).
See above, chapter 9.
See above, chapter 5, pp. 100-3, an d chapter 7, pp. 153-8.
Principia, Book I, Scholum to Laws of Motion.
As opposed to his treatment of the problem in unpublished MSS. See my
Background to Newton's Principia (Oxford, 1965), chapter 5.
As opposed to the very evident mathematical manipulation and transformation
of these equations which is always given, in part at least, in the finished work.
Especially his Etudes Galileennes.
Greene, pp. 7-8.
Quoted in Jourdain (2), p. 245.
See above, chapter 10, pp. 197-202.
Especially the paper referred to in n. 8 above.
See above, chapter 10, pp. 203-4.
Analytical Theory of Heat, p. xvii.
Ibid., pp. xvii-xviii.
Ibid., p. xxii.
Ibid., p. xvii.
Ibid., p. xxviii.
Ibid., p. xxiv.
Ibid., p. xxv.
Ibid., pp. xxv-xxvi.
Ibid., p. xxiii.
Ibid., p. xxiii.
Ibid., p. xxii.
Quoted by Jourdain (1), p. 249.
Analytical Theory of Heat, p. xxiv.
Ibid., p. xv.
Ibid., p. xxi.
Ibid., p. xxviii.
Ibid., p. xxi.
Quoted — slightly incorrectly — by Fourier at p. xvi.
Analytical Theory of Heat, p. xvi.
Ibid., p. xxviii.
Thus Hermite {Oeuvres, 4, p. 287) states that: 'For Laplace and Poisson pure
analysis was not the object but the instrument, the applications to physical
phenomena were their essential objectives.'
Thus Maupertius in his Discours sur la figure des astres states :
It is a justice which one must render to Newton; he never regarded attraction as an
explanation of the weight of one body towards another : he often warned that he used
the term to designate a fact not a cause ; that he only used it to avoid explanations and
systems : that it could even be that this tendency was produced by a subtle matter from
bodies and was the effect of an actual impulse ; but that, whatever was the case, it was
always a prime fact from which one could proceed to explain facts depending on it.
1
240 EPILOGUE
Maupertius, Oeuvres, i, p. 92. Or d'Alembert, in his Discours Preliminaire to
the Encyclopedic who points out that in certain regions of physics where it has so
far proved impossible to apply mathematical calculations the only resource is
to
collect as many facts as possible, to dispose them in the most natural order, to connect
them to a certain number of principle facts from which the others can be drawn as
consequences.
68. A particularly striking account of Lavoisier's attitude is given in the Discours
Preliminaire to his Traite Elementaire de la Chimie (Oeuvres, 1 (1864), pp. 1 ff.
69. For an account of ideologue thought see Picavet, Van Duzer.
70. Especially his Essai sur Vorigine des connaissances humaines. For a recent
account of Condillac's philosophy see the work by Knight.
71. Thus d'Alembert, Discours Preliminaire to the Encyclopedic
The universe, if we may be permitted to say so, would only be a single fact and a great
truth for whoever wished to embrace it from a single point of view :
or Laplace
All phenomena, even those which by their smallness seem to be independent of the
great laws of nature, are in fact the consequences of these laws every bit as necessary
as the revolutions of the sun. In our ignorance of the links which connect them to the
whole system of the universe they have been made to depend on final causes or on
chance, depending on whether they occur regularly or without apparent order, but
these imaginary causes have been successively pushed back with the bounds of our
knowledge, and they disappear entirely before the wise philosophy which sees in them
the expression of our ignorance of the true causes.
Essai Philosophique sur les Probabilites (3rd ed., Paris, 1816), p. 2.
72. Thus for Lavoisier truth was only to be found 'in the natural linkage of experi-
ments and observations' (op. cit., p. 4).
73. Op cit., fol. 158.
74. Analytical Theory of Heat, p. xvi.
75. See below p. 334.
76. See Gouhier, vol. 3, p. 235.
77. Comte, vol. 1, p. 17.
78. Ibid., vol. 2, p. 435.
79. Ibid., vol. 2, p. 648.
80. Some consideration has been given to this question as regards the physical
sciences in Herivel (1), Fox (especially pp. 262 ff.) and Boughey (unpublished
thesis). For the biological sciences see the interesting account of attitudes in
Cahn, chapter 26.
81. See Herivel (2).
82. See above, chapter 6, p. 135.
83. See above, chapter 4, p. 75.
84. See below, Letter II, Appendix, p. 251.
85. See Grattan-Guinness (3), p. 82, n. 6.
86. See Biot, Melanges, vol. 3, p. 122, n. 1.
87. See below, Letter VI, Appendix, p. 259.
88. For example, in a letter of around 1806 found in BN MS. 22501, fol. 71.
89. See below, Letter XX, Appendix, p. 316.
90. On the other hand we must remember how Fourier excused himself for lack of
references to earlier works on trigonometrical expansion on the grounds that
EPILOGUE
241
no mathematical works were available in Grenoble. See Letter XXI, Appendix,
p. 320.
91. See above, chapter 8, pp. 162-6.
92. See above, chapter 5, p. 99.
93. Op. cit., chapter 1, sect. 6.
94. See above, chapter 5, pp. 100-103, chapter 7, pp. 153-8.
95. See below, Letters XVII-XXI, Appendix, pp. 302-321.
96. See below, Letter XVII, Appendix, p. 303.
97. Poisson (5).
98. Cousin, p. 39.
1
APPENDIX: LETTERS
Fourier to Bonard, May 1788
This 22 May 1788.
Sir,
On occasion others have graciously forgiven me too long a silence ; I hope
for the same indulgence from you. This accursed habit follows me every-
where, call it what you will ; the fact remains that I like and infinitely esteem
people, and yet do not write to them. However, I only wrong myself, it is
one pleasure the less and you know that I have said goodbye to pleasures
for the moment.
I allow myself few details on my present situation: sunt bona mixta malts.
I am present at studies, classes, recreations, and arithmetic lessons; we
shall soon be at fractions ; all these petty concerns and a thousand others
render me neither less content nor less happy. I did not want to devote
myself to pleasures, but rather to study and to religion. Esteem and friend-
ship make up for everything. Many people here are predisposed in my
favour, but I honestly fear that I may not live up to the notion they have of
my talents. I have made so exclusive a study of mathematics and science
that in literature I am only left with a taste for the subject and very little
expertise in it.
I have quite lost sight of what I wrote in algebra, 1 I really must busy
myself with it one day. I wait for news. I should be enchanted to know the
opinion of the mathematicians ! But it would be pointless to hope for any-
thing else, [though] I have no doubt of your interest in the matter. 2
I pay with interest to Morphee all the nights I stole from him at Auxerre :
there is no time left for living when one sleeps eight hours [a night], and my
nights are not those of Descartes. 3 My health 4 is as good as it can be : rest
and a regular life no doubt contribute to its improvement. In short, up to
the moment I am far from repenting a step taken against the advice of many
persons.
I have examined your solution of this little question in analysis, it is very
elegant: the result agrees with mine, and hardly with that of M. de Guis-
tiniani; 5 he must be consoled for this mischievously; I shall write to him
244
I. FOURIER TO BONARD, MAY 1788
perhaps one of these days ; I should like to know how he is getting on in
his new position, and what is your opinion on this subject and that of
Dom Laporte 6 and his [Guistiniani's] pupils. I still do not know if I shall
be able to send you on this present occasion a certain memoir that I cannot
decently keep any longer, for it is certainly yours. I have not forgotten it.
Here is a little problem of a rather singular nature : it occurred to me in
connection with certain propositions in Euclid we discussed on several
occasions. Arrange 17 lines in the same plane so that they give 101 points
of intersection. 7 It is to be assumed that the lines extend to infinity, and
that no point of intersection belongs to more than two lines. The problem
must be reduced purely to analysis so that given m and n one can arrive at
the necessary equations.
Your memoir on a curve with double curvature should have been returned
to you. The author of this memoir is to a good mathematician as are
alchemists to competent chemists.
Dom Vaudret 8 and I recommend our sundial to you ; if he who made the
style has acquitted himself badly, I charge you to revenge me for his
clumsiness.
I am sure that as soon as M. de Montuclas 9 [sic] has replied to you, you
will not fail to inform me.
You could also send me some mathematical, physical and astronomical
news etc. ; M. de Guemadeuc 10 is in a position to instruct you. I would like
to know if the Marquis de Condorcet 11 has had published what he is said to
have written on modern calculus; if it is true that M. de la Grange 12 and
other academiciens employ eight months of the year in visiting the Fcoles
Militaires; I cannot persuade myself to believe it.
As to political news : those that fight each other destroy each other.
I have surrendered to Du Plessis 13 my subscription to the Journal de
Genive. 1 * The world and I are going to grow several years older without
knowing each other.
I end a letter which is already too long, you could revenge yourself by
the length of yours ; there would also be a way of correcting my negligence,
namely by setting me an example of the opposite quality. I recommend
you to try this method, you will oblige him who with sentiments of esteem
and attachment has the honour to be
Your very humble and obedient servant,
Fourier
To M. [Bonard], M. Fourier, at the royal abbey of St. Benoit-sur-Loire.
Notes
1. Navier,* in his introduction to the posthumous edition (1831) of Fourier's
Analyse des equations determines, refers to an early work by Fourier entitled
I. FOURIER TO BONARD, MAY 1788
245
Recherches sur Valgebre. Navier had seen an incomplete copy of fourteen pages
of this work certified by Fourier's close friend Roux to have been in the hand
of Bonard who told Roux that it had been composed by Fourier when scarcely
eighteen years old (i.e. early in 1786). Bonard also said that a more careful
copy of this paper was sent to Paris in 1787. This is presumably the work to
which Fourier refers here.
* Navier, L. M. H. (1785-1836). Mathematician and engineer. He entered
the Ecole Polytechnique in 1802 and passed on to the ficole des Ponts et
Chaussees becoming an engineer in the department of the Seine in 1807. He
entered the Academie des Sciences in 1824 and the same year was put in
charge of a suspension bridge over the Seine. Navier had the unfortunate
experience of seeing this bridge collapse before his eyes, but his reputation
was very great and was little affected. He was called to one of the chairs of
analysis and mechanics at the Ecole Polytechnique in 1831. He was the author
of a number of important papers on elasticity and on the movement of fluids
and is remembered by the so-called Navier-Stokes equations for the motion of
viscous fluids. He was a close friend of Fourier who entrusted him with the
care of his mathematical papers after his death, especially the manuscript of his
work on algebraic equations (Bio. Gen. ; Gde. Encycl.).
2. Reading between the lines it would seem that Fourier had originally some hope
that the brilliance of his paper would not only impress the 'mathematicians'
but would also lead to 'something else' perhaps a teaching position in mathe-
matics. In fact we know that on leaving St. Benoit he returned to Auxerre to
assist Bonard in the Ecole Royale Militaire.
3. Meaning that Fourier's nights were not spent usefully like those of Descartes
in dreams which suggested the strategy of his philosophical researches.
4. According to a curriculum vitae of Fourier (Fourier Dossier AN) he suffered in
1783-4 from a serious illness possibly brought on by excessive application to
his studies including those carried on surreptitiously by candle-light in the suffo-
cating atmosphere of the 'cupboard'.
5. No trace of a de Guistiniani has survived in the local records. Possibly it was a
pseudonym.
6. Charles Marie Laporte. Born at Ambournay around 1755. He obtained a
position in the Ecole Royale Militaire where he was for a number of years
deputy principal under the principal, Rosman.* In 1790 he was one of a list of
teachers proposed to the municipality by Dom Rosman. He was dismissed
from the college in April 1793 with the other so-called professor-priests on the
demand of the local Popular (Jacobin) Society. On leaving the college he
became cure-doyen of Touchy. We do not know when he resigned this living
but on returning to Auxerre he offered his services to the college following its
reorganization by Dom Rosman in 1794-5. He was evidently not accepted, and
in November 1795 we find him president of the council of the commune of
Auxerre. He was still in this position when he was admitted as professor of
legislation to the ficole Centrale in 1796. When a secondary school was to be
set up to take the place of the ficole Centrale the municipality at first proposed
Laporte as director. Ultimately, however, a Monsieur Choin was chosen for
that position and Laporte did not enter the school until 1806 when he suc-
ceeded Choin. He was accompanied by his close friend Ducastel who had
refused two years earlier to enter the school in the absence of Laporte.
Laporte continued as director till 1825 and during the whole of this time
246 I. FOURIER TO BONARD, MAY 1788
there were excellent relations between the school and the town. His administra-
tion had a strong religious tincture, something which suited the temper of the
majority of the townsfolk who (like Fourier) had long abandoned the revolu-
tionary fervour of 1789-94. However, judging by the following extract from a
letter written in 1821 not all the pupils found the instruction or tone of the
school to their liking :
M. Laporte made me stay in again yesterday during the walk. He has recently done
certain things which would make one think him a trifle mad. He confiscated a very
instructive geography book which spoke of all the departments of France and their
origin, of their productions, of the great men born in the different towns, of the various
wars, of the remarkable things which one finds there, because among these numerous
citations there was one of a gentleman from a certain part who thus commenced his
testament: 'I leave my soul to the Devil, my immodesty to the Capucins and my wine
cellar to the monks . . .' He preached on this for half an hour and ordered that the
person who had the book should have several impositions and should not go for a
walk, and on the score of it treated us as impious libertines and atheists. He so tor-
mented a young man of Autun that he was forced to write to his parents to come and
fetch him and he left at 1 1 .00 in the evening. As for myself, I do not bother myself
much with what he says, I do my duty in class the best I can.
And he continues later,
if you knew how arid and boring are the things we have to do you could not imagine it.
When I have worked an hour or an hour and a half I assure you that I have had enough;
we only work on 'letters' which have no more sense for us than Hebrew. M. Roux
tells us that it is only the beginnings which are difficult and that the rest is amusing. I
hope so.
Laporte lived on for four years after retiring from his position at the school.
He died in 1829 with a great reputation for saintliness and generosity, mourned
by all sections of the community, and two busts were erected to his memory,
one in the cathedral and one in the cemetery (Arch. Yon. Cestre (2)).
* See below Letter XII, n. 5.
7. The data given by Fourier leads to an impossible 35 pairs of parallel lines. If
1 01 were an error for 131 the answer would be 5 pairs of parallel lines and 7
other lines.
8. On the closure of St. Benoit-sur-Loire at the time of the Revolution its archives
were placed in the departmental archives of Loiret in Orleans. These latter
were largely destroyed by bombing in 1940. No record therefore remains of
Dom Vaudret or other humble inmates of the abbey.
9. Montucla, J. E. (1725-99). Historian of mathematics. Educated by the Jesuits
at Lyons he came to Paris where he made the acquaintance of d'Alembert,
Diderot, and their circle, and obtained a position in the Gazette de Paris. He
was appointed secretary to the Intendant at Grenoble in 1761, and was a mem-
ber of the astronomical expedition to Cayenne in 1764. Soon after his return
to France he was appointed head clerk of the royal buildings and royal censor,
positions which he later lost as a result of the Revolution. He retired to Ver-
sailles and devoted himself to the composition of his Histoire des Mathematiqu.es
of which the first two volumes were left incomplete at his death but were
finished by Lalande {Bio. Gen. ; Gde. Encycl.).
10. Armand Henri Baudoin de Guemadeuc. Born Colmar, 1734, died Paris 1814.
Around 1785, with the aid of two other citizens, he constructed inside the
church of the hospital of Tonnerre an astronomical sundial which is still
I. FOURIER TO BONARD, MAY 1788
247
standing. He was a member of the 'Lycee de PYonne' an historical and scientific
society founded after the Revolution in Auxerre by the Prefect of Yonne,
Rougier de la Bergerie. Fourier, who was a member of this society, was often in
correspondence with Guemadeuc on astronomical topics (M. Richard, Auxerre,
private communication).
11. Caritat, M. J. A. N., Marquis de Condorcet (1743-94). Educated by the Jesuits,
and at the College Mazarin, he early attracted the attention of the foremost
mathematicians of the day by his 'Essai sur le calcul integral' (1765). He was
elected to the Academie des Sciences in 1769 and produced a number of
important works on mathematics including a memoir on integral calculus
(1772) said by Lagrange to have been 'filled with sublime and fruitful ideas
which could have furnished material for several works'. About this time he
became acquainted with Turgot and Voltaire and on the latter's advice and
that of D'Alembert he began to train himself in the composition of academic
eloges. This may have contributed to his election as permanent secretary to the
Academie des Sciences instead of Bailly, but it also seriously interfered with his
mathematical output and thereafter he produced no further works of importance
in that subject.
When Turgot became controller general of finances in 1774 he had Con-
dorcet elected inspector general of moneys, a position which he retained after
Turgot's disgrace — his own resignation being refused — and which he con-
tinued to fill up to 1 79 1. When the Revolution broke out he became one of the
foremost champions of the liberal cause. He was especially prominent for plans
for the reform of French education later to be taken up by the 'Ideologues'.
After Varennes he became a Republican and thus lost most of his friends.
Elected a member of the Convention by Aube, he mostly voted with the
Girondists. With his friend Thomas Paine he pleaded in vain for the life of the
King.
When the Gironde fell Condorcet imprudently attacked the new constitution
which had been hastily drawn up to replace the one for which he himself had
largely been responsible. As a result he was denounced by Chabot, decreed
arrested, and forced into hiding. In March 1794 he left Paris and after wander-
ing for a few days in the suburbs was arrested as a suspect and died in prison
(possibly by his own hand) on 29 March 1794.
Like his uncle, for a time bishop of Auxerre, and from whom he had a small
inheritance, Condorcet was no politician. His uncompromising directness of
manner and inability to suffer illogical windbags in silence made him many
enemies and few friends. His weak voice, lack of oratorical powers, and ten-
dency to bore the Convention by the excessive height of his arguments was
one of the tragedies of the Revolution. If his intellect had been matched by the
eloquence and charm of a Fourier he might conceivably have saved the life of
the King with incalculable consequences for the later history of the Revolution
both in France and Europe.
After a long absence from mathematics Condorcet took up his treatise on
integral and differential calculus again including an entirely new treatment of
infinitesimals. The printing of this new work began in 1786 but terminated at
p. 17 and was never continued. No doubt it was this still-born work to which
Fourier referred (Bio. Gen. ; Gde. Encycl. ; Robinet).
12. Lagrange, Joseph Louis (1736-1831). Born in Turin of parents of mainly
French descent, being connected to Descartes on his father's side. He had at
248 I. FOURIER TO BONARD, MAY 1788
first a great love of letters with no special interest in mathematics but by the
age of seventeen he had already become a master, and a few years later had
drawn to himself the attention of the foremost mathematicians of the day by his
publications in the Academy of Turin. In 1764 he was awarded the grand prize
of the Academie des Sciences for a memoir on the libration of the moon in
which he made use of the principle of virtual velocities which was later to form
the basis of his Mecanique Analytique. In 1766 he replaced Euler as director
of the mathematical section in the Academy of Berlin remaining there until 1787
when he moved to Paris at the invitation of the French government and became
a member of the Academie des Sciences of which he had been a foreign asso-
ciate since 1772. After the publication of his masterpiece the Mecanique Ana-
lytique in 1788 he lost interest in mathematics for a time and devoted himself to
other subjects, especially chemistry. In 1792 he became a member of the com-
mission of weights and measures on which he continued to serve as president
after the removal of Lavoisier, Borda, Laplace, Coulomb, and Delambre. He
retired for a time during the Terror being saved from exile by the influence of
Guyton de Morveau. On hearing of the execution of Lavoisier he remarked to
Delambre: 'it has taken them but a moment to lop off this head but perhaps a
hundred years will not suffice to produce the like again.' The foundation of the
Ecole Polytechnique re-aroused his interest in mathematics and led to the
composition of his Theorie des function analytiques (1797) for the use of the
pupils of that school. At the very end of his life he had a final burst of creative
activity aroused through a paper by S. D. Poisson which led him to undertake
a second edition of his Mecanique Analytique containing much new material.
Lagrange was married twice, once in Berlin where he lost both his wife and
their only child. In 1792 he married the young and beautiful daughter of the
astronomer Lemmonier who rendered the last twenty years of his life ideally
happy. Lagrange was a man of few words whose favourite expression was 'I
do not know'. He always refused to allow his portrait to be drawn believing
with Pascal that 'penser fait le grandeur de I'homme' and that only the pro-
ductions of the mind have a right to immortality. He was of a naturally delicate
constitution and was extremely moderate in all things except work. Besides his
work in analytical dynamics, Lagrange made important contributions to the
theory of sound, to the theory of numbers, and to various branches of analysis
especially the calculus of variations of which in company with Euler he was
essentially the founder (Bio. Gen.; Gde. Encycl.; notice by Delambre (La-
grange, CEuvres, 1, pp. ix-li); Biot, J. B., (5), Vol. 3, pp. 117-24).
13. Possibly the same as the Duplessis who signed the 'patriotic address' of 15
October 1792 of the Society of Friends of the Republic in Auxerre in company
with Bonard and other radicals, or the Huet-Duplessis listed as one of the
professors of the college in Auxerre following the expulsion of the remaining
'teacher-priests' and its takeover by the radical party led by Balme and Fourier.
14. There were two 'Journal de Geneve' appearing in 1788. One appeared only
between August 1787 and January 1791 and was purely a depot of facts and
information relating to the district of Geneva. The other, founded by
Panckoucke under the tide Journal historique et politique (45 Vol., 1772-83),
and continued by Mallet du Pan the elder (16 Vol., 1784-7), was given the
title Journal historique et politique de Geneve (18 Vol., 1788-92). During its last
period the printed cover bore the sole title Journal de Geneve. Fourier is
evidently referring to this latter journal. According to E. Hatin (Bibliographie
I. FOURIER TO BONARD, MAY 1788
249
historique et critique de la presse periodique franpaise Paris, 1866, p. 73), 'The
long duration of this sheet, founded by Panckoucke, which had the advantage
of appearing three times a month, sufficiently proves the regard in which it
was held by contemporaries : it can be consulted as a faithful resumee of all the
gazettes and public papers of the period'. Fourier would therefore have been
well informed of events in the external world at least up to the time of the
surrender of his subscription.
II
Fourier to Bonard, March 1789
22 March 1789.
Sir,
I am going to take you away for a moment from possibly more agreeable
and certainly more profitable occupations. I shall try not to be lengthy, but
shall still be too long-winded. At a time when everything resounds with the
news of the day, you nevertheless do not expect me to talk about it with
you; it was only recently that I learnt that the States are to be held at
Orleans, 1 and I would perhaps still not know about it if I did not know that
the Father Prior is at present there to take part in the election. I would,
however, be able to tell you that M. Favre is no longer the Knight of
Hongry; he tells me in a letter dated 21 December that he is a postulant
with the Bernadins, 2 a very strange metamorphosis. He wrote to me at the
FJcole Militaire. I replied to him from Saint-Benoit. I shall not talk to you
of the accidents caused by the Loire; 3 they frightened many, and did harm
to some, but to me neither one nor the other.
A misfortune which I feel much more is the lack of books. Is it not to be
condemned to ignorance not to be able to read any other books but one's
own? It is a privation not to be consoled by all philosophy. I have no
books to read but a miserable copy of Montaigne lacking certain pages
which I am reduced to guess at; I busy myself a little with Greek; you
can well believe that it is for reading Euclid and Diophantus rather than
Pindar and Demosthenes. My health is not too good. For the last five
weeks I have constantly had a weak stomach and difficulty in sleeping. I
sometimes think that I have bought very dearly 4 some rather fragile
knowledge for which it will be difficult to find a market.
I have worked at these methods of elimination again ; it is not difficult to
see how defective are those commonly employed, but it is very difficult to
replace them by better ones. You can certainly see that I would need to have
the work of M. Bezout 5 on the same subject before me. Alone and without
help one can meditate but one cannot make discoveries ; often by flying the
world one becomes better, but not wiser; the heart gains and the mind
loses. Montaigne likes to preach incuriosity, he cannot make a proselyte of
me. I have put in order everything contained in the memoir you have on
numerical equations. 6 Everything is explained and demonstrated, but
nothing is written. If I could be judge in my own case I would assure you
again that these are the true methods, that the Italian ones are absurd and
II. FOURIER TO BONARD, MARCH 1789
251
opposed to all that is most certain in analysis, that they have held up the
progress of algebra, that it is to them one must attribute all the disorder and
imperfection that one is grieved to find in a science more than twenty
centuries old; that it is impossible that a genuine mathematician should
reject such powerful evidence. So, my dear sir, you can be certain that
these truths only need to be known to be approved. But will they be?
Admit that I have a right to doubt it. I begin to take M. Montuclas [sic] at
his word when he tells us he has fallen out with learned analysis: I wait
calmly for him to be reconciled with it. 7 To you, Sir, who have brought
to the matter the concern of friendship, I can only offer my sincere but
worthless gratitude. I was telling you that I have thought about the
question of numerical equations ; I have discovered a very inexact passage
in the memoir in your possession; it concerns a theorem on the nature of
the roots when certain of the coefficients are zero, its enunciation is de-
fective. The application made of it in an example is no less incorrect. I beg
you — and to do so is the first object of this letter after the pleasure of
assuring you of my friendship — to make a little note on it, I shall tell you
another time what the enunciation should be. This remark is of some
consequence, one must not replace errors by errors.
Forgive me the trouble this letter has caused you, all the disorder and
bitterness you will find in it. If you only knew the effect of a passion for the
truth when it is constrained to be sterile, and all the treachery which un-
grateful truth reserves for her devotees. But if it is hard to suffer her
caprices, it is very pleasant to complain of them. And who would grudge me
this pleasure ? For me pleasures are so rare.
With all the esteem which is due to you and with the most sincere
friendship, I am
Your very humble and very obedient servant,
Fourier
Yesterday was my 21st birthday, at that age Newton and Paschall [sic] had
[already] acquired many claims to immortality. 8
Notes
1. He is referring to the preliminary meeting of the three estates (clergy, nobility,
bourgeoisie) of the Orleans district to draw up lists of grievances and elect
delegates to the forthcoming meeting of the States General at Versailles. The
meeting of the assembly of clergy took place in the church at the Cordeliers,
Orleans, from 17 March to 2 April, 1789. From the minutes of this meeting
(which have been preserved) it appears that the prior of the Abbey of St. Benoit,
Dom Charpentier, played a leading part in the proceedings : he was a member of
one of the bureaux for verifying the credentials of delegates, was one of twenty-
six commissioners responsible for drawing up the 'Cahiers de doleances' of this
252
II. FOURIER TO BONARD, MARCH 1789
assembly, and was elected scrutineer at the election of delegates from the assembly
to the States General. He himself proclaimed the results (MS. 993, Bib. Mun.
d' Orleans).
2. The name often given to the reformed order of Cistercians founded by St.
Bernard of Clairvaux. Originally the order had been noted for its piety and the
strictness of its rule, so that by implication the Knight of Hongry — who has left
no other trace behind, though he was presumably one of the nobler kind of
pupils at the Ecole Militaire — was something of a gay dog before his meta-
morphosis.
3. A flooding of the Loire took place in January 1789 following a sudden thaw
after a period of extreme cold. The bridge at Orleans was damaged, that of
Jargeau was carried away, and four of the middle arches of the main bridge at
Tours were destroyed. There was also a flooding of the valley of the Loire
following the breaking of one of its banks downstream from Orleans. No doubt
all these events were interpreted as portents of future misfortunes.
4. Referring possibly to the effect on his health of excessive study while at the
ficole Militaire which in turn may have been responsible for the serious illness of
I784-5-
5. He is probably referring to Bezout's Theorie generate des equations algebraiques
(Paris, 1779)-
6. In the introduction to the posthumous (1831) edition of Fourier's Analyse des
equations determinees Navier refers to a meeting of a seance of the Academie
Royale des Sciences on 9 December 1789 at which Fourier 'commenced to read a
memoir on algebraic equations'. This could have been the memoir referred to
here. According to Navier there is no further reference to it in the minutes of
later seances. But Fourier himself in a letter of 1 1 April 181 6 to the president of
the Academie des Sciences refers to a memoir on which a report had been made,
'twenty-six years ago [i.e. in 1790] by Messrs. Cousin and Monge who particu-
larly desired to encourage my zeal'. This report would have been on the memoir
referred to by Navier.
7. He would seem now to be referring to the paper on algebra sent to Montucla for
an opinion by Bonard. (See above Letter I, n. 1.) The circumstances of Mon-
tucla's 'falling out with learned analysis' are unknown.
8. Pascal's early 'claims to immortality' would have been known to all aspiring
French mathematicians. In the case of Newton — that unavoidable English
phenomemon — Fourier would have read of the story of the apple in Voltaire
(Elements de la Philosophie de Newton) while Newton himself relates the history
of his early researches in light at the beginning of his first paper to the Royal
Society.
Ill
Fourier to Bonard, September 1789
St. Benoit, Sunday, September, 1789.
Sir,
On this occasion I shall no longer complain of your silence; I must
declare myself since you have done so. This correspondence with which
you yourself had charmed me was no more than a pleasing chimera; but
what is there that cannot be consoled by time and reason ?
The wish to publish what I have discovered in algebra, the long silence
of M. Montuclas, 1 and perhaps the fear of being forestalled, all this has
recently induced me to make some attempts to broadcast those truths
which I believe are important and of which Bonnardot 2 promised to
communicate an abstract to M. Monge, 3 and even to have them published.
I recalled that you might have been able to present your copy to M.
Legendre, 4 for I remember you mentioned the matter to me. You would
oblige me by informing me, as soon as your affairs will permit you, if M.
Legendre has read this paper; and if so what is his answer. I should like to
know before offering the abstract I have been telling you of to M. Monge.
If you were to put between your reply and my letter too long an interval
I might perhaps lose the opportunity which is going to present itself to
send what I have written to Paris.
I am your very humble and very obedient servant,
Fourier
P.S. Kind regards to Mme Bonard. It is not with her that I am annoyed.
M. Aubry 5 senior passed through here the day before yesterday. He is a
friend of M. Montuclas. He has promised to talk to him of my memoir.
Notes
1. For the long silence of M. Montucla see Letters I, II above.
2. He has left no trace behind.
3. Monge, Gaspard (1746-1818). Educated at the oratorian schools at Beaune
and Lyons, he was destined for the Church but withdrew on the advice of his
father and went instead as a draughtsman to the military engineering school at
Mezieres. There his talent was soon recognized and he was appointed to the
chair of physics in 1768. He was elected an associate of the Academie des
Sciences in 1789. He became an ardent revolutionary and served as Minister of
Marine from August 1792 to April 1793. Later he was a leading member of the
small group of scientists including Berthollet, Guyton de Morveau, and Four-
croy who put their talents at the disposal of the Committee of Public Safety
254 HI. FOURIER TO BONARD, SEPTEMBER 1789
during the dark days of 1793-4. He played a major part in the foundation and
early organization of the Ecole Polytechnique where he was also an inspiring
teacher. In 1797 he was sent to Italy with Berthollet to supervise the 'collection'
of works of art. There he was recognized by Napoleon who as a young officer
had been treated graciously by Monge while the latter was Minister of Marine.
Berthollet and Monge were later entrusted by Bonaparte with carrying the
treaty of Campo-Formio to Paris. A member of the Egyptian Campaign, he was
the driving force behind the Institute of Cairo of which he was the first president.
With Berthollet he again supervised the collection of works of art and other
valuables. He accompanied Bonaparte on the Syrian Campaign, and was
fortunate to recover from a serious illness at the siege of Acre. He returned to
France with Bonaparte in 1799 to take up his position again in the Ecole Poly-
technique which he always regarded (with justice) as his own particular creation.
He was forced to accept various honours from Napoleon including the title of
count and a seat in the senate. At the First Restoration his part in the Revolution
was overlooked, but on the Second Restoration it was remembered that he had
been a minister at the time of the execution of the King and he was expelled
from the Academie des Sciences and forbidden to enter the Ecole Polytechnique.
Heartbroken by these measures and the fall of Napoleon his last years were
spent in a state of deep melancholia with gradual loss of powers. Monge was
effectively the creator of descriptive geometry, a method of representing three-
dimensional bodies on a plane, and he also did distinguished work in the theory
of surfaces. Apart from Fourier his pupils included Dupin, Servois, Hachette,
Biot, and Poncelet (Gde. Encycl. ; Aubry; Taton (1)).
4. Legendre, A. M. (1752-1833). He studied at the College Mazarin and there-
after devoted himself entirely to mathematics especially the works of Euler
which he is said to have known by heart. On the recommendation of d'Alembert
he obtained a chair at the Ecole Militaire in Paris. He was a member of the
Academie des Sciences (1783) and of the Bureau des Longitudes. He made
important contributions to the theory of numbers and to analysis, especially
to the theory of elliptic and Eulerian functions. His Elements de Geometrie
(twelve editions 1794 to 1823) and his Theorie des Nombres (2 Vol. 1830) became
classics (Bio. Gen. ; Gde. Encycl. ; see also Beaumont).
5. This could have been J. B. Aubry (1756-1809), a member of the Benedictine
Congregation of St. Vannes, and the author of a number of books including
VAnti-Condillac, ou Harengue aux ideologues modernes (Paris 1801) (Bio. Univ.).
IV
Fourier to Bonard, October 1793
Equality or Death.
This 7th day, 2nd month,
2nd year of the French
Republic one and indivisible.
Joseph Fourier, national agent, to citizen Bonard.
I beg you, my very dear fellow- citizen and colleague, 1 to do me two
equally important services immediately on receipt of the present letter.
In the first place, I would like you to visit citizen Roux, 2 the mathema-
tician, to find out from him if he has received a letter from me in which I
requested him to let me have about 400 francs : I have spent much more
than I anticipated on my journey, and out of 550 francs, I only have 5 left
at the most. This amount will not suffice for the remainder of my journey.
I anticipated this and had applied to citizen Roux ; I do not know if he has
fulfilled this commission. It could be that the registered letter has remained
at Orleans which I left quite a time ago.
If citizen Roux has not been able to render me this service, I beg you to
do it for him, at least for half the sum. And in the event of him having sent
it to Orleans you could inform me accordingly.
However, in this latter case, I would beg you still to send me some
additional money no matter what the amount so that I may be able to wait,
or rather since it looks as if I shall not return to Orleans, I shall write
immediately to have the letter returned to Auxerre, where I shall go,
moreover, without delay for my mission is finished and with every possible
success. The horses and military equipment will arrive directly.
I pass on to the second matter : you will have heard that the Department
of Loiret is not absolutely quiet and that the town of Orleans is somewhat
disturbed: I played some part in this matter and I behaved in it in con-
formity with the principles of the Revolution.
I realized how things stood with regard to certain difficulties which I
resolved with too much success not to irritate my adversaries. I have been
informed that they are going to denounce me to Ichon 3 by whom I was
delegated. I should like to know the details and consequences of this
denunciation which is no more than a trifle for me and which will, I hope,
in time rebound dreadfully against its authors.
I have written about this to Milon. 4 I should like to know if he has
received my letter, and the attitude taken by Ichon. I was expecting, I
256 IV. FOURIER TO BONARD, OCTOBER 1793
must confess, to be recalled temporarily. But now there is no longer time
for that since everything is completed. Please deal with this matter, I beg
you, with the speed of lightning. I am accustomed to this language, I who
for fifteen 5 days have been hurrying on night and day.
The most urgent thing, you will agree with me, is the money; let me
have it by return of post. That which remains to me will not last for two
days, since I have to feed two horses and my coachman. If citizen Roux
has already made the advance I have demanded of him, I beg you to tell
him that it will be returned to him as soon as I arrive. I thank you in
advance for all the trouble I am about to give you. Your kindness leads
people to importunate you and you will add this service to all that I owe
you.
Fourier.
National agent in the department of Loiret,
at Montargis, at the Angel Hotel.
Notes
i. Bonard and Fourier were both on the staff of the college at Auxerre and also
both belonged to the revolutionary committee.
2. Roux, Jean Louis (1769-?). Born at Cluny, he is given as professor in charge of
the sixth class in Dom Rosman's list of 1790 where he is styled as an abbe.
He was one of those who continued in the school under Balme's directorship
after the dismissal of Dom Rosman and the other professor-priests. He was
appointed one of the teachers in the new system of education inthe commune
of Auxerre on 26 Brumaire Year III and in 1795 was called to the Ecole Normale.
He was appointed professor of physics and chemistry at the foundation of the
ficole Centrale in 1796. In 1804 he became professor of mathematics at the
Fxole Secondaire a position he still occupied in 1823. Following a visit to
Auxerre, the Inspector General of Universities, Joubert, reported that Roux
was first rate but that HI ne connait pas le del'. He was, however, very careful to
hide it {Arch. Yon. ; Cestre (3) ; Tessoneau).
3. Ichon, Pierre-Louis (1757-1837). He entered the congregation of the Oratoire
and became professor of theology at the College of Condon in 1783. He was
elected deputy of Gess for the Legislative Assembly and for the Convention
where he voted for the immediate execution of the King. He was sent on a
mission to oversee recruitment of the levee of 300 000 in Gess and Landes in
March 1793. After several other missions (including that to Yonne) he returned
to the Convention after 9 Thermidor where he remained faithful to the Moun-
tain, defending Jagot against Merlin. He filled several administrative positions
under the Directory, the Consulate, and the Empire. In spite of being a regicide,
and of signing the Acte Aditionnel during the Hundred Days he escaped exile*
by reason of 'powerful protecting interests' (Kucinski).
Like so many other ex-ecclesiastics in the Revolution — it is not necessary to
go beyond Goyre-Laplanche for another, even more extreme example — Ichon
showed himself a decided enemy of the clergy both regular and secular, especi-
ally of the non-juring priests. A curious example of this anti-clerical bias is
IV. FOURIER TO BONARD, OCTOBER 1793
257
provided by an account of Ichon's contribution to a discussion in the Directory
of the department of Yonne on 25 Brumaire Year II (i.e. six days after the
seance at which the decree confirming Fourier's dismissal from his commission
was promulgated) relating to the destruction of the fleurs de lis sculptured on
the arches of the vaults of the cathedral of St. Etienne at Auxerre.
Citizens [said Ichon], one of our most important duties is to remove from the sight
of our fellow citizens all signs of priestly idolatry; for too long the people have been
both the vitctim and the dupe of all these vain marvels thought up by the priests to
propagate their superstitious empire. It is for you, in whom the people place their
trust, to obliterate the baubles of a religion disfigured by their ambitious hypocrisy. I
am going to tell you something of which you are no doubt unaware, for I scarcely
remember it myself. I was a priest, but lo, scarcely ordained, I recognized the error
into which I had been led, and in the space of six or seven years I carried out the
involved practices of that perverse institution no more than ten times {Arch. Yon. ;
Bio. Gen. ; Bio. Univ. (Ed. 1858); Kucinski).
* According to Bio. Univ. (Ed. 1858) he was forced into exile in 1816 and re-
turned in 1830.
Was probably the Paul Milon who headed the list of signatories of the address
of the Popular Society of Auxerre to the convention demanding the trial of the
King. Professor of the college of Auxerre under Balme's principate between
August 1793 and Messidor Year II, he was appointed one of the instituteurs to
the new system of education in the commune of Auxerre in Brumaire Year III.
He was dismissed from his position in Prairial Year III as a former Jacobin
and was not 'reintegrated' till Ventose Year IV. In July 1796 he was appointed
co-librarian in the new Ecole Centrale. A certain Milon is said (Cousin, p. 32)
to have been a close relation of Fourier {Arch. Yon. ; Cestre (3)).
Implying that Fourier left Auxerre on 22 Vendemiaire, that is the day before the
promulgation of Ichon's order of the 23rd.
V
Fourier to administrators of the Department of Yonne,
January 1794
Equality, Liberty.
This 24 Nivose, Year II of the
French Republic, one and
indivisible.
Joseph Fourier to the Administrators of the Department of Yonne.
Citizens, the National Convention has desired that there should be a
public library in all the principal department towns.
This wish has been fulfilled in the majority of the divisions of the
Republic.
The administration proposes to appoint a person to direct this establish-
ment in the commune of Auxerre.
Joseph Fourier, professor of eloquence, presents himself to fill this place.
Domiciled in this commune he has successively occupied there the
public chairs of mathematics, history, eloquence, and philosophy. Having
devoted himself since childhood, and possibly with too much ardour, to
the study of the exact sciences, passing his nights in instructing himself,
and his days instructing others he has need of several years repose.
He has no inheritance except time and no acquired wealth except public
esteem. His morals are beyond reproach and his civisme, sufficiently well-
known, is also attested by the election of the people who have placed him in
a public position. The place in question would suit a man of letters residing
at Auxerre and he solicits it as a national recompense.
He will only suspend his course of public eloquence when a citizen
agreeable to the administration has presented himself to replace him.
VI
Fourier to Bonard, January/February 1795
[Notes on the Ecole Normale and the persons attached to that Establish-
ment]
The Fxole Normale holds its sessions at the Jar din des Plantes, 1 in a
middling-sized place of circular shape; daylight only enters from above;
the pupils, who are very numerous, are seated in rows on the tiers of a very
high amphitheatre ; there is not room for everyone, and every day there are a
fair number who find the door closed ; if one is obliged to leave during the
session, one cannot enter again. Only pupils are admitted, on presentation
of their cards to the officer on guard or the sentry. Some exceptions are
made, however, in the case of a small number of loyal citizens and of
several women. At the back of the room, and within an enclosure separated
by a railing, are seated several Parisian scientists and the Professors. In
front, and on a slightly higher platform are three armchairs for the pro-
fessors who are to speak and their assistants. Behind them, and on a
second, still higher platform, are the two representatives of the people
Lakanal 2 and Deleyre, 3 in the uniform of deputies on detached service.
The session opens at 1 1 o'clock when one of the deputies arrives; there is
much applause at this moment and when the professor takes his place.
The lessons are almost always interrupted and terminated by applause.
The pupils keep their hats on, the professor who is speaking is uncovered;
three quarters of an hour or an hour later, a second professor takes his
place, then a third, and the usher announces that the session is ended. The
names of the professors are familiar to the men of letters who attend the
sessions and conferences. I have noticed Cousin, 4 Lalande, 5 Brisson, 6 the
bookseller Panckoucke, 7 several professors of the Lycee. 8 Several are
brought in official carriages or with the deputies; the professors never
come any other way. Here are some particulars about the professors:
these minutiae may appear superflous, but I am writing them because the
papers give no account of them. Lagrange, 9 the first among European men
of science, seems to be between 50 and 60 years old. He is however younger ;
there is a dignity in his features and a delicacy in his countenance: he
seems a trifle thin and pale; his voice is very weak, except when he becomes
animated; he has a very pronounced Italian accent and pronounces s like z;
he is very modestly dressed in black or brown; he speaks very familiarly
and with some difficulty; there is in his speech the hesitation and simplicity
of a child. Everyone sees clearly that he is an extraordinary man, but it is
260 VI. FOURIER TO BONARD,
necessary to have seen him to realize he is a great man. He only speaks at
the conferences, and there are certain of his phrases which might excite
derision. He said the other day: 'There are still on this matter many
important things to say, but I shall not say them'. The pupils, who for the
most part, are incapable of appreciating him, give him a rather poor
reception but the professors make up for it. Laplace 10 who is also like him
[Lagrange] professor of analysis had been nominated at Melun a pupil of
theScole Normale and had accepted [the nomination] ; the government has
repaired this administrative error. 11 Laplace is among the first rank of men
of Science, he is known in Europe as an excellent mathematician, physicist,
and chemist; he seems quite young, with a weak though distinct voice, and
he speaks with precision, but not without a certain difficulty; he has quite
an agreeable appearance and is dressed very simply; he is of medium build.
The mathematical teaching he gives has nothing extraordinary about it
and is very rapid.
Haiiy, 12 former abbe 13 is extraordinarily modest and simple; he is not
old; his dress is still almost that of a churchman moreover he refused to
take the oath. His speech is very distinct, he makes himself perfectly
understood and speaks with great elegance and ease. It would be impossible
to express oneself better. It is said that he knows his lecture by heart. It
seems that he reads part of it, although it is not always easy to be sure of
this for the professors are far away and they always have their lecture
notes in front of them. He is so timid that if anyone interrupts to ask for an
explanation he becomes confused and answers badly or not at all. It is not
that he is not very learned, and if he does not shine with the genius of the
first two (professors), he has at least all the brilliance of method and the
display of the most elegant demonstration.
D'Aubenton 14 is an old broken man who is almost carried to his chair;
he reads and speaks alternatively and is understood by no-one. There are
some repetitions in his lessons, but they are full of reason and knowledge.
There has never been a naturalist more completely and wisely learned.
There is a touch of good humour in his speech which adds to the respect
which he inspires.
Berthollet 15 is the greatest chemist we have, either in France or abroad :
he is not old and has a rather ordinary appearance. He only speaks with
the most extreme difficulty, hesitates and repeats himself ten times in one
sentence, and seems to find difficulties in the least important details of an
experiment. His course is only understood by those who study much or
understand already, and it is for this reason that he displeases the great
majority. His course is a collection of useful dissertations, very wise and
very learned : he has much difficulty in making himself understood.
Monge 16 speaks in a loud voice, he is active, ingenious, and very learned.
JANUARY/FEBRUARY 1795
261
As one knows, he excels in geometry, physics and chemistry; the science on
which he lectures is presented with infinite care, and he expounds it with
all possible clarity. One finds even that he is too clear, or rather that his
method is not sufficiently rapid. He will give private lessons in practical
work. He speaks very familiarly, usually in a precise way. He is not only to
be recommended for his deep knowledge, he is said to be very admirable
in all public and private respects. His appearance is very ordinary.
Thouin 17 is a very learned naturalist; he is now in Belgium, where the
government makes use of his talents. 18
La Harpe 19 is well known, and speaks with great elegance and taste; he
has not the charlatan tone with which one can reproach several others, but
he has a bantering and decisive way of speaking ; he speaks without having
any hint of constraint and he has a very clear voice. A very learned man of
letters, he makes no display of his knowledge, and only shows it when
appropriate, does not try, like others, to vaunt his art above all others, and
makes himself heard with pleasure by people of good taste. He has made no
secret of being a professed partisan, as one can see in his programme, and
is only approved in that respect by the crowd. The unjust persecution
which he says he underwent is not a sufficient excuse, for one must be
tolerant, even with regard to those who are not always so themselves.
Nevertheless, I find that of all the professors he is the one who speaks the
best.
Volney 20 is a rather young man, very well dressed, tall with a very
agreeable appearance. I know little of his writings. 21 He speaks easily and
chooses his words very carefully; his speech is slow and he seems to take a
pleasure in it. If knowledgeable people are not flattered on the score of his
taste, they are at least astonished by the glitter of his diction. He has tried
to fill his course with too much philosophy, and in the midst of these
brilliant accessories, the principal object of his teaching disappears.
Sicard 22 is well known as a teacher of deaf-mutes. Of short stature, still
young, he has a strong voice, distinct and vibrant. He is ingenious, interest-
ing, active and knows how to keep the attention of a large audience. He
pleases the crowd who bring down the roof in applause. He praises his
subject, his method and his principles, and at every turn talks of the
natural man, whom he claims to be deaf and dumb. He is a man of great
wit, without genius, who seems to be very sensitive and, is (I think), in
reality modest, but he has been beguiled by some sort of grammatical
system which he claims to be the clue to the sciences. He often speaks for a
long time and pompously, and there is something capricious in his accent
and diction. His theory of grammar, which is brilliant in certain respects,
is one of the craziest I know of. In spite of this there [is] talk of adopting it,
and even prescribing it in all the schools of the Republic. If this comes
262
VI. FOURIER TO BONARD,
about we shall have something to laugh about. Apart from this, Sicard is
full of enthusiasm and of patience and is a paragon of all the virtues, but he
is mad : that makes me think that he pleases the ladies, although he is small
and rather ugly.
Mentelle 23 is known at Auxerre. 24 His lessons are extremely informed
and have nothing in them worthy of the institution ; he talks reasonably, as
far as I can judge, for I scarcely every listen to him. Buache 25 is a very well
known geographer who speaks very badly and gives some indication of a
knowledge of the subject. Garat 26 is a rather young man of medium height,
and of a rather agreeable appearance. He has a loud voice with a very lively
and oratorical tone. His speech is loud and eloquent, he has less taste than
La Harpe but more warmth and vivacity. As for the substance of what he
says I find his ideas a trifle fanatical: he talks of nothing less than the
perfection of human organization and of opening up ways to the human
spirit hitherto unknown. He greatly and almost exclusively praises Bacon,
Locke, and Condillac of whom he is an enthusiastic admirer. However, one
would have to be unfair to deny Garat superior and extraordinary talents :
he is, after La Harpe, the one I most like to hear talk.
You will find me very bold to dare thus to judge these superior men, but I
only give you the first impressions made on me, and I shall admit my
errors as I recognize them. In another note 27 I shall give my opinion of the
pupils, I shall speak of them with that liberty of thought which I have
always cherished and which I shall never give up. I shall also send a note of
the books which could most usefully steer education in the direction which
the government wishes to give to it today.
Notes
i. Founded in 1635 the jfardin des Plantes had at first been a centre for the culture
and study of medicinal plants. With the appointment of Buffon as director in
1739 the field of study was gradually extended to the whole of biology. It was
reorganized by the Convention's law of 10 June 1793 and had had its name
changed officially to Museum d'Histoire Naturelle under which name it had
been opened to the public on 7 September 1794. But the old name lingered
on.
2. Lakanal, Joseph (1762-1845). Educated by the 'doctrinaires' he entered their
congregation and taught in various colleges. Elected to the Convention for the
department of Ariege he voted for the immediate execution of the King without
stay or appeal to the people. He was elected to the Committee of Public
Instruction in January 1793 and was one of the most active and influential
of its members. He was largely responsible for reorganizing the Museum
d'Histoire Naturelle. He instituted a competition for composition of books for
public instruction and presented a plan for national education (26 June, 1793).
On the replacement of the Committee of Public Instruction on 6 July he was
JANUARY/FEBRUARY 1795
263
elected one of six members of the new committee. Elected secretary of the Con-
vention on 21 August 1793 he had the Ecoles Militaires suppressed, and
decreed (15 September) the setting up of three progressive degrees of education,
universal, secondary, and special. He returned to the Committee of Public
Instruction after 9 Thermidor. On 28 October 1794 he presented his report on
public education, and on 30 October decreed the formation of the Ecole
Normale. On 12 November he was named with Sieves representative of the
Convention at that school and on 18 November he had the law of public
education passed. On 25 February 1795 he presented a project for the estab-
lishment of Ecoles Centrales. He co-operated in the establishment of the
Institut being himself admitted to the Second Class. After the coup d'etat of 18
Brumaire he took over the chair of ancient languages at the Ecole Centrale de la
Rue St. Antoine. In 1807 he became inspector general of weights and measures.
At the Restoration he was dismissed from his employment and from the
Institut, and was proscribed as a regicide. He sought refuge in the United
States becoming president of the University of New Orleans and did not return
to France until 1833 when he was readmitted to the Academy of Moral and
Political Sciences in succession to Garat (Bio. Gen. ; Gde. Encycl.).
3. Deleyre, Alexandre (1726-97). Educated by the Jesuits he became acquainted
in Paris with Rousseau, Duclos, Diderot, and d'Alembert and contributed an
article on Fanaticism to the Encyclopedic Elected to the Convention for the
Gironde, he voted for the death of the King. He was elected to the Council
of Ancients in 1795 in which year he also became a member of the Second
Class of the Institut. He was the author of several comedies and published a
French translation of an English analysis of the philosophy of Bacon (Bio.
Gen. ; Gde. Encycl.).
4. Could have been: Cousin, J. A. J. (1739-1800), professor of physics at the
College de France. Became a member of the municipality of Paris in 1791 and
later sat on the Council of Ancients. He was elected to the Academie des
Sciences in 1772 and was the author of a number of well-known text books
including 'Lecons sur le calcul differentiel et le calcul integral' (Paris 1777).
Or Cousin, C. Y., known as Cousin d'Avallon (1769-1840). Historian and
compiler, author of a large number of books including many collections of
anecdotes (Bio. Gen.).
5. Lalande, Joseph Jerome (1732-1807). Educated by the Jesuits he changed
from Law to Astronomy following a visit to the observatory of Paris. On
returning to Paris in 1753 after a mission to Berlin he became a member of the
Academie des Sciences. In 1760 he succeeded Deslisle as professor of astro-
nomy at the College de France where his lectures attracted pupils from all parts
of Europe. He directed the Paris observatory from 1768 until his death. He
composed many eloges for the Academie des Sciences. His desire for public
recognition rendered him increasingly eccentric towards the end of his life. He
was the author of many works including his Traite d'Astronomie (1764) and his
Histoire celeste francaise (1801). His nephew Michel Lalande (1766-1839) was
also an astronomer who devoted himself more exclusively to astronomical
tasks than his uncle whose deputy and later successor at the College de France
he was, and with whom he collaborated in the Histoire celeste francaise (Bio.
Gen.; Gde. Encycl.; see also Aimable).
6. Probably J. M. Brisson (1723-1806). Naturalist and physicist. He acted as
assistant to Reaumur in his youth and succeeded Nollet in the chair of physics
264
VI. FOURIER TO BONARD,
in the College de Navarre. He was a member of the commission of weights
and measures. Elected a member of the Institut in 1795 (Bio. Gen.; Gde.
Encycl.).
7. Panckoucke, Charles Joseph (1736-98). He continued the trade of erudite
bookseller and printer commenced by his father Andre Joseph (1700-53) of
Lille. An enlightened and wise editor he attached himself in Paris to the ablest
savants and literary men of the day with whose help he was able to undertake
important publications including the Encylopedie Methodique (1781-1832), the
so-called Kehl edition of Voltaire revised by Beaumarchais, the works of
Buffon, and the memoirs of the Academie des Sciences. Under his editorship
the Mercure de Paris at one time counted no less than 15 000 subscribers. He
founded the Gazette Nationale or Moniteur Universel, from its first appearance
in November 1798 the unwearying and largely faithful witness of the wayward
course of the Revolution. His son Charles (1780-1844) continued the great
tradition of his father and among many other important works was publisher
of the revised edition of the Description of Egypt (1820-30) (Bio. Gen.; Gde.
Encycl.).
8. Almost certainly the Lycee founded in Paris in 1787 by Pilatre de Rozier for
teaching literature and sciences. It numbered among its professors at various
times Fourcroy, Chaptal, Thenard, Cuvier, Guinguine, La Harpe, and Biot.
Later (1803) it took the name 'Athenee de Paris'. Alternatively, but less likely,
Fourier could be referring to the less famous Lycee des Arts, founded in 1792,
whose title was changed to 'Athenee des Arts' in 1802. Unlike the Lycee, the
Lycee des Arts was exclusively concerned with scientific subjects, its main
object being the organization of courses of public lectures and the recognition
by means of prizes and medals of discoveries useful to industry and the arts.
Prominent early members were Lavoisier, Berthollet, Fourcroy, Lalande, and
Lamarck (Gde. Lar.; Gde. Encycl.; Crosland).
9. See above Letter I, n. 12.
10. Laplace, Pierre (1749-1827). Son of a poor cultivator, he had the good fortune
to encounter a first class teacher at the University of Caen, Christophe Gadbled
(1731-82) who was imbued with that strict sense of rigour essential to the
serious study of mathematics. Later he returned to the Ecole Militaire of his
native town of Beaumont-en-Auge from whence he proceeded to Paris with
letters of recommendation for d'Alembert. These were at first ignored, but
after Laplace had written d'Alembert a letter which was in reality an original
mathematical memoir the latter immediately summoned him and said 'Sir, you
see that I do not bother much about recommendations : you have no need of
them . . .'. Soon after d'Alembert had Laplace appointed professor of mathe-
matics at the ficole Militaire in Paris. In 1773 he entered the Academie des
Sciences and he also held positions as examiner at the school of artillery (where
he succeeded Bezout) and at the Bureau des Longitudes (of which he ulti-
mately became president). He was a member of the Metric Commission, and
of the Committee of Public Instruction and traversed the Terror safely in
spite of his earlier close friendship and collaboration with Lavoisier. Apart
from lecturing at the ficole Normale (Year III) he played an influential role in
the early years of the Ecole Polytechnique, being a foundation member of the
jury of examiners. Later he was president of the Conseil de Perfectionnement of the
school. After the coup d'etat of 18 Brumaire Laplace was appointed Minister of
the Interior only to be replaced some six weeks later by Napoleon's brother
JANUARY/FEBRUARY 1795
265
Lucien. In his memoirs Napoleon describes how Laplace quickly disappointed
his hopes and proved himself totally unfitted for the position :
He never grasped any question from the right end: everywhere he searched for
subtleties, had nothing but hypothetical ideas, and finally carried the spirit of the
infinitely small into administration.
Later Laplace was created a senator and count of the Empire, though this
did not prevent him signing the act of deposition of Napoleon. Towards the
end of his life, in 1826, he incurred much odium among the more liberal-
minded of his colleagues in both the Academie des Sciences and the chamber
of peers by his support for the infamous press law 'of justice and love'. Like
Newton, however, any personal defects in Laplace were overshadowed by his
single-minded devotion to science and the towering nature of his achievements
in his chosen fields of study, especially in celestial dynamics. Here he vastly
extended and refined all previous applications of the theory of gravitation, and
greatly reduced the number of cases where theory and observation failed to
agree, thus (ironically) paving the way for Einstein's general theory of relativity.
Apart from celestial dynamics he also made a major contribution to the theory
of probability in which his treatise was the point of departure for all later work
in the subject for the remainder of the nineteenth century. Laplace's approach
to mathematics was in sharp contrast to that of his friend and colleague
Lagrange. For the latter mathematics was a world in itself in which question
of elegance, clarity and harmony were primordial, whereas for Laplace mathe-
matics was above all a tool to help unlock the secrets of nature. But he was at
one with Lagrange (and Newton) in his humbleness before Nature, remarking
on his death bed: 'what we know is a small thing: what we do not know is
immense' (Bio. Gen. ; Gde. Encycl. ; Andoyer; Hahn).
11. This story could well have been apocryphal. But it epitomizes that undue, and
indeed unnecessary, regard for authority which seems always to have charac-
terized Laplace. In the gentle sarcasm of Fourier's account, and the placing of
Laplace among the first rank of savants behind Lagrange, the first of European
savants, there may be detected the beginning of an antipathy on Fourier's part
which — if Cousin is to be believed — eventually became fairly strong, although
Fourier was probably always careful to hide it, at least until he had become
permanent secretary to the Academie des Sciences, and which in any case he
would never have allowed to cloud his respect for Laplace's magnificent
achievements in theoretical physics.
12. Haiiy, Rene Just (1743-1822). Educated at the colleges of Navarre and Cardinal
Lemoine. Through attending the course of natural history of d'Aubenton he
became interested in mineralogy and later made fundamental contributions to
crystallography which entitled him to be regarded as the father of that subject.
He gave lectures on his new theory of crystals at the college of Cardinal
Lemoine before distinguished audiences which included Lagrange, Lavoisier,
Laplace, and Berthollet. Under the Revolution he first lost his benefice on
refusing to take the oath of allegiance to the State, and later his university
position. After 10 August he was arrested as a non-juring priest. Geoffroy
Saint Hilaire, who had been one of his pupils, determined to free Haiiy and
with the aid of members of the Academie des Sciences and the Jardin des
Plantes succeeded in obtaining an order for his release. But it was only with
great difficulty that he managed to persuade Haiiy to leave prison a few days
before the massacres of 2 September. He became a member of the commission
266
VI. FOURIER TO BONARD,
of weights and measures in September 1793 and keeper of the Cabinet des
Mines in August 1794. He was elected to the old Academie Royale des Sciences
in 1783, and to the Institut on its foundation in 1795. His Traite de Mineralogie
was published in 1801 and the next year he became professor of mineralogy at
the Musium d'Histoire Naturelle (Bio. Gen. ; Gde. Encycl. ; Lacroix).
13. Fourier himself is styled abb£ on Dom Rosman's list of professors at the ficole
Royale Militaire Auxerre in 1790. Although this is the only occasion on which
he seems to be given this title in the records, it fits in well with his public
avowal on 21 April 1790 (see above chapter I, p. 13). But if he was in fact an
abbe like Haiiy, unlike Haiiy he would have had no compunction in taking the
oath of allegiance to the State. Perhaps these thoughts passed through Fourier's
mind as he wrote of the former abbe in the almost ecclesiastical dress, and
Bonard on reading the letter might well have recalled how a few years previously
this same [abbe] Fourier had christened his eldest child Joseph Antoine Rene
Bonard whose first name Joseph was no doubt given him for Fourier.
14. D'Aubenton, L. J. M. (1716-1800). Educated by the Jesuits, he became assis-
tant to Buffon in the composition of his Histoire Naturelle. He entered the
Academie des Sciences in 1744 and was Professor at the College de France
and the Jardin des Plantes. He was one of the first to realize the importance of
the study of comparative anatomy for the determination of fossils, a work
carried on by his pupil Cuvier. Entirely without worldly ambition, he devoted
himself wholly and exclusively to his subject. He was one of the most con-
scientious lecturers at the Ecole Normale giving sixteen lessons packed with
detail and laced with a certain amount of unconscious humour including his
memorable opening words: 'we are all here gathered together by a decided
taste for natural history' (Bio. Gen. ; Gde. Encycl. ; Alain).
15. Berthollet, Claude Louis (1748-1822). He graduated in medicine and in 1780
became one of the doctors to Madame de Montesson the mother of the Duke
of Orleans (Philippe Egalite). Thereafter he devoted himself increasingly to the
study of chemistry, in which he at first upheld the phlogiston theory. The seven-
teen memoirs which he published in support of this theory in the Academie
des Sciences marked him out as one of the most determined opponents of the
new views of Lavoisier. But in 1783 he made his amende honorable before the
Academie des Sciences of which he had become a member in 1780. Thereafter
he was one of the principal collaborators in the revolution in chemistry initiated
by Lavoisier. He made many original contributions to both inorganic and
physical chemistry. He was president of the scientific commission set up by the
Committee of Public Safety to study problems of physics, chemistry, and
mechanics important for national defence. In 1797 he was sent on a mission to
Italy with Monge to supervise the 'collection' of works of art. He performed the
same function in Egypt. In the revolt in Cairo in 1799 his firmness (and that of
Monge) under great danger contributed much to the saving of the Cairo
Institute with all its instruments and collections. He prospered greatly under
the Empire becoming a senator and grand officer of the legion of honour. In
1 8 14 he voted for the deposition of Napoleon out of horror of war, and was
rewarded by Louis XVIII with the title of count and a seat in the Chamber of
Peers. In his house at Arcueil he entertained many visiting scientists including
Davy, Watt, and Berzelius. In 1807, in company with Laplace, he founded the
short-lived but very influential Societi d' Arcueil (Bio. Gen. ; Gde. Encycl.).
16. See above, Letter III, n. 3.
JANUARY/FEBRUARY 1795 267
17. Thouin, Andre (1747-1824). At the age of seventeen he replaced his father as
chief gardener at the Jardin des Plantes, increasing the cultures and greenhouses
and making many contacts with botanists in similar establishments in other
countries. He was elected a member of the Academie des Sciences in 1786, and
became professor at the Museum d'Histoire Naturelle in 1793 (Gde. Encycl.).
18. A somewhat malicious reference by Fourier to Thouin's activities in Belgium
and Holland where he had been appointed by the French Government as one
of their commissioners to oversee the 'collection' of works of art. He later
performed the same function in Italy.
19. La Harpe, Jean Francois (1739-1803). Soon after completing a brilliant course
of studies at the College d'Harcourt he was imprisoned for verses lampooning
various members of the college. This harsh treatment, added to the grinding
poverty of his early years, embittered his spirit. After writing for a time for the
theatre where the great success of his early play Warwick was not repeated, he
turned to his true profession of literary and critical studies. In 1776 he was
elected to the Academie Francaise where in 1780 he read an eloge of Voltaire
whose affection and interest he repaid by a somewhat shocking flippancy and
lack of deference. He opened a course of literature at the Lycee de la Rue St.
Honore in 1786, which, apart from a period spent in prison, he continued till
1798. This course, which was enormously successful, was the first example of
literary teaching in France and contained a particularly brilliant, if somewhat
superficial, description of French literature in the seventeenth century. In 1793
he came out strongly in favour of the Terror in whose honour he composed an
ode. In spite of this he was imprisoned as a suspect in April 1794. Entering
prison as a confirmed Voltairian he left it after 9 Thermidor as a militant
Catholic turning savagely on his former heroes and principles, and he played
a prominent part in the Thermidorians ruthless anti-Jacobin press campaign
of 1794/5. The very favourable impression made on Fourier at the Fxole
Normale (Year III) by La Harpe's excellent delivery is in sharp contrast with
the impression evidently made on the stenographer whose record of his lec-
tures was judged by Alain (p. 183) as 'very mediocre, without order or method,
and containing nothing practical' as opposed to the order and clarity of the
records of the geographers Buache and Mentelle whom Fourier in turn found
deadly dull (Bio. Gen. ; Gde. Encycl.).
20. Volney, C. F. Chasse Boeuf, Comte de (1757-1820). Son of an advocate he
went to Paris after completing brilliant classical studies and studied first law
then medicine. But he was soon captivated by the then prevalent philosophical
discussions about oriental languages and civilizations and the study of an-
tiquity, and this led him to spend an unexpected legacy on travels in Egypt and
Syria from 1782-7. His description (1787) of these travels brought him great
fame. On the outbreak of the Revolution he was called first to the States Gen-
eral, and later to the Constituant Assembly where he played a distinguished part.
His attachment to the Girondins led to his imprisonment for a time during the
Terror. He was released after 9 Thermidor and was charged with a course of
history at the Ecole Normale. Sent to the U.S.A. in 1795 he was at first well
received by Washington but was later accused by John Adams of being a spy
sent to prepare for the return of Louisiana to France. He returned to France in
1798.
After 18 Brumaire he was at first a supporter of Napoleon, having known him
previously for his republican sympathies, and he was created a senator. Later
268
VI. FOURIER TO BONARD,
he became increasingly critical of the dictatorial tendencies of Napoleon. He
offered to resign in 1804 when the Empire was proclaimed. Napoleon tried to
humour him by electing him to the Legion of Honour but until the end of the
Napoleonic era Volney in company with Destutt de Tracy, Lanjuinais, and
other 'ideologues' continued a decided critic of the Napoleonic regime.
Created Count by Louis XVIII at the First Restoration he did not rally to
Napoleon during the Hundred Days and after the Second Restoration played
little or no part in politics, devoting all his time to the study and publication of
works on languages. A member of the second class of the Institut from 1795
onwards, he was elected to the Academie Francaise at the time of the suppres-
sion of the second class. He left money to the Institut for the Prix Volney for
the study of languages and comparative grammar (Bio. Gen. ; Gde. Encycl.).
21. Volney's best known writings prior to 1795 were his Voyage en Egypte et Syrie
(1787) and his Raines ou Meditations sur les Revolutions des Empires (1791),
especially the latter which was a best-seller and very influential in the Romantic
Revival in France.
22. Sicard, Roch Ambroise, Abbe (1742-1822). He entered the Church, and hav-
ing been initiated in Paris into the methods of the Abbe de L'Epee was placed
by Archbishop Cice of Bordeaux in charge of a school of deaf mutes. In 1789
he succeeded de L'fipee at the Paris school. He took the oath after the fall of
the throne on 10 August 1792 but was nevertheless imprisoned as a suspect on
26 August and would have been murdered in the prison of the Abbaye during
the September massacres if a certain Monnot, a watchmaker, had not covered
him with his own body. He was freed on 4 September and thereafter traversed
the Terror in safety. He was elected to the Institut on its foundation in 1795.
After the purging of Royalist sympathizers on 18 Fructidor he escaped deporta-
tion by hiding. For some unknown reason Napoleon could not abide him and in
spite of Chaptal's protection he was for a time reduced to a state of penury
until his fortunes revived at the Restoration when he received many sinecures
(Bio. Gen. ; Gde. Encycl.).
23. Mentelle, Edme (1730-1815). He tried his hand at finance and poetry before he
turned to geography and history in which subjects he became professor at the
Fxole Militaire in Paris 1760. He became a member of the Institut on its
creation in 1795. His brother Francois-Simon (1731-99) was a well-known
explorer and geographer.
24. Possibly as one of the inspectors of the Ecoles Royales Militaires.
25. Buache, Jean Nicholas (1741-1825). Through his uncle the celebrated geogra-
pher Philippe Buache (1700-73) he became a tutor in geography to the sons of
Louis XV and was later appointed first geographer to King Louis XVI. In this
position he received a salary of 24 000 francs a year with an apartment at the
Louvre. His lack of any knowledge of foreign languages often led him into
serious errors in the construction of maps. He entered the old Academie des
Sciences in 1781 and was elected a member of the Institut at its foundation. In
spite of his close association with the crown he traversed the Revolution in safety
and continued as chief geographer to King Louis XVIII under the restoration
(Bio. Univ. ; Gde. Encycl.).
26. Garat, Dominique Joseph (1749-1833). A lawyer by profession, he established
himself as a journalist in Paris. He became a member of the Lycee on its founda-
tion in 1786 and made a name for himself as a brilliant lecturer. He was a
member of the National Assembly where he played little part in the debates
JANUARY/FEBRUARY 1795
269
27.
but gave an excellent account of them in the Journal de Paris. He was nominated
Minister of Justice on 9 October 1792 on the recommendation of Danton. He
excused the September massacres on 22 October. He was responsible for notify-
ing the King of the death sentence and for supervising the execution. He suc-
ceeded Rolland as Minister of the Interior. His report of 27 May 1793 which
found Paris absolutely quiet a few days before the insurrection of 30 May
earned him the title of the 'optimist of the Revolution'. He retired from his
position of Minister of the Interior on 15 August 1793 and was arrested on 2
October but was soon released and passed through the Terror safely thanks to
the friendship of Barere and Robespierre whose oratorical and literary pre-
tensions he lost no opportunity of flattering.
He tried to save Condorcet, abandoned Robespierre on 9 Thermidor, and
was himself denounced on 9 March 1795 for his apology of the September
massacres, but escaped imprisonment although he was removed from his
position on the Committee of Public Instruction for a time. He became a
member of the Institut on its foundation in 1795 and took up his chair at the
Lycee again. He was president of the Council of Ancients in 1798 and continued
a staunch republican up to but not beyond the coup d'etat of 18 Brumaire. He
was rewarded by Napoleon for his support by the title of senator. He became
ever more sympathetic to Napoleon, but deserted him in 1814 to work for the
King. He was ignored by Napoleon on his return from Elba and equally at the
Second Restoration, but was not exiled in spite of his role in the execution of
King Louis XVIII, presumably because he had not voted over the question of
sentence (Bio. Gen.; Gde. Encycl.).
This note, if it was ever written, has apparently not survived.
VII
Fourier to Bonard, March 1795
Paris 28 Ventose, Year III
of the French Republic.
I write to you, my dear Bonard, to discover more clearly what is happen-
ing about me in the Commune of Auxerre; no-one has written to me about
it yet. I have vague news that I have been accused and condemned in the
sections 1 there. However disagreeable the details may be it is nevertheless
important that I should be informed of them. It is stated categorically that
the Abbe d'Avigneau 2 is among my denunciators and I hear all sorts of
stories on this score. I would never give credence to such absurdities, and
what renders this still more unbelievable is that I am said to be held up as a
peculator and a drunkard. Certainly I would only laugh at all that if I did
not know of what excesses 3 the armed vengeance of the factions are capable.
I beg you to transmit me some details which could help me to correct
these denunciations and to forestall them if necessary. I await this sad
service of your friendship for me.
I know that the assemblies of the sections, in the meeting last decadi*
decided that I should be denounced in their name and that they demand
at the same time my exclusion from the Fcole Normale. To whom is this
denunciation 5 addressed? On what grounds is it based? What was its
form and what result has it had up to the moment ? I beg to satisfy me on
these points. You could add, if you like, a notice of the discussion which
preceded the decision taken, as I am assured, in the four sections. This
deliberation seems to be very irregular, for before whom is the denuncia-
tion supposed to be brought ? Can it be supposed that I fall under the law of
5 Ventose ? 6 But it is entirely inapplicable to me. I am neither dismissed
from my office nor accountable. If I were able to consider myself as dis-
missed from office that could only be by the letter of the former Committee
of Public Safety which ordered my arrest but before 9 Thermidor. However,
the operation of this law is suspended. But from another point of view,
being attached to a national establishment and even employed in a specific
way by the government at the College de France, 7 only material facts can
harm me; and who will find these facts? Who can reproach me with an
act unauthorized by law ? I cannot believe that I shall be asked to give any
financial account, unless it be of my own money, nor of the blood I have
spilled, nor of the wine I have drunk. Is it then the terror I have inspired ?
My goodness, I cannot see that I have inspired much of it among the most
VII. FOURIER TO BONARD, MARCH 1795 271
feeble creatures — among women. And if I have understood some of them,
they seemed ready to make enormous sacrifices.
However, my opponents can leave it to my conscience, and I am judged
by it much more rigorously than they themselves would judge. Let them
take it as certain that I have done nothing arbitrarily and nothing that does
not emanate directly from a law. That is enough for me to feel no anxiety
under a good government. But it is perhaps not enough to satisfy myself,
and so I can add that my heart was never party to the evil produced by
circumstances. I voluntarily did what I thought was just and useful to the
cause which I embraced : what went beyond this I did not impede, but for
the most part I could not have done so without rushing to certain ruin. It
will be said that I should have taken the risk rather than tolerate injustice
and act as its instrument; that may be true, but at least let me be blamed
only by those who would have done so themselves in my place.
There is in Auxerre one man who is justified in hating me, that is
Moreau, 8 whom you know: I contributed indirectly to his arrest, but I did
so in public, and I refused to be involved in legal action against him. Soon
after, it was I who had him set free. Far from repenting this denunciation,
I would do the same again for a man of this sort should be unmasked.
Apart from this individual, I can swear by all that is most sacred that I have
not contributed in any manner to the arrest of any person, that those who
have experienced this misfortune ought to put it down to circumstances,
and that there are several persons who are indebted to me for the tran-
quillity which they have always enjoyed. 9 Moreover I believe firmly that
there are times of public danger when such measures are justified. Since I
am not able to pretend to myself that I have not done almost everything I
could without certain peril, I have a perfectly quiet conscience, and that is
no small thing.
I am, as you know, much disposed to become extremely anxious and so
all these rumours have greatly affected me: however, on reflection, I tell
you I cannot see how my enemies can succeed, because I am supported
here by persons of high repute. 10
I had wanted to write to the section in which my domicile is situated,
that of fraternity, I think; I would have presented my justification briefly,
and if it had been appropriate I would have obtained permission to visit
Auxerre for several days, to exonerate myself in person. Do you think it
would be fitting to do this, or to write a letter to the Assembly? I am
completely ready to take this action; you will tell me if you think it would
be useful, also the points which need to be emphasized and which seem to
have made the most impression.
I depend on your friendship for this service and I await a reply from
you as soon as possible. You will tell me also the news of your family; I
272
VII. FOURIER TO BONARD, MARCH 1795
know that you are a father for the third time, it is an occasion for my con-
gratulations and respects to citizen Bonard your wife.
Up to now my health has been fairly good ; this miserable affair greatly
disturbs me; whether it is mental uneasiness or excessive work, I am not
at all well ; I have been obliged to keep to my room today.
I devote myself to studying with more enthusiasm than ever, and I
would be perfectly content if only I were left in peace by your part of the
world. You know, perhaps, that I have been appointed director of the
mathematical conferences; 11 they take place every day, it is altogether
exhausting. You will sometimes see my name in the journal of the
school, 12 not the most pleasing thing for me, since they mangle everything
I say.
I spoke to you of a proof of the famous rule of Descartes, 13 I gave it to
Laplace and Lagrange who told me they would have it published : 14 I am on
very good terms with these two mathematicians, I sometimes talk with
them about Auxerre. The method of organizing the Jicoles Centrales 15 is
still uncertain. Laplace who is on the council of the Committee of Public
Instruction, still does not know if they will be organized immediately. It
seems that several professors will be chosen from the Jicole Normale,
something which does not exclude those like you who already hold an
appointment; it is possible that those persons who are not already in-
structors and those who are, but are not well enough known, might be
required to come to Paris to be examined, this is Laplace's opinion, but I
believe it impracticable. As to the pupils of the Jicole Normale, 16 they will be
examined here. All the indications are that the present organization of
primary schools will be abolished. The number of instructors who could
be called to the chairs of the licoles Centrales is very small. That is why all
those of recognized talent are sure of being appointed.
I beg you to remember me to our common friends : I salute and embrace
you.
Fourier
Notes
i. The number of sections into which the commune of a town was divided
depended on its size. Thus the commune of Paris had forty-eight sections
whereas Auxerre had only four.
2. D'Avigneau, Abbe. He was professor of Rhetoric at the college of Auxerre in
1790 under Dom Rosman. He became a member of the Societe d' Emulation
founded by Fourier in 1790. On 22 September 1797 he was awarded the prize
for poetry at the Fete of the Foundation of the Republic to the displeasure of
certain extreme republicans who evidently regarded his former clerical status
with suspicion (Arch. Yon.; Quantin; Cestre (2)).
VII. FOURIER TO BONARD, MARCH 1795
273
3. Fourier is thinking of the massacres of 'patriots' which had commenced in
certain parts of France, especially in the south of the country, towards the end
of the previous year (1794).
4. Each month of the revolutionary calendar contained thirty days which were
divided into three decadi.
5. This denunciation, which has been preserved, eventually reached the Com-
mittee of Public Instruction and initiated the process which led to Fourier's
second arrest as described in chapter 3 above.
6. On 23 February 1795, i.e., 5 Ventose Year III a decree had been passed on the
report of Merlin de Douai that all civil and military officials who had been
removed from their office after 9 Thermidor should return to the communes
where they had been living before that date and remain there under the super-
vision of municipal authorities. As Lefebvre says, this was a law of suspects in
reverse and those who were unfortunate enough, or foolish enough, to comply
with its terms sometimes suffered with their lives especially in the Midi where
their return to the scenes of their revolutionary 'activities' often 'marked them
out for massacre' (Lefebvre (3), p. 57).
7. As one of 10 mditres de conferences in mathematics at the F-cole Normale. See
Guillaume, vol. 5, p. 478.
8. He has left no trace.
9. The mother of Nicolas Davout, later Marshal of France, and Dom Rosman
are two of the persons Fourier is traditionally said to have 'protected* during the
Terror.
10. No doubt he is thinking of Lagrange, Laplace, and Monge, perhaps especially
the latter. After the attempted insurrection of the royalists against the Con-
vention on 13 Vendemiaire had been crushed by Napoleon's 'whiff of grape-
shot', J. B. Biot,* later a colleague and enemy of Fourier in the Academie des
Sciences, was one of those taken prisoner by the government forces. He owed
his freedom — and possibly his life — to Monge who recognized him as one of
his best pupils at the Ecole Polytechnique and had him freed (C. A. St. Beuve,
Nouvelles Lundis, z (1864) p. 76).
* Biot, Jean Baptiste (1774-1862). A pupil at the college of Louis-le-grand
he entered the army in 1793, and then became a pupil at the Ecole Polytechnique
where he attracted the attention of Monge. He was one of the insurgents
on 13 Vendemiaire, was captured and owed his release to Monge. He became
Professor at the Ecole Centrale at Beauvais in 1797. Through the influence
of Laplace he was appointed Professor of Physics at the College de France
in 1800 and a member of the first class of the Institut in 1803. In 1806 he
visited Spain with Arago to complete the measure of the arc of meridian
commenced by Lalande and Machais. In 1809 he was appointed Professor
of Physical Astronomy at the Faculty of Sciences. He worked in many dif-
ferent branches of physics and is remembered by the law of Biot and Savart
for the mechanical force produced by a magnetic field on an element of
current carrying wire. But his most important work was on the shape of
the earth as described in his Memoire sur la figure de la terre (1827), and
on the rotation of the plane of polarization of light by various liquids and
crystals. This latter work was the origin both of polarimetry as an analytical
method and of Pasteur's pioneering researches in stereochemistry. Having
prepared himself for the position of perpetual secretary at the Academie
des Sciences by literary productions such as his Essai sur VHistoire Generate des
274 VII. FOURIER TO BONARD, MARCH 1795
Sciences pendant la Revolution and his Eloge de Montaigne he was bitterly dis-
appointed to be passed over twice, first for Fourier (1822) and then for Arago
(1830). He was elected to the Academie des Inscriptions et Belles Lettres in 1841,
and to the Academie Franfaise in 1856.
The explanations of Biot's relative lack of success as a scientist in spite of the
enormous quantity of work he undertook is perhaps best explained by C. A. St.
Beuve who in an interesting essay on Biot (Nouvelles Lundis, vol. 2, 1864, pp.
70-109) relates that the 'competent' persons from whom he demanded an
opinion of Biot as a scientist were generally in accord that he was 'endowed
to the highest degree with all the qualities of curiosity, finesse, penetration,
precision, ingenious analysis, method, clarity, in short with all the essential
and secondary qualities, bar one, genius, in the sense of originality and in-
vention' (Op. cit., p. 71), (Bio. Gen., Gde. Encycl.).
1 1 . Taken by him at the College de France. See n. 7 above.
12. He is referring to the Ecole Normale.
13. For an interesting account of the history of this rule, and of the new proof
given of it by Fourier in his lectures at the Ecole Polytechnique, see Grattan-
Guinness (3), pp. 8-12.
14. But it seems to have passed into the canon by other means.
15. The famous Ecoles Centrales of the Directory formed part of a new system of
primary and secondary education — the first to take the place of the system
of the ancien regime which had largely been destroyed by the Revolution— laid
down in the decree of 26 October 1795. The thinkers responsible for this new
system — later contemptuously dubbed the ideologues by Napoleon — included
Ginguen6, Daunou, Volney, Francois de Neufchatel, Destutt de Tracy,
Cabanis, Lakanal, and Garat, based their educational beliefs on the sen-
sualism of the Abbe Condillac, especially in the interpretation of Cabanis
and de Tracy, the two foremost theorists of the movement. The Ecoles Cen-
trales marked a genuine educational innovation of great value, and although
these schools largely failed to achieve the aims of their founders, and were
soon to be abolished (1802 onwards) nevertheless they exercised an enduring
influence both inside and outside France. The full course of study in the
Ecoles Centrales was to extend over six years divided into three cycles of two
years each. The first cycle was devoted to Latin, design, and natural history.
Through an enlightened method of teaching pupils were supposed to acquire
in two years -a knowledge of Latin previously only attained in five or six. The
language was taught not for its own sake, nor out of respect for ancient tradi-
tions, but because of its utility in medicine and law, and for the training of the
mind it provided. Design provided a training of the pupils' observational
powers, and could contribute equally either to the prosperity of the future
artisan or to the enjoyment of the man of leisure. Natural history was of par-
ticular importance as it provided a prototype of sound scientific method based on
observations. It also brought the pupil into contact with nature, and this among
other things might lead to a much-needed improvement in French agricultural
practice which was in many respects backward compared with that in other
countries, especially in England. The second cycle was devoted entirely to
mathematics and the physical sciences, mathematics being studied for two
years and physics and chemistry for one year each. Apart from their obvious
utility, these studies could train the mind and rid it of the errors and super-
stitions of a priest-ridden gothic outlook. The final cycle was intended (by
VII. FOURIER TO BONARD, MARCH 1795
275
16.
the ideologues) as the crown of the whole course of education provided by the
ficoles Centrales. It was made up of grammaire generate, consisting of ideology —
that of the ideologues — and the principles of language and logic with especial
reference to the views of Condillac and his ideologue interpreters Cabanis and de
Tracy. There were also to be courses in legislation, history — to be taught from
a strictly unbiased, international point of view — and belles-lettres. The last
course was peripheral to the other studies, and was intended to give students
polish rather than a deep knowledge of literature.
The decree of October 1795 envisaged one ficole Centrale in every depart-
ment, the towns chosen in almost every case having a building of a former
college available. The departmental administrations were to be responsible
for the organization of the schools. This was probably a mistake, at any rate
from the point of view of the inculcation of ideological views, since many of the
administrators failed to follow the views of the ideologues closely enough. The
performance of the Ecoles Centrales from their foundation in 1795 until their
dissolution under Napoleon in 1802 varied greatly both from department to
department, and from subject to subject. Thus design and mathematics seem
to have been the most popular courses — pupils had freedom of choice —
followed by natural history and physical sciences, though the popularity of the
latter subject depended largely on the availability of apparatus. One general
factor which militated greatly against the success of the schools was the uni-
versally low level of primary education. Much of the time of the professors in
the Ecoles was thus taken up with elementary teaching instead of the more ad-
vanced courses envisaged by the ideologues. Needless to say, the course of
grammaire generate was the least popular of all the courses (Barnard; Fayet;
Williams).
In fact the Ecole Normale was closed down without examinations.
VIII
Fourier to Bergoeing, June 1795
Paris, 24 Priarial, Third
year of the Republic.
To Citizen Bergoeing, 1 Representative of the People.
Citizen ; I was arrested several days ago thanks to the civil committee of
the Section of Social Contract ; you will know the reasons for this detention
by taking cognizance of the order of the representative of the people
Mailhe 2 and of the printed letter 3 of the public prosecutor of the commune
of Auxerre. From these papers it follows that I have been included in the
number of citizens to be disarmed in the commune of Auxerre; my
personal defence had not been heard when this order was taken with
respect to me. I was then a pupil at the ficole Normale. Independently of
the duties which this position prescribed me, the Committee of Public
Instruction had imposed on me a more special duty by instructing me to
give a public course of mathematics in the College de France. I was not
able to visit Auxerre 4 to explain the grounds of my justification. They
were not known to the representative of the people, and I was informed by
letters from my relations that I had been included among those to be
disarmed before I knew the matter was being considered at Auxerre. I had
no kind of notification of the order concerning me. I had two brothers at
Auxerre neither of whom received this document. The citizen Mailhe
made a new order on 11 Prairial carrying the pain of detention against
those who resisted the disarmament pronounced against them. A statement
of this order was sent to each of the persons concerned. I was not at Auxerre
and the municipality of Auxerre knew that I was living temporarily in
Paris with the intention of studying medicine. 5 Neither myself nor any of
my relations received this new order. Nevertheless, I wrote to the muni-
cipality that / intended to obey without delay the order of the representative
of the people directing my disarmament, and in spite of the fact that I only
had an indirect knowledge of the order I would hasten to conform to it. I
declared that I was neither the owner nor the holder of any arms, and that if I
had had any, I would instantly have put them in safe custody, requesting this
declaration should be regarded as equivalent to the surrender of my arms. 6
Moreover no one contested the truth of my declaration and all those who
were acquainted with me knew well that I was never armed. This letter was
VIII. FOURIER TO BERGOEING, JUNE 1795
277
dated 12 Prairial and I protested that I had no knowledge of the later order
of the citizen Mailhe. In any case my country was distant forty-two leagues
from Paris. Fearing that this declaration would not appear adequate to the
municipality of Auxerre, I invited it in a second letter to indicate the
constituted authority before which it wished me to present myself to
effect my disarmament in a regular manner, in case my (original) declara-
tion was not approved. All this sufficiently proves, citizen, that I had no
intention of avoiding the measure directed against me, and that conse-
quently I did not come under the order of the representative of the people
dated 1 1 Prairial which had in any case been addressed neither to myself
nor my family. It seems to me that in accordance with natural justice I
should have been interrogated before suffering detention. When I was
arrested I was assured that I was only to be conducted to the Committee of
General Security to give an account of my conduct. I was placed provision-
ally in the prison Des Orties and the principal object of this petition is to
ensure that you should be so good as to proceed yourself, or be present at
my interrogation.
As to the charge of terrorism, I am unable here to advance all the reasons
which will convince you that these charges are unfounded. I shall only
insist on the incontestable facts that no-one in the commune of Auxerre
was condemned to death or judged by the Revolutionary Tribunal at Paris;
that no revolutionary tax was established of any kind whatsoever, that the
property of those detained was never confiscated, that no cultivator, artisan,
or merchant was arrested, that in what concerns me personally I believe
that I introduced into my conduct and my opinions a moderation which I
did not find in my adversaries, that far from having shared the revolutionary
madness of many men I regarded it with horror and blamed it publicly;
that I have experienced terror more than I have inspired it, as I was the
victim of it precisely on the same date a year ago, that I was arrested and
even condemned to death, 7 delivered by the unanimous demands of the
assembled sections, the same which abandoned me or pursued me today,
arrested again so that I owed to 9 Thermidor both life and liberty, so that
there is no one of my compatriots who has known more danger than I.
The representative of the people Guillemardet 8 sent to this department
after 9 Thermidor was familiar with the general facts which I have related
to you ; the citizen Mailhe did not think it proper to order any arrest, and
there is not any really just and lawful reason for my arrest. I confidently
address my complaints to you and I beg you to excuse the disorder and
length of this letter. I have scarcely enough freedom of mind left to justify
myself; your humanity will make up for that.
Fourier, Joseph
278
Notes
VIII. FOURIER TO BERGOEING, JUNE 1795
i. Bergoeing, Francois (1755-1820). A surgeon by profession, he was elected to
the Convention by the Department of the Gironde and sat and voted on the
right with the Girondins. At the trial of Louis XVI he voted for a reprieve and
imprisonment and appeal to the people. On 21 May 1793 he was named one of
the committee of twelve empowered to investigate the commune of Paris and
the plots against public order and liberty. On 2 June he was ordered to be
arrested. He fled to Caen, took part in the insurrection there, and was declared a
traitor to the country on 28 July. But he escaped and reappeared at the Con-
vention with the remnants of the Gironde in Year III, and was one of the most
ardent post-thermidorians. On the day of 1 Prairial he was one of those who
marched to the deliverance of the Convention. On 8 Prairial he denounced Panis
and contributed to his arrest. Later he entered the Committee of General
Security. He was a member of the Council of 500 where he opposed the royalist
reaction. A friend of Barras, he resigned on 19 Brumaire. He served Murat in
Naples under the empire and returned to Paris in 1815 where he lived in ob-
scurity till his death (Bio. Gen. ; Gde. Encycl.).
2. Mailhe, J. B. (1754-1839). A lawyer by profession, he was a deputy to the
Legislative Assembly. On 10 August 1792 he was able to save the lives of a
large number of royal guards. In the Convention he presented the report on the
question of the judgement of the King and came out in favour of a trial. He
voted for the death of the King, but for a reprieve. He lay low during the Terror
but after 9 Thermidor was one of the most fervent accusers of the ex-terrorist
Carrier. As a member of the Council of 500 he demanded in March 1796 the
dissolution of all Popular Societies. He was included under the proscription of
19 Fructidor Year 5 (5 September 1797) but was recalled by the Consuls and
nominated Secretary General of the Department of Hautes-Pyrenees. On his
return to Paris he gained a great reputation as a lawyer at the court of appeal and
the council of state. He was exiled as a regicide by the law of 12 January 1816
but returned to France after the July revolution (Bio. Gen.).
3. Unfortunately not in the file with the other documents of the case in the Archives
Nationales.
4. This should be compared with the apparent willingness to visit Auxerre ex-
pressed in Fourier's letter of 28 Ventose Year III to Bonard where he also
mentions his position at the College de France.
5. This is the only indication we have that Fourier ever thought of forsaking
mathematics for medicine.
6. Italics Fourier's.
7. Fourier must be referring here to his imprisonment in Auxerre in Messidor
Year II. But his condemnation to death is difficult to accept as he would need
first to have been transferred before the revolutionary Tribunal at Paris, and
there is no trace of this.
8. Guillemardet, Ferdinand Pierre (1765-1808). When the Revolution broke
out he was a Doctor at Autun. He was elected to the Convention where he
voted for the death of the King. On his motion the Convention had a medal
struck to commemorate 10 August. He was sent on a mission to the departments
of Seine and Marne, Yonne and Nievre in December 1794. At Nevers he ordered
VIII. FOURIER TO BERGOEING, JUNE 1795 279
the arrest of members of the revolutionary committee who had been responsible
for various illegal acts. He was appointed Ambassador to Spain in 1798 but was
recalled by Napoleon because of his inactivity and was appointed Prefect of
Charente-Inferieure. In 1806 he was transferred to Allier where he behaved
unwisely dying two years later of mental illness (Bio. Gen.).
IX
Fourier to Villetard, June/July 1795
To Citizen Villetard 1 Representative of the People
Citizen,
You have wished me to set forth the grounds of a justification rendered
necessary by unexpected calumnies. The notes which I address to you on
this subject will contain facts known publicly or privately which I claim to
be true. The exactitude and the veracity of this report will contrast with the
vague denunciations of certain obscure adversaries who are trying to turn
public opinion against me.
You know what my profession was at the time of the Revolution.
Devoted to the study of the exact sciences from childhood with an ardour
greater than would seem called for in such a calling, I achieved that suc-
cess in it which steady application hardly ever fails to produce. At i6^ years
I was appointed Professor of Mathematics at the military school of
Auxerre ; the memoirs 2 which I wrote four years later and which I read at
the Paris Academie des Sciences sufficiently prove my exclusive taste for
such researches. I recall these facts as at least plausible proof of the regu-
larity of my principles ; and, in fact, which one of my compatriots would
dare to question these principles, have I not passed all the days of my
youth in the strictest propriety, in the calm of passions which are even
excusable, 3 in the obscurity and silence of the study?
The first events of the Revolution did not change my way of life. Because
of my age I was still unable to speak in public ; and impaired by night studies
my health scarcely sufficed for the work my position required of me.
From another point of view I will admit frankly that I regarded these
events as the customary disturbances of a state in which a new usurper
tends to pluck the sceptre from his predecessor. History will say to what
extent this opinion was justified. Republican principles still belonged to an
abstract theory. 4 It was not always possible to profess them openly. As the
natural ideas of equality developed it was possible to conceive the sublime
hope of establishing among us a free government exempt from kings and
priests, and to free from this double yoke the long-usurped soil of Europe.
I readily became enamoured of this cause, in my opinion the greatest and
the most beautiful which any nation has ever undertaken.
The public duties which I carried out did not allow me either to wish for
or to undertake any others. The law of 21 March 1793, old style, having
established sectional committees for receiving the declarations of strangers
IX. FOURIER TO VILLETARD, JUNE/JULY 1795 281
and travellers, I was afterwards chosen in the General Assembly as a
member, something which nobody then regarded as a public position.
However the duties of these committees were successively modified, and
various laws entrusted them with a universal surveillance which soon
degenerated into very extensive powers since the law of 17 September
ordered them to proceed to the arrest of suspects. I had no doubt that this
measure was legitimate, and one could cite the illustrious Montesquieu 5 in
support of this opinion. However I considered myself much less fitted than
many others to enforce this law. I offered, even sent in, my formal resigna-
tion of the commission which had been given me — the original of my letter is
in the Public Archives 6 — and I ended by stating that if any of my co-citizens
were opposed to my resignation being accepted, I declared that I was determined
to persist in it, that any attempt to change my mind would be useless and em-
barrassing . . . that I would not be less zealous in defence of the liberty of the
people. 1
This move produced an effect opposite to what I had intended. In the
reply sent to me I was reminded of a law which forbade any official from
abandoning his post, and my resignation was rejected. At the same time
other persons openly accused me of abandoning my colleagues at a moment
when my help was about to become most useful to them. I was reproached
with the feebleness of my conduct, and some even seemed to doubt the
purity of my intentions.
I remained a member of the committee of surveillance of the commune
of Auxerre up to the time not long time past when a choice was allowed
between that position and that of school teacher. 8 That was the source of
all the persecutions which I have undergone.
In the month of Frimaire last when I was Professor of Mathematics at
the College of Auxerre, and unbeknown to me, the administrators of a
neighbouring district nominated me as a pupil of the ficole Normale. I did
not wish to accept without the authorization of the constituted bodies of the
commune of Auxerre. I informed the district administration of this
nomination, they confirmed it, and in the order addressed to me included a
fair testimonial of my civisme and principles. These administrators are
today still public officials. The Committee of Public Instruction and the
professors of the ficole Normale having entrusted me with giving mathe-
matical lessons to the pupils at the College de France, I was not, as I
wished, able to visit the commune of Auxerre to reply to my denunciators. 9
They realized all the advantage my absence gave them and employed it to
good effect. They had tried unsuccessfully to make use of the authority of
the citizen Guillemardet 10 — then on mission in this department — against
me. When the representation of the people Mailhe 11 succeeded him they
demanded my disarmament and obtained it. This measure was not taken
282 IX. FOURIER TO VILLETARD, JUNE/JULY 1795
against any one of my co-citizens without him being heard, but in my
case this was not possible. They managed to inspire the representative
of the people with the most fearful and even the most improbable
prejudices.
To the denunciation of terrorism which is habitual with them, and to the
reproach of having been a member of the Committee of Surveillance, I
reply with the following declarations.
I was entrusted by their own votes with a surveillance determined by the
law. I received this position without soliciting 12 it, I continued in it without
the power of withdrawing from it, and I exercised it without passion.
I had no grounds for hatred, I had up to that time formed so few links
with other people that I had no enemies. I respected the power which was
given to me; I said and repeated a hundred times that we would have to
render an account of it one day.
Let my opponents recall any act in which I participated and I will cite
the article of law on which it was founded. As regards the internal regime of
the house of internment, I argued that everything not expressly forbidden
by the law should be allowed.
Over a long period the committee was advised to sequester the goods of
those detained. I constantly opposed it; my opinion in this matter was
always that of my colleagues, and they all constantly rejected whatever
seemed to them to exceed the limits of the law.
No revolutionary tax was imposed of any kind whatsoever, and there
were never any domiciliary visits. 13 The National Convention never had
any need to free any tradesman, artisan, or cultivator. No family had to
grieve at this time for a father or a relation. The Revolution cost the life of
several of our co-citizens at this time, but it was on the frontiers of the state
that they lost their lives while fighting the enemies of the freedom of the
state. If there were dangers, it was our kith and kin who ran them, it was
my two brothers of whom the youngest fought from the beginning of the
first campaign, and who for the last two years have both maintained the
most alarming silence.
There remain, therefore, those citizens 14 who being nobles or priests
or relations of emigres found themselves included under the law of 17
September, and who experienced a temporary detention when they showed
themselves declared enemies of the Revolution. They accuse me of not
having been opposed to their arrest and will never pardon me for having
signed the warrants for their arrests. They pretended to believe that I
could have released them, and wanted me to make this use of the trust
which had been placed in me.
Being unable to accuse us of abusing our powers they reproach us with
excessive rigour, but far from having merited this insult I believe that I have
IX. FOURIER TO VILLETARD, JUNE/JULY 1795 283
accorded to humanity, friendship, generosity even, all that was allowed by
the letter of the law and the rigour of the times.
I could cite citizens that I defended against injust denunciations, those
that I protected by secret warning, 15 those that owed me their release from
prison. May I not recall also, since my adversaries stop at nothing, that I
was in the habit of defending innocence, feebleness, and error in the
courts. I never considered the profession, fortune, or the opinion of those
accused. I usually defended the poor, but some nobles, and even prisoners
charged with criminal offences, have asked me to speak in their defence.
Of all those who devoted themselves to these affairs I was the only one
who drew no profit from them, and I accepted from those that I defended
no recompense of any kind whatsoever. I am ashamed to make a show of
this disinterestedness, it is not for me to recall it, but I am reduced to
proving that I am not a monster of immorality and inhumanity.
The only fact that they cite in support of their denunciations is the
reproach of my having drawn up inflammatory addresses. Here is my reply
to this charge, the only one which is not devoid of all plausibility. I pass
over the inconvenience which would arise through regarding as punishable
today opinions advanced some two years ago, but I insist that my opponents
produce a writing of mine in which humanity is not respected ; that they
take care not only to recall isolated passages but that they cite the whole
writing. They have had sufficiently little discernment to attribute to me ad-
dresses in which I took no part instead of those which I did in fact compose.
If I were to be judged at the tribunal of Coblenz 16 I certainly would not be
acquitted, but I have nothing to fear if one has the honesty not to transform
into crimes errors and faulty opinions, and even exaggerations, which the
distance of the places, the actual sequences of events or a feeling of peril
may have caused. I have never provoked or approved any of the revolu-
tionary excesses or violent measures which have dishonoured the popular
cause in France. However, if one wishes to try me on that score the docu-
ments are extant, they are printed in the Bulletin of the Convention, for I
can assert that there was not one of the addresses which I drew up either
before or after 9 Thermidor which did not receive honourable mention, a
circumstance which I know is little calculated to justify me in the eyes of
my accusers.
Citizen, you know as well as I do the persecutions which I experienced
two months before the fall of the government brought down by 9 Thermi-
dor. You know that the defence — perhaps imprudent but at least disin-
terested — which I dared to make of three paterfamilies 17 was the reason
for my disgrace; proceeded against on the basis of the report of Barere, I
was soon arrested at Auxerre by two emissaries, 18 one of whom was out-
lawed on 10 Thermidor. You will remember with what ardour and with
284 IX. FOURIER TO VILLETARD, JUNE/JULY 1795
what a universal agreement of witnesses my release was demanded by my
fellow citizens. Released at first, I was arrested again three days later on the
same grounds and detained until 24 Thermidor. Ultimately I experienced
every degree of persecution and misfortune, none of my adversaries have
run more dangers, and I am the only one of our compatriots who was
condemned to death. 19 Nevertheless, they have the injustice to forget the
terror which I experienced only to speak endlessly of that which I am said
to have inspired.
They formed a plot to get me out of public teaching. All the pupils
whom I taught in the school of Auxerre are today employed in civil or
military engineering, and yet they want to say that I am incapable of public
teaching. There is no sophism which has not been invented to that end in
the sectional assemblies, they repeat there continually that as a member of
the Popular Society of Auxerre I was a Jacobin (that is to say an immoral
terrorist), that there is the most extreme danger in entrusting me with
teaching mathematics and physics. I reply to this that my morals are beyond
reproach and that there is neither a liar nor a fool who could say otherwise,
that it is not a matter of terror here but of truth, that being a professor of
mathematics I do not bring up children but instruct those who want to
better themselves, that they themselves are in bad faith, that if they had
sons whom they destined for employment of this kind they asked me to
look after their education.
I add finally that to exclude me from a school of mathematics is to take
away from me an entirely legitimate possession 20 which I have acquired by
my work and which I retain by cultivating it daily.
At the time when attempts were made in Auxerre to perpetrate this use-
less and absurd injustice, I was put in charge of public classes 21 in Paris
under the auspices of the government ; it was then that they broke out in
denunciations which they addressed to the Committees of General Security
and of Public Instruction. They did not have the effect they desired since
they bore the evident mark of persecution. Soon afterwards, without having
ever solicited it, I was called to the Central School of Public Works. 22 This
circumstance infuriated them anew and I never managed to disarm this im-
placable coalition of ignorance, hate, and envy. I finally declared that
I was ready to renounce all the positions given me by the government, and
trying the line of giving way for a time before oppression I gave up a right
which I had acquired by study and vigils. Once again they refused me the
shade of tranquillity which I requested. My disarmament had been notified
neither to me or to any of my relations, although this was done in the case
of all the others. In spite of my repeated declarations they treated me as
if I wished to escape and their pursuits affected my arrest. What follows is
known to you.
IX. FOURIER TO VILLETARD, JUNE/JULY 1795 285
Citizen ; there are the facts which I wish to draw to your attention. You
will judge whether it is I or my adversaries who are terrorists and per-
secutors. For my part I accuse them of having violated in my regard all the
rules of natural justice, of being ignorant and evil, of profaning the words
humanity and justice in invoking them, just as tyranny was organized in
the name of liberty. Finally, of having given themselves up to a boundless
revolutionary fury which ought to cover them with disgrace and scorn.
Fourier, Joseph
Notes
1. Villetard, Edme Pierre Alexandre (1755-1824). A wine merchant in his native
town of Auxerre, he was elected a substitute deputy to the National Convention
for Yonne. On 25 January 1793 he was called to replace the assassinated Michel
le Pelletier. He became a deputy member of the Military Committee of the
Convention on 18 Fructidor Year II and was maintained in this position in
Year III. He was secretary of the Convention from 16 Vendemiaire Year IV to
the end of the session. In 1799 he became a member of the senate and he was
created a Count of the Empire in 1808. He retired on the fall of Napoleon and
lived in private thereafter. According to local tradition Villetard was a very
cautious man who had every intention of dying in his own bed unlike his unfor-
tunate colleagues Le Pelletier, Maure, Boileau, and Bourbotte of whom the
first was assassinated, the second committed suicide, and the remaining two
were guillotined.
2. He would be referring to the memoir on numerical equations read to the
Academie des Sciences in December 1789. See reference to this above in
Letter II, n. 6.
3. 'Dans le calme des passions meme excusables.' The sense being that the
'strict propriety' of his life even extended to his passions, which being directed
towards study were themselves not subject to blame.
4. That is before they came into the open following the flight of the King to
Varennes on 20 June 1791. See above, chapter 2, n. 2.
5. Citation unknown.
6. This letter has disappeared.
7. Italics Fourier's.
8. This is confirmed by Arch. Yon. Reg. L. 557 1 .
9. This is to be compared with a similar excuse in Letter VIII above (to Bergoeing)
as opposed to the possibility of visiting Auxerre mentioned in Letter VII (to
Bonard).
10. See Letter VIII above, n. 8.
11. Ibid., n. 2.
12. In one of his applications for a retirement pension following his return to
Paris in 1 81 5 Fourier made exactly the same apologia regarding his appoint-
ment by Napoleon as Prefect of the Rhone. He makes the same claim again in
the penultimate paragraph of the present letter in regard to his appointment to
the Ecole Centrale des Travaux Publics (later Ecole Polytechnique).
IX. FOURIER TO VILLETARD, JUNE/JULY 1795
As opposed, for example, to those carried out in Orleans in August 1793 by the
forty commissioners appointed to investigate the hoarding of grain by mer-
chants. See Lefebvre (2), vol. 2, p. 134-
Such as the Francois Leblanc part of whose letter from prison of 1 1 Germinal
Year II describing his interrogation by Fourier and Maure is reproduced above
in chapter 2, p. 41.
Such as the citizen of Tonnerre he saved from arrest by an agent of the Com-
mittee of Public Safety. See account of Cousin's story above in chapter 2,
p. 40.
Coblentz was the chief emigre centre until its occupation by French republican
forces in 1794.
For the identification of these three paterfamilias see above, chapter 2, p. 34.
It is tempting to assume that one of these emissaries was Robespierre's agent
Demaillot. See above, chapter 2, p. 43.
The reasons why it is difficult to accept this statement at its face value have
already been given above in chapter 2, p. 44.
The inviolability of private property continued to be observed, at least in
principle, throughout the most radical phases of the Revolution.
21. He is referring to his position as one of the mattres des conferences in mathe-
matics at the Ecole Normale, Fourier's class being held in the College de
France. See Letter VII above.
22. Later Ecole Polytechnique.
286
13'
14.
IS-
16
17-
18.
19
20.
X
Fourier to Bonard, October 1795
Paris, 30 Vendemiaire, Year IV
My friend, I reply in great haste to the letter you were good enough to
write to me. I know you have been appointed to examine candidates for
the ficole Polytechnique although I do not believe I have had anything to
do with this.
You ask me for information that I am hardly in a position to give you ; it
seems to me the text of your commission should sufficiently inform you
what you are to do at this juncture. The marks arising from your examina-
tion are passed on to a jury composed of several distinguished scholars who
compare them, in so far as that is possible, with those sent by the other
examiners, and they choose the candidates whom it seems right to them to
place higher on the list. The members of the jury are Laplace, 1 Cousin, 2
Legendre, 3 and Lacroix, 4 unless I am mistaken over the last name. You can
see all the imperfections of this examination procedure. Whatever unifor-
mity one attempts to enforce in the marks it is obvious that one can obtain
nothing satisfactory in this way. Once chosen in this way the candidates
undergo no further examination. At least there has been none up to the
moment. I do not believe it will be different this year. If they had to be
interrogated again on their arrival at the school, I would probably be the
only one detailed to do it. 5 I think that the members of the jury will be all
the more satisfied with the individual examiner the more they appear to
have conformed to the method prescribed to them. In my own mind, what
I most desire is to see young people entering the school who have outstand-
ing talents regardless of how much they have actually been taught. What
they may have learnt matters little to me if they do not have a marked
taste for mathematics and extraordinary aptitudes, accompanying these
qualities with aversion, or at least indifference, to the frivolities of which
Paris offers so many opportunities. The worst of all faults would be non-
chalance. I have unfortunately noticed it too often in the young people who
come from Auxerre. This is also the viewpoint of the professors of the
school who, moreover, do not contribute in any way to the choice of
candidates. For that it has been considered necessary to consult savants
outside the establishment. 6
I am assured that the number of candidates presenting themselves is
less than it has been in other years. 7 On Roux's 8 evidence it seems to me
288
X. FOURIER TO BONARD, OCTOBER 1795
that the two young men of whom you spoke to me are in a position to be
admitted.
I shall fortunately have the opportunity to write to you again and I shall
[then] enter into the details which lack of time obliges me to omit. Please do
not neglect this correspondence; you must not doubt the pleasure you will
give me. I very much approve of Madame Bonard's intention to leave
Saint-Georges which is not perhaps a very healthy place to live in. Your
post, which up to the moment has availed you nothing, cannot fail to be-
come very favourable, and it provides a security which makes it preferable
to all others. I have it on good authority that the state system of education
may be modified in many respects, but not as regards mathematics.
Remember me to Madame Bonard and embrace for me all your little
family, and especially our little Rene. Write to me sometimes and be
assured that I shall never forget our long standing friendship of which I
offer you the most sincere assurances.
Your friend,
Fourier
Notes
i. See above, Letter VI, n. 10.
2. See above, Letter VI, n. 4.
3. See above, Letter III, n. 4.
4. Lacroix, Sylvestre Francois (1765-1843). The son of poor parents, he obtained
the position of Professor of Mathematics at the school of gardes de marine at
Rochefort at the age of seventeen through the influence of Monge. He was
professor of the Ecole Normale and later at the Ecole Centrale des Quatre
Nations. In 1799 he entered the Institut and took the chair of analysis at the
Ecole Polytechnique which he left in 1815 for the Sorbonne and the College de
France where he succeeded his master Mauduit. Lacroix made important con-
tributions to the teaching of mathematics through his textbooks including his
Traite de Calcul differentiel et integral (3 vols, 1797-1800) and the different
volumes of his Cours de Mathematiques (10 vols, 1797-9)- Both of these ran
through many editions, and in English translation played an important part in
the transmission of continental methods in mathematics and theoretical physics
to the British Isles (Bio. Gen.; Gde. Encycl.).
5. Judging by Fourier's letter to Villetard (see above, Letter IX, n. 22) Fourier had
originally been appointed to a position in the Ecole Centrale des Travaux
Publics. This must have been in 1795 before his second imprisonment. Fourcy
(p. 94) relates that Fourier was appointed to the 'police des etudes' in 1796, by
which time he was already responsible for 'a part of the analysis course' and that
in 1797 (probably in June) he was continued as assistant to the mathematics
teachers, the three positions in 'police des etudes' having been suppressed.
6. Referring to the selection 'jury' for entry to the school whose members he had
already listed.
7. There had, in fact, only been one previous year.
8. See above, Letter IV, n. 2.
XI
Fourier to Bonard, November 1797
Paris, 20 Brumaire [Year VI]
I have just, my friend, left a person from Avallon who is very interested
in a young man of that district who hopes to enter the Fcole Polytechnique.
Villetard, 1 to whom he was recommended as well, has asked my advice
on the matter.
I replied that there was only one door by which to enter this school, and
that it was neither his business nor mine to introduce the young man there
other than by way of examination.
Citizen Boileau, the brother of a man 2 whose patriotism and misfortune
had rendered him somewhat celebrated, has assured me that this young
man had entirely satisfied you, and that he had devoted himself to the study
of mathematics with an enthusiasm which promises great talent. You will
doubtless easily have recognized the aptitudes shown by this boy, and in
that case I very much wish him to enter the school.
It will be very difficult to be admitted this year. Things have turned out
precisely opposite to what I had been told. The number of candidates at
Paris is considerable, the examiners have told me that they are much more
satisfied, and that there is no comparison between this year and the pre-
ceding ones ; they kindly attribute this change in part to my lectures 3 which
have become widely known.
On the other hand, the number of pupils will be greatly reduced by the
government, 4 and many will be forced to leave the school. These circum-
stances will make entry very difficult, so that it will be necessary to give
very high marks to young people whose entry one desires since they will be
regarded, in effect, as capable of making great progress in mathematics.
Having foreseen these difficulties, and knowing that the members of the
election jury greatly distrust the abilities of several departmental examiners
who are unknown to them, I have given them advance notice of the
candidates they might receive from Auxerre, and Laplace 5 in particular,
whose opinion carries most weight, agrees with me that special attention
should be paid to these candidates since their recommendations originate
from a just and very learned man.
I have seen no other means than this of responding to the wish of
Villetard and the citizens of Avallon, while at the same time bearing wit-
ness to the truth.
Roux 6 will also have spoken to you of a young pupil 7 of citizen Billy,
290 XI. FOURIER TO BONARD, NOVEMBER 1797
professor at Fontainebleau. All those that he has sent us have had adequate
ability and he himself is an entirely adequate teacher.
I thought, my friend, that you would be pleased to receive this informa-
tion, and that gives me the opportunity to reiterate to you and to your wife
and family the assurance of the sincere attachment with which I am
Your friend
signed: Fourier.
Embrace for me Madame Bonard and little Rene. 8 My regards to all
your colleagues.
Notes
i. See above, Letter IX, n. i.
2. Boileau, Jacques (1752-93). A judge of the peace, he was elected to the Con-
vention for the district of Avallon in the department of Yonne. He demanded a
decree of accusation against Marat on 25 September 1792. He voted for the
immediate execution of the King without stay or appeal to the people. There-
after he voted with the Gironde and was elected a member of the ill-fated com-
mission of twelve on 21 May 1793. He was arrested on 2 June. He retracted
before the Revolutionary Tribunal: 'I have searched for the truth. I have found
it among the Jacobins and I am now a Jacobin.' Nevertheless he was guillotined
with the Girondin leaders on 31 October 1793. Boileau was succeeded at the
Convention by his brother (Bio. Gen.; Gde. Encycl.).
3. For details of the extant part of these see Grattan-Guinness (3), pp. 6-7.
4. The successive numbers of entrants in the years 1794, 1795, 1796, 1797 were
396, 3ss, 361, and 266 respectively. The present letter can therefore confidently
be dated as 20 Brumaire Year VI, i.e. 10 November 1797. The reduction in
numbers was due to the financial situation.
5. See above, Letter VI, n. 10.
6. See above, Letter IV, n. 2.
7. Poisson, S. D. (1781-1840). Poisson's mathematical powers were first awakened
through reading the journal of the Fxole Polytechnique which was sent to his
father as leader of the local commune. In 1798 he headed the list at the Ecole
Polytechnique, where his genius for mathematics was quickly recognized by J. L
Lagrange whose course in analysis he attended. In 1800 he was appointed
demonstrator at the ficole, and in 1802 became assistant to Fourier whose Chair
he assumed when the latter became Prefect of Isere. In 1808 he was appointed
astronomer at the Bureau des Longitudes and in 181 2 became a member of the
Academie des Sciences. He was appointed mathematician at the Bureau des
Longitudes in succession to Laplace in 1827.
In his fundamental memoir of 181 2 Poisson adopted a two-fluid theory of
electricity in which like fluids repelled and unlike attracted according to the
inverse square law. Taking over mathematical results from the theory of
gravitational attraction, including Lagrange's potential function, Poisson
showed that this function would be constant over the surface of an insulated
conductor. Acting on a suggestion of Laplace, he gave an ingenious proof of the
formula for the force at the surface of a charged conductor. He also gave solu-
XI. FOURIER TO BONARD, NOVEMBER 1797
291
tions to various problems, including the calculation of the surface densities of
charge for two spherical conductors placed at any distance apart, his theoretical
results being in excellent agreement with those already obtained experimentally
by Coulomb. In an equally fundamental paper of 1824 Poisson gave a wonder-
fully complete theory of magnetism based on Coulomb's two-fluid model
deriving a general expression for the magnetic potential at any point as the sum
of two integrals due to volume and surface distributions of magnetism res-
pectively. He also investigated the problem of induced magnetism. Apart from
his work in electricity and magnetism, Poisson made important contributions to
the calculus of variations, differential geometry, and to probability theory in
which he is remembered by the distribution bearing his name. He contributed
also to the theory of elasticity in which field the ratio of lateral contraction to
longitudinal extension is known as Poisson's ratio. He also contributed to the
theories of capillarity, heat, and dispersion. In astronomy, he wrote many
important memoirs especially that of 1833 on the movement of the moon
(Arago (2)).
8. Joseph Antoine Rene Bonard, became chief medical officer of the military
hospital in Calais, chevalier of the Legion of Honour, and retired as surgeon-
major first class. He died at Calais in 1858 (Challe (2), p. 130, footnote 1). From
Letter XII below it appears that Fourier had baptized him.
XII
Fourier to Bonard, November 1801
Toulon, 29 Brumaire, Year X
My Dear Bonard,
I have just at last completed my voyage from Egypt which leaves me with
nothing but the most agreeable memories. 1 I entered the port of Toulon a
few days ago and I am in as good health as I could hope for after such pro-
longed hardships. I hope that you will have retained your friendship 2 and
that you will be glad to hear of my happy return to France ; one could not
return in more favourable circumstances. The study of the antiquities of
Egypt and the positions that I filled in the civil government of the country
in no way diverted me from the study of mathematics ; up to the moment I
have not actually published any of my researches. I shall not delay doing so,
if, as I greatly desire, I am last fortunate enough to enjoy a substantial
period of leisure in Paris, but it will be necessary for me to devote my first
days to the publication of my work on the astronomical monuments 3 we
have discovered in Upper Egypt. As it is possible that you have not yet been
informed of these results I will tell you, merely to give you a general idea,
that the ancient inhabitants of the region of Thebes represented the state of
the sky as then observed by them in the sculptures decorating religious
buildings, and that the arrangement of that ancient celestial sphere is very
different from the one which we observe today, a change which is princi-
pally due to the precession of the equinoxes ; the amount of this movement,
and even the reason for it, are today perfectly known, so that one can deter-
mine the epoch which the Egyptians intended to represent. A host of
additional circumstances, and the interpretation of a hieroglyphic emblem,
confirm the deductions that can be drawn from these sculptures for arriving
at the age of the monuments. One can thus fix the time when the Egyptian
people cultivated astronomy and the arts, and place within their true limits
chronological epochs which seemed destined to remain for ever unknown.
I shall not go into greater detail today, and I reserve your attention for
another time.
Present my regards to Madame Bonard and embrace in my name all your
charming family. But I retain an altogether special affection for that one
of your children whom I baptized. 4 If M. Rosman 5 still lives in Auxerre
express to him the token of my regards and unalterable attachment which
reflection and age can only increase.
I should like also to be remembered to our common friends, Roux, 6
XII. FOURIER TO BONARD, NOVEMBER 1801
293
Professor of Physics and Mathematics, Mathon, 7 and Ame. 8 I do not know
if citizens Defrance 9 and Balme 10 are still your colleagues; please greet
them and their families on my behalf. I think I have not yet lost all the
friends that I have had since childhood among your fellow citizens ; truly
I believe I have kept them all, to judge only by my own feelings; please,
therefore, announce my arrival to those to whom this news would be
neither indifferent nor disagreeable.
[If] you have time to write to me at Marseille, where I shall go without
delay, I shall learn your news with the most lively satisfaction. Address
your letters to Marseille, poste restante, to Citizen Fourier, ex-commissaire
of the government in Egypt. I should like to be informed in some detail of
the position in your part of the world more with respect to personalities
than affairs with which I have less and less to do.
I request you specially to inform my relations of my safe return, and
more particularly to assure my friendship to that one of my brothers 11
whom I saw in Paris ; he might give you a letter which you could address to
me at Marseille.
I renew the assurances of my attachment to you and I desire that you
may always want to retain your friendship for me.
Notes
i. By the terms of capitulation the remaining French forces were transported
from Egypt to Toulon in British ships. Fourier's voyage from Egypt to
Toulon would therefore have been much more comfortable than it would have
been in the brig Oiseau in which the scientific commission had originally
attempted to escape from Alexandria.
2. Possibly implying that Fourier had not been in correspondence with Bonard
during his stay in Egypt: the postal service between Egypt and France was
understandably somewhat erratic.
3. Altogether six astronomical monuments were found during the Egyptian
Campaign, all containing signs of the Zodiac, the most famous being in the
temple of Denderah in Upper Egypt. In all these monuments different signs
of the Zodiac were found in the 'first' positions, and it was assumed that this
was due to the precession of the equinoxes, the sign given 'first' being supposed
to be that corresponding to the solstice at the time of the construction of the
buildings in question. This gave very remote ages of the order of 5 to 6000
years for the construction of all the buildings. When the results were published
they were welcomed by some, but others were alarmed by the apparent con-
tradiction with the sacred writings. Fourier prudently rejected with some
warmth rumours that he was in favour of such ancient datings. No reference to
the estimated age of the buildings containing the Zodiacs was given in the first
draft of his Introduction to the Description of Egypt of 1809, although the pub-
lished edition of 1810 contained a short reference of a somewhat ambiguous
nature. But in the Description of Egypt itself he dated two of the monuments to
around 2000 B.C. Soon after, the whole question was shelved by order of
294
XII. FOURIER TO BONARD, NOVEMBER 1801
Napoleon as disturbing to religious sensibilities. When the circular Zodiac of
Denderah reached Paris in 1822 the controversy broke out anew. J. B. Biot
fixed the epoch of this Zodiac at 717 B.C. though this was contested by Cham-
pollion-Figeac the younger. In September 1822 the reading of hieroglyphic
inscriptions by the latter led to the realization that the temples of Esne and
Denderah — where two of the Zodiacs had been erected — had been completed
at the time of the Roman occupation of Egypt. Fourier was somewhat taken
aback at this refutation of his calculations. But if these Zodiacs were omitted
then his general views on the great antiquity of Egyptian civilization were later
confirmed by Champollion-Figeac the younger and others who pushed the
limits back even further into the past (A. L. Champollion-Figeac (1), pp. 123-
S ; J. J. Champollion-Figeac, chapter 5).
4. The 'little Rene' referred to in the postscript to the preceding letter written
some five years earlier.
5. Rosman, Henri Antoine, born at Hesdin (diocese of St. Omer) around 1742.
He became a professor at Jumieges in 176 1 and in 1775 was appointed prior of
the Abbey St. Germain. In 1777 he became principal of the Ecole Royale
Militaire at Auxerre. He was removed by his order from both these positions
in 1783 — in spite of a storm of public interest — after a commission appointed
in that year had found the school heavily in debt and the affairs of both the
school and the abbey in an inextricable state of confusion. His successor was a
certain Dom Joseph Philippe Rousseau, previously Professor of Humanities at
Lyons. On the retirement (or transfer) of Rousseau in 1788 Rosman returned as
prior of the abbey and director of the school. On the provisional suppression
of the regular orders at the beginning of 1790 Rosman was confirmed as
principal, and had evidently no scruples in taking the oath of allegiance to the
State recognizing its authority on at least four occasions.
In April 1793 certain of the so-called professor-priests (including the vice-
principal Laporte) were dismissed from the college on the demand of the local
Popular (Jacobin) Society. Rosman continued as principal till the following
June when he was replaced by Balme. After his dismissal he hid for a time in the
district of St. Georges close to Auxerre but was later discovered and placed in
detention. Rosman was evidently a man of spirit, for the communal records
note that he received a grave warning that any further acts of insubordination
towards the guardian of the house of detention would result in his transfer to
prison.
He was released some time after 9 Thermidor, being reinstated as principal
of the college on 14 Ventose Year III. When the college was replaced by an
Fxole Centrale in the following year Rosman retired to St. Georges where he
announced the setting up of a boarding school for some twelve or so pupils
in the following terms: 'Rosman, former principal of the college of Auxerre,
informs the public that in order to satisfy the demands of a number of parents
he has just set up his pensiomtat at St. Georges, in the former country house of
the college. Those who wish to confide the education of their children to him
should make application. There follows the programme of the courses.' He
spent the rest of his life peacefully at St. Georges apart from a period around
1797 when he was denounced for certain supposedly anti-Republican actions.
He seems to have had little difficulty in defending himself against these charges.
He died at St. Georges on 26 April 1799 in his fifty-seventh year (Arch. Yon.;
Cestre (2); Moiset).
XII. FOURIER TO BONARD, NOVEMBER 1801
295
6. See above, Letter IV, n. 2.
7. Mathon . He was one of the professors of the College of Auxerre in Messi-
dor 1793 following the dismissal of all the professor-priests including Dom
Rosman. He was one of those whose departure from the college in February/
March 1795 had led to its complete disorganization. But in July 1796 he
returned to become economic-director of the new Ecole Centrale which had
replaced the college and where he became Professor of Belles-lettres in Novem-
ber 1798. He was a professor for a short time in the ficole Secondaire which
replaced the ficole Centrale in 1804 but by 1805 had left to set up a private
pensionnat (Arch. Yon. ; Cestre (3)).
8. Ame, Gerard. Born at Beru near Rheims, 1759. Studied at the college of 'Good
Children', at the University of Rheims where he acquired the degree of Master
of Arts. He figured among the list of professors at the College of Auxerre on
6 August, 1793, and also on several other occasions before 9 Thermidor. He
was a member along with Fourier and Bonard of the provisional revolutionary
committee on 23 Fructidor Year II. Later he returned to teach being named as
an instituteur of the new system of education in the Commune of Auxerre on
26 Brumaire Year III. For some reason or other Ame never taught at the
Ecole Centrale. In 1805 he was appointed Professor of the fifth and sixth
classes in the new Ecole Secondaire which replaced the Ecole Centrale. He
generously gave up one of these chairs in favour of the ex-director of the school
Choin. In 1808 he became regent of the third class. He retired in 1817 and was
awarded a pension by the State who thus evidently did not know about his
revolutionary activities in 1794 (Arch. Yon.; Cestre (3)).
9. Defrance . He appears as one of the professors of the college of Auxerre
in Messidor Year II after the dismissal of all the 'professor-priests' including
Dom Rosman. He was still a professor in August 1793. He interceded with
Gautherot for Fourier before the Committee of General Security at the time
of the latter's first arrest in Messidor Year II and he was one of those who
successfully argued for the reintegration of Fourier and Balme into the
Popular Society of Auxerre in the winter of 1794/5. Shortly afterwards he
left the college which became 'thoroughly disorganized' owing to his departure
and that of Fourier, Balme, Roux, and Mathon (Arch. Yon.).
10. Balme, J. G. Born around 1764, died 1841. A tonsured clerk at the outbreak of
the Revolution he is said (Moiset, pp. 22-8) to have embraced its principles with
enthusiasm. He does not appear on Dom Rosman's list of professors at the
Ecole Royale Militaire in 1790. Having acted for a time as secretary to Nicolas
Maure, one of the representatives of Yonne at the Convention, he returned to
Auxerre where he was elected a member of the General Council of Yonne. In
June 1793 he was sent into the district of St. Florentin to recruit for the war
against the Vendee. The same month he was appointed principal of the college
at Auxerre in succession to Rosman. At the time of his appointment as principal
the college at Auxerre was still a military college though naturally no longer a
royal one. This explains the following letter of 22 June 1798 from the Minister
of War Bouchotte to Maure :
I have been informed, citizen, of the dismissal of principal Rosman, and of the choice
of citizen Balme to replace him . . . The interest which you take in citizen Balme
justifies his appointment in my eyes even more, and I am persuaded in advance of
the good which he will do in this place.
296 XII. FOURIER TO BONARD, NOVEMBER 1801
Maure evidently passed on this letter to Balme as appears from the following
postscript:
I salute and embrace my friend Balme but he will have to believe in my good wishes,
because I have not the time to express them to him in a long discourse.
Balme was one of the six commissioners sent to collect horses by Ichon's
order of 23 Vendemiaire Year II. Unlike Fourier he does not appear to have
been a member of the revolutionary committee of Auxerre. After 9 Thermidor,
he was one of those appointed on 26 Brumaire Year III to the new system of
education in the commune of Auxerre. Like Fourier he was purged from the
Popular Society of Auxerre at the time of the first post-Thermidorian reaction,
but was 're-integrated' (once again with Fourier) on 26 Nivose Year III. He
was appointed to the ficole Normale in company with Fourier, Roux, and
Bonard. While in Paris he was condemned by the commune of Auxerre for his
part in the Terror, but there is no trace of his having been arrested in Paris
so that he may possibly have returned to Auxerre in time to comply with the
disarmament order issued against him as a former Jacobin. In any case he was
're-armed' in company with Fourier, Bonard, and Maure Junior on 13 Fructi-
dor Year III. Thereafter he played an increasingly important part in the local
administration. In Year IV he became commissioner of the executive directory
of the department at Vermenton, administrator of the department in Year VI,
and vice-president in Year VIII. Under the Empire he was a judge of the peace
at Avallon. After the Restoration he founded a 'pensionnat' at Auxerre.
1 1 . Probably the brother Jean Baptiste who wrote to the Committee of General
Security at the time of Fourier's second imprisonment. See above, chapter 3,
p. 56.
XIII
Fourier to Bonard, November 1802
Grenoble 4 Brumaire, Year XI
The Prefect of the Department of Isere
Will you allow me, my dear Monsieur Bonard, to entrust you with
several small tasks relating to my personal affairs ?
I am writing to Paris to have transferred to Messrs. Bastide & Son, Mont-
Blanc Street, Paris, the sum of 1000 francs which will be paid out to you by
the post office director of the department of Isere. I have informed M.
Sauvalle in advance that I am sending the money; he will indicate to you
the small payments which you are to make to M. Ame 1 and my nephew.
Further, one of my brothers who is in the Army, and whom I wish to
buy out, but who is at present at Auxerre on six months leave, is apparently
in need of money; please pay him 100 francs and inform him that he is to
tell me the sum required to obtain his discharge — I shall give him this if it
does not exceed what I am able to afford. As soon as he has retired from the
service I shall give him a small pension and inform him how I wish him to
use it; it is also my intention that he remain at Auxerre.
If you would be good enough to look after his initial correspondence
with me I would be very obliged to you, please ask him how easy he expects
to find it to buy his discharge in his corps ; M. Sauvalle can give you very
precise details in this matter ; moreover the brigade commander wrote to me
some time ago, he is quite ready to assist him ; my dear Bonard, please take
some interest in this affair. I should also very much like you to give me news
of your family; no one desires more than I that you should enjoy the
happiness which you so much deserve. Embrace on my behalf all your family
and continue to be my friend.
I am writing today to Paris ; the money will arrive within eight days ; you
will receive a letter of advice from M. Lefort, an employee in Paris.
Fourier
Note
1. See above, Letter XII, n. 8.
XIV
Fourier to Bonard, January 1804
To M. Bonard
Professor of Mathematics
Fcole Centrale of the Department of Yonne
Grenoble 9 Pluviose Year XII
My Dear M. Bonard,
If I were not myself guilty of the greatest carelessness in my personal
correspondence I would reproach you with your silence. But I am not in a
position to accuse anyone. Be so kind as to give me from time to time news
of yourself, of your family, and of our old colleagues in public education.
How are Mathon, 1 Millon, 2 and Roux, 3 and what are you working on your-
self at present?
I think that it would not be very difficult to have one or two of your
children placed in a lycee. 4 Could I be of help to you in that connection ? I
do not know the names of the inspectors of studies in your district, but it
would be easy for me to write to them and they might have some friends in
common with me. Give me an idea of your intentions in this matter. M.
Sauvalle must be in touch with you about the little scheme you two may be
hatching. Please let him have these details. He will be good enough to
pass them on to me.
Remember me to your wife and all your family and be sure of the
devotion of your friend.
J. B. Fourier
Prefect of Isere
Notes
1. See above, Letter XII, n. 7.
2. See above, Letter IV, n. 4.
3. Ibid., n. 2.
4. The French lycees played a very important part in the educational system of the
Consulate and Empire. They were founded by a decree of 2 Floreal Year X
(1 May 1802). There was to be at least one in every region containing a court of
appeal. The emphasis was much more on Latin and literature compared with
the Ecoles Centrales of the Directory with their bias towards science and mathe-
matics. There was equally a new attention to discipline and this increased
steadily under the Empire. Auxerre was unsuccessful in its attempt to have its
Ecole Centrale replaced by a lycee, and it had a content itself with a much less
advanced ficole Secondaire. It only acquired a lycee — today the lycee Amygot —
later in the century.
XV
Fourier to Bonard, no date
Grenoble the — Floreal —
To M. Bonard, Professor of
Mathematics at Auxerre
My dear Bonard,
I have a thousand apologies to make to you and I do not know how to
justify myself for having remained so long without writing to you. Your
friendship for me is a real refuge.
I shall be pleased if you will remember me to your wife and embrace all
your family for me. Tell me what are your plans regarding the education
of that one of your children of whom you spoke to me. If you wish him to
enter a lycee I shall write specially to Fourcroy, 1 and if I am not deceived by
the offer of help which he made me recently I hope you will quickly succeed
in finding a place for him.
If you have some points to make to an old friend you must make up your
mind to come and see me at Grenoble, and I believe it is the quickest way
for us to agree together on an infinity of things. For you are not very
regular in your correspondence and I am unpardonably negligent.
I have entirely forgotten how our accounts stand and I am sending the
sum of 300 francs just in case. Kindly let me know what the position is
about this.
Remember me to our old friends and colleagues, Messrs. Daru, 2
Mathon, 3 and Ame, 4 and if as I hope, you will be able to spend a few days
with me, we shall talk about them here.
I beg you my dear Bonard to excuse my scrawl and to believe me your
devoted and sincere friend.
J. B. Fourier
P.S. Be good enough to call in at my brother's and find out from him about
the matter he is so keen for me to complete. I shall gladly do whatever he
likes to suggest.
Notes
Fourcroy, Antoine Francois, Count (1755-1809). He belonged to an ancient
legal family much reduced in circumstances, his father being a pharmacist in the
House of Orleans. He left the College d'Harcourt at the age of fourteen with few
attainments beyond a passion for music and poetry. Through the encouragement
300
XV. FOURIER TO BONARD, NO DATE
of Vicq-d'Azyr he entered for medicine and became interested in chemistry. He
made the acquaintance of Lavoisier in 1782 and was elected to a chair of chemis-
try at the Jardin du Roi in 1784 in preference to Berthollet. His lectures were
celebrated for their brilliance and charm. He made important contributions to
chemistry, both in collaboration with colleagues, especially Lavoisier, and by his
analysis of various compounds. He became a member of the Academie des
Sciences in 1785. He was elected a substitute deputy for Paris in the Convention
and took his seat in July 1793 after the death of Marat, having worked un-
remittingly during the preceding eighteen months on ways and means of
extracting and purifying saltpetre which had become in critically short supply as
a result of the war between France and the European coalition. He became a very
active member of the Committee of Public Education, playing a leading part in
the dissolution of the ancient academies including the Academie des Sciences.
He managed to have Desault, Chaptal, and Darcet released from prison but
could — he later claimed — do nothing for Lavoisier. Later he was blamed for
Lavoisier's death and though he defended himself from the charge with vehe-
mence he could never entirely free himself from some measure of blame. He
became a member of the Committee of Public Safety for a time after 9 Thermi-
dor where he contributed to the establishment of the Ecole Polytechnique. As
Director General of Education under Napoleon from 1801 onwards he was
largely responsible for the institution of the Napoleonic system of education
including the setting up of lycees and the foundation of three schools of medicine
at Paris, Montpellier, and Strasbourg. When Fontanes was chosen in 1808 as
head of the Imperial University — a position to which Fourcroy had good claims
and which he would have gladly filled — Fourcroy had to give up the educational
side of his ministry, a surrender which he felt very keenly, and which may have
contributed to his death the following year (Bio. Gen.; Gde. Encycl).
A Daru is listed as one of Fourier's friends by Mauger.
See above, Letter XII, n. 7.
Ibid., n. 8.
XVI
Fourier to Bonard, no date
To M. Bonard,
Professor of Mathematics at
ficole Centrale
Melun 13 Germinal
From the Prefect of Isere
My dear Bonard,
Sauvalle whom I saw several times at Paris will have warned you that I
was going to ask permission to sleep one or two nights at your house on the
occasion of my visit to Auxerre. As you see I have made use of this liberty
which your friendship allows me.
I left Paris this evening, and, as I have promised to stop at Sens, I shall
not arrive at Auxerre till the evening of the 15th. Once there I shall reply
to your letter or rather I shall excuse myself if I can for having put off
answering them.
I hope thus to renew with you an acquaintance which is beginning to
become venerable and which will, I hope, never be broken.
Receive the assurance of my sincere [friendship].
J. B. Fourier
XVII
Fourier to an unknown correspondent, around 1810
I have the honour to send you :
(1) The work of M. Prevost on Radiant Heat. 1
(2) An extract from the review which was given of this book in the
Mercure de France. 2
I had a search made for the whole number without success but have
transcribed the part 3 of the review where the author of the articles des-
cribes the researches of M. Laplace 4 and the discoveries which were the
fruit of these researches. Except by expressing oneself in a false and unjust
manner I cannot be included among those who have been held up by this
supposed analytical difficulty, 5 which a cursory examination soon dispels. It
arises from the fact that (1) a differential quantity has been taken as a finite
quantity, namely the heat that each section loses at its surface (2) a finite
quantity has been expressed as a differential, namely the heat which one sec-
tion communicates to the following one.
I have omitted to point out to you that this same author, who aided by
the advice of M. Laplace has attempted to apply the equation of the linear
movement of heat, thinks he has demonstrated the following result: that an
iron bar whose extremity is immersed in a furnace at a given temperature
cannot be heated sensibly at a distance of six feet from that extremity. He
does not take account of the fact that the distance to which heat can be
propagated in a bar depends on its thickness, and he could easily have seen
this by establishing rigorously the equation in question. He first published
this pretended discovery in the Bibliotheque Brittanique. 6 Since then he has
referred again to the same proposition in a work on physics translated from
Fischer 7 (see p. [ ]). M. Haiiy 8 has also borrowed this error. I
found it again in the work of M. Prevost, 9 p. 1. However the contrary is
amply proved by experiment, and calculation demonstrates that the dis-
tance to which heat can be effectively propagated increases with the square
root of the thickness. 10 This comment will provide you with a new proof
of the small amount of care which he has given to the mathematical
examination of these questions.
To treat with such lack of care one of the most important questions in
analytical physics, to rush into publishing in periodical works speculations
which are still uncertain and even erroneous, to found his reputation on a
mutual exchange of [ ] and ridiculous flattery, to make use of pub-
lic newspapers to foist on, and attribute to, others his own errors, and to
AROUND 1810
303
predispose others against a work which he does not dare to attack directly,
and to attempt by a servile and calculated flattery to display as the inventor
of an idea a person who is by no means such: that, Sir, is what I cannot
observe without scorn. One can be assured that the majority of the public
share this sentiment [ ]. I sincerely regret that M. Laplace does
not realize that it is he himself who is supporting this attitude which is so
false and so contrary to the progress of the sciences. The artifices that an
author employs to exalt his own reputation beyond that which is reasonable
never have lasting success and often involve him in bitter regrets.
As to the general principle about which M. Biot 11 talks which consists in
the fact that the molecules of bodies which are immediately adjacent to each
other act the one on the other for the transmission of heat, I do not under-
stand why one would wish to set it up as a new truth. It has seemed incon-
ceivable to me that the action in question could be restricted solely to sur-
faces in contact, and it is evident, or so it appears to me, that each point of
an element should act on every point of neighbouring elements. It is no
less certain that when the surface of a body is heated the heat which dissipates
itself into the colder air comes not only from the extremity of the
surface, but also from points which are beneath it at a very small distance.
I can assure you that I have often employed these considerations in my
researches. But I have recognized very clearly that it was not necessary
[ ] for founding the theory of heat. Everything can be reduced to a
proposition for which it is easy to give a rigorous demonstration: if a solid
is contained between two infinite parallel planes whose distance is e : if the
temperatures of each section decrease in arithmetic progression from the
interior surface up to the opposite surface, the state of the system will be
permanent, that is to say it will subsist in itself once it has been set up, and
there will thereafter be no change in the temperature provided that one
holds the two extreme sections (^4) and (B) in the states which have just
been assigned to them.
It is impossible to deny that this proposition is true and rigorously
proved. Equally one cannot deny that it suffices to establish all the equa-
tions of the movement of heat. Finally, one cannot deny that the integrals
given by the author exactly reproduce the phenomena. It is therefore false
and unjust to insinuate indirectly that he has been held up by any analytical
difficulty.
It is true that one can derive these same equations by considering the
mutual actions of neighbouring molecules, 12 and that can be done also for
the interior of a solid as I have shown in a note sent to M. Laplace. 13
But the application employed by M. Biot relative to the surface is entirely
false. It is not thus that one should do it. Unless I am mistaken myself the
temperatures of the extreme envelope of a body are not as M. Laplace or he
304 XVII. FOURIER TO UNKNOWN CORRESPONDENT
[Biot] represent them to be. 14 But I reserve for another time an observation
in this matter.
I shall end this long letter by citing to you another example of the little
care with which this theory has been examined. It has been pretended that
the differential equations given by the author of the memoir had imaginary
roots. For example, the equation tan * = o 15 was cited and it was continually
objected that this equation had an infinity of imaginary roots, something
which is contrary to the simplest elements of the calculus.
I could multiply remarks of this kind but the trouble which I would
take would be importune and useless. The work I have given to the Institut
would be for me the occasion of an embarrassing discussion. I propose to
give up. I would prefer to lose so just a cause rather than defend it by means
of public papers. I shall abandon this noble theatre to those who desire it
for a career equally worthy. I shall restrict myself to devoting to science
certain moments of leisure and I shall leave to others the difficult task of
pointing out and [ ] intrigue. But that which I shall always retain
is a just and sincere obligation to those, who like you Sir, are the true
founders. May you long enjoy a glory so pure and so merited and bring
back all minds to the true path by the authority of your lessons and of your
examples. I beg you, Sir, to participate in the homage of my attachment and
respect with which I am . . .
Notes
i. Prevost (2). Prevost, P. 1751-1839. From 1780-4 he was a member of the Berlin
Academy and Professor of Philosophy in Berlin. Later he became Professor of
Philosophy and Physics at the Academy of Geneva.
2. Biot (2). For a note on Biot see above Letter VII, n. io, p. 273.
3. Ibid., p. 336.
4. Laplace (3), pp. 290-4.
5. Referred to in Biot (2), p. 336 and Laplace (3), p. 291.
6. Biot (i), p. 328.
7. Fischer.
8. It is not clear to which work of Haiiy he refers.
9. PreVost (2).
io. This result is given in the 1807 memoir, art. 21.
1 1. Biot (2), p. 336 and Laplace (3), p. 291 maintained that the 'analytical difficulty'
could be overcome by taking account of points of the bar other than those
immediately adjacent to the point under consideration.
12. As in Laplace (3), pp. 291-4.
13. Possibly Letter XIX below.
14. See above, chapter 8, pp. 17c— r for a discussion of this.
15. This question continued to cause difficulties even after the publication of the
Analytical Theory of Heat. See above, chapter 7, p. 155.
XVIII
Fourier to an unknown correspondent, around 1810
I see myself also obliged to discuss with you the memoir on the propaga-
tion of heat. I was imperfectly aware of the reflections 1 that M. Biot had
inserted in the Mercure de France. 2 But having read this article myself I
saw that [ ] the unfavourable intention of the author.
Without expressing oneself in a false and unjust manner one could not
say that all the persons who undertook to treat this matter had been held
up by an analytical difficulty 3 whose solution has just been discovered.
This unkind allegation should not have been inserted in a newspaper, and
it applies directly to my own researches announced long ago in the me-
moirs of a literary society of which M. Biot is a member. 4
Far from having myself been held up in endeavouring to submit the
theory of heat to calculation, I completely resolved questions of this kind
and the table of matters given in my work alone proves that the allegation
of M. Biot is unjustified.
Moreover the equations of movement of heat present themselves
naturally and this first step encounters no difficulty. Doubtless by founding
oneself on other considerations one can obtain the same equations. 5 They
have this in common with all mathematical propositions, and it is the
essence of truth. But it does not follow from that that the work of the
author [ ] on heat is defective and that the results which he has
discovered do not belong to him. When M. Biot considered the extremely
simple case in which a solid reaches a constant state he was led certainly to
an equation whose terms were not comparable. 6 But this arose uniquely
from the small amount of attention which he gave to the establishment of
the calculation, and not from any difficulty inherent in the question itself.
Let x be the distance of the section from the furnace and y the temperature,
then the quantity of heat which an elementary section transmits to the air
is not represented by a finite term proportional to y but the differential
term Chy dx, C being the circumference of the cross-section, h the measure
of the exterior conductivity and dx the thickness of the section. On the
other hand, the quantity of heat which passes from one section to another
should not be represented by a differential term proportional to Ay, but by a
finite quantity which is a function of x, and this is very evident because the
quantity of heat which traverses a section compensates exactly all that
which diffuses through the rest of the surface. So M. Biot expresses in
finite form a quantity which is differential, and on the other hand he
306 XVIII. FOURIER TO UNKNOWN CORRESPONDENT
represents a finite quantity by a differential quantity; this double irregu-
larity would express a quantity infinitely small by a finite term, and on the
other hand he writes a magnitude which is evidently finite by a differential
term. But in that way this double omission has held him up himself. It is
not reasonable to make a similar judgment on my own work where the
question is treated and resolved with the most rigorous exactitude. It
would be necessary that at least he expresses his opinion in a precise
manner, and that he should, for example, among the large number of new
propositions which I have derived indicate one single one which was either
false or uncertain. But he shall never do this, and it is in fact impossible to
attack the theory [ ] he can only retreat into vague expressions
which exclude all formal replies. I beg you to consider, Sir, that the Institut
should propose ... as subject of a prize to treat the same question . . . 7
Notes
i. See above, Letter XVII, para. 2.
2. Biot (2), p. 336.
3. Referred to in Biot (2), p. 336 and Laplace (3), p. 291.
4. A reference to Poisson's review (Poisson (2)) in the Bulletin of the Societi
Philomatique.
5. A reference to the derivation given by Laplace in Laplace (3), pp. 291-4.
6. This was the analytical difficulty encountered by Biot (see Biot (2), p. 336) to
which reference was made in the second paragraph above.
7. Continuation illegible. Possibly the beginning of the campaign which led to the
propagation of heat in solid bodies being chosen as the topic for the grand
mathematical Prize of the Institut for 181 1.
XIX
Fourier to an unknown correspondent, around 1810
When one began to determine by calculation the movement of heat in
solid bodies one was held up by an analytical difficulty which consisted in
the fact that the equations seemed to be made up of non-comparable terms. 1
It is asked 2 if the same difficulty subsists in the work which has been
presented to the Institut on the theory of heat. The author of this memoir
made no mention of the difficulty in question, he considered it unnecessary
to recall the unfruitful attempts which had been made before him, but one
can easily recognize that the equations which he proposes are made up of
exactly comparable terms, and that there is no remaining uncertainty
about the truth of these equations since they are all rigorously deduced
from a principle 3 long since adopted and confirmed by all experiments.
This principle can be annunciated as follows :
If two molecules A and B have different temperatures the quantity of
heat which the warmer one transmits during an instant to the less warm
one is, other things being equal, proportional to the difference of the two
temperatures. Thus supposing that this difference were zero the molecules
A and B would not exercise on one another any action which tends to
change their temperatures. But if the initial difference of temperature is a
the colder molecule will acquire during an instant 8t a new quantity of heat,
and if this initial difference had been za, ^a, 4a, . . . the quantities of heat
transmitted during the same instant by the hotter molecule would have
been zy, 37, 47, . . . That is to say, the excess of the initial temperature
being composed of a certain number of equal parts a, each of these parts
acts as if it had produced an effect y, in such a way that the total effect
contains as many multiples of y as the total excess of temperature contains
a. Also if one adds to the initial temperature of the molecules a common
magnitude the result of their mutual actions will not be changed. This
principle must now be applied. A bar of any length whatsoever is held by
its extremity A at the constant temperature 1, and from the point A is
plunged in air which remains at temperature o. It is supposed that the solid
has acquired in each of these points a permanent temperature, and that all
the points of a given section perpendicular to the length have sensibly
the same temperature; x is the distance of a point of the axis to the point
A, y is the temperature of this point. Here is how one attempted to deter-
mine by calculation the value of y in terms of x. The quantity of heat
which a section placed at distance x transmits to that which follows it is
308 XIX. FOURIER TO UNKNOWN CORRESPONDENT,
according to the preceding principle proportional to y—y' or Sy. The
quantity of heat that the second section transmits to that which follows it
is proportional to y' —y" or — Sy'. Therefore the quantity of heat which
any particular section actually acquires in an instant as a result of its
position is proportional to the second difference 8 2 y. On the other hand
this same section allows a quantity of heat to escape into the air which is
proportional to the excess of the temperature y over that of the air which is
zero. But it is necessary that this loss should be compensated since the
state of the bar is constant. Therefore in order to form the equation one
should equate a term proportional to 8 2 y to a term which is proportional
to y. These two terms are not comparable as they are, in this state, but
since they become so on dividing the first by 8 2 x one has written the equa-
tion 8 2 yj8x 2 = Ay, A 4, being an undetermined constant. This way of estab-
lishing the calculation seemed inexact because it furnished two terms
which were not comparable, and in fact one cannot equate them except by
making a change in the first for which one gives no reason drawn from the
question itself. 5 On the other hand, the equations expressing the interior
state of the solid, and that of the surface, cannot be obtained by this
method in other problems; only a complete analysis of the conditions of
the question can furnish these equations.
In spite of the simplicity of the preceding question the solution which
has just been referred to is not satisfactory because it does not tell us
how the dimensions of the solid, and the convective qualities, enter into
the coefficient A. 6 It has even led to erroneous deductions, for example
that a bar of iron held by one extremity in a furnace of heat cannot sensibly
heat itself at a distance of six feet from the furnace. 7 If one tried in this way
to determine the conductivity of different substances one would only
obtain results which were vague and inapplicable. In order to judge if this
defective manner of establishing calculations has been followed in the
memoir on the theory of heat one should recall the principles employed by
the author.
Since the solid has arrived at a permanent state the quantity of heat
which traverses during unit time a single section placed at distance * is
always the same. Moreover this quantity, which we designate by z, is
necessarily equal to that which escapes during the same time in the air by
all the parts of a surface which is to the right of the point x. Equally the
quantity z' of heat which escapes by another section x' is equal to that which
is lost in the same time by the part of the surface which is to the right of x'.
Thus the difference z — z' is equivalent to the quantity of heat which is
lost during unit time by the part of the surface which is comprised between
* and x' . However the quantity of heat which in unit time will flow out of a
unit of surface held at all its points at temperature i has been denoted by
AROUND 1810
309
h. It is therefore manifest that z and z' are quantities which are comparable
to this number h. The quantity which measures the heat flowing through
the section x is evidently a finite quantity which is a function of x, and the
temperature y being represented by f[x) the quantity z should be another
function <f>(x) of x. If C is the [circumference] of the section and the dis-
tance x — x' is dx one will have
— 8z = chy 8x or — 8z/8x = chy
It remains to determine the function z. But whatever it is, since it is
certain that it represents, like the number h, a finite quantity, the equation
is formed by terms which are exactly comparable and no change needs to
be made to bring about that situation. But it has been rigorously proved
in the memoir 8 that the function z is no other than — kSf'(x), k being the
conductivity proper of the solid, S the surface of a section, and jf'(x) denoting
dy/dx. One will then have the equation
kS d 2 yjdx 2 = chy.
To sum up, one sees why it is the solution which we have presented gives
comparable terms.
i. The quantity of heat lost by the surface of the section is not only
proportional to y but should also be expressed by chydx which reduces this
term at first to a differential of the first order.
2. The quantity of heat which passes from one section to another is pro-
portional to the differential dz. This quantity [z] is a fixed magnitude
which is proportional to the function f'(x) or dyjdx. It is therefore the
differential of this function, or f"{x) dx, which should be compared to
chy dx, and now there is no sort of inhomogeneity whatsoever.
Thus everything reduces to noting that the magnitude designated by z
is not a differential but a finite quantity which is a certain multiple of the
number h. But of all the ways of being assured of the truth of this there
can be no other which is clearer or more simple than that which precedes.
It consists in noting that this quantity is necessarily equivalent to the
quantity of heat which is lost in the same time by the whole surface of the
solid which is to the right of the point x.
Later one will see the means which have been employed to establish the
equations of the motion of heat in much more complicated questions. One
will find that they are no less rigorous and that there is no sort of uncer-
tainty on the nature of the terms compared.
Doubtless by basing oneself on different considerations one can obtain
the same equations. They have that in common with all mathematical
propositions and it is the characteristic of that which is true. But just
310 XIX. FOURIER TO UNKNOWN CORRESPONDENT,
because one discovers another way to arrive at the same result it does not
follow that the author's work has been defective or that his results do not
belong to him. 9 Without expressing oneself in a false and unjust manner one
cannot say that all persons up to date who have attempted to submit to
calculation the theory of heat have been held up by the above mentioned
difficulties 10 . . . and the contrary is proved by the table of matters treated
in the memoir alone. The persons to whom this work is presented and who
wish to examine it cannot but disapprove of such an unfounded allegation.
It is unseemly to insert it in advance in public periodicals 11 , and to lecture
the public on questions which one has studied so badly. It is to make a very
unworthy use of both talent and time.
To render the preceding notes more complete it is necessary to recall
how one proves that the function designated by z has the expression
— kSf'(x). For that one considers [ ] of the prismatic bar as a
solid comprised between two infinitely prolonged planes one of these
faces being maintained at the constant temperature y and the other at the
constant temperature y+dy. But it is easy to determine the movement of
heat in such a solid and subsequently to apply the result to the section
whose thickness is dx.
Let 12 M be a solid comprised between two parallel infinite planes, e
the distance between the planes, a the permanent temperature of the first
surface, and b that of the opposite surface. One sees easily that when the
state of the solid has become steady the interior temperatures decrease
from A to B as the ordinates of a straight line. In fact, if the temperatures
were so there would be no change in the state of the solid and the heat
would continue to move uniformly from A to B. To assure oneself of this
it is sufficient to remark that the temperatures being unequal at every
instant a new quantity of heat traverses any particular section of the prism.
But one proves that this quantity which flows during a given time is the
same for the section m as for any other section n. Therefore the solid
comprised between m and n receives [ ] as much heat as it loses.
It should therefore maintain its state, and it is the same for all the other
parts. It remains to prove this equality of the quantities of heat traversing
any two sections. For that we shall consider a part AD of the solid which
can be divided in two equal parts at point C. Let us compare the state of
the part CD to that of the part AC. It is clear that if one adds a common
quantity to all the temperatures of the solid CD one will change in no way
the mutual action of the molecules, and in consequence the same quantity
of heat will still traverse the mean section n. But by this addition of a cer-
tain common quantity to all the temperatures of CD one makes them
equal to the temperatures of AC. Therefore there flows by the mean sec-
tion m [of AC] just as much heat as by the mean section n [of CD]. From
AROUND 1810
311
this one sees that if the temperatures decrease as supposed in arithmetical
progression the solid will be continually traversed by a uniform current of
heat, and consequently its state should not change, which was what had to
be proved.
It is necessary now to find the nature of this quantity of heat which
traverses the part AB. Suppose that in another equal solid one of the faces
is at temperature za and the other at temperature zb. When its state be-
comes permanent the interior temperatures will decrease from za down to
zb in arithmetic progression. They will therefore be very different from
those which were found in the first solid. If two molecules p and q in the
first case had temperatures whose difference was a, the same molecules of
the second solid would have temperatures whose difference would be za. If
therefore [ ] transmit heat the result of this action being in the
first case a it will be 2a in the second case, and it will be the same for any
two molecules whatsoever equally placed in one and the other solid. From
this it necessarily follows that the whole quantity of heat which crosses a
section m of the second solid is double the quantity which traverses the
same section of the first. Therefore, in general, to compare the state of two
equal solids whose faces are maintained at unequal temperatures it suffices
to compare the temperatures of two molecules p and q whose distance is r,
to those of two molecules of the second solid which are at the same distance
r. If the excess of the temperatures is a in the first solid and a' in the second,
the quantities of heat which traverse uniformly one or other prism will be
between themselves in the ratio a to a'.
It follows from this that the measure of this quantity of heat in the first
solid considered is kS(a-b)e, the number k being the same for the bodies
formed of the same substance but different for solids of another material,
and S being the extent of the surface of the section traversed by the current
of heat [ ]. By applying this result to the infinitely small section
whose thickness is dx, whose extreme temperatures are y and y + dy, and
whose section is S one has
-kS(dyldx) or -kSf\x)
The demonstration that one has just given may give rise to the following
questions :
i. It is asked 13 if in the solid comprised between the two planes A and B
the quantity of heat which crosses a point of a section m arises solely from
the action of two molecules p and q infinitely close together, or if there are
not other molecules/)' and q' which being even separated by the preceding
p and q act one on the other, in such a way that the colder q' receives from
the warmer p' a certain quantity of heat. We reply as follows to this
question.
312 XIX. FOURIER TO UNKNOWN CORRESPONDENT,
If two molecules p' and q' separated by the molecules p and q are also
sufficiently close to transmit a certain quantity of heat y', and the two
molecules p' and q' exercise their action in a solid whose extreme tem-
peratures are a and b, and in one in which the extreme temperatures are
2fl and zb. If in the first case the difference of their temperatures is a' and
the result of their action y', this difference will be 2a! in the case of 2a and
2b, and consequently p' will transmit to q' a quantity of heat equal to 2y'.
It is therefore certain that the quantity of heat which crosses the point m
is twice as great in the second solid as in the first whether the heat trans-
mitted arises solely from the action oip and q or from that of a multitude
of systems of two molecules. The preceding demonstration applies to each
part of the total effect and consequently to the sum of these effects.
Moreover one cannot reduce the effect in question to that of two indi-
vidual parts in contact. That is inconceivable in continuous solids and it is
the whole slice mpp'P which acts on the whole slice mqq'Q. One cannot
doubt but that this action consists in a sort of radiation, and that heat
transmits itself in the interior of solids in the same manner as in air and at
the surface of bodies. Only the distance up to which two molecules exercise
on one another a sensible action is incomparably smaller in a solid than in
an elastic fluid. This distance is very considerable in air and from the
experiments of M. Leslie one knows that a leaf of gold even when it has
become transparent and of the greatest thinness stops the direct transmission
of heat. The preceding demonstration neither supposes nor excludes these
physical considerations, and whether the distance in question be infinitely
small or finite, it is incontestable that the quantity of heat transmitted has
for its expression the term kS(a — b)fe. Although in what follows one makes
application of this result to the varied movement of heat in solids, one
supposes implicitly that the distance at which two points no longer exercise
any sensible action is extremely small as is shown by all experiments.
2. If one objects that it is not obvious that the principle given by Newton
can serve as a basis for the theory of heat, the author would reply that the
proposition in question is confirmed by multiple observations and that it is
accepted by all physicists. One can moreover go back to the origin of this
principle or replace it by other considerations. But if it is always necessary
to start with a primordial fact that can be verified by experiment alone let
us imagine, for example, that two such material points p and q act one on
the other for the transmission of heat in the interior of a solid, and that
there is between these molecules an exchange of heat as there would be an
exchange of light if they were both illuminated. Let r be their distance, U
the quantity of heat accumulated in the point p, V the heat of the point q,
and a the difference V— U which is infinitely small compared to V. The
AROUND 1810
313
quantity of heat sent by q would be given by <f>(r, V), </> indicating a certain
function which depends on the nature of the solid and also [ ],
<f>(r, U) for the quantity of heat sent by the point p. Therefore the result of
the mutual action which would be necessary to change the temperatures is
given by <f>(r, V) — >fs{r, U) or a<f>'{rU). Now if one adds a common quantity
A to the two quantities V and U one knows by repeated observations that
the mutual action of the two molecules will not be changed. Therefore
a<f>'(r, U+ A) is the same thing as a<f>'(r, U). By that one sees that the co-
efficient <j>'(t, U) in the expression atf>'(r, U) is a quantity independent of U,
and that all other things being equal the action of the molecules is pro-
portional to the difference a of the temperatures, which is the principle
of Newton. One ought to substitute for this principle the general fact
which has just been mentioned. It consists in the fact that phenomena
depending on the transmission of heat remain sensibly the same when all
temperatures are increased by a constant quantity. But this last result
[ ] by the observations of Newton, Rickmann, and Kraft, those of
Lambert, of Count Rumford, and of Messrs. Leslie and Biot. 14 In a word
by all those persons who have made the most varied experiments on the same
subject. No matter what the outcome of the preceding considerations, and
even if one does not agree with them, it has nevertheless always been
rigorously proved that the results announced in the memoir are the necessary
consequences of a single principle adopted by all the physicists who have
studied the phenomena of heat.
It suffices to look at the table of matters which have been treated in the
memoir on the Propagation of Heat to recognize that the author has taken
the greatest care to deepen this theory and that he has solved all the funda-
mental questions. He has given the general equations for the movement of
heat and those belonging to the state of the surface, and has applied them
to the most important cases, and he has later given integrals of these
equations in the forms most appropriate to the nature of the physical
questions which he has treated. The formulae which he has deduced can
be applied easily. They represent in the clearest manner all the circum-
stances of the propagation of heat in the interior of solids. They contain
exact definitions of the diverse properties of bodies relative to this trans-
mission, namely the capacity of heat 15 and the conductive qualities. 16 They
furnish the means of distinguishing and measuring these properties. They
show the nature of the movement of heat in a sphere, 17 in a ring, 18 in a
cubic solid 19 and in a prismatic solid. 20 This theory is applicable to that of
the problem of terrestrial temperatures. 21 It is confirmed by experiments
which the author has made himself with attention and perseverance. 22 One
should not therefore announce, even indirectly, that he has been held up
in this theory, for the contrary is proved by the table of matters alone.
314 XIX. FOURIER TO UNKNOWN CORRESPONDENT,
In order that one might judge more easily whether or not the equations
which express the movement of heat are established on sound principles
one will recall the propositions which are in question :
i . The quantity of heat which flows in a given time across the section of a
prismatic bar which has reached a permanent temperature, is equal to
that which escapes in the air by a definite part of the surface of a solid.
This quantity is represented, like the temperature, by a function z of
the distance x. The equation sought for is — dz/dx = chy which involves
only comparable terms.
2. That if a solid comprised between two infinite parallel planes at distance
e apart acquires permanent temperatures, one of the faces being held at
temperature a and the opposite face at temperature b, the intermediate
sections [ ] will have temperatures decreasing from a to b in
arithmetic progression, and the quantity of heat which flows uniformly
in the solid by a section S of the section is equal to the quantity — kS
(a — b)je, k being the specific conductibility.
3. The function designated by z in the second [sic] proposition is equal to
kSf'(x) and the equation which expresses the linear movement of heat is
kS d 2 y/dx 2 = chy.
For one to be able to consider as non-rigorous the methods adopted by
the author for establishing these equations it would be necessary to
indicate as either false or doubtful one or other of the preceding proposi-
tions.
Notes
1. He is evidently referring to his treatment in the Draft Paper. See above,
chapter 8, p. 164-5.
2. By Biot and Laplace among others.
3 . Newton's principle, first enunciated for the case of the loss of heat at the surface
of a heated sphere immersed in air maintained at a constant temperature. See
entry under Newton in Bibliography.
4. Fourier employs this symbol here in spite of its quite different earlier meaning
as one end of the bar.
5. For the 'argument* given in the Draft Paper see above, chapter 8, p. 164-5.
6. This was also a weakness of Laplace's derivation in Laplace (3): see above,
chapter 9, p. 184.
7. This unfortunate 'deduction' was made in Biot (1), p. 338.
8. See 1807 memoir, art. 17.
9. The passage back to the beginning of the paragraph should be compared with
that given in para. 4 of Letter XVIII above.
10. He refers to the same difficulty in para. 1 of Letter XVII above.
AROUND 1810
315
11. The same complaint is made in Letters XVII and XVIII above. Fourier him-
self was careful to restrict his criticisms of Biot — and later Poisson — to private
correspondence. As he said in a note to Letter XXI 'it will be more difficult to
cite M. Biot because I wish to avoid saying in public what I think of his
writing on the subject'.
12. The following derivation of the expression for the heat flux represents a funda-
mental improvement on that given in the 1807 memoir. See above, chapter 9,
p. 186.
13. Probably by Biot and Laplace who had implied (Biot (2), p. 336 and Laplace
(3). P- 291) that the famous 'analytical difficulty' could only be surmounted by
taking account of 'molecules' other than those immediately adjacent to the
point of the bar considered.
14. In the case of Lambert and Leslie he would be referring to the works given in
the Bibliography. The other references are uncertain apart from Biot (1).
15. See 1807 memoir, art. 15.
16. Ibid., arts. 16, 17.
17. Ibid., arts. 100-14.
18. Ibid., arts. 76-94.
19. Ibid., arts. 152-8.
20. Ibid., arts. 140-51.
21. As given for the first time in arts. 80-8 of the Prize Essay.
22. Fourier refers to such experiments in the Historical Notes, and in the Historical
Precis fol. 162. They are recounted in arts. 159-67 of the 1807 memoir.
XX
Fourier to Laplace, around 1808-9
I have the honour to offer to M. Laplace the homage of my regards in
sending him the attached note on certain analytical expressions in con-
nection with the theory of heat.
The function cos * is developed in terms of multiple arcs as follows: 1
■^7tcosa;= (-j- + i)sin 2a;+(J + ^-)sin4Je + (j+7) sin 6a;+ • • • (i)
The function sin * is developed in terms of multiple arcs as follows: 2
1 . 1 cos 2x cos ajx cos 6x cos Sx
-tt sin x = -
4 2 1.2 3.5 5.7 7.9
(2)
These theorems are not contrary to the principles of the calculus. 3 They
may be demonstrated rigorously and the demonstration not only consists
in the procedure which serves to determine the coefficients ; it consists also
in proving that if one sets in place of x in the equations (i) and (2) any
value whatsoever comprised between certain limits the second number is a
determined value which is equal to that of the first.
The series (1) and (2) are convergent and in general this property holds
without exception for all the series which I have employed in the Analytical
Theory of Heat.
For example the infinite series 4
smx +
sm 3* sin 5*
To I
+
is convergent and it expresses the ordinate of the contour of an isosceles
triangle the value of x being comprised between certain limits. Of all the
propositions of this kind the most simple is the principal one
1 . sin ix sin zx
-n = sinaH - — I — + ■ • •
4 3 5
which contains the series of Leibniz.
One can demonstrate in different ways the convergence of these series.
Here is the procedure 5 which I have most often employed because it
cannot leave any doubt. One considers first the number m of terms as
finite and known. One looks for the exact expression of the sum of the
terms as a function of x and m. One develops this function according to
XX. FOURIER TO LAPLACE, AROUND 1808-9
317
reciprocal powers of m and one recognizes that the more the number m
increases the more each term diminishes except the first. One remarks that
this latter term is the limit of the series. But this term is the first number of
the equation. The same calculation clearly shows between which limits
the calculation holds.
The question of the convergence of the series is here considered only in
regard to an understanding of the validity of the equation and disregarding
the use made of the same series to find numerical values. This kind of
approximation would be too slow. But in the equations of the theory of heat
the terms of these theories are multiplied by exponentials which contain the
time as a result of which the convergence is extremely rapid. 6
Notes
1. See 1807 memoir, p. 222.
2. Ibid., p. 228.
3. Presumably Laplace had said they were.
4. See 1807 memoir, p. 227.
5. First given in section 4 (fol. 142) of the Draft Paper and reproduced in article 47
of the 1807 memoir.
6. A good example of Fourier's intensely pragmatic approach to mathematics, at
least in the Analytical Theory of Heat, as a tool for obtaining workable solutions
to physical problems.
7
XXI
Fourier to an unknown correspondent, around 1808-9
I have the honour to send you two notes concerning the memoir on heat.
The first 1 is the one which was read at the Institut in place of the reading
of the memoir. The second 2 contains a more detailed discussion of the
equation
\x — sin x— ^sin zx+^sin 3* . . .
I beg you instantly to cast your eyes on this second note which clearly
establishes the convergence of this series and of which the essential
part was already in the memoir (article [44-]). 3 You will easily recognize that
this matter is not a question of faith but of mathematics, a very different
thing, and it seems to me that if such demonstrations are to be forbidden,
it will be necessary to give up writing anything exact in mathematics. I can
assure you, Sir, that I have advanced in this memoir nothing whose truth
has not been established by the most careful examination in which very
different methods have been brought to bear. But I have suppressed these
details which would have rightly been regarded as unnecessary.
I arrived at the developments of functions in sines or cosines of multiple
arcs by the method of elimination. Having later* solved the problem posed
by an infinity of bodies communicating heat between each other, I recog-
nized that the development would also apply to an arbitrary function and I
arrived by an entirely different 5 method at the same equation
W(«)
sin x \<f>(x)
sin #03:+ sin 2X
Ji(*)
sin zx&x +
which I had obtained previously. I transmitted this part of my work two
years ago to M. Biot and M. Poisson who then knew the use I was making
of it to express the integrals of partial differential equations in trigono-
metrical or exponential series : they did not point out to me that d'Alembert
or Euler had employed these integrations to develop a trigonometrical
solution. I was ignorant of the fact myself or I had entirely forgotten it; it
was in attempting to verify a third theorem that I employed the procedure
which consists in multiplying by cosi * dx the two sides of the equation
<f>(x) = <*(, + «! cos x+a 2 cos zx+ • • •
and integrating between x=o and x=ir. I am sorry not to have known the
mathematician who first made use of this method because I would have
AROUND 1808-9 319
cited him.* Regarding the researches 6 of d'Alembert and Euler could one
not add that if they knew this expansion they made but a very imperfect use
of it. They were both persuaded that an arbitrary and discontinous function
could never be resolved in series of this kind, and it does not even seem
that anyone had developed a constant in cosines of multiple arcs, the first
problem which I had to solve in the theory of heat. It was also necessary to
know the limits between which this development took place. For example
it has to be realized that the equation 7
xjz = sin x— % sin 2x+$ sin 3* . . .
is no longer true when the value of x is between n and 377. However, the
second side of the equation is still a convergent series but the sum is not
equal to xjz. Euler, who knew this equation, gave it without comment. It is
very clear that if the method used to develop certain functions in trigo-
nometrical series had been entirely exact it would have made known the
limits between which the equations held true. Finally, this development of a
function in sines or cosines of multiple arcs is only a particular case among
those which I have had to treat, and these latter offered analytical diffi-
culties of a very different order. It was necessary, for example, for deter-
mining the movement of heat in a cylindrical body to develop an arbitrary
function in a series whose terms depended on a transcendental function
given by a differential equation of the second order. 8 I beg you, Sir, to be
good enough to examine this part of my work which is really the only part
worthy of your attention.
I did not intend to denigrate the work which had been done before me
by mathematicians as illustrious as Messrs d'Alembert and Euler for I hold
their memories in the deepest respect. But I have wished to make it clear
that the procedure which they made use of was not adequate to solve the
problems relating to the theory of heat.
Moreover, Sir, if I had to cite certain works it would have been princi-
pally yours of which I have made an attentive study in the past and which
contain in fact on the question of series, on partial differential equations,
the elimination of coefficients, and the consideration of an infinite number
of differential equations, a multitude of elements similar to those employed
by me. Accept this as a reason for claiming your attention, and I beg you
instantly to read all the section of my work where I consider the develop-
ment of series. After this reading you will readily see that there is nothing
which is not incontestable. In fact one can well object that there exists in
the analysis certain trigonometrical series whose values are vague, that
often in this matter the results present themselves in diverse and opposed
forms, that several of the results of the memoir have paradoxical implica-
tions, and that in dealing with propositions of this kind the more they lack
320 XXI. FOURIER TO AN UNKNOWN CORRESPONDENT,
solid proofs the more one attempts to justify them. But those are the sort of
general reasonings which apply universally, for example to the quadrature
of the circle, which have not even the advantage of being new and with
which one can combat either error or truth as the need arises. These
maxims do not dispense with the need for examining things in themselves
in order to avoid lumping together those which are entirely different, and
because there were formally certain obscurities in the theory of infinite
limits it does not at all follow that these obscurities are in my work. Finally,
Sir, the end which I have proposed to myself is to determine the movement
of heat in solid bodies by means of the analysis of partial differential
equations. This question is in itself sufficiently important to merit the
attention of mathematicians, and it is really useful to know if the results
announced are erroneous or if applications can be made of them.
I desire, above all, to recommend my work to your attention for other
reasons and to remind you of the tokens of your benevolence which you
have given to the author. My heart will always guard their memory
and I attach to these relations an entirely different value than to cold,
and as it were indifferent, truths.
Excuse therefore, Sir, the length of this letter, and be very sure that it is
written by one who honours you and admires you and who joins to the
public gratitude which is due to you, the personal homage of the most
respectful attachment.
I have the honour to be with these sentiments, Sir, your very humble
and very obedient servant Fourier.
note * I was not able to consult any mathematical works at the time of
undertaking these researches, but when I publish them I shall re-
gard it as my duty to insert the missing (historical) citations. For
this reason I shall endeavour to find out about the work of Lambert
which seems to have treated the same subject. It will be more diffi-
cult to cite M. Biot because I wish to avoid saying in public what I
think of his writing on the subject.
Notes
i. This was the abstract (extrait) of Fourier's 1807 memoir which has been
retained in the MS. 1851 of the library of the Nationale F-cole des Ponts et
Chaussees, Paris. It must therefore be dated 1807, and not 1809 as suggested by
Grattan-Guinness (3), p. 497.
2. Also found in above MS. 1 85 1 . It is effectively identical with the treatment of the
same series given in art. 44 of the same memoir, as Fourier himself notes
below.
3. The question of convergence of certain trigonometrical series had first been
treated in the Draft Paper.
AROUND 1808-9
321
4. Sometime between the composition of the Draft Paper and the completion
of the 1807 memoir.
5. Different, that is, from the method based on elimination by which he had first
obtained this equation, as given in the 1807 memoir, arts. 50-61. The different
method is evidently that based on integration to which he refers immediately
afterwards.
6. See a recent discussion of this in Grattan-Guinness (3), chapter 10.
7. See 1807 memoir, arts. 122-39.
8. Some forty years later William Thomson, Lord Kelvin, was full of admiration
for this part of Fourier's treatise :
when it was printed in 1821 [sic], and published after having with the rest of Fourier's
work been buried alive for fourteen years in the archives of the French Academy,
and when Bessel found in it so thorough an investigation and so strikingly beautiful
an application of the Besselsche Funxtion we can imagine the ordinary feeling towards
those qui ante nos nostra dixerunt reversed into the pleasure of genuine admiration.
(Thomson, W., Math. Phys. Pap., z, p. 52).
XXII
Fourier to Bonard, February 1810
Paris, 25 February 1810
My dear old friend,
I do not know how to ask your forgiveness for the continual delays in my
correspondence, though they can only in part be blamed on my negligence;
for the circumstances in which I have found myself for several months have
demanded my exclusive and total attention.
I have written today to Grenoble and instructed the person responsible
for my affairs to send you immediately the sum of 800 francs to which you
refer in your letter.
My letter will arrive on 1 February [sic] and you will certainly receive the
sum in question by the 6th and 7th of next month. If, however, you find
this delay somewhat inconvenient please be good enough to write to M.
Guichard, the post office director, and request from him on my behalf
the sum of 800 francs. I know his friendship for me well enough to be cer-
tain that he will accede to your request. Please give my regards to Mme
Bonard and thank her for what she has done for my niece. I shall do my
best on my return to spend a day or two at Auxerre. When you remember
me to M. Guichard, tell him how much I regret not having seen him when
he was last at Paris; I often meet M. Dumoland, his friend, at court and we
talk about him.
At last I am coming to the end of my troubles, the printing of my
discourse 1 will soon be finished. I shall then devote more time and care to
my personal affairs. In continuing to have recourse to your kindness I shall
try to repay it better than I have done up to the present. Please remember
me to M. Roux 2 - and give me news of his health.
Accept the assurance of all the feelings of gratitude which I owe to your
long standing friendship.
P.S. J. Fourier
Prefect of Isere
Notes
1. His Introduction to the Description of Egypt.
2. See above, Letter IV, n. 2.
XXIII
Fourier to the Minister of the Interior, March 1815
Lyons 25 March 181 5
Sir,
I have the honour to address to your excellency 1 a certified copy of the
imperial decree of the 12th of this month by which his majesty was pleased
to call me to the office of the Prefect of the department of the Rhone in
which I was installed the same day in accordance with the enclosed report.
I am with respect, Sir, your excellency's most humble and most obedient
servant.
The prefect of the department of the Rhone,
Fourier
Notes
1. Carnot, L. N. M. (1753-1823). Having completed his early studies at the
College of Autun, his remarkable aptitude for mathematics and science promp-
ted his father to send him to a preparatory school in Paris for prospective cadets
for the engineers and artillery run by a friend of D'Alembert. From here he
passed to the school of Military Engineering at Mezieres (1771) where he was a
pupil of his compatriot Gaspard Monge. He left Mezieres in 1773 and entered
the corps of engineers where he found time to compose an Moge de Vaubin and
his important Essai sur les Machines en General (1783) containing the theorem on
colliding bodies bearing his name. In 1788 he was imprisoned for a time through
a lettre de cachet resulting from his somewhat ungallant action in relation to a
certain Mile Bouillet. In September 1789 he addressed a memoir to the National
Assembly against the oppressive regime governing the engineering corps in
which he demanded the creation of a committee of officers elected by their
peers. In 1792 he was elected (along with his brother Claude-Marie) to the
Legislative Assembly where he became a member of the Committee of Public
Instruction and made a name for his interventions in military affairs. He was
elected to the Convention where he voted for the death of the King. His role in
the period 1793 to 1797 belongs to European History. He disapproved of the
Empire and spent the period 1804 to 18 14 in retirement devoting himself to the
education of his children, his scientific work, and to playing a full part in the day
to day life of the First Class of the Institut to which he had been elected in 1796.
He emerged from retirement in 1814 to become governor of Antwerp, and during
the Hundred Days he was Minister of the Interior. This led to his exile after
Waterloo and he died in Magdeburg in 1823. Carnot's stature as a savant has
tended to be ignored in comparison with the political and military side of his
life, but is now under active consideration (Bio. Gen.; Gde. Encycl.; see also
Gillispie).
XXIV
Fourier to the Minister of the Interior, March 1815
Lyons 30 March 1815.
Sir,
I have the honour to acknowledge reception of your excellency's letter
written to me on 22nd of this month informing me that his majesty the
Emperor had recalled you to the Ministry of the Interior.
France will find in this change, Sir, a new proof of the clear views of
his majesty; but while France and Europe applaud this striking testimony
rendered to you, the administrative authorities will be particularly conscious
of its value.
I will not talk to your excellency of the sentiments of devotion which
attach me to his majesty. They have been long known. Public opinion
in the department which I have the honour to administer has expressed
itself in a manner to leave no doubt as to the opinion of the inhabitants, and
if there still exist some partisans of the previous government they are few in
number and without influence.
All the official proclamations printed in the Moniteur have been printed,
published, and displayed at various times in all the communes of the
department. The official bulletins and telegraphic dispatches have also
been published immediately after their arrival and help to strengthen public
opinion which could still be led astray by some new lies spread about
intentionally. And so from this point of view your excellency's instructions
have already been carried out and will continue to be punctually.
As to municipal officers, very few changes have been made, they have
been restricted to a few members . . .
XXV
Fourier to sub-prefects of the Department of the Rhone,
May 1815
Lyons 1 May 1815
M. Sub Prefect,
I have the honour to address to you the enclosed circulars which I have
written to mayors of the communes concerning the publication of the
acte additionel 1 to the imperial constitution and to the execution of the
imperial decree which orders the opening of registers on which the votes of
Frenchmen are to be inscribed.
I enclose with the present letter several copies of this act which should
remain in the secretariat of the sub-prefecture so that the voters can acquaint
themselves with it.
I request you, M. Sub Prefect, to pass on immediately, and by express
post, to the mayors of the communes of your district the packets which are
intended for them, and to make sure that the registers are opened wherever
they should be.
I have fixed the closing of the registers for the 12th of this month and I
have instructed the mayors to see that they reach you in the course of the
15th.
On the 1 6th you are to make a report of the votes cast in the communes
of your district. This report, in conformity with model 2, and which you
will prepare in advance, should be sent the next day in duplicate with the
registers of the votes. Under no circumstances, M. Sub Prefect, should this
dispatch be subject to the least delay. It is indispensable that on the 17th
of this month all the papers should be returned to me.
I request you to bring all possible promptness and speed to these
matters so that I may be able to send his excellency the Minister of the
Interior, within the delay fixed by his instructions, the results for submis-
sion to the assembly of the Field of May.
Receive M. Sub Prefect the assurance of my distinguished regard.
The Prefect of the Rhone
Count Fourier
Note
1. See above, chapter 5, n. 78, p. 116.
XXVI
Fourier to the Ministers of War, Police, and the Interior,
May 1815
Lyons, 6 May 181 5
Sir,
The examining council finished its operations on the 3rd of this month.
The number of returned soldiers available has risen to 12 900. The first
departure took place today, 220 men were dispatched for various corps;
new detachments will be sent off every day.
I shall have the honour to send you, Sir, without delay the municipal
returns of the soldiers called before the council, of those who appeared, and
the decisions which were taken.
The recruiting officers occupy one of the offices of the prefecture, and I
have them supplied with the material necessary for their writing. There are
already some white forms left by the former recruiting captains, but they
will not be enough to provide for duplicate copies: I am having others
printed . . .
Fourier
XXVII
Fourier to the Minister of the Interior, March 18 16
Paris,
28 March, 1816
To His Excellency the Minister and Secretary of State for the Interior. 1
Sir,
I received with the keenest sorrow the reply which your Excellency has
just sent me concerning my demand for a retirement pension. I have
devoted to the State my life and talents during thirty consecutive
years, namely thirteen years in public education and seventeen in adminis-
tration. I have contributed as Professor of Analysis to the establishment of
the Fcole Polytechnique of France. Your Excellency knows the part I
played in the composition of the memoirs on Egypt. I am the only one of
the authors of this great work who has received no payment, nor pension,
nor indemnity. I administered the department of Isere during thirteen
years and I leave public office without any fortune. The principles which
directed my conduct in this period are perhaps forgotten today by the
government, but they are well known in the ancient province of the Dau-
phinee. The services I rendered to so many families then in need of support
deserve to be taken into consideration. The drying of the marshes of
Bourgoin was commenced and entirely completed under my administration.
The agricultural territory of France received considerable increase (about
19 000 acres). The annual illnesses which cut short men's lives have ceased
for ever in this region. Public wealth has been augmented by many millions.
Your Excellency knows the deliberations of the forty interested communes
and of the general council of the department, those of the proprietors and
of the concessionaries, and in the light of their expression of gratitude and
their formal declarations one cannot doubt that I was the principal author
of this enterprise. It required a special effort on my part continued over
eleven years, and considerable expenses for which I have never been com-
pensated. I have served France in difficult times, full of dangers of every
kind; I have served her in towns, in camps, in far countries, in the midst
of seditions, wars, and contagious diseases. As a man of letters I have
contributed gratuitously to a precious monument which honours our
country and which will long be remembered in the history of the arts. My
youth was consecrated to teaching the sciences in the foremost places of
education; finally as an administrator I participated in the greatest and
328 XXVII. FOURIER TO THE
most useful public work which has been executed in France in recent
times. No political motive should efface the memory of so many services
from which the State and many generations will receive real and lasting
advantages. I realize how out of place it is to speak thus of oneself, and it is
as painful to me as it is contrary to good manners thus to recall the out-
come of my efforts; but I may be excused if one remembers the absolute
obligation under which I find myself to make the most of my services by all
means consistent with the truth.
As to the political facts which have been brought against me, one cannot
judge them fairly without taking careful account of the circumstances in
which I found myself .
The outcome of the inquest into the trial of General Marchand has
just proved that I made the greatest efforts to check the spirit of sedition
in the department of Isere. Your Excellency has moreover an incontestable
proof of this in the attached letter which I beg you instantly to read. 6 I
shall restrict myself to enumerating the principal facts the formal evidence
for these facts being cited in my memoir.
I had arrested and conducted to the prisons of Grenoble and other towns
fifteen of the principal agitators.
An act entitled 'Imperial Decree' dated Grenoble, 9 March, published
and displayed in this town and in the neighbouring departments, dismissed
me from my position and required me to leave the territory of the Seventh
Military Division under penalty of being treated as an enemy of the State. 3
I upheld the exercise of the King's authority wherever I was, and this
authority did not cease till I had been arrested by the advance guard and
conducted to Bourgoin to Bonaparte's headquarters.
I visited the banks of the Rhone to co-operate in the destruction of
bridges and the removal of ferry boats, important and decisive measures
which I constantly advocated orally and in writing and which could alone
have prevented the usurpation of the territory beyond that river. I was on
the way to Lyons when from that town I received a written order 4 from
His Royal Highness, Monsieur, ordering me to return to the department of
Isere and go back towards Grenoble. It was in obeying this instruction that
I was captured at Lerezin by order of Bonaparte and conducted to his head-
quarters at Bourgoin in the midst of an immense crowd of mutineers and
soldiers. From that moment I lost all liberty of action and what I did could
not be imputed to me as a voluntary act. It is well known that I resisted as
long as possible what Bonaparte intended for me, and I yielded to a violent
and formidable power to which my previous actions had been opposed. It is
at least certain that I made use of my authority only to prevent, stop, and
repair great misfortunes. I only exercised this authority after the reiterated
demands of a large number of the principal inhabitants who were exposed to
MINISTER OF THE INTERIOR, MARCH 1816
329
great peril through their attachment to the royal cause. I may add that I
refused absolutely to participate in any act of dismissal, replacement, or
arrest. I will not attempt to justify my sustained opposition to Messrs. de
Grouchi, Brayer, and the extraordinary commissioner M. Maret. These facts
are public property in the two departments of Isere and of the Rhone. It is
equally well known that I refused formally and in writing to participate
in the acts required of me. I was then replaced by Monsieur Pons as is
proved by an act entitled 'Imperial Decree' dated Paris, 17 May. 5
If the facts I advance are true, and if my previous services actually
are as I have related them, are the rights to which these services entitle me
to be irrevocably destroyed? Should neither my disinterestedness nor my
zeal count for something, nor my constant opposition to all oppressive
measures, nor the benefits which I have obtained for the State, nor the
principles which I have followed during thirteen consecutive years in a
time when these principles certainly could not have been suggested to me
by any political consideration. The King's justice and virtue will not allow
one of the most senior administrators of France, one who has consecrated
his life to useful works, and to the progress of science and letters, to remain
without any personal fortune and unindemnified while the state and [other]
individuals alone enjoy the fruit of his labours. It is from this point of view,
Excellency, that I am obliged to renew my demands to your Ministry for a
pension as former professor of the Ecole Polytechnique, as one of the
principal authors of the Egyptian collection, and as a former prefect. Allow
me to call again on your benovolence and support in such a just cause which
concerns both administration and the arts.
I have the honour to be with respect, my dear Sir, your Excellency's very
humble and very obedient servant.
Baron Fourier, former Prefect of Isere.
Notes
(a) There is a marginal reference here to an address of thanks to Fourier from the
principal proprietors of the land adjoining the swamps of Bourgoin for his part
in the draining of these swamps.
(b) There is a marginal reference here to an attached copy of a letter to Fourier's
successor as Prefect of Isere which proves the active steps he took to attempt to
suppress any moves in Grenoble in favour of Napoleon.
1. Vaublanc, Vincent Marie Vienot, Count of (1756-1845). A pupil at the Ecole
Militaire in Paris he originally entered the army but resigned to become a
member of the Legislative Assembly where he belonged to the Constitutional
Party. He was a supporter of the monarchy though a decided liberal. He
opposed the Girondins and defended Lafayette on 8 August 1792. On 10 August
he owed his life to General Bertrand. He was not elected to the Convention and
330 XXVII. FOURIER TO MINISTER OF THE INTERIOR
escaped the Terror by wandering about from place to place. After 9 Thermidor
he returned to Paris but was proscribed after 18 Fructidor (4 September 1797).
He returned to France after the coup d'etat of 18 Brumaire and became one of
the most enthusiastic supporters of Napoleon. He was made Prefect of Moselle
and continued in office after the First Restoration. During the Hundred Days
he fled to Luxembourg and later joined the King at Ghent. He entered the
Ministry of Richelieu as Minister of the Interior on 24 September 1815. He
adopted a most reactionary policy especially towards prefects who had supported
Napoleon in the Hundred Days and this earned him the approval of the 'cham-
bre introuvable'. He was a favourite of the King's brother the Comte D'Artois.
He was responsible for purgings of supporters of Napoleon from the Institut and
he dissolved the ficole Polytechnique. His conduct became so intolerable in
the cabinet that he was finally replaced on 8 May 1816 by Laine (Bio. Gen.;
Gde. Encycl.).
2. Marchand, Jean Gabriel (1765-1851). Before the Revolution he was a lawyer in
the' parlement of Grenoble and a friend of Barnave. Elected captain by the
volunteers of the 4th Battallion of Isere in 1791 he fought through all the cam-
paigns of the Republic in the armies of Italy and the Rhine. He distinguished
himself at Jena and Friedland, in various engagements in Spain and Portugal
including the battle of Busaco, and he fought in the rear-guard in the retreat
from Moscow. He continued in his position under the First Restoration and
refused to join Napoleon during the Hundred Days. He was court martialled in
June 1 816 for his failure to hold Grenoble for the king but was acquitted. He
was created a peer of France in 1837 (Bio. Gen.; Gde. Encycl.).
3. A copy of this act is preserved in Fourier Dossier AN where it is listed as item 15
of the pieces justificatives to the present letter.
4. A copy of this order, in the form of a letter from the Comte de Chabrol, Prefect
of the Rhone, is preserved in the Fourier Dossier AN. It is listed as item 16 of
the pieces justificatives to the present letter.
5. A copy of this act is preserved in the Fourier Dossier AN. It is listed as item 18
of the pieces justificatives to the present letter.
XXVIII
Fourier to the president of the first class of the Institut
11 April 1816
To the President 1 of the First Class of the Institut
Mr. President Sir,
The Academie Royale des Sciences having proposed the election of
several people as free academiciens, 2 I have the honour to express to you
my desire to obtain one of these places. I presented myself to the members
of the commission whose report must precede the election. I wished to
entreat their goodwill and their vote personally. But several of these
gentlemen were not to be found at home. I beg you to allow me to express
in writing to the commission how grateful I would be if it were to include
me on its presentation, placing me in the position which it deems appro-
priate.
I offered to the former Academie Royale des Sciences the results of my
first researches in analysis. A report 3 was made on it twenty-six years ago
by Messrs. Cousin 4 and Monge 5 who particularly desired to encourage my
zeal. Since then I have not ceased to cultivate the sciences, and I have
treated various questions in geometry, mechanics, and physics. I have often
been diverted by other literary tasks or by civil occupations from the
sciences, but my intention [now] is to consecrate myself entirely to them
and to contribute to their progress to the best of my ability.
My attachment to science is in truth the only claim which I should
advance to win your vote : but to some extent I am entitled to recall another
which is very dear to me, since it was you yourself who awarded it: I wish
to refer to the mathematics prize which the Institut was pleased to award
for my researches on the theory of heat. I am in the process of publishing
the work which will have about 480 quarto pages : 360 pages are already
printed.
I beg you, Mr. President, to receive favourably and to present to the
members of the committee the desire which I have the honour to express
to you, and to receive with an equal kindness the homage of my respect.
With these sentiments Mr. President, Sir, I am your very humble and
very obedient servant,
Fourier
332
FOURIER TO THE PRESIDENT OF THE INSTITUT
Notes
i. Charles, J. A. C. (1746-1833). Experimental physicist.
2. As a result of Royal Ordinance of 21 March 1816.
3. No trace of this report is to be found in the archives of the Academie des Sciences.
4. See above, Letter VI, n. 4.
5. See above, Letter III, n. 3.
PROVENANCE OF LETTERS
LETTER
LOCATION
PREVIOUS PUBLIC/
I-IV
Bib. Mun. Auxerre MS. 335.
Challe (2)
V
Arch. Yon.
Quantin
VI-VII
Bib. Mun. Auxerre MS. 335.
Challe (2)
VIII
ANMSF 7 . 4710.
Unpublished
IX
Fourier Dossier AdS.
Unpublished
X-XIII
Bib. Mun. Auxerre MS. 335.
Challe (2)
XIV-XVI
Arch. Yon. MS. 470.
Unpublished
XVII
BNMS ff. 22501 fol. 67, 75.
Unpublished
XVIII
Ibid., fol. 66.
Unpublished
XIX
Ibid., fol. 76-81.
Unpublished
XX
Ibid., fol. 68.
Unpublished
XXI
Ibid., fol. 72-73V, 74.
Unpublished
XXII
Bib. Mun. Auxerre MS. 335.
Challe (2)
XXIII
Fourier Dossier AN.
Unpublished
XXIV
Bib. Mun. Lyon MS. 2270.
Unpublished
XXV
Ibid., MS. 2271.
Unpublished
XXVI
Ibid., MS. 2272.
Unpublished
XXVII
Fourier Dossier AN.
Unpublished
XXVIII
Fourier Dossier AdS.
Unpublished
BIBLIOGRAPHY
Primary sources
Fourier's papers passed on his death to his friend Navier and ultimately found
their way into the Bibliotheque Nationale where they are catalogued under
MSS. ff. 22501-29. A summary list by content of these manuscripts will be found
on pp. 496-7 of Grattan- Guinness (3). They are largely made up of mathematical
and scientific writings, many of them drafts of published papers and works. All
the letters in the collection are found in 22501 and 22529. The most important of
these are reproduced in English translation in the Appendix of the present work
as Letters XVII-XXI. In addition there are two sets of letters from Fourier to
Sophie Germain in MS. ff. 91 18 and MS. na. 4073. The Archives Nationales,
Paris contain two major collections of manuscripts relating to Fourier. The dossier
of the prefect Fourier (Fourier Dossier AN) MSF 1B1 160 contains a rich
collection of material relating to Fourier's life in Grenoble and during the
Hundred Days, much of it in the form of certified copies attached as pieces
justificatives to various letters by Fourier in support of his application for a pen-
sion after his return to Paris in 181 5. The second collection in the Archives
Nationales is found in the series F 7 of the secret police relating to Fourier's
second arrest in 1795 including the important letter to Bergoeing (Letter VIII).
There are also certain other relevant manuscripts at various places in the Archives
mostly relating to the Orleans affair and referred to above in Chapters 4 and 5.
The Fourier dossier in the archives of the Academie des Sciences in Paris (Fourier
Dossier AdS) contains a number of letters from Fourier including the very
important letter to Villetard (Letter IX, Appendix) and in addition certain
material relating to his election to the Academic Part of his lectures at the ficole
Polytechnique are found in the Bibliotheque de Vlnstitut (MS. 2044) together
with a certain amount of other material. There is also a small amount of material
relating to Fourier in the archives of the Academie Francaise. The original text of
the 1807 memoir is contained as MS. 1851 in the archives of the Fxole Nationale
des Ponts et Chaussees, Paris. The same MS. contains an abstract (extrait) of the
memoir together with a set of ten numbered notes referring to specific places in
the text of this abstract.
The departmental archives of Yonne at Auxerre contain a particularly rich
collection of material in section L relating to the Revolution in Auxerre. Thanks
to a succession of devoted local historians including Quantin, Poree, and Fores-
tier many of these documents and other related ones in the Archives Nationales
and the Municipal Library of Auxerre have now been published. All the material
on Fourier located in these manuscripts either published or unpublished has
been incorporated in the present work. The Municipal Library of Auxerre also
contains the precious collection of letters from Fourier to Bonard reproduced
above in the Appendix. Lefebvre's Etudes OrUanaises contains an account of
BIBLIOGRAPHY
335
Laplanche's activities in Orleans in 1793, including some references to Fourier's
intervention. This account was rendered doubly valuable by the destruction in
1940 of the documents on which it was based in the departmental archives of
Loiret in Orleans. The departmental archives of Isere at Grenoble contain a
large mass of material relating to Fourier's administration as prefect in Isere.
This has not been drawn on directly in the present work as opposed to at second
hand through extracts given in the writings of the various Champollion-Figeacs
and those of Letonnelier. It would be necessary to make more extensive use of
this material in a definitive biography of Fourier. Certain letters relating to
Fourier's actions during the Hundred Days are located in the departmental
archives at Lyons. These have all been referred to in the text. There are also a
small number of Fourier letters at various municipal libraries in France including
those of Amiens, Avignon, Grenoble, Nantes, and Versailles.
Fourier
(a) Major works and MSS. referred to in present work other than Letters re-
produced in English translation in the Appendix. In each case the short title is
given first.
Draft Paper BN MS. ff. 22525, fol. 107-49 r ^^ v -
1807 memoir Mimoire sur la propagation de la chaleur.
Read in abstract before the Institut on 20 December 1807. The original memoir
is preserved in MS. 1851 of the ficole Nationale des Ponts et Chaussees, Paris.
The full text is reproduced with commentary in Grattan-Guinness (3).
Prize Essay Theorie du mouvement de la chaleur dans les corps solides.
The winning entry for the 181 1 Prize competition of the Institut on the subject
of the propagation of heat in solid bodies. The original manuscript is preserved in
the archives of the Academie des Sciences. Page references are to the version of
the essay published in two parts in the Memoir es de V Academie Roy ale des Sciences.
(vol. 4 (1819-20); 185-555, 5 (1821-2), 153-246). The second part of this publi-
cation is given in Oeuvres, 2, 1-94.
Historical Precis Pricis historique de la propagation de la chaleur. BN MS.
ff. 22525 fol. 152-68 r. and v.
Analytical Theory Thiorie analytique de la chaleur, Paris 1822.
Page references throughout will be to the version published in Oeuvres, 1.
Oeuvres Oeuvres de Fourier (Ed. G. Darboux, 2 Vols.), Paris,
1888-90.
Fourier Dossier AN AN MS. FIBI 160.
Fourier Dossier AdS Dossier of J. B. Fourier, Archives de I' Academie des
Sciences, Paris.
Historical Notes BN MS. ff. 22529 fol. 102.
336
BIBLIOGRAPHY
(b) Other works and MSS.
The full title and/or location of all other Fourier works or MSS. referred to
in the present work are given in the notes. For an extensive list of Fourier's pub-
lished works see Grattan- Guinness (3), pp. 491-5.
Other authors
Amontons, G. Histoire de V Academic Paris (1703).
Aulard, F. V. A. (1) (Ed.) Recueil des actes du ComiU de Salut Public. First vol.,
1899. Paris.
Biot, J. B. (1). Memoire sur la propagation de la chaleur. Bibliotheque Brittanique
37 (1804), 310-29.
(2) Du calorique rayonnant, par Pierre Prevost. Mercure de France, 38
(1809), 327-38.
■ (3). Traite de physique experimentale et mathimatique. 4 Vols., Paris (1816).
ficole Normale, An. II. Siances desFcoles Normales Ricueillis par des Stenographs
et Revues par les Professeurs (2nd ed.). 10 Vols., Paris (1800-1).
Geoffroy Saint Hilaire, E. Lettres ecrites d'Egypte (Ed. E. T. Hamy), Paris
(1901).
Guillaume, J. (Ed.). Proces verbaux du ComiU d' Instruction Publique de la
Convention Nationale. 7 Vols., Paris (1891-1957).
Hermite, C. Oeuvres. 4 Vols., Paris (1905-17).
Ingenhouss, J. Nouvelles experiences et observations sur divers objets de physique.
2 Vols., Paris (1785-9).
Lambert, J. H. Pyrometrie. Berlin (1779).
Laplace, P. S. (1) Extrait d'un memoire sur la theorie des tubes capillaires.
J. Physique, 62 (1806), 120-8 {Oeuvres, 14, 217-27).
(2) Memoire sur divers points d'analyse. J. Ecole Polytech. cah., 15, 8
(1809) 229-65 {Oeuvres, 14, 178-214).
(3) Sur les mouvements de la lumiere dans les milieux diaphanes. Mdmoires
de la classe des sciences mathematiques et physiques de I'Institut de France, Ser. 1,
10 (1810), 300-42 {Oeuvres, 12, 265-98).
Leslie, J. An experimental enquiry into the nature and propagation of heat.
London (1804).
Malus, E. L. L' agenda de Malus. Souvenirs de V expedition d'Egypte, iyg8-i8oi.
Paris (1892).
Mayer, J. T. Gesetze und Modificationen des Warmestbffes. Erlangen (1791).
Moland, F. et al. Proces verbaux de V administration de I'Yonne, iygo-1800. 7
Vols., Auxerre (1889).
Napoleon, I. Correspondence. Selection by Bingham. 3 Vols. London (1884).
Poisson, S. D. (1) Memoire sur les solutions particulieres des equations differen-
tielles et des equations aux differences. J. Ecol. Polytech. cah., 13, 6 (1806),
60-116.
(2) Memoire sur la propagation de la chaleur dans les corps solides (extrait).
Bull. Soc. phil., 1 (1808), 1 12-16 {Oeuvres, 2, 213-21).
BIBLIOGRAPHY
337
— (3) Extrait d'un memoire sur la distribution de la chaleur. J. Phys. Chim., 80
(1815), 434-41.
■ (4) Memoire sur la distribution de la chaleur dans les corps solides. Bull.
Soc. phil. (1815), 85-91.
■ (5) Theorie mathimatique de la chaleur. Paris (1835).
Pictet, M. A. Essai sur le feu. Geneva (1790).
Poree, C. Sources manuscrits de Vhistoire de la Revolution dans I'Yonne. 2 Vols.,
Auxerre (1918-27).
Prevost, P. (1) Memoire sur l'equilibre du feu. Phys. {Fr.), 38 (1791), 314-23.
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Secondary sources
The general history of Auxerre and neighbourhood, including certain relevant
details of the revolutionary period, is given in Challe (3), Chardon, Henry,
Lebeuf, Phelipeaux, and Pinsseau. Challe (1), Cestre (2), Moiset, and Schmidt
give a well- documented account of the history of the College d' Auxerre especially
during the period 1 789-1 804. The general background to the Benedictine
teaching order of St. Maur is given in the article by Lemoine in Taton (3), which
is also useful for its bibliographic references including that to Tassin. The main
sources for Fourier's early life up to 1798 are Cousin, Mauger, and Arago.
Cousin's account is largely based on first-hand witnesses. It stands up well to
comparisons with other, primary sources of information and must be judged a
most reliable, careful, and scholarly account. It is also much the most extensive
and detailed account. Mauger's account, though much shorter than Cousin's,
and possibly influenced by Cousin, is nevertheless valuable as coming from a
friend of Fourier's, and for certain details not found elsewhere. Arago's dloge,
though lively and well written, evidently depended for various details on Cousin,
and has its value reduced still further by a total lack of documentation. Among
the many histories of the French Revolution, some excellent, Soboul and
Lefebvre (1) proved particularly useful for setting Fourier's life within the
general framework of the Revolution. Of more specialized works Egret was
particularly valuable for the so-called Aristocratic Revolution, Aulard (2) for the
early effect of the Revolution on the religious orders, Sirich for the changing role
of the revolutionary committees of 1793, Lefebvre (2) for the background to
Fourier's intervention in Orleans, and Lefebvre (3) for the Thermidorian reac-
tion. For the role of science in the saving of the Republic in 1793-4 Biot (4),
Fayet, and Pouchet were particularly useful, for the short-lived ficole Normale
of Year II, Allain, Barnard, Fayet, and the Notice historique, and for the founda-
tion of the ficole Polytechnique, Allain, Barnard, Fayet, Fourcy, Pinet, and the
Livre de centenaire. For Fourier's life in the period 1793-5 Cousin is the best
secondary source, followed by Mauger and Arago in that order. Apart from two
brief references in Fourcy and a few lines in Cousin and Arago there appears to
be nothing on Fourier's time at the ficole Polytechnique in 1795-8. Herold,
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340
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Germain, S. Oeuvres philosophiques de Sophie Germain suives de pensees et de
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Gillispie, C. C. Lazare Carnot savant. Princeton (1971).
Gouhier, H. Lajeunesse d'Auguste Comte et la formation du positivisme. 3 Vols.,
Paris (1933-41).
Grattan-Guinness, I. (1) Joseph Fourier and the revolution in mathematical
physics. J. Inst. Math. App., 5 (1969), 230-53.
(2). The development of the foundations of mathematical analysis from Euler
to Riemann. Cambridge, Mass. and London (1970).
(3) (in collaboration with J. R. Ravetz). Joseph Fourier, 1768-1830. Cam-
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Green, G. Mathematical papers (Ed. N. M. Ferrars). London (1871).
Hahn, R. (i) Quelques nouveaux documents sur Jean-Sylvain Bailly, Rev. Hist.
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(2). Laplace as a Newtonian scientist. Los Angeles (1967).
Henry, J. B. Histoire del'Abbaye de St. Germain. Auxerre (1853).
Herivel, J. W. (1) Aspects of French theoretical physics in the 19th century.
Br. J. Hist. Sci. 3 (1966), 109-32.
(2). The influence of Fourier on British mathematics. Centaurus, 17 (1972),
40-57-
Herold, C. J. Bonaparte in Egypt. London (1963).
Jourdain, P. E. B. (i). Note on Fourier's influence on the conceptions of mathe-
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526-7, Cambridge (19 1 3).
(2). The influence of Fourier's theory of the conduction of heat on the
development of pure mathematics. Scientia, 22 (1917), 245-54.
Kucinski, A. Dictionnaire des conventionels. Paris (1917).
Kelland, P. Theory of heat. Cambridge (1837).
Knight, I. F. The geometric spirit. New Haven and London (1968).
Lacour-Gayet, G. Bonaparte, membre de VInstitut. Paris (1921).
Lacroix, A. La vie et l'oeuvre de l'Abbe Rene- Just Haiiy. Bull. Soc. franpaise
Mineral, 47 (1944), 15-226.
La Jonquiere, T. de. L'Expedition en Egypte, 1798-1801. 5 Vols., Paris (1899-
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Langer, R. Fourier series, the genesis and evolution of a theory. Am. math.
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BIBLIOGRAPHY
341
Lebeuf, J. Memoires concernant I'histoire ecclesiastique et civile d' Auxerre. With
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Lefebvre, G. (i). The French Revolution from its origins to 1793. Translated by
E. M. Evanson. London (1962).
(2). Etudes Orleanaises. 2 Vols., Paris (1962-3).
(3). The Thermidorians. English translation R. Baldick. London (1965).
Lefort, F. Notice sur la vie et les travaux de Biot. Paris (1867).
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Mach, E. Die Principien der Wdrmelehre. Leipzig (1896).
Maras, R. J. Napoleon: patron of science. Historian, 21 (1958), 46-62.
Mauger, G. G. Joseph Fourier. Ann. Stat. Dep. de V Yonne, p. 270
(1837)-
Moiset, C. Le College Royale Militaire d' Auxerre. Bull. Soc. Sci. hist. not. Yonne,
(1893), 5-22.
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Pinsseau, P. Auxerre historique et pittoresque. Auxerre (1943).
Pouchet, G. Les sciences pendant la Terreur. Paris (1896).
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(2). Histoire anecdotique des rues d' Auxerre. Auxerre (1870).
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mathematical physics, Actes du IX Congres International d' Histoire des Sciences,
pp. 574-8. Barcelona and Madrid (1959).
(2). Vibrating strings and arbitrary function. The logic of personal knowledge:
essays presented to Michael Polyani on his 70th birthday, pp. 71-88. London
(1961).
Robinet, J. F. E. Condorcet, sa vie, son oeuvre, 1743-1794. Paris (1893).
Schmidt, C. Le college d' Auxerre en 1792. Ann. Stat. Dep. del' Yonne, pp. 29-36
(1899).
Sirich, J. B. The Revolutionary Committees in the Departments of France, 1793-4.
Cambridge, Mass. (1943).
Smith, E. B. Jean-Sylvain Bailly — astronomer, mystic, revolutionary — 1736-
1793. Trans. Am.phil. Soc, 44(1954), 427-538.
Soboul, A. Precis d'histoire de la Revolution franpaise. Paris (1962).
Tassin, R. P. L'histoire litteraire de la congregation de St. Maur. Paris (1770).
Taton, R. (i). L'oeuvre scientifique de Monge. Paris (1951).
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Melanges Alexandre Koyre, Vol. 1., pp. 552-64, Paris (1964).
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(1964).
342 BIBLIOGRAPHY
Tessoneau, R. Joseph Joubert, educateur, d'apres des documents inedits, 1754-
1824. Paris (1944).
Vinot, J. Bezout. Sa vie et ses oeuvres. Nemours (1883).
Vleck, E. B. van. The influence of Fourier's series upon the development of
mathematics. Science, 39 (1914), 113-24.
Vuillemin, J. B. La vie du St. Pierre Fourier. Paris (1897).
Williams, L. P. Science, education and the French Revolution. Isis, 44 (1953),
INDEX
The names of persons who are neither mathematicians nor scientists are entered
only where they occur in a context having some direct connection with Fourier's life
or work. Entries in bold type indicate biographical notes.
Bezout, E., 7, 7 n. 14, 250, 250 n. 5.
Bio. Ben. passim.
Biot, J. B., 102, 103, 125, 129, 130.
Academie des Sciences; passim; see also
under Fourier and the Academie des
Sciences.
Academie Francaise, Fourier election to,
137-
Aignan, E., 33, 33 n. 19
Allain, E. 66.
Alembert, J. Le R. D., 221, 224, 225, 226,
223, 240; and trigonometrical series,
154, 157, 172.217,318,319-
Am<5, G., 133, 293, 293 n. 8, 297, 299.
Amontons, G., 163
Ampere, A. M., 129, 129 n. 97, 209, 220,
233, 234-
Ancelot, M. L. V. ,143.
Andreossy, A. F., 72, 72 n. 20.
Anguoleme, Duchess of, 105.
Arago, F., 108, 116, 125, 125 n. 57, 129,
144, 234.
Artois, Count of, 105, 106, 108, 109.
Aubrey, 253, 253 n. 5.
Auger, L. S., 137, 137 n. 130.
Auxerre; Abbey St. Germain, 5, 6, 14;
Cathedral St. Etienne, 5, 6, 257;
Ecole Royale Militaire of, 7, 13, 14-15,
39-40 ; educational tradition at, 6 n. 6 ;
Society of Emulation of, 14, 14 n. 45 ;
post thermidorian reaction in 45, 45 n.
65; and French Revolution, 15-16,
277, 282.
Avallon, Fourier's mission to, 29.
Bailly, J. S., 7, 7 n. 13.
Balme, J. G., 40, 54, 55, 60, 61, 293,
293 n. 10.
Barere, B., 35 n. 26; his decree against
Fourier, 35, 36, 37, 229, 283.
Barnard, H. C, 66.
Barrow, J., 91.
Bedel, J., 17.
Belliard, A. D., 74, 74 n. 31.
Bergoeing, F., 44, 56, 57, 58, 60, 236, 276,
276 n. 1.
Bernouilli, D., 157, 217.
Berthollet, C. L., 52, 71, 72, 76, 77, 104,
118, 147, 260, 260 n. 15.
Bertrand, H. C, 108, 108 n. 61, 109.
Bessel, F.W., 319 n. 8.
138,
141, 144, 151, 154, I5S, 159, 172, 177,
180, 181, 183, 211, 212, 213, 219, 220,
225, 227, 235, 236, 240, 271 n. 10,
311 n. 13, 313, 313 n. 14, 318; Fourier,
opinion of, 127; his boundary con-
dition criticised by Fourier, 170, 303-4;
his candidature for position of perma-
nent secretary (mathematics) to Acadd-
mie des Sciences; 125; his claim to
priority rejected by Fourier, 126; his
criticism of Fourier's form of solution,
176; his criticism of Fourier's three-
slice approach, 183-4; his 'general
principle' 185, 303, 303 n. 11; his im-
plied criticism of Fourier regarding a
certain analytical difficulty in treatment
of thin bar, 101, 302, 302 n. 2, 5, 305,
305 n. 2, 3, 310, 310 n. 10; his re-
ferences to Laplace's treatment of
thin bar, 102, 302, 302 n. 4;
his treatment of temperature distribution
in a thin bar; 149, 162-4, 3°5-6>
305 n. 6, 308 n. 7; its probable in-
fluence on Fourier, 149; Fourier's
praise for, 149, 165; Fourier's criti-
cism of, 127, 302-3, 305-6, 310, 308 n.
7, 320 note.
Blanchin, J. B., 137, 137 n. 133.
Boileau, J., 28911. 2.
Bonaparte, N.; and expedition to Upper
Egypt, 73 ; and Fourier's appointment
as prefect of Isere, 76-7; and Fourier's
Introduction to Description of Egypt,
97-8; and the Cairo Institute, 71-2;
his granting of a pension to Fourier,
112; his journey to Elba, Fourier's
rerouting of, 105; his knowledge of
Fourier's revolutionary past, 87; his
order expelling Fourier, 109, 119, 328;
his refusal to move Fourier from Gre-
noble, 104; Fourier's accounts of 133-
134; Fourier's encounter with at
Bourgoin, 109, 328; Fourier's letter
to, 108; Fourier's support for during
100 Days, 119.
344
INDEX
Bonard, C. L., passim; 9 n. 34; his friend-
ship with Fourier, 82-5 ; his position as
provincial^ examiner for intending
pupils of Ecole Polytechnique, 62, 217,
287, 288; letters of, 83, 84; see also
Fourier's letters to.
Bonard, J. A. R., 62, 288, 290, 29011.9;
his baptism by Fourier, 292.
Bonard, Mme. C.L., 253, 272, 288, 290,
292, 298, 322.
Bonnardot, 253, 253 n. 2.
Bose, A. C, 161, 177, 238.
Bossut, C, 7, 7 n. 15.
Boughey, C. J., 240.
Brisson, J. M., 52, 259, 259 n. 6.
Brucker, G., 21.
Buache, J. N., 262, 262 n. 25.
Caferelli, L. M. J. M., 90 n. 21.
Cahn, T., 240.
Cantor, G., 218.
Caritat, M. J. A. N., Marquis de Con-
dorcet, 39, 230, 244, 244 n. 11.
Carnot, L. N. M. ,110, 112, 323 n. 1.
Carnot, S., 141.
Casimir, A., 25, 26.
Cauchy, A. L., 237; his controversy with
Fourier, 127.
Cestre, C, 23, 95.
Chabrol, C. J. G., 118, 118 n. 2, 121, 130,
J 38, 143, 144, 230.
Challe, A., 7. 13. 1 8, 19, 22, 23, 24, 46, 48.
Champollion-Figeac, A. L., 93, 94, 114,
Champollion-Figeac, J. F., 96, 96 n. 1.
Champollion-Figeac, J. J., 92, 94, 97, 103,
104, 105, 106, 108, 109, 113, 114, 115,
116, 117,232.
Chaptal, J. A., 77, 77 n. 40.
Charbonnet, P. M., 7, 7 n. 11.
Charles,J. A. C.,33in. 1.
Clairaut, A. C, 233.
Cicd, J. B. M., Champion de, 8, 8 n. 22.
Coblentz, tribunal of, 283.
College Montaigu, 8, 224.
Colombat, M., 6.
Combes, A., 20.
Committee of General Security; 56, 57, 58,
277, 284; order of, effecting Fourier's
arrest, 42 ; order of, effecting Fourier's
release, 44; report on Fourier by
Mailhe forwarded to, 55; order of,
effecting Fourier's provisional release,
56; letter of Fourier to Chairman of,
56, 277; letter of Fourier's brother to,
56-7; rearmament of Fourier by order
of, 61.
Committee of Public Instruction; 276, 281,
284; address against Fourier to, 55;
report against Fourier to, 55.
Committee of Public Safety; 43, 44, 60,
270; letter of Maure to, 34-5 ; letter of
administrators of Orleans to, 35;
decree of Barere on behalf of, 35;
letter of Ichon to, 36; letter of Maure
to, 37; delegation on behalf of Fourier
to, 42, 42 n. 50, 42 n. 54; orders of re-
lease and imprisonment of Fourier, 42 ;
intervention of agent Demaillot against
Fourier before, 43.
Comte, A., possible influence of Fourier on,
226, 227-8.
Conte\ N. J., 71, 71 n. 11.
Corbiere, J. J. G. P., 121, I2 i n. 21, 132 .
Costaz, L., 73, 73 n. 35, 104.
Costabel, P., 206, 206 n. 48.
Coulomb, C, 234.
Cousin, C. Y., 259, 259 n. 4.
Cousin, J. A. J., 259, 259 n. 4, 287, 331.
Cousin, V., 13, 23, 37, 46, 48, 68, 72, 77,
79, 81, 89, 92, 94, 108, 116, 129, 130,
133, 133 n- "6, 134, 138, 143, 146,
241; his friendship with Fourier, 133.
Crosland, M., 86, 115.
Cubieres, S. L. P., 122, 122 n. 33.
Cuvier, G. D., 128, 12811.82, 138, 143,
228; Fourier's membership of his
salon, 129.
Daubenton, J. L. M., 52, 260, 260 n. 14.
Darboux, G., 205.
Dauphine, ancient province of, 93-4.
Davigneau, Abb6, 270, 270 n. 2.
Davout, N., 22, 271 n. 9.
DeCoinces, D., 33, 33 n. 20.
Defrance, 61, 293, 293 n. 9.
Delambre, J. B., 103, 103 n. 45, 115, I2 2,
124, 156, 156 n. 72; Fourier's eloge
of, 125.
Deleyre, A., 51, 259, 259 n. 3.
Denon, D. V., 71, 71 n. 14.
Demaillot, agent of Robespierre, 43, 60,
286.
Derreal, H., 17.
Desaix, L. de V., 74, 74 n. 39.
Descartes, R., 243, 243 n. 3; Fourier's
proof of his rule, 54, 272, 272 n. 13.
Dirichlet, P. G. J., 129, 129 n. 88, 217.
Doublet, E., 21.
Duplessis, 244, 244 n. 13.
Dupuy, P., 66.
Dupuytrin, G., 138, 138 n. 134.
INDEX
345
Dubouchage, F. J. Viscount de Gratet,
120, 120 n. 14; his letter in support of
Fourier, 123.
Duhamel, J. M., 129, 129 n. 90.
Duzer, C. H. van, 240.
Ecole Polytechnique; foundation of, 61-2;
early years of, 62—3 ; examining jury
of, 62, 64, 287; entry to, 63-4, 287,
289; contribution to Egyptian cam-
paign of, 130; Fourier's lectures at,
64, 64 n. 71, 289; Fourier's succession
to chair of Lagrange at, 64.
Ecoles Centrales, 272, 272 n. 15.
Ecoles Centrale des Travaux Publics,
Fourier's position at, 56, 284, 284 n.
22.
Ecoles Normale year II; foundation of, 51
51 n. 1, 51 n. 2; closure of, 53; nomi-
nation of former terrorists to, 45;
Fourier's nomination to, 44-5, 281;
Fourier's notes on, 51-3, 259-262;
Fourier's position of maitre des con-
ferences (in College de France) at, 53,
54, 55, 270, 270 n. 7, 272, 272 n. 11
276, 281, 284, n. 21; demand for
Fourier's exclusion from, 54, 284.
ficole Royale Militaires, 6-7, 6 n. 7; at
Auxerre 7 ; at Soreze 7, 7 n. 9, 21 ;
ficole Royale Militaire, Rebais, Fourier's
supposed stay at, 24.
Egypt, French Campaign in :
Commission of Arts and Science; re-
cruitment for, 69 n. 1; Fourier's
secondment to, 64.
Cairo Institute; its foundation, 71-2;
Fourier's position as secretary of, 71,
71 n. 15.
Expedition to Upper Egypt, 173.
Description of Egypt, 97 ; see also under
Fourier, his Introduction to.
See also under Fourier, his study of
Astronomical monuments of Egypt.
Einstein, A., 216, 219.
Euler, L., 157, 217, 220; and trigonometri-
cal series, 154, 172, 318, 319.
Faraday, M., 209.
Fayet,J.,66.
Fischer, E. G., 302, 302 n. 7.
Fontanes, L. M. de, 98, 98 n. 17.
Fortin, F. J. F., 22.
Fourcroy, A. F., 62, 299, 299 n. 1.
Fourcy, A., 68.
Fourier, Jean B., 132, 293 n. 1 1 ; his letter to
Committee of General Security, 56-7.
Fourier, Joseph,
and Acte Additional, no.
and Egyptian Campaign: See under
Egypt.
and Lazare Carnot's appointment as
Minister of the Interior, no, 324.
and Napoleon: See under Bonaparte.
and Pension granted by Napoleon, 112.
and Society of Arts and Science of Gre-
noble, 96.
and Statistics, 73, 96, 96 n. 6, 118.
and Study of Medicine, 276, 276 n. 5.
and the Academie des Sciences; his
early memoir to, 13, 13 n. 39, 250 n.
6, 280 n. 2 ; his unconfirmed election of
1816, 122-3, 33 1 . his election of 1817,
124; his service on commissions of
Academie, 125, 125 n. 50; his election
as permanent secretary to 125; his
eloges 125, 125 n. 65; his annual re-
ports on state of mathematical sciences,
125, 125 n. 66. See also under 1807
memoir, Prize Essay, and Analytical
Theory of Heat.
and the Ecole Normale, year II: see
under ficole Normale.
and the First Restoration, 104-6.
and the 100 Days; 106-12, 323-9;
flight from Grenoble, 106-108; en-
counter with Napoleon 109, 328 ; posi-
tion as prefect of the Rh6ne, 1 10-12,
323-6; justification of his conduct
during 100 Days, 119, 328-9.
and the French Revolution 27-61;
growth of his political views, 27, 280;
entry into local politics, 27-28, 281;
membership of committee of surveil-
lance (revolutionary committee) of
Auxerre, 28-30, 280-1; missions to
Avallon, 29, St. Brie, 30, Loiret, 30-38
and Tonnerre, 41 ; his defence of three
pater-familias at Orleans, 34, 283 ; let-
ter demanding Fourier's recall, 35;
decree of Barere, 35, 36, 37, 229, 283;
order of Ichon, 35 ; defence of Fourier
by Maure, Popular Society of Auxerre,
and Committee of Surveillance, 37;
his arrest in Messidor year II, 42, 283,
and reasons for 42-3, 60, 283 ; delega-
tion of intercession for Fourier to Com-
mittee of Public Safety, 42, 42 n. 50,
42 n. 54, 284; his supposed condemna-
tion to death, 44, 277, 277 n. 7, 284;
his release from prison, 44, 284; his
resignation from revolutionary com-
mittee of Auxerre, 44 ; his arrest in
344
INDEX
Bonard, C. L., passim; g n. 24; his friend-
ship with Fourier, 82-5 ; his position as
provincial examiner for intending
pupils of Ecole Polytechnique, 62, 217,
287, 288; letters of, 83, 84; see also
Fourier's letters to.
Bonard, J. A. R., 62, 288, 290, 290 n. 9;
his baptism by Fourier, 292.
Bonard, Mme. C.L., 253, 272, 288, 290,
292, 298, 322.
Bonnardot, 253, 253 n. 2.
Bose, A. C, 161, 177, 238.
Bossut, C, 7, 7 n. 15.
Boughey, C. J., 240.
Brisson, J. M., 52, 259, 259 n. 6.
Brucker, G., 21.
Buache, J. N., 262, 262 n. 25.
Caferelli, L. M. J. M., 90 n. 21.
Cahn, T., 240.
Cantor, G., 218.
Caritat, M. J. A. N., Marquis de Con-
dorcet, 39, 230, 244, 244 n. 11.
Carnot, L. N. M. ,no, 112, 323 n. 1.
Carnot, S., 141.
Casimir, A., 25, 26.
Cauchy, A. L., 237; his controversy with
Fourier, 127.
Cestre, C, 23, 95.
Chabrol, C. J. G., 118, 118 n. 2, 121, 130,
138, 143, H4. 230.
Challe, A., 7, 13, 18, 19, 22, 23, 24, 46, 48.
Champollion-Figeac, A. L., 93, 94, 114,
Champollion-Figeac, J. F., 96, 96 n. 1.
Champollion-Figeac, J. J., 92, 94, 97, 103,
i°4» i°5> i°6, 108, 109, 113, 114, 115,
116, 117,232.
Chaptal, J. A., 77, 77 n. 40.
Charbonnet, P. M., 7, 7 n. 11.
Charles, J. A. C, 331 n. 1.
Clairaut, A. C, 233.
Cice, J. B. M., Champion de, 8, 8 n. 22.
Coblentz, tribunal of, 283.
College Montaigu, 8, 224.
Colombat, M., 6.
Combes, A., 20.
Committee of General Security; 56, 57, 58,
277, 284; order of, effecting Fourier's
arrest, 42 ; order of, effecting Fourier's
release, 44; report on Fourier by
Mailhe forwarded to, 55; order of,
effecting Fourier's provisional release,
56; letter of Fourier to Chairman of,
56, 277 ; letter of Fourier's brother to,
56-7; rearmament of Fourier by order
of, 61.
Committee of Public Instruction; 276, 281,
284; address against Fourier to, 55;
report against Fourier to, 55.
Committee of Public Safety; 43, 44, 60,
270; letter of Maure to, 34-5 ; letter of
administrators of Orleans to, 35;
decree of Barere on behalf of, 35;
letter of Ichon to, 36; letter of Maure
to, 37; delegation on behalf of Fourier
to, 42, 42 n. 50, 42 n. 54; orders of re-
lease and imprisonment of Fourier, 42 ;
intervention of agent Demaillot against
Fourier before, 43.
Comte, A., possible influence of Fourier on,
226, 227-8.
Cont6, N. J., 71, 71 n. 11.
Corbiere, J. J. G. P., 121, 121 n. 21, 132.
Costaz, L., 73, 73 n. 25, 104.
Costabel, P., 206, 206 n. 48.
Coulomb, C, 234.
Cousin, C. Y., 259, 259 n. 4.
Cousin, J. A. J., 259, 259 n - 4, 287, 331.
Cousin, V., 13, 23, 37, 46, 48, 68, 72, 77,
79, 81, 89, 92, 94, 108, 116, 129, 130,
133, 133 "• "6, 134, 138, 143, 146,
241; his friendship with Fourier, 133.
Crosland, M., 86, 115.
Cubieres, S. L. P., 122, 122 n. 33.
Cuvier, G. D., 128, 12811.82, 138, 143,
228; Fourier's membership of his
salon, 129.
Daubenton, J. L. M., 52, 260, 260 n. 14.
Darboux, G., 205.
Dauphine, ancient province of, 93-4.
Davigneau, Abb£, 270, 270 n. 2.
Davout, N., 22, 271 n. 9.
DeCoinces, D., 33, 33 n. 20.
Defrance, 61, 293, 293 n. 9.
Delambre, J. B., 103, 103 n. 45, 115, 122,
124, 156, 156 n. 72; Fourier's eloge
of, 125.
Deleyre, A., 51, 259, 259 n. 3.
Denon, D. V., 71, 71 n. 14.
Demaillot, agent of Robespierre, 43, 60,
286.
Derreal, H., 17.
Desaix, L. de V., 74, 74 n. 29.
Descartes, R., 243, 243 n. 3; Fourier's
proof of his rule, 54, 272, 272 n. 13.
Dirichlet, P. G. J., 129, 129 n. 88, 217.
Doublet, E., 21.
Duplessis, 244, 244 n. 13.
Dupuy, P., 66.
Dupuytrin, G., 138, 13811. 134.
INDEX
345
Dubouchage, F. J. Viscount de Gratet,
120, 120 n. 14; his letter in support of
Fourier, 123.
Duhamel, J. M., 129, 129 n. 90.
Duzer, C. H. van, 240.
Ecole Polytechnique; foundation of, 61-2;
early years of, 62-3; examining jury
of, 62, 64, 287; entry to, 63-4, 287,
289; contribution to Egyptian cam-
paign of, 130; Fourier's lectures at,
64, 64 n. 71, 289; Fourier's succession
to chair of Lagrange at, 64.
Ecoles Centrales, 272, 272 n. 15.
Ecoles Centrale des Travaux Publics,
Fourier's position at, 56, 284, 284 n.
22.
Ecoles Normale year II; foundation of, 51
51 n. 1, 51 n. 2; closure of, 53; nomi-
nation of former terrorists to, 45;
Fourier's nomination to, 44-5, 281;
Fourier's notes on, 51-3, 259-262;
Fourier's position of maitre des con-
ferences (in College de France) at, 53,
54, 55, 270, 270 n. 7, 272, 272 n. 11
276, 281, 284, n. 21; demand for
Fourier's exclusion from, 54, 284.
Ecole Royale Militaires, 6-7, 6 n. 7; at
Auxerre 7 ; at Soreze 7, 7 n. 9, 21 ;
Fxole Royale Militaire, Rebais, Fourier's
supposed stay at, 24.
Egypt, French Campaign in:
Commission of Arts and Science; re-
cruitment for, 69 n. 1; Fourier's
secondment to, 64.
Cairo Institute; its foundation, 71-2;
Fourier's position as secretary of, 71,
71 n. 15.
Expedition to Upper Egypt, 173.
Description of Egypt, 97; see also under
Fourier, his Introduction to.
See also under Fourier, his study of
Astronomical monuments of Egypt.
Einstein, A., 216, 219.
Euler, L., 157, 217, 220; and trigonometri-
cal series, 154, 172, 318, 319.
Faraday, M., 209.
Fayet,J.,66.
Fischer, E. G., 302, 302 n. 7.
Fontanes, L. M. de, 98, 98 n. 17.
Fortin, F. J. F., 22.
Fourcroy, A. F., 62, 299, 299 n. 1.
Fourcy, A.,68.
Fourier, Jean B., 1 32, 293 n. 1 1 ; his letter to
Committee of General Security, 56-7.
Fourier, Joseph,
and Acte Additional, no.
and Egyptian Campaign: See under
Egypt.
and Lazare Carnot' s appointment as
Minister of the Interior, no, 324.
and Napoleon : See under Bonaparte.
and Pension granted by Napoleon, 112.
and Society of Arts and Science of Gre-
noble, 96.
and Statistics, 73, 96, 96 n. 6, 1 18.
and Study of Medicine, 276, 276 n. 5.
and the Academie des Sciences; his
early memoir to, 13, 13 n. 39, 250 n.
6, 280 n. 2 ; his unconfirmed election of
1816, 122-3, 33 1 ! ms election of 1817,
124; his service on commissions of
Academie, 125, 125 n. 50; his election
as permanent secretary to 125; his
eloges 125, 125 n. 65; his annual re-
ports on state of mathematical sciences,
125, 125 n. 66. See also under 1807
memoir, Prize Essay, and Analytical
Theory of Heat.
and the Ecole Normale, year II: see
under Ecole Normale.
and the First Restoration, 104-6.
and the 100 Days; 106-12, 323~9;
flight from Grenoble, 106-108; en-
counter with Napoleon 109, 328; posi-
tion as prefect of the Rh6ne, 1 10-12,
323-6; justification of his conduct
during 100 Days, 119, 328-9.
and the French Revolution 27-61;
growth of his political views, 27, 280;
entry into local politics, 27-28, 281;
membership of committee of surveil-
lance (revolutionary committee) of
Auxerre, 28-30, 280-1; missions to
Avallon, 29, St. Brie, 30, Loiret, 3°~38
and Tonnerre, 41 ; his defence of three
pater-familias at Orleans, 34, 283 ; let-
ter demanding Fourier's recall, 35;
decree of Barere, 35, 36. 37. 229, 283 ;
order of Ichon, 35 ; defence of Fourier
by Maure, Popular Society of Auxerre,
and Committee of Surveillance, 37;
his arrest in Messidor year II, 42, 283,
and reasons for 42-3, 60, 283; delega-
tion of intercession for Fourier to Com-
mittee of Public Safety, 42, 42 n. 50,
42 n. 54, 284; his supposed condemna-
tion to death, 44, 277, 277 n. 7, 284;
his release from prison, 44, 284; his
resignation from revolutionary com-
mittee of Auxerre, 44; his arrest in
346
INDEX
Joseph Fourier (cont.)
Prairial year III, 56, 284, (and back-
ground to) 54-56, 284; letters from
prison to Bergoeing, 276-7, and Ville-
tard, 280-5; presumed support by
Lagrange, Laplace and Monge 271 n.
10; provisional release from prison,
56; letter from Fourier's brother de-
manding his interrogation following
his rearrest, 56-7; his reply to charge
of terrorism, 57-9, 282-3; his final
release from prison, 61 ; see also under
Committee of General Security, Com-
mittee of Public Instruction, and Com-
mitte of Public Safety,
his achievement as a physicist, 209-16;
in relation to : his 1798 paper on virtual
velocities 209; his paper on elastic
surfaces, 209; his work on terrestrial
heat, 210; his work on radiant heat,
21c— 11 ; his derivation of the equation
of motion of heat, 211; his expression
for the heat flux, 21 1-14 ; his definition
of interior conductivity; 213-14; his
separation of processes of interior and
exterior conduction of heat, 214-15.
the main underlying features of, 215-
216.
his Analyse des equations determines, 23,
243 n. 1, 250 n. 6.
his application for the position of li-
brarian in Auxerre, 39, 258.
his application for a retirement pension,
118-22; services to the state in teach-
ing, administration and writing 327-8;
apologia for his conduct during the 100
Days, 328-9.
his appointment as bibliographical com-
missioner, 39, 39 n. 41.
his appointment as Director of Statistical
Bureau of the Seine, 118
his brother Jean Baptiste, 132, 293 n. 1 1 ;
his letter of intercession for Fourier,
56-7.
his brothers in Army, 282.
his controversy with Cauchy, 127.
his early life; parents, 5-6; birth, 6;
education 7-8; illness, 8; application
to enter artillery or engineers rejected,
8; membership of Society of Emula-
tion of Auxerre, 14, 14 n. 45; teaching
positions in Auxerre, 13, 14, 14 n. 43,
14, n. 44, 258, 280, 281.
his early work in pure mathematics, 11,
12, 13, 243 n. 1, 280, 280 n. 2.
his election to Academie Francaise, 137.
his health, 8, 11, 137, 243, 243 n. 4, 250,
250 n. 4.
his Introduction to Description of
Egypt', origin of, 97; and Bonaparte,
97-8 ; contents of, 98 ; opinion of Fon-
tanes. on, 98-9; printing of, 322, 322
n. 1.
his lectures at ficole Polytechnique, 64,
64 n. 71,289.
his letters to; administrators of the
department of Yonne, 258; Auger
(extract), 137; Bergoeing, 276; Bo-
nard, 243, 250, 253, 255, 259, 270,
287, 289, 292, 297, 298, 299, 301, 322;
Germain (extract), 125, 134-5; Hu-
zard, 124; Laplace (extract), 127, 316;
PHerminier, 135-6; Madame Cuvier,
135; Minister of Interior, 323, 324,
327; Ministers of War, Police, and
Interior, 326; President of First Class
of Institut, 331; Sub-prefects of the
Department of the Rii6ne, 325; un-
known correspondents, 302, 305, 307
(Laplace?), 318 (Lagrange ?) ; Villetard,
280.
his opinion of; Biot, 127, 320 note;
Laplace, 52, 130, 227, 260 n. n ; Pois-
son, 127, 128.
his position as Abb£, 14, 266.
his position at Ecole Centrale des Tra-
vaux Publics, 56, 284, 284 n. 22.
his proof of rule of Descartes, 54, 272,
272 n. 13.
his reading of Demosthenes, Diophan-
tus, Euclid, Montaigne and Pindar II,
250.
his servant Joseph, 133.
his study of astronomical monuments of
Egypt, 76, 292, 292 n. 3.
his succession to Chair of Lagrange at
Ecole Polytechnique, 64.
opinion of; by Geoffrey St. Hilaire, 75;
by Jomard, 75-6.
Prefect of Isere, 76-85 ; his appointment
as, 76-7; his administration as, 78;
his duties as, 79; his reconciliation of
different parties behind government,
79; his relations with different groups
of society, 79-80; his contribution to
draining of swamps of Bourgoin, 80-1,
327-8; his contribution to construc-
tion of road from Grenoble towards
Turin, 81-2.
Work on heat:
Analytical theory of heat; passim;
comparison with Prize Essay, 159;
INDEX
347
presentation to Academie des Sciences
159; printing of, 126, 159, 159 n - 93-
boundary conditions; 169-71; use of, in
solution, 173-4; criticism of, 155,
155 n- 59. 170. 170 n. 42.
communication of heat between discrete
bodies; 149, 192-7; influence on early
researches, 197, 197 n. 15, 235.
conductivity of heat, external, 169-70.
conductivity of heat, internal, 151, 151
n. 17, 152, 181.
derivation of equation of motion of heat;
in a cube, 152, 152 n. 26, 152 n. 36; in
a cylinder, 152, 152 n. 25, 152 n. 35,
168; in a prism, 152, 152 n. 37, 168;
in a semi-infinite strip, 150, 151, 152,
230; in a sphere 152, 152 n. 24, 152 n.
34, 168; in a thin ring, 152, 152 n. 23,
152 n. 32, 168.
derivation of equation of motion of heat
in a thin bar; early incorrect treatment,
150, 164-5, 307-8; three-slice treat-
ment in 1807 memoir, 152, 165-6;
transition to one-slice treatment, 166-
7 ; one-slice treatment (in Letter XIX),
308-9 (in Prize Essay), 167-8, (in
Analytical Theory of Heat), 168; see
also criticisms of, under Biot, Laplace
and Poisson.
derivation of general equation of motion
of heat in three dimensions; early,
incorrect equation, 150; correct equa-
tion, 152, 152 n. 27, 169.
Draft Paper: 149-53. 164-5; Part n
passim.
experimental considerations, 151, 15 1
n. 14, 151 n. 15, 152, 152 n. 29, 209,
209 n. 1, 209 n. 2.
expression for heat flux, 151, 151 n. 18,
152, 152 n. 21, 165-6, 180-91 ; implicit
use of in Draft Paper, 181 ; derivation
of, in 1807 memoir, 18 1-2: use of 3
slice approach to, in 1807 memoir, 183 ;
transition to one-slice treatment of,
185; one-slice treatment of (in Letter
XIX), 185-7, 310-11, (in Prize Essay)
187-9, (in Analytical Theory of Heat)
189.
his criticisms of; Biot, 126, 127, 163,
163 n. 8, 170, 302-3, 3°4. 3°5-6, 31°.
320 note; Laplace, 236, 303; Poisson,
127, 158, 176-7-
hypothetical considerations on mecha-
nism of heat interchange, Fourier's
reason against employing, 189-90,
190 n. 39.
influence of Fourier's work in heat; in
pure mathematics, 217-18; in applied
mathematics, 218-19; in theoretical
physics, 219-21.
mathematical aspects:
cylinder or Bessel functions, Fourier's
use of, 178, 319, 319 n. 8.
equation of diffusion of heat in infinite
bar ; Fourier's solution to, (and pos-
sible influence of Laplace) 156.
normal mode, assumption of, 173,
orthogonality, 171,
roots of equation (tanx = o, controversy
over; 304, 304 n. 15 ; see also under
Poisson
separation of variables, 173,
trigonometrical expansions, 150, 152,
152 n. 31, 157, 172-3, 174. 176-7.
criticisms of Laplace, 101, 154, 156,
235-6, 310 n. 3; criticism of Pois-
son, 126, 157, 175-6; convergence
of 150, 316-7; origin of Fourier's
use of, 318; range of validity, 319.
uniqueness of solution, 157, 157 n.
80, 175-7.
memoir of 1807; Part II passim; com-
position of, 99 ; comparison with Draft
Paper, 152-3; presentation to Acade-
mie des Sciences, 100; abstract of, 153,
153 n. 39, 318, 318 n.i; commission
of Academie appointed to report on,
100, 153, 153 n. 44; review by Poisson,
100, 153, 153 «• 4i. 305 n. 4; contro-
versy over, 101-2, 235-6.
Preliminary Discourse to Analytical
Theory of Heat, 221-8; philosophy of
science, 223; philosophy of mathe-
matics, 223; 'separatist* attitude to
theory of heat, 224, (possible explana-
tion of this attitude) 226-7, (possible
influence on Comte) 226, 227-8.
Prize Essay of 181 1 ; setting of, 102, 156,
306 306 n. 7 ; comparison of contents
with those of 1807 memoir, 156, and
Analytical Theory of Heat, 159!
commission of Academie set up to
report on, 103, 156, 156 n. 71; Fou-
rier's protest at criticisms of report on,
103, 156, 156 n. 72; publication of,
103, 158, 158 n. 90, 159 n. 91, 331-
radiant heat; 202-205; possible in-
fluence on subsequent work, 22 1 .
solution to equations of motion of heat,
171-6.
specific heat, 141, 151 n. 16, 168.
348
INDEX
Joseph Fourier (cont.)
terrestrial heat; 197-202, 210; its im-
portance for Fourier's early researches,
T 97> 19711.20; influence on subse-
quent work, 221.
Fourier, Pierre, 66 n. 3, 94, 231.
Fox, R., 24.
Fresnel, A. J., 129, 139 n. 96, 151, 233, 234.
Galileo, G., 210, 213, 219, 224.
Garat, D. J., 53, 134, 262, 263 n. 36
Gautherot, C, 15, 15 n. 54, 45, 61.
Gardien, J., 17.
Gauss, J. C. F., 141, 143.
Gde. Encycl. Passim.
Geneve, Journal de., 10, 10 n. 30, 244, 244
n. 14.
Geoffroy St. Hilaire, E., 71, 71 n. 12, 72,
74. 92, 129, 143, 229; his opinion of
Fourier, 75.
Germain, S., 125, 12511.58, 134-5, 138,
160, 161, 172, 172 n. 51, 174, 175.
Gouhier, H., 240.
Grattan-Guinness, J. J., 68, 142, 238, 240,
318 n. 1, 319 n. 6.
Greene, G., 221.
Grenoble, Society of Arts and Science of,
196.
Guemadeuc, A. H. B. de., 244, 244 n. 10.
Guillaume, J. (Ed.), 66, 67.
Guillemardet, F. P., 277, 277 n. 8, 281.
Guistiniani, de, 243 n. 5.
Hahn, R., 21
Haiiy, R. J., 52, 66, 156, 260, 260 n. 12, 302
n. 8.
Hardy, G. H., 232.
Haten, E., 23.
Herivel, J. W., 239, 240.
Hermite, C, 239.
Herold, C.J., 191.
Humboldt, A. von, 128, 138 n. 81, 129, 143.
Huygens, C, 221.
Huzard, J. B., 124, 124 n. 44.
Ichon, P. L., 30-38 passim, 255, 255 n. 3.
Ind. Bio. passim.
Ingenhouss, J., 163.
Jacobi, C. G. J., 223.
Jacobin Society, 42.
Jardin des Planus, 52, 52 n. 7, 259, 259 n. 1.
Jomard, E. F., 114, 130, 13011.103, 132,
138, his opinion of Fourier, 75-6.
Jourdain, P. E. B., 177, 238, 239.
Kelland, P., 174, 174 n. 62.
Kelvin Lord; See Thomson, W.
Keralio, L. F. G., de, 7; 7 n. 10.
Kirchoff, G. R., 210.
Kleber, J. B., 69, 69 n. 5, 73, 97, 230.
Knight, I. F., 240.
Koyre, A., 220.
Kraft, G. W. 313.
Kucinski, A., 25, 47.
Lacroix, S. F., 100, 153, 287, 287 n. 4.
Lagrange, J. L., 10, 10 n. 29, 45, 53, 55, 61,
100, 104, 122, 141, 232, 233, 237, 244,
34411.13, 271 n. 10; and Fourier's
proof of rule of Descartes, 54, 272;
Fourier's letter to (?) 318; Fourier's
opinion of, 52, 259-60; Fourier's
succession to his chair at Fxole Poly-
technique, 64; his criticism of David
Bernouilli, 157; his criticism of
Fourier's use of trigonometrical series,
101, 154, 235-6; his lecturing manner,
52, 259; his views on problem of
vibrating string, 217; his membership
of commission on Fourier's 1807
memoir, 100, 153, 235-6; his member-
ship of commission on Prize Essay for
181 1, 103, 156; listed among Fourier's
friends, 128; superiority commonly
accorded to him in Paris, 75; the re-
newal of his interest in analytical
dynamics, 234.
Laharpe, J. F., 52, 261, 261 n. 19.
Lain£, E. H. J., 120, 120 n. 13, 121, 122,
123, 132.
Lakanal, J. , 5 1 , 259, 259 n. 3.
Lalande, J. J., 52, 83, 259, 259 n. 5.
Lambert, J. H., 163, 163 n. 6, 188, 211, 313,
313 n. 14, 320 note.
Langer, R., 116, 177.
Laporte, Dom, 7, 244, 344 n. 6.
Laplace, P. S., 45, 61, 118, 122, 126, 129,
151, 171, 180, 212, 213, 219, 220, 224,
232. 233, 237, 239, 240, 360 n. 10:
and Fourier's attitude to analytical
dynamics, 234 ; and Fourier's proof of
Descartes' rule, 54: his criticism of
Fourier's derivation of equation of
motion of heat for thin bar, 155, 156,
'85, 315; his criticisms of Fourier's
use of trigonometrical series, 101, 154,
!56, 235-6, 316 n. 3; his derivation of
equation of motion of heat, 155, 167,
184, 189, 225, 302, 314; his friendly
letter to Fourier, 130; his lecturing
manner, 260; his membership of
INDEX
349
commission for 1807, memoir, 100,
153; his membership of commission
for Prize Essay of 1811, 103, 156; his
membership of Committee of Public
Instruction, 55, 55 n. 31; his member-
ship of election jury for Ecole Poly-
technique, 64, 287, 289 ; his opposition
to Fourier's 1807 memoir, 101, 235-6;
his integral solution to equation for
propagation of heat (and possible in-
fluence on Fourier) 156, 157; his
suggestion for boundary condition,
155. 155 n. 61, 170, 303, 304 n. 14; his
presumed support for Fourier in 1795,
271, 271 n. 10; Fourier's criticism of,
236, 303; Fourier's eloge of, 125, 231;
Fourier's letter to, 3 16 ; Fourier's letter
to concerning Poisson, 127, 158;
Fourier's note to, 303, (and possible
original of) 303 n. 13; Fourier's opi-
nion of, 52, 1 30, 227, 260 n. 1 1 .
Laplanche, Goyre, J. L., 31-4 passim,
31 n. 18, 60, 236.
Larrey, D. J., 137, 137 n. 133.
Lavoisier, A., 221, 224, 225, 240.
Lebegue, E. H., 6.
Leblanc, F., 41.
Lebeuf, J., 24.
Lefebvre, G., 46, 49.
Legendre, A. M., 7, 141, 143, 156, 253,
253 n. 4, 287.
Lemontey, P. C. M., 137, 137 n. 128, 244.
Lepelletier, de St. Fargeau, L. M., 15,
IS *»• 53. 230.
Leslie, J., 203, 210, 313, 313 n. 14.
Letonnelier, G., 43, 94, 115, 115.
Libri, G. B., 129, 129 n. 89.
Liouville, J., 215.
Loiret, Fourier's mission, to 30-8.
Lycees, 298, n. 4.
Lycee, de Paris or des Arts, 259, 259 n. 8.
Mach, E., 161, 238.
Mailhe, J. B., 55, 56, 57, 60, 276, 276 n. 2,
277, 281.
Malus, E., 7, 70, 70 n. 7, 71, 85, 130, 156,
234-
Marchand, J. G., 104, 108, 328, 338 n. a.
Maret, Count.
Mathon, 293, 393 n. 7, 298, 299.
Mauger, G. G., 8, 13, 17,23,24,46,48, 128.
Maupertuis, P. L. M., 224, 225, 239.
Maure, N., 15, 15 n. 51, 34-5, 37, 38, 40,
41,46.55,61,230.
Maxwell, J. C, 216, 219, 220, 228.
Meaule, J. N., 29, 39 n. 6.
Menou, J. F., 73, 73 n. 38, 74.
Mentelle, E., 262, 262 n. 23.
Milon, P., 61, 255, 255 n. 4, 298.
Monge, G., 45, 52, 53, 55, 61, 66, 71, 72,
77, 97, 100, 104, 118, 122, 128, 147,
153, 232, 253, 253 n. 3, 260, 271 n. 10,
33i-
Moiset, C, 18, 19, 48.
Monna, A. F., 238.
Montalivet, J. P. B., 97, 97 n. 12.
Montesquieu, C. L., de S., 281, 281 n. 5.
Montucla, J. E., 10, n, 244, 24411. 9, 251,
25m. 7, 253, 253 n. 1.
Moreau, 271, 271 n. 8.
Navier, L. M. H, 23, 128, 129, 138, 243
n. 1, 250 n. 6.
Newton, I., 149, 151, 192, 213, 216, 219,
220, 221, 224, 233; his claim to im-
mortality, 12, 251, 251 n. 8: his prin-
ciple of transmission of heat, 150, 181,
187-8, 213, 307 n. 3, 312; his paper on
heat, 163, 170, 313; Fourier's deriva-
tion of his principle of transmission of
heat, 187-8, 312-13.
Oersted, H. C, 234.
Orleans, Fourier intervention in, 30-8.
Pallais, J., 6, 6 n. 4.
Panckoucke, C. J., 52, 259, 259 n. 7.
Pascal, B., 12, 124, 233, 251, 251 n. 8.
Perier, A., 81, 81 n. 53, 132, 138.
Perier, C, 132, 132 n. 111.
Picavet, F., 240.
Pictet, M. A., 203.
Pigiere.J., 93.
Poincar6, H., 221.
Poisson, S. D., 64, 101, 103, 126, 129, 130,
138, 180, 189, 212, 213, 219, 220,
221, 233, 234, 236, 237, 239, 289 n. 7;
his criticisms of Fourier's boundary
condition, 155, 178; his criticisms of
Fourier's derivation of equation of
motion of heat in thin bar, 158; his
criticism of Fourier's treatment of
equation tan x = o, 155-6; his criti-
cism of Fourier's use of trigonometrical
expansions, 126, 157, 175-6, (and Fou-
rier's reply thereto) 126-7, 157, 176-7;
his paper of 18 15 on theory of heat,
!57. J 57 n - 74! hi s review of Fourier's
1807 memoir, 100, 153, 153 n. 41,
305 n. 4; his solutions to equation of
motion of heat, 157, 157 n. 77, 222;
350
INDEX
S. D. Poisson (cont.)
Fourier's criticisms of, 127, 158, 176-
177; Fourier's opinion of, 127, 128;
other controversies with Fourier, 127.
Polignac, Count of, 108, 108 n. 68.
Porte, C, 46.
Pouillet, C, 129, 129 n. 91.
Prevost, P., ioi, 156, 203, 211, 302, 302
n. 1, 302 n. 9.
Quantin, M., 17, 24.
Ravetz.J. R., 161,238.
Riemann, B., 217.
Robespierre, M., 42, 42 n. 49.
Rochon, A. D., de., 124, 134 n. 43.
Rosenberger, F., 238.
Rosily-Mesros, F. E., 122, 122 a. 32.
Rosman, H. A., 14, 40, 271 n. 9, 292, 292
n.5.
Roux, J. L., 40, 133, 243 n. 1, 255, 255 n. 2,
256, 287, 289, 292, 298, 322.
Rumford, B., 313.
Say, J. B. 71, 71 n. 13.
Schmidt, C, 24.
Sicard, R. A., 53, 261, 261 n. 22.
Smith, E. B., 21.
Smith, W. S., 72, 72 n. 22, 73, 131-2.
St. Benoir-sur-Loire, Abbey of; prior of,
11, 11 n. 31, 13, 250, 250 n. 1; Fou-
rier's life at 8-13; Fourier's letters to
Bonard from, 243-57.
St. Brie, Fourier's mission to, 30.
Stefan, J. ,210.
St. Just, A., 42.
St. Maur, Benedictine Congregation of,
6n. 8, 13.
Sturm, C, 215.
St. Vallier, Count of, letter in support of
Fourier, m.
Tallien, J. L., 69, 69 n. 6.
Taton, R., (Ed), 19, 20, 22.
Thomson, W., (Lord Kelvin), 174, 174
n. 63, 211, 221, 228, 319 n. 8.
Thouin, A., 261, 261 n. 17.
Tonnerre, Fourier's mission to, 41.
Vaublauc, V. M. V. de, 120, 123, 327 n. I.
Vaudret Dom, 244 n. 8.
Villetard, E. P. A., 44, 49, 55, 57, 58, 59, 63,
236, 280, 280 n. 1, 289.
Vinot, J., 21.
Vleck, E. B., Van, 177, 238, 239.
Volney, C. F. de, 53, 261, 261 n. 20, 261 n.
21.
Vuillemin, J. B., 17.
Weirstrass, K., 217.
Young, T., 234.