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Full text of "Joseph Fourier { The man & the physicist }"

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 



Oxford University Press, Ely House, London W.i 

GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON 

CAPE TOWN IBADAN NAIROBI DAR ES SALAAM LUSAKA ADDIS ABABA 

DELHI BOMBAY CALCUTTA MADRAS KARACHI LAHORE DACCA 

KUALA LUMPUR SINGAPORE HONG KONG TOKYO 



ISBN O I 



9 858149 1 



© 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 



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PRINTED IN GREAT BRITAIN BY 
WILLIAM CLOWES & SONS, LIMITED 
LONDON, BECCLES AND COLCHESTER 



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. 



EARLY LIFE 



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. 



104 



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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133 



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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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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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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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- 



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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 



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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. 



214 



EPILOGUE 



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 



EPILOGUE 



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 



216 



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EPILOGUE 



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 



EPILOGUE 



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 



220 



EPILOGUE 



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 



EPILOGUE 



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. 



222 



EPILOGUE 



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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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 



EPILOGUE 229 

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 



230 



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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 



EPILOGUE 



235 



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. 

(2) Essai sur le calorique rayonnant. Geneva (1809). 

Rumford, B. (Count). An enquiry concerning the nature of heat and the mode 

of its communication. Phil. Trans. R. Soc. (1804), 77-182. 



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 



BIBLIOGRAPHY 



Fayet, J. La Revolution franpaise et la science. Paris (1960). 

Fischer, E. G. Physique mecanique. Translated from German by Mme Biot 

with notes by J. B. Biot. Paris (1806). 
Forestier, H. et al. L' Yonne au 19 siecle. 4 Vols., Auxerre (1959-67). 
Fortin, F. J. F. Souvenirs. 2 Vols., Paris (1865-7). 
Fourcy, A. Histoire de V ecole poly technique. Paris (1828). 
Fox, R. The caloric theory of gases from Lavoisier to Regnault. Oxford (1971). 
Gardien, J. L'organe et les organistes en Bourgogne. Paris (1943). 
Germain, S. Oeuvres philosophiques de Sophie Germain suives de pensees et de 
lettres inedites et procedes d'une notice sur sa vie et ses oeuvres par H. Stupuy. 
Paris (1879). 
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- 
bridge, Mass. and London (1972). 
Green, G. Mathematical papers (Ed. N. M. Ferrars). London (1871). 
Hahn, R. (i) Quelques nouveaux documents sur Jean-Sylvain Bailly, Rev. Hist. 
Sci., 8 (1955), 338-53. 

(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- 
matics. Proceedings of the 5th International Congress on Mathematics, Vol. 2, pp. 
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- 

1907). 
Langer, R. Fourier series, the genesis and evolution of a theory. Am. math. 
Man., 54 (1947), supplement. 



BIBLIOGRAPHY 



341 



Lebeuf, J. Memoires concernant I'histoire ecclesiastique et civile d' Auxerre. With 

additions by A. Challe and M. Quantin. 2 Vols., Paris (1848). 
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). 
Letonnelier, G. Le prefet Fourier. Bull. Acad. Delphinale, (5) 13 (1922: pub- 
lished 1923) 131-47. 
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. 
Newton, I. Scala Graduum Caloris. Phil. Trans., 22 (1701), 824. 
Phelipeaux, M. R. Auxerre se penche sur son passe. Auxerre (1966). 
Picavet, F. Les Ideologues. Paris (1891). 

PiGEiRE, J. La vie et l'oeuvre de Chaptal (1756-1832). Paris (1932). 
Pinet, G. Histoire de l'£cole Poly technique. Paris (1887). 
Pinsseau, P. Auxerre historique et pittoresque. Auxerre (1943). 
Pouchet, G. Les sciences pendant la Terreur. Paris (1896). 
Quantin, M. (i). La societe d' emulation d' Auxerre. Bull. Soc. Sci. hist. not. 

Yonne, (1849), 131. 

(2). Histoire anecdotique des rues d' Auxerre. Auxerre (1870). 

Ravetz, J. R. (1). Joseph Fourier and the nineteenth century Revolution in 

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). 
(2). L'Fcole Polytechnique et le renouveau de la geometrie analytique, 

Melanges Alexandre Koyre, Vol. 1., pp. 552-64, Paris (1964). 
■ (3). (Ed). Enseignement et diffusion des sciences en France au 18 siicle. Paris 



(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.